A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Finite stature proven for cube complexes with cyclonormal edges.
Study on planar graph braid groups' second homology.
Connected components of Morse boundaries are studied in graph of groups.
New method improves grouped convolutions on edge devices.
This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poinca…
This paper characterizes a specific type of twisted Artin groups embedded in knot groups.
This note demonstrates how both the concept of distance and the concept of holonomy can be constructed from a suitable network with directed edges (and no lengths). The number of different edge types depends on the signature of the metric and the dimension of the holonomy group. If the holonomy group is of dimension on…
Research explores hyperbolic space groups and their fundamental domains.
The study shows that certain groups can be uniquely identified by their finite abelian summands.
Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of infinite index. As a corollary, the same holds for limit groups. We also obtain a ch…
We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group is not one-ended, then we can blow up vertex groups to graphs of groups with simp…
Constructs weight 1/2 multiplier systems for a specific group and relates to geometric edge paths.
We prove that the Cayley graph and the coset geometry of the von Dyck group are linked by a vertex-to-edge duality.
The paper examines how edge subdivisions affect the vanishing of -homology in Coxeter groups.
The paper calculates the number of closed cycles in a specific complex group.
Timelike minimal surfaces in Lorentzian Heisenberg group have singular points.
A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces are negatively curved 2-complexes, and whose edge spaces are points …
New method solves group synchronization with cycle-edge message passing.
Square percolation determines threshold for group divergence in random graphs.
We consider triangulations of surfaces with edges painted three colors so that edges of each triangle have different colors. Such structures arise as Belyi data (or Grothendieck dessins d'enfant), on the other hand they enumerate pairs of permutations determined up to a common conjugation. The topic of these notes is l…
Researchers describe and compare decompositions of Poincaré duality pairs.
Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat loose, network clusters or groups are generally considered as nodes with enriched in…
In this article we determine the structure of a twisted first cohomology group of the first homology of a trivalent graph with a coefficient associated with the quantum Clebsch-Gordan condition. As an application we give a characterization of a combinatorial property, the external edge condition, which is defined by th…
The {\em Wiman-Edge pencil} is the universal family $\Cs/\mathcal B$ of projective, genus , complex-algebraic curves admitting a faithful action of the icosahedral group $\Af_5$. The goal of this paper is to prove that the monodromy of $\Cs/\mathcal B$ is commensurable with a Hilbert modular group; in particular is …
We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These last two unstable groups are the "edge" in our title.) Applying our results to auto…
Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex in vertex groups, we prove that vertex groups are relatively quasiconvex if and only if all the vertex groups have finite relative height in the f…
EoS selectively shapes learning, affecting some groups more than others.
Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale …
Our goal is to better understand the relationship between the polyhedron and the group associated with a fundamental domain in H^3. In this paper, we will study torsion-free groups and determine a formula for how many edge classes a given abstract polyhedron must have. We will use that result to classify all fundamenta…
Incremental methods for structure learning of pairwise Markov random fields (MRFs), such as grafting, improve scalability by avoiding inference over the entire feature space in each optimization step. Instead, inference is performed over an incrementally grown active set of features. In this paper, we address key compu…
Paper studies Wiman-Edge pencil and Wiman curve, providing uniformizations and modular interpretations.
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes. While learning arbitrary graphs with nodes and edges is known to be hard in the sense of requiring $Ω( \min\{ k^2 \log n, …
It is shown that for any locally knotted edge of a 3-connected graph in , there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in .
New model captures time series dependence across and within blocks.
A dessin is a 2-cell embedding of a connected bipartite graph into an orientable closed surface. An automorphism of a dessin is a permutation of the edges of the underlying graph which preserves the colouring of the vertices and extends to an orientation-preserving self-homeomorphism of the supporting surface. A dessin…
Paper solves isomorphism problem for specific Baumslag-Solitar groups.
The PC algorithm allows investigators to estimate a complete partially directed acyclic graph (CPDAG) from a finite dataset, but few groups have investigated strategies for estimating and controlling the false discovery rate (FDR) of the edges in the CPDAG. In this paper, we introduce PC with p-values (PC-p), a fast al…
Consider a group G and a family of subgroups of G. We say that vertex finiteness holds for splittings of G over if, up to isomorphism, there are only finitely many possibilities for vertex stabilizers of minimal G-trees with edge stabilizers in . We show vertex finiteness when G…
We show that if X is a minimal length carrier graph in a hyperbolic 3-manifold, M, then if X contains a sufficiently short edge, it must contain a short circuit, as well. The meaning of "short" depends only on the rank of the fundamental group of M. We also expand the class of manifolds which are known to have minimal …
The (torsion) complexity of a finite edge-weighted graph is defined to be the order of the torsion subgroup of the abelian group presented by its Laplacian matrix. When G is d-periodic (i.e., G has a free action of the rank-d free abelian group by graph automorphisms, with finite quotient) the Mahler measure of its Lap…
The paper clusters hypergraphs to find diverse and experienced groups based on past experiences.
Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality group with probability tending to 1 as n goes to infinity. This includes random ri…
Bounds on conformal dimension for certain Coxeter group boundaries.
Explicit presentations found for asymptotically rigid mapping class groups.
We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homology by the polynomial ring generated by the set of edges, and we show that this homology module is finitely generated. An analogue of class…
Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing such data is that inference at the individual edge level is not particularly biolog…
Threshold found for hyperbolicity in random Coxeter groups.
Generalized Baumslag-Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester proved (in "On uniqueness of JSJ decompositions of finitely generated groups", Comment. Math. Helv. 78 (2003) pp 740-751) that in most cases the defining graphs are cyclic JSJ …