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math-PVS: A Large Language Model Framework to Map Scientific Publications to PVS Theories
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in formalizing mathematics, and discovering connections between different mathematical areas, to name a few.
A Dynamic Mode Decomposition Approach for Decentralized Spectral Clustering of Graphs
Our proposed method uses the existing wave equation clustering algorithm that is based on propagating waves through the graph.
Sampling via Controlled Stochastic Dynamical Systems
Given a target distribution and a reference stochastic differential equation (SDE), the Doob $h$-transform produces a controlled stochastic process whose marginal at a finite time $T$ will be equal to the target distribution.
Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms
Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$.
A Chaotic Dynamical System that Paints
Can a dynamical system paint masterpieces such as Da Vinci's Mona Lisa or Monet's Water Lilies?
