#eigenvectors

[stary-night]

Eigens your vectors

[dnieperrobot69420]

Taking a slight tangent from classical optics, I decided to delve more into non-linear optics.

As someone who never had to use Gaussian form of Maxwell's equations, never used Tensors, and had never used Einsteins notation for summation; let me just say the algebra of the book proved to be a hard nut to crack!

What am I learning about? Anisotropy! Who knew that the direction at which you observe/propagate through a material such as a crystal plays a role in the material properties you will experience!!

I still don't believe you can determine eigenvalues and eigenvectors for an arbitrary 3x3 permittivity matrix (I need to use numerical examples to really see it) and that there exists rotational matricies that let us make the math all neat and proper.

But, slowly and with growing pains, I am continuing to slowly tread the waters of this fascinating topic!

[gayarograce]

if i pass my linear algebra exam tomorrow i think that means grant 3b1b and i have to go get gay married i'm sorry i don't make the rules

[abalidoth]

broke: I was sold to One Direction

woke: I was sold one direction

theyre selling WHAT on ebay now

[possibly-j]

Hanging out with a bunch of sorority girls while doing math and watching them all suddenly look over at me when I say a Greek letter then immediately lose interest has been a great experience

[empiricalscotus]

Using Network Analysis to Gauge the Justices’ Relative Importance in Oral Arguments

Anecdotes and research support the notion that oral arguments do not often influence case outcomes. Chief Justice John Roberts said as much in an interview with Bryan Garner for the Scribes Journal in 2010: “The oral argument is the tip of the iceberg — the most visible part of the process — but the briefs are more important.”  In fact, a series of studies including my own work points to the…

[laz-ofthestars]

DAAAMN LINEAR ALGEBRA IS SICK

[sublightdrive]

from this perspective it's a very math-y idea, and it's pretty understandable that someone who learns about surreal numbers in that way could completely miss out on their more playful origins.

I feel like this is actually a pretty common phenomenon in mathematics, where an idea has an intuitive, often geometric, and even playful origin. But then the idea gets formalized, and the language used to describe it is made more generic in order to make it easier to manipulate, and fold it into the greater universe of mathematics it exists within. And in doing so, you lose the original context that made that idea interesting or easily understood in the first place.

I'm not saying that's necessarily a bad thing, since formal, "generic" notation is like, a huge reason that mathematics as a field can even exist in the first place, but it is a tradeoff that I think often falls harder on the "formal notation" side of things than the "intuitive ideas" side.

another really specific game theory (field of mathematics) poll

[charl0ttan]

scary how probably all of your friends are friends with someone who you would either hate or be hated by. the set of all such friends forms an eigenvector of assholes

[covid-safer-hotties]

Also preserved on our archive

Whenever you hear someone trying to blame kid's poor test scores "post pandemic" on "lockdowns," show them this.

By Dr. Sushama R. Chaphalkar, PhD.

New research shows that mild COVID-19 alters brain structure and connectivity in key areas responsible for memory and cognition, emphasizing the lasting effects on young people’s brain health.

In a case-control study published in the journal Translational Psychiatry, researchers used magnetic resonance imaging (MRI) and cognitive tests to examine brain structure, function, and cognition in adolescents and young adults with mild coronavirus disease 2019 (COVID-19) compared to healthy controls in a pandemic hotspot in Italy. They identified significant changes in brain regions related to olfaction and cognition, with decreased brain volume and reduced functional connectivity in areas like the left hippocampus and amygdala, which were linked to impaired spatial working memory. Notably, no significant differences were observed in whole-brain connectivity, suggesting that these changes were localized rather than widespread.

Background COVID-19, primarily known for respiratory symptoms, also affects the central nervous system, leading to neurological issues like headaches, anosmia, and cognitive changes. MRI-based studies reveal anatomical brain changes in COVID-19 patients, such as reduced gray matter and decreased volume in regions like the hippocampus and amygdala, often linked to cognitive deficits.

While research mostly focuses on severe cases and older adults, a majority of infections with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative agent of COVID-19, occur in adolescents and young adults who also experience long-lasting cognitive symptoms.

