L^2$-sense
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Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion
arXiv:2502.03205v3 Announce Type: replace Abstract: We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm approximates the solution of the SDE in the $L^2$-sense without the curse of dimensionality. The latter means that its computational cost grows at most polynomially in both the dimension and the...
Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time
arXiv:2401.02878v5 Announce Type: replace-cross Abstract: Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the $L^{q}$ sense.
Predicting every game of the entire World Cup: All...
Everyone is using artificial intelligence to do, well, everything. With the World Cup starting on June 11, you can't scroll for more than a couple of minutes without hitting another post or video or reel of someone telling you how they used AI to predict the World Cup. So, I decided to use my own supercomputer to predict every game of the 2026 World Cup -- the supercomputer is called "my brain."
The Preisach Extremum Stack is a Shannon-Minimal Sufficient Statistic for Rate-Independent Functionals
Announce Type: new Abstract: Let R denote the class of all computable, causal functionals that are rate-independent in the classical sense (invariant under monotone time reparametrizations), and let Pi_n be the Preisach extremum stack of an input sequence u_{0:n}. We prove a characterization theorem establishing that every F in R satisfies Fu = f(Pi_n) for a computable f, and derive two information-theoretic results. First, under any probability measure on u_{0:n}, the equality I(u_{0:n};...
Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator
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Efficient and accurate neural-field reconstruction using resistive memory
Abstract Applications such as medical imaging, augmented and virtual reality, and embodied artificial intelligence (AI) depend on the ability to reconstruct complex signals from sparse observations. These applications are characterized by incomplete measurements and limited computational resources. Traditional approaches to digital hardware face the following challenges: explicit signal representations require heavy sampling and storage, data movement across the von Neumann bottleneck...
Diverse binding poses of agonistic neurotoxins on human Na<sub>v</sub>1.6
Abstract Voltage-gated sodium (Nav) channels are key targets of various venomous toxins. Deciphering the binding poses and mechanisms of action of representative toxins will help to dissect the functional mechanism of the channels and facilitate therapeutic development targeting Nav channels1,2. Here we present cryo-electron microscopy (cryo-EM) structures of distinct binding poses of three agonistic peptide toxins on the human Nav1.6–β1 channel complex.
Molecular glue degraders of HuR suppress BRAF-mutant colorectal cancer
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Abstract The Arctic is undergoing rapid warming, resulting in retreating sea ice and glaciers1, yet how cryospheric changes propagate into the deep ocean remains poorly understood2. Here we identify a climate-driven mechanism linking accelerating glacier disintegration to an increase in deep-sea hard-bottom habitats far beyond calving fronts. Seafloor observations in Fram Strait show a localized increase in the density and patchiness of dropstones delivered by debris-laden icebergs.
The Frame Problem
The Frame Problem To most AI researchers, the frame problem is the challenge of representing the effects of action in logic without having to represent explicitly a large number of intuitively obvious non-effects. But to many philosophers, the AI researchers' frame problem is suggestive of wider epistemological issues. Is it possible, in principle, to limit the scope of the reasoning required to derive the consequences of an action?