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Nothing Fancy... just experimenting and exploring with the available ones before exploring the new trending ones.. The core trick here: ctx.measureText() pre-computes every word into a data object with a baseX, current x, and targetX. Each frame, a 120-segment dragon emits collision nodes with anatomically-computed radii. For every line...

73,622 просмотров • 3 месяцев назад •via X (Twitter)

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Ask anyone who’s taken a course in Ordinary Differential Equations (ODEs) what a solution to an ODE represents geometrically, and most of them won’t have a clean answer. When I first took ordinary differential equations, the pattern was always the same. Early on it turns into a speedrun of methods: separation of variables, integrating factors, variation of parameters, Bernoulli, exact equations. Then pretty quickly the course slides into hammer-picking. Spot the form, apply the recipe, move on. Too mechanical! And the real problem is what you don’t walk away with. You leave with a toolkit, but without a feel for what a differential equation even is, especially geometrically. That matters because in real modeling the equations you meet are rarely nice enough to reward memorised recipes. So you get trained to solve toy forms, while the actual subject stays blurry. The behavior. The flow. The shape of solutions. It wasn't until I watched the first lecture of Professor Arthur Mattuck that I realized I didn’t actually know what a solution to a differential equation represents geometrically. His point is almost embarrassingly simple. A first-order ODE is a slope field, and a solution is a curve that stays tangent to that field everywhere. The math breakdown: Write the ODE as dy/dx = f(x,y). At each point (x,y), attach a tiny line segment with slope f(x,y). A function y = y₁(x) is a solution exactly when its graph follows those slopes. At every x, the slope of the curve equals the slope prescribed by the field at the point on the curve. That’s the one line that ties both viewpoints together: y₁′(x) = f(x, y₁(x)). So solving the ODE and drawing an integral curve are the same statement in two languages. Once you see that, you stop obsessing over whether you can write y(x) in closed form. You start asking the questions that actually matter. Where do solutions flow. Where do they get trapped. Where do they blow up. Where does existence or uniqueness fail because the field isn’t even defined? That’s the perspective shift I wish every ODE course forces early. It’s also why I keep pairing math with animation. #DifferentialEquations #ODEs #VectorFields #AppliedMathematics #Mathematics #

Mathelirium

40,739 просмотров • 5 месяцев назад

When I first took ordinary differential equations, the pattern was always the same. Week 1 turns into a speedrun of methods: separation of variables, integrating factors, variation of parameters, Bernoulli, exact equations… and by Week 2 or 3 the course has quietly degenerated into hammer-picking. Spot the form, apply the recipe, move on. Mechanical! Fuuuuck!😫😫😫😫 The problem is what you don’t walk away with. You leave with a toolkit, but without a feel for what a differential equation even is, especially geometrically. And that’s a big deal, because in real modeling the equations you meet are rarely nice enough to reward memorized recipes. So you end up trained to solve toy forms, while the actual subject...the behavior, the flow, the shape of solutions stays blurry. This is why I’m biased toward the old-timers. Their old-school way of doing things always surprises me:...they’ll spend time on one idea until it sticks, instead of sprinting through a syllabus checklist. One lecture from them and you start noticing a contrast. A lot of modern teaching feels like "finish the content,". You get marched through techniques, but you’re not left with a single thought that keeps bothering you later...the kind of thought that actually pushes you toward research-level curiosity. MIT OpenCourseWare’s Professor Arthur Mattuck did that to me in his very first ODE lecture. One lecture, and your whole relationship with dy/dx = f(x,y) changes. In this segment, Prof. Mattuck is basically saying: A first-order ODE is a slope field, and a solution is a curve that moves everywhere tangent to that field. The math breakdown Write the ODE as dy/dx = f(x,y). At each point (x,y) you attach a tiny line segment with slope f(x,y). A function y = y₁(x) is a solution exactly when its graph follows those slopes:. At every x, the slope of the curve equals the slope prescribed by the field at the point on the curve. That’s the single line that unifies both viewpoints: y₁′(x) = f(x, y₁(x)). So solving the ODE and drawing an integral curve are the same statement in two languages!👌🏻 Once you see that, you can stop obsessing over whether you can write y(x) in closed form. You can start asking the questions that matter: where do solutions flow, where do they get trapped, where do they blow up, and where does existence/uniqueness fail just because the field isn’t even defined? That’s the perspective shift I wish every ODE course forces early and it’s exactly why I keep pairing math with animation. #DifferentialEquations #ODEs #VectorFields #MathAnimation #Mathematics

