#Calculation of Standard Deviation in Continuous Series | Explore Tumblr Posts and Blogs

full-of-jams · 4 years

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Tangsuyuk Love

Pairing: Jungkook x Reader

Summary: College student Jungkook passes cute notes with a customer who always orders take-out tangsuyuk at his part-time job. Meanwhile he’s trying not to miserably fail his Math class, while hiding his ever-growing crush on you.

Genre: college au, f2l, fluff, smut, one shot, did I mention FLUFF?

Warnings: mild swearing, sexual content, hold your heart palpitations!

Word Count: 11.5k

A/N: I wanted to write something light and sweet before I continued with Good Riddance. It will be easy, she said. It will be fun, she said. It will be quick, she said. Ha. haha. ha. ha. Ignore my pain. Enjoy!

°°°°°°°

[09/04 18:34 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY] 1 Tangsuyuk (large) 1 Jjamppong 2 Kimchi Mandu ---------------- Note: Without pineapple! Please make the jjamppong extra spicy, my boyfriend just broke up with me T-T

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: JK ------------------- TO GO

1 Tangsuyuk (large) -- 20,000 1 Jjamppong -- 5,000 2 Kimchi Mandu -- 6,000 1 Soju -- 0

Total: 31,000 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

Note: Service! Nothing’s better than the fresh taste of soju to lighten a heavy heart :) Cheer up LatteIsHorse-Nim!

Paper Note: JK-nim, thanks for the soju. It sweetened my bitter night. This is Tokki, please give him a loving new home! TT-TT

Jungkook was fucking terrified of you. If it weren’t for the fact that he was close to failing Statistical Analysis, he would’ve considered faking a stomach flu and making a beeline straight out of the library.

“If you have a box containing 3 white, 4 red and 5 black balls what is the probability that you will draw a white ball on your first draw and a black ball on your second draw?” you asked again through gritted teeth.

You looked up at Jungkook and were met by an empty stare. Usually you enjoyed tutoring your fellow classmate. He was a smart and funny guy, maybe a bit awkward at times, but always trying his best. Today every little thing grated on your nerves. It took you every ounce of energy to get out of bed and look like a presentable human being this morning. You really didn’t want to sit here for another hour if the boy was just going to stare at you like a petrified statue. “It’s really not that difficult. You just have to apply conditional probability.”

Jungkook let out a frustrated huff and pulled at his hair, “I really don’t know, this doesn’t make any sense! Why do I even need this stuff for my major? Who cares if I pull out a white ball or a black ball first? It’s not like I’m planning on becoming Houdini!”

Sometimes you pitied him, but who on Earth had an irrational fear of Gauss distributions and probability?! They were beautiful, harmless, abstract concepts of life. Your sympathy was muffled by a thrumming headache. All the late-night crying already had you chugging water and slapping ice cubes on your face at breakfast. Right now you just wanted to go home, change into your pjs, order some tangsuyuk and binge watch Boys Over Flowers. The cringy acting and Go Jun Pyo’s luscious locks were the only things that made your miserable life feel a bit less pathetic at the moment. “Jungkook, we went over this last time. Just apply the damn formula,” you snapped.

“Why are you being so scary today?” he asked wide-eyed and apprehensive.

You took a deep breath, rubbed your temples and tried to calm your inner turmoil. It wasn’t his fault; you were just in a really shitty mood. “I’m sorry. It’s not my day today. Is it okay if we rain check? I promise I’ll make it up to you next week.”

Jungkook wasn’t used to seeing you this distraught. He wracked his brain on how to lift your spirit. “Hey, do you want to hear this math joke my friend Jin told me the other day? What do you call an angle that is adorable?”

The boy scrunched his nose adorably and waited for your response. He was really handsome, you noticed that back when you two first met. Back then you just didn’t have a reason to care. Back then you still had a boyfriend.

“I don’t know, tell me,” you answered.

“Acute angle!” he said with a timid smile.

Despite your foul mood you had to snort at his joke.

Jungkook’s smile grew wider. It wasn’t a full laugh, but at least your frown disappeared. He discovered early on that you had a soft spot for bad math puns.

Although he absolutely detested Statistical Analysis, he has come to enjoy your study sessions over the past couple of weeks. The TA of his class, Namjoon, was a close friend of Jungkook’s and a sunbae of yours. Once he discovered that his favorite dongsaeng was abysmal at reading a z-score table, he immediately referred him to you.

At first Jungkook was very reluctant to accept any help. He was a mechanical engineer for fuck’s sake! He calculated distributed load across uneven surfaces and directional derivatives all the time!

His inner protests died down during your first session when you unwittingly asked him if he was constipated while he tried to calculate the standard deviation. During your second session he noticed you liked to doodle small geometric and fractal comics on his work sheets whenever he was solving a problem.

‘What did the triangle say to the circle?’ ‘You’re pointless!’

By the time your third session rolled around he still hated statistics, but it was too late and he’d developed a hopeless crush on you. Your monologues about dead mathematicians and the beauty of an infinite series were oddly captivating. He didn’t think he’d ever met anyone who was so passionate and animated about anything in all his life.

“Is everything okay?” Jungkook asked carefully. You seemed tired and a bit wary. “I-I mean, you don’t have to tell me if you don’t feel like it. Sorry, it’s none of my business,” he immediately added.

You smiled at his flustered state. Jungkook’s heart stumbled when your smile turned sad and you said, “No not really, but I’m sure I’ll be fine sooner or later.”

[13/04 19:12 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY]

1 Tangsuyuk (large) 1 Jjajangmyeon 1 Jjajangbap ---------------- Note: JK-nim! Omg your tangsuyuk is the best! I could drown in that sauce! How is Tokki doing?

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: JK ------------------- TO GO

1 Tangsuyuk (large) -- 20,000 1 Jjajangmyeon -- 4,500 1 Jjajangbap -- 5,500

Total: 30,000 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

Note: LatteIsHorse-nim! Little Tokki is doing well and bravely guarding our store! Don’t drown, but here’s some extra sauce for you to enjoy. I asked for it to be without pineapple. Hwaiting!

“Yah! Why does it smell like rotten take-out in your bedroom?” Jisoo asked.

Scowling has become your new go-to expression. “Too soon. Just let me wallow in my self-pity and sorrow.”

If you didn’t know any better you would’ve thought your friend was playing ‘The Floor Is Lava’ considering how gingerly she walked across your room. Safely on the other side, she ripped open a window to let some much needed fresh air in.

“I think you’re going to be wallowing in mold and fungus instead,” Jisoo commented with disgust. “Wallow all you want, I’m here to support you, girl. But I can’t allow you to turn your place into a biohazard zone. Isn’t your sister bothered by this?”

“My sister doesn’t care; our rooms are off limits to each other. As long as we both keep the common area clean, she won’t complain,” you said.

Jisoo sat down on your bed and patted the empty spot next to her. She immediately retracted her hand. “Eww, is that tangsuyuk sauce on your sheets?” she asked, completely appalled.

You shrugged and thumped onto your bed.

“So what are your plans for tonight?” she asked, trying to suppress a shudder.

“It’s Monday night. What plans could I possibly have?”

“We’re in college! Weekdays, weekends, they’re all the same!” your friend exclaimed. She looked at your sprawled-out figure. “I told you from the very beginning he wasn’t good for you. I know it doesn’t feel like this right now, but you’re lucky he’s out of your life. I really can’t watch you torture yourself over a jerk like him. Let’s go out to Hongdae!”

“I can’t go out. I already have plans.”

“Didn’t you just say you didn’t have any plans?”

“I lied. I have a date.”

Jisoo paused for a second, unsure how to respond. “Really? With whom?”

“Gong Yoo. We promised to kiss each other on first snowfall,” you responded listlessly.

“Yah!” Jisoo yelled and smacked your butt.

“Oww! What was that for?” you cried in surprise, rubbing the tender spot.

“Re-watching Goblin is not a date! You scared me for a second,” Jisoo said.

“How is it not a date? I meet a hot oppa, multiple hot oppas, we have dinner together, I giggle and blush and at the end of the night I get kissed to sleep.” You sat up and gave your friend a weary look. “I really don’t want to go out right now, but also don’t want to be on my own. Can’t we just stay in and watch a drama?” you asked with the saddest face you could muster.

Jisoo wanted to argue, but she couldn’t resist your pout. “Fine. But first you change your bedsheets, I’m not gonna sit in moldy tangsuyuk sauce all night. And I get to choose the drama.”

“Call!”

[16/04 17:58 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY]

1 Tangsuyuk (small) 1 Kimchi Kimbap 1 Beef Kimbap ---------------- Note: JK-nim thanks for the extra sauce! It was delicious. Are you a dipper or a pourer?

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: JK ------------------- TO GO

1 Tangsuyuk (small) -- 13,000 1 Kimchi Kimbap -- 2,500 1 Beef Kimbap -- 2,500 1 Soup -- 0

Total: 18,000 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

Note: LatteIsHorse-nim! Personally, I’m a dipper, but I don’t discriminate! I added some broth as service for you. It’s chilly tonight. Don’t catch a cold!

Paper Note: JK-nim, let’s be friends? I’m also a dipper! Did you know that butterflies can’t fly when they’re cold? Here is one that I folded, sending back my warmest thoughts to you on this frosty spring night.

The first thing that caught your eye was Jungkook who was patiently waiting at the library entrance. Despite the steaming goods in his hands, his entire body was shivering. The temperature suddenly dropped last night, but he couldn’t be bothered to dig up his padded jacket when he left the house this morning.

Before you could even greet him, he shoved a hot milk tea towards you and mumbled, “Here, it’s cold today so I thought you could use something warm.”

You were surprised by this sweet gesture. “Thanks,” you reached for it and examined the drink in your hand, ”How did you know I like black milk tea?”

He ducked his head and mumbled something into himself.

“Sorry, what did you say?”

Jungkook lifted his head. His cheeks and nose were a lovely wash of pink from the cold. “You mentioned once that you’re an OG milk tea drinker, so I just guessed” he repeated again, louder. “I saw this bungeoppang cart on the way here. We can share them while studying?” he said, holding up a small paper bag.

Your heart warmed and for the first time in weeks your face split into big smile, “Sure, I love bungeoppang! We’re not allowed to eat inside the library. So how about we eat everything first before they get cold and then go in?”

The both of you took a seat on a bench. By now Jungkook definitely regretted being too lazy to find his jacket this morning, but he was determined not to let it show. He passed the bag full of bungeoppangs to you.

You happily reached for one of the fish-shaped pastries and started munching on it. Your face crinkled, steam came out of your mouth. Jungkook’s heart skipped as he watched you in fascination. Your cheeks were flushed. A sudden instinct to stroke your rosy skin overcame him. Instead he reached for a bungeoppang and took a careful bite. “Are you feeling better today?”

“A little bit,” you said between bites, “I’m really sorry about last time. I feel bad now. I ditched you and now you’re treating me to snacks.” You went on and stabbed your straw through your milk tea. “I should be the one treating you instead.”

“I like to treat you,” Jungkook said, mesmerized by the way your lips moved against the straw. He suddenly realized what he was doing and cleared his throat, “A happy teacher is a good teacher! You’re already spending your time tutoring me.”

A laugh slipped out of you, “Jungkook, you’re paying me for your lessons. But it’s okay, this bungeoppang and tea definitely hits the spot, so I’ll accept it with a grateful heart. What are you drinking?”

Jungkook looked down on his drink and gave it a shake, the black pearls swirled around buoyantly. “Banana milk tea, I prefer sweet drinks.”

You leaned back against the bench and looked up at the clear blue sky. “Sweet things are the best combat against the bitter taste of life,” you sighed. You closed your eyes and soaked in the crisp air. Jungkook felt your melancholy, he could warm your body, but he didn’t know how to warm your heart.

“Sorry that I’m bothering you with my personal stuff. It’s just that I had a really bad breakup recently. I shouldn’t let it affect our lessons,” you said with a wistful smile as you lifted your head again.

The boy next to you remained silent. You turned and saw a contemplative look on his face. “It’s alright, everyone can have a bad day,” he finally said, “You don’t have to pretend to be okay when you’re not. If you’re never angry or sad, you won’t know when you’re happy.”

His words stunned you. Has Jungkook always been this thoughtful? You turned away from his gaze and looked down at the pastry in your hand. “They’re rhombus shaped,” you muttered in an attempt of distraction and showed your bungeoppang to Jungkook. “The fish scales,” you added when he looked confused.

“Ah yeah, the scales. It’s actually erroneous since most of the bungeoppangs depict a ganoid scale structure when in fact carps have cycloid scales to allow for a greater flexibility,” Jungkook explained.

A blank look appeared on your face. Probably the same blank look he had whenever you tried to explain the Bayes’ theorem to him. He let out an awkward laugh, “We studied the mechanics of fish scale structures in Material Science. You can correlate the flexibility of a scaled surface depending on its underlying geometric structure and material. It’s pretty cool stuff.”

“I can’t believe you can geek out about the geometry of fish scales, but don’t know how to define your probability population,” you snorted in disbelief.

“Hey, when will I ever need to calculate the probability of two people with the same birthday in a room? I just have a hard time learning stuff I never have to apply,” he said defensively.

Then you suddenly had an idea. “Tell you what, how about this? If you pass your statistics final, I’ll treat you to the best Chinese take-out in town! You can order whatever you want!”

Jungkook didn’t want to dampen your excitement by telling you that his part-time job already allowed him to eat as much Chinese take-out as he wanted. “Okay, but don’t complain when you go broke. My record was five jjajangmyeon and two tangsuyuk in one sitting.”

You batted away his challenge. “First you have to pass your finals,” you teased.

“I’ll pass,” Jungkook said.

You smiled at his cute determination. “Then it’s a date.”

Jungkook beamed back at you. “It’s a date.”

[05/05 18:21 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY]

1 Tangsuyuk (large) 2 Pork Mandu 1 Tteokkguk 1 Jjajangmyeon 1 Tteokkbokki ---------------- Note: No pineapple plz. JK-nim! Happy Children’s Day! For this special occasion I’ve decided to order all of my childhood favorites. Life is too short to eat bad food. I hope today you treat yourself to something delicious as well!

“Yah! JK! Your girlfriend placed an order again!” Yugyeom yelled across the store.

A mop of black hair peaked out from the back of the shop. “She’s not my girlfriend, she’s just a regular,” Jungkook yelled back.

“A regular you flirt with,” Yugyeom snickered, “I saw all the notes you left her in the system. ‘Don’t catch a cold!’, ‘Hwaiting!’ Don’t tell me that’s not your lame attempt at flirting.”

Suddenly an angry Yoongi stomped out of the kitchen. “Keep it down boys, we have guests here.”

Jungkook went up to the register and printed out the online order. “Hyung, can you make a large tangsuyuk without pineapple?”

“It’s a national holiday, there’s like two people here tonight,” Yugyeom muttered under his breath.

“What did you say, Yugyeom?”

“Nothing, hyung!”

Yoongi snatched the order out of Jungkook’s hand and gave both boys another irritated glance before he headed back into the kitchen.

“Hey JK,” Yugyeom said in a lower voice as he moved next to his friend, “aren’t you ever curious how LatteIsHorse is like? I mean, she must have some sense of humor judging by her username.”

“Sometimes. Don’t you ever wonder how our regulars are like? But it’s not like I’m ever gonna meet them or know it’s them when they come into the store,” Jungkook said with a shrug.

“You could though. Mingyu’s out on delivery, Eunwoo’s off so we have a free bike. The store is dead tonight. You could go deliver the order and have a look,” Yugyeom spurred him on.

Jungkook considered his friend’s suggestion. Every time he opened his locker a little origami bunny and butterfly stared back at him and brightened his day. It was true, he was curious how LatteIsHorse was like. “Okay I’ll go, but don’t pretend you’re doing me a favor. You just don’t want to do delivery tonight.”

A pretty girl in a Yonsei hoodie and shorts opened the door. She somehow looked familiar, but Jungkook couldn’t place from where. Maybe he met her on campus before.

“Delivery from Golden Bang,” Jungkook said, holding up his metal box.

“Ah great! I’m starving!” the girl said.

Jungkook started unloading the box and handed the dishes to the girl. Once he was done, he lingered awkwardly in the doorway. The girl gave him a curious look, clearly wondering why he wasn’t leaving. Jungkook gathered his courage and said, “I’m JK by the way.”

What followed was a beat of silence. Jungkook could feel his ears burn.

“Err, it’s nice to meet you, I guess? Is there anything else you need?” the girl asked after the painful pause. “Ah got it! Just a sec!” She ran into the apartment and came back with her wallet. “Here’s a tip, we’ll put the dishes back outside for pick up,” she said as she scrunched a bill into Jungkook’s hand, “Thanks for your hard work. Happy holiday!” And then she shut the door right into his face.

What just happened? Jungkook was stupefied. After an eternity he finally moved and mechanically pulled out his phone. He checked the delivery order on his app. LatteIsHorse – this was the address. She didn’t recognize him. Why was he so naive to believe that she would remember him? All he wanted in that moment was for the ground to open and swallow him up.

