Recent developments in big data and analytics research have produced an abundance of large sets that are too to be analyzed their entirety, due limits on computer memory or storage capacity. To address these issues, communication-free parallel Markov chain Monte Carlo (MCMC) methods been developed for Bayesian analysis data. These partition into manageable subsets, perform independent MCMC each subset, combine the subset posterior samples estimate full posterior. Current approaches combining...

Abstract The objective of this article is to introduce a fairness interpretability framework for measuring and explaining the bias in classification regression models at level distribution. In our work, we measure model across sub-population distributions output using Wasserstein metric. To properly quantify contributions predictors, take into account favorability both predictors with respect non-protected class. quantification accomplished by use transport theory, which gives rise...

Recent advances in big data and analytics research have provided a wealth of large sets that are too to be analyzed their entirety, due restrictions on computer memory or storage size. New Bayesian methods been developed for only sample sizes. These partition into subsets perform independent Markov chain Monte Carlo analyses the subsets. The then combine subset posterior samples estimate density given full set. approaches were shown effective models including logistic regression models,...

We consider the equations describing dynamics of radial motions for isotropic elastic materials; these form a system non-homogeneous conservation laws.We construct variational approximation scheme that decreases total mechanical energy and at same time leads to physically realizable avoid interpenetration matter.

We present a general framework for the approximation of systems hyperbolic balance laws.The novelty analysis lies in construction suitable relaxation and derivation delicate estimate on relative entropy.We provide direct proof convergence smooth regime wide class physical systems.We results arising materials science, where presence source terms presents number additional challenges requires treatment.Our is spirit introduced by Tzavaras [23] conservation laws.

We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001), 325–344] that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. establish convergence time-continuous interpolates constructed in to solution before shock formation. The proof is based on relative entropy estimation for time-discrete approximants an environment L^p -theory bounds, provides error estimate approximation...

We introduce a new notion of solution, which we call weak* solutions, for systems conservation laws. These solutions can be used to handle singular situations that standard weak cannot, such as vacuums in Lagrangian gas dynamics or cavities elasticity. Our framework allows us treat the ODEs Banach space. Starting with observation act linearly on test functions $α\in X$, require take values dual space $X^*$ $X$. Moreover, weaken usual requirement measurability solutions. In order do this,...

We develop a framework in which to make sense of solutions containing the vacuum Lagrangian gas dynamics. At and near vacuum, specific volume becomes infinite, enclosed vacuums are represented by Dirac masses, so they cannot be treated usual weak sense. However, weak* recently introduced authors can extended include vacuums. present definition these natural provide explicit examples demonstrate some their features. Our isentropic for clarity, we briefly discuss extension full $3\times3$...

We introduce various models for cellulose bio-degradation by micro-organisms. Those rely on complex chemical mechanisms, involve the structure of chains and are allowed to depend phenotypical traits population then use corresponding in context multiple-trait populations. This leads classical, logistic type, reproduction rates limiting growth large populations but also, more surprisingly, which too small a manner similar effects seen requiring cooperative interactions (or sexual...

This paper deals with relaxation approximations of nonlinear systems hyperbolic balance laws. We introduce a class schemes and establish their stability convergence to the solution laws before formation shocks, provided that we are within framework compensated compactness method. Our analysis treats source terms satisfying special mechanism which induces weak dissipation in spirit Dafermos [Hyperbolic dissipation, J. Hyp. Diff. Equations 3 (2006) 505–527.], as well more general terms. The...

The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem cavitation in nonlinear elasticity, order re-assess an example non-uniqueness entropic weak (with polyconvex energy) due a forming cavity.

In this article we perform an asymptotic analysis of parallel Bayesian logspline density estimators. Such estimators are useful for the datasets that partitioned into subsets and stored in separate databases without capability accessing full dataset from a single computer. The estimator introduce is spirit kernel introduced recent studies. We provide numerical procedure produces normalized itself place sampling algorithm. then derive error bound mean integrated squared posterior estimator....