Related papers: On proximal contractions via implicit relations an…
In recent years, the success of deep learning has inspired many researchers to study the optimization of general smooth non-convex functions. However, recent works have established pessimistic worst-case complexities for this class…
Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class…
We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions.
The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth…
We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically, via identifying appropriate $\mathbb{Z}_m$-gradings (and their generalizations) on the parent algebra. This includes…
In this work, we generalized and unified recent two completely different works of Jascha \cite{sohl2014fast} and Lee \cite{lee2012proximal} respectively into one by proposing the \textbf{prox}imal s\textbf{to}chastic \textbf{N}ewton-type…
The magnitude of traction forces exerted by living animal cells on their environment is a monotonically increasing and approximately sigmoidal function of the stiffness of the external medium. This observation is rationalized using active…
In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…
In this paper we introduce three Markovian couplings of Brownian motions on smooth Riemannian manifolds without boundary which sit at the crossroad of two concepts. The first concept is the one of shy coupling put forward in…
The goal of this paper is to put the theory of approximate fibrations into the framework of higher topos theory. We define the notion of an approximate fibration for a general geometric morphism of $\infty$-topoi, give several…
In this paper we study the class of brutal base contractions that are based on a bounded ensconcement and also the class of severe withdrawals which are based on bounded epistemic entrenchment relations that are defined by means of bounded…
We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this kind of problems can be classified into three classes.…
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. At first, we review…
We investigate inexact proximity operators for weakly convex functions. To this aim, we derive sum rules for proximal {\epsilon}-subdifferentials, by incorporating the moduli of weak convexity of the functions into the respective formulas.…
For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the…
The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates.…