Related papers: Recent advances in rigorous computation of Poincar…
This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…
In this talk I will focus on theoretical issues related to high precision determinations of the top mass. Several mass definitions are reviewed and their respective advantages and disadvantages are discussed. Precision determinations of the…
Measures of uncertainty and divergence are introduced for interval-valued probability distributions and are shown to have desirable mathematical properties. A maximum uncertainty inference procedure for marginal interval distributions is…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…
Interval-valued computing is a relatively new computing paradigm. It uses finitely many interval segments over the unit interval in a computation as data structure. The satisfiability of Quantified Boolean formulae and other hard problems,…
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
Accuracy-driven computation is a strategy widely used in exact-decisions number types for robust geometric algorithms. This work provides an overview on the usage of error bounds in accuracy-driven computation, compares different approaches…
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…
We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the…
Over the last few decades, various methods have been proposed for estimating prediction intervals in regression settings, including Bayesian methods, ensemble methods, direct interval estimation methods and conformal prediction methods. An…
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…
Our rigorous path integrals costruction for the evolution operators is extended to metric-affine manifolds.
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
In the paper we develop a method to evaluate the topological degree of the Poincare map of the mathematical model of narrow lagoon subject to a T-periodic forcing. Using the method developved we arrive to the conditions for the parameteres…
The margin of victory is easy to compute for many election schemes but difficult for Instant Runoff Voting (IRV). This is important because arguments about the correctness of an election outcome usually rely on the size of the electoral…
In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…
Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…