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Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences, engineering or even finance. For example, in physical systems, the Allen-Cahn equation describes pattern f ...

In this article, we want to find a map u : (Omega) over bar -> R-n solving, in Omega, the equation ...

Succinct non-interactive arguments of knowledge (SNARKs) are cryptographic proofs with strong efficiency properties. Applications of SNARKs often involve proving computations that include the SNARK verifier, a technique called recursive composition. Unfort ...

We introduce a notion of complexity of a complex of -adic sheaves on a quasi-projective variety and prove that the six operations are “continuous”, in the sense that the complexity of the output sheaves is bounded solely in terms of the complexity of the i ...

Motivation: Astrocytes, the most abundant glial cells in the mammalian brain, have an instrumental role in developing neuronal circuits. They contribute to the physical structuring of the brain, modulating synaptic activity and maintaining the blood-brain ...

This paper presents an input parameterization for dynamic optimization that allows reducing the number of decision variables compared to traditional direct methods. A small number of decision variables is likely to be beneficial for various applications su ...

Given n continuous open curves in the plane, we say that a pair is touching if they have finitely many interior points in common and at these points the first curve does not get from one side of the second curve to its other side. Otherwise, if the two cur ...

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Solving Non-linear Kolmogorov Equations in Large Dimensions by Using Deep Learning: A Numerical Comparison of Discretization Schemes

On the equation (Du)(t) H Du = G

On Succinct Non-interactive Arguments in Relativized Worlds

Quantitative Sheaf Theory

Metaball skinning of synthetic astroglial morphologies into realistic mesh models for visual analytics and in silico simulations

On reducing the number of decision variables for dynamic optimization

Many touchings force many crossings