Visualization of the incompressible Navier–Stokes equation.
Showing how pressure, inertia, viscosity, and external forces govern fluid motion, from smooth laminar flow to vortices, smoke advection, and turbulence.
Number lines pair open circles with strict inequalities (excluding endpoints) and filled circles with inclusive ones, converting exactly to interval notation via parentheses or brackets.
x > 5 becomes (5, ∞)
x ≥ 5 becomes [5, ∞)
1 < x < 5 becomes (1, 5)
1 ≤ x ≤ 5 becomes [1, 5]
x ≤ 1 or x ≥ 5 becomes (−∞, 1] ∪ [5, ∞)
In order to activate cooling systems, engineers set temperature safety thresholds in industrial sensors as 1 ≤ T ≤ 5 °C above baseline.
Three fundamental integrals stand out for their elegant closed forms despite spanning infinite domains.
- The Gaussian ∫_{-∞}^{∞} e^{-x²} dx equals √π.
- The Lorentzian ∫_{-∞}^{∞} 1/(x² + 1) dx totals π.
- The sinc function ∫_{-∞}^{∞} sin(x)/x dx also equals π.
These identities, established through techniques such as contour integration, link analysis across mathematics.
Engineers apply the sinc integral within the sampling theorem to perfectly reconstruct continuous-time signals from discrete samples in digital communications systems.
RAG just got replaced by... screenshots.
PixelRAG is a 100% open-source retrieval system that skips HTML parsing completely.
instead of scraping a page into text and embedding chunks, it screenshots the page, embeds the pixels with a vision model, and searches 8.28M wikipedia articles like it's nothing.
→ HTML parsers drop 40%+ of a page. Screenshots drop nothing.
→ 30M+ Wikipedia screenshots indexed
→ perfect tables, perfect math, perfect code blocks
it even ships a Claude Code plugin that gives Claude eyes..
point it at any URL and it reads the rendered page like a human. One setup script. No MCP. No backend.
100% open source.
My team at @Google has just open sourced GNM, our parametric 3D statistical model of the human head, which is learned from a large dataset of 3D scans. It provides fine-grained control over facial identity (170 head and 80 teeth components), expressions (383 components, with a range of -3 to +3) and head pose.
You can get all the data here! https://t.co/kj1vkbXR0x
Congratulations to everyone for the release, and stay tuned for the next ones ;-)
✅ Claude Code
✅ Claude Cowork
✅ Claude Design
✅ Claude Finance
✅ Claude Science
✅ Claude Teacher
⬜ Claude HR
⬜ Claude Analytics
⬜ Claude Marketing
⬜ Claude Sales
⬜ Claude Legal
⬜ Claude R&D
⬜ Claude Procurement
⬜ Claude Accounting
⬜ Claude Engineering
Freiheit verschwindet selten mit einem Knall.
Meist wird die Temperatur nur ein kleines Stück höher gedreht – jedes Mal angeblich für mehr Sicherheit:
NetzDG. DSA. Chatkontrolle. EUDI-Wallet.
Und wenn der Bürger endlich merkt, dass das Wasser kocht, steht der Regler längst auf Anschlag.
#Meinungsfreiheit #Chatkontrolle #DSA #EUDIWallet #Überwachung
Netzfund, 17 Jahre alt. Heute Journal Bericht aus 2009 zu Ursula von der Leyens Plänen, zum Schutz der Kinder "Netzsperren" (Stoppschilder) in Deutschland einzuführen.
Erkennt ihr die Parallelen?
Dieses völlig wirkungslose Gesetz trat dann am 23.02.2010 doch in Kraft und wurde am 29.12.2011 bereits wieder aufgehoben. Damit war sie in Deutschland endgültig an den Kritikern gescheitert, die den technischen Sachverstand hatten, und die von Anfang an vor Unwirksamkeit und vor den Gefahren der damit geschaffenen Zensurwerkzeuge gewarnt hatten.
Heute ist der Hebel über die EU wesentlich länger. Mit Chatkontrolle und EUid App ist man dem eigentlichen Ziel, der Kontrolle des freien Internets und dem Ende der Anonymität aller EU Bürger, einen gewaltigen Schritt näher gekommen. Wenn sich die Bürger jetzt nicht dagegen wehren, haben sie ihr Ziel endgültig erreicht.
This is an elegant way to simulate falling sand:
Define simple rules for all 16 possible 2×2 grids and let a cellular automaton do the rest!
Watch the grains cascade, spread, and pile up realistically.
Conditional probabilities link events via their intersections in the sample space.
Nodes show regions A ∩ B, Ā ∩ B, A ∩ B̄, Ā ∩ B̄ and events A, B, Ā, B̄ around Ω. Arrows label conditionals such as P(B|A), P(A|B), P(Ā) and P(B). The equality P(A|B) ⋅ P(B) = P(A ∩ B) = P(B|A) ⋅ P(A) holds.
It lets one calculate joint probability using a conditional and the event's probability.
Medical diagnostics uses it to revise the probability of a disease given a positive test by incorporating prevalence and test accuracy.
An open-source, self-hostable PaaS alternative to Vercel, Heroku & Netlify that lets you easily deploy static sites, databases, full-stack applications and 280+ one-click services on your own servers.
https://t.co/HTZQ0iOyqd