Related papers: Fault-Equivalent Lowest Common Ancestors

Let $\ell \geqslant 0$ be an integer, and $G$ be a graph without loops. An $\ell$-link of $G$ is a walk of length $\ell$ in which consecutive edges are different. We identify an $\ell$-link with its reverse sequence. The $\ell$-link graph…

We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero…

Clustered Federated Learning has emerged as an effective approach for handling heterogeneous data across clients by partitioning them into clusters with similar or identical data distributions. However, most existing methods, including the…

Federated learning (FL) has emerged as an important machine learning paradigm where a global model is trained based on the private data from distributed clients. However, most of existing FL algorithms cannot guarantee the performance…

Let $\Gamma$ be a locally finite graph, $L$ the normalized Laplacian of $\Gamma$. If $\Gamma$ is uniformy locally finite, i.e. if each vertex has no more than $d$ adjacent vertices, then the matrix of $L$ (with respect to the standard…

We study the distributed detection problem in the context of a balanced binary relay tree, where the leaves of the tree correspond to $N$ identical and independent sensors generating binary messages. The root of the tree is a fusion center…

We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics…

We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer k, we can in fixed-parameter time construct a data structure that can…

Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…

Let $G$ be a simple undirected graph, $\theta(G)$ be the circuit rank of $G$, $\eta_M(G)$ and $m_M(G,\lambda)$ be the nullity and the multiplicity of eigenvalue $\lambda$ of a graph matrix $M(G)$, respectively. In the case $M(G)$ is the…

Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

We construct a filtered simplicial complex $(X_L,f_L)$ associated to a subset $X\subset \mathbb{R}^d$, a function $f:X\rightarrow \mathbb{R}$ with compactly supported sublevel sets, and a collection of landmark points $L\subset…

An even factor of $G$ is a spanning subgraph $F$ such that every vertex in $F$ has a nonzero even degree. Note that $\delta(G)\geq2$ is a trivial necessary condition for a graph to have an even factor, where $\delta(G)$ is the minimum…

Let $k$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $\delta$. A graph $G$ is said to have property $P(k, d)$ if it contains $k$ edge-disjoint spanning trees and an additional forest $F$ with edge…

Formal Concept Analysis (FCA) is an approach to creating a conceptual hierarchy in which a \textit{concept lattice} is generated from a \textit{formal context}. That is, a triple consisting of a set of objects, $G$, a set of attributes,…

This paper revisits alternating low-rank updates for federated fine-tuning and examines their behavior in decentralized federated learning (DFL). While alternating the LoRA matrices has been shown to stabilize aggregation in centralized FL,…

We prove an analogue of Jacquet's conjecture on the local converse theorem for \ell-adic families of co-Whittaker representations of GL_n(F), where F is a finite extension of Q_p and \ell does not equal p. We also prove an analogue of…

There are important conjectures about logarithmic conformal field theories (LCFT), which are constructed as kernel of screening operators acting on the vertex algebra of the rescaled root lattice of a finite-dimensional semisimple complex…

We show that given any two minimal models of a generalized lc pair, there exist small birational models which are connected by a sequence of symmetric flops. We also present some applications.