“Dinner’s here,” your sister said as you came out of the shower. “Did you order banana milk?”

“No? Why?” you joined her at the dinner table and started rummaging through the dishes. “Where’s the receipt?”

“I threw it in the trash,” she said. When she saw you opening up the trash can and fishing for it, she added, “Gross! What are you doing? Why do you need it?”

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: JK ------------------- TO GO

1 Tangsuyuk (large) -- 20,000 2 Pork Mandu -- 6,000 1 Tteokkguk -- 4,500 1 Jjajangmyeon -- 4,500 1 Tteokkbokki -- 3,000

Total: 38,000 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

Note: LatteIsHorse-nim! Happy Children’s Day to you too! I added my favorite childhood drink, banana milk! I hope it brings back as many happy childhood memories for you as it does for me.

There, sitting on the table, was a small bottle of banana milk. A smile spread across your face. “I need to file it away for tax purposes.”

Your sister looked at you like you were crazy. “Let’s eat already, I’m starving. Wash your hands.”

[14/05 16:55 PM] User: LatteIsHorse ---------------- ORDER [TAKE AWAY]

1 Tangsuyuk (small) 1 Jjajangbap ---------------- Note: JK-nim, hope you’re doing well. I’m in the area today, so I thought I’d stop by and say hello in person! Is it weird that I feel a bit nervous?

The restaurant door wasn’t going to open itself. The past 15 minutes of you standing in front of it has proven that. You had some errands to run in Hongdae after school and decided on a whim to place a pickup order at your favorite take-out place.

Why was it so difficult to enter a restaurant? If you steeled your nerves any more, they’d probably break from how brittle they’ve become. You just had to open that damn door.

Sometimes you wondered if you liked that place more because of its great tangsuyuk or because of JK’s little notes which always managed to put a smile on your face.

One thing was for sure, you weren’t stalling because of the tangsuyuk.

“Welcome to Golden Bang!” a bright male voice rang across the restaurant as you passed through the door.

You walked up to the register and sneaked a peek at the boy’s name tag, ‘Yugyeom’. You felt a slight twinge of disappointment.

“I’m here to pick up my order? LatteIsHorse?” you asked tentatively.

A sign of recognition flashed across Yugyeom’s face. “Of course, your order’s ready! I’ll just bag it up for you,” he said cheerfully. He walked away and quickly came back with a white plastic bag full of food. Then he printed out your receipt and handed both to you.

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: YG ------------------- TO GO

1 Tangsuyuk (small) -- 13,000 1 Jjajangbap -- 5,500

Total: 18,500 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

You looked around the restaurant, it was empty since dinnertime was still a while away. You wondered if Yugyeom was managing the store alone right now. At least the cook must be in. “Your tangsuyuk is really delicious. It’s probably my favorite.”

Yugyeom gave you a big smile, “Happy to hear that you enjoy our food so much. The tangsuyuk is our chef’s family recipe. It’s one of our most popular menu items!”

You wringed your hands and finally decided to bite the bullet and straight out ask, “Is JK here? He usually takes my orders when I order delivery, so I just wanted to say hi.”

“JK’s shift doesn’t start until 6, so he should be here in about half an hour. If you want, I can relay a message,” he said with a knowing smile, “Or you can also take a seat and wait for him. I’m sure he’d be thrilled to meet you.”

No way you were going to sit here for half an hour and wait up for a stranger. “Ah no, that’s alright. If you could just say hi from me, that’d be great,” you quickly replied with a flush. JK would probably think you’re a creepy stalker.

“Sure, can do! Enjoy your day!” Yugyeom said merrily as you walked out the store.

A feeling of both relief and sadness passed through you. You slowly walked down the busy streets of Hongdae as you reprimanded yourself for being so stupid. What were you going to say to JK anyway if you met him? Thanks for being nice to me? You’re the reason I don’t burst into tears every single night? You’re the reason why I don’t feel completely alone when I’m sobbing into my food over Song Joong Ki’s acting? Thanks for making me gain 3 kilos in the last month?

Whatever you said, it would’ve only made you sound pathetic.

A crippling wave of desperation suddenly washed over you and rooted you in your tracks. A single tear rolled down your face. Then another. You dropped down into a crouch and started to bawl. You couldn’t fathom how you’ve reached this all-time low in your life. Why did you feel so incredibly sad about being stood up by a stranger? Especially when that stranger didn’t even know you were coming?

“Y/N?” an alarmed voice asked. You looked up when you felt a soft shake against your shoulder.

Through your tear-blurred eyes you recognized Jungkook’s face. He crouched down next to you and asked, “Is everything okay? Are you hurt?”

You shook your head and tried to wipe away your tears. It was a useless attempt as they kept on streaming down your face.

Jungkook hesitantly pushed your hair out of your face and asked, “Do you want to go somewhere else so you can tell me what happened?”

You gave him an imperceptible nod.

His hand gently moved down to your arm, afraid that you were going to push him away. With a steady grip he slowly helped you back onto your feet. Then he slid his hand through yours and led you down the hustle and bustle of Hongdae until you ended up in front of a convenience store located in one of the quieter residential side streets. He sat you down in a plastic chair and told you to wait. After a while he came back with a packet of tissues, a bottle of water and two red bean popsicles.

You gratefully took the tissues and loudly blew your nose. A small part of your brain told you to act more ladylike, especially in front of Jungkook, but the bigger part didn’t really care and just wanted to drag you back down into the pits of loneliness. A strangled sound came out of your mouth as you started to hiccup, making you sound like a drowning cat.

You expected Jungkook to laugh at your weird orchestra of emotions. Even you found it absurd and would’ve laughed if you weren’t already crying and hiccupping at the same time. But all he did was quietly open the water bottle and hand it to you.

As soon as you lifted the bottle to your mouth another hiccup made you almost spill the water on yourself. You held your breath for a few seconds and then took a careful sip. It seemed to work. You took a bigger sip, when another hiccup racked your body and you squeezed water all over your face.

There was a bewildering moment of shock, then you started to laugh deliriously. Forget before, this was your lowest point in life. This was so pathetic that it was hilarious again. Your laughter garbled whenever you hiccupped, only causing you to laugh even harder. You would’ve continued laughing for another long minute if you weren’t choking for air.

A small smile played around Jungkook’s mouth. He took another tissue and started wiping down your face. You hiccupped under his touch. He must think you’re a nutcase.

“I have a question. We have to do some statistical testing in my Quality Management class. What would a hypothesis look like if I wanted to analyze any deviation in a spare parts production line due to temperature conditions?” Jungkook asked.

Did he really forget hypothesis testing already? He finally managed to get it after four sessions! You frowned slightly. “You could set up a null hypothesis stating that a variation in temperature does not significantly impact the parameter of measurement in your production line. Jungkook did you seriously forget this?!” you said indignantly.

Jungkook gave you a playful laugh, “No, I think you drilled it so hard into my brain, I could probably recite all variables of the standard deviation formula if you woke me up in the middle of the night. Your hiccups stopped though.”

They did.

Embarrassment set in as you realized your predicament. Maybe your hormones were going crazy, maybe you were going crazy. You were getting whiplash from the emotional roller coaster you were on. In an attempt to hide your disgrace, you picked up another tissue and wiped away the remaining water, snot and tears.

There was tangible awkwardness in the air.

“I hope you like red bean,” Jungkook said shyly as he unwrapped a popsicle, “Red bean is my favorite. My friends keep on calling me old fashioned, but it just reminds me of the time when my mom used to buy me these after taekwondo class. I think I liked the popsicles more than I liked going to class.” He sighed in reverie and held up the popsicle for you.

You stared at his hand. You remembered how it felt against yours just a few moments ago. Firm, warm and steady. Then you looked up at Jungkook. He hid it well, but you could tell that there was concern behind his encouraging smile.

“This is so embarrassing,” you said as you accepted the popsicle and turned your head away from him, “I don’t know what is wrong with me right now. I’m usually not like this.”

“Did something happen earlier?” Jungkook asked cautiously as he unwrapped his own popsicle and took a bite out of it.

Did something happen earlier? Why did you cry? Where you really crying just because you didn’t meet JK?

“No,” you said and slowly shook your head, “I don’t know. I just suddenly felt overwhelmed.”

Jungkook hesitated before he asked, “Are you sad because of your breakup?”

Were you sad because of your ex-boyfriend?

“I don’t think so. In the beginning when we broke up I was devastated, but I don’t think that’s the case anymore,” you said more to yourself than to Jungkook. “Everyone told me I was lucky to be rid of him. I really didn’t understand why. But I think it’s becoming clearer now. Maybe it’s not sadness. Maybe it’s fear. I think I just feel lost. I don’t know who I am anymore. Maybe it scares me to know that I was able to lose myself and I don’t know if I can find a way back.”

Before you knew it, you spilled your heart, your deepest and darkest fears to Jungkook. You barely knew this boy, yet it still felt oddly comforting. He remained quiet and listened.

“I wanted to meet someone today, but they weren’t there,” you continued, “I think in that moment I just realized how utterly lost I was on my own.”

Jungkook searched for the appropriate words. How do you respond to someone’s most vulnerable thoughts? “I mean you know what they say. It’s not about how much you’ve lost, it’s about how much you have left.”

He peeked at you to check if it worked.

“Jungkook, did you just quote Iron Man at me?” you asked incredulously before a giggle slipped from your lips.

You noticed how his cheeks dimpled when he gave you an embarrassed laugh, “Sorry, I was trying to say something that would cheer you up. I’m probably not doing a very good job.”

In that second you realized how kind-hearted Jungkook actually was. Your heart squeezed. “Don’t say that. Thanks for listening to my problems. And thanks for the red bean popsicle. I also ate this a lot in my childhood. Mainly because my sister hated them. She always used to steal my ice cream out of the freezer so at some point I asked my parents to only buy me red bean popsicles. She never touched those,” you reminisced.

Jungkook laughed at your story, “Your sister sounds like a piece of work.”

“We used to fight a lot, we used to never get along,” you became thoughtful, “At some point that stopped. I think we just grew up and grew to understand and accept our differences. She doesn’t steal my food anymore. I don’t steal her clothes anymore. We may not always agree, but we respect each other’s decisions.”

“You know, for someone who just said she feels lost, you sound pretty self-reflected right now,” Jungkook mused, “Maybe you need to do the same as you did with your sister. Understand yourself and accept the differences of your past and present.”

You paused at this. He was right. You were so desperately trying to fend off these negative emotions that you never took the time to actually think. You were chasing an image that never existed. Not in the past nor in the present.

“You’re surprisingly good at giving advice. Thanks, Jungkook,” you said.

“Surprisingly? What’s that supposed to mean?” he asked, offended. The glint in his eyes gave his teasing away.

Laughter pealed from you. Jungkook was captivated by the sound. He drank in the way your eyes creased with mirth and followed your fingers as they brushed back your hair.

Jungkook’s phone vibrated. “Oh shit!”

“Is everything alright?”

“Yeah, don’t worry. I was actually on my way to work and my boss is asking me where I am,” he said as he stuffed his phone back in his pocket.

Jungkook startled when you suddenly jumped up. “Then you should get to work! You should’ve said something sooner. I’m so sorry for keeping you here!”

“No, it’s really fine. I’ve done enough overtime. He won’t complain if I’m a few minutes late,” he said, “Are you feeling better?”

You ignored his question and pushed against his shoulders to get him out of the chair. “Go to work, Jungkook. I’ll be fine, your red bean popsicle did wonders,” you responded placatively.

When he still didn’t move, you grabbed his arm and pulled him back onto the main street. Jungkook’s skin scorched under your touch. “Go to work, Jungkook,” you said again with more emphasis.

“Are you sure…?” he asked, unwilling to let you out of his sight before he knew you weren’t just going cry again at the next street corner.

“I won’t burst into tears,” you said as if reading his mind. “You were right, I need to reconcile with myself. So I’ll go home, enjoy my dinner and think about who I am and who I want to be. And you,” you said giving him another gentle shove, “need to go to work.”

Jungkook saw the stubborn look on your face. He wondered if you realized you were using your teaching voice right now. You weren’t going to take no for an answer. “Okay fine, text me when you get home?”

You waved away his concerns. “Sure. Go already,” you said with a big reassuring smile. “See you tomorrow at school!” you added before you turned around and walked away.

“You’re late,” Yugyeom said as soon as Jungkook entered the store.

Jungkook gave Yugyeom a sheepish look and only muttered, “Yeah sorry, something came up on my way here.” Then he rushed past him to the back of the restaurant and changed into his uniform.

Once he came back out he noticed Yugyeom throwing him strange looks.

“What?”

“Your girlfriend says hi,” Yugyeom said with a hint of amusement.

“Who?”

Yugyeom gave Jungkook a meaningful look, “LatteIsHorse. She ordered pick up. I think she was hoping to meet you. She’s cute. She looks like she’s probably a college student around here.”

“I know,” was all Jungkook replied.

Yugyeom’s eyes bulged in curiosity, “You know? You know she’s cute or you know she’s a student? You never told me what actually happened that night!”

Jungkook gave him a tired look and said, “She didn’t recognize me. She wore a Yonsei hoodie, so I guess she goes there. Nothing else happened.”

“Hmm, that’s weird. She was asking for you today, so she definitely knows your name,” Yugyeom said.

“Who knows, maybe she was having a lot on her plate that day,” Jungkook said with a shrug. He wondered where you lived and if you already got home safely. “Why are you obsessing over this so much?”

“Man, do you know how painful it is to watch your sorry attempts at flirting? I’m just trying to help you out, mate,” Yugyeom quipped.

“I wasn’t flirting! I was just trying cheer someone up who was obviously feeling down! It’s called being a decent human being,” Jungkook exclaimed.

Yugyeom gave him the side eye, “Yeah, that’s still not gonna get you laid.”

[19/05 18:47 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY]

1 Tangsuyuk (small) 1 Bibimbap ---------------- Note: JK-nim, I visited you at the store last week, but you weren’t there. TT-TT I hope you don’t think I’m weird, I just really like talking to you. You always manage to put a smile on my face when I’m having a hard day. We’re still friends, right?

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: JK ------------------- TO GO

1 Tangsuyuk (small) -- 13,000 1 Bibimbap -- 5,000

Total: 18,000 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

Note: LatteIsHorse-nim! I’m sad that I missed your visit to our store. I’ll try harder the next time! I added some extra bulgogi to make up for it. :) Of course we’re still friends. I don’t wish any hard days upon you, but I’m glad to hear that my words have a healing effect. In case you ever need a friend to talk to, feel free to talk to me. 010-1234-5678.

The study sessions with Jungkook continued per usual. He still struggled and had frustrated outbursts from time to time, especially when you forced him to revise probability distributions. When you finally reached regression analysis, things became easier.

Although your sessions remained the same, something in your dynamic changed. The both of you became looser and more playful around each other. He wouldn’t clamp up anymore and you felt more at ease around him. You became friends. He never once mentioned that disasterous afternoon.

At home, on the evening of the incident, you shot Jungkook a text and slumped down on the couch. Your sister was out that night, so it was just you in the apartment. Normally, the eerie quiet would’ve unsettled you and you would’ve distracted yourself from your deafening thoughts. But that night you just let them scream, yell and tear at you.

It was an excruciating process, but in the end your head was clearer, your heart calmer. You still weren’t quite there yet, but at least you made a first step out of the endless pit of desperation.

There were other things you noticed about yourself. Gradually you realized you didn’t mind being on your own anymore. You rediscovered your love for drawing and created you own mandala art. You also learned to code your own website and now had a clickable version of your cv on the go. Although you made time for yourself, you weren’t a hermit. You went out for drinks with Jisoo and soon asked Namjoon to take you along to your university’s Math Club. There you met a lot of familiar faces that you’ve encountered in class but never talked to. With them you spent animated evenings discussing stimulating math problems and exchanging incredibly bad math puns.

You also started noticing things about Jungkook. He wasn’t as timid and shy as you initially thought. Once he got over his awkwardness, he turned out to be quite a cheeky and goofy guy. He teased you or told you silly jokes whenever you were on a break. Despite his obvious aversion for statistics, he still took your lessons very seriously. Diligently listening to your explanations and trying to solve the problems to the best of his abilities. His study-mode showed you other sides of him. The cute pout he had whenever he tried to hide his confusion. Or the two little ridges which formed between his eyes whenever he was concentrated and deep in thought. More often than not you fought the urge to smooth them out with your touch or even better, with a kiss.

“Is something wrong?” Jungkook asked when he caught you staring.

“No,” you quickly said, “I was just thinking that you don’t seem to have much trouble with regression analysis.”

“I don’t know, the relationship between the variables just makes much more sense,” Jungkook said.

You looked at him and considered, “Hmm, maybe you don’t need my tutoring anymore?”

Brief dismay crossed Jungkook’s face. “My finals are in three weeks. I think I’d still prefer if you helped me revise the earlier chapters,” he said, “Unless you need more time to study for your own finals.”