This age group, undergoing key brain development, is impacted by changes in spatial working memory and brain structure, which are crucial for cognitive functions shaped by social interactions, significantly disrupted by the pandemic.

Given that this is the largest and most understudied population affected by COVID-19, understanding the brain and cognitive impacts in adolescents and young adults is vital.

Therefore, researchers in the present study compared anatomical, functional, and cognitive outcomes, utilizing a longitudinal design that allowed them to assess both pre- and post-infection differences, in COVID-19-positive and negative adolescents and young adults from Lombardy, Italy, a global hotspot during the pandemic.

About the study The present study involved participants from the Public Health Impact of Metal Exposure (PHIME) cohort, a longitudinal investigation of adolescents and young adults in northern Italy. Between 2016 and 2021, 207 participants, aged 13 to 25 years, were included in a sub-study with MRI scans and cognitive tests. After COVID-19 restrictions were lifted, 40 participants (13 COVID+ and 27 COVID−) participated in a follow-up study, which replicated the MRI and cognitive assessments.

The mean age of participants was 20.44 years and 65% were female. COVID+ status was confirmed through positive reverse transcription polymerase chain reaction (RT-PCR) tests within 12 months of follow-up. Neuropsychological assessments used the Cambridge Neuropsychological Test Automated Battery (CANTAB) to evaluate spatial working memory.

MRI and functional MRI data were acquired using a 3-Tesla scanner, processed, and analyzed for structural and local functional connectivity using eigenvector centrality mapping (ECM) and functional connectivity (FC) metrics. Whole-brain functional connectivity metrics showed no significant differences between COVID+ and control groups, indicating that the observed changes were specific to key brain regions rather than generalized across the entire brain.

Statistical analysis involved the use of pairwise Student's t-tests, Kolmogorov–Smirnov test, linear regression, two-waves mediation analysis, negative binomial regression, and linear regression, all adjusted for covariates.

Results and discussion Significant differences were observed in the two groups regarding the time between assessments, COVID-19 symptoms, and vaccine status. The research identified five localized functional connectivity hubs with significant differences between the two groups, including the right intracalcarine cortex, right lingual gyrus, left frontal orbital cortex, left hippocampus and left amygdala, which is vital for cognitive functions. Only the left hippocampal volume showed a significant reduction in COVID+ participants (p = 0.034), while whole-brain connectivity remained unchanged, reinforcing the localized nature of the brain changes.

The left amygdala mediated the relationship between COVID-19 and spatial working memory "between errors" (p = 0.028), a critical finding that highlights the indirect effect of amygdala connectivity on cognitive function in COVID+ individuals. This mediation analysis underscores the role of specific brain regions in influencing cognitive deficits, as only the indirect effect was statistically significant for spatial working memory errors. The orbitofrontal cortex, involved in sensory integration and cognitive functions, also showed decreased connectivity in COVID+ individuals, supporting previous findings of structural and functional changes in this region during COVID-19.

The study is limited by small sample size, lack of diversity, potential confounding factors due to the long interval between MRI scans, treatment of certain subjects as COVID-negative based on antibody testing beyond the 12-month threshold, and the possibility of non-significant findings in mediation analysis due to these factors.

Conclusion In conclusion, the findings indicate persistent structural and functional alterations in specific brain regions of COVID-19-positive adolescents and young adults, including changes in gray matter volume and localized functional connectivity, which correlate with diminished cognitive function, particularly in working memory.

Further research is necessary to evaluate the longevity and potential reversibility of these brain and cognitive changes post-infection, enhancing our understanding of post-COVID outcomes and informing future interventions and treatments. The longitudinal design of this study, with pre- and post-COVID data, strengthens these findings by allowing direct comparisons over time, offering robust insights into the impact of COVID-19 on adolescent brain development.

