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The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…
We consider sampling strategies for a class of multivariate bandlimited functions $f$ that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating $f$ to the…
Previously, the authors reported direct evidence of channel saturation and conductance quantization in atomic-sized gold constrictions through mechanical perturbation studies, and also showed that peaks in conductance histograms are…
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…
Why do deep networks generalize well? In contrast to classical generalization theory, we approach this fundamental question by examining not only inputs and outputs, but the evolution of internal features. Our study suggests a phenomenon of…
On a triangulated category $\mathbf D$ equipped with a semiorthogonal decomposition $\mathbf D=\langle{\mathbf D_{1}},{\mathbf D_{2}}\rangle$, Collins and Polishchuk develop a gluing construction of stability condition on $\mathbf D$. The…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
The absence, so far, of any graviton signatures at the LHC imposes severe constraints on the Randall-Sundrum scenario. Although a generalization to higher dimensions with nested warpings has been shown to avoid these constraints, apart from…
Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let $\overline{M}_\Gamma$ be a Galois $\Gamma$-covering. Under additional assumptions on $\overline{M}$, satisfied for example by Witt…
We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.
We analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of…
We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behavior. We give sufficient conditions for the continuous variation (in the $L^1$-norm) of the densities of absolutely continuous…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
Stochastic gradient descent (SGD) performed in an asynchronous manner plays a crucial role in training large-scale machine learning models. However, the generalization performance of asynchronous delayed SGD, which is an essential metric…
The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. However, the "stability of physical theories principle" seems to be the one that provides, through the tools of algebraic deformation theory,…
We study the recently introduced stability training as a general-purpose method to increase the robustness of deep neural networks against input perturbations. In particular, we explore its use as an alternative to data augmentation and…
Suppose that the origin is globally asymptotically stable under a set of continuous vector fields on Euclidean space and suppose that all those vector fields come equipped with -- possibly different -- convex Lyapunov functions. We show…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
We prove sharp regularity estimates for solutions of highly degenerate fully nonlinear elliptic equations. These are free boundary models in which a nonlinear diffusion process drives the system only in the region where the gradient…
In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…