Being in college meant that you were always in dire need of more time. That constant nagging voice in the back of your head telling you to study was an occupational disease. But you didn’t have to kid yourself, those four hours a week spent on Jungkook weren’t going to make or break your grade. Besides, you enjoyed spending time with him. You wondered if he felt the same.

“It’s alright, I’ll help you revise. Just don’t embarrass me on your finals. I don’t want Namjoon to tell me afterwards that you didn’t manage to calculate the mean of the population or worse, read the scoring table upside down,” you teased him light-heartedly.

Jungkook’s ears turned bright red. “That happened once!” he said, “How long are you going to hold that over my head?”

You laughed at his indignation. “Don’t forget, you’ll get endless tangsuyuk if you pass.”

[26/05 20:09 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY]

1 Tangsuyuk (small) 1 Jjamppong ---------------- Note: JK-nim, I’d like to get the advice of a friend. There’s this kind, sweet boy that I really like. I would like to tell him how I feel, but he’s seen me in my lowest and ugliest moments. Maybe he’ll think I’m just baggage? I guess I’m afraid of his rejection.

Golden Bang 7 Wausan-ro 29-gil, Seogyo-dong

Server: JK ------------------- TO GO

1 Tangsuyuk (small) -- 13,000 1 Jjamppong -- 5,000 1 Soju -- 0

Total: 18,000 -------------------- Thanks for ordering at Golden Bang! Have a golden day!

Note: LatteIsHorse-nim! It’s only human to fear rejection. I can completely understand. I also have someone I really like. She’s really pretty, smart and funny. Spending time with her makes me really happy, but I never managed to tell her. Maybe we should both gather our courage and cheer each other on? I’m not saying that drunken confessions are the way to go but consider this soju a symbolism for (liquid) courage.

Paper Note: This is a flexagon. Whenever you need a word of encouragement give it a flip!

Jungkook examined the hexagonal origami in his hands. On the outside it read ‘Flip Me!’

He gave the flexagon a flip. ‘JK you’re the best!’ And another. ‘The world needs more people like you!’ And another. ‘Don’t forget that LatteIsHorse is always rooting for you!’ And another. ‘Aja, aja, hwaiting!’ And another. ‘Thank you for being my friend!’

Jisoo barged into you room and flopped onto your bed. ‘Ahhh! I’m so glad you finally cleaned in here. Seriously, if I find another rancid noodle stuck to my clothes, I’ll call in a hazmat team.”

“I don’t know why you’re complaining so much. It’s not even your room,” you said.

“Hey, where are you ever going to find a friend like me?”

Your friend sacrificed many a night away from college parties to binge watch handsome oppas sweep equally beautiful unnies off their feet with you. And she wasn’t shy telling you that.

“Let’s go out tonight,” Jisoo suggested. She rolled back onto her feet and started walking around, inspecting your cleaning job.

“Our finals start in two weeks; I really don’t want to spend my weekend nursing a hangover.”

“I’m not saying you have to get wasted. Tonight is the Pre-Game Night. We have to go!” Jisoo demanded.

The Final’s Pre-Game Night was a campus-wide tradition. Every semester on the Friday a week before finals huge parties were thrown to signal the beginning of the end. It was like a dare – were you confident enough to get completely drunk and still hope to pass your finals? Naturally everybody on campus joined in and drank.

“Not getting wasted at a Pre-Game party? That’s like saying you’ve decided you don’t need to breathe. I really don’t think…”

“What’s this?” Jisoo suddenly interrupted. “LatteIsHorse-nim! Personally, I’m a dipper, but I don’t discriminate! I added some broth as service for you. It’s chilly tonight. Don’t catch a cold!” she read aloud, “LatteIsHorse-nim! Happy Children’s Day to you too! I added my favorite childhood drink, banana milk! I hope it brings back as many happy childhood memories for you as it does for me.”

You flung yourself across the room and almost tripped over your own feet trying to rip the receipts out of Jisoo’s hands.

“Oh. My. God. Is your take-out guy flirting with you?!” she asked.

“No! He’s just a friend. We send encouraging notes to each other,” you tried to explain.

Jisoo threw her hands in the air. “Okay that’s it! We’re going to the Pre-Game party, whether you want or not. You can’t tell me that the only flirting interaction you have is with a stranger who delivers you tangsuyuk!”

The place Jisoo picked out was ram packed and buzzing with energy. It was an open dorm party; all the common rooms were transformed into dancefloors. Different types of music played from each corner of the building. Crates of alcohol were stacked against the walls.

The both of you grabbed a beer and made your way through the crowd.

“You’re going to have fun tonight, alright?”

“I don’t think this works that way,” you laughed.

“Then put some effort into it. We look way too cute for it to go to waste,” she said as you roamed around the floors and explored the different areas. You looked down on your dress. It was a pretty warm night; you had opted for a flowy summer dress with a blush pink floral pattern. Jisoo was right, it was cute.

You discovered a familiar face at the edge of the crowd. “Sunbae!” you said.

Namjoon turned around gave you a surprised smile. “Y/N! Out of all the places on campus, we meet each other here tonight. What are the chances?”

He was surrounded by a group of friends, you spotted Jungkook right behind him. The boy gave you an excited wave. A slow smile spread across your face. “I don’t know, but why don’t we ask Jungkook to calculate it for you?”

Namjoon let out a hearty laugh while Jungkook groaned in exasperation.

“Do you see what I have to put up with every week, hyung?”

“Didn’t you just say it’s the best thing that happened to you?” Namjoon taunted, “You have some nerve showing up in front of me tonight. You better ace your SA finals. Do you know how many favors I had to pull to get Y/N to tutor you?”

“What do you expect me to do?” Jungkook sputtered, “Go home and lock myself up on Pre-Game Night?”

If it weren’t for Jisoo you would’ve done just that. Speaking of Jisoo, your friend cleared her throat and gave you a painful nudge in the side.

“Ah yes, uhm, Jisoo you already know Namjoon. This is Jungkook. You know, the guy I’m tutoring.”

Jungkook gave her a small wave.

Jisoo didn’t even try to hide her amazement. “This is Jungkook? But you’re like wayyy cute!” She turned to you and added still loud enough for everyone to hear, “Why didn’t you tell me he was cute?!”

The embarrassment was obvious on Jungkook’s face. You could tell that Namjoon was getting a rush out of his dongsaeng’s reaction and before he could provoke him any further you decided to jump in.

“Who wants to go dance?” you asked loudly. You turned around and headed to the dancefloor without waiting for any of them to respond.

“Why didn’t you tell me you were tutoring a hunk?” Jisoo muttered under her breath.

“He’s not a hunk. Don’t call him that.”

“Yeah but he’s hot. You made him sound like he was a nerd.”

“He is a nerd.”

Your friend gave you a glare, “Why are we arguing about this? I know you’re not that oblivious.”

Of course you weren’t oblivious to Jungkook, but you weren’t going to tell Jisoo that.

“Let’s dance.” You grabbed Jisoo’s hand and twirled her around.

Namjoon and his friends joined you on the dancefloor. The mood of the crowd was electric. Music pulsed through your veins. Drinks flowed, shots were downed, people pulled out their best, lamest, craziest dance moves. Everyone celebrated like the world was going to end.

After a while you became hot and needed a new drink. You looked around for Jisoo and saw her grinding up against one of Namjoon’s friends. She’d be busy for a while. You inconspicuously moved away from the group and decided to go get some fresh air.

“Wait up,” Jungkook said as he appeared next to you, “are you getting something to drink? I’ll join you.”

His dark curls were slightly matted with sweat. His baggy t-shirt clung to his body. You weren’t sure if it was the alcohol or Jisoo’s damn voice whispering into your ear. He was hot.

You circled your arm through his and pulled him through the crowd. His muscles shifted under your touch. You grabbed two drinks from a crate and handed one to Jungkook, your nerves tingled when his hand brushed against yours. The both of you remained in comfortable silence, leisurely walking through the dorm, neither of you in a hurry to get back to your friends. You explored the facility areas, weaving through pounding and quiet parts of the building.

“You look really nice tonight,” he said after a while.

The heels of your shoes echoed against marble floor of the dark hallway. “Thanks, Jisoo raided my closet.”

“She’s really something isn’t she?”

“She’s the best. I’m grateful to have her as my friend.”

Somewhere further down the hallway you made out two figures pressed against the wall, probably trying to find a quiet place of their own.

“You also look nice,” you said to Jungkook.

“I’m wearing the same things I always do,” Jungkook said, his voice turning shy.

You were getting closer to the couple. You could see how the guy was sticking his tongue down the girl’s throat. She seemed to enjoy it from the sounds she was making. Lucky them.

Your next words were definitely fuelled by your tipsy state, “I guess that means you always look nice.” Jungkook missed a step. You had to laugh at his blunder.

The couple in front of you broke apart and looked in your direction. More annoyed about being interrupted rather than embarrassed being caught. You were about to make a funny comment to Jungkook when your heart stopped and you froze.

A string of saliva still clung to the guy’s lips. His eyes widened when he recognized your face in the darkness. “Y/N?”

Your breath hitched and your grip tightened around Jungkook’s arm. He glanced between you and the guy, the situation slowly dawning on him.

“Why did you stop? Who’s that?”, the girl whined.

“No one,” the guy responded as he returned his attention to her and they started making out again.

Jungkook didn’t know if he wanted to puke or punch that guy. A sharp pain in his arm brought him back to his senses. Your nails dug into his skin. He put his hand around yours and loosened your iron grip.

“Let’s go,” he said and quickly pulled you past the couple. You followed him in a daze. He stopped once you were outside of the building, hidden away in a quiet corner.

His hands reached for your face and he lifted your eyes to his. “Breathe.”

You closed your eyes, let out a long breath and let your head fall against the wall behind you. The horrible encounter replayed in your mind. You had to open your eyes again.

There he was right in front of you. Worried Jungkook, kind Jungkook, beautiful Jungkook.

Your hands reached behind his neck and you pulled him a bit closer. You tried to decipher his gaze, it was dark and yearning. Everything was a haze, the alcohol in your blood made you daring.

“Kiss me,” you whispered.

His mouth crashed against yours. Your hands slipped up into his hair and your bodies entwined. You opened your lips and sucked in his hot breath. Your tongues found each other; he groaned at your taste.

He moved one of his hands down your side until he found purchase on your leg and hitched it up against his waist, pressing his body further into you. You let out a moan when his hips ground into yours.

All your senses drowned in Jungkook. You drowned in his scent, you drowned in his touch, you drowned in his heat. You tried to use Jungkook to drown out the grotesque image from before. Suddenly the heat of the moment disappeared, and a cold shower ran down your spine.

You broke away from your breathless kiss and put your hands against Jungkook’s chest to put some distance between you. He gave you a disoriented look.

“I’m sorry. We shouldn’t have kissed.”

Jungkook’s eyes grew wide and alarmed. “Did I do something wrong?”

His lips were swollen, his hair was mussed. You wanted nothing more than to pull him back in, but you couldn’t. Not here. Not like this. He deserved better.

You pushed yourself off the wall and gave him a small shove. He immediately let go of you and stepped back. “I shouldn’t have kissed you like this,” was all you said before you ran back into the building.

The next day you woke up to a splitting headache and a heart full of regret. You really needed to talk to Jungkook and explain to him why you ran away the previous night, but you were too much of a coward to pick up your phone and contact him. You decided it was better to talk to him in person at school.

The following week at school you waited for him in the library. Your heart was in your throat. Your prepared speech played in an endless loop in your head.

‘I’m sorry I ran away. I shouldn’t have kissed you in that state. It wasn’t fair to you. You deserve better than that.’

You looked down on your phone to check the time. A message blinked. You opened and read through it. Your heart sank. He wasn’t coming. He wanted to study the last week before finals on his own. He thanked you for your time.

Slowly you got up and packed your bag. You blew it. You wanted to do him right, but you only caused him pain. Thinking back, you realized he gave and gave and gave and all you did was take. He was right to stay away from you. There was no way he’d be happy with someone like you.

The week passed and finals week commenced. You immersed yourself in your exams and tried to get over your heavy heart. You were pretty sure you aced Geometry II, but the Numerical Analysis exam was nothing but a blur.

Although your heart ached, you didn’t fall back into the same dark pit of the past. You didn’t feel lost, you got on with your life. Nobody noticed the Jungkook-sized hole in your heart except for you. You wanted to talk about your feelings, but you didn’t think Jisoo or your sister would understand. They’d probably just tell you to get out there and find a new guy.

Another week passed. You were walking out of your professor’s office, finalizing the details of your summer internship, when you bumped into Namjoon.

“Y/N! What are you doing here? Aren’t you off for summer break yet?” he asked.

“I was just discussing my internship with Prof. Kim,” you said.

“Ah you’re participating in his research program?” Namjoon said, “I heard it’s really interesting, he’s intense though.”

“I think intense is fine for me, I need something to do with my brain. Otherwise I’ll just go crazy,” you said with a smile.

“Speaking of intense, what did you do to that kid?” Namjoon suddenly asked.

You tensed. Did something happen to Jungkook? “What do you mean?”

“Did you brainwash him or something? He got a 98 on his SA final! When I handed him over to you, he was still asking me why the positive and negative z-scores tables had different values,” Namjoon said in awe.

Relief washed through you and your chest filled with pride. “Watch out sunbae, I might be coming for your TA position,” you said with a wink.

At home you sprawled out on the couch. Your sister’s classes ended earlier than yours so now she was away with her friends travelling the countryside. Your mind wandered as you stared up at the ceiling of your quiet apartment. You really wanted to call Jungkook and congratulate him, but you didn’t think you should. He clearly didn’t want to be in contact with you, you hadn’t heard anything from him since his text canceling your study sessions.

A pang of sadness washed through you. It should have been a happy moment for the both of you, you should be eating tangsuyuk together right now. You really wanted to tell someone about your joy and your grief.

Then you suddenly remembered your friend. Your friend who never judged and always had something wise to say. Maybe he would understand the conflicts of your heart. You got up and dug through the receipts on your desk until you found the one with his phone number on it.

You hoped he wouldn’t think you were crazy, but then again, he was the one who offered himself to talk to you any time. You typed in the number and hit call. Your phone dialed when suddenly the number displayed switched to a name. Jungkook.

You quickly hit the cancel button and stared at your phone. Did you accidentally hit Jungkook’s contact? Was your phone broken? This time you typed in the number more carefully and hit call. Again, the display switched to Jungkook’s name. You hit cancel.

Your heart began to race. You opened up Jungkook’s contact and compared it with the number on the receipt.

Holy shit.

JK was Jungkook. Jungkook was JK.

The stranger who cheered you on and made you smile whenever you felt down was Jungkook. You combed through all your receipts and reread them one by one. What was the probability for this to happen? This was so bizarre, but it made so much sense. Jungkook was the kindest person you knew. Why wouldn’t he be kind to a stranger who needed some uplifting words and comforting tangsuyuk?

[13/06 18:20 PM] User: LatteIsHorse ---------------- ORDER [DELIVERY]

3 Tangsuyuk (large) 6 Jjajangmyeon ---------------- Note: JK-nim, I hope you’re doing well! Can I ask you for a strange favor? Would you mind delivering today’s order to me? I would really like to meet you and thank you in person for always being by my side! <3

The doorbell rang. Your heart pounded painfully in your chest. You slowly walked up to the door and opened it.

“Delivery from Golden…,” Jungkook’s voice faltered.

“Hi JK-nim,” you said quietly. You opened the door wider. “Thanks for coming today.”

“Y/N? What are you doing here?” he asked.

You had to smile at his look of utter confusion. “I live here. Come in, you can put the food on the dining table.” You turned around and walked back into the apartment.

Jungkook hesitated before he followed you inside. He moved up to the table and unloaded his box. He tried to steady himself. “You’re LatteIsHorse-nim?” he asked skeptically, “I’ve been here before. Last time someone else opened the door.”

He has visited you before? “Oh, that was probably my sister. I live here with her. She’s out travelling right now.”

“So you’re on your own right now? Why did you order so much food?” he asked. A giant mountain of neatly stacked dishes graced the table.

You came up and pried the metal box out of his hand. Then you moved in front of him and unclasped his bike helmet. He flinched at your sudden closeness.

“To celebrate. Congratulations on passing your Statistical Analysis exam. Namjoon told me you passed in flying colors,” you said in a gentle voice. “I promised you the best Chinese take-out in town, didn’t I?”

Jungkook still looked shell-shocked and simply stared at you.

“I’m sorry about that night at the Pre-Game party. I’m sorry I ran away. I owe you an explanation.”

Jungkook regained his wits and swallowed. “It’s okay, you don’t have to explain yourself. I get it, we were drunk. It was a mistake.” He looked down and tried to turn back around.

You grabbed onto his hands before he could move away. “Jungkook, look at me.”

He stopped turning, but his eyes remained on the floor.

You took a deep breath and squeezed his hands. “I really like you. I’ve really liked you for a while now.”

His eyes shot up to your face.

“The reason why I ran away that night was because I felt guilty. I probably would’ve ended up kissing you anyway, but in that moment, I kissed you because I wanted to forget. I didn’t want our first kiss to be like that. I wanted it to be the me who liked you and not the me who tried to drown out her shitty ex-boyfriend. I’m sorry if I hurt you.”

