#adjacency matrix number of paths

[ryunumber]

Does Keanu Reeves have a ryu number?

Keanu Reeves has a (Standard) Ryu Number of 3/4/does not have a Ryu Number.

(CORRECTION: Per @kchasm, Keanu Reeves has a much less ambiguous path to 3. See here.)

(old image and clarification below)

Right off the bat: Reeves's only appearance as himself in anything even video game-adjacent is the Unreal 5 tech demo/Matrix Resurrection advertisement. If that's a non-starter for you, then Keanu Reeves does not have a Ryu Number and we're done here. Have a nice day.

If you're still around, Reeves shows up in the intro to talk the talk and walk around in-engine recreations of Matrix scenes, like the bullet dodging scene.

One of those is when Morpheus talks to Thomas Anderson for the first time in the Construct.

I'm assuming that's a still digital recreation of Laurence Fishburne as Morpheus, which is a bit clearer when you see it in action. Whether or not you count this is a valid Morpheus appearance determines which route applies above. It's unmistakably meant to be Morpheus, but there's also the matter of it maybe being textually a digital recreation of Morpheus, and as to how that interacts with both the original context of the scene, the new context it's been transplanted into, and the conceit of The Matrix as a whole is... not something I'm particularly interested in adjudicating. So, you know, take your pick.

Also complicating matters: the demo was pulled roughly seven months after release. Whether or not this disqualifies the above as a Standard Ryu Number is largely dependent on whether or not it was always intended to be pulled at a later date, and from what articles I can glean around release time, I don't think this was the case? And anyone who claimed the demo is able to redownload it at any time, so in theory if you really wanted to get your hands on the demo, it's very well possible to do so.

There's probably something apt about defined boundaries, so to speak, breaking down when something Matrix-related is brought up. I dunno.

[jeremy-ken-anderson]

An adjacency list in a graph is a series of numbers that tells you how many nodes are adjacent to each node. So if you imagine a 3x3 square of rooms that all connect with a door in the center of each wall, the corner rooms would have a value of 2 (the side rooms adjacent to them), the side rooms would have a value of 3 (the adjacent corner rooms and the center), and the center would have a value of 4 (being adjacent to all 4 side rooms).

An adjacency matrix for a graph is possibly more confusing, depending on how your brain works, but defaults to containing more info and has faster lookups in terms of computer processing. It would represent those 9 rooms as a 9x9 grid and mark each door you could go out of as a 1 instead of a 0. So

becomes

And you can see it's symmetrical (split down the line of Xs), because you can go through a door either direction. If these were streets in a city and the street going from intersection E to F was a one-way street, the E,F would be a 1 but the F,E would be a 0.

To get a 2-hop option - everything available in 2 jumps from each point, allowing for overlap - you do slightly different things depending on whether List or Matrix is your representation.

For a List, you have a nested for loop, grabbing the set of adjacent options in the outer loop, and asking for them to spit out a list of their adjacent options in the inner loop. Imagine a 4-square of rooms

J Q K A

the outer loop would say, What's adjacent to J? Q- What's adjacent to Q? J and A are adjacent to Q K- What's adjacent to K? J and A are adjacent to K What's adjacent to Q? J- What's adjacent to J? Q and K are adjacent to J A- What's adjacent to A? Q and K are adjacent to A and so on. So the 2-hop for J ends up with J,A,J,A, for Q it's Q,K,Q,K, for K it's Q,K,Q,K, and for A it's J,A,J,A.

For matrices you do Matrix Multiplication. For square matrices of the same size (which works perfectly for us because we're trying to square the matrix in the first place) you take the row and column that meet at each point in the matrix and multiply across. If you were squaring a matrix

your new A would be A*A + B*D + C*G. Your new B would be A*B + B*E + C*H.

So the square of

For A,A it's a,a(0)*a,a(0) + b,a(1)*a,b(1) ... + i,a(0)*a,i(0) = 2 For B,A it's a,a(0)*b,a(1) + b,a(1)*b,b(1) ... + i,b(0)*b,i(0) = 0

And this makes sense. Remember, this is representing how many paths there are to go from one space to another in exactly 2 jumps. A,A means "how many paths go from A back to A in 2 steps." You can see there are 2: A -> B -> A and A -> D -> A. There's no way to actually take 2 steps starting from B and get to A. Using this logic we can guess by looking at the "map" that B,H would give us a value of 1, because there's only one way to get from B to H in 2 hops.

If we do the same cross-section trick to multiply it out, we have 1*0 + 0*0 + 1*0 + 0*0 + 1*1 + 0*0 + 0*1 + 0*0 + 0*1 and sure enough, we have just one spot where the numbers match up.

[leetcode1]

LEETCODE PROBLEMS 1-100 . C++ SOLUTIONS

Arrays and Two Pointers   1. Two Sum – Use hashmap to find complement in one pass.   26. Remove Duplicates from Sorted Array – Use two pointers to overwrite duplicates.   27. Remove Element – Shift non-target values to front with a write pointer.   80. Remove Duplicates II – Like #26 but allow at most two duplicates.   88. Merge Sorted Array – Merge in-place from the end using two pointers.   283. Move Zeroes – Shift non-zero values forward; fill the rest with zeros.

Sliding Window   3. Longest Substring Without Repeating Characters – Use hashmap and sliding window.   76. Minimum Window Substring – Track char frequency with two maps and a moving window.

Binary Search and Sorted Arrays   33. Search in Rotated Sorted Array – Modified binary search with pivot logic.   34. Find First and Last Position of Element – Binary search for left and right bounds.   35. Search Insert Position – Standard binary search for target or insertion point.   74. Search a 2D Matrix – Binary search treating matrix as a flat array.   81. Search in Rotated Sorted Array II – Extend #33 to handle duplicates.

Subarray Sums and Prefix Logic   53. Maximum Subarray – Kadane’s algorithm to track max current sum.   121. Best Time to Buy and Sell Stock – Track min price and update max profit.

Linked Lists   2. Add Two Numbers – Traverse two lists and simulate digit-by-digit addition.   19. Remove N-th Node From End – Use two pointers with a gap of n.   21. Merge Two Sorted Lists – Recursively or iteratively merge nodes.   23. Merge k Sorted Lists – Use min heap or divide-and-conquer merges.   24. Swap Nodes in Pairs – Recursively swap adjacent nodes.   25. Reverse Nodes in k-Group – Reverse sublists of size k using recursion.   61. Rotate List – Use length and modulo to rotate and relink.   82. Remove Duplicates II – Use dummy head and skip duplicates.   83. Remove Duplicates I – Traverse and skip repeated values.   86. Partition List – Create two lists based on x and connect them.

Stack   20. Valid Parentheses – Use stack to match open and close brackets.   84. Largest Rectangle in Histogram – Use monotonic stack to calculate max area.

Binary Trees   94. Binary Tree Inorder Traversal – DFS or use stack for in-order traversal.   98. Validate Binary Search Tree – Check value ranges recursively.   100. Same Tree – Compare values and structure recursively.   101. Symmetric Tree – Recursively compare mirrored subtrees.   102. Binary Tree Level Order Traversal – Use queue for BFS.   103. Binary Tree Zigzag Level Order – Modify BFS to alternate direction.   104. Maximum Depth of Binary Tree – DFS recursion to track max depth.   105. Build Tree from Preorder and Inorder – Recursively divide arrays.   106. Build Tree from Inorder and Postorder – Reverse of #105.   110. Balanced Binary Tree – DFS checking subtree heights, return early if unbalanced.

Backtracking   17. Letter Combinations of Phone Number – Map digits to letters and recurse.   22. Generate Parentheses – Use counts of open and close to generate valid strings.   39. Combination Sum – Use DFS to explore sum paths.   40. Combination Sum II – Sort and skip duplicates during recursion.   46. Permutations – Swap elements and recurse.   47. Permutations II – Like #46 but sort and skip duplicate values.   77. Combinations – DFS to select combinations of size k.   78. Subsets – Backtrack by including or excluding elements.   90. Subsets II – Sort and skip duplicates during subset generation.

Dynamic Programming   70. Climbing Stairs – DP similar to Fibonacci sequence.   198. House Robber – Track max value including or excluding current house.

Math and Bit Manipulation   136. Single Number – XOR all values to isolate the single one.   169. Majority Element – Use Boyer-Moore voting algorithm.

Hashing and Frequency Maps   49. Group Anagrams – Sort characters and group in hashmap.   128. Longest Consecutive Sequence – Use set to expand sequences.   242. Valid Anagram – Count characters using map or array.

Matrix and Miscellaneous   11. Container With Most Water – Two pointers moving inward.   42. Trapping Rain Water – Track left and right max heights with two pointers.   54. Spiral Matrix – Traverse matrix layer by layer.   73. Set Matrix Zeroes – Use first row and column as markers.

This version is 4446 characters long. Let me know if you want any part turned into code templates, tables, or formatted for PDF or Markdown.

[theactsoftheapostles]

"The Schvitz." From the Acts of the Apostles 2: 22-24.

Underneath the flesh and hidden in the coils of the mind is what is called the Self, the secret entity only we can discover, and cannot in any way nor are we required to explain it. Everyone who finds the hidden language of the Self understands how it is custom and also universal all at once; this process of complete awareness of all is called the Pentecost.

To understand as much as possible about this sacramental experience Luke says we have to backtrack to the Supreme Self, a being we call Jeshua. On earth He is called Jesus of Nazareth. We can come to know the Self in All, but this mightiest of beings is their Cause. To know the effect, oneself, one must first know the Cause, the Zara, or "the seat of might."

Notice Luke like yours truly is rolling the Torah forward so it inlcudes the vital data about this Causal Self for the benefit of all who seek the Hem of the Holy Ghost and the Communion of Saints with their fellow man:

22 “Fellow Israelites, listen to this: Jesus of Nazareth was a man accredited by God to you by miracles, wonders and signs, which God did among you through him, as you yourselves know. 

23 This man was handed over to you by God’s deliberate plan and foreknowledge; and you, with the help of wicked men,[d] put him to death by nailing him to the cross. 

24 But God raised him from the dead, freeing him from the agony of death, because it was impossible for death to keep its hold on him. 

The Self as I have said is self-defined. Once the Self is loosed, the matrix from it was made is cast aside. As Luke says at that point, life and death have no more hold over the actions of a person. This is explained below:

The Values in Gematria are:

v. 22: Listen to this. Jesus was a man. The Number is 14102, ידק‎ב‎, "yadak, use the Gemara, thin things out and be accurate."

Jesus did not sin, no not once. We have nothing to lose if we read the Gospels and learn how Jesus said we can overcome sin and achieve Shabbat. A self that sins is not knowable. Who would want to do that?

v. 23: This man was handed over to you. Deliberately follow in His footsteps and impersonate Him in all your ways. The Number is 9908, ט‎ץח‎, tzach, "be fresh, pure, clean, and neat."

v. 24: But God raised Him from the dead and freed Him. As sad as it sounds, Jesus does not fit in with us as individual persons or as a community. As we impersonate Him, what is not of the Self will dissipate leaving the remnant in the flask, the objective of this book called the Acts. All reverence of Jesus is to stop after the remnant is attained and Shabbat is celebrated instead. Just like one must one day walk off the college campus and practice one's trade, one must also plan to leave the Church behind.

The Number is 4715, םזי״ה‎, mezayeta, "from sweat."

The Hebrew term for sweat is schvitz. A schvitz "can afford to sweat."

One undertakes the Torah and the Gospels and does the "backbreaking work" in hopes one day all the sweating one does will be restricted to the moments one is engaged in physical exercise alone. In terms of Gemara this means all self-doubt must be schvitzed out.

The final Gemara is ידק‎ב ט‎ץח‎םזי״ה‎, yedek‎be t‎tzach‎mezayeta‎, "will stick to you through the teachings of the Zeyata, 'the order that is coming."

