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.
New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.
Extends folding techniques to study subgroups of CAT(0) cube complexes.
Stochastic Gradient Descent (SGD) is widely used in machine learning problems to efficiently perform empirical risk minimization, yet, in practice, SGD is known to stall before reaching the actual minimizer of the empirical risk. SGD stalling has often been attributed to its sensitivity to the conditioning of the probl…
The ellipticity graph of a free group was defined by I. Kapovich and M. Lustig in order to study the outer automorphism group of , which acts on this graph. The graph was constructed to be analogous to the curve complex of a surface. It is a