There was an unreadable look in his eyes. Your heart fluttered in nervousness. “How long have you known I was JK? How long did you know I had a crush on you?” he asked.

You could feel your blood rushing through your ears, the butterflies in your stomach beat like crazy. “Since today. I was sad because I thought I couldn’t share the promised meal with you. I wanted a friend to talk to, so I thought to call you. You who was always kind to me, even when I wasn’t kind to myself. Isn’t fate strange? We cheered each other on to find each other.” You had to laugh at the irony of it all.

Your hand hesitantly moved up to his face and stroked across his cheek, “I’m sorry I hurt you. I’m sorry I made you sad.”

Jungkook melted against your touch. “If I’m never sad, I won’t know when I’m happy.” Then he closed the gap and pressed his lips against yours.

It was a sweet but sad kiss. Filled with happiness and sorrow. Every touch was filled with an ‘I missed you’ or an ‘I’m sorry’.

Jungkook pressed you against the edge of your dining table, he lifted you up and you wrapped your legs around his waist. You both deepened your kiss. Your hands snaked through his hair and pulled him closer into you. Jungkook braced his hands against the table and instinctively ground his hips against your core. You moaned his name at the sensation. The both of you broke apart to catch your breaths, you pulled at his jacket and removed his layers of clothing.

You stilled at the sight of his bare chest. He was truly beautiful. Your fingers traced along his skin and marvelled at its silkiness. Jungkook shuddered under your touch. His hands moved under your shirt and you both lifted it off your head. Then you gripped his hands and slowly led them around your back, urging him to take off your bra. You wriggled out of your jeans and laid yourself completely bare in front of him. Jungkook stopped and stared at you, equally amazed.

“You’re so beautiful,” he whispered.

Your heart swelled and you pulled him back into a kiss. Both his kisses and his hands left a burning trail down your body. His mouth sucked on the soft skin of your neck while his hands moved across your breast, across your stomach, lower and lower. Wetness gathered between your legs.

“Jungkook,” you sighed. The muscles of his back shifted under your touch.

He released your neck with a loud smack and looked at the artwork he created. He still couldn’t get over how overwhelmingly beautiful you were. Your cheeks flushed, eyes bright and his name at the tip of your tongue. He felt himself strain against his confines.

“Please,” you whimpered. You looked down at his hand and tried to silently command him to touch you.

He kept his eyes trained on your face when his fingers moved lower and slid through your folds. Another moan left your lovely lips. He teased you with his touches, gathering your wetness until he finally pushed down where you wanted him most. Your hands dug into his back, your hips bucked, and you threw your head back in pleasure. He steadied your hips with his other hand and slowly pushed a finger inside of you. Another loud moan echoed through the room.

Jungkook was transfixed by you. He added a second finger and started pushing in and out. Your eyes squeezed shut in pleasure and small breathless pants left your mouth. Jungkook increased the speed of his movement and marvelled at the way you reacted under his touch. Then he moved his mouth to your breast and closed his lips around your nipple. You raked your hands through his hair and arched into him. Your core tightened around his fingers. All your nerves were on fire.

You pulled him away from your breast and guided his mouth back to yours. Your tongue traced his lips and you swallowed his moan. You wanted more, you wanted him closer. His fingers curled and his thumb pressed down on you. Jungkook held you tight as you shuddered and fell apart around him.

He rested his forehead against yours, your breath mingled as you both panted into each other. He slowly removed his hand from you and traced his mouth with his slicked fingers, then he moved them to your lips. Your tongue licked the tips of his fingers. His grip tightened around your waist.

“I want to feel you,” you said.

Jungkook shuddered at your words. “Where is your room?”

“The door behind you.”

Jungkook lifted you off the table, you tightened your legs around him and gave him another kiss. He walked you both to your room and gently laid you down on your bed. He took off his pants, then slowly moved onto the bed and hovered above you.

“Tell me what you want,” he said.

Your fingers caressed his face. “I want you to be happy.”

Another shudder ran through him. “I am happy. What else?”

You traced his eyes, his nose, his lips. “I want to be the one making you happy.”

Jungkook couldn’t contain himself anymore. His heart felt like it was about to explode. He covered your body with his and pressed himself into you. Your eyes rolled back as he entered you slowly. You felt so full you wanted to burst out of your skin. You could feel how the Jungkook-sized whole in your heart filled up again.

He rocked into you and took your breath away. Your nails raked across his back and left red lines against his smooth skin. Jungkook ducked his head into the crook of your neck and moaned against your skin. Every pull dragged pleasure out of you, every push brought you closer together.

You wanted more. Jungkook gave you more.

You wanted him closer. Jungkook pushed deeper into you.

With every moan, Jungkook pushed harder, pushed deeper. He wanted to melt into you. He wanted the lines between you and him to disappear. Your desire was his desire. His pleasure was your pleasure.

Jungkook could feel you tightening around him. He moved his mouth over yours and gave you an ardent kiss. The light of your desire turned brighter and brighter until it burst apart into a thousand little flames. You cried against his lips and let the heat consume you. Your body pulsed around his and the overwhelming sensation brought him right over the edge with you.

The both of you laid on your bed and clung to each other. Neither of you willing to let the other go. Your pounding chests beat in tandem. Jungkook stroked his hand across your hair and kissed your head.

“I want you to be happy too,” he said.

“I know,” you said as you smiled against his chest, “You make me happy.”

Jungkook pulled you tighter into him and you remained silent for a while. His hand traced lazy patterns against your skin. Your breathing evened out.

“Are you allergic to pineapple?” he suddenly asked.

You looked up at him in surprise. “No. Why?”

“Because you always order tangsuyuk without pineapple.”

“Oh. That’s because my sister hates pineapple.”

Jungkook frowned, you pulled yourself up and kissed the little ridges between his eyes.

“What?” you asked.

“I think the jjajangmyeon is all soggy by now,” he said.

You had to laugh. “Probably, but the tangsuyuk should still taste great.”

Jungkook kissed you with a smile. “You’re right, tangsuyuk always tastes great.”

°°°°°°°

02/05/20

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spacetimewithstuartgary · 4 years

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Tracking down the mystery of matter Researchers at the Paul Scherrer Institute PSI have measured a property of the neutron more precisely than ever before. In the process they found out that the elementary particle has a significantly smaller electric dipole moment than was previously assumed. With that, it has also become less likely that this dipole moment can help to explain the origin of all matter in the universe. The researchers achieved this result using the ultracold neutron source at PSI. They report their results today in the journal Physical Review Letters. The Big Bang created both the matter in the universe and the antimatter - at least according to the established theory. Since the two mutually annihilate each other, however, there must have been a surplus of matter, which has remained to this day. The cause of this excess of matter is one of the great mysteries of physics and astronomy. Researchers hope to find a clue to the underlying phenomenon with the help of neutrons, the electrically uncharged elementary building blocks of atoms. The assumption: If the neutron had a so-called electric dipole moment (abbreviated nEDM) with a measurable non-zero value, this could be due to the same physical principle that would also explain the excess of matter after the Big Bang. 50,000 measurements The search for the nEDM can be expressed in everyday language as the question of whether or not the neutron is an electric compass. It has long been clear that the neutron is a magnetic compass and reacts to a magnetic field, or, in technical jargon: has a magnetic dipole moment. If in addition the neutron also had an electric dipole moment, its value would be very much less - and thus much more difficult to measure. Previous measurements by other researchers have borne this out. Therefore, the researchers at PSI had to go to great lengths to keep the local magnetic field very constant during their latest measurement. Every truck that drove by on the road next to PSI disturbed the magnetic field on a scale that was relevant for the experiment, so this effect had to be calculated and removed from the experimental data. Also, the number of neutrons observed needed to be large enough to provide a chance to measure the nEDM. The measurements at PSI therefore ran over a period of two years. So-called ultracold neutrons, that is, neutrons with a comparatively slow speed, were measured. Every 300 seconds, an 8 second long bundle with over 10,000 neutrons was directed to the experiment and examined. The researchers measured a total of 50,000 such bundles. "Even for PSI with its large research facilities, this was a fairly extensive study," says Philipp Schmidt-Wellenburg, a researcher on the nEDM project on the part of PSI. "But that is exactly what is needed these days if we are looking for physics beyond the Standard Model." Search for "new physics" The new result was determined by a group of researchers at 18 institutes and universities in Europe and the USA, amongst them the ETH Zurich, the University of Bern and the University of Fribourg. The data had been gathered at PSI's ultracold neutron source. The researchers had collected measurement data there over two years, evaluated it very carefully in two teams, and through that obtained a more accurate result than ever before. The nEDM research project is part of the search for "new physics" that would go beyond the so-called Standard Model. This is also being sought at even larger facilities such as the Large Hadron Collider LHC at CERN. "The research at CERN is broad and generally searches for new particles and their properties", explains Schmidt-Wellenburg. "We on the other hand are going deep, because we are only looking at the properties of one particle, the neutron. In exchange, however, we achieve an accuracy in this detail that the LHC might only reach in 100 years." "Ultimately", says Georg Bison, who like Schmidt-Wellenburg is a researcher in the Laboratory for Particle Physics at PSI, "various measurements on the cosmological scale show deviations from the Standard Model. In contrast, no one has yet been able to reproduce these results in the laboratory. This is one of the very big questions in modern physics, and that's what makes our work so exciting." Even more precise measurements are planned With their latest experiment, the researchers have confirmed previous laboratory results. "Our current result too yielded a value for nEDM that is too small to measure with the instruments that have been used up to now - the value is too close to zero", says Schmidt-Wellenburg. "So it has become less likely that the neutron will help explain the excess of matter. But it still can't be completely ruled out. And in any case, science is interested in the exact value of the nEDM in order to find out if it can be used to discover new physics." Therefore, the next, more precise measurement is already being planned. "When we started up the current source for ultracold neutrons here at PSI in 2010, we already knew that the rest of the experiment wouldn't quite do it justice. So we are currently building an appropriately larger experiment", explains Bison. The PSI researchers expect to start the next series of measurements of the nEDM by 2021 and, in turn, to surpass the current one in terms of accuracy. "We have gained a great deal of experience in the past ten years and have been able to use it to continuously optimise our experiment - both with regard to our neutron source and in general for the best possible evaluation of such complex data in particle physics", says Schmidt-Wellenburg. "The current publication has set a new international standard."

#space #science #Astronomy #physics #particle physics

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lupine-publishers-oajess · 4 years

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Lupine Publishers|Effect of Interaction Between Ag Nanoparticles and Salinity on Germination Stages of Lathyrus Sativus L.

Abstract

The aim of the study was to effect of interaction between Ag nanoparticles and salinity on Germination Stages of Lathyrus Sativus L. Treatments included in the study were viz. To 3 levels of salinity (0 as control, 8 and 16 dS/m NaCl), 8 and 16 dS/m and four levels of silver nanoparticles (0, 5, 10 and 15 ppm) on grass pea seed were tested. An experiment was conducted to evaluate the effects of silver nanoparticles (AgNPs), on the seed germination factors, root and shoot length (RL and SL) and proline content of grass pea Survival under Salinity Levels. Results showed a significant reduction in growth and development indices due to the salinity stress. The salt stress impaired the germination factors of grass pea seedlings. The application of Ag in combination improved the germination percentage, shoot and root length, seedling fresh weight and seedling dry weight and seedling dry contents of grass pea seedlings under stressed conditions. The results suggest that Ag nanoparticles enhancement may be important for osmotic adjustment in grass pea under salinity stress and application of Ag mitigated the adverse effect of salinity and toxic effects of salinity stress on grass pea seedlings.

Keywords: Ag nanoparticles; Salinity; Germination Stages; Grass Pea; Lathyrus Sativus L.

Introduction

High salinity is a common abiotic stress factor that causes a significant reduction in growth. Germination and seedling growth are reduced in saline soils with varying responses for species and cultivars [1]. Soil saltiness may impact the germination of seeds either by causing an osmotic potential outside to the seed averting water uptake, or the poisonous effects of Na+ and Cl− ions on germinating seed [2]. Salt and osmotic stresses are responsible for both inhibition or delayed seed germination and seedling establishment [3]. The majority of our present-day crops are adversely affected by salinity stress [4]. NaCl causes extensive oxidative damage in different legumes, resulting in significant reduction of different growth parameters, seed nutritional quality, and nodulation [5,6]. To mitigate and repair damages triggered by oxidative stress, plants evolved a series of both enzymatic as well as a non-enzymatic antioxidant defense mechanism. Ascorbate and carotenoids are two important non-enzymatic defenses against salinity, whereas proline is the most debated osmoregulatory substances under stress [7].

Lathyrus Sativus L. (Grass pea) is an annual pulse crop belonging to the Fabaceae family and Vicieae tribe [8]. Grass pea has a long history in agriculture. The crop is an excellent fodder with its reliable yield and high protein content. This plant is also commonly grown for animal feed and as forage. The grass pea is endowed with many properties that combine to make it an attractive food crop in drought-stricken, rain-fed areas where soil quality is poor and extreme environmental conditions prevail [9]. Despite its tolerance to drought it is not affected by excessive rainfall and can be grown on land subject to flooding [10,11]. Compared to other legumes, it is also resistant to many insect pests [12-15]. Nanoparticles (NPs) are wide class of materials that include particulate substances, which have one dimension less than 100 nm at least [16]. The importance of these materials realized when researchers found that size can influence the physiochemical properties of a substance e.g. the optical properties [17]. NPs with different composition, size, and concentration, physical/ chemical properties have been reported to influence growth and development of various plant species with both positive and negative effects [18]. Silver nanoparticles have been implicated in agriculture for improving crops. There are many reports indicating that appropriate concentrations of AgNPs play an important role in plant growth [19,20]. The application of Nano silver during germination process may enhance germination traits, plant growth and resistance to salinity conditions in basil seedlings [21]. The use of Silver Nanoparticle on Fenugreek Seed Germination under Salinity Levels is a recent practice studied [22]. Nanomaterials have also been used for various fundamental and practical applications [23]. Although the potential of AgNPs in improving salinity resistance has been reported in several plant species [24,25], its role in the alleviation of salinity effect and related mechanisms is still unknown. Therefore, the main objective of this work was to study the effect of Silver Nanoparticles on salt tolerance in Lathyrus Sativus L.

Material and Methods

In order to investigate salinity stress on Lathyrus Sativus L. germination indices, an experiment was carried out in Iran from April to Juan 2017 at Ferdowsi University of Mashhad, to creation salinity, sodium chloride at the levels of 8 dS/m, 15 dS/m and 0 (as control), four levels of silver nanoparticles (0, 5, 10 and 15 ppm) on Grass pea were tested. The Ag NPs were obtained from US Research Nanomaterial’s, Inc. Transmission electron microscopy (ТЕМ) images of silver nanoparticles with diameters of 20 nm, shown in Figure 1. Seeds of Lathyrus Sativus L. where from seed bank of Research Center for Plant Sciences, Ferdowsi University of Mashhad. These all were washed with deionized water. Seeds were sterilized in a 5% sodium hypochlorite solution for 10 minutes [26], rinsed through with deionized water several times. Their germination was conducted on water porous paper support in Petri dishes (25 seed per dish) at the controlled temperature of 25 ± 1°C. After labeling the Petri dishes, seed were established between two Whatman No. 2 in Petri dishes. Silver nanoparticles in different concentration silver nanoparticles (0, 5, 10 and 15ppm) were prepared directly in deionized water and dispersed by ultrasonic vibration for one hour. Each concentration was prepared in three replicates. Every other day supply with 0.5 ml silver nanoparticles per every test plantlet was carried out for 21 days along with control. Germination counts were recorded at 2 days’ intervals for 21 days after sowing and the seedlings were allowed to grow. The germination percentages of the seeds were finally determined for each of the treatments. After 21 days of growth, the shoot and root lengths were long enough to measure using a ruler. The controlled sets for germinations were also carried out at the same time along with treated seeds (Figure 2).

Figure 1: Silver Nanopowder, Coated with ~0.2wt% PVP (Poly Viny Pyrrolidone) surfactant for low oxygen content and easy dispersing. True density: 10.5 g/cm3 Purity: 99.99% APS: 20 nm SSA: ~18-22 m2/g Color: black, Morphology: spherical.

Figure 2: Effect of Ag Nanoparticles on Germination Stages of Lathyrus Sativus L. in Salinity level( 8 dS/m NaCl).

Parameters Measured in this Study were:

A. Germination Stages

Total germination percentage (GT) was calculated as Gt = (n/N ×100), where n = total number of germinated seeds (normal and abnormal) at the end of the experiment and N = total number of seeds used for the germination test.

B. Germination Speed Index (GSI)

Conducted concomitantly with the germination test, with a daily calculation of the number of seeds that presented protrusion of primary root with length ≥2 millimeter, continuously at the same time amid the trial. The germination speed index was calculated by Maguire formula [27]: aguire formula (1962):

Where:

GSI = seedlings’ germination speed index;

G = number of seeds germinated each day;

N = number of days elapsed from the seeding until the last count.

