Related papers: Structure and Stability of the 1-Dimensional Mappe…
We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…
We prove an analytic version of the stable graph regularity lemma from \cite{MaSh}, which applies to stable functions $f\colon V\times W\to [0,1]$. Our methods involve continuous model theory and, in particular, results on the structure of…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical…
We study the stability of resonance poles in pi-N P_11 partial wave, particularly the Roper resonance, by varying parameters significantly within the EBAC dynamical coupled-channels model, keeping a good fit to the empirical amplitude. We…
For a connected locally path-connected topological space $X$ and a continuous function $f$ on it such that its Reeb graph $R_f$ is a finite topological graph, we show that the cycle rank of $R_f$, i.e., the first Betti number $b_1(R_f)$, in…
The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based…
A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and 1<p<\infty. Generalisations are obtained for the Laman and…
The stability of persistence diagrams is among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the $\infty$-norm of…
Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like…
In this paper we study the regularity of stationary and minimizing harmonic maps $f:B_2(p)\subseteq M\to N$ between Riemannian manifolds. If $S^k(f)\equiv\{x\in M: \text{ no tangent map at $x$ is }k+1\text{-symmetric}\}$ is $k^{th}$-stratum…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
We discuss smooth functions which are Morse on preimages of values not being local extrema. We call such a function internally Morse or I-Morse. The Reeb graph of a smooth function is the space of all connected components of preimages of…
We present a new sufficient condition on stability number and toughness of the graph to have an f-factor.
In this paper, we first study the $\alpha-$energy functional, Euler-Lagrange operator and $\alpha$-stress energy tensor. Second, it is shown that the critical points of $\alpha-$ energy functional are explicitly related to harmonic maps…
Learning representations of nodes has been a crucial area of the graph machine learning research area. A well-defined node embedding model should reflect both node features and the graph structure in the final embedding. In the case of…
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of solutions snapshots, what…
A function $f:\RR \to \RR$ is called \emph{vertically rigid} if $graph(cf)$ is isometric to $graph (f)$ for all $c \neq 0$. We prove Jankovi\'c's conjecture by showing that a continuous function is vertically rigid if and only if it is of…