IA Scholar Query: On the 2-Cyclic Property in 2-Regular Digraphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSun, 25 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Hierarchical Cyclic Pursuit: Algebraic Curves Containing the Laplacian Spectra
https://scholar.archive.org/work/vud3fnhivncvfgv7umt4ow4pha
The paper addresses the problem of multi-agent communication in networks with regular directed ring structure. These can be viewed as hierarchical extensions of the classical cyclic pursuit topology. We show that the spectra of the corresponding Laplacian matrices allow exact localization on the complex plane. Furthermore, we derive a general form of the characteristic polynomial of such matrices, analyze the algebraic curves its roots belong to, and propose a way to obtain their closed-form equations. In combination with frequency domain consensus criteria for high-order SISO linear agents, these curves enable one to analyze the feasibility of consensus in networks with varying number of agents.Sergei E. Parsegov, Pavel Yu. Chebotarev, Pavel S. Shcherbakov, Federico M. Ibáñezwork_vud3fnhivncvfgv7umt4ow4phaSun, 25 Sep 2022 00:00:00 GMTIntrinsic Simulations and Universality in Automata Networks
https://scholar.archive.org/work/nqinjlbxnje53atvstfn74kceu
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. They are studied both from the dynamical and the computational complexity point of view. Inspired from well-established notions in the context of cellular automata, we develop a theory of intrinsic simulations and universality for families of automata networks. We establish many consequences of intrinsic universality in terms of complexity of orbits (periods of attractors, transients, etc) as well as hardness of the standard well-studied decision problems for automata networks (short/long term prediction, reachability, etc). In the way, we prove orthogonality results for these problems: the hardness of a single one does not imply hardness of the others, while intrinsic universality implies hardness of all of them. As a complement, we develop a proof technique to establish intrinsic simulation and universality results which is suitable to deal with families of symmetric networks were connections are non-oriented. It is based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks. As an illustration, we give a short proof that the family of networks were each node obeys the rule of the 'game of life' cellular automaton is strongly universal. This formalism and proof technique is also applied in a companion paper devoted to studying the effect of update schedules on intrinsic universality for concrete symmetric families of automata networks.Martín Ríos-Wilson, Guillaume Theyssierwork_nqinjlbxnje53atvstfn74kceuWed, 21 Sep 2022 00:00:00 GMTPositive matching decompositions of graphs
https://scholar.archive.org/work/ipl5mu4vo5bwzcwh7r2itp76na
A matching M in a graph Γ is positive if Γ has a vertex-labeling such that M coincides with the set of edges with positive weights. A positive matching decomposition (pmd) of Γ is an edge-partition M_1,...,M_p of Γ such that M_i is a positive matching in Γ-M_1∪⋯∪ M_i-1, for i=1,...,p. The pmds of graphs are used to study algebraic properties of the Lovász-Saks-Schrijver ideals arising from orthogonal representations of graphs. We give a characterization of pmds of graphs in terms of alternating closed walks and apply it to study pmds of various classes of graphs including complete multipartite graphs, (regular) bipartite graphs, cacti, generalized Petersen graphs, etc. We further show that computation of pmds of a graph can be reduced to that of its maximum pendant-free subgraph.Mohammad Farrokhi Derakhshandeh Ghouchan, Shekoofeh Gharakhloo, Ali Akbar Yazdan Pourwork_ipl5mu4vo5bwzcwh7r2itp76naWed, 21 Sep 2022 00:00:00 GMTDIGRAC: Digraph Clustering Based on Flow Imbalance
https://scholar.archive.org/work/ey3lgxetkrgsrjjm4uxszkegim
Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing graph neural network methods, and can naturally incorporate node features, unlike existing spectral methods. Extensive experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering when compared against 10 state-of-the-art methods from the literature, for a wide range of noise and sparsity levels, graph structures and topologies, and even outperforms supervised methods.Yixuan He and Gesine Reinert and Mihai Cucuringuwork_ey3lgxetkrgsrjjm4uxszkegimSun, 18 Sep 2022 00:00:00 GMTA System of Interaction and Structure III: The Complexity of BV and Pomset Logic
https://scholar.archive.org/work/ndvjbeywrnderitb6xx3qj4mru
Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, and proof systems. Both logics enjoy a cut-admissibility result, but for neither logic can this be done in the sequent calculus. Provability in pomset logic can be checked via a proof net correctness criterion and in BV via a deep inference proof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate the complexity of the two logics, exhibiting a huge gap between the two. Whereas provability in BV is NP-complete, provability in pomset logic is Σ_2^p-complete. We also make some observations with respect to possible sequent systems for the two logics.Lê Thành Dũng Nguyên, Lutz Straßburgerwork_ndvjbeywrnderitb6xx3qj4mruFri, 16 Sep 2022 00:00:00 GMTOn the geometry of two state models for the colored Jones polynomial
https://scholar.archive.org/work/srzxwhqaizfpjdz5lp2pdtbmaa
Using the flow property of the R-matrix defining the colored Jones polynomial, we establish a natural bijection between the set of states on the part arc-graph of a link projection and the set of states on a corresponding bichromatic digraph, called arc-graph, as defined by Garoufalidis and Loebl. We use this to give a new and essentially elementary proof for a knot state-sum formula of Garoufalidis and Loebl. We will show that the state-sum contributions of states on the part arc-graph defined by the universal R-matrix of U_q(sl(2,ℂ)) correspond, under our bijection of sets of states, to the contributions in the formula of Garoufalidis and Loebl. This will show that the two state models are in fact not essentially distinct. Our approach will also extend the formula of Garoufalidis and Loebl to links. This requires some additional non-trivial observations concerning the geometry of states on part arc-graphs. We will discuss in detail the computation of the arc-graph state-sum, in particular for 3-braid closures.Uwe Kaiser, Rama Mishrawork_srzxwhqaizfpjdz5lp2pdtbmaaWed, 14 Sep 2022 00:00:00 GMTOn generalized Schur groups
https://scholar.archive.org/work/zzsyp4coczcclmyrhulwzp6ani
An S-ring (Schur ring) is called central if it is contained in the center of the group ring. We introduce the notion of a generalized Schur group, i.e. such finite group that all central S-rings over this group are schurian. It generalizes in a natural way the notion of a Schur group and they are equivalent for abelian groups. We establish basic properties and provide infinite families of nonabelian generalized Schur groupsGrigory Ryabovwork_zzsyp4coczcclmyrhulwzp6aniMon, 12 Sep 2022 00:00:00 GMTReinterpreting the Middle-Levels Theorem via Natural Enumeration of Ordered Trees
https://scholar.archive.org/work/ecww2ebdrzfhnfmhjebhgd3d7a
Let 0<k∈ℤ. A reinterpretation of the proof of existence of Hamilton cycles in the middle-levels graph M_k induced by the vertices of the (2k+1)-cube representing the k- and (k+1)-subsets of {0,...,2k} is given via an associated dihedral quotient graph of M_k whose vertices represent the ordered (rooted) trees of order k+1 and size k.Italo J. Dejterwork_ecww2ebdrzfhnfmhjebhgd3d7aWed, 07 Sep 2022 00:00:00 GMTOASIcs, Volume 106, ATMOS 2022, Complete Volume
https://scholar.archive.org/work/k3l2xowdkvfxdelwxhf2xrcp6y
OASIcs, Volume 106, ATMOS 2022, Complete VolumeMattia D'Emidio, Niels Lindnerwork_k3l2xowdkvfxdelwxhf2xrcp6yTue, 06 Sep 2022 00:00:00 GMTOn the functional graph of the power map over finite groups
https://scholar.archive.org/work/zrqdyqplznfwhfy2uurmmliwl4
In this paper we study the description of the functional graphs associated with the power maps over finite groups. We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower groups, which is a special class of non abelian groups introduced in this paper. Unlike the abelian case where all the trees associated with periodic points are isomorphic, in the case of flower groups we prove that several different classes of trees can occur. The class of central trees (i.e. associated with periodic points that are in the center of the group) are in general non-elementary and a recursive description is given in this work. Flower groups include many non abelian groups such as dihedral and generalized quaternion groups, and the projective general linear group of order two over a finite field. In particular, we provide improvements on past works regarding the description of the dynamics of the power map over these groups.Claudio Qureshi, Lucas Reiswork_zrqdyqplznfwhfy2uurmmliwl4Tue, 06 Sep 2022 00:00:00 GMTGIT stability of linear maps on projective space with marked points
https://scholar.archive.org/work/w5mq3vm6tra3vfwnvc7eue7lyu