Root and Shoot Length

Root length was taken from the point below the hypocotyls to the end of the tip of the root. Shoot length was measured from the base of the root- hypocotyl transition zone up to the base of the cotyledons. The root and shoot length were measured with the help of a thread and scale.

Seedling Vigour Index

The seedling vigor index was determined by using the formula given by Abdul baki and Anderson [28].

Fresh and Dry mass

The fresh mass was quantified through weighing on precision scale, and the dry mass was determined through weighing on a precision scale after permanence of the material in a kiln with air forced circulation, at a temperature of 70°C, until indelible weight. At the ending of the experiment, At the end of the experiment, radical and plumule length and fresh weight measured. Plants were placed in the oven at 70°C for 48 h and weighted with sensitive scale.

Proline Contents

Proline was determined spectrophotometrically following the ninhydrin method described, using L-proline as a standard [29]. Approximately 300 mg of dry tissue was homogenized in 10ml of 3% (w/v) aqueous sulphosalicylic acid and filtered. To 2ml of the filtrate, 2ml of acid ninhydrin was added, followed by the addition of 2ml of glacial acetic acid and boiling for 60 min. The mixture was extracted with toluene, and the free proline was quantified spectrophotometrically at 520nm from the organic phase using a spectrophotometer. Statistical analysis each treatment was conducted, and the results were presented as mean ± SD (standard deviation). The results were analyzed by one-way ANOVA with used Minitab Version 16.

Results and Discussion

The present study showed clearly that salinity had a negative effect on the yield and its components of grass pea. It is well known that seed germination provides a suitable foundation for plant growth, development, and yield [30]. Increased salt concentration caused a decrease in germination percent (Table 1). Seed germination decreased as the doses increased. The Strong reduction in germination (-47%) was observed mainly at the highest level of salt concentration as compared to control treatment. Delayed germination causes increased irrigation cost and irregular and weak seedling growth in the establishment of legume crops. Relevant results were reported by Gunjaca and Sarcevic [31] and Almansouri et al. [32]. They reported that increasing osmotic potential decreased water uptake and slow down germination time. The average time of germination increases with increasing levels of salinity. In view of mean germination time, there was a considerable increase in this character at 0 (as control), 8 and 16 DS/m salinity levels as compared to the others. Emergence was significantly affected by salinity levels. Moreover, many researchers have reported developmental delay of seed germination at high salinity [33]. The germination rate decreased as salt concentration increased to a 16 dS/m and delayed for the high salt dosage (Table 1). Since higher salinity limited water absorption, it has prevented nutrient assimilation, as a result, germination rate declined with increasing salinity. The findings from this study were like to the findings of Kaydan and Yagmur [34] and Akhtar and Hussain [35].

Table 1: The interaction effect of NaCl and AgNPs on Germination Speed Index.

Table 2: Analysis of variance of the measured traits.

Shoot fresh weight was significantly influenced (P<0.05) by salinity levels. The highest shoot fresh weight was obtained from 0dSm salinity level while the lowest weight was at 16dSm. Shoot fresh weight significantly decreased as salinity level increased above 8dSm (Table 2). Salinity stress significantly (P<0.05) affected shoot dry weight as the salt concentration dosage increased. Shoot dry weight significantly decreased in salt levels over 8dSm. When the salinity level was raised above, the proline content increased in grass pea. Culturing excised roots has demonstrated to be a really great test show for the early detection of tolerance to abiotic stresses such as saltiness [36-38].

Proline was studied in numerous works dealing with plant selection against abiotic stresses such as dry and salinity [39,40], and it may play a defensive part against the osmotic potential produced by salt [41,42]. The proline substance of the expanded with the NaCl concentration of the culture medium. At 16 dS/m NaCl, the proline concentration appeared a huge increment in reaction to salt stress, although the activity of the roots at this concentration was negligible, with no grateful longitudinal development. Proline, which happens broadly in higher plants and collects in bigger sums than other amino acids [43], regulates the aggregation of useable N. Proline collection normally occurs within the cytosol where it contributes significantly to the cytoplasmic osmotic alteration [44]. It is osmotically very active and contributes to membrane stability and mitigates the impact of on NaCl cell membrane disturbance [45]. In the present experiment application of Ag NPs enhanced seed potential by increasing the characteristics of seed germination (Tables 1 & 2). The results showed that the impact of Ag NPs was significant on germination percentage in P≤0. 05. The results about of this test appeared that utilization of Ag NPs nanoparticles can increment the germination in grass pea. Seed germination results indicate that Ag Nanoparticles at their lower concentrations advanced seed germination and early seedling growth in grass pea, anyway at higher concentration showed slight antagonistic impacts. Parameters of seed germination were expanded with increasing levels of Ag NPs up to 10 ppm. Among the treatments, application of 10 ppm of Ag NPs proved best by giving the highest values for percent seed germination, germination rate and germination mean time. It is well watched that the exogenous application of Ag NPs decreased the reduction of germination resulted from salt treatments. In the interim, the control treatments of salt and Ag nanoparticles gave the tallest plants contrasted with the other studied treatments. Darvishzadeh et al. [21] found that the utilization of Ag Nano particles at the concentration of 40 mg.kg-1 prompted the increases in germination percentage and improved the resistance to salinity conditions in basil. The proline content increased with increasing severity of salinity stress. Additionally, proline content significantly (P.0.01) increased when silver nanoparticles were applied in connected in serious saline stress in comparison without silver nanoparticles (Figure 3).

Figure 3: Effect of interaction between ag nanoparticles and salinity on germination stages of Lathyrus Sativus L. a - Main effects plot for Root length (mm); b - Main effects plot for dry weight of shoot and root (gr); c - Interaction Plot for fresh weight of shoot and root (gr); d - Interaction Plot for dry weight of shoot and root (gr); e - Interaction Plot for Proline (mg/gr).

Conclusion

Salt stress through enhancement of osmotic pressure leads to the decrease of germination percentage, germination rate, germination index and an increment in mean germination time of Lathyrus sativus seeds. For overcoming the negative impacts of salinity on the plant growth and yield can be to attempt to new strategies. The dry and fresh weight of seedlings diminished as seedling length declined with increasing salinity levels since root number, shoot number, root length and shoot length decreased essentially. Results demonstrate that Ag NPs at lower concentration enhances seed germination, promptness index, and seedling growth. The positive effect of Ag on physiological properties was in conditions that the plant grew under salt stress was more increasingly exceptional in examination with the conditions that plant grown under normal conditions. The results of this study showed that Ag can be involved in the metabolic or physiological activity in higher plants exposed to abiotic stresses.

Acknowledgment

I would like to thank the Research Center for Plant Sciences, and Dr. Jafar Nabati for providing the necessary facilities.

#Lupinepublishers #Lupine Publishers Group #open access journals #Earth and Environment Journals #ecology

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theliberaltony · 5 years

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via Politics – FiveThirtyEight

As the Ukraine scandal continues to dominate the headlines, former Vice President Joe Biden remains the most-mentioned candidate on cable news. But even though Biden has been getting so much attention, Sen. Elizabeth Warren has been slowly and steadily rising in popularity (although not at his expense). Last Tuesday, Warren surpassed Biden in the RealClearPolitics average of polls for the first time. It should come as no surprise, then, that Warren is the next most-mentioned candidate on cable news after Biden and that her share of coverage increased last week from the previous week, according to data from the TV News Archive,1 which chops up TV news into 15-second clips. Though this column typically also includes data from Media Cloud, a database of online news stories, that data is temporarily unavailable due to site maintenance.

Warren got more attention on cable news last week

Share of 15-second cable news clips mentioning each candidate

Cable TV clips the week of … Candidate 9/29/19 10/6/19 diff Joe Biden 69.3% 65.7% -3.6 Elizabeth Warren 12.8 20.2 +7.3 Bernie Sanders 13.9 13.9 +0.0 Kamala Harris 4.0 3.8 -0.2 Beto O’Rourke 1.7 2.3 +0.7 Tom Steyer 0.5 1.4 +0.9 Amy Klobuchar 1.1 1.3 +0.2 Pete Buttigieg 2.1 1.3 -0.9 Cory Booker 2.0 1.2 -0.8 Julián Castro 0.3 0.5 +0.3 Andrew Yang 0.9 0.5 -0.5 Tulsi Gabbard 0.3 0.3 +0.0 Michael Bennet 0.1 0.1 -0.1 John Delaney 0.0 0.1 +0.1 Steve Bullock 0.3 0.0 -0.3 Marianne Williamson 0.1 0.0 -0.1 Tim Ryan 0.2 0.0 -0.2 Joe Sestak 0.0 0.0 +0.0

Includes all candidates that qualify as “major” in FiveThirtyEight’s rubric. Each network’s daily news coverage is chopped up into 15-second clips, and each clip that includes a candidate’s name is counted as one mention. Our search queries look for an exact match for each candidate’s name, except for Julián Castro, for whom our search query is “Julian Castro” OR “Julián Castro.” Percentages are calculated as the number of clips mentioning each candidate divided by the number of clips mentioning any of the 2020 Democratic contenders for that week.

Sources: Internet Archive’s Television News Archive via the GDELT Project

But Warren’s rise in coverage isn’t all about how well she’s doing in the polls, and it’s also not evenly distributed across the three networks that we monitor (CNN, Fox News and MSNBC). This week she was mentioned in 327 clips on Fox News, but only 176 on MSNBC and 108 on CNN, marking the second week in a row that she has been mentioned significantly more on Fox News compared to the other networks.

And it’s not just the amount of coverage that differs. Fox News is also focusing on stories that the other two networks are not devoting as much time to. “Hillary Clinton” and “visibly pregnant” are among the top three two-word phrases most particular to Fox News in clips about Elizabeth Warren last week.2 The phrase “Hillary Clinton” — which appeared in 17 clips on Fox that mentioned Warren, but only two on each CNN and MSNBC — appeared often in segments about Clinton’s response to a tweet from President Trump suggesting Clinton should run for president and “steal it away” from Warren. And the phrase “visibly pregnant,” which appeared in 14 Fox News clips last week but wasn’t mentioned at all on CNN or MSNBC, occurred in segments about Warren’s response to allegations that she misrepresented the details of her departure from a job as a special education teacher in the early 1970s.

If Warren continues to rise in the polls, she could get more media attention (and scrutiny) than she has in the past. We’ll be monitoring just how much attention she gets in cable and online news, and whether the amount and content continues to diverge across different media sources. Stay tuned!

Check out the data behind this series and check back each week for an update on which candidates are getting the most coverage on cable and online.

#IFTTT #Politics – FiveThirtyEight #politics #538 #Dhrumil Mehta

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lilybeige25 · 3 years

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WHY GOAN 스포츠토토커뮤니티 RECRUITMENT ADVERTISEMENTS IN NEPAL?

A railway also passes through the commune with a station near the town and the railway line coming from Azerailles in the north-west continuing to Bertrichamps in the south-east. http://edition.cnn.com/search/?text=코인카지노 Like single-roll bets, hard way bets can be lower than the table minimum; however, the maximum bet allowed is also lower than the table maximum. The Seminoles fought the system and won, setting a precedent for other tribes to open high-stakes gambling businesses on their land (reservation land is sovereign). If the dealer has at least one ace and one king, a comparison of the combinations is made and the winner is determined. As in classic poker, the winner is the one who has collected the biggest combination. Bets are made using chips of different rank.

Each suit contained ten "spot" cards (cards identified by the number of suit symbols or "pips" they show) and three "court" cards named malik (King), na'ib malik (Viceroy or Deputy King), and thani na'ib (Second or Under-Deputy). This fully custom card deck desin was created by Renáta Farkas with the help of consultant Csongor G Szigeti. This would be the first occurrence of a network linked progressive jackpot on a table game allowing for a jackpot that is contributed to by players in many different casinos simultaneously. This is called a reach (or reachi) and sometimes longer animations are played called super reaches.

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karonbill · 3 years

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Fortinet NSE 5 - FortiSIEM 5.2 NSE5_FSM-5.2 Exam Questions

If you are new to NSE5_FSM-5.2 exam and taking the Fortinet NSE 5 - FortiSIEM 5.2 exam for the first time, then don't worry about your exam preparation and success. You will get the best quality Fortinet NSE 5 - FortiSIEM 5.2 NSE5_FSM-5.2 Exam Questions in pdf format at PassQuestion for the preparation of your Fortinet NSE5_FSM-5.2 exam.The real and reliable NSE5_FSM-5.2 Exam Questions will enable you to get through your Fortinet NSE 5 - FortiSIEM 5.2 exam in just your first attempt without any problem. Our Fortinet NSE 5 - FortiSIEM 5.2 NSE5_FSM-5.2 Exam Questions will help you to pass the Fortinet NSE5_FSM-5.2 exam smoothly.

Fortinet NSE 5 - FortiSIEM 5.2

Anyone who is responsible for day-to-day management of FortiSIEM can choose this NSE5_FSM-5.2 exam to get certified. You will learn how to use FortiSIEM, and how to integrate FortiSIEM into your network awareness infrastructure.You will learn about initial configurations, architecture, and the discovery of devices on the network. You will also learn how to collect performance information and aggregate it with syslog data to enrich the overall view of the health of the environment. Additionally, you will learn how you can use the configuration database to greatly facilitate compliance audits.

Exam Details

Fortinet NSE 5 - FortiSIEM 5.2

Exam series: NSE5_FSM-5.2

Number of questions: 30

Exam time: 60 minutes

Language: English

Product version: FortiSIEM 5.2

Status: Available

NSE5_FSM-5.2 Exam Objectives

SIEM and PAM Concepts

Discovery

FortiSIEM Analytics

CMDB Lookups and Filters

Group By and Aggregations

Rules

Incidents and Notification Policies

Reports and Dashboards

Maintaining and Tuning

FortiSIEM Agents

View Online Fortinet NSE 5 - FortiSIEM 5.2 NSE5_FSM-5.2 Free Questions

Which two FortiSIEM components work together to provide real-time event correlation? A. Collector and Windows agent B. Supervisor and worker C. Worker and collector D. Supervisor and collector Answer:D

Which database is used for storing anomaly data, that is calculated for different parameters, such as traffic and device resource usage running averages, and standard deviation values? A.Profile DB B.Event DB C.CMDB D.SVN DB Answer: B

Which process converts Raw log data to structured data? A.Data enrichment B.Data classification C.Data parsing D.Data validation Answer: D

In the rules engine, which condition instructs FortiSIEM to summarize and count the matching evaluated data? A. Time Window B. Aggregation C. Group By D. Filters Answer: C

What are the four categories of incidents? A.Devices, users, high risk, and low risk B.Performance, availability, security, and change C.Performance, devices, high risk, and low risk D.Security, change, high risk, and low risk Answer: B

In FotiSlEM enterprise licensing mode, if the link between the collector and data center FortiSlEM cluster a down what happens? A.The collector drops incoming events like syslog. but slops performance collection B.The collector continues performance collection of devices, but stops receiving syslog C.The collector buffers events D.The collector processes stop, and events are dropped Answer: D

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biomedgrid · 4 years

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Biomed Grid | Assessment of Serum Lipid Profile among Male Cigarette Smokers in Jos Metropolis

Introduction

Smoking is now acknowledged to be one of the leading causes of preventable morbidity and is one of the largest single preventable causes of ill health in the world. Smoking as an environmental factor can alter normal lipid profile and cause heart diseases [1,2]. Nearly every cigarette smoker begins as a teenager. The average smoker tries their first cigarette at the age of 12 [3] and may be a regular smoker by the age of 14 years [4]. Smokers always crave for more cigarettes most especially after an overnight abstinence due to the effect of Nicotine, acetylcholine, and dopamine on Central Nervous System (CNS), which causes addictiveness. On average, smoking increases the risk of cardiovascular heart disease by 70% when compared with nonsmoking. The start of even modest cigarette smoking during adolescence and early adulthood alters the serum lipid and lipoproteins levels [5,6]. Smokers have high risk for coronary artery disease (CAD) compared to non-smokers, partly attributed to some altered physiological factors including altered coagulation state, damages vascular walls, and an alteration in lipid and lipoprotein content [6].Davis [7] described various mechanisms leading to lipids alteration by smokers to include:

a) Stimulation sympathetic adrenal system by Nicotine leading to increase secretion of catecholamine resulting in increased lipolysis and increased concentration of plasma free fatty acids (PFFA) which further result in increased secretion of hepatic free fatty acids (HFFA) and hepatic triglycerides,

b) Fall in estrogen level which occurs due to smoking that further leads to decreased HDL-cholesterol,

c) Presence of hyperinsulinaemia in smokers leading to increased cholesterol, LDL-Cholesterol, VLDL- cholesterol and triglycerides due to decreased activity of lipoprotein lipase.

