相关论文: Verifications of primal energy identities for vari…
We verify functional a posteriori error estimate proposed by S. Repin for a class of obstacle problems. The obstacle problem is formulated as a quadratic minimization problem with constrains equivalently formulated as a variational…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
We study a nonlinear equation in the half-space $\{x_1>0\}$ with a Hardy potential, specifically \[-\Delta u -\frac{\mu}{x_1^2}u+u^p=0\quad\text{in}\quad \mathbb R^n_+,\] where $p>1$ and $-\infty<\mu<1/4$. The admissible boundary behavior…
The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2)…
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…
We propose using performance metrics derived from zero-failure testing to assess binary classifiers. The principal characteristic of the proposed approach is the asymmetric treatment of the two types of error. In particular, we construct a…
Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound).…
Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We…
A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…
Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…
Bell inequalities rest on three fundamental assumptions: realism, locality, and free choice, which lead to nontrivial constraints on correlations in very simple experiments. If we retain realism, then violation of the inequalities implies…
An approach to implementing variational Bayesian inference in biological systems is considered, under which the thermodynamic free energy of a system directly encodes its variational free energy. In the case of the brain, this assumption…
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More…
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We…
In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…