相关论文: A stability result for balanced dictatorships in $…

We consider a quantum system composed of a spatially infinitely extended free Bose gas with a condensate, interacting with a small system (quantum dot) which can trap finitely many Bosons. Due to spontaneous symmetry breaking in the…

We introduce a fairly general concept of functional equation for $k$-tuples of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The homomorphy equations for mappings between groups and other algebraic systems, as well as…

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…

We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…

In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…

This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…

We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding…

We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…

We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a…

In this paper, we prove that the Fourier entropy of an $n$-dimensional boolean function $f$ can be upper-bounded by $O(I(f)+ \sum\limits_{k\in[n]}I_k(f)\log \frac{1}{I_k(f)})$, where $I(f)$ is its total influence and $I_k(f)$ is the…

We show that on every product probability space, Boolean functions with small total influences are essentially the ones that are almost measurable with respect to certain natural sub-sigma algebras. This theorem in particular describes the…

We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We…

We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol…

We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schrodinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the…

The Laplacian $\Delta_{\mathbb{S}^{n-1}}$ on the unit sphere $\mathbb{S}^{n-1}\subset \mathbb{R}^n$ has the property that it can explicitly be expressed in terms of $\Lambda$, the Dirichlet-to-Neumann map of the unit ball, as…

Let $G$ be a finite abelian group acting faithfully on a finite set $X$. As a natural generalization of the perfect nonlinearity of Boolean functions, the $G$-bentness and $G$-perfect nonlinearity of functions on $X$ are studied by Poinsot…

We establish the existence and fundamental properties of the equilibrium measure in uniformly quasiregular dynamics. We show that a uniformly quasiregular endomorphism $f$ of degree at least 2 on a closed Riemannian manifold admits an…

We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…

We analyse the complexity of approximate counting constraint satisfactions problems $\mathrm{\#CSP}(\mathcal{F})$, where $\mathcal{F}$ is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is…

Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…