Research has shown a correlation between the number of cigarettes smoked and cardiovascular morbidity and mortality. Cigarette smoking leads to increase in the concentration of serum total cholesterol, triglycerides, LDL-cholesterol, VLDL-cholesterol and fall in the levels of anti-atherogenic HDL- cholesterol. The smoke described as plaque sticks to the inside walls of the vessels causing the vessels to narrow and the Platelets get trapped in the plaque, causing further narrowing and blood clotting. When the artery is completely occluded, the part of the heart muscle supplied by that coronary artery can be cut entirely from blood supply, causing heart attack. Inhaling cigarette smoke also leads to an increased free radicals in the body which can cause damages to the body in a large amount to cells and tissues, and could also triggered an immune response [2,8,9,10]. Smoking in different form is a major risk factor for atherosclerosis and coronary Heart Disease (CHD) due to the chemical components of cigarette which provides for research interest to check the effect of smoking on lipid profile in Jos Metropolis which hosts several higher institutions in the State.

Methods

A total of 100 apparently health males subjects within the ages of 15-45years were used in this study, made up of 80 smokers and 20 non-smokers as the control. All the subjects reside within Jos Metropolis. The subjects were selected through self-administered questionnaire containing series of question for proper screening and selection of suitable subjects. The lipid profile was determined using the methodology as described by Ochei & Kolhaktar [11]. Statistical Analysis employed was Mean, Standard Deviation and Students t-test Ethical Consideration was duly followed ranging from the volunteers giving consent of participation and obtaining ethical committee approval from Federal School of Medical Laboratory Technology, Jos before the research was carried out.

Result

A total of 100 fasting samples; 80 smokers and 20 non-smokers were estimated (essayed) for total cholesterol (TC), high-density lipoprotein-cholesterol (HDL-C), Triglycerides (TG) and Lowdensity lipoproteins cholesterol (LDL-C) using respective methods. All data were expressed as Mean ± Standard Deviation (X±SD) for control (non-smokers), and smokers with varying numbers of cigarettes per day as shown below in Table 1 and 2 and the statistical significance was evaluated by student t-test at confident interval of 95%. The smokers mean and standard deviation of Total cholesterol (TC), Triglyceride (TG), High density lipoproteincholesterol (HDL-C) and Low density lipoprotein-cholesterol (LDL-C) were 6.40±1.41, 1.90±0.66, 1.80±0.52 and 3.60±1.21 mMol/L respectively whereas non-smokers’ mean and standard deviation of Total cholesterol, (TC), Triglyceride (TG), High density lipoprotein-cholesterol (HDL-C) and Low density lipoproteincholesterol (LDL-C) were 3.20+0.71, 1.30±0.40, 2.00±0.20 and 1.30±0.80mMol/L, greater than those of non-smokers, showing a significant value at P< 0.05 but the HDL-C of smokers were less than that of non-smokers.

Table 1:The mean and standard deviation (X±SD) of Non-smokers and smokers.

Note: NB: Calculated Value is greater than tabulated value showing significance at P<0.05. Key: C: Calculated value; T: Tabulated value.

Table 2:The mean and standard deviation (X±SD) of control (non-smokers) and smokers of 1-10 cigarettes per day and smokers of 11-20 cigarettes per day subjects.

Discussion

In this study, the serum total cholesterol levels in smokers as compared to that of controls. The cholesterol concentration increases with increase in number of cigarettes smoked as shown in this study. It has been reported that incidence of coronary Heart Disease (CHD) is directly related to number of cigarettes smoked and smoking more than 10 cigarettes regularly constitutes a major risk factor for Ischemic Heart Disease (ISHD) by Vasudevan & Sreekumari [12]. Similarly, higher levels of triglycerides (TG) were found in smokers as compared to controls Some studies have suggested that triglyceride levels are the most important factors leading to coronary heart disease (CHD), although in fact, triglycerides as a risk factor has been suggested by various research workers [13]. The values of serum triglycerides were significantly higher in subjects smoking 11-20 cigarettes per day as compared to those smoking 1-10 cigarettes per day [2]. HDL serum level showed decrease in smokers as compared to controls. The results are in conformity with Zamir et al. [13] who observed that levels of HDL in smokers as the result of threat of developing atherosclerosis and Coronary Heart Disease (CHD) could be increased. The level of HDL in those smoking 11-20 cigarettes per day showed no significant difference statistically with those smoking 1-10 cigarettes per day. On the other hand, the level of serum LDL-Cholesterol levels are significantly increased in smokers as compared with the control. It has been described that nicotine contained cigarettes increased the circulating pool of atherogenic LDL through accelerated transfers of lipid from HDL and impaired clearance of IDL from plasma compartment and hence LDL Cholesterol in the arterial wall increased. LDL values were significantly higher in those smoking 10-20 cigarettes per day as compared to those smoking 10-10 per day. This study is in agreement with the earlier works [1,5,8,9,12,13].

Conclusion

From the results of this study, the serum anti-atherogenic HDL- Cholesterol level is significantly low in smokers irrespective of the number of cigarettes they smoked. The serum level of total cholesterol, LDL-cholesterol and triglycerides (TG) are significantly increased in smokers as compared to non-smokers, and in those smoking 11-20 cigarettes per day as compared to those smoking 1-10 cigarettes per day and therefore raising the cardiovascular disease risk. From this study, it is good to recommend to all smokers and intending smokers in Jos Metropolis and the world at large that:

a) Smoking should be avoided as much as possible by smokers and intending smokers for the benefit of cardiac health.

b) Young people should be continually educated on the dangers of smoking in order not to take up smoking.

c) Legislative laws should be enacted prohibiting people from smoking in public places like cinema halls, studio, inside vehicles, institutions of learning especially secondary schools and higher institutions of learning in Jos Plateau State by the State House of Assembly.

d) Tobacco companies should be taxed heavily to discourage production and distribution in Jos-Nigeria.

e) There should be prohibition of advertisement or any form of cigarette on the mass media.

f) Health workers should discourage their patients from smoking as a take home message after visiting any health facility in Jos.

Read More About this Article:https://biomedgrid.com/fulltext/volume3/assessment-of-serum-lipid-profile-among-male-cigarette-smokers-in-jos-metropolis.000732.php

For more about: Journals on Biomedical Science :Biomed Grid

#biomedgrid #American Journal of Biomedical Science & Research #Journals on Biomedical Engineering #Journals on Medical Microbiology #Journals on Biomedical Intervention #Journals on Biomedical Science #Journals on Medical Casereports

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endivesoftware · 4 years

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1. Introduction

Introduction: Why Economics?, Meaning and Definitions of Economics, Economic and Non-economic Activities, Economic Groups, Introduction: Statistics, Meaning and Definition of Statistics, Importance of Statistics in Economics, Limitation of Statistics, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Higher Order Thinking Skills [HOTS], Value Based Questions, Multiple Choice Questions (MCQs).

2. Collection of Data

Introduction, Meaning of Collection of Data, Types of Data (Sources of Data), Methods of Collecting Primary Data, Questionnaire and Schedule, Census and Sample Investigation Techniques, Sampling and Non-Sampling Errors, Sources of Secondary Data, Census of India And NSSO, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Higher Order Thinking Skills (HOTS), Value Based Questions, Multiple Choice Questions (MCQs).

3. Organisation of Data

Introduction, Meaning and Definition of Classification, Objectives of Classification, Methods of Classification, Variable, Statistical Series, Individual Series, Discrete Series (Ungrouped Frequency Distribution or Frequency Array), Continuous Series or Grouped Frequency Distribution, Types of Continuous Series, Bivariate Frequency distribution, General Rules for Constructing a Frequency Distribution, or How to prepare a frequency distribution?, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Higher Order Thinking Skills (HOTs), Value Base Questions, Multiple Choice Questions (MCQs).

4. Presentation of Data : Tabular Presentation

Introduction, Textual Presentation of Data (Descriptive Presentation), Tabular Presentation of Data, Objectives of Tabulation, Essential Parts of Table, Type of Table, Solved Examples, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Higher Order Thinking Skills (HOTS), Value Based Questions, Multiple Choice Questions (MCQs).

5. Presentation of Data : Diagrammatic Presentation

Introduction, Utility or Advantages of Diagrammatic Presentation, Limitations of Diagrams, General Principles/Rules for Diagrammatic Presentation, Types of Diagrams, Bar Diagram, Pie Diagram, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Question, Long Answer Type Question, Numerical Questions, Higher Order Thinking Skills (HOTS), Multiple Choice Questions (MCQs).

6. Presentation of Data: Graphic Presentation

Introduction, Advantages of Graphic Presentation, Construction of a Graph, False Base Line (Kinked Line), Types of Graphs, Limitation of Graphic Presentations, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Higher Order Thinking Skills (HOTS), Multiple Choice Question (MCQs).

7. Measures of Central Tendency Arithmetic Mean

Introduction, Meaning and Definition, Objectives and Significance or uses of Average, Requisites or Essentials of an Ideal Average, Types or Kinds of Statistical Averages, Arithmetic Mean (X), Calculation of Arithmetic Mean in Different Frequency Distribution (Additional Cases), Calculation of Missing Value, Corrected Mean, Combined Arithmetic Mean, Mathematical Properties of Arithmetic Mean, Merits and Demerits of Arithmetic Mean, Weighted Arithmetic Mean, List of Formulae, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Miscellaneous Questions, Multiples Choice Questions (MCQs).

8. Measures of Central Tendency Median and Mode

Median, Determination of Median, Calculation of Median in Different Frequency Distribution (Additional Cases), Partition Values (Measures of Position or Positional Values based on The principle of Median), Mode (Z), Computation of Mode, Calculation of Mode in Different Frequency Distribution (Additional Cases), Relationship between Mean, Median and Mode, Comparison between Mean, Median and Mode, Choice of a Suitable Average, Typical Illustration, List of Formulae, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Miscellaneous Questions, Higher Order Thinking Skills (HOTS), Value Based Questions, Multiple Choice Questions (MCQs).

9. Measure of Dispersion

Introduction, Meaning and Definition, Objectives and Significance, Characteristics of Good Measure of Dispersion, Methods of Measurement of Dispersion, Types of Dispersion, Range, Inter-Quartile Range and Quaritle Deviation, Mean Deviation (Average Deviation), Standard Deviation (s), Relationship between Different Measures of Dispersion, Lorenz Curve, Choice of A Suitable Measure of Dispersion, Typical Illustrations, List of Formulae, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Higher Order Thinking Skills (HOTS), Multiple Choice Questions (MCQs).

10. Correlation

Introduction, Meaning and Definitions, Types of Correlation, Coefficient of Correlation (r), Degree of Correlation, Techniques or Methods for Measuring Correlation, Scatter Diagram (Dotogram Method), Karl Pearson’s Coefficient of Correlation, Spearman’s Rank Correlation, Typical Illustrations, List of Formulae, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Miscellaneous Questions, Higher Order Thinking Skills (HOTS), Value Based Questions, Multiple Choice Questions.

11. Index Numbers

Introduction, Characteristics or Features, Precautions in Constructions of Index Numbers (Problems), Types or Kinds of Index Numbers, Methods of Constructing Price Index Numbers, Simple Index Number (Unweighted), Weighted Index Numbers, Some Important Index Numbers, Significance or Uses of Index Numbers, Limitations of Index Numbers, List of Formulae, Key Points, Question Bank, Very Short Answer Type Questions, Short Answer Type Questions, Long Answer Type Questions, Numerical Questions, Higher Order Thinking Skills (HOTS), Value Based Questions, Multiple Choice Questions (MCQs).

12. Mathematical Tools Used in Economics

Slope of a Line, Slope of a Curve, Equation of a line.

13. Developing Projects in Economics

Introduction, Steps Towards Making A Project, Suggested List of Projects.

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faissalb · 4 years

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Machine Learning for Data Analysis-Week4-Running a K-Means Cluster Analysis:

For this week I will continue with gapminder dataset to identify the impact of similar groups of variables on Life expectancy using K-Means cluster analysis by identifying subgroups of countries based on their similarity response to the following 6 variables: income per person incomeperperson, employment rate: employrate, HIVrate, alcohol consumption rate :alcconsumption, urban rate: urbanrate, amount of CO2 emission co2emissions.A series of k-means cluster analyses were conducted on the training data specifying k=1-9 clusters, using Euclidean distance. The variance in the clustering variables that was accounted for by the clusters (r-square) was plotted for each of the nine cluster solutions in an elbow curve to provide guidance for choosing the number of clusters to interpret.

Import libraries and load the dataset :

subset clustering variables :

standardize predictors to have mean=0 and sd=1 :

split data into train and test sets :

k-means cluster analysis for 1-9 clusters :

Plot average distance from observations from the cluster centroid to use the Elbow Method to identify number of clusters to choose :

Interpret 4 cluster solution :

plot clusters :

Begin multiple steps to merge cluster assignment with clustering variables to examine cluster variable means by cluster.

create a unique identifier variable from the index for the cluster training data to merge with the cluster assignment variable:

create a list that has the new index variable:

create a list of cluster assignments :

combine index variable list with cluster assignment list into a dictionary :

convert newlist dictionary to a dataframe :

rename the cluster assignment column :

Repeat the same for the cluster assignment variable.

create a unique identifier variable from the index for the cluster assignment dataframe to merge with cluster training data :

merge the cluster assignment dataframe with the cluster training variable dataframe by the index variable :

cluster frequencies :

Finally calculate clustering variable means by cluster :

validate clusters in training data by examining cluster differences in lifeexpectancy using ANOVA .

First have to merge lifeexpectancy with clustering variables and cluster assignment data:

split lifeexpectancy data into train and test sets :

Means for lifeexpectancy by cluster :

standard deviations for lifeexpectancy by cluster :

The elbow curve was inconclusive, suggesting that the 2, 4,5, 6,7 and 8-cluster solutions might be interpreted. The results above are for an interpretation of the 4-cluster solution.

In order to externally validate the clusters, an Analysis of Variance (ANOVA) was conducting to test for significant differences between the clusters on life expectancy rate. A tukey test was used for post hoc comparisons between the clusters. Results indicated significant differences between the clusters on life expectancy rate (F=35.39, p<.0001). The tukey post hoc comparisons showed significant differences between clusters on life expectancy rate, with the exception that clusters 0 and 3 were not significantly different from each other. Countries in cluster 0 had the highest life expectancy rate (mean=80.38, sd=2), and cluster 1 had the lowest life expectancy rate (mean=60.37, sd=8.25).

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little-p-eng-engineering · 4 years

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Hierarchy of Piping Design Documents

September 27, 2017

P.Eng.

Meena Rezkallah

In today’s atmosphere of complex projects, extended liabilities, tight cost controls, and strict quality standards, it is essential that all phases of a project, from inception to operation, be effectively communicated and correctly executed. To this end, contract documents, design documents, fabrication details, procedures, and speciﬁcations are developed to communicate, monitor, and document the design, fabrication, and erection of piping systems precisely. The number and variety of documents to be prepared for a particular piping system are determined not so much by the importance of the piping system as by the complexity of the system and by the interface requirements of the owner, the design organization, the contractor, the material suppliers, and the regulatory agencies. In the following sections, the documentation requirements of a complex project are illustrated to provide a broad overview of the hierarchy of documents. However, since the speciﬁc requirements of a project are driven by many variables, such as the owner’s requirements, budgets,market conditions, company practice, and licensing requirements, the discussion here should be considered as a guideline only.

In this post all the principal design documents normally prepared for a complex piping system are identiﬁed, and their roles in the overall project are described. Note, however, that future developments in engineering tools might dictate variations from the documents described here. With the ongoing development of sophisticated computer software, several related design documents maybe developed from one database with the capability to extract information as required. For example, pressure drop and pipe stress analysis calculations may be executed from a physical piping drawings database.

The production and management of design documents may be inﬂuenced by outside parties. There are many industry and national standards that provide guidance in the preparation and control of design documents. Conformance to certain international standards is often mandatory. The references listed below contain standards for the preparation and control of design documents. The list is based on current practices in the United States. Where need for clarity exists, the reference is accompanied by a statement of ﬁeld of applicability. The list is not all-inclusive; engineers responsible for the preparation of design documents must, from time to time, review the current codes and standards in order to comply with and take advantage of the changes in the industry which are expected to continue as computerized drafting and preparation of text and record keeping improve. Additionally,where unique requirements exist, as in shipbuilding, the system design evolution process is governed by specialized methods. One reference is provided below for ship system design practice.

The military (MIL) and Department of Defense (DOD) standards and speciﬁcations referenced below provide a number of generally useful concepts and procedures for producing and maintaining design documents. Not all the information may be directly applicable to the ﬁeld of interest of this handbook; however, the referenced documents should not be ignored by anyone setting up a system of design document production and control because the information is of fundamental importance to an organized approach to the task.

ASME Boiler and Pressure Vessel Code, Section III, NCA-3252: Contents of Design Speciﬁcations. (The American Society of Mechanical Engineers, Three Park Avenue, New York, NY 10016–5990, USA.)

ANSI/ASME N626.3: Qualiﬁcations and Duties of Personnel Engaged in ASME Boiler and Pressure Vessel Code Section III, Division 1 and 2 Certifying Activities. (The American National Standards Institute, 11 West 42nd St., New York, NY 10036.)

