Related papers: Almost All Vectorial Functions Have Trivial Extend…

It is an open problem whether one can always extend an absolutely continuous function (in the sense of Ashton and Doust) on a compact subset of the plane to a larger compact set. In this paper we show that this can be done for a large…

While the beta-VAE family is aiming to find disentangled representations and acquire human-interpretable generative factors, like what an ICA (from the linear domain) does, we propose Full Encoder, a novel unified autoencoder framework as a…

Under certain assumptions we derive a complete semiclassical asymptotics of the spectral function $e_{h,\varepsilon}(x,x,\lambda)$ for a scalar operator \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*}…

Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or…

We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…

We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader-Shalom and Nevo-Zimmer, we show that the action stabilizers, and all irreducible…

In this paper we classify endofunctors on the simplex category, and we identify those that induce weak equivalence preserving functors on the category of simplicial sets.

We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $\mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists…

We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an…

Almost perfect nonlinear (APN) functions play an important role in the design of block ciphers as they offer the strongest resistance against differential cryptanalysis. Despite more than 25 years of research, only a limited number of APN…

We construct a new type of convergent, and asymptotic, representations, dyadic expansions. Their convergence is geometric and the region of convergence often extends from infinity down to $0^+$. We show that dyadic expansions are…

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…

Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…

We give conditions on the subgroups of the circle to be realized as the subgroups of eigenvalues of minimal Cantor systems belonging to a determined strong orbit equivalence class. Actually, the additive group of continuous eigenvalues…

We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly…

We prove a new weak mean ergodic theorem (Theorem A) for 1-cocycles associated to weakly mixing representations of amenable groups. Let $G$ be a finitely generated, discrete, amenable group $G$ which admits a controlled Folner sequence. We…

We develop an asymptotic theory of adversarial estimators ('A-estimators'). They generalize maximum-likelihood-type estimators ('M-estimators') as their average objective is maximized by some parameters and minimized by others. This class…

We prove that a solution of an elliptic operator with periodic coefficients behaves on large scales like an analytic function, in the sense of approximation by polynomials with periodic corrections. Equivalently, the constants in the…

In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder.…

For \Omega a C^{2}-smooth domain, and a positive bounded continuous map a \in C(\Omega), we prove existence of a minimizer of the functional u \mapsto $\int_{\Omega} a|Du| over the space BV(\Omega) of functions of bounded variation with…