Simulating a Planet on the GPU: Part 1 — Patrick Celentano

Simulating a planet is hard work. The GPU makes it easer.

Simulating Фахівець-85

Simulating and Visualising the Central Limit Theorem

I completed a Computer Science degree at uni, and bundled a lot of maths subjects in as electives: partial differential equations, vector calculus, discrete maths, linear algebra. For some reason however I always avoided statistics subjects.

Centaur: A Controversial Leap Towards Simulating Human Cognition

Explore the discussions around Centaur, an AI model designed to imitate human behavior, as experts evaluate its capabilities and challenges in cognitive science.

Simulating Time With Square-Root Space

We show that for all functions $t(n) \geq n$, every multitape Turing machine running in time $t$ can be simulated in space only $O(\sqrt{t \log t})$. This is a substantial improvement over Hopcroft, Paul, and Valiant's simulation of time $t$ in $O(t/\log t)$ space from 50 years ago [FOCS 1975, JACM 1977]. Among other results, our simulation implies that bounded fan-in circuits of size $s$ can be evaluated on any input in only $\sqrt{s} \cdot poly(\log s)$ space, and that there are explicit problems solvable in $O(n)$ space which require $n^{2-\varepsilon}$ time on a multitape Turing machine for all $\varepsilon > 0$, thereby making a little progress on the $P$ versus $PSPACE$ problem. Our simulation reduces the problem of simulating time-bounded multitape Turing machines to a series of implicitly-defined Tree Evaluation instances with nice parameters, leveraging the remarkable space-efficient algorithm for Tree Evaluation recently found by Cook and Mertz [STOC 2024].

ECCC - TR25-017

Homepage of the Electronic Colloquium on Computational Complexity located at the Weizmann Institute of Science, Israel

Evolutionary Scale · ESM3: Simulating 500 million years of evolution with a language model