U.S. Department of Defense Index of Speciﬁcations and Standards (DOD ISS). Naval Publication and Form Center ATT: NPODS, 5801 Tabor Avenue, Philadelphia, PA 19120–5099:

MIL-STD-481A Conﬁguration Control; Engineering Changes, Deviation and Waivers, Short Form

DOD-STD-480A Conﬁguration Control; Engineering Changes, Deviations and Waivers

MIL-STD-483A Conﬁguration Management Practices for Systems, Equipment, and Computer Programs

DOD-D-1000B Drawing, Engineering and Associated List

MIL-D-8501B Drawing, Undimensioned, Reproducibles, Photographic and Contact, Preparation of

ANSI Y14.1, to be ordered from ASME unless the request or is in the Navy

ANSI Y14.1, Drawing Sheet Size and Format (For ANSI ‘‘Y,’’ use ASME address.)

ANSI Y14.2, Line Conventions and Lettering. Drawings prepared under this standard usually are adequate for micro-graphic reproduction. (For ANSI ‘‘Y,’’use ASME address.)

ANSI Y14.5M, Dimensioning and Tolerancing (For ANSI ‘‘Y,’’ use ASME ad-dress.)

ISA-S5.1: Instrument Symbols and Identiﬁcation. This reference includes a standard for the amount of instrumentation detail that the piping designer would show on the piping and instrumentation diagram. The U.S. Nuclear Regulatory Commission has adopted a fairly current edition; users should verify that subsequent editions remain acceptable for U.S. nuclear work. (Instrument Society of America, 67 Alexander Drive, P.O. Box 12277, Research Triangle Park, NC 27709.)

NMA MS102, National Micrographics Association Drafting Guide for Micro-ﬁlm has been superseded by ANSI Y14.2, Line Conventions and Lettering, and by MS23. Contact the Association for Information and Image Management International, 1100 Wayne Ave., Silver Spring, MD 20910, for current information. Also, government regulations may dictate certain documentation requirements.

ISO 9000 Series Standards relating to quality control and quality assurance.

Harrington, Roy L., ed., Marine Engineering, Society of Naval Architects and Marine Engineers, Pavonia, NJ, 1992; ISBN 0-939773–10–4.

References 1 and 2 cover the ASME Code requirements for the Design Speciﬁcation and the certifying activities incidental to completion of the manufactured and erected work. References 3–8 have been required for some projects or they have been used as sources of guidance in the physical aspects of design and drafting.Reference 9 provides quality assurance and control requirements, which are being speciﬁed increasingly for piping and other equipment, including services. References 10 and 11 contain information on piping design and the design process itself.

In the United States, federal, state, and local laws apply to various piping systems; in other countries, similar laws may prevail. For example, the U.S. Code of Federal Regulations (CFR), Title 10, Part 50 mandates strict requirements for the design, construction, and operation of piping systems in a nuclear production or utilization facility. State and local governments generally invoke the ASME B31, Pressure Piping Code (Section B31.1 for Power Piping; B31.3 for Process Piping; etc.); and the ASME Boiler and Pressure Vessel Code (Section I, Power Boilers; Section II, Materials; etc.). Laws aimed at protecting the environment may also impact the design of some systems. Parts of the International Standards Organization (ISO) requirements, Ref. 9, are often imposed on piping design projects worldwide. The designer becomes familiar with the regulations prevailing at the location of the project by independent research and conference with the owner and local authorities.

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jparkau · 4 years

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K-means Cluster Analysis

In order to create groups of similar bottles of wine, we conducted a k-means cluster analysis and found subgroups of wines based on the similarity of responses on 11 variables. Clustering variables included quantitative variables (which work best on k means analysis): fixed acidity, volatile acidity, citric acid, residual sugar, chlorides, free sulfur dioxide, total sulfur dioxide, density, pH, sulphates, and alcohol level.

CODE:

Call in the libraries.

from pandas import Series, DataFrame import pandas as pd import numpy as np import matplotlib.pylab as plt from sklearn.model_selection import train_test_split from sklearn import preprocessing from sklearn.cluster import KMeans

Call in the data (I used kaggle.com to retrieve the data) data = pd.read_csv("redwinequality.csv")

Make all Dataframe columns uppercase data.columns = map(str.upper, data.columns)

Clean the dataset and delete all of the data with missing information

data_clean = data.dropna()

Assign the following clustering variables cluster=data_clean[['FIXED','VOLATILE','CITRIC','RESSUGAR','CHLORIDES','FSDIO', 'TSDIO','DENSITY','PH','SULPHATES','ALCOHOL']] cluster.describe()

Standardize clustering variables to have mean=0 and sd=1, because the variables should have the same scale to be fair. Astype float 64 ensures numeric format. clustervar=cluster.copy() for col in ['FIXED','VOLATILE','CITRIC','RESSUGAR','CHLORIDES','FSDIO', 'TSDIO','DENSITY','PH','SULPHATES','ALCOHOL']: clustervar[col] = preprocessing.scale(clustervar[col].astype('float64'))

Split data into train and test sets. We set 30% of the data set into the testing set and 70% into training. clus_train, clus_test = train_test_split(clustervar, test_size=.3, random_state=123)

Perform K-means cluster analysis for 1-9 clusters. We use Euclidean distance to measure similarity. from scipy.spatial.distance import cdist clusters=range(1,10) meandist=[]

for k in clusters: model=KMeans(n_clusters=k) model.fit(clus_train) clusassign=model.predict(clus_train) meandist.append(sum(np.min(cdist(clus_train, model.cluster_centers_, 'euclidean'), axis=1)) / clus_train.shape[0])

In order to see how many clusters we should choose from, we plot average distance from observations from the cluster centroid and use the Elbow Method.

plt.plot(clusters, meandist) plt.xlabel('Number of clusters') plt.ylabel('Average distance') plt.title('Selecting k with the Elbow Method')

We assume that we choose 3 clusters. Because this is a subjective conclusion, let us interpret the k=3 clustering. model3=KMeans(n_clusters=3) model3.fit(clus_train) clusassign=model3.predict(clus_train)

Use canonical discriminant analysis, which will reduce the number of clustering variables. Plot the first two most influential canonical variables to see the discriminant plot and see cluster within variance as well as overlapping points.

from sklearn.decomposition import PCA pca_2 = PCA(2) plot_columns = pca_2.fit_transform(clus_train) plt.scatter(x=plot_columns[:,0], y=plot_columns[:,1], c=model3.labels_,) plt.xlabel('Canonical variable 1') plt.ylabel('Canonical variable 2') plt.title('Scatterplot of Canonical Variables for 3 Clusters') plt.show()

We can now merge cluster assignment with clustering variables to examine the cluster variable means by cluster clus_train.reset_index(level=0, inplace=True) cluslist=list(clus_train['index']) labels=list(model3.labels_) newlist=dict(zip(cluslist, labels)) newlist newclus=DataFrame.from_dict(newlist, orient='index') newclus newclus.columns = ['cluster']

newclus.reset_index(level=0, inplace=True) # merge the cluster assignment dataframe with the cluster training variable dataframe # by the index variable merged_train=pd.merge(clus_train, newclus, on='index') merged_train.head(n=100) # cluster frequencies merged_train.cluster.value_counts()

We can now calculate clustering variable means by cluster clustergrp = merged_train.groupby('cluster').mean() print ("Clustering variable means by cluster") print(clustergrp)

To validate clusters in training data, we can examine the cluster differences in QUALITY using ANOVA quality_train, quality_test = train_test_split(quality_data, test_size=.3, random_state=123) quality_train1=pd.DataFrame(quality_train) quality_train1.reset_index(level=0, inplace=True) merged_train_all=pd.merge(quality_train1, merged_train, on='index') sub1 = merged_train_all[['QUALITY','cluster']].dropna()

import statsmodels.formula.api as smf import statsmodels.stats.multicomp as multi

qualitymod = smf.ols(formula='QUALITY ~ C(cluster)', data=sub1).fit() print (qualitymod.summary())

print ('means for QUALITY by cluster') m1= sub1.groupby('cluster').mean() print (m1)

print ('standard deviations for QUALITY by cluster') m2= sub1.groupby('cluster').std() print (m2)

mc1 = multi.MultiComparison(sub1['QUALITY'], sub1['cluster']) res1 = mc1.tukeyhsd() print(res1.summary())

By visualizing the elbow method, we can see that k=2 or k=3 will be an appropriate number of clusters. To further analyze this, let us use the canonical discriminant analyses to interpret the k=3 cluster solution. The canonical discriminant analyses reduced the 11 clustering variables down to 5 that affected most of the variance in clustering variables. We then plot the 2 most influential canonical variables on a scatterplot and see the density or overlap between the points.

We can see from the scatterplot that clusters 1 and 2 are all densely packed with relatively low within cluster variance. Cluster 3 was generally distinct, but the observations had greater spread than cluster 1 and 2 which suggests that it has a higher within cluster variance. Clusters 1, 2, and 3 do not overlap with one another very much. The plot does suggest that a 2 cluster solution is also feasible.

The means on the clustering variables show that compared to the other clusters, types of wine in cluster 1 are low in fixed and volatile acidity, while cluster 2 are low in fixed but relatively higher in volatile acidity. Wine types in cluster 3 are high in fixed acidity and lower in volatile acidity. This indicates that wines in cluster 1 are not acidic, while cluster 2 wine types are not acidic but tend to vary as time continues, and cluster 3 wine types are acidic but tend to vary with time. Both cluster 1 and 3 are low in pH (with cluster 3 being more), while cluster 2 is higher in pH. Wines low in sulphates include cluster 1 and 2, while cluster 1 has a lower alcohol level than others.

In order to externally validate the clusters, we conducted an Analysis of Variance to test for significant differences between the clusters on Quality. We used the turkey test for post hoc comparisons between the clusters, and the results showed us moderate differences between the clusters on Quality (although not significant). On a scale of 10, cluster 2 had similar quality means compared to cluster 1 and 3, with cluster 2 quality mean being 5.56 and cluster 1 and 3’s quality means being 5.375 and 5.972 respectively. When comparing cluster 1 and 3 there is a more noticeable difference in quality mean. Wine in cluster 1 is the lowest in quality, while wine in cluster 3 is the highest in wine quality.

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sbayarri · 4 years

Text

Fourth Assignment; k-means cluster analysis

This post shows the result of applying k-means cluster analysis to detect ideological/political population clusters using the Outlook On Life 2012 survey.

* A set of 11 variables which may have relation to the political or ideological position of the observed subjects have been chosen for the analysis. They are listed in the Python code.

* In addition one more variable representing the position of subjects on the “American dream” expectations has been chosen to validate the cluster division.

* As in the previous assignment, all columns data preparation and scaling has been encapsulated in the adjust_column function.

This is the Python code of the initial run:

=================================

from pandas import Series, DataFrame import pandas as pd import os import numpy as np import matplotlib.pyplot as plt from sklearn.model_selection import train_test_split from sklearn import preprocessing from sklearn.cluster import KMeans

""" Data Management """ os.chdir("D:\Documentos\Personal\Curso Data Analytics\Datasets")

data = pd.read_csv("ool_pds.csv")

#upper-case all DataFrame column names data.columns = map(str.upper, data.columns)

# Data Management

data_clean = data.dropna()

# W1_A5A: Who did you vote for? # W1_A10: How often, if ever, do you discuss politics with your family or friends? # W1_A12 Obama approval: 1 approve, 2 disapprove, -1 Refused # W1_B4 Anger about country situation: 1 more angry, 5 less angry # W1_C1C: Do you think of yourself as closer to the Republican Party or to the Democratic Party? # W1_E2A: Are you extremely [optimistic/pessimistic], moderately [optimistic/pessimistic], or slightly [optimistic/pessimistic]? # W1_E4: Were you ever willing to date outside of your racial group? # W1_H1: Society has reached the point where Blacks and Whites have equal opportunities for achievement. # W1_J1_D: [Require that an equal number of the top leadership positions in government go to women? ] What is your opinion about each of them? # W1_L5_A: [Helped in a voter registration drive ] Please indicate whether or not you have engaged in these political activities in the last TWO years? Have you... # W1_M5: How often do you attend religious services? # W1_A4: In 2008, John McCain ran on the Republican ticket against Barack Obama who ran on # the Democratic ticket. Do you remember whether or not you voted in that election? # W1_A11: How many days in the past week did you watch national news programs on # television or on the Internet? # W1_B1: How much do government officials care what people like you think? # W1_B2: How much can people like you affect what the government does? # W1_B4: Generally speaking, how angry do you feel about the way things are going in the # country these days? # W1_C2: We hear a lot of talk these days about liberals and conservatives. Where would you # place YOURSELF on this 7 point scale? # W1_D11: [The Republican Party] How would you rate: (1-100) # W1_D12: [The Democratic Party] How would you rate: # W1_E3: Some people engage in interracial relationships, while others do not. Have you dated # outside of your racial group? (Yes/no) # W1_F2: And when you think about the future of the United States as a whole, are you # generally optimistic, pessimistic, or neither optimistic nor pessimistic? # W1_F3: A basic American belief has been that if you work hard you can get ahead and reach # the goals you set and more. Is this true or false today? # W1_F6: How far along the road to your American Dream do you think you will ultimately get on # a 10-point scale where 1 is not far at all and 10 nearly there?

# subset clustering variables cluster=data_clean[['W1_A5A','W1_A12','W1_B4','W1_C1C','W1_E2A', 'W1_H1','W1_J1_D','W1_C2','W1_D11','W1_D12','W1_F2']] cluster.describe()

# Function to normalize data columns from sklearn import preprocessing def adjust_column(column): column = pd.to_numeric(column, errors='coerce') average = column.mean() column = column.fillna(value=-1) column = column.replace(-1, average) return preprocessing.scale(column.astype('float64')) # standardize predictors to have mean=0 and sd=1

# standardize clustering variables to have mean=0 and sd=1 clustervar=cluster.copy() clustervar['W1_A5A']=adjust_column(clustervar['W1_A5A']) clustervar['W1_A12']=adjust_column(clustervar['W1_A12']) clustervar['W1_B4']=adjust_column(clustervar['W1_B4']) clustervar['W1_C1C']=adjust_column(clustervar['W1_C1C']) clustervar['W1_E2A']=adjust_column(clustervar['W1_E2A']) clustervar['W1_H1']=adjust_column(clustervar['W1_H1']) clustervar['W1_J1_D']=adjust_column(clustervar['W1_J1_D']) clustervar['W1_C2']=adjust_column(clustervar['W1_C2']) clustervar['W1_D11']=adjust_column(clustervar['W1_D11']) clustervar['W1_D12']=adjust_column(clustervar['W1_D12']) clustervar['W1_F2']=adjust_column(clustervar['W1_F2'])

# split data into train and test sets clus_train, clus_test = train_test_split(clustervar, test_size=.3, random_state=123) print(clus_train.shape) print(clus_test.shape)

# k-means cluster analysis for 1-9 clusters from scipy.spatial.distance import cdist clusters=range(1,10) meandist=[]

""" Plot average distance from observations from the cluster centroid to use the Elbow Method to identify number of clusters to choose """

f1 = plt.figure(1) plt.plot(clusters, meandist) plt.xlabel('Number of clusters') plt.ylabel('Average distance') plt.title('Selecting k with the Elbow Method')

# Interpret 3 cluster solution model3=KMeans(n_clusters=3) model3.fit(clus_train) clusassign=model3.predict(clus_train) # plot clusters

from sklearn.decomposition import PCA pca_2 = PCA(2) plot_columns = pca_2.fit_transform(clus_train)

f2 = plt.figure(2) plt.scatter(x=plot_columns[:,0], y=plot_columns[:,1], c=model3.labels_,) plt.xlabel('Canonical variable 1') plt.ylabel('Canonical variable 2') plt.title('Scatterplot of Canonical Variables for 3 Clusters') plt.show()

""" BEGIN multiple steps to merge cluster assignment with clustering variables to examine cluster variable means by cluster """ # create a unique identifier variable from the index for the # cluster training data to merge with the cluster assignment variable clus_train.reset_index(level=0, inplace=True) # create a list that has the new index variable cluslist=list(clus_train['index']) # create a list of cluster assignments labels=list(model3.labels_) # combine index variable list with cluster assignment list into a dictionary newlist=dict(zip(cluslist, labels)) newlist # convert newlist dictionary to a dataframe newclus=DataFrame.from_dict(newlist, orient='index') newclus # rename the cluster assignment column newclus.columns = ['cluster']

# now do the same for the cluster assignment variable # create a unique identifier variable from the index for the # cluster assignment dataframe # to merge with cluster training data newclus.reset_index(level=0, inplace=True) # merge the cluster assignment dataframe with the cluster training variable dataframe # by the index variable merged_train=pd.merge(clus_train, newclus, on='index') merged_train.head(n=100) # cluster frequencies merged_train.cluster.value_counts()

""" END multiple steps to merge cluster assignment with clustering variables to examine cluster variable means by cluster """

# FINALLY calculate clustering variable means by cluster clustergrp = merged_train.groupby('cluster').mean() print ("Clustering variable means by cluster") print(clustergrp)

# validate clusters in training data by examining cluster differences in another variable using ANOVA # first have to merge GPA with clustering variables and cluster assignment data gpa_data=data_clean['W1_F6'] # split GPA data into train and test sets gpa_train, gpa_test = train_test_split(gpa_data, test_size=.3, random_state=123) gpa_train1=pd.DataFrame(gpa_train) gpa_train1.reset_index(level=0, inplace=True) merged_train_all=pd.merge(gpa_train1, merged_train, on='index') sub1 = merged_train_all[['W1_F6', 'cluster']].dropna()

import statsmodels.formula.api as smf import statsmodels.stats.multicomp as multi

gpamod = smf.ols(formula='W1_F6 ~ C(cluster)', data=sub1).fit() print (gpamod.summary())

print ('means for W1_F6 by cluster') m1= sub1.groupby('cluster').mean() print (m1)

print ('standard deviations for W1_F6 by cluster') m2= sub1.groupby('cluster').std() print (m2)

mc1 = multi.MultiComparison(sub1['W1_F6'], sub1['cluster']) res1 = mc1.tukeyhsd() print(res1.summary())

=================================

Output description and discussion

The observations are divided into a training set of 1604 and a test set of 688.

