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In this paper, we prove bounds for the unique, positive zero of O G (z) := 1 −O G (z) , where O G ( z ) is the socalled orbit polynomial [1]. The orbit polynomial is based on the multiplic ity and cardinalities of the vertex orbits of a graph. In [1] , we have shown that the unique, positive zero δ≤1 of O G (z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ.

Research on the structural complexity of networks has produced many useful results in graph theory and applied disciplines such as engineering and data analysis. This paper is intended as a further contribution to this area of research. Here we focus on measures designed to compare graphs with respect to symmetry. We do this by means of a novel characteristic of a graph G, namely an ``orbit polynomial.'' A typical term of this univariate polynomial is of the form czn, where c is the number of orbits of size n of the automorphism group of G. Subtracting the orbit polynomial frommore »

Online consumer reviews contain rich yet implicit information regarding consumers’ preferences for specific aspects of products/services. Extracting aspects from online consumer reviews has been recognized as a valuable step in performing finegrained analytical tasks (e.g. aspectbased sentiment analysis). Extant approaches to aspect extraction are dominated by discrete models. Despite explosive research interests in continuousspace language models in recent years, these models have yet to be explored for the task of extracting product/service aspects from online consumer reviews. In addition, previous continuousspace models for information extraction have largely overlooked the role of semantic information embedded in texts. In this study, wemore »

A bstract A search for a heavy resonance decaying into a top quark and a W boson in protonproton collisions at $$ \sqrt{s} $$ s = 13 TeV is presented. The data analyzed were recorded with the CMS detector at the LHC and correspond to an integrated luminosity of 138 fb − 1 . The top quark is reconstructed as a single jet and the W boson, from its decay into an electron or muon and the corresponding neutrino. A top quark tagging technique based on jet clustering with a variable distance parameter and simultaneous jet grooming is used tomore »Free, publiclyaccessible full text available April 1, 2023

Free, publiclyaccessible full text available March 1, 2023

Free, publiclyaccessible full text available January 1, 2023

A bstract A search for a heavy resonance decaying to a top quark and a W boson in the fully hadronic final state is presented. The analysis is performed using data from protonproton collisions at a centerofmass energy of 13 TeV, corresponding to an integrated luminosity of 137 fb − 1 recorded by the CMS experiment at the LHC. The search is focused on heavy resonances, where the decay products of each top quark or W boson are expected to be reconstructed as a single, largeradius jet with a distinct substructure. The production of an excited bottom quark, b *more »Free, publiclyaccessible full text available December 1, 2022