Block Diffusion: Interpolating Autoregressive and Diffusion Language Models
https://m-arriola.com/bd3lms/
#ycombinator #block_diffusion #discrete #masked #diffusion #language_models #BD3_LM #BD3_LMs
#discrete
Mean: Share and Balance allows students to explore four different conceptualizations of #mean, in four different contexts. Create, predict and modify the mean of a data set in #continuous and #discrete contexts. https://phet.colorado.edu/en/simulations/mean-share-and-balance/ #AvailableInPhETStudio #CentralTendency
@dawisco no there has been a ton of work already on it, no tech debt issue more of a policy/admin glitch. it is a good idea but not something to get on coercion train about, it is more about privacy, surveillance capitalism, morals and morays. we can agree options would be nice #discrete indiscretions
The #volute is the most striking element of the #IonicOrder, even more than the #scrolls, for there would be no scrolls without volutes.
The #IonicVolute is constructed as a spiral, of which there's a bewildering array of types that have fascinated artists, philosophers, and mathematicians alike for millennia. Most #CAD tools have a built-in primitive for spirals, but you will only waste your time with them because they strive for #continuous curvature changes, when only a #discrete spiral made from circular arcs will work in this design. I spent years trying different kinds and learned a lot in the process.
Even within the family of discrete spirals, there's only one that fits. Dürer's approximation of #logarithmicSpirals with 90° arcs comes close, but still doesn't fit. The only one that works is contrived to fit the measurements of the #IonicCapital, and it's not a general spiral. It's specifically designed for 3 turns, and you can only proceed in one direction — toward the eye. You cannot start at the eye and diverge outward.
The process is not complicated. I purposely left out the measurements in the sketch because they cluttered the area near the eye, but I describe them here.
When µ = 144, you will need to start with a square that is exactly 1 part (8 units) wide and divide it into smaller portions — initially 6, but eventually 24. This is the first time you might regret choosing µ = 144. If you had chosen a value 3x larger, then one part would be 24 units instead of 8. That would certainly have made understanding the volute a little easier but the other measurements would also be 3x and too unwieldy to work with.
There is a happy compromise: Temporarily scale everything up by 3x just for the volute, and once it has been constructed, scale it down to 1/3 to fit with the rest of the design.
So, the first step is to divide the square into a 24x24 grid. Then make 3 concentric squares 4 units apart and mark their ends with points 1 through 12 as shown here.
The #IonicVolute is constructed as a spiral, of which there's a bewildering array of types that have fascinated artists, philosophers, and mathematicians alike for millennia. Most #CAD tools have a built-in primitive for spirals, but you will only waste your time with them because they strive for #continuous curvature changes, when only a #discrete spiral made from circular arcs will work in this design. I spent years trying different kinds and learned a lot in the process.
Even within the family of discrete spirals, there's only one that fits. Dürer's approximation of #logarithmicSpirals with 90° arcs comes close, but still doesn't fit. The only one that works is contrived to fit the measurements of the #IonicCapital, and it's not a general spiral. It's specifically designed for 3 turns, and you can only proceed in one direction — toward the eye. You cannot start at the eye and diverge outward.
The process is not complicated. I purposely left out the measurements in the sketch because they cluttered the area near the eye, but I describe them here.
When µ = 144, you will need to start with a square that is exactly 1 part (8 units) wide and divide it into smaller portions — initially 6, but eventually 24. This is the first time you might regret choosing µ = 144. If you had chosen a value 3x larger, then one part would be 24 units instead of 8. That would certainly have made understanding the volute a little easier but the other measurements would also be 3x and too unwieldy to work with.
There is a happy compromise: Temporarily scale everything up by 3x just for the volute, and once it has been constructed, scale it down to 1/3 to fit with the rest of the design.
So, the first step is to divide the square into a 24x24 grid. Then make 3 concentric squares 4 units apart and mark their ends with points 1 through 12 as shown here.
The #Capital is the last essential component of the complete #IonicOrder. The column #flutes remain, but they are #decorativeElements, and I will cover them later when I cover the decorative elements of the capital like the #EggsAndDarts motif on the #ovolo and the #3StrandBraid on the ribbon or belt around the middle of the smooth #scrolls.
The Ionic capital is complex, but not unapproachable. We will systematically construct everything in this draft rendering using just straight lines and arcs as promised in https://pixelfed.social/p/Splines/789956327130679640, with the exception of the #cymaReversa near the top and the 3-strand braid on the ribbon.
In this rendering, the cyma reversa near the top is made using a flattened half-turn of a #helix, but it can also be constructed using elliptical arcs as I described in earlier posts.
The braid is a #periodic shape with infinite variety and is also based on a helix. You can vary the number of strands, their thickness, pitch, and so on, none of which are essential to the Ionic Order itself. They're only a jumping point for further exploration.
The eggs in the 'eggs and darts' motif can have different shapes. They can be convex like real eggs or concave as shown here, but the top is almost always sliced off. The total depth of the convex or concave shapes can vary, but only within a range of 1 part, or 8 units.