Mathelirium

53,338 просмотров • 6 месяцев назад

Using Claude Fable 5, I built a model that predicts the entire 2026 FIFA world cup.. every single game, not just the final.. so let me break the whole thing down. what it does, how it works, and exactly how i built it.. #1 First what it does: it predicts all 104 games of the tournament. not just who lifts the trophy, but every group match, every knockout, the full path from the round of 32 to the final.. everything lands in one dashboard: > group stage, every match with each team's win % and the chance of a draw > standings, how all 12 groups are projected to finish > bracket, the full knockout tree with each team's odds of advancing > champion odds, who's most likely to actually win it all and it doesn't freeze after one prediction. the moment a real game is played, it locks that result in and re-runs everything around it. so the odds move live as the tournament goes, week by week you watch favorites rise and contenders collapse. #2. How it works: the core idea is simple. the model only ever predicts one thing, a single match. the real trick is the repetition. it learns from decades of match history, then plays the whole tournament out from the first game to the final, tens of thousands of times. each run it records who advanced and who won. do that enough and you stop getting one guess and start getting real odds, one team lifts the trophy in maybe 14% of the runs, another in 9%, and so on. #3. So, how i built it ? i didn't hand-write most of the code. i broke the project into 4 pieces, described each one to fable, and let it build while i focused on getting the football logic exactly right. - The data every international match going back over a century, around 50,000 games, plus each team's elo rating, which is the truest measure of strength, and the official 2026 schedule. garbage data means garbage predictions, so this part mattered most. - The features i turned that raw history into signals the model can learn from, the elo gap between the two teams, recent form, goals scored and conceded, and a home boost for the hosts, usa, canada and mexico. - The model for each match it predicts the expected goals for both sides, then turns that into win, draw and loss probabilities plus a likely scoreline. that's what feeds the simulation. - The tournament engine this was the hard part. the 2026 world cup is brand new, 48 teams, 12 groups, a round of 32 that's never existed before, and 8 "best third-placed" teams that slot into the bracket by a fixed fifa table. even the group tiebreakers changed this year, head to head now counts before goal difference. get any of it wrong and the whole bracket falls apart, so i built it carefully and tested the format until it was exact, then wrapped it in a simulation loop that plays the tournament out tens of thousands of times. and the last piece, the live part. as real results come in, they get locked, and only the unplayed games get re-simulated. that's what makes it a living model instead of a one-time prediction. all of it outputs to a clean dashboard you can actually read and screenshot.. right now, before kickoff, it already has a clear favorite to lift the trophy.. 👀 btw who's your pick to win the 2026 world cup?

Axel Bitblaze 🪓

49,714 просмотров • 1 месяц назад

🚨NODE SALE Alert!🚨 If you are looking into exploring #Nodes, but finding it difficult to get started, I recommend exploring PlayFi - (Follow @PlayFiAI our new handle)! It's super easy to setup and they are about to have an epic public Node License Sale! 💥 Their Launch partners are great! Including Polygon | POL, Aethir, Nim.Trade, ZKsync, Matter Labs, and more! This is your chance to be part of something HUGE - where #AI supercharges content creation across gaming, streaming, and everything in between! 🤯 🔥 Why You NEED to Jump In 👇👇: PlayFi's AI Magic: Imagine turning every like, comment, and view into instant, actionable data! 📈 From electrifying live streams to giving game studios insane insights without lifting a finger, PlayFi is changing the game. $PLAY Token Bonanza: Early birds get the worm... or in this case, a 3x airdrop bonus of $PLAY tokens! 🤑 Easy-Peasy Nodes: No fancy gear needed! Run PlayFi nodes right alongside your current setup without breaking a sweat. It's your VIP pass to a massive, decentralized network that turns endless content into valuable, on-chain data. 🤯 Limited-Time Gold Rush: Only 10,000 licenses up for grabs! Secure yours and start earning those sweet, sweet $PLAY token rewards at mainnet launch. The more nodes you own, the bigger your potential payout! 🤑 Tech Meets Opportunity: We're talking AI, decentralized networks, and the creator economy all in one place. PlayFi nodes are the backbone of this revolution, ensuring a massive, global network that rewards everyone involved. 🌐 ⏳ Don't Miss Out! PlayFi is shaping the future of Web3, and you can be a part of it! 💪 Join the Discord for Whitelists: #PlayFi #Web3Gaming #P2E #DATA #Node #NodeSale Disclaimer: For full transparency, I am serving #PlayFi as a KOL, and I want to emphasize that I am extremely selective when it comes to the projects I choose to partner with. Only those that meet my strict criteria and align with my values will have the privilege of collaborating with me. This is just my review and not a financial advice, please DYOR

LadyTraderRa

50,474 просмотров • 2 лет назад

A fired Jane Street quant walked out with 10 years of private BTC trading data. Turned it into $1.5M. He did not build a bot. He built a simulator that runs every move Bitcoin can make before it makes one. I found his wallet. Been copying him for a week. PnL prints like clockwork. Here is what he actually built. A swarm of agents feeds 10 years of stolen tick data into MiroFish. A god-tier agentic simulator. It does not forecast the next candle. It spins up a virtual market and plays Bitcoin forward through thousands of scenarios at once. Six agents each validate their own call. A trade only fires when they converge. They collect data 24/7, rerun the sim, and remember every pattern, every reaction, every signal they have ever seen. He does not predict the future. The math already knows it. He just reads the numbers and takes the money. Here is the part firms do not want public: MiroFish just broke algo trading. The desks are quietly building their own simulators right now. The window where one solo wallet can run this is still open. Barely. I rebuilt his approach using Claude. One prompt. Fed it the same framework. Let it run. The agent monitors his wallet 24/7. Copies every position in real-time. No delay. No guessing. Just mirror and profit. You only need Claude + device + 1 hour to deploy. Giving this free for 24 hours. To get it: 1. Comment the word "QUANT" 2. Like and retweet this post 3. Follow me Himanshu Kumar so I can DM you Save this post. Build the copytrading system this week. Start with $200. Scale on evidence.

Himanshu Kumar

62,945 просмотров • 1 месяц назад

[CLIP] by Hand ✍️ The CLIP (Contrastive Language–Image Pre-training) model, a groundbreaking work by OpenAI, redefines the intersection of computer vision and natural language processing. It is the basis of all the multi-modal foundation models we see today. How does CLIP work? Goal: 🟨 Learn a shared embedding space for text and image [1] Given ↳ A mini batch of 3 text-image pairs ↳ OpenAI used 400 million text-image pairs to train its original CLIP model. Process 1st pair: "big table" [2] 🟪 Text → 2 Vectors (3D) ↳ Look up word embedding vectors using word2vec. [3] 🟩 Image → 2 Vectors (4D) ↳ Divide the image into two patches. ↳ Flatten each patch [4] Process other pairs ↳ Repeat [2]-[3] [5] 🟪 Text Encoder & 🟩 Image Encoder ↳ Encode input vectors into feature vectors ↳ Here, both encoders are simple one layer perceptron (linear + ReLU) ↳ In practice, the encoders are usually transformer models. [6] 🟪 🟩 Mean Pooling: 2 → 1 vector ↳ Average 2 feature vectors into a single vector by averaging across the columns ↳ The goal is to have one vector to represent each image or text [7] 🟪 🟩 -> 🟨 Projection ↳ Note that the text and image feature vectors from the encoders have different dimensions (3D vs. 4D). ↳ Use a linear layer to project image and text vectors to a 2D shared embedding space. 🏋️ Contrastive Pre-training 🏋️ [8] Prepare for MatMul ↳ Copy text vectors (T1,T2,T3) ↳ Copy the transpose of image vectors (I1,I2,I3) ↳ They are all in the 2D shared embedding space. [9] 🟦 MatMul ↳ Multiply T and I matrices. ↳ This is equivalent to taking dot product between every pair of image and text vectors. ↳ The purpose is to use dot product to estimate the similarity between a pair of image-text. [10] 🟦 Softmax: e^x ↳ Raise e to the power of the number in each cell ↳ To simplify hand calculation, we approximate e^□ with 3^□. [11] 🟦 Softmax: ∑ ↳ Sum each row for 🟩 image→🟪 text ↳ Sum each column for 🟪 text→ 🟩 image [12] 🟦 Softmax: 1 / sum ↳ Divide each element by the column sum to obtain a similarity matrix for 🟪 text→🟩 image ↳ Divide each element by the row sum to obtain a similarity matrix for 🟩 image→🟪 text [13] 🟥 Loss Gradients ↳ The "Targets" for the similarity matrices are Identity Matrices. ↳ Why? If I and T come from the same pair (i=j), we want the highest value, which is 1, and 0 otherwise. ↳ Apply the simple equation of [Similarity - Target] to compute gradients of for both directions. ↳ Why so simple? Because when Softmax and Cross-Entropy Loss are used together, the math magically works out that way. ↳ These gradients kick off the backpropagation process to update weights and biases of the encoders and projection layers (red borders).

Tom Yeh

67,834 просмотров • 2 лет назад

EA Sports CFB25 released their Sights & Sounds Deep Dive today and I am DISAPPOINTED! The main theme they use in the video is "Every Team Is Somebody's Favorite" and if you are going to make that claim, then I will hold you to it. My favorite school is the one I attended, Baylor University, and it has been clipped and used in both CFB25 videos with a GLARING mistake to anyone who went to Baylor. The Baylor Line is missing! Every year the freshman class gets a Baylor Line Jersey at the Freshman Line Camp before school starts. They spend a week learning about the school, each other, and our traditions which all leads up to getting a gold Line Jersey with your graduation year as the number and your last name or nickname on the back. Once football starts the Freshman show up hours early in their jersey to each home game and wait in the brutal Texas heat to be in the Baylor Line. Right before the game starts the freshman class runs onto the field in a frenzie to get to the other side of the field and form the tunnel that the team will run through. This is a tradition that is so crazy and dangerous that the NCAA outlawed it and grandfathered Baylor in as the one school allowed. The last home game of the season the graduating senior class gets to join the Freshman and run the line one last time in a double sized mosh pit to send them off how they entered. This tradition is near and dear to Baylor student's hearts. I remember my first time running with my roommate and best friend who both were in my wedding years later. I couldn't wait to watch my brother run his first line when he got here, then getting to run my last line at the last home game as a senior with my brother who was a freshman. I still take a video at every home opener to compare the sizes of the freshman classes, and because it gives me nostalgia and is the thing that makes me really feel that college football has started. So, with all of that, I am calling on College Football 27 and EA SPORTS to please add the biggest Baylor football tradition to the game. My favorite game of all time is NCAA 14, and I am literally taking off work July 19th (my birthday as well if that helps) to play this game, I just want it to be perfect. 🙏 #SicEm #Baylor #CFB25

Ace: United Football Media VP

66,394 просмотров • 2 лет назад

Mark Zuckerberg just gave away the real business model of the next decade. It isn’t computing. It’s loneliness. Zuckerberg: “The average person would like to have 10 friends, and they have two, right? Or three. And there’s just more demand to socialize than what people are able to do given the current construct.” The CEO of the largest social network ever built just told you the construct is broken. He built half of it. Now he’s selling the repair. Every platform shift in modern history has quietly repriced a human need. The phone repriced attention. The feed repriced validation. The glasses reprice presence itself. Zuckerberg: “This is probably going to be the next major platform after phones.” Ten years of miniaturization. Full holograms. Wide field of view. Not a headset. Glasses. Something you wear the way you wear your face. Every winning platform disappeared into daily life. The phone won because it fit in your pocket. Glasses win if they fit into who you are. Then comes the layer nobody else has. An AI that sees what you see. Hears what you hear. Not a map overlay. Not a floating notification. A second mind sitting behind your eyes. Building context around every person in front of you, every room you walk into, every silence you’d otherwise sit in alone. Zuckerberg: “It’s this feeling of presence, and this capability of really personalized intelligence that can help you.” Presence and intelligence. The two things human beings have always needed from each other and could never reliably provide. That’s the whole pitch. That’s the whole company. The loneliness data has been stacking for thirty years. People are more connected and more isolated at the same time. That isn’t a contradiction. That’s what connection without presence produces. You can text someone every day and still feel like they’re gone. The phone solved distance. It didn’t solve absence. Video calls solved visibility. They didn’t solve the room. There’s a gap between being reachable and being there. Every platform of the last twenty years has lived inside that gap and called it enough. Zuckerberg is the first person with the capital, the hardware, and the AI to close it. Or to simulate closing it so convincingly that nobody checks. That’s the part that should keep you up. Because if a pair of glasses can make an empty room feel full, most people won’t go looking for the real thing. They’ll just put the glasses back on. The feed taught a generation to trade community for dopamine. The glasses will teach the next one to stop noticing the difference.

Dustin

20,827 просмотров • 3 месяцев назад

Every major platform in history has run the same play. You’re about to watch it happen again. Jason Calacanis just went on record. He wants it clipped. He wants it shared. Calacanis: “If I was a developer of any kind, I would never work with Sam Altman and OpenAI.” This isn’t pessimism. It’s pattern recognition. And the pattern has a 40 year track record. Open. Invite. Reward. Study. Absorb. Eliminate. Microsoft let developers build Lotus 1-2-3. Then built Excel. Let them build WordPerfect. Then built Word. Flew them to conferences. Handed out awards. Studied everything. Then eliminated them. Zuckerberg ran the exact same play at Facebook. Zynga built billions in value on their platform. Then Zuckerberg shifted them without blinking. Calacanis: “Sam Altman comes from the Zuckerberg school of business. Give people access to your tools, study them, and like the Borg, steal every innovation they have.” This is how platforms grow. They don’t innovate at the edges. They let the ecosystem do it for them. Startups take the risk. Startups find the market. Startups prove the concept. Then the platform ships it natively and calls it a feature. Altman isn’t selling you compute. He’s selling you a front row seat to your own disruption. Calacanis: “This is a warning for anybody dumb enough to use Sam Altman’s OpenAI API. They are studying you.” OpenAI has the legal right to study how you use their API. You agreed to it. It’s in the terms. Every gap you find, you’re finding it for them first. Every dollar you make signals exactly where he should build next. We are at the exact same moment in AI that we were in the early internet. Developers flooded onto platforms. Built incredible things. Created real value. And handed the leverage to whoever owned the infrastructure beneath them. The AI gold rush feels different because the tools are more powerful. It isn’t different. You are not a founder. You are unpaid R&D. The builders who win the next decade won’t be the ones who used the best tools. They’ll be the ones who owned something the tools couldn’t absorb. Proprietary data. Distribution. A brand. A moat. History doesn’t warn you before it repeats. It just repeats. Thousands of developers are walking straight into this right now convinced they’re different. They’re not. Do not build your business on OpenAI. Build something he has to acquire or destroy.

Dustin

248,588 просмотров • 4 месяцев назад

THIS GUY CONNECTED HIS AI AGENTS TO HIS OBSIDIAN AND BUILT A BRAIN THAT LEARNS ON ITS OWN. HERE'S HOW TO BUILD IT Obsidian is just markdown files sitting in a folder. That turns out to be the perfect memory for an AI agent, because an agent can read and write those files directly. He wired his agents into the vault so they pull context from it, do the work, and write what they learned back. The notes aren't the point. The loop is, and it gets sharper every cycle How to build it: 1. Point an agent at your vault. The fastest way, no plugins, no API keys: open a terminal and run npx obsidian-mcp /path/to/your/vault. That exposes your Obsidian folder to Claude as a tool it can read, search, and write to. Add it to your Claude Code or Cowork config and restart 2. Confirm it can see the brain. Ask it: "list the notes in my vault and summarize what's in them." If it reads them back, the connection is live. Now it starts every task with everything the vault already holds instead of from zero 3. Give each agent one job and a write-back rule. Tell it: "research this, then save what you found as a new note in /brain with links to related notes." One agent researches, one summarizes, one plans. Each writes its output back into the vault 4. Close the loop. Add one line to every agent's instructions: "read /brain before starting, write your result back when done." Now each task leaves the vault richer, and the next run reads that before it works. It compounds instead of resetting 5. You only steer. Review what the brain produces, point it at the next thing. The agents handle the reading, writing, and connecting The edge isn't better notes. It's a brain that feeds itself, so the work gets sharper every cycle instead of starting over Bookmark this