Journal reference: COVID-19 related cognitive, structural and functional brain changes among Italian adolescents and young adults: a multimodal longitudinal case-control study. Invernizzi, A. et al., Translational Psychiatry, 14, 402 (2024), DOI: 10.1038/s41398-024-03108-2, www.nature.com/articles/s41398-024-03108-2

[goyardgoyangi]

𐙚 bad habit pt. 1 ໒꒱ ‧₊˚

⌗ pairings: ino takuma x reader, slight! choso x reader

⌗ summary: you met in your first computer science course— not because either of you were brilliant, but because you were both bombed the first quiz and were too stubborn to quit. he’s the guy you kept bumping into at the campus convenience store at 1AM and a habit of muttering “chat, we’re so cooked” under his breath during quizzes. you? you just wanted to pass. and maybe cry in peace. you study together now— a little too often, a little too late. he makes fun of your variable names. you wear his hoodie during all-nighters. and no one says it out loud, but maybe friends who suffer through CS together… fall for each other a little, too.

⌗ word count: 1.8k

♥ pt. 2 ♥ masterlist ♥

You thought getting into the computer science major would be the hardest part.

Beating out a 71% application rate had to mean something.

Surviving weed-out courses, crafting a personal statement that didn’t make you sound like every other overachiever who taught their grandparent how to restart a computer— that was supposed to be your final boss.

Wrong.

Apparently, the game’s just beginning.

Because it’s Week 1 and there’s already a test. Not even a quiz, a full-blown exam worth 15% of your grade.

Not a quiz. A test. The syllabus had said something vague about "assessment checkpoints," but you hadn't realized they'd be checking if you were built for this within the first five days of class.

The professor just breezes through the rest of the syllabus like it’s Terms and Conditions, casually mentioning that attendance points will also be cumulative and mandatory.

Like it was a fun little bonus. Like it wasn’t about to completely derail your mental health.

You are, in every definition of the word, cooked.

Especially since you, in your infinite optimism, decided to skip linear algebra and now he’s name-dropping matrix multiplication like you’re all old friends.

Which, sure, is a prereq— but you thought you could squeeze it in next quarter. Because you thought, “How bad could it be?”

So now you're here, sitting in the second row with your laptop open, staring blankly at the slides you’ve written meticulous notes about, trying to decode phrases like "eigenvector interpretation" while suppressing the urge to scream.

Long story short: you’re fucked.

But you can’t drop. Not when you clawed your way in. Not when you’ve already fantasized about the stupid little LinkedIn post you'll write when you graduate.

You wanted this. This major, this future— you chose it. So now you get to suffer for it.

So instead of clicking “Unenroll,” you find yourself at the campus convenience store at 12:03AM, hoping a Celsius will give you the will to survive reviewing the sheer number of questions you got wrong on that first quiz.

You don’t expect anyone else to be there this late, except maybe the sad grad students.

But while you’re squinting at the flavors, someone rounds the corner of the aisle. There’s the low rumble of skateboard wheels and the crinkle of plastic as he picks up a Red Bull. He’s tall, broad-shouldered, wearing a worn black hoodie and plaid pajama pants like it’s a uniform. And he's—

He’s cute.

Boyish, really. His hair’s a little messy, his under-eye bags dramatic and kind of adorable, and you can’t help but admire how youthful he looks for someone also up past midnight.

You’re not in the mood to crush, not when you’re running on 3 hours of sleep and academic shame, but… God. His eye bags are really cute.

You try not to stare.

You also try not to fall asleep standing up, but your body is fighting you on all fronts. When you move toward the counter to check out, your foot catches on the edge of the aisle carpet.

You stumble forward.

And suddenly, someone’s hand is on your elbow— steady, warm. Holding you up.

You meet his gaze, honey brown eyes, amused and warm.

"Be careful, yeah?"

You mumble a thanks and practically flee to the self-checkout, embarrassed beyond belief. You don’t look back.

The next day, you drag yourself to your professor’s office hours. You’re so tired your vision blurs a little. You’d spent the whole night trying to understand where you went wrong— how you could have possibly missed that many questions on the quiz.

You’re five minutes early. The office is quiet except for the hum of a desk fan. There’s someone already there.

You freeze.

It’s him.

Red Bull guy. Skateboard guy. “Be careful” guy.

He’s sitting across from the professor, leaning over the desk with a notebook open and pen in hand, looking deeply focused. His hoodie’s different today, but just as lived-in.

How the hell did you not notice him in class?

You convince yourself he must be from a different section. You would’ve noticed someone like that, right? The bone structure? You definitely would’ve noticed.

