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We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative…

This work presents several improvements to the closed-loop stability verification framework using semialgebraic sets and convex semidefinite programming to examine neural-network-based control systems regulating nonlinear dynamical systems.…

This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic subgradient method, on any semialgebraic locally Lipschitz…

This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…

We give a new proof of the NIP arithmetic regularity lemma for finite groups (due to the authors and Pillay), which describes the approximate structure of "NIP sets" in finite groups, i.e., subsets whose collection of left translates has…

The steepness property is a local geometric transversality condition on the gradient of a $C^2$-function which is fundamental in order to ensure the stability of sufficiently-regular nearly-integrable Hamiltonian systems over long…

In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific…

We study the basic computational problem of detecting approximate stationary points for continuous piecewise affine (PA) functions. Our contributions span multiple aspects, including complexity, regularity, and algorithms. Specifically, we…

We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…

The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish…

We show that if the principal graph of a subfactor planar algebra of modulus \delta>2 is stable for two depths, then it must end in A_{finite} tails. This result is analogous to Popa's theorem on principal graph stability. We use these…

The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many…

For the simulation of rectilinearly moving conductors across a magnetic field, the Galer-kin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline…

This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs…

In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\xi)=-i\beta(x)\xi+\gamma(x)|\xi|^{\alpha(x)},$ where $\alpha(x)\in(0,2)$, $\beta(x)\in\R$ and…

Generalizing both Substable FSMs and Indicator FSMs, we introduce alpha-stabilized subordination, a procedure which produces new FSMs (H-sssi symmetric stable processes) from old ones. We extend these processes to isotropic stable fields…

In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ng\^o's Geometric Stabilization. To achieve this, we follow the strategy from the recent proof by Groechenig, Wyss and Ziegler which avoided the use of…

We study sparse hypergraphs which satisfy a mild pseudorandomness condition known as $L_p$ regularity. We prove appropriate regularity and counting lemmas, and we extend the relative removal lemma of Tao in this setting. This answers a…

This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the…

In analogy with the regularity lemma of Szemer\'edi, regularity lemmas for polynomials shown by Green and Tao (Contrib. Discrete Math. 2009) and by Kaufman and Lovett (FOCS 2008) modify a given collection of polynomials \calF =…