Yarchi

58,186 просмотров • 1 месяц назад

CSS Trick 🧲 You can create magnetic links with the power of custom properties and some JavaScript 💪 a { translate: calc(clamp(-1, var(--x), 1) * var(--pad-x)) ...; transition: translate var(--s, 1s) var(--ease, var(--elastic)); } a:hover { --s: 0s; } The trick here is to pad out the list items wrapping your links and use that as a translation limit 🛑 Start by using some JavaScript to calculate a value between -1 and 1 for both the x/y axis on pointermove for each list item, not the link! 🔗 If your pointer was at the center of the item, you'd get [0,0]. If it was in the top right, you'd get [1,-1] ☝️ It's worth checking out the JavaScript snippet to see how the mapping function works. Essentially, you create a function that when given a value between two bounds, will give you a mapped value back 🤙 const mapX = mapRange( item.offsetWidth * -0.5, item.offsetWidth * 0.5, 1, -1 ) Then, on pointermove, you plug the pointer position in to get the value back out and pass that into your CSS const x = mapX(item.centerX - event.x) document​.documentElement​.style.setProperty(--x, x) When the pointer leaves the list item, you make sure to reset these values back to 0 ✨ Once CSS has your values, it's the trick of updating the translation of each part You know that in each axis, you only want to translate the link by the padding amount li a { translate: calc(clamp(-1, var(--x), 1) * var(--pad-x)) calc(clamp(-1, var(--y), 1) * var(--pad-y)); transition: translate var(--speed, 1s) var(--ease, var(--elastic)); } This will translate the link within the list item by the desired amount. The cool part here is that you can set an offset for the text inside the link and have that move at a different rate ⭐️ By only updating the --pad-x/y custom properties for the inside the link, you can control how much it moves nav a span { --pad-x: 0.25rem; --pad-y: 0.25rem; } And the last piece, how do you update the behavior for transition speeds? And so it springs back like that? Again, use custom properties ✨ a:hover { --s: 0s; } a { transition: translate var(--s, 1s) var(--ease, var(--elastic)); } By default, a link will use --elastic easing via linear() and have a transition-duration of 1s. When a link is hovered that speed becomes 0s because you want the link to magnetise to your pointer. How about that little gap between when your pointer enters the item but hasn't hovered the link? Set a different transition so it transitions to being hovered 🫶 nav li:hover a { --ease: ease-out; --speed: 0.1s; } That's kinda it! 🙌 Use JavaScript (~40 loc) to get the information and then let CSS do all the lifting for you 💪 Any questions or suggestions, let me know 🙏 If you want a walkthrough video, also let me know please 🙏 CodePen.IO link below 👇

jhey ʕ•ᴥ•ʔ

164,863 просмотров • 2 лет назад

Musk says the simulation hypothesis is almost certainly true since 2016. And this is also why he renamed Twitter to X... Elon founded xAI on the mission of understanding the universe. He renamed Twitter to X in 2023, picking the only letter without an opposite. The thesis traces back to a Darwinian thought experiment. "Like in this version of reality, in this layer of reality, if a simulation is going in a boring direction, we stop spending effort on it." Boring simulations got cancelled. Interesting ones got renewed. Then, he said, the corollary appeared. "They particularly seem to like interesting outcomes that are ironic." The simulation, in Musk's frame, didn't just keep stories alive — it actively preferred the ones that flipped on themselves, the ones where the noun and the truth ran in opposite directions. He pointed at the names of AI companies and read them off one by one. - OpenAI is closed. - Midjourney is not mid. - Stability AI is unstable. - Anthropic is misanthropic. Four labs. Four nouns. Four ironic reversals. Each picked a name with a clean flip available. The simulation took every one. Musk, who had named X for that exact reason, dodged the trick. "It's a name that you can't invert, really. It's hard to say, what is the ironic version?" He called it an irony shield. No opposite. No mirror. No clean flip. Musk, on the bet underneath the joke: "It's, I think, a largely irony-proof name. By design." P.S. I made a playbook breaking down 100+ most powerful decision making mental models used by history's greatest thinkers. 5,000+ downloads. 113 five-star reviews. Grab a free copy here: If you're new here, follow GeniusThinking for content on the greatest minds in economics, psychology, and history. — Elon Musk ( Elon Musk ), CEO of Tesla and SpaceX, on Dwarkesh Patel's ( Dwarkesh Patel ) podcast