The #volutes in the front and back of the capital are based on #spiral shapes, of which there are many different kinds. Some have #continuous curvature changes, while some do it in #discrete steps, like #fibonacci spirals that can approximate #logarithmic spirals seen in nature, e.g., nautilus. When curvature changes are discrete, the spiral arms can diverge in #arithmetic, #geometric, or some other sequence.
We will construct all of these, and most notably the smooth, sweeping surface of the scrolls using just straight lines and arcs, and let the #CAD software deal with delicate #NURBS curves and surfaces.
The Ionic capital is complex, but not unapproachable. We will systematically construct everything in this draft rendering using just straight lines and arcs as promised in https://pixelfed.social/p/Splines/789956327130679640, with the exception of the #cymaReversa near the top and the 3-strand braid on the ribbon.
In this rendering, the cyma reversa near the top is made using a flattened half-turn of a #helix, but it can also be constructed using elliptical arcs as I described in earlier posts.
The braid is a #periodic shape with infinite variety and is also based on a helix. You can vary the number of strands, their thickness, pitch, and so on, none of which are essential to the Ionic Order itself. They're only a jumping point for further exploration.
The eggs in the 'eggs and darts' motif can have different shapes. They can be convex like real eggs or concave as shown here, but the top is almost always sliced off. The total depth of the convex or concave shapes can vary, but only within a range of 1 part, or 8 units.
The #volutes in the front and back of the capital are based on #spiral shapes, of which there are many different kinds. Some have #continuous curvature changes, while some do it in #discrete steps, like #fibonacci spirals that can approximate #logarithmic spirals seen in nature, e.g., nautilus. When curvature changes are discrete, the spiral arms can diverge in #arithmetic, #geometric, or some other sequence.
We will construct all of these, and most notably the smooth, sweeping surface of the scrolls using just straight lines and arcs, and let the #CAD software deal with delicate #NURBS curves and surfaces.
La #discrète #révolte des #salariés de la #tech ( #US #USA ) contre le #virage #trumpiste ( #trump ) de leurs #patrons
www.courrierinternational.com/article/etat...
La discrète révolte des salari...
時序資料的異常偵測方式
剛好上個禮拜才整理舊的資料，寫了一篇關於用 z-score 偵測時序資料 (time-series data) 中的異常：「用 z-score 抓出異常的量」。
昨天就在 Hacker News 上面看到有論文整理這十年來對時序資料的異常偵測方式：「Time-Series Anomaly Detection: A Decade Review (arxiv.org)」，論
#Computer #Murmuring #Science #algorithm #anomaly #data #detection #discrete #fourier #series #time #transformer
Homer Simpson's Orbit
https://youtu.be/slfS7j_7L6s
#discrete #fourier #transform #mathart
Electronic Etch-A-Sketch, No Microcontroller Required https://hackaday.com/2024/06/20/electronic-etch-a-sketch-no-microcontroller-required/ #7400-series #demultiplex #etchasketch #multiplex #ToyHacks #discrete #encoder #matrix #logic #sram #led
Small #soldering excercise: a #discrete #NE555 timer built with #SMD #transistor.
I tried it out on my #breadboard and verified it with my #oscilloscope.
#electronics
2⃣ feComponentTransfer allows us to play with individual RGBA channels of input separately and feFuncA is for alpha channel.
type='discrete' means input alpha is split in as many intervals as values we have in tableValues. Alphas in [0,.5) become 0 and alphas in [.5,1] become 1. Kinda like round(input_alpha) in this particular case.
#css #alpha #transparency #svg #filter #svgFilter #discrete #stepFunction #maths #mathematics #code #coding #frontend #web #dev #webDev #webDevelopment
And it's another reminder that #continuous measurement beats #discrete measurement every time. As true 150 years ago as it is today, #sixsigma #statistics
Interesting #math video on sparse rulers, which has applications ranging from #stellar #interferometry to #ElectricalEngineering designing voltage taps on transformers (ok, these days we have switchmode PS, but it's still cool).
I feel so #alone tonight. Can’t sleep and everyone else is asleep. Closed all my dating app accounts because I got tired of being hit up for money. I have so few friends that I have no one to talk to. No one seems to understand what #discrete means. And yes, sex is good, but it is not all there is to life. I haven’t had any in about 3 months and yes, I miss it, but I haven’t died from lack of it. Guess I will lay here staring at the dark ceiling.
Google refuses to develop gaming Chromebooks with discrete graphics cards
#cards #Chromebooks #develop #Discrete #gaming #Google #graphics #refuses
https://gadgetpreeks.com/google-refuses-to-develop-gaming-chromebooks-with-discrete-graphics-cards/
Now at #ICFCA2023: #Late #Breaking Talk by Christian on《Breaking the Barrier: A Computation of the Ninth #Dedekind Number》#WorldRecord #FCA #Applied #Discrete #Maths https://www.kde.cs.uni-kassel.de/icfca2023/latebreaking.html
Algebraic Structure of Discrete-Event Dynamical Systems, and Applications - call for abstracts.
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