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This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method…
Differential equations have void applications in several practical situations, sciences, and non sciences as Euler Lagrange equation in classical mechanics, Radioactive decay in nuclear physics, Navier Stokes equations in fluid dynamics,…
Failure Mode Reasoning (FMR) is a method for formal analysis of system-related faults. The method was originally developed for identifying failure modes of safety-critical systems based on an analysis of their programs. In this paper, we…
We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem…
Confounding matters in almost all observational studies that focus on causality. In order to eliminate bias caused by connfounders, oftentimes a substantial number of features need to be collected in the analysis. In this case, large p…
Many-Objective Feature Selection (MOFS) approaches use four or more objectives to determine the relevance of a subset of features in a supervised learning task. As a consequence, MOFS typically returns a large set of non-dominated…
We prove the existence and uniqueness of non-negative entropy solutions of the obstacle problem for stochastic porous media equations. The core of the method is to combine the entropy formulation with the penalization method.
Using methods of statistical mechanics, we analyse the effect of outliers on the supervised learning of a classification problem. The learning strategy aims at selecting informative examples and discarding outliers. We compare two…
This is a chapter of the forthcoming Handbook of Multiple Testing. We consider a variety of model selection strategies in a high-dimensional setting, where the number of potential predictors p is large compared to the number of available…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Classifying states as entangled or separable is a fundamental, but expensive task. This paper presents a method, the forest algorithm, to improve the amount of resources needed to detect entanglement. Starting from 'optimized' methods for…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Object recognition technologies hold the potential to support blind and low-vision people in navigating the world around them. However, the gap between benchmark performances and practical usability remains a significant challenge. This…
In this survey, we discuss the challenges of executing scientific workflows as well as existing Machine Learning (ML) techniques to alleviate those challenges. We provide the context and motivation for applying ML to each step of the…
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality…
Arithmetic complexity is considered simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic…
The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First,…