You also assume he’s a TA or grader or something. He just looks so comfortable in here, like he knows what he’s doing. Probably here to help debug someone's recursion disaster.

Until—

“I just don’t get how I got the lowest score,” he mutters, rubbing the back of his neck. “Like, I thought I did alright, but when I checked Canvas it said 35 out of 100. That’s... beyond terrible.”

Your jaw drops.

Thirty-five?

You’re not even sure if that’s comforting or depressing, and nearly choke on your own breath.

You’re not sure if you want to laugh or cry.

On one hand: thank��God you’re not the only one struggling. On the other: there’s someone who actually did worse than you

You take a hesitant seat next to him. His gaze flicks toward you.

It takes a second, but he recognizes you too. “Yo,” he says, like you didn’t almost faceplant in front of him nine hours ago.

You blink. “Hi.”

And just like that, you’re no longer alone in your academic downfall.

Because after office hours, just as you’re packing up your laptop with a sense of mild defeat, Ino clears his throat beside you.

“You wanna come study with my tutor?” he asks, eyes hopeful but tired. “Nanami. Took the class last year, has a file of all the assignments. And he interned for Riot Games over the summer, so he actually knows his shit.”

You blink, surprised. “You have a tutor?”

He shrugs, the corner of his mouth twitching in a sheepish grin. “I mean… tutor might be a strong word. More like a friend who’s already survived this mess and doesn’t mind explaining it to the rest of us.”

You hesitate for a moment, but honestly, you really need help, and the idea of learning from someone who’s already been through this feels like a lifeline.

“Okay,” you say, finally giving in. “I’ll come. Riot intern, huh? That’s pretty cool— you actually know someone like that?”

“Yeah, we used to skate together all the time when we were younger. Then we both ended up interning at Riot. He did backend dev, and I was doing data science for Valorant.”

He shrugs, flicking a loose strand of hair behind his ear. “Not that I play PC anymore— too busy trying not to fail this class, honestly.”

His grin turns sheepish but still has that effortless cool that makes you smile back without even trying.

You step out together into the crisp evening air. The campus is quiet, lights flickering on the pavement as students scurry past or lounge on benches, headphones on, notebooks out.

He doesn’t rush like you expect. Instead, Ino slows his pace to match your tired steps. You notice he’s watching you carefully, adjusting his stride so you don’t have to sprint just to keep up.

The gesture is small but feels... considerate. Like he’s already looking out for you, even though you barely know each other.

The walk to the undergrad library takes about ten minutes. Ino casually talks about how he’s been skating since middle school and how he prefers skating at night because the cool breeze helps him relax. When you mention you’ve never learned to skateboard, he laughs and teases that you’d probably be the type to rent a Lime scooter instead.

The library’s glass doors slide open smoothly. Inside, the quiet hum of fluorescent lights and the soft tapping of keyboards greet you. It’s comforting, familiar.

You both find a table tucked in a corner, away from the main clusters of students.

“Here’s the plan,” Ino says, pulling out his laptop. “We wait for Nanami to finish his lecture downstairs, and in the meantime, we try to finish as much of the homework as we can before he gets here to review it.”

You nod, setting up your laptop. You try to start on the first problem, the one about recursion, but your brain immediately threatens to shut down.

Ino leans over your screen, pointing at your code. “You named that variable ‘ballerinaCappuccina’? Dude, what?”

You laugh despite yourself. “More memorable than ‘x’ or ‘temp’, okay?”

He snickers, shaking his head. “You're so brainrot.”

Time slips by as you swap dumb jokes and lament the professor’s cryptic hints. You find yourself relaxing, your earlier dread melting into something softer.

Then the door opens again, and Nanami steps in.

He moves with an easy confidence, glasses sliding down his nose, hair a little tousled but neat. His tee sports a pixelated game logo you recognize, and he’s carrying a backpack that looks surprisingly clean for a CS major.

You glance up, surprised by how different he is from Ino.

If Ino’s energy was all skater-boy charm and casual cool, Nanami's would be hot, slightly nerdy, and intensely focused— like someone who clearly spent all night grinding out code but still somehow looks handsomely tired in the morning.

You catch your breath for a moment.

Cute, you think. Definitely cute.