Jesus was a man, then He was a literary figure, a mechanism God used to explain the Supreme Self to persons who do not know what that means. He has always been a product and a progenitor of the natural order. Whether we think of Him as a man or a Spirit, He can always be found in what is adjacent; what is rooted in reality and inseparable from it.

In other words, Jesus can never be a thing of fiction or fantasy, only exactly as He is. Life here would not work without it. Comprehension of this is the shortest path to the Self. To schvitz away all the nonsense people say about this phenomenon is a great favor one can do for oneself.

The fukchucks think we have to accept this, but all we really have to do is understand it. Acceptance of an immutable thing is silly, there is no need to believe. One does not need to accept the light of the sun or the wetness of water. The natural substance of this Being is the same. All one needs to do is move about and proof of these things appears. Persons that teach acceptance of Jesus are fools. In any case they are not in charge, not of themselves, not of anything.

[fortunatelycoldengineer]

What Does Big O(N^2) Complexity Mean?

It's critical to consider how algorithms function as the size of the input increases while analyzing them. Big O notation is a crucial statistic computer scientists use to categorize algorithms, which indicates the sequence of increase of an algorithm's execution time. O(N^2) algorithms are a significant and popular Big O class, whose execution time climbs quadratically as the amount of the input increases. For big inputs, algorithms with this time complexity are deemed inefficient because doubling the input size will result in a four-fold increase in runtime.

This article will explore what Big O(N^2) means, analyze some examples of quadratic algorithms, and discuss why this complexity can be problematic for large data sets. Understanding algorithmic complexity classes like O(N^2) allows us to characterize the scalability and efficiency of different algorithms for various use cases.

Different Big Oh Notations.

O(1) - Constant Time:

An O(1) algorithm takes the same time to complete regardless of the input size. An excellent example is to retrieve an array element using its index. Looking up a key in a hash table or dictionary is also typically O(1). These operations are very fast, even for large inputs.

O(log N) - Logarithmic Time:

Algorithms with log time complexity are very efficient. For a sorted array, binary search is a classic example of O(log N) because the search space is halved each iteration. Finding an item in a balanced search tree also takes O(log N) time. Logarithmic runtime grows slowly with N.

O(N) - Linear Time:

Linear complexity algorithms iterate through the input at least once. Simple algorithms for sorting, searching unsorted data, or accessing each element of an array take O(N) time. As data sets get larger, linear runtimes may become too slow. But linear is still much better than quadratic or exponential runtimes.

O(N log N) - Log-Linear Time:

This complexity results in inefficient sorting algorithms like merge sort and heap sort. The algorithms split data into smaller chunks, sort each chunk (O(N)) and then merge the results (O(log N)). Well-designed algorithms aimed at efficiency often have log-linear runtime.

O(N^2) - Quadratic Time:

Quadratic algorithms involve nested iterations over data. Simple sorting methods like bubble and insertion sort are O(N^2). Matrix operations like multiplication are also frequently O(N^2). Quadratic growth becomes infeasible for large inputs. More complex algorithms are needed for big data.

O(2^N) - Exponential Time:

Exponential runtimes are not good in algorithms. Adding just one element to the input doubles the processing time. Recursive calculations of Fibonacci numbers are a classic exponential time example. Exponential growth makes these algorithms impractical even for modestly large inputs.

What is Big O(N^2)?

An O(N2) algorithm's runtime grows proportionally to the square of the input size N.

Doubling the input size quadruples the runtime. If it takes 1 second to run on 10 elements, it will take about 4 seconds on 20 elements, 16 seconds on 40 elements, etc.

O(N^2) algorithms involve nested iterations through data. For example, checking every possible pair of elements or operating on a 2D matrix.

Simple sorting algorithms like bubble sort, insertion sort, and selection sort are typically O(N^2). Comparing and swapping adjacent elements leads to nested loops.

Brute force search algorithms are often O(N^2). Checking every subarray or substring for a condition requires nested loops.

Basic matrix operations like multiplication of NxN matrices are O(N^2). Each entry of the product matrix depends on a row and column of the input matrices.

Graph algorithms like Floyd-Warshall for finding the shortest paths between all vertex pairs is O(N^2). Every possible path between vertices is checked.

O(N^2) is fine for small inputs but becomes very slow for large data sets. Algorithms with quadratic complexity cannot scale well.

For large inputs, more efficient algorithms like merge sort O(N log N) and matrix multiplication O(N^2.807) should be preferred over O(N^2) algorithms.

However, O(N^2) may be reasonable for small local data sets where inputs don't grow indefinitely.

If you want more learning on this topic, please read more about the complexity on our website.

[lifeafterthelayoff]

Day 82

My first foray into financial services: job number 19. In June 2011, I found myself on the receiving end of my second layoff. I didn't really formally apply for that job, so my resume was woefully out-of-date. And I hadn't really been in the market for a new role since 2001. Rusty would be an understatement. A consolation: my daughter was three years old, so I looked forward to spending some time with her over the summer. We reduced our 5-day child care arrangement down to three days; we saved money and I still had time to fully dedicate to the job search when she was with her tiny pals and teachers at daycare. I pulled together the resume, added a landing page to the blog, and started applying for roles. I still have that tracking spreadsheet; it bears a pretty close resemblance to the one I'm using today. I landed an interview at one of the major financial services companies in the Twin Cities: Ameriprise Financial. I had a few interviews and a 15-minute presentation slot. On the elevator ride down to the lobby after the interview, I handed the hiring manager (and soon boss-to-be) one of my custom-made business cards, all clever with a slogan and a QR code. This was well before QR codes were cool. It worked. I got the job as the Senior Manager of Digital Content Strategy. This was my first experience in the corporate world, having spent my career thus far at a startup, a non-profit, and then an agency. It was an easier transition than I anticipated. I got to do some standard content strategy work, some user journey development, and a major project revamping the messaging and copy on the home page and the top-level supporting pages. I learned so much along the way about retirement services and financial planning. Gathering domain knowledge along the way like a lint roller is one of the benefits of a varied career path. Choosing the biggest takeaway from this role is easy: I got a crash course in navigating a matrixed organization. From influencing designers in adjacent disciplines to getting approval from SVPs and above. I still think about lessons learned there to this day. After a few years, a friend asked if I would be interested in joining him at an agency. Initially I said no, but later changed course... (The photo shows me taking a self-portrait in the screen of a TV/VCR combo in one of the Ameriprise conference rooms. And yes, that is a regular tie.)

[delves-n-denizens]

Delve: Count's Castle

This is the Castle of a strange Count, very well known and even feared throughout the neighboring regions. The Count is very reserved and rarely seen outside of his domain; some even believe that he is some sort of cultist, possessed by a demon, or even a vampire. Whichever the nature, he is usually blamed for every mishap and horror that plagues the surrounding villages... Although quietly, lest he focus his attention on us, the commoners say in fear.

The Castle has supernatural abilities of its own; Rumors say that it can disappear and reappear in different locations and points in time. Of course, the heavy mist and dangerous tangle woods that surround the palace make these claims hard to prove right or wrong. Most of the times it cannot even be seen through the fog; It's on the rare full moon of a cloudless night that its silhouette appears to rise ominously as a shadow over the cliffside.

Many have ventured into the Castle, through different entrances and areas, and with different objectives. Some went looking for missing wives, others to banish a supposed demon or source of blasphemies. None ever returned.

⛨

Delving into the Castle

The Count's Castle is an Epic Delve. Locating your Objective usually means confronting the Count himself in his throne room, but your heroes might have different reasons to explore his castle. Adjust your objectives accordingly, but keep in mind that if you are looking to face the Count himself, the castle is a maze of Epic proportions.

The Theme and Domain of the Count's Castle vary a lot, depending on the area (the palace's geography is very varied and... odd).

Castle Zones

The different Zones of the Castle (and their recommended Theme/Domain) are:

Lower Zones

Entrance and Gardens: Wild Tanglewood

Alchemy Laboratory and Common Quarters: Corrupted Stronghold

Marble Gallery: Ancient Ruin

Colosseum: Infested Underkeep

Underground Zones

Underground Caverns: Infested Cavern

Abandoned Mine: Haunted Mine

Catacombs: Corrupted Barrow

Upper Zones

Library: Ancient Stronghold

Clock Tower: Haunted Stronghold

Chapel: Hallowed Ruin

Keep and Count's Throne room: Fortified Underkeep

They are roughly interconnected in the order of the list above, but there are many secret passages that you could find that connect one Zone with another (from the same subgroup or an adjacent subgroup). As a rough estimate, assume that each Zone is comprised of at least 5 areas or rooms that you can Delve into.

How to traverse Zones

After traversing 5 areas when you Delve the Depths, or when you Find an Opportunity and obtain a result of 1-25 ("The terrain favors you, or you find a hidden path") after at least having traversed 3 areas, you can envision a passage to a different Zone (in the same Zone subgroup or in an adjacent subgroup). If you do, switch the Delve Theme + Domain to those recommended for the Zone. A result of 99 or 00 in the roll of the Area: Features Oracle table could also be interpreted as a Zone transition.

Alternate Entrances

The main and usual entrance is through the main gates, across the twisted Garden that surrounds the castle. But there are other passages that connect the outer world with the Abandoned Mines and the Underground Caverns zones. A savvy adventurer that Gathers Information might find out about these secret entryways before the Delve.

Denizens of the Castle

The Denizens in the Count's Castle are as varied as the zones and their themes and domains. As a rule of thumb, any creature that fits in the gothic horror or grimdark fantasy genres would feel right at home in the castle. Legendary creatures of mythology like Gorgons, Minotaurs, Cyclops and Hydras also have their place in certain zones of the castle.

Denizen Matrix by zones

Denizen Ranks

For their Rank, the risk increases as you delve deeper: It's as the Castle could feel the intruders and reacted instinctively to eliminate them.

From 0 to 3 Progress boxes: Low Risk - Denizens are Troublesome or Dangerous

From 4 to 7 Progress boxes: Medium Risk - Denizens are Dangerous or Formidable

From 8 to 10 Progress boxes: High Risk - Denizens are Formidable or Extreme

Treasure

The Count collected all sorts of treasure and art throughout his very, very long life. Adventurers would most likely find interesting pieces of equipment and magic items in zones like the Laboratory, the Marble Gallery and the Library.

It's alive!

If you somehow manage to escape from the Castle to return at a later time, don't expect it to be the same or have the same layout as it did the first time. As per Discover a Site, when returning you'll have to clear a number of Progress boxes. "The Count's Castle is unmappable", some rumors say. It's as the Castle's corridors twisted and changed, its halls shifted as if it were a living creature. Maybe it is, in a way.

[dzamie-oc]

6: Hidden

“...so by adjusting the variable theta here in the matrix, you can alter the angle of rotation.”

Ocellus kept her eyes on her note paper, making clean, orderly brackets to house the grids of numbers and trigonometric functions. She flicked her forked tongue, getting a cursory taste of the emotions in the room. The delicious, cool flavor of learning and understanding, soured slightly by a smattering of confusion. A couple spicy motes of frustration, largest from where Smolder sat. The changeling glanced towards the dragon, finding that her friend’s own eyes were darting between the chalkboard, Headmare Starlight, and... her. Pulling herself back from the draw of nibbling on the emotions, Ocellus startled when she realized she had missed two entire equations being written. That they were just the first steps in a practice problem was small comfort to the blue-chitin changeling; who knew what verbal instructions she could have missed, too?

After catching back up in her notes, she chanced another taste, intending to take more of a passive taste, paying more attention to class. However, what she intended was overruled harder Princess Celestia denying Prince Blueblood the last bite of her cake; an intoxicating wave of lust filled her tastebuds, overpowering nearly every other emotion in the room. Reflexively, Ocellus turned towards its source, both surprised and suddenly hungry - although she hated to admit it. Not only was it filling yet almost nutritionally useless, the taste and her reaction recalled memories in her from before the Great Reformation, when she had been drawn towards and fed on such strong love-adjacent emotions.

Nonetheless, she found herself staring at her dragon friend, who was now staring entirely at her. A light blush crept onto her cheeks as she considered the implications: her unsubtle, willful dragon friend was focused wholly on her, and thinking incredibly lewd thoughts at her. Her thoughts were once more diverted when the lust suddenly cut off, replaced by a more platonic desire. In the back of her mind, she acknowledged that Headmare Starlight was going over the answer to the problem on the board, almost unconsciously copying down the correct answer for later comparison; at present, though, she noticed Smolder repeatedly moving her hand. Thumb and fingers together, save for an extended pinky, rocking back towards the dragoness twice. Pause, hand still in position, and another two rocks. It was a sign the two of them had worked out - miming the high-society griffon etiquette for holding a teacup.

Ocellus smiled and nodded ever so slightly, then waited until Smolder smiled back, put her hand down, and turned back to the front of the class before doing the same herself. She mentally kicked herself for dropping her attention from class, but reassured herself that friends were important, as well. After all, the School of Friendship has “friendship” right in its name... as well as school, so she resolved to stay focused on the lesson until after class. Her pencil once more found the paper when the headmare moved onto three-dimensional transformation matrices, and her tail subconsciously began to sway back and forth as she drank in the learning - almost literally, as an emotivore!

After class, Ocellus met up with the dragon, who was leaning against the wall outside of the classroom. “Was that... necessary?” she asked, her blush returning with the memory of the wave of lust, “I mean, you could have asked me after class; I tend to linger the longest to speak with our professors.”

Smolder smirked. “No, but I wanted to make sure you wouldn’t stay for an hour or two after Starlight Glimmer dismissed us and take up all the time we could’ve used. Seeing your reaction was just a bonus. So, same place as before?”

Ocellus nodded, starting to walk with her friend. “That works. I’ll drop off my stuff back in our room first, and then we can head out.”

“Sounds good. I’ll tag along; I’ve gotta grab a-” the dragoness cut herself off, looking around at the ponies and creatures around, “a... a thing. My thing.”

Back in their room, the two students swapped out their schoolbooks for a small selection of carefully-folded dresses. Ocellus levitated a tube of lipstick into Smolder’s bag for her, and added a bottle of hoof polish and a compact of blush to her own. Loaded up with their secret payload of fancy fittings, the two girls strode out of their room, sharing fanged smiles.

They made it to the main hall before somecreature noticed and approached them. Silverstream, with her distinctly bubbly step, strode up to the pair. Ocellus flicked out her tongue and got back a hefty dose of curiosity from the hippogriff, fighting against that spicy taste of frustration (and the faintest hint of shame) from the dragon beside her.

“Hi Celly, Smolder! Are you two heading out?”

The changeling nodded. “Yep. Just the two of us.”

“Ooh, girl’s night! Or, girl’s afternoon. Whatcha gonna do?” Her bright, innocent smile was infectious, and Ocellus found her own lips curling up. She stayed silent, however, unwilling to tell her friend where she was going with the dragon.

Fortunately for her, Smolder had had years of hiding her secret interest. Unfortunately for her, Smolder was Smolder. “We’re going to set a new record for longest two-creature lesbian makeout session. Do you want to come?”

The sarcasm flew straight over the hippogriff’s head, and her enthusiastic nodding only abated when Smolder’s deadpan expression and admission that she had just been messing with her sunk in. With a promise to have a good time given, the pair strode out of the building, before making their way through the meandering, misleading path to a secret spot in the woods.

Ocellus and Smolder walked up to the large, flat stump in the middle of the forest clearing and set about setting up. From Smolder’s pack came a white tablecloth, fringed with lace. From Ocellus’s, a teapot, two saucers, and two teacups. The makeup came out next, and finally, the dresses. Smolder slipped hers on with an ease that came from far more practice than she would ever admit. As for the changeling...

“So, myself or Professor Rarity? She has the accent and mannerisms for it.” Ocellus held two dresses aloft in her teal magic, looking between them.

“Hmm... Probably not Rarity, but...” Smolder’s off-center stance and stroking of her chin were a stark contrast to the frilly, pale pink dress she wore as she thought, “I think, maybe... Oh! Could you do Gallus? I bet he’d look ADORABLE in a dress!”

That drew a grin and a giggle from the changeling. A wave of fire washed over her form, and in the next moment, a pair of yellow eagle claws caught the two floating dresses before they could hit the ground. ‘Gallus’ handed one to Smolder to fold and return to Ocellus’s bag, and the griffon set about fitting into the other one. After a little difficulty, getting stuck twice, and ultimately asking Smolder for help with the wings, ‘Gallus’ was proudly sporting a pale yellow dress. “Well? How do I look?” ‘he’ asked the dragoness.

“Heh. Actually, not bad. The next time we play Truth or Dare with the boys, I think I’ve got a good idea.” Smolder leaned to one side, then the other, taking in the griffon’s form. “But, I think you’re missing something very important.”

The grinning dragon held up a couple of the makeup implements before setting them down. The pair of friends spent some time matching blush to their scales and feathers, picking out the right lipstick - or beakstick, as it were - painting each other’s claws, and otherwise gussying themselves and each other up until they both looked like slightly exaggerated versions of the fanciest fancy bourgeoisie to be found in Canterlot - nay, all of Equestria.

Smolder cleared her throat. “Now then, Madam Gallus, shall we?” she prompted in a Received Equestrian accent, “it would be a terrible shame to come all the way here for some tea, and to then forget the beverage in entirety!”

‘Gallus’ gave a proper curtsey, then stepped up to the stump. ‘He’ picked up the teapot in one hand, held the lid on with the other, and gracefully tipped it over, pouring a cup for Smolder, and then a cup for ‘himself.’ With two steaming cups of tea properly set on their saucers, the well-dressed duo took their seats. ‘Gallus’ added two sugar cubes to the cup in front of ‘him;’ Smolder added only one. Keeping their pinky claws extended, they lifted their cups and politely toasted their friendship. 

Hidden away in the calm, peaceful grove, the disguised changeling and her dragon friend traded light gossip, homework tips, and compliments. Their table manners would put several Canterlot nobles to shame, and over time, the level of tea in the teapot declined. The pair were in the middle of discussing which creature in their friends group had the shapeliest rear when Sandbar wandered into the clearing and promptly did a double-take.

The three of them stared at each other for a minute, before ‘Gallus’ finally spoke up, “we... lost a bet to Ocellus. Why she has these dresses, I haven’t the foggiest, but she’s, uh...” the griffon turned his head to look around, “well, she’s one of these branches around, to make sure we keep the deal.”

Smolder’s look of shock faded as her friend spun the tale. “Yeah, but look. This whole thing? Never happened. You’re gonna leave, and next time we see each other, it’s like we weren’t even here, even if you ask. Right, Gallus?”

‘Gallus’ nodded. “Yeah, you’re actually lucky I’m not denying this right now. Anyway, we’ve got, like, another teacup to finish before this is over. See you back at school.”

Content with their answer, the pony silently nodded and walked back off through the forest. Once they were sure he was out of sight and hearing, both of the well-dressed creatures let out a big sigh of relief. Their secret was safe. And they still had some tea left to talk over.

[codezclub]

C Program to find Path Matrix by powers of Adjacency matrix

Path Matrix by powers of Adjacency Matrix Write a C Program to find Path Matrix by powers of Adjacency Matrix. Here’s simple Program to find Path Matrix by powers of Adjacency Matrix in C Programming Language. Adjacency Matrix:  Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an…

[htvewor]

Matlab 2017 sum every element matrix

#MATLAB 2017 SUM EVERY ELEMENT MATRIX CODE#

Note: If the length of the array is odd then the right half will contain one element more than the left half. Your program should use ~ 2 lg n compares in the worst case. The basic brute force approach to this problem would be generating all the subarrays of the given array, then loop through the generated subarray and calculate the sum and if this sum is equal to the given sum then printing this subarray as it is the part of our solution. so 1 0 1 1 0 0 0 0 0 would give the following matrix: 1 3 0 1 3 1 1 1 0.

#MATLAB 2017 SUM EVERY ELEMENT MATRIX CODE#

I am using that code & to me this is looking fine. Note : You do not need to print anything, it has already been taken care of. im looking for a way to sum all adjacent elements in a matrix with 1s and 0s. Hi every one, I want to make a function that take two dimensional matrix as input and return sum of its diagonal (index for row and col will be same) and element right to this diagonal (sum of upper triangular elements). Given five positive integers, find the minimum and maximum values that can be calculated by summing exactly four of the five integers. reduce and how cool it is, the first and sometimes the only example you find is the sum of numbers. It is used to show the summation of data as it grows with time (updated every time a. Input: grid =, , ] Output: 7 Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum. Explanation: Value of each node is replaced by the sum of all its subtrees and the node itself.The same result is obtained in MATLAB, e.g. However, the result you show with numpy is simly the addition of the scalar to all matrix elements. Given an array of integers arr consisting of N integers, the task is to minimize the sum of the given array by performing at most K operations, where each operation involves reducing an array element arr to floor(arr/2). I looks like you mean that in MATLAB or numpy matrix scalar addition equals addition with the identy matrix times the scalar.To find the sum of the list in Python, use the sum() function.To calculate the sum of elements in each column: Two loops will be used to traverse the array where the outer loop select a column, and the inner loop represents the rows present in the matrix a. Now this task can simply be solved by saying $,0) Steps to Find the Sum of Prime Numbers. First we’ll measure distance from center of the image to every border pixel values. If any element is less than the selected element then swap the values. Read or initialize the lower and upper limit. The second line contains N space-separated. Given an array of N integers, can you find the sum of its elements?.We can still reduce the A in which to search for tuple. Adding an array with the same dimensions adds only the. TCS CodeVita is one of the toughest coding competition throughout the world. Adding a scalar to an array adds the scalar to every element in the array. Your task is to minimize the sum of the final array and print the minimum sum.

[kitwallace]

Finding Eulerian circuits

As discussed previously, Eulerian circuits are useful in 3D printing because they enable continuous extrusion which increases the strength of the printed object . In addition the lack of a seam improves its visual appearance.  

However finding a Eulerian circuit in a design is not always easy, and finding the ‘best’ even harder.

For a rectangular grid  (3 x 2) 

a braiding program I developed a while ago finds a circuit.  It attempts to find a braid on an N x M grid.  If N and M are relatively prime, one rope (ie. a Eulerian circuit) completes the grid  but if not (like this 6 x 3), multiple ropes are needed.

This restriction on the size of this mesh is not helpful.  Since every N x M mesh of this style is Eulerian, they must all have a Eulerian circuit. This could  be constructed if we were able to join up the separate partial loops. Start somewhere and follow a chain of unvisited edges until you get back to the start.  If all edges have been visited, you are done. If not, go back to the last vertex with unvisited edges and start a new circuit at that point, with those points inserted into the current circuit .This is the Hierholzer algorithm.

Hierholzer algorithm

I searched for a pseudo code implementation but wasn’t satisfied with any that I found.  Any implementation depends heavily on the data structures used: for the graph itself in a form in which edges can be removed as they are visited and for the path as it is constructed, adding a vertex to the end and rotating the path to backtrack. 

One representation of a graph with V vertices and E edges is as a V x V adjacency matrix where adj[i,j] =1 indicates the edge i to j which will be symmetric across the diagonal if the graph (as here) is undirected.  Updating is straightforward but  navigating from vertex to vertex requires a scan through a row.  

Alternatively, the graph can be represented as an array of lists of the connected vertices  - easy to navigate, more compact for a sparse graph (as these are)  but harder to update.  

The JavaScript array structure can implement the vertex list and the evolving path. I found this is a useful summary of operators. push() and pop()  will add and remove the head of the list;  unshift() and shift() do the same at the tail of the list.  myArray[myArray.length - 1] and myArray[0] return the head and tail of the list respectively.

Minimizing turns in the circuit

The Hierholzer algorithm mechanically selects the next vertex by taking any vertex (the first or the last perhaps) from the list of possible vertices. This does find a circuit but not necessarily a good circuit.  For the purposes of 3D printing, good means a circuit with a minimum number of turns since straight runs will be stronger and faster.  To get a good, though not necessarily the best, circuit, I added a kind code to each edge and then choose a vertex in the same kind if possible.  For the rectangular mesh above, there are two kinds , coded +1 for the right diagonal, -1 for the left.  (note that we don’t need to distinguish between the direction of travel on a diagonal since we can’t reverse direction at a vertex as that edge has just been traversed)

JavaScript Implementation

In the Fottery suite, the algorithm is implemented as a method in a Graph class which includes the adjacency structure adj and supporting functions:

find_circuit(kind-0,start_vertex = 0 ) {    // assumes graph is connected and a euler circuit exists         var cpath =[];        var vertex, next_vertex, edge, edges;        cpath.push(start_vertex);        while (cpath.length < this.n_edges  ) {            vertex = cpath[cpath.length - 1];  // the last vertex in the constructed path            edges = this.adj[vertex];  // get its  adjacent nodes (untraversed edges)            if (edges.length == 0) {  // if no untraversed edges                cpath.pop();   // rotate back to the previous vertex                if (!(vertex == initial_vertex && cpath[0]==vertex)) { // dont  include the start at the end                  cpath.unshift(vertex);                 }            } else {                  edge = this.best_edge(edges,kind);                  next_vertex= edge[0];                kind = edge[1];                cpath.push(next_vertex);  // add  vertex to the path                this.remove_edge(vertex,next_vertex); // remove the traversed edge            }         }

       // get start back to the first in the path        while (cpath[0] != start_vertex)                  cpath.push(cpath.shift());        return cpath;

[damn discovered a use-case where this implementation fails!   

16 April 2024 - fixed edge case with the bold change ] 

Example

A  rectangular N x M  mesh like the one above is more useful if the vertices at the edges are connected to make a border.  This addition does not change the Eulerian nature of the graph, but introduces two more directions, horizonal and vertical.  This is the resultant 2 x 3 mesh.

and this a box constructed from rectangular meshes.  The sides are bevelled by insetting the top layer from the bottom by the thickness of the tile to make a 45 degree bevel.  Assembled with plastic glue (UHU).

Stars (stellated polygons)

This algorithm has been applied to other structures such as a triangular mesh and stars.   

A pentagram can be constructed with 5 vertices and 5 edges connecting pairs of vertices.This is a closed path so Eulerian.

A hexagram looks Eulerian, but if constructed by connecting the vertices of the star, the graph is not connected (two separate triangular paths).

To make a circuit so it can be printed continuously, we have to compute the 6 intersections and the 18 edges (of 3 kinds)  which result from the intersections, and then use the modified Hierholzer algorithm to find a good circuit.  

A fully connected star is only Eulerian if the number of vertices is odd - which makes for a kind of infill pattern.

Nearly Eulerian graphs

Structures which are Eulerian are rather limited. An hexagonal tiling is not Eulerian because vertices are order 3. However it and many others are nearly Eulerian in the sense that small modifications to the graph will make the graph Eulerian. The basic idea is to duplicate ( the minimum number of ) edges. If this is a problem with printing, the edge could be omitted or an additional edge inserted.

This problem  is called the Chinese Postman Problem or Route Inspection Problem and the subject of extensive research. 

This is work for another day -.April 2024 see Non-Eulerian graphs

References

Fleischner, Herbert (1991), "X.1 Algorithms for Eulerian Trails”   https://archive.org/details/euleriangraphsre0001flei/page/

Gregory Dreifus,Kyle Goodrick,Scott Giles,Milan Patel Path Optimization Along Lattices in Additive Manufacturing Using the Chinese Postman Problem June 2017  https://www.researchgate.net/publication/317701126_Path_Optimization_Along_Lattices_in_Additive_Manufacturing_Using_the_Chinese_Postman_Problem

Prashant Gupta, Bala Krishnamoorthy, Gregory Dreifus  Continuous Toolpath Planning in a Graphical Framework for Sparse Infill Additive Manufacturing  April 2021 https://arxiv.org/pdf/1908.07452.pdf

https://algorithms.discrete.ma.tum.de/graph-algorithms/directed-chinese-postman/index_en.html

https://www.stem.org.uk/resources/elibrary/resource/31128/chinese-postman-problems

https://ibmathsresources.com/2014/11/28/the-chinese-postman-problem/

http://www.suffolkmaths.co.uk/pages/Maths%20Projects/Projects/Topology%20and%20Graph%20Theory/Chinese%20Postman%20Problem.pdf

[jeremy-ken-anderson]

A matrix representation of a graph of a square with doors going from 1-2 and back, 2-3 and back, 3-4 and back, and 4-1 and back, would look like this 0101 1010 0101 1010 Each node has a total degree of 4. In spite of using a door as an analogy the "degree" counts the fact that there's a path out to and in from those adjacent rooms. Looking at the matrix you can get the same result by adding up the number of 1s in the matching row and column. In row 3 there are two 1s, indicating the means to go out to rooms 2 and 4. In column 3 there are two 1s, indicating the ability to come in from rooms 2 and 4.

Now imagine the same square but it's all 1-way streets. You can only go from 1-2, from 2-3, from 3-4, and from 4-1. It looks like so: 0100 0010 0001 1000 You can see that the matrix still shows the correct information. Row 1 column 2 has a 1 in it, so you can go from 1 to 2. Row 4 column 1 has a 1 in it, so you can go from 4 to 1. And between row 1 and column 1 you have a total of two 1s, so the first node has a degree of two.

The adjacency list representation of the "doorways" is like this:

1 - (2,4) 2 - (1,3) 3 - (2,4) 4 - (1,3)

The list representation is nice when you've got big areas described, because you may have noticed that even with just a square there's a lot of needless 0s telling you "there's not a line between these two points going this direction." With the list you only bother to say something exists when it's something existing.

[dreamipie]

10/01/21

Imagine a grid of hexagon. Each one has a dome overtop to keep the atmosphere in, above us was pure open space, stars abound. In the domes was terrain, lakes and trees and gardens. Paths leading from one dome to the next. I don’t remember how it started, but the earliest memory from the dream, I’m coming back with one of the giant robots from scouting. (they resembled transformers but none of them were real-life transformers except the dead and rusty ones that littered the domes) we come back and one of the human members of the expedition is dead, we had just found his medication in a building and we were rushing back to give it to him. There was a giant mud pit by the lake that we were told he dug himself in anticipation that we wouldn’t make it back in time. The other human members said they didn’t want to bury him there because his corpse would get water logged and that we should bury him on the edge of the dome connecting to a university that he went to. We were patrolling the border of the dome looking for a good stop when some stumbled upon the corpse of megatron and accidentally set off a missile he had set up that fired off and destroyed the still standing corpses of bumblebee and arcee (the only female transformer in the og cartoon). We moved to another dome and one of the twin girls wasted some of our saved up money on an app for her phone but it was too late to refund it and I realized as the head of the group it would keep her morale up as well as not really having much use for our money except for the vending machines we occasionally ran into. Then I woke up.

A lot to unpack, so first off. The hexagon grid (or the cybertron matrix) represents the number six repeating, an esoteric number that ties into my research into sacred geometry, specifically it represents half of the sacred number 12. Half of the whole. Just as the team I’m with splits in two to scout and set up base camp respectfully. Although this number is 3 and 3, dropping down to a total of five as we move together again below the number 6. We encountered a total of 3 dead transformers, one decepticon and two autobots. So the number three comes up again. There are three domes we move through in my dream, the one I scouted out, the one base camp is at and the one containing the university. There are two transformers and four humans, though in the end there are three humans. So there are three sets of the number three in this dream by the end, all based around a hexagonal grid of infinitely repeating sixes. Moving on to the actual component parts of this dream and away from the sacred numbers… the transformers. Alien being he represent the change from one state to another, though none of them actually transform in the dream and all remain as human form. This represents a stagnation, as they are no longer flowing freely from one form to the next. The twins represent two sides of one whole, one that conserves and one that wastes. The conscious and the unconscious. The man that died had dug his own grave, symbolizing a tendency towards morbid thought, something shared with the rusted out and broken dead transformers we could see both the three within our bubble and the many in adjacent bubbles. Morbid statues of death. The missile firing off was a trap set centuries ago, representing a fear of the distant past. The university representing the future.

TL;DR: this dream represents anxieties about how the distant past will affect the far future, how my brain is split in two and how little control of the subconscious I have at this moment. 3s and 6s representing Allah and perfection in various orders of organization, and how ultimately I’m just a child playing in Allah’s playground, surrounded by death and stagnation, trying to find a way to transform into the next stage of existence.

[holytheoristtastemaker]

Have you ever solved a real-life maze? The approach that most of us take while solving a maze is that we follow a path until we reach a dead end, and then backtrack and retrace our steps to find another possible path. This is exactly the analogy of Depth First Search (DFS). It's a popular graph traversal algorithm that starts at the root node, and travels as far as it can down a given branch, then backtracks until it finds another unexplored path to explore. This approach is continued until all the nodes of the graph have been visited. In today’s tutorial, we are going to discover a DFS pattern that will be used to solve some of the important tree and graph questions for your next Tech Giant Interview! We will solve some Medium and Hard Leetcode problems using the same common technique. So, let’s get started, shall we?

Implementation

Since DFS has a recursive nature, it can be implemented using a stack. DFS Magic Spell:

Push a node to the stack

Pop the node

Retrieve unvisited neighbors of the removed node, push them to stack

Repeat steps 1, 2, and 3 as long as the stack is not empty

Graph Traversals

In general, there are 3 basic DFS traversals for binary trees:

Pre Order: Root, Left, Right OR Root, Right, Left

Post Order: Left, Right, Root OR Right, Left, Root

In order: Left, Root, Right OR Right, Root, Left

144.  Binary Tree Preorder Traversal (Difficulty: Medium)

To solve this question all we need to do is simply recall our magic spell. Let's understand the simulation really well since this is the basic template we will be using to solve the rest of the problems.

At first, we push the root node into the stack. While the stack is not empty, we pop it, and push its right and left child into the stack. As we pop the root node, we immediately put it into our result list. Thus, the first element in the result list is the root (hence the name, Pre-order). The next element to be popped from the stack will be the top element of the stack right now: the left child of root node. The process is continued in a similar manner until the whole graph has been traversed and all the node values of the binary tree enter into the resulting list.

145. Binary Tree Postorder Traversal (Difficulty: Hard)

Pre-order traversal is root-left-right, and post-order is right-left-root. This means post order traversal is exactly the reverse of pre-order traversal. So one solution that might come to mind right now is simply reversing the resulting array of pre-order traversal. But think about it – that would cost O(n) time complexity to reverse it. A smarter solution is to copy and paste the exact code of the pre-order traversal, but put the result at the top of the linked list (index 0) at each iteration. It takes constant time to add an element to the head of a linked list. Cool, right?

94. Binary Tree Inorder Traversal (Difficulty: Medium)

Our approach to solve this problem is similar to the previous problems. But here, we will visit everything on the left side of a node, print the node, and then visit everything on the right side of the node.

