Related papers: Iterated LD-Problem in non-associative key establi…
This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
We study algorithms in the distributed message-passing model that produce secured output, for an input graph $G$. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the…
Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction…
In this paper we propose three iterative greedy algorithms for compressed sensing, called \emph{iterative alternating direction} (IAD), \emph{normalized iterative alternating direction} (NIAD) and \emph{alternating direction pursuit} (ADP),…
We investigate structural and rigidity properties of \emph{Lie skew braces} (LSBs), objects essentially known in the literature as \emph{post--Lie groups}, obtained by endowing a manifold with two compatible group laws that share the same…
Federated learning (FL) is a privacy-preserving distributed management framework based on collaborative model training of distributed devices in edge networks. However, recent studies have shown that FL is vulnerable to adversarial examples…
Federated Learning (FL) that extracts data knowledge while protecting the privacy of multiple clients has achieved remarkable results in distributed privacy-preserving IoT systems, including smart traffic flow monitoring, smart grid load…
A new presentation of the $n$-string braid group $B_n$ is studied. Using it, a new solution to the word problem in $B_n$ is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes…
Addition of higher nonlinear terms to the well known integrable nonlinear Schr\"odinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel…
The aim of the paper is to define noncommutative cluster structure on several algebras ${\mathcal A}$ related to marked surfaces possibly with orbifold points of various orders, which includes noncommutative clusters, i.e., embeddings of a…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
Federated learning algorithms perform reasonably well on independent and identically distributed (IID) data. They, on the other hand, suffer greatly from heterogeneous environments, i.e., Non-IID data. Despite the fact that many research…
This paper presents a significant advancement in the estimation of the Composite Link Model within a penalized likelihood framework, specifically designed to address indirect observations of grouped count data. While the model is effective…
A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric…
In the present paper we propose a coupled multigrid method for generalized Stokes flow problems. Such problems occur as subproblems in implicit time-stepping approaches for time-dependent Stokes problems. The discretized Stokes system is a…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
This paper addresses a complex parallel machine scheduling problem with jobs divided into operations and operations grouped in families. Non-anticipatory family setup times are held at the beginning of each batch, defined by the combination…
We present an untyped linear lambda calculus with braids, the corresponding combinatory logic, and the semantic models given by crossed G-sets.