Ino waves him over. “Yo, Nanami! This is my study buddy— also failing this class with me.”

Nanami gives a small smile as he slides into the seat next to Ino. “Ino, try not to embarrass yourself. It’s not that hopeless— yet.”

With a calm confidence, he starts breaking down the first week's concepts— functions, APIs, database calls— with a precision and clarity that almost makes you think you could pass this class if you had him as your professor.

You and Ino trade notes, nodding along, asking questions, laughing when Nanami mocks the actual professor’s habit of using vague buzzwords.

Between explanations, Nanami looks at you briefly and says, “You’re doing better than most first-timers. Keep at it.”

You feel a warmth spread through your chest.

Hours pass, the late-night study session stretching into the early morning. The three of you share snacks from Ino’s backpack— a sad assortment of Takis, a couple of peach ring gummies, and a can of Red Bull you suspect was bought last night at the convenience store.

You realize, with a little startle, that this is the first time you’ve felt truly at ease since the quarter began.

The three of you fall into a rhythm— Ino’s lighthearted jokes, Nanami's steady patience, and your stubborn determination.

The future still looks impossible.

But for now, with these two by your side, it feels a little less like you’re totally cooked.

[stromblessed]

pretty much all analysis naming Mel any kind of "flawed" character, villain, or as problematic in any way, is terrible analysis. which is a phenomenon that goes against all my instincts but it is so real all the energy and interest I possess leaves my body every time

the thing is, Mel is a hero, Mel's intentions in season 1 are not as pure as the driven snow, Mel benefited from class divide pre-canon and during canon, yet Mel would have benefited from war and colonialism pre-canon only for her to reject it, she is both noticeably "nice" to all the protagonists in season 2 and removed from most of the plot, she is so many things because of her story and because of her writers and (unfortunately) because of the fandom -

and these "nuanced" analyses of her flaws and negative impact on the narrative are worthless

i can't even explain it. i get one sentence in and it immediately sucks. doesn't matter how true or technically correct the words are. i would rather read my linear algebra textbook and make a fandom for eigenvectors than engage with any level of Mel "criticism" no matter how mild. it could be one sentence in an otherwise long and carefully thought-out essay and i will quit that thing faster than my anxiety medication makes me fall asleep

the fandom or the writers can call Mel a manipulator, a liar, a capitalist, a billionaire, a seductress, "benefiting from zaun just like all the privileged characters", "kind of mean that one time, she should've been more polite" - whatever anyone can dream up - as many times as they want, and it won't be anything the entire fandom hasn't seen approximately 1,000 times since 2021. and it won't be anything every person who consumes any kind of media hasn't seen approximately 10,000 times since we each took our first breath in this world - when that media has women in it

why push this same analysis over and over again. what do you get out of this. does it make everybody feel smart to point out the obvious without bothering to go even one level deeper. do you think it makes her character more interesting to equate well-recognized surface-level negative tropes with negative morality, even when all of those tropes are either actively subverted or massively outweighed by her true role in the story? (it doesn't.) no amount of pointing at and highlighting and underlining Mel's morality or lack thereof will make her any less of an interesting character worth loving and engaging with, and she is probably the most interesting character in the entire show even considering season 2. it won't make the other characters around her "better" by comparison either. nor will it make competing ships more compelling or more justified

[clementine-kesh]

if i was a scifi tv writer i’d take so much joy in taking real scientific terms that already kind of sound like technobabble and using them in ways that are total nonsense. i’d be writing shit like we need to transpose the eigenvector of the latin hypercube. then nerds on the internet would get mad about it and it would be funny

[intervex]

Term proposal: gender sodality

As is, we have terms like:

Intergender: when your gender is connected, linked, or influenced by being intersex

Neurogender: when your gender is connected, linked, or influenced by being neurodivergent

Somatogender: when your gender is connected, linked or influenced by having a somatic disability

Indigender: when your gender is connected, linked, or influenced to being part of an Indigenous culture

These aren't gender modalities. While sometimes they get used as gender identities, they often aren't: they're descriptors of the influence(s) on one's gender identity.