We construct moduli spaces of linear self-maps of projective space with marked points, up to projective equivalence. That is, we let the special linear group act simultaneously by conjugation on projective linear maps and diagonally on (ℙ^N)^n, and we take the geometric invariant theory (GIT) quotient. These moduli spaces arise in algebraic dynamics and integrable systems. Our main result is a dynamical characterization of the GIT semistable and stable loci in the space of linear maps T with marked points. We show that GIT stability can be checked by counting the marked points on flags with certain Hessenberg functions relative to T. The proof is combinatorial: to describe the weight polytopes for this action, we compute the vertices and facets of certain convex polyhedra generated by roots of the A_N lattice.Max Weinreichwork_w5mq3vm6tra3vfwnvc7eue7lyuTue, 06 Sep 2022 00:00:00 GMTCOVID-19 INFODEMIC IN THE TWITTERVERSE: CHARACTERIZATION OF MISINFORMATION SPREAD AND TWITTER BOT ACTIVITY BY CRITICAL MASS, ENERGY DECAY, ENTANGLEMENTS, AND NODE SYNCHRONIZATION USING MULTILAYER AND SPECTRAL GRAPH VISUALIZATIONS, KURAMOTO MODELING, SONIFICATION, AND WAVEFUNCTION SIMULATION
https://scholar.archive.org/work/gk6ei767mfgdpiyf4hohftjhau
No communication framework for "infodemiology" or investigative techniques within the discipline of communication have covered measurement of Twitter bots' "virality" and (massive) "misinformation spread" by energy with mass and energy equivalence because these are relegated to quantum mechanics. To posit infodemical measurements, this study of "COVID-19 infodemic" on Twitter characterizes misinformation spread and Twitter bot activity by critical mass, energy decay, entanglements, and node synchronization using multilayer and spectral graph visualizations, Kuramoto modeling, sonification, and wavefunction simulation. The Python-based analytics pipeline was developed based on fundamental conceptualizations of 7 communication theories and quantum mechanics. Simulation and (stochastic) modeling were implemented to investigate the intra- and interlayer relationships between bots, humans, and tweets. This study endeavored on: (1) theorizing "virality" and bot activity, (2) data mining using Hoaxy® and bot detection set at ≥.43 using Botometer®, and (3) comprehensive analysis using state-of-the-art techniques and statistics. Misinformation spreads more frequently with user replies than with retweets and faster through interlayer edges. Super spreaders were detected using centrality-based metrics. Bots that had high betweenness and eigenvector centralities, random walk score, and PageRank score were false human accounts. Bot cliques emerged inconsistently by edge entanglement with humans. False human accounts were central spreaders and were detectable by an increase in percolation centrality, random walk and PageRank scores. Spammers were peripheral spreaders with scores decreased or unchanged whenever indirectly connected to human hubs. False human accounts connect by power-law distribution. Many cross-links were shown between bots and humans. Overall, bots (re)produce the intrinsic "virality" of tweets with human users. Bots synchronized (partially) around 400 seconds (6.67 minutes) at peak befo [...]JOANNES PAULUS TOLENTINO HERNANDEZ, SERLIE BARROGA-JAMIASwork_gk6ei767mfgdpiyf4hohftjhauFri, 02 Sep 2022 00:00:00 GMTMinimal Path and Acyclic Models
https://scholar.archive.org/work/drcmh3tdlbhfrkviudkcw5vgbm
In this paper, firstly, we will study the structure of the path complex (Ω_*(G)_ℤ,∂) via the ℤ-generators of Ω_*(G)_ℤ, which is called the minimal path in . In particular, we will study various examples of the minimal paths of length 3. Secondly, we will show that the supporting graph of minimal graph is acyclic in the path homology. Thirdly, we will consider the applications of the acyclic models.Xinxing Tang, Shing-Tung Yauwork_drcmh3tdlbhfrkviudkcw5vgbmTue, 30 Aug 2022 00:00:00 GMTOn Certain Edge-Transitive Bicirculants of Twice Odd Order
https://scholar.archive.org/work/lihyfxwyjbaqxdetl4liwwipb4
A graph admitting an automorphism with two orbits of the same length is called a bicirculant. Recently, Jajcay et al. initiated the investigation of the edge-transitive bicirculants with the properties that one of the subgraphs induced by the latter orbits is a cycle and the valence is at least $6$ (Electron. J. Combin., 2019). We show that the complement of the Petersen graph is the only such graph whose order is twice an odd number.István Kovács, János Ruffwork_lihyfxwyjbaqxdetl4liwwipb4Fri, 26 Aug 2022 00:00:00 GMTConvergences of looptrees coded by excursions
https://scholar.archive.org/work/tpufedoctjd2pf5n7ax5yyb5ey
In order to study convergences of looptrees, we construct continuum trees and looptrees from real-valued c\'adl\'ag functions without negative jumps called excursions. We then provide a toolbox to manipulate the two resulting codings of metric spaces by excursions and we formalize the principle that jumps correspond to loops and that continuous growths correspond to branches. Combining these codings creates new metric spaces from excursions that we call vernation trees. They consist of a collection of loops and trees glued along a tree structure so that they unify trees and looptrees. We also propose a topological definition for vernation trees, which yields what we argue to be the right space to study convergences of looptrees. However, those first codings lack some functional continuity, so we adjust them. We thus obtain several limit theorems. Finally, we present some probabilistic applications, such as proving an invariance principle for random discrete looptrees.Robin Khanfirwork_tpufedoctjd2pf5n7ax5yyb5eyWed, 24 Aug 2022 00:00:00 GMTA Trivariate Dichromate Polynomial for Digraphs