323. Number of Connected Components in an Undirected Graph (Difficulty: Medium)

Our approach here is to create a variable called ans that stores the number of connected components. First, we will initialize all vertices as unvisited. We will start from a node, and while carrying out DFS on that node (of course, using our magic spell), it will mark all the nodes connected to it as visited. The value of ans will be incremented by 1.

import java.util.ArrayList; import java.util.List; import java.util.Stack; public class NumberOfConnectedComponents { public static void main(String[] args){ int[][] edge = {{0,1}, {1,2},{3,4}}; int n = 5; System.out.println(connectedcount(n, edge)); } public static int connectedcount(int n, int[][] edges) { boolean[] visited = new boolean[n]; List[] adj = new List[n]; for(int i=0; i<adj.length; i++){ adj[i] = new ArrayList<Integer>(); } // create the adjacency list for(int[] e: edges){ int from = e[0]; int to = e[1]; adj[from].add(to); adj[to].add(from); } Stack<Integer> stack = new Stack<>(); int ans = 0; // ans = count of how many times DFS is carried out // this for loop through the entire graph for(int i = 0; i < n; i++){ // if a node is not visited if(!visited[i]){ ans++; //push it in the stack stack.push(i); while(!stack.empty()) { int current = stack.peek(); stack.pop(); //pop the node visited[current] = true; // mark the node as visited List<Integer> list1 = adj[current]; // push the connected components of the current node into stack for (int neighbours:list1) { if (!visited[neighbours]) { stack.push(neighbours); } } } } } return ans; } }

200. Number of Islands (Difficulty: Medium)

This falls under a general category of problems where we have to find the number of connected components, but the details are a bit tweaked. Instinctually, you might think that once we find a “1” we initiate a new component. We do a DFS from that cell in all 4 directions (up, down, right, left) and reach all 1’s connected to that cell. All these 1's connected to each other belong to the same group, and thus, our value of count is incremented by 1. We mark these cells of 1's as visited and move on to count other connected components.

547. Friend Circles (Difficulty: Medium)

This also follows the same concept as finding the number of connected components. In this question, we have an NxN matrix but only N friends in total. Edges are directly given via the cells so we have to traverse a row to get the neighbors for a specific "friend". Notice that here, we use the same stack pattern as our previous problems.

That's all for today! I hope this has helped you understand DFS better and that you have enjoyed the tutorial. Please recommend this post if you think it may be useful for someone else!

[ada-open-new-place]

                        activism | research | intervention

              Park, Kisač local community , Novi Sad, Serbia

                                      September 28 2019

       New Places - DANS (Association of Novi Sad Architects)  

                                       COMPETITION

                                                     X

   "The wider site of the competition is the contact zone along the eastern edge of the park,  the sports complex of the Tatra Football Club. The narrower site, which is the subject of the competition, is the space at the main entrance to the park, east of the walkway leading to the summer stage. Within this space it is necessary to propose the arrangement of a zone for gathering of citizens (sitting), exhibiting of products (in the form of a small market) with the accompanying elements of an urban furniture. The solution should define the greening of the area , the lighting appropriate to the park and proposal of paving, which can also be used as a model matrix for paving other paths in the park. Within the narrower scope of the site, there is a public restroom whose remodeling and moving within this space is advisable." *

* Description of locations for the New Places Competition - 46 urban pockets

  …For the third year in a row, in September 2019, the "Novi Sad 2021" Foundation and the Association of Novi Sad Architects (DANS) are hold the "Nova Mesta (New Places)" , the urban-design call for improvement of small public spaces in the territory of the city of Novi Sad, when Stefan takes part in a series of these competitions for the second time. However, unlike the standard design approach to the competition assignment, this time Stefan is experimenting with both the concept of the competition work and its content, introducing active site involvement into the product of his competition material. Like the action on the bob and sled track on Trebević, a practical approach to the competition is self-initiated as a personal condition for participation in the competition, making AΔA and its members the first ones in this area to act in architecture in this way. Prior to intervening in the park forest perimeter of the Kisač local community, Stefan is playing with the concept, designing an "outdoor social network"...

       CONCEPT

 "Participants emphasize that the mentality of the residents of Kisač is that the locals generally spend time at home - children on social networks, and adults following a television program."

         SOCIAL NETWORK

Forest Park in Kisač Local Community is defined as a gathering place for citizens of all ages. However, at the border between the forest and the landscaped park, this site is "in transition" as an undefined public space, for which citizens' need for socialization and new contents is recognized. It is this need that transforms the problem into potential, so the solution is conceptualized as an open-air social network. The social network, as an online space for meeting, content exchange and leisure, is becoming a new place, materialized in the physical space of the park. The social network, as a regenerative remix of various contents, implies a transformable spatial programming scheme and the possibility of updating it, available to different users in a continuous timeline.

        The forest park, on which the proposed site is located, is seen as an open network whose basic units of structure are tree trunks, between which the flow and connection of natural and social contents take place. Cut, copy and paste digital tools are interpreted as principles of design methodology.

         SPATIAL SCHEME

   The spatial concept of the project is conceived as a modular network of variable raster of the basic unit of structure - the trunk, i.e. its variable height and disposition (density), depending on the potential content - program zones.

Trunks, as nodes of a spatial scheme, are connected by content elements that, as links, mutually form spatial ambients - program zones. Within the transformable network, trunks are positioned and programmed to support and combine different sets of pre-determined content elements (project-defined), as well as to embrace new, unpredictable elements (by addition and improvisation in the future). In this way, the social network, as an open spatial-program system, enables different variations depending on the actors, number and type of basic units of the structure and content elements, ie size, layout and combinatorics of the program zones, as well as the existing situation on the site (layout of the park greenery, trail, etc).

          At the proposed site, the intervention zone  contents  concentrate and overlap along the existing dirt path which remains undisturbed by designed elements whose network tends to extend inland to the park forest. Initially, it is generated as the program optimum version of the contents the participants cited. In order to achieve a unique spatial composition of the park greenery and the designed structure, it is envisaged to plant additional low and high vegetation on the perimeter of the park.

          TECHNICAL DESCRIPTION

  For the intervention at the site, for the basic units of the structure - trunk, a module of 300 cm was initially taken, which represents the width of the dirth path connecting the access to the location at the vehicle entrance of FC "Tatra" to the motor club "Kisač Crows". The module width, as a common denominator, is convenient for supporting various smaller modules: 50/75/150 cm and / or 30/60 cm for content element positions within the network. The trunks, as nodes of the modules they create, are made of 15 cm thick wooden poles with vertical modularity: 25/50/100/150/200/250/350/450. The disposition and combinatorics of trunks, as well as the content elements between them, leads to the development of the concept and the variability of programming zones.

             In addition to greenery, a stone cube has been proposed for the flooring, which, with its technical and aesthetic characteristics, is suitable as a paving in the natural ambience of the park. Its formation and occupation within the modular network is initially free, depending on the layout of ambient zones. In addition to the program contents, it is used for the access path and can also be considered as an element of paving throughout the park.

                 Content elements, ie program zones, are concentrated within the field of intervention at the site, but some, which are general, can be extended further into the park: lighting columns along the path, bins, benches, tables, etc. In addition to the design elements, the project also envisages additional greening of the perimeter of the park, between the driveway and the adjacent parcel of the football field.

            > Segments from submitted project documentation. The publication is on  this link. <

          …By setting the project optimum of the wide variability solution, Stefan and Majda fill the trunk with prepared materials and tools and go to Kisač. Along the perimeter of the park, in the central part of the competition site, Stefan sets up a segment of the spatial-program concept, the so-called 3D model in a 1:1 ratio, as an object of use, an urban furniture…

                                     The  structure of installation consists of three trunks, interconnected by three content elements:

1) swing (E8.1) - O:TVORENO concept-project leitmotif, segment of playground zone (Z3) 2) bench (E5.1.1) - segment of rest and recreation zone  (Z2) 3) birdhouse (E3.1) - segment of all zones, intended for park residents

  In art and aesthetic terms, the installation is mostly left in the natural texture of the wood, while certain accents of the content elements and their spots of links (connections) are painted in the colors of the competition graphics, that is, the colors of programmatically pre-determined and unpredictable sets.

                                                  …By refining the park's neglected space, AΔA manages to surpass its own goal of participating in this competition, forming another (ad hoc) NEW PLACE on its o:pen journey, which will in a few days lead to a Jury Award in the form of Honorable Mention...

                                                                               ***

                                     contact & connection

                                                  AΔA

                                I  II  III  IV  V  VI  VII  VIII IX  X

[juniperpublishers-dentistry]

Oral Health, Diseases, Examination, Diagnosis, Treatment Plan &Mouth Preparation- Juniper Publishers

For more Open Access Journals in Juniper Publishers please click on: https://juniperpublishers.com For more articles in Open Access Journal of Dentistry & Oral Health please click on: https://juniperpublishers.com/adoh/index.php To know more about Open Access Journals please click on: https://juniperpublishers.com/journals.php

Abstract

Aim of the study: To research the perceptions of patients in the Diyarbakir region in respect of the toxicity of mercury in amalgam fillings.

Materials and methods:The study included 500 patients with at least one amalgam filling who attended the clinic for routine dental treatments. Data were gathered using a single-page questionnaire The questions on the form related to age, gender, marital status, level of education, economic status, types of dental filling, whether or not the amalgam filling included mercury and whether or not mercury was harmful to human health. Questions were also asked to ascertain the patient’s level of knowledge in respect of mercury, amalgam fillings and human health.

Results:A total of 500 patients were included in the study, comprising 283 (56.6%) females and 217 (43.4%) males. When economic status was questioned, 267 (53.4%) patients reported monthly income of 0-1000TL and 233 (46.6%) patients reported more than 1000TL. The level of education was primary school in 110 (22%) patients, high school in 159 (31.8%), university or post-graduate in 190 (38%) and 41 (8.2%) were illiterate. The type of dental filling was unknown by 64.4% of patients and 59.6% did not know that the amalgam filling contained mercury. 52.6% of the patients did not know whether or not mercury was harmful and 72% did not know whether or not mercury in amalgam was harmful.

Conclusion:A low level of awareness was determined in the study participants in respect of the toxicity of mercury in amalgam fillings.

Keywords: Awareness; toxicity; Mercury; Dental Amalgam

    Introduction

The oral cavity composed of:

a. Hard tissues as: Bones of the upper jaw (maxilla ) & lower jaw ( mandible ), bone of the palate, and teeth.

b. Soft tissues as: Periodontium, soft palate, tongue, floor of the mouth, cheeks & lips.

The most common diseases always affect the teeth and the periodontium.

The Periodontium is composed of :

Gingiva:The normal gingiva is firm and pink in color and composed of :

a) Free gingival:It is the movable part of the gingiva that extent from the gingival crest to the bottom of the gingival sulcus (normal sulcus depth is 1-2 mm).

b) Attached gingival:It is the stippled part of the gingiva.

Periodontal ligaments:The periodontal ligaments are arranged in 5 bundles in different directions. It is responsible for the nutrition and attachment of the teeth in addition to act as foundation for the prosthesis.

Alveolar bone crest:The alveolar bone crest is 2 mm away from the gingival sulcus. The periodontium is a connective tissue structure attached to the periosteum of both the maxilla & the mandible that serves to anchor the teeth in the maxillary and the mandibular alveolar processes. It provides attachment & support, nutrition, synthesis & resorption, and mechanoreception.

The main element of the periodontium is the periodontal ligament (PDL), which consists of collagenous fibers (Sharpey’s fibers), embedded in bone and cementum, and giving support to the tooth in function.

There are five principal fiber groups in the PDL that traverse the space between the tooth root & alveolar bone, providing attachment and support :-

Trans-septal fibers: extending interproximally between adjacent teeth; their ends embedded in cementum.

Alveolar crest fibers: beginning just apical to the epithelial attachment and extending from cementum to the alveolar crest.

Horizontal fibers: coursing at right angles from cementum to the alveolar bone.

Oblique fibers: extending in an oblique direction apically, attaching cementum to the alveolar bone. They are the most numerous fibers.

Apical fibers:radiating from cementum into the alveolar bone at the apex of the root.

There are also smaller irregularly arranged fibers interspersed between the principal fiber groups. Cellular elements found in PDL included - fibroblast [the main synthetic cell, producing collagen & other proteoglycans], cementoblasts & cementoclasts, osteoblasts & osteoclasts, and mast cells & epithelial rests [playing a role in pathologic conditions of the periodontium].

At the base of the gingival sulcus is the epithelium - tooth interface named dentogingival junction (DGJ). This structural relationship between hard and soft tissues is unique in the body, which anchor the epithelial cells to the enamel and cemental surfaces. The depth of the sulcus is variable in healthy individuals, averaging 1.8 mm. In general, the shallower it is, the more likely is the gingiva to be in a state of health.