I'd like to propose that we call them gender sodalities. 🎉

The word "sodality" is used in theology and anthropology as a contrast to "modality". It comes from Latin sodalis ("companion") and is used to refer to non-kin groups organized a shared purpose or affiliation. I like it here because these gender terms indicate that one's gender is in conjunction with being part of a community.

Right now these gender terms tend to get grouped under exclusive genders, and they are exclusive, but I want a way to talk about the the influence descriptors that doesn't apply to the exclusive gender identities and/or exclusive gender modalities.

I considered calling them "gender influences" but that word pair gets used a lot to refer to things like how one's gender influences what occupation you pursue and stuff. Also: "gender identity", "gender modality", and "gender quality" all end in -ity and so I wanted to keep the trend going. @GoingRampant helped brainstorm ideas for terms with me and helped pick "sodality" out of the options.

Gender sodalities can be combined: for example, one who feels like their gender is a function of being both intersex and autistic could then say their gender sodality is interautigender.

I'm also going to coin two non-exclusive gender sodality terms:

1. Coenogender for when one has a sense of gender that feels connected, linked, or influenced by being part of the common hegemonic zeitgeist of Global North / Western society. Coeno- is used in scientific terminology to denote something is common or general. Does *not* mean the individual approves of Global North binarism! One can be influenced by something and also feel like it is a negative/restrictive influence! (Coeno- is usually pronounced /si:no/ in English, like see-no. It comes from Greek, and in Greek it's pronounced closer to kee-no. I personally consider both correct.)

2. Eigengender for when one has a sense of gender that feels inherent to one's self and unrelated to their intersex status, disability status, culture, etc. So one is not intergender, not neurogender, not somatogender, not indigender, nor coenogender. Eigen- in reference to the prefix used math: an eigenvector is one which is unchanged under transformation. It comes from German, meaning "one's own", characteristic of a given individual. Pronounced /ˈaɪ̯ɡən/ (like eye-gun - sound recording here)

Note: I am intergender, and do not identify as eigengender, though I do feel at least partly coenogender. Eigengender is coined in response to an anonymous ask for a term more general than extergender (not-intergender). Coenogender is coined as an option for those who feel none of the above and/or the "default" sodality.

Note for Americans: the spelling of coeno- with the o is intentional. This is because a different scientific prefix, caeno- (new/recent) gets Americanized as ceno- (e.g. Cenozoic). The two prefixes have different etymologies. It's standard to spell coeno- with the o to avoid confusion, including in the US.

Tagging for archival: @liom-archive @radiomogai @themogaidragon

[misspepeshi]

Get to Know You/Catch Up Tag ✨

Thank you for the tag, @edmunderson! 💛

📖 Currently reading: Daredevil: To Heaven Through Hell, and Heaven Official’s Blessing!

🎶 Last song I listened to: She Is Beautiful by Andrew W.K. I’ve been listening to this song a little bit too much! 🥲

📺 Last series: Outer Range. I have to take breaks with this one. The episodes always leave my brain overwhelmed.

🎞️ Last movie: McFarland, USA.

📺 Currently watching: My Deer Friend Nokotan and The Master of Diabolism. I love, LOVE, Nokotan. 🦌

🍱 Sweet/Savoury/Spicy: 50% sweet, 50% savoury. ¿? Unfortunately I have IBS and cannot tolerate well sugary and/or spicy food anymore.

❤️ Relationship status: In a relationship with Mister Pepeshi, who isn’t Pepeshi-sized at all. 😆

🖌️ Favorite color: I’ve always pondered on this. What color does truly define me? Black, Purple, and Royal Blue. ¿?

🫡 Current obsession: Chicken sandwiches with no pickles……… and wanting to make a Caribbean, sun-kissed, green or turquoise-eyed, light/dark brown hair sim. With nice legs and booty. A tropical-esque occult. ¿? Second one will have to wait.

🫖 Tea or Coffee: Chocolate milk! 🤠

❔Last thing I Googled: What Linear Algebra is used for within your career path. 🫠 Lovely, lovely eigenvectors, eigenvalues, matrices……… *brain combusts*.

Tagging: @aching-joints, @bloody-soda, @herzblau, @itawdoris, @kagumiya, @strangegrapefruit. 🌼

As always, you don’t have to do it if you don’t want to!