https://scholar.archive.org/work/h77xvmww6rcmnp2wjnqb2uko3u
We define a trivariate polynomial combining the NL-coflow and the NL-flow polynomial, which build a dual pair counting acyclic colorings of directed graphs, in the more general setting of regular oriented matroids.Winfried Hochstättler, Johanna Wiehework_h77xvmww6rcmnp2wjnqb2uko3uWed, 24 Aug 2022 00:00:00 GMTDagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issue
https://scholar.archive.org/work/scntyrlsivecdcac4psbic4qzy
Dagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issuework_scntyrlsivecdcac4psbic4qzyTue, 23 Aug 2022 00:00:00 GMTComputation and Reconfiguration in Low-Dimensional Topological Spaces (Dagstuhl Seminar 22062)
https://scholar.archive.org/work/em4rf2iiergt7k43eyfmd2keza
This report documents the program and the outcomes of Dagstuhl Seminar 22062 "Computation and Reconfiguration in Low-Dimensional Topological Spaces". The seminar consisted of a small collection of introductory talks, an open problem session, and then the seminar participants worked in small groups on problems on reconfiguration within the context of objects as diverse as elimination trees, morphings, curves on surfaces, translation surfaces and Delaunay triangulations.Maike Buchin, Anna Lubiw, Arnaud de Mesmay, Saul Schleimerwork_em4rf2iiergt7k43eyfmd2kezaTue, 23 Aug 2022 00:00:00 GMTOn Upward-Planar L-Drawings of Graphs
https://scholar.archive.org/work/6hnoujxgbvdbzbmrcjlts5v62y
In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge e is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail of e and of a horizontal segment ending at the head of e. Distinct edges may overlap, but not cross. Recently, upward-planar L-drawings have been studied for st-graphs, i.e., planar DAGs with a single source s and a single sink t containing an edge directed from s to t. It is known that a plane st-graph, i.e., an embedded st-graph in which the edge (s,t) is incident to the outer face, admits an upward-planar L-drawing if and only if it admits a bitonic st-ordering, which can be tested in linear time. We study upward-planar L-drawings of DAGs that are not necessarily st-graphs. On the combinatorial side, we show that a plane DAG admits an upward-planar L-drawing if and only if it is a subgraph of a plane st-graph admitting a bitonic st-ordering. This allows us to show that not every tree with a fixed bimodal embedding admits an upward-planar L-drawing. Moreover, we prove that any acyclic cactus with a single source (or a single sink) admits an upward-planar L-drawing, which respects a given outerplanar embedding if there are no transitive edges. On the algorithmic side, we consider DAGs with a single source (or a single sink). We give linear-time testing algorithms for these DAGs in two cases: (i) when the drawing must respect a prescribed embedding and (ii) when no restriction is given on the embedding, but the DAG is biconnected and series-parallel.Patrizio Angelini, Steven Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Stefan Szeider, Robert Ganian, Alexandra Silvawork_6hnoujxgbvdbzbmrcjlts5v62yMon, 22 Aug 2022 00:00:00 GMTDigraph Networks and Groupoids
https://scholar.archive.org/work/sv4uu3arnjhzxlxd5nhsvq22zq
We answer a question posed by Dougherty and Faber in [3], "Network routing on regular directed graphs from spanning factorizations." We prove that every vertex transitive digraph has a spanning factorization; in fact, this is a necessary and sufficient condition. We show that 1-factorization of a regular digraph is closely related to the notion of a Cayley graph of a groupoid and as such, the theorem we prove on spanning factorizations can be translated to a 2006 theorem of Mwambene [4; Theorem 9] on groupoids. We also show that groupoids are a powerful tool for examining network routing on general regular digraphs. We show there is a 1-1 relation between regular connected digraphs of degree d and the Cayley graphs of groupoids (not necessarily associative but with left identity and right cancellation) with d generators. This enables us to provide compact algebraic definitions for some important graphs that are either given as explicit edge lists or as the Cayley coset graphs of groups larger than the graph. One such example is a single expression for the Hoffman-Singleton graph.Nyumbu Chishwashwa, Vance Faber, Noah Streibwork_sv4uu3arnjhzxlxd5nhsvq22zqMon, 22 Aug 2022 00:00:00 GMT