The Tooth is composed of :

Enamel:The hardest outer part of the tooth composed from enamel prisms embedded in a matrix which bonds the prisms together.

Dentin:The resilient part of the tooth which contains tiny tubes called dentinal tubules through which pass nerve filaments to collect at the junction between enamel & dentin ( dentino- enamel junction ) forming the nerve plexus.

Pulp:The soft connective tissues contain blood vessels and nerves, and fill the inner space of the tooth which called pulp chamber & root canal. It is responsible for nutrition of the tooth & sensation.

Cementum:The outer layer of the root covering the dentin. It is responsible for attaching the 5 bundles of PDL from one end to insure tooth anchor (Figure 1).

    Common Oral Diseases

Tooth decay

Tooth decay, which is also called dental cavities or dental caries, is the destruction of the outer surface (enamel) of a tooth. Decay results from the action of bacteria that live in plaque, which is a sticky, whitish film formed by a protein in saliva (mucin) and sugary substances in the mouth. The plaque bacteria sticking to tooth enamel use the sugar and starch from food particles in the mouth to produce acid. Tooth decay is a common health problem, second in prevalence only to the common cold. It has been estimated that 90% of people have at least one cavity, and that 75% of people had their first cavity by the age of five. Although anyone can have a problem with tooth decay, children and seniors are the two groups at highest risk. Other high-risk groups include people who eat a lot of starchy and sugary foods; people living in areas without a fluoridated water supply; and people who already have numerous dental restorations (fillings and crowns).

Etiology and prognosis

Tooth decay requires the simultaneous presence of three factors: plaque bacteria, sugar, and a vulnerable tooth surface. Although several microorganisms found in the mouth can cause tooth decay, the primary disease agent appears to be Streptococcus mutans. The sugars used by the bacteria are simple sugars such as glucose, sucrose, and lactose. They are converted primarily into lactic acid. When this acid builds up on an unprotected tooth surface, it dissolves the minerals in the enamel, creating holes and weak spots (cavities). As the decay spreads inward into the middle layer (the dentin), the tooth becomes more sensitive to temperature and touch. When the decay reaches the center of the tooth (the pulp), the resulting inflammation (pulpitis) produces a toothache. The general term periodontal disease is used to describe any condition of the periodontium other than normal (Figure 2).

Etiology

Most gingival & periodontal diseases result from microbial plaque. Other contributors to inflammation, however, are calculus, acquired pellicle, materia alba, and food debris.

Terminology

Microbial plaque:It is a sticky substance composed of bacteria & their byproducts in an extra cellular matrix & also containing substances from the saliva, diet, and serum. It is basically a product of the growth of bacterial colonies & is the initiating factor in gingival & periodontal disease.

Calculus:It is a chalky or dark deposit attached to the tooth structure. It is essentially microbial plaque that has undergone mineralization with the passage of time.

Acquired pellicle:Pellicle is a thin brown or gray film of salivary proteins that develops on teeth after they have been cleaned. It frequently forms the interface between the tooth surface and dental deposits.

Materia alba:It is a white coating composed of microorganisms, dead epithelial cells, and leukocytes that is loosely adherent to the tooth. It can be removed from the tooth surface by water spray or by rinsing.

Pathogenesis:Sequence of events in the development of a gingivitis - periodontitis lesion is a very complex. It involves not only local phenomena in the gingiva, PDL, tooth surface, and alveolar bone, but also a number of complex host response mechanisms.

The chronic plaque induced lesion has been investigated & analyzed, so, divided into initial, early, established, and advanced stages.

Tooth Loss:

Trauma: Trauma due to accident may cause:

Avulsion of tooth from its socket.

Fracture of the tooth crown with part of the root.

Internal fracture of the root with separation of the fractured part.

Alveolar bone fracture with gingival trauma and exposure of the root to oral cavity.

Unrestorability: Unrestorability of the tooth may be due to:

Mutilation from caries with complete destruction of the crown and part of the root.

Root caries with fraction involvement.

Failure to do R.C.T for the tooth.

Occlusion & path of insertion problems: Severe tilting of the tooth which causing problem with occlusion & fabrication of other prosthesis.

Periodontal problems: Severe periodontal problems which cause looseness of the tooth or furcation involvement with other complications as caries of roots & furcation area (Figure 3).

    Introduction

Fixed Prosthodontics treatment can offer exceptional satisfaction for both patient & dentist. It can transform an unhealthy, unattractive dentition with poor function into a comfortable, healthy occlusion capable of giving years of further service, while greatly enhancing esthetics. To achieve that goal, meticulous attention to case selection through right diagnosis, treatment planning & mouth preparation must be done within the first visit in sequence, with great accuracy.

    Diagnosis

Diagnosis is defined as “The procedures of collecting data and information through different channels, so that, a proper line of treatment can be proposed. “

Fundamentals of diagnosis are

History

Examination

Articulated Diagnostic Casts

History

Chief Complaint:Is the patient’s primary reason (s) for seeking treatment.

It’ll be one or more of 4 categories

Comfort: discomfort may be from pain, sensitivity or swelling.

Function: malfunction may be during mastication or speech.

Social: unpleasant appearance may be due to mouth bad taste or odor.

Appearance: unpleasant appearance may be due to bad restoration or teeth discoloration (Figure 4).

Personal Details:Name, age, sex, address, education, occupation, marital status, children, and telephone number

Medical History:Could be achieved under 4 categories :

Conditions affecting the treatment methodology, e.g., any disorders that necessitate the use of antibiotic premedication, any use of steroids or anticoagulants, & previous allergic response to medication or dental materials.

Conditions affecting the treatment plan, e.g., previous radiation therapy, hemorrhagic disorders, extremity of age, and terminal illness.

Systemic conditions with oral manifestations, e.g., + Periodontitis= diabetes, menopause, pregnancy, or the use of anticonvulsant drugs. + Erosion of teeth= stomach acid regurgitation in case of hiatal hernia, bulimia, or anorexia nervosa. + T.M.J. disorders or reduced salivary flow= as side effect of certain drugs.

Possible risk factors to dentist & auxiliary personnel, e.g., patients who are suspected or confirmed carriers of hepatitis, AIDs, or syphilis.

Dental History: Includes :

Periodontal history and oral hygiene

Restorative history: filling and F.P.Ds

Endodontic history

Orthodontic history

Removable Prosthodontic history

Oral surgery history

Radiographic history

T.M.J. dysfunction history

    Methods of Clinical Examination

General examination

General appearance, skin color, and vital signs as respiration, pulse, temperature, and blood pressure.

Extra oral examination: special attention to facial asymmetry = may hint at serious conditions. Cervical lymph nodes are palpated, as are the T.M.J., & the muscles of mastication. Lips position during smiling is critical in treatment planning.

Intra oral examination: Reveals considerable information concerning the condition of the soft tissues, teeth, and supporting structures. Lips tongue, floor of the mouth, vestibules, cheeks, and the hard & soft palates are examined; and any abnormalities are noted.

A.Periodontal examination:

Gingiva: Color, texture, size, contour, consistency, and position.

Periodontium: Pocket’s depth, tooth mobility or malpositions, open or deficient contacts, and furcation involvement must be recorded after thorough examination (Figure 5).

B. Diagnosis of caries:Accurately diagnosing early dental caries is a challenge for the dentist. The following methods are used for detecting dental caries, and each has specific limitations:-

Dental explorer: When a sharp explorer tip is pressed into an area of suspected caries, it will “stick” when being removed. N.B. This technique is not effective in diagnosing carious lesions on teeth that have been exposed to fluoride.

Radiographs: Although useful for detection of interproximal caries, early caries on occlusal surfaces is not visible on radiographs. In addition, the extent of caries can easily be misdiagnosed because the caries is often two times deeper and more widespread than it appear on the radiograph.

Visual appearance: The appearance of dark-stained grooves in the teeth may indicate caries. However, the grooves may simply be stained from coffee or tea (Figure 6).

Laser caries detector: The recently introduced laser caries detector is used to diagnose caries and reveal activity under the enamel surface. A small battery-operated unit directs a laser beam into the tooth. When the beam encounters a change in the integrity of the tooth, it gives off a fluorescent light of different wave-lengths. The laser caries detector is equally effective in both primary & permanent teeth. The laser wave-length is translated through the handpiece into a number from 0 - 99, according to the degree of fluorescence based on the amount of decay. The laser cannot be used to diagnose inter-proximal caries due to the limited access. In addition, it cannot detect caries under dental sealants or amalgam restorations (Figure 7).

C. Diagnosis of teeth required R.C.T:The diagnosis of a tooth requiring endodontic treatment is based on an examination that has both subjective and objective components.

Subjective examination:includes an evaluation of symptoms or problems described by the patient, which include the following:

+ Chief complaint

+ Character and duration of pain

+ Painful stimuli

+ Sensitivity to biting and pressure

Objective examination:is conducted by evaluating the status of the tooth and surrounding tissues in regard to the following:

+ Extent of caries

+ Periodontal conditions surrounding the tooth in question

+ Presence of an extensive restoration

+ Tooth mobility

+ Swelling or discoloration

+ Pulp exposure (visual examination)

Several techniques are used to test pulp vitality in determining whether endodontic treatment is required or the pulp is still vital and able to repair itself.

When testing a questionable tooth, a control tooth is selected for comparison ( healthy tooth, usually of the same type, in the opposite quadrant ). The use of control tooth shows that the stimulus is capable of achieving a response.

    Methods of vitality evaluation

a. Percussion & Palpation:Are tests used to determine whether the inflammatory process has extended into the periapical tissues. Positive test results indicate that there is inflammation in the periodontal ligament and the endodontic treatment is required.

b. + Percussion test:by tapping on the occlusal or incisal surface of the tooth with the end of the mouth mirror handle, which is held parallel to the long axis of the tooth?

c. + Palpation test:by applying firm pressure to the mucosa above the apex of the root.

d. - Thermal sensitivity:Are tests with temperature extremes to determine the status of the pulp. The thermal stimulus is never placed on a metallic restoration or the gingival tissue, which would result in an abnormal response and could cause damage to the tissues.

e. + Cold test:The dentist uses ice, dry ice, or ethylchloride to determine the response of a tooth to cold. The control tooth and the suspect tooth are isolated and dried, then the source of cold is applied first to the cervical area of the control tooth, and after to the cervical area of the suspect tooth.

f. + Heat test:Is generally the least useful of the vitality tests because a painful response to the heat could indicate either reversible or irreversible pulpitis. Only, the necrotic pulp will not respond to the heat. A small piece of guttapercha, or the end of an instrument, is heated in a flame and applied to the facial surface of the tooth.

g. - Electric pulp testing:is used to determine whether a pulp is vital or non-vital. Like other testing devices, it can produce a false response; therefore, the test results must be supported by other diagnostic findings.

Electric pulp testers deliver a small electrical stimulus to the pulp. Factors that influence the reliability of the pulp tester include the following:

Teeth with extensive restorations can vary in response.

In teeth with more than one canal, one canal may be vital and the others may be non-vital.

A failing pulp can produce a variety of responses.

Control teeth may not respond as anticipated.

Moisture on the tooth during testing may produce an inaccurate reading.

6- The batteries in the tester may weaken over time.

- Cavity test: By the use of small inverted cone carbide bur with high speed hand-piece, a small cavity done without using anesthetic solution. If the suspect tooth is vital the patient will feel pain. This test is only used, if there is still doubt about the tooth vitality.

- Radiographic evaluation: radiographs are a necessity for diagnostic testing as well as in root canal treatment. Good quality radiographs are required for optimal information.

D.Radiographic full-mouth examination:

1. Intra-oral full-mouth radiographs:are composed of both periapical and bite-wing films. They are used to examine the teeth and the supporting structures. For the average adult, a full-mouth series consists of 18 - 20 films are needed. Occlusal films, also, are needed to detect the position of impacted teeth, or a lesion in bone (Figure 8).

