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An overview of some methods of statistical physics applied to the analysis of algorithms for optimization problems (satisfiability of Boolean constraints, vertex cover of graphs, decoding, ...) with distributions of random inputs is…

In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is…

The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for…

We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…

In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the…

The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…

Fine-grained information on translation errors is helpful for the translation evaluation community. Existing approaches can not synchronously consider error position and type, failing to integrate the error information of both. In this…

We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output…

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional…

We present a generalized FDTD scheme to simulate moving electromagnetic structures with arbitrary space-time configurations. This scheme is a local adaptation and 2+1-dimensional extension of the uniform and 1+1-dimensional scheme recently…

We propose a flat nonlinear placement algorithm FFTPL using fast Fourier transform for density equalization. The placement instance is modeled as an electrostatic system with the analogy of density cost to the potential energy. A…

The alignment of large language models (LLMs) aims to ensure their outputs adhere to human values, ethical standards, and legal norms. Traditional alignment methods often rely on resource-intensive fine-tuning (FT), which may suffer from…

This tutorial provides an introduction to the development of fast matrix algorithms based on the notions of displacement and various low-rank structures.

To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…

In this article, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem…

The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…

This paper presents LEXR, a framework for explaining the decision making of recurrent neural networks (RNNs) using a formal description language called Linear Temporal Logic (LTL). LTL is the de facto standard for the specification of…

We present the Eisenhart-lift formalism in which the dynamics of a system that evolves under the influence of a conservative force is equivalent to that of a free system embedded in a curved manifold with one additional generalised…

Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…