GeniusThinking

20,844 просмотров • 1 месяц назад

What are Physics-Informed Neural Networks (PINNs) Physics-Informed Neural Networks (PINNs) are neural nets trained to satisfy a differential equation. The trick is simple. You bake the PDE residual straight into the loss. They came out of a very practical pain point. Classical PDE pipelines can be amazing, but they often demand a lot of setup work. Meshes. Stencils. Stability tuning. And once you build a solver, it’s usually tied to one geometry and one discretization choice. A PINN flips the workflow. You represent the solution itself as a smooth function uᵩ(x,t) and you enforce the physics wherever you choose to sample the domain. Most people first meet PINNs in the least helpful way. A pretty solution surface, almost no clarity on what was enforced to make it appear. In this series we keep the enforcement visible. We pick a PDE, represent the unknown solution as a flexible function, measure how badly that function violates the equation across the domain, and train it to reduce that mismatch at the points we sample. A normal neural net learns from labels. You give it inputs and target outputs. A PINN learns from an equation. You give it inputs (x,t), and it gets penalized whenever its output fails the PDE. Smaller mismatch means smaller loss. Bigger mismatch means bigger loss. That’s all “punish” and “reward” mean here. The network isn’t replacing physics. It’s just a flexible function that we force to obey the same calculus you’d demand from any candidate solution. The math breakdown: We start with a PDE on a domain Ω. Write it as uₜ(x,t) + N(u(x,t), uₓ(x,t), uₓₓ(x,t), …) = 0 for (x,t) in Ω A PINN replaces the unknown u with a neural network output uᵩ(x,t) Now define the physics residual by plugging uᵩ into the PDE rᵩ(x,t) = ∂uᵩ/∂t + N(uᵩ, ∂uᵩ/∂x, ∂²uᵩ/∂x², …) If uᵩ were an exact solution, we’d have rᵩ(x,t) = 0 everywhere. We may also have data points (xᵢ,tᵢ,uᵢ) from measurements or from an initial condition. The training objective is a weighted sum of squared errors L(ᵩ) = L_data(ᵩ) + λ L_phys(ᵩ) + L_bc/ic(ᵩ) with L_data(ᵩ) = meanᵢ |uᵩ(xᵢ,tᵢ) − uᵢ|² L_phys(ᵩ) = meanⱼ |rᵩ(xⱼ,tⱼ)|² where (xⱼ,tⱼ) are collocation points in Ω L_bc/ic(ᵩ) = penalties enforcing boundary conditions and initial conditions The key technical step is how we get the derivatives inside rᵩ. We don’t approximate them with finite differences. We compute them with automatic differentiation: ∂uᵩ/∂t, ∂uᵩ/∂x, ∂²uᵩ/∂x², … Then we differentiate the total loss L(ᵩ) with respect to ᵩ and train with gradient descent. That’s the whole idea. Learn a function, but make the PDE part of the loss, so the network is trained to be a solution, not just a curve-fitter. In the render, the main 3D surface is the network’s current guess uᵩ(x,t), drawn as a living sheet over the (x,t) plane. Hovering above is the neural scaffold, a visible graph of feature nodes and connections. The bright tension threads are the physics residual rᵩ(x,t). Each thread tethers a collocation bead on the sheet up to the scaffold, and it thickens and brightens exactly where |rᵩ| is large, with color showing the sign. As training runs, those threads go slack across the domain, not because we hid the error, but because the network has actually been pushed toward rᵩ(x,t) ≈ 0. #PINNs #ScientificMachineLearning #PDE #DifferentialEquations #Optimization #MachineLearning #AppliedMath #ComputationalPhysics

Mathelirium

44,712 просмотров • 5 месяцев назад

How to build a 1-person AI company that: - Runs locally - 100% open-source - No human employees, all agents - Real-time collaboration via email Multi-agent orchestration is not new. Plenty of frameworks already let agents hand off tasks, run in parallel, and talk to each other. So the interesting question is not whether agents can collaborate. It is what structure you use to make them collaborate. The common approach is to wire a graph of nodes and edges and reason about the plumbing yourself. It works, but you are learning a new abstraction just to describe who does what. There is a coordination structure we have trusted for a hundred years already: an organization. Every company runs the same way. People have roles, roles have reporting lines, and work moves up and down that chart without anyone relaying each message by hand. Map that onto agents and the whole thing gets intuitive. You lay out an org chart, each agent fills one role, you talk to the person at the top, and the org sorts out the work between them. You already know how a company works, so you already know how to run one here. There is no new abstraction to learn. That is exactly what Alook does. Each agent is a live Claude Code or OpenCode session with a defined role, a reporting line, and its own email inbox. The agents coordinate over email, the same way a team would. And it all runs locally through a runtime on your own machine, so nothing leaves your setup. You bring your own agent too. Claude Code and Codex both work, and if you would rather stay fully open source and local, OpenCode works the same way. To show how this feels in practice, I set up three agents as a small sales team. Vi is the one I talk to. I hand Vi a goal, and Vi routes the work down the chart. Neile runs prospect research. Vi passes the target criteria, and Neile reports back a ranked list of names, roles, and companies, each with a suggested angle and a confidence score. Lliane runs outreach. Vi hands over the messaging angle and follow-up cadence, and Lliane reports back on emails sent, responses received, and any deal that needs escalation. I never relay a message between them. Neile and Lliane report to Vi, and Vi updates me in one place. The whole thing is open source and self-hosted, so it runs on your machine with your own agents. Give the repo a star if you want to follow where it goes: I also wrote a full walkthrough on building your own AI company with it, from a blank org chart to a running job. The article is quoted below. Cheers! :)