2. Extra-oral & digital radiography:provides an overall image of the skull and jaws. In some cases the extra-oral film is used because the patient has swelling or severe pain and is unable to tolerate the placement of intra-oral films. It may be used alone or in conjunction with intra-oral films. The images seen on an extra-oral film are not as well defined or as sharp as the images seen on an intra-oral radiograph.

Indications for extra-oral radiographs are:

- To identify trauma or fractures.

- To determine the size and area of large lesions.

- To identify T.M.J. disorders.

- To detect diseases of the jaws.

- To identify the location of impacted teeth.

- To determine jaw growth and development.

Types of extra-oral radiographs used in dentistry are:

3. Panoramic radiograph:allow the dentist to view the entire dentition and related structure on a single film.

Intra-oral films are used to supplement a panoramic film for detection of dental caries or periapical lesions (Figure 9).

4. Lateral jaw radiography:is used to view the posterior region of the mandible. It is very useful in children, patient with limited jaw opening, and patients who cannot tolerate intra-oral film placement.

5. Skull radiography:is used most often in oral surgery and orthodontics.

The most common skull radiographs used in dentistry include the following:

+ Lateral cephalometric:is used to evaluate facial growth and development, trauma, and disease & developmental abnormalities.

It shows the bones of face and skull as well as the soft tissue profile.

+ Posteroanterior:is used to evaluate facial growth & development, trauma, and disease & developmental abnormalities.

It shows the frontal & ethmoid sinuses, the orbits, and the nasal cavities (Figure 10).

+ Waters projection:is used to evaluate the sinus area. It shows the frontal and ethmoid sinuses, the orbits, and the nasal cavities.

+ Submentovertex:  is used to identify the position of the condyles, show the base of the skull, and evaluate fractures of the zygomatic arch. Also, shows the sphenoid and ethmoid sinuses and the lateral wall of the maxillary sinus.

+ Reverse towne:is used to identify fractures of the condylar neck and ramus. Imaging technique:- as the T.M.J. area can be very difficult to be examined radio-graphically because of the multiple adjacent bony structures, also radiography cannot be used to examine the articular disc and other soft tissues of the T.M.J.. Instead, special imaging techniques such as arthrography & MRI must be used.

6. Digital radiography:uses an electronic sensor to record the penetration of the x-ray photons and then sends this information to a computer that digitizes these electronic impulses. This allows the computer to produce a diagnostic image on a monitor almost instantaneously.

E. Occlusal examination :

General alignment.

Lateral and protrusive contacts.

Centric relation.

Jaw maneuverability (Figure 11).

A. Articulated diagnostic casts:They are essential in treatment planning. Static and dynamic relationships of the teeth can be examined without interference from protective neuro-muscular reflexes. The unencumbered views reveal aspects of the occlusion not detectable within the confines of the mouth.

+ Steps for accurate diagnostic casts are :-

B. Impression making:Accurate alginate impression of both dental arches are required.

C. Articulator selection:Articulators are classified according to how they can reproduce mandibular border movements.

Types of articulators are:

2 types:

D. Centric relation record:Provides the orientation of mandibular to maxillary teeth at CR in the terminal hinge position, where opening & closing are a purely rotational movement. Casts articulated in the IP don’t permit evaluation of the CR & contact relationships. Therefore, the relation of diagnostic casts in CR is of significant diagnostic value.

E. Jaw manipulation:Accurately mounted casts depend on precise manipulation of the patient’s mandible by the dentist.

The condyles should remain in the same place throughout the opening - closing arc. The load - bearing surfaces of the condylar processes, which face anteriorly, should be manipulated into apposition with the mandibular fossae of the temporal bones, with the disc properly interposed. The best technique to be used, is “Dawson” technique.

Anterior programming device, plastic leaf gauge, or cotton rolls, can be used first to prevent tooth contact before manipulation to ensure that there are no muscular reflexes during manipulation (Figure 12,13).

+ Uses of articulated diagnostic casts are:-

I) Distribution & dimensions of edentulous span:

1. Distribution of edentulous are:could be properly evaluated to decide whether to construct R.P.Ds or F.P.Ds.

2. Mesio - distal dimension:Short M.-D. width = short span Long M.-D. width = long span, leads to bending of the bridge, therefore increase the number of the abutments and F.-F. type is indicated.

3. Occluso - gingival height:this will determine the type of the selected pontic & retainers.

II) Type of bite & occlusal prematurities:The main advantage of the study cast is to study the “Lingual occlusion”. Abnormal bite as deep bite, cross bite, and edge to edge bite can be easily recognized. Any premature contact, which may be caused by tilted or over erupted teeth will prevent the maximum intercuspation with undue stress and this should be detected & corrected. Proper mounting is essential to study occlusion.

III) Occlusal discrepancies & occlusal plane:Some cases may need to establish a new occlusal plane. With the aid of radiograph, over erupted teeth can be easily evaluated and the amount of reduction needed could be determined.

IV) Axial inclination & common path of insertion:Due to the changes of the tooth axial inclination, some problems may arise in attaining a common path of insertion. With the aid of radiograph & dental surveyor, the amount of reduction needed, without endangering the pulp vitality, can be measured; accordingly the type of the bridge and its retainers could be selected.

V) Concerning the abutment teeth:

1) Size and form of the coronal portion:-these are well visualized on the cast, so, we can determine the type of retainers & the required retentive means.

2) Amount and location of tooth reduction:-on the cast we can determine the amount of reduction that may be increased in certain areas.

3) Evaluation of the available tooth structure:-we can visualize the remaining tooth structure & the occlusal load imposed on the tooth, after removal of decay.

VI) Alteration of midline:This is easily measured on the cast & the suitable solution can be reached.

VII) Planning the suitable design:On a second study cast the suitable design can be visualized & the treatment plan for the entire mouth is decided.

VIII) Trial preparation and waxing - up:Dentist could rehearse a proposed treatment plan on another cast. This enables him to visualize & realize the difficulties that might face him during tooth preparation. Also through waxing - up, the final shape of the prosthesis could be properly assessed.

    Treatment Planning

Treatment planning consists of formulating a logical sequence of treatment in steps designed to restore the patient’s dentition to good health, with optimal function and appearance. It should be presented in written form & discussed in detail with the patient.

Successful treatment planning is based on proper identification of the patient’s need.

A. Treatment is required to accomplish one or more of the following objectives:

O Correction of existing disease.

O Prevention of future disease.

O Restoration of function.

O Improvement of appearance.

B. Sequence of treatment:

A logical sequence of steps must be decided on - including :

O Treatment of symptoms.

O Stabilization of deteriorating conditions.

O Definitive therapy.

O Program of follow - up care.

I. Treatment of symptoms:The relief of discomfort attending an acute condition is a priority item in planning treatment. A fully examination is neither desirable nor generally possible until the symptoms of the acute condition have been addressed. Also, urgent treatment of non acute problems such as a lost anterior crown, a broken porcelain veneer or fractured R.P.D., should receive priority attention.

II. Stabilization of deteriorating conditions:Such as dental caries or periodontal disease.

Replacement of defective restorations.

Removal of carious lesions.

Re contouring of over contoured prosthesis.

Removal of plaque & proper oral hygiene instructions.

III. Definitive therapy:When the stabilization phase has been completed, successful elective long - term treatment aimed at promoting dental health, restoring function, and improving appearance can begin. Several therapeutic proposals may be applicable to a single patient. The advantages & disadvantages of each should be thoroughly explained to the patient, with a diagnostic casts and waxing - up used as guides. Usually oral surgical procedures are scheduled first, followed by periodontics, endodontics, orthodontics, fixed Prosthodontics, and finally removable Prosthodontics.

Oral surgery:The treatment plan should allow time for healing & ridge remodeling. All preprosthetic surgical procedures (e.g. ridge contouring) should be undertaken during the early phase of treatment.

Endodontics:Some endodontic treatment may have been accomplished as part of the relief of discomfort & stabilization of conditions. Elective endodontics may be needed to provide adequate space for a cast restoration or to provide retention for a badly damaged or worn tooth.

- Orthodontics:Minor orthodontic tooth movement is a common adjunct to fixed Prosthodontics, especially if tooth loss has been neglected & drifting has occurred.

- Fixed Prosthodontics:Is initiated only after the preceding modalities have been completed. This will permit modification of the original plan , as unforeseen difficulties should surface during treatment.

+ Occlusal adjustments:are often necessary before the initiation of fixed Prosthodontics. Where extensive F.P.D. is to be provided, an accurate & well-tolerated occlusal relationship may be obtainable only if a discrepancy between IP & CR is eliminated first.

+ Anterior restorations:are usually done first because they influence the border movements of the mandible & thus the shape of the occlusal surfaces of the posterior teeth.

+ Posterior restorations:it is often advantageous to restore opposing posterior segments at the same time. This permits the development of an efficient occlusal scheme through the application of an additive wax technique.

+ Complex prosthetics:carefully planned treatment sequencing is particularly important when complex Prosthodontic treatments involving alteration of the vertical dimension or a combination of fixed & removable prosthesis are required. Two sets of diagnostic casts are accurately mounted, so, they can be precisely interchanged on the articulator. Definitive tooth preparation starts in one arch only, preserving the occlusal surfaces of the opposing arch to act as an essential reference for mounting the working cast. The definitive restorations are waxed against the diagnostically waxed cast, establishing optimal occlusion. When one arch has been completed, the opposing cast can be restored, achieving the predicted result.

- Removable Prosthodontics:Are the final procedures, but start to be planned for during fixed Prosthodontic treatment.

- Follow up:A specific program of follow up care and regular recall is an essential part of the treatment plan. The aim is to monitor dental health, identify the signs of disease early, and initiate prompt corrective measures as necessary.

IV.Clinical Tips:

Factors affecting the selection of prosthesis type:

(I) Biomechanical Considerations

1) The decision to remove a tooth:Is part of the treatment planning process & is made after the advantages & disadvantages associated with retention of the tooth have been assessed.

2) The edentulous span:

a- Distribution:

+ Cases with free end saddle will usually require a R.P.Ds.. Alternative treatment are:

- A distal fixture with implant.

- Cantilever bridge in selected cases.

+ Multiple edentulous spaces, though each of which may be restored with a fixed bridge, yet due to expenses & technical complexity, a R.P.Ds. May be used.

b- Length:All fixed bridges, long or short, possess a certain degree of bending when subjected to load; the longer the span, the greater the flexing.

Bending varies directly with the cube of the length & inversely with the cube of occluso-gingival thickness of the pontic considering other factors being equal.

+ Excessive flexing or bending under occlusal force may lead to:

- Fracture of porcelain veneer

- Connector breakage

- Retainer loosening

- An unfavorable soft tissue response

+ To minimize bending:

- Construct pontics & connectors of greater occluso-gingival dimensions

- Use an alloy of higher yield strength

+ Clinical considerations of the bridge flexing in treatment planning:

- The length of the edentulous area will affect the type of restoration to be suitable for replacing one or two missing teeth.

- Three posterior teeth is better to be replaced with R.P.D. as F.P.D. will be very questionable.

- Constructing a long span F.P.D. on short teeth is expected to have a very disappointing prognosis. + Alternative treatment modalities for long edentulous span:

An implant supported F.P.D. {requires sufficient alveolar bone, broad flat ridge & favorable opposing occlusion}.

- Removable partial denture.

c- Arch form: The arch curvature affects the amount of stresses occurring in F.P.Ds constructed in the anterior segment, especially in the upper teeth.

In cases of pointed arch (V-shaped), pontics of F.P.D would lie far outside the inter abutment axis line, thus acting as lever arm producing torque movement on the supporting abutment. + Measures to be taken in bridge design: If the distance between the inter abutment axis & the pontic is increased = the force arm will be increased; this will need to increase the number of the abutments, to increase the resistance arm for this force.

