Related papers: Universally consistent vertex classification for l…
In this paper we show that all nodes can be found optimally for almost all random Erd\H{o}s-R\'enyi ${\mathcal G}(n,p)$ graphs using continuous-time quantum spatial search procedure. This works for both adjacency and Laplacian matrices,…
This paper deals with the convergence analysis of the SUCPA (Semi Unsupervised Calibration through Prior Adaptation) algorithm, defined from a first-order non-linear difference equations, first developed to correct the scores output by a…
Graphical data is comprised of a graph with marks on its edges and vertices. The mark indicates the value of some attribute associated to the respective edge or vertex. Examples of such data arise in social networks, molecular and systems…
We consider the offline change point detection and localization problem in the context of piecewise stationary networks, where the observable is a finite sequence of networks. We develop algorithms involving some suitably modified CUSUM…
Besides finding trends and unveiling typical patterns, modern information retrieval is increasingly more interested in the discovery of surprising information in textual datasets. In this work we focus on finding "unexpected links" in…
A graph $G$ is said to be a $k$-degenerate graph if any subgraph of $G$ contains a vertex of degree at most $k$. Let $\kappa$ be any non-negative function on the vertex set of $G$. We first define a $\kappa$-degenerate graph. Next we give…
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…
Almost forty years ago, Connes, Feldman and Weiss proved that for measurable equivalence relations the notions of amenability and hyperfiniteness coincide. In this paper we define the uniform version of amenability and hyperfiniteness for…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
Starting from Sinclair's 1976 work {\it Automatic Continuity of Linear Operators}, Cambridge University Press, (1976), on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear…
We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability…
This paper proposes a task-agnostic discovery layer for multivariate time series that constructs a relational hypothesis graph over entities without assuming linearity, stationarity, or a downstream objective. The method learns window-level…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
Self-supervised contrastive learning has predominantly adopted deterministic methods, which are not suited for environments characterized by uncertainty and noise. This paper introduces a new perspective on incorporating uncertainty into…
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
For vector lattices $E$ and $F$, where $F$ is Dedekind complete and supplied with a locally solid topology, we introduce the corresponding locally solid absolute strong operator topology on the order bounded operators $\mathcal…
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery…