Related papers: Obstacles problems with measure data

This note is devoted to continuity results of the time derivative of the solution to the one-dimensional parabolic obstacle problem with variable coefficients. It applies to the smooth fit principle in numerical analysis and in financial…

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…

Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.

We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small…

We propose here selected actual features of measurement problems based on our concerns in our respective fields of research. Their technical similarity in apparently disconnected fields motivate this common communication. Problems of…

Explaining predictions based on multivariate time series data carries the additional difficulty of handling not only multiple features, but also time dependencies. It matters not only what happened, but also when, and the same feature could…

General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

For the general obstacle problem, we prove by direct methods an epiperimetric inequality at regular and singular points, thus answering a question of Weiss (Invent. Math., 138 (1999), 23--50). In particular at singular points we introduce a…

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…

In this paper we put forward a new solution of the well-known problem of relevant logics, i.e. we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the…

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…

Data values in a dataset can be missing or anomalous due to mishandling or human error. Analysing data with missing values can create bias and affect the inferences. Several analysis methods, such as principle components analysis or…

When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…

Validation is a major challenge in differentiable programming. The state of the art is based on algorithmic differentiation. Consistency of first-order tangent and adjoint programs is defined by a well-known first-order differential…

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…

We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence -- the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We prove an…