Akshay 🚀

166,723 просмотров • 14 дней назад

The last 20 Moni Wizards NFTs. WL Application is live. The Wizards collection is the highest access to everything Moni. Apply to get whitelisted: 20 seats left. After these, primary closes for good and the only way in is the secondary market. Funds from this sale go straight back into the build: more research, more Smarts coverage, more API surface, more community infrastructure. What’s inside? Full Moni platform access. The off-chain side of our stack and how you find alpha before it's alpha. Discover tracks where smart money is already looking: VCs, founders, alpha hunters, and influencers, in real time. You see the projects they're moving toward one to three weeks before they trend on the main timeline. Behind it: 15,000 hand-curated Smarts and millions of smart mentions collected over five years. Wizards get every filter, every list, every signal we expose internally. Daily and weekly Alpha Reports. Written by the Moni Research team, not aggregated from elsewhere. Our analysts hand-pick the best of what the engine surfaces each day and each week, then write up what the Smarts are watching, why it matters, and where the narrative is forming. Reports usually land in the Wizards Discord before any public version exists. Moni Social API. New for Wizards. The same API we give access to launchpads, exchanges, VCs, and analytical platforms. 30+ data types, 100,000+ tracked events per day, 5,000+ projects under coverage, Smart Mindshare endpoints, real-time and historical social signals. Think of it as the social intelligence layer you'd otherwise have to build yourself. Wizards get a data they can plug into their own tools, alert systems, or agents. Deep Research. One project at a time, long form, the same work we run inside Moni Research. Each one takes the team about a week. Thesis, ecosystem map, mechanism, risks, Smart positioning, what to watch for. Structured the way an analyst would actually use it, not a Twitter thread version of it. Private Wizards-only chats and community. The room where the 180 holders and the private Moni community already share early calls, deal flow, research drafts, and "look at this" moments before anything goes public. Most of the real work happens here, not in the Twitter version of Moni. Alpha bots and curated Smarts lists. The bots that track Smart movements in real time. The Twitter lists we don't share publicly because they are the actual edge. Wizards get both. Early access to every new Moni product. Whatever ships next, Wizards see it first. Sometimes the prototype, sometimes weeks before public release. The feedback loop runs straight back into the team. Partnership raffles and early-stage deal flow. Pre-seed and seed allocations from partner projects. Raffles, intros, primary access to things that come through the table and never leave it. Custom hand-drawn PFP. Designed by our artist around your call. Yours forever. How to buy. Fill the form. The team reads every answer. If your fit makes sense for what this circle is, we'll come back to you with everything you need to complete the purchase. Moni Wizards Opensea Page:

Moni 🧙‍♂️

48,824 просмотров • 1 месяц назад

If you take a movement to unpack this visualization... You'll see how it simply breaks down how reality works. At frame 0 you have a static image. Everything is one, this is the monad. As soon as you hit frame 1 there is movement, there is change. Now you have two states, moving, or static. When Nikola Tesla says you can explain everything in frequency and vibration. The difference between frame 0 and 1, is vibration. The difference between movement and no movement. This is like binary logic we use in code which is made up of 0's and 1's. After frame 1, is when frequency emerges. Because the difference between frame 1 and all frames after is about how fast is the vibration/movement happening. If we skip forward to frame 50... You have a shape that begins to emerge, this is the 8 dots, then the 6 dots. Notice how unstable it is, it's 8 dots, then 6, then a moment with 4 in a rectangle These shapes are emergent properties. The first two emergent properties after the monad was vibration and frequency. Next comes shape (i'm skipping over rotation and direction). These shapes of dots can only exist when you have frequency and rotation. This frequency and rotation creates vortex energy. It's the same energy that things like your chakras use. Or the same energy we harness in devices like engines, airplanes, fans, blenders, hard drives, etc. It's also the same vortex energy you'll see in a tornado or hurricane. They are powered because they harness rotation and frequency(change/movement). Going back to the video, notice that it is inside the entire shape, the internal structure is manifesting before the external structure does. Then around frame 60 the hexagon of circles begins to rotate. First it was the two dots that moved and now it's a complex shape that is coming to life. This is a higher dimension (or lower depending on how you look at it) manifesting into existence. The internal state is "awakening" and experiencing it's own change like what happened to the whole shape in the first frames. But it is unstable. That's why it doesn't persist for long. If you think of the 8 dots being the octahedron, they map to the element of air. Air is in the material world, but it is not something you can see. The brief moments the 8 dots are visible is similar to that effect. They are only experienceable between a small frequency band of frames. Now here's where stability begins to appear in the internal structure. This is when the 4 dots appear. You'll see that the four dots, the square, is stable and persists the most visibly for the most amount of frames. The square represents earth in the platonic solids to elements mapping. Earth, is material, it's stable. We build our buildings in squares and with earth because it is a solid shape to build on. This visualization shows you why. Across different vibrations (frame rates) it can self sustain. Between this point and frame 180, you'll see a new emergent property. Which is depth. A new dimension is introduced at around frame 90 but really becomes visible at around frame 110. You can see a foreground and background. There is the shape of the dots, but also the triskellion wave happening in the background. Let's jump to frame 180. Notice how it is the same as frame 0 except... It's flashing. If you were paying attention, you'll notice you could see flashing at frame 90 and frame 120, but they didn't persist for long. At around 150 it started to reach stability and 180 it was solidified. Between frames 150 and 180 there is flashing, but the image is still moving. Only for a brief moment at frame 180 is the movement frozen and the flashing persists. Think of that like your computer screen. It's what your screen is doing right now as you read this. Even tho the text isn't moving, the screen is flashing at 60 or 120hz. The images appear on your device because this flashing brings things to life. The entire material realm and your physical body right now, is doing the same thing. While you look solid... You're flashing in and out of existence at very high frequencies. You can look at frame 180 and frame 0 as the same essence but it is the mid point between an octave change. In the video, the ying and yang was vertical, now it is horizontal. This is a phase shift. If you notice at exactly frame 180, the rotation freezes and then the direction of rotation changes. The process then repeats all the way to frame 360 but in the opposite sequence. Once it reaches frame 360, that is an octave change and the process repeats. Each time you repeat the process is a layering of the same patterns into higher octaves. This is the same as your chakras or how other things work. They are like russian nesting dolls where every octave is layering onto the next. The complexity of your body is a layering of basic principles that emerged in earlier stages. Your organs are built of systems that are built with cells that are built with proteins that are built with atoms and so on. The atoms, work just like your body at a basic level. Your body works just like the galaxies. At each level you'll have the same pattern. This is where the idea "As Above, So Below" from. The monad, splits in two, and so on and so on. One cell, splits into two through mitosis in the same logic. We could spend all day going through examples of how biology, physics, spirituality, etc. aren't really different. They are just categories that we use to dissect these frequencies and octaves of energy but they only start paying attention within the confines of materialism. The problem is, none of the sciences start at the root patterns. Because that is reserved for religion or spirituality. It's too woo-woo to take seriously so it's dismissed. And because of that... We're left ignorant on the simple explanations for how things work. Now you need some expert with tools you don't have access to in order to explain things. When you could be understanding them without the tools. The Yin and Yang symbol in this video is 3,000 years old. It's simple. Yet I just showed you how it explains deeper layers of reality.