The first significant output is the plot showing the evolution of the average distance within each cluster, depening on the number of clusters. We can see significant bend points for K=3 and K=4, so we will focus on those numbers of clusters.

3-cluster analysis

This is the result of plotting the observations (with a cluster color code for the k=3 case) in the plane defined by the two principal components resulting from PCA.

We can see that most observations lie on a continuous group along the horizontal axis, and the k-means algorithm has divided this subset into two clusters with some overlap (the algorithm does not favor elongated clusters). On the other hand, it has grouped together two other subsets, clearly separated in the vertical axis.

To interpret this graphical result, we can look into the meaning of the two canonical variables resulted from the PCA:

Based on the coefficients of each canonical variable (table rows), we can summarize the meaning like this:

* Variable 0 (horizontal axis) correlates most with the original variables 0, 1 and 7, which represent the vote and approval of president, and the position in the liberal-conservative scale. We can summarize it as an “ideological position” coordinate.

* Variable 1 (vertical axis) correlates most with the original variables 8 and 9, which represent the rating given to Republican and Democratic political parties, so we can summarize it as a “political position” coordinate.

The interpretation would be, then, that the observations are mostly continuous along the ideological axis, but k-means divides the longest group in two halfs which we can interpret as a somewhat arbitrary liberal/conservative division. On the other hand, the political axis clearly divides the observations in three separated groups. We would need to look into the PCA coefficients for the canonical variables and the values of these variables to interpret this division, but it is clear that the two upper groups (yellow cluster) have a smaller number of observations and higher variance, so it may make sense to cluster them together.

If we look at the variable means by cluster below, we confirm that cluster 2 is defined by strong political party identification, probably one subset for Republicans and another for Democrats, while clusters 0 and 1 are divided by the vote/approval behavior in the Obama election.

Validation with external variable

We now perform the OLS regression with the W1_F6 variable, which represents the expectations regarding the “American dream”.

We can see that the average value for this variable is significantly different for cluster 2, which also has a larger standard deviation.

Larger number of clusters

When we select 4 as the number of clusters in the second part of the analysis, we find that it is the largest group which is divided along the “ideological” axis, not the other separated groups, which remain in a single cluster. So, in order to analyze this groups as different clusters we probably would need to use a different cluster analysis method that emphasyzes more continuity/discontinuity than average distance.

The failure of the k-means method to capture the divide in the vertical axis is even more clear with k=5, when the observations between different subsets start overlapping:

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bentonpena · 4 years

Text

Beginner's Guide to Statistics and Probability Distribution

Beginner's Guide to Statistics and Probability Distribution http://bit.ly/39yJ24M

By Anupriya Gupta and Ishan Shah

We have all realised that a working knowledge of statistics is essential for modelling different strategies when it comes to algorithmic trading. In fact, data science, one of the most sought after skills in this decade, employs statistics to model data and arrive at meaningful conclusions. With that aim in mind we will go through some basic terminologies as well as the types of probability distributions which are employed in the domain of algorithmic trading.

We will go through the following topics:

Historical Data Analysis

Probability distribution

Correlation

Historical Data Analysis

In this section, we will try to answer the fundamental question, “How do you analyse a stock’s historical data and use it for strategy building?” Of course, for the analysis, we first need a data set!

Dataset

In order to keep it universal, we have taken the daily stock price data of Apple, Inc. from Dec 26, 2018, to Dec 26, 2019. You can download historical data from Yahoo Finance. If you are interested in downloading the data using python, you can visit the following link.

For the time being, we will use the following python code to download it from yahoo finance;

import yfinance as yf aapl = yf.download('AAPL','2018-12-26', '2019-12-26')

This is a time-series data set with daily closing prices and volumes for Apple. We’ll base our analysis on the closing prices for this stock. We’ll just touch upon the basic statistical properties for the daily stock prices in this post, which would be followed by a breif on correlation.

Mean? Mode? Median? What’s the difference!!!

We will just take 5 numbers as an example: 12, 13, 6, 7, 19, 21, and understand the three terms.

Mean

To put it simply, mean is the one we are most used to, i.e. the average. Thus, in the above example, the mean = (12 + 13 + 6 + 7 + 19 + 21)/6 = 13.

In the AAPL dataset, the mean of closing prices is 204.84. The rolling mean is a widely used measure in technical trading strategies. The traders place great importance to cross over of 50 days and 200 days rolling mean. And initiate trade based on it.

For the AAPL dataset, we will use the following python code:

mean = np.mean(aapl['Adj Close']) mean

The output is: 204.84638595581055

Mode

In a given dataset, the mode will be the number which is occurring the most. In the above example, since there is no value which is repeated, there is no mode. You can argue that every element is a mode. But that doesn't help in summarizing the dataset.

In the AAPL dataset, the mode of closing prices does not exist as there is no repeating value.

When we try to run the following code to find the mode in python, it throws the following error

import statistics mode = statistics.mode(aapl['Adj Close']) mode

Also, if your dataset is as below, which value of mode you will go with?

It is difficult to answer that question, and some other measure should be used. Also, the mode doesn’t really make much sense for closing prices or other continuous data. A mode is especially useful when you want to plot histograms and visualize the frequency distribution.

Median

Sometimes, the data set values can have a few values which are at the extreme ends, and this might cause the mean of the data set to portray an incorrect picture. Thus, we use the median, which gives the middle value of the sorted data set.

To find the median, you have to arrange the numbers in ascending order and then find the middle value. If the dataset contains an even number of values, you take the mean of the middle two values. In our example, the median is (12 + 13)/2 = 12.5

In our data set, the median of the closing price is 201.05

The python code for finding the median is the following:

median = np.median(aapl['Adj Close'])

Great! We now move on to a term which is very important when we start learning about statistics, i.e. Probability distribution.

Probability distribution

We have all gone through the example of finding the probabilities of a dice roll. Now, we know that there are only six outcomes on a dice roll, i.e. {1, 2, 3, 4, 5, 6}. The probability of rolling a 1 is 1/6. This kind of probability is called discrete, where there are a fixed number of outcomes.

Now, as the name suggests, the probability distribution is simply a list of all outcomes of a given event. Thus, the probability of the dice roll event is the following:

Dice roll number

Probability Distribution

1/6

Listing all the values here works because we have a limited set of outcomes, but if the outcomes are large, we use functions.

If the probability is discrete, we call the function a probability mass function. In the case of dice roll, it will be P(x) = 1/6 where x = {1,2,3,4,5,6}.

For discrete probabilities, there are certain cases which are so extensively studied, that their probability distribution has become standardised. Let’s take, for example, Bernoulli's distribution, which takes into account the probability of getting heads or tails when we toss a coin. We write its probability function as px (1 – p)(1 – x). Here x is the outcome, which could be written as heads = 0 and tails = 1.

Now, there are cases where the outcomes are not clearly defined. For example, the heights of all high school students in one grade. While the actual reason is different, we can say that it will be too cumbersome to list down all the height data and the probability. It is in this situation that the functions are essential.

Earlier, we said that for discrete values, the probability function is the probability mass function. In comparison, for continuous values, the probability function is known as a probability density function.

Let us take a step back and understand some terms related to the probability distribution.

Range

Range simply gives the difference between the min and max values of the data set.

In the data set taken, the minimum value of the closing price is 140.08 while the maximum value is 284.26. Thus, the range = 284.26 - 140.08 = 144.18. Now, we will move towards standard deviation.

In python, we can find the values by a simple line of code:

aapl['Adj Close'].describe()

The output is as follows:

Standard Deviation

In simple words, the standard deviation tells us how far the value deviates from the mean. Let us use the full dataset and try to understand how the standard deviation helps us in the arena of trading.

We are taking into account the closing price for our calculations. As specified previously, the mean of our dataset is 204.84. The python code for Plotting the graph with the closing price and the mean should give us the following figure.

import matplotlib.pyplot as plt aapl['Adj Close'].plot(figsize=(10,7)) plt.axhline(y=mean, color='r', linestyle='-') plt.legend() plt.grid() plt.show()

The standard deviation is calculated as:

Calculate the simple average of the numbers (mean)

Subtract the mean from each number

Square the result

Calculate the average of the results

Take square root of the answer in step 4

For the data set given, the code is as follows:

std = np.std(aapl['Adj Close'])

The standard deviation of the closing price would be 34.05.

Now we will plot the above graph with one standard deviation on both sides of the mean. We will write it as (+S.D.) = 204.84 + 34.05 = 238.89, and (-S.D.) = 204.84 - 34.05 = 170.79.

The code is as follows:

aapl['Adj Close'].plot(figsize=(10,7)) plt.axhline(y=mean, color='r', linestyle='-') plt.axhline(y=mean+std, color='r', linestyle='-') plt.axhline(y=mean-std, color='r', linestyle='-') plt.legend() plt.grid() plt.show()

In the graph, the mean is shown as the middle red line while the +S.D. and -S.D. are the other red lines.

So tell us, what can you observe by looking at the above graph?

Well, a quick look tells us that most of the closing price values are in between the two standard deviations. Thus, this gives us a rough idea about the majority of the price action.

But you might still be wondering, what is the use of knowing a certain range of price values? Well, for one thing, standard deviation plays an important role in Bollinger Bands, which is a quite popular indicator. You can use the upper standard deviation as a sign of a breakout. And initiate a buy trade when the price moves above the upper band.

The volatility of the stock can be calculated using the standard deviation. The stock volatility is an important feature used in many machine learning algorithms. It is also used in Normal probability distribution, which we will cover in a while.

Wait! Normal distribution?

Normal distribution is a very simple and yet, quite profound piece in the world of statistics, actually in general life too. The basic premise is that given a range of observations, it is found that most of the values centre around the mean and within one standard deviation away from the mean. Actually, it is said that 68% of the values are within this range. If we move ahead, then we see 95% of the values within two standard deviations from the mean.

Wait, we are going ahead of ourselves now. Let us first take the help of something called the histogram to understand this.

Histogram

Let’s take an example of the heights of students in a batch. Now there might be students who have heights of 60.1 inch, 60.2 inches and so on till 60.9. Sometimes we are not looking for that level of detail and would like just to find out how many students have a height of 60 - 61 inches. Wouldn’t that make our job easier and simpler? That is exactly what a histogram does. It gives us the frequency distribution of the observed values.

When it comes to trading, we usually use the daily percentage change instead of the closing prices.

For our dataset, we will use the following code:

aapl['daily_percent_change'] = aapl['Adj Close'].pct_change() aapl.daily_percent_change.hist(figsize=(10,7)) plt.ylabel('Frequency') plt.xlabel('Daily Percentage Change') plt.show()

The output is as follows:

Recall how we said that the majority of the values are situated close to the mean. You can see it clearly in the histogram plotted above.

In fact, if we draw a line curve around the values, it would look like a bell.

We call this a bell curve, which is another name for the normal probability distribution, or normal distribution for short. You can see the majority of the values lying between the standard deviations, i.e. (+S.D.) = 239.6, and (-S.D.) = 172.64.

You might want to keep in mind that in a normal distribution, 68% of the values lie between one standard deviation and 95% of the values lie between two standard deviations. Moving further, we will say that 99.7% of the values lie between 3 standard deviations of the mean.

Normal distribution

When the distribution of your data meets certain requirements, such as symmetry around the mean and bell-shaped curve, we say your data is normally distributed.

Statistically speaking, if X is Normally distributed with mean µ and standard deviation σ, we write X∼N(µ, σ^2), where µ and σ are the parameters of the distribution.

Why is it useful to know the distribution function of your dataset?

If you know that your data sample is, say, normally distributed, you can make ‘predictions’ about your population with certain ‘confidence’.

For example, say, your data sample X represents marks obtained out of 100 in an entrance test for a sample of students. The data is normally distributed, such as X∼N(50, 102). When plotted, this data would look as follows:

If you increase the number of observations in your sample data set from 100 to 1000, this is what happens:

It looks more bell-shaped!

Now that we know, X has normally distributed data with mean at 50 and standard deviation of 10, we can predict the marks of the entire student population or future students (from the same population) with a certain confidence. With almost 99.7% confidence, we can say that students would not get less than 20 or greater than 80 marks. With 95% confidence, we can say that students would get marks between 30 and 70 points.

Statistically speaking, distribution functions give us the probability of expecting the value of a given observation between two points. Hence, using distribution functions, also called probability density functions, we can ‘predict’ with certain ‘confidence’.

Are closing prices normally distributed?

Before we try to answer the question, let us take another dataset and see how its histogram looks like.

We have plotted the histogram of Tesla, Inc. for the same period and see the following:

Here, the mean(Closing price) is 270.9 and the +S.D. and -S.D. is 319.14 and 222.66 respectively. So what conclusion can you draw from the above histogram?

To sum it up, probability distribution functions are used in every step of technical analysis, and it is the core of the quantitative analysis. These analyses constitute the core part of any strategy building process.

So far, we have gone through some basic concepts in the world of statistics. Now, we shall try to go a bit further in this fascinating world and see its application in trading. We will first start with correlation.

Correlation

Am I related to you or not?

Well, in a way, correlation tells us about the relationship between two sets of values. Until now, we have taken the data set of Apple from Dec 26, 2018 to Dec 26, 2019. Now, we should point that Apple is part of the S&P 500 index. Thus, any change in Apple stocks could in some way reflect on the S&P index.

Let us take the dataset of the S&P500 for the same time period and find the correlation.

The code is as follows:

import yfinance as yf spx = yf.download('^GSPC','2018-12-26', '2019-12-26') spx['daily_percent_change'] = spx['Adj Close'].pct_change() plt.figure(figsize=(10,7)) plt.scatter(aapl.daily_percent_change,spx.daily_percent_change) plt.xlabel('AAPL Daily Returns') plt.ylabel('SPY Daily Returns') plt.grid() plt.show()

from scipy.stats import spearmanr correlation, _ = spearmanr(aapl.daily_percent_change.dropna(),spx.daily_percent_change.dropna()) print('Spearmans correlation is %.2f' % correlation)

Understanding correlation

Correlation is a unit free number lying between -1 and 1 which gives us the measurement of the relationship between variables. A highly positive correlation value lying between 0.7 and 1.0 means that the change in one variable is positively related to the change in the other variable. That means, if one variable increases, there is a high probability that other one will increase as well. The behavior will be consistent in other cases of decrease or no change in value as well.

On the other hand, a highly negative correlation value lying between -0.7 to -1.0 tells us that the change in one variable is negatively related to the change in the other variable. That means, if one variable increase, there is a high probability that the other one will decrease.

The low correlation value around -0.2 and 0.2 tells us that there is no strong relationship between the two variables.

A point to note is that correlation doesn’t tell us anything about causality. We have all heard of the statement, “Correlation doesn’t imply causation”. For instance, it is possible that instances of lung cancers are correlated with the number of cigarettes smoked in a lifetime among a population, that does not establish causality of smoking to lung cancer. One would be required to do a controlled group study keeping constant all other influential factors to establish such a causality relation. Machine learning based trading models are very good at extracting such causality between different indicators.

Correlation is the measure of the linear relationship. For instance, the correlation between x and x2 might be as close as 0. Even though there is a strong relationship between the two variables, it would not be captured in the correlation value.

Great! We have gone through a lot of concepts related to Statistics. You can move further to regression; in fact, the blog on Linear regression is a perfect next step in your quest to master the art of algorithmic trading.

Conclusion

We have gone through basic concepts of mean, median and mode and then understood the probability distribution of discrete as well as continuous variables. We looked into normal distribution in detail and touched upon the topic of correlation to figure out if two datasets are related or not.

If you want to learn various aspects of Algorithmic trading and automated trading systems, then check out the Executive Programme in Algorithmic Trading (EPAT®). The course covers training modules like Statistics & Econometrics, Financial Computing & Technology, and Algorithmic & Quantitative Trading. EPAT® equips you with the required skill sets to build a promising career in algorithmic trading. Enroll now!

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