Related papers: Notes on the stable regularity lemma
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
The canonical double cover $\mathrm{D}(\Gamma)$ of a graph $\Gamma$ is the direct product of $\Gamma$ and $K_2$. If $\mathrm{Aut}(\mathrm{D}(\Gamma))=\mathrm{Aut}(\Gamma)\times\mathbb{Z}_2$ then $\Gamma$ is called stable; otherwise $\Gamma$…
Nowadays we are witnessing a transformation of the business processes towards a more computation driven approach. The ever increasing usage of Machine Learning techniques is the clearest example of such trend. This sort of revolution is…
This paper addresses the ubiquity of remarkable measures on graphs, and their applications. In many queueing systems, it is necessary to take into account the compatibility constraints between users, or between supply and demands, and so…
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…
In the present paper, complete designs of graphs are considered. The notion of (regular) sampling is introduced and analyzed in detail, showing that the trivial necessary condition for its existence is actually sufficient. Some examples are…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…
As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…
We study non-orthogonality of symmetric, regular types and show that it preserves generic stability and is an equivalence relation on the set of all generically stable, regular types. We will also prove that some of the nice properties from…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
The goal of this expository note is to give a short, self-contained proof of nearly optimal lower bounds for the second largest eigenvalue of the adjacency matrix of regular graphs.
These notes give a brief introduction to the category of spectra as defined in stable homotopy theory. In particular, Section 5 discusses an extensive list of examples of spectra whose properties have been found to be interesting.
This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality, with explicit stability constants.
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the…
We present new combinatorial insights into the calculation of (Castelnuovo-Mumford) regularity of graphs.
We correct some errors in the earlier version of this paper. Most importantly, the definition of isogeny of marked stable graphs has changed.
This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete…