相关论文: Uniqueness of a constrained variational problem an…

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…

The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a…

Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…

This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…

We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In…

It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…

This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility,…

The unfolding problem formulation for correcting experimental data distortions due to finite resolution and limited detector acceptance is discussed. A novel validation of the problem solution is proposed. Attention is drawn to fact that…

We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energy-minimizing solutions support defects having the same character as what is seen…

The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…

Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…

Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small $BV$ functions which are global solutions of this equation. For any small $BV$ initial data, such global…

The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…

Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…

Designs which are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. This mean…

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…

In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…