相关论文: Direct Statistical Simulation Using Generalised Cu…

Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard…

Analog quantum computation offers a route to machine learning using controllable physical dynamics as a computational resource. However, many existing approaches rely on task-specific protocols or observables that are difficult to access…

Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to…

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…

Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…

This is Part II of a two-part work on the estimation for a multi-layer generalized linear model (ML-GLM) in large system limits. In Part I, we had analyzed the asymptotic performance of an exact MMSE estimator, and obtained a set of coupled…

A Two-Stage approach is described that literally "straighten outs" any potentially nonlinear relationship between a y-outcome variable and each of p = 2 or more potential x-predictor variables. The y-outcome is then predicted from all p of…

Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of…

We propose Deep Companion Learning (DCL), a novel training method for Deep Neural Networks (DNNs) that enhances generalization by penalizing inconsistent model predictions compared to its historical performance. To achieve this, we train a…

There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…

This article introduces the Generalized Fourier Series (GFS), a novel spectral method that extends the clas- sical Fourier series to non-periodic functions. GFS addresses key challenges such as the Gibbs phenomenon and poor convergence in…

A principled framework to generalize variational perturbation approximations (VPA's) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting…

We introduce CaLES, a GPU-accelerated finite-difference solver designed for large-eddy simulations (LES) of incompressible wall-bounded flows in massively parallel environments. Built upon the existing direct numerical simulation (DNS)…

When deriving a master equation for a multipartite weakly-interacting open quantum systems, dissipation is often addressed \textit{locally} on each component, i.e. ignoring the coherent couplings, which are later added `by hand'. Although…

The quantum statistics of damped optical solitons is studied using cumulant-expansion techniques. The effect of absorption is described in terms of ordinary Markovian relaxation theory, by coupling the optical field to a continuum of…

In this work we investigate the statistical mechanics of a family of two dimensional (2D) fluid flows, described by the generalized Euler equations, or $\alpha$-models. These models describe both nonlocal and local dynamics, with one…

Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…

The Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to…

We develop a general strategy for constructing the explicit Local Langlands Correspondences for $p$-adic reductive groups via reduction to LLC for supercuspidal representations of proper Levi subgroups, using Hecke algebra techniques. As an…

We present a machine learning-based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier-Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models…