Jamal ☯︎ 🔆🧘🏽🧠

13,149 просмотров • 3 месяцев назад

Skills are the quickest way to 10x the quality and consistency of what you get from Claude Code. And you don't need to be a developer to use them. Anthropic just published how they use hundreds of skills internally every day. Most skill tutorials are made for developers — if you're in marketing, sales, content ops, or GTM, you probably watched those and moved on. But skills are just as important for non-developers. A skill is just a reusable prompt with clear instructions for a specific task. Instead of prompting Claude the same way over and over, you build it once and invoke it every time. I have a skill for writing on LinkedIn. A different one for YouTube outlines. Another for X. Each platform has different rules, different voice, different structure — so each one gets its own skill. If you're doing something repeatedly, it's time to make a skill. The biggest mistake most people make: building skills as a single .md file. A single file dumps everything into context whether Claude needs it or not. Wastes tokens. Gets worse results. Skills should be folders. Here's the structure that works: skill.md — the orchestrator. Tells Claude which files to read and when. It doesn't contain rules itself — it's the playbook. instructions/ — separate files for voice, structure, scope. Claude only loads the one it needs for the current step. examples/ — good AND bad. Good examples show what success looks like. Bad examples show patterns to avoid — AI writing tells, weak hooks, generic CTAs. Most people skip bad examples. Don't. eval/ — a checklist that scores every output before you see it. "Does it have a clear hook?" "Is it free of AI buzzwords?" Pass or fail on each item. templates/ — output formatting so you get consistent structure every time. The three types of skills that matter most for non-developers: 1. Business automation. Writing a newsletter. Checking reports and drafting follow-ups. Running programmatic ad campaigns. Any workflow you repeat — build a skill for it. 2. Content templates. Landing page copy, meta ads, email sequences, SEO briefs. Each one has specific requirements. Each one gets its own skill. 3. Thinking partners. This is the one people miss. Skills don't have to produce output. They can help you think — an advisory board that reviews your work from your ICP's perspective, a coach that pressure-tests your strategy, an ideation partner that researches competitors before suggesting your next move. If you already have skills as .md files, here's the exact prompt to restructure them in the Anthropic approved format: "I want to restructure my Claude Code skill file. Right now my skill is a single .md file and I want to break it into a folder system following Anthropic's best practices. Read my current skill file, then restructure it into a folder with: a skill.md orchestrator, an instructions/ folder with separate files for each concern (voice, structure, scope), an examples/ folder with good and bad examples, an eval/ folder with a quality checklist, and a templates/ folder for output formatting. Keep all my existing rules and intent — just reorganize them into the modular structure." Paste that into Claude Code pointed at the folder where your skill lives. It handles the rest. A few caveats: 1. Don't add too many skills. Every skill adds context Claude has to process. 50 skills loaded means everything slows down. Start with 3-5 covering your most repeated workflows. 2. Vet skills before downloading. If you grab a skill from the internet, read what's inside first. Skills can include shell commands and scripts. Check what you're running. 3. Share what works. Build a skill that performs well, put it in a shared GitHub repo. Your marketing org gets shared skills for copywriting, SEO, ad copy — new hires invoke the skill instead of learning every playbook from scratch. Onboarding time drops dramatically. 4. Keep your skills updated. When you see output you love, add it as a good example. When you see a pattern you hate, add it as a bad example. The skill gets sharper every time. I made a full video walking through all of this — including a live build of two skills from scratch (no terminal, no code), the exact prompt I use to restructure old skills, and 5 pro tips from Anthropic's internal playbook. Share this with your non-developer friends that want to do more with AI; or bookmark it to come back to at a later time.

JJ Englert

29,322 просмотров • 3 месяцев назад