(II) The Prospective Abutment:

1) The pulpal condition:

a- Vital sound tooth:the unrestored vital caries-free tooth is an ideal abutment as it facilitates conservative preparation for strong retentive restoration with good esthetics.

b- Carious tooth:after caries removal as well as all the undermined enamel, assessment of the remaining sound tooth structure & the pulpal condition should be performed. The existing situation would influence the line of treatment as following:

+ Selecting the most suitable type of restorative material & the necessary retentive means {e.g. pins, grooves or boxes}.

+ Doubtful pulpal condition or those teeth with pulpal capping should not be used as F.P.D abutments unless being endodontically treated.

c- Endodontically treated abutments:A perfectly endodontically treated tooth (clinically & radio- graphically) can be used successfully as an abutment with a post & core for retention & strength.

+ Clinical consideration of endodontically treated abutments:

- As posts & cores are usually constructed to compensate for the lost coronal part, thus extreme care is needed to get sufficient retention from the post.

- Before deciding an endodontic treatment for a tooth to be used as abutment, it should be evaluated whether this tooth is restorable or not.

- In complex & expensive prosthesis whose success is dependent on an abutment that will require endodontic treatment, endodontic surgery or implants may be a better treatment choice.

2) Coronal variations and tooth alignment:

a- Over erupted teeth:to restore the dentition to complete function, free of interference, over- erupted teeth should be adjusted to the normal occlusal plane. In some situations intentional RCT may be necessary to permit enough shortening to correct the occlusal plane.

b- Short crowns:abutments with short clinical crown would create problems in constructing F.P.Ds. Careful selection of the bridge design, with suitable retentive retainers & types of pontics should be highly stressed on. Considerations in bridge design:

- F.-F. Bridge is the most indicated type.

- Full coverage retainer with additional retentive means are to be used.

- Establishing relative least convergence.

- Extend stump of preparation more cervically.

- To avoid excessive shortening = occlusal reduction to receive retainer with occlusal metal coverage. - Pontics & connectors should be of considerable occluso-gingival dimension to resist bending.

- Replacing missing 2 or 3 teeth in short occluso-gingival edentulous areas with R.P.D should be highly considered.

c- Mesially tilted 2nd molar:early loss of 1st mand. molar would create problems if the space is ignored, as mesial tilting of the 2nd molar. Constructing of F.P.D would face the problem of attaining a common path of insertion. Different treatment modalities:

Up-righting the tilted abutment orthodontically then normal F.-F bridge is considered the treatment of choice.

A proximal (mesial) ½ crown can be used as a retainer on the tilted abutment.

F.-S bridge with non rigid connector on the distal aspect of the premolar; so, the path of insertion of the bridge is parallel to the tilted molar.

]

F.F bridge with telescopic crown on the distal abutment.

+ Telescopic crown is consisted of:

- Thin thimble crown that prepared, constructed & cemented alone parallel to the long axis of the tilted abutment.

- The external surface is especially designed to be covered by the retainer of the bridge, which will not cover the distal surface as it will be inserted parallel to the normal path of insertion.

Mouth preparation

It has become clear that failures are often attributed to inadequate mouth preparation. In this case mouth preparation refers to the dental procedures that need to be accomplished before fixed prosthodontics can properly be undertaken. This is because the etiologic factors that lead to the need for F.P.Ds, also promote other pathologic conditions. F.P.Ds will be successful only if restorations are placed on well restored teeth in a healthy environment.

Comprehensive treatment planning will ensure that mouth preparation is undertaken in a logical & efficient sequence, and aimed at bringing the teeth & their supporting structures to optimum health. Equally important is the need to educate & motivate the patient to maintain long-term dental health through meticulous oral hygiene practices. As a general plan, the following sequence of treatment procedures in advance of F.P.D should be adhered to:-

Relief of symptoms {C.C.}

Removal of etiologic factors {caries & deposits}

Repair of damage

Maintenance of dental health

+ A typical sequence in the treatment of a patient presenting with extensive dental disease, could be as follows:

- Preliminary assessment

- Emergency treatment for symptoms {C.C.}

- Definitive data collection & assessment of needs

- Oral surgery

- Caries control & replacement of defective restorations

- Endodontic treatment

- Definitive periodontal treatment, possibly in conjunction with preliminary occlusal therapy

- Orthodontic treatment

- Definitive occlusal treatment

- F.P.D. treatment

- R.P.D. as immediate transient before implant treatment or permanent restoration

- Implant treatment

- Follow up care

Oral Surgery

Oral SurgeryAny abnormality that may require surgical intervention.

+ Elective soft tissue surgery may include:

- Alteration of muscle attachments

- Removal of soft tissue wedge distal to molars

- Increase of the vestibular depth

- Modification of edentulous ridges to accommodate F.P.Ds. or R.P.Ds.

B- Hard tissue procedures:It should be performed as early during treatment as possible to allow the maximum time of healing & osseous recon touring.

+ It may include:

- Simple tooth extraction or remaining roots removal

- Tuberosity reduction or, max. or mand., tori excision

- Impacted or unerupted supernumerary tooth or 3rd molar removal

C- Orthognathic surgery:Patients who are candidates for orthognathic surgery require3 careful restorative evaluation & attention before treatment. Otherwise, an expected improvement in the facial skeleton may be accompanied by unexpected occlusal dysfunction. After surgery, the connection between plaque control, caries prevention, and periodontal health should be stressed to the patient.

D- Implant-supported fixed prosthesis:Successful implant dentistry necessitates that both, the patient be meticulously selected & the technique chosen be skillfully executed.

E- Caries and Existing Restorations

Generally, when a crown is needed, the dentist should plan to replace any existing restorations. Although, most teeth will require foundation restorations, & small defects resulting from less extensive lesions, can often be incorporated in the design of a cast restoration or be blocked out with cement. Assessment is more difficult when an existing crown or F.P.D is being replaced. Then the extent of damage can be seen only after the defective restoration has been removed.

+ Foundation restoration or core: Is used to build a damaged tooth to ideal anatomic form in advance of it’s being prepared for a crown. It should provide the patient with adequate function & be contoured and finished to facilitate oral hygiene. Subsequent tooth preparation is greatly simplified if the tooth is built up to ideal contour.

+ Selection criteria of the foundation material depends on:

The extent of tooth destruction.

The overall treatment plan.

Operator preference.

It is important to consider the effect of subsequent tooth preparation for the cast restoration on the retention & resistance of the foundation. Retention features such as grooves or pins should be placed sufficiently pulpal to allow adequate room for the definitive restoration. Adhesive retention may be helpful in preventing lose of the foundation during tooth preparation.

F- Endodontics:

+ Assessment: the clinical examination should include:

- Tenderness to percussion should be noted.pulpal health.

- Any abnormal sensitivity, soft tissue swellings, fistulous tracts, or discolored teeth.

- Carefully examined radiographs for signs of periapical disease, if there is doubt concerning pulpal health.

+ Treatment:it should be a general rule to perform conventional rather than surgical endodontics, if possible; because apicoectomy adversely affects the crown/root ratio & thus the support of the planned prosthesis. When a post & core restoration is needed, 3-5 mm of apical seal should be retained. The post can usually be removed to access recurrent periapical lesion, using a “ Masserann Kit “. It may be desirable to perform elective endodontics in the following situations:-

When there are problems in obtaining a completely compatible line of withdrawal between multiple abutments.

When it is impossible to gain adequate retention in a badly worn tooth.

When the pulpal prognosis of an abutment tooth is compromised & additional preparation is likely to further jeopardize its longevity.

G- Definitive Periodontal Treatment:Certain specific periodontal procedures may be indicated to improve the prognosis of a restoration.

H- + Mucosal reparative therapy:It is recommended that a tooth to be treated with restoration extending into the gingival sulcus should have approximately 5 mm of keratinized gingiva, at least 3 mm of which is attached gingiva. Where less keratinized gingiva is present, or in areas of localized gingival recession, a grafting procedure should be considered.

- Free autogenous gingival graft.

- Laterally positioned pedicle graft.

- Coronally positioned pedicle graft.

+ Crown lengthening procedure:- May be indicated:

To improve the appearance of an anterior tooth.

When the clinical crown is too short to provide adequate retention without the restoration’s impingement on the soft tissue { biologic width }.

In some patients with extensive sub gingival caries, sub gingival fracture, or root perforation resulting from endodontics.

When crown lengthening is the treatment of choice it may be accomplished either surgically or with combined orthodonticperiodontic techniques depending on the patient & dental situation.

I-Orthodontic Treatment:

Minor orthodontic tooth movement can significantly enhance the prognosis of subsequent restorative treatment. Up righting of malpositioned abutment tooth can improve axial alignment, create more favorable pontic space, and improve embrasure form in the fixed prosthesis. Additionally, it can direct occlusal forces along the long axis of the tooth & often lead to a substantial conservation of tooth structure.

J- Definitive Occlusal Treatment:

Mouth preparation often involves reorganization of the patient’s occlusion, typically to make IP coincide with CR & remove eccentric interferences. The coincidence of CR & IP greatly facilitates accurately transferring the patient’s casts to an articulator. When selective grinding of the natural dentition is being considered, it should be remembered that this is a purely subtractive procedure (tissue is removed) and is limited by the thickness of the enamel.

Obviously, before any irreversible changes are made in the dentition, a careful diagnosis must establish whether indeed restorations will be needed.

+ Diagnostic adjustment:-2sets of articulated diagnostic casts are required. One set will serve as a reference; the other will be used to evaluate how much tooth structure has been removed and how much more must be removed to meet the objectives of the procedure. This will reveal the efficacy of the treatment plan before anything is done.

The primary objectives of selective occlusal grinding are:

To redistribute forces parallel to the long axes of the teeth by eliminating contacts an inclined planes & creating cuspfossa occlusion.

To eliminate deflective occlusal contact; CR coincides with IP.

To improve worn occlusal anatomy, enhance cuspal shape, narrow occlusal tables, & reemphasize proper developmental & supplemental grooves in otherwise flat surfaces.

To correct marginal ridge discrepancies & extrusions, so oral hygiene will be easier.

To correct tooth malalignment through selective reshaping.

It will not always be possible to achieve every one of these goals.

If a choice must be made, corrective therapy should not be at the expense of functional surfaces & should not destroy any functional contact.

+ Clinical occlusal adjustment:

A- Patient selection:careful analysis of the diagnostic occlusal adjustment must be made to determine whether the patient is a good candidate for such irreversible subtractive treatment.

Precise reduction & close attention to the sequence are essential. A written record of each reduction is also recommended.

The following should be considered as contraindications to definitive occlusal adjustment:

A bruxer, whose habit cannot be controlled,

When the diagnostic correction indicates that too much tooth structure will be removed.

A complex spatial relationship [e.g. Angle class II & skeletal class III].

When max. Palatal cusps contact mand. buccal cusps.

An open anterior occlusal relationship.

Excessive wear.

Before orthodontic or orthognathic treatment.

Before physical or occlusal appliance therapy.

A patient with T.M.J pain.

A patient whose jaw movements cannot be manipulated easily.

B- Occlusal adjustment:it needs to be undertaken in a logical sequence of steps, so, this will avoid repetition & improve the efficacy of treatment.

The steps are:

(1) Elimination of CR interferences:

mandibular tooth follows its own arc of closure. If IP & CR positions don’t coincide, premature contacts will be unavoidable. Manipulate the mand. & mark the tooth, so that, the initial contact in CR & the extent and direction of jaw movement to IP are seen. This movement, or slide, can be in either an anterior or a lateral direction. Find any interference that because the condylar processes to be displaced & adjust it by selective grinding of the cuspal inclined planes.

(2) Elimination of lateral & protrusive interferences:

The goal of this phase of adjustment are to eliminate contacts between all posterior teeth during protrusive movements, mediotrusive [non working], & latero-trusive [working]. In certain patients, group function of the working side contacts should be considered rather than the more ideal mutually protected occlusion; especially when there is mobility, poor bone support, wear, or malpositioning of the canines. It is essential during this phase of adjustment, that no centric contacts be removed. In general, lateral & protrusive interferences are eliminated by creating a groove that permits escape of the centric cusp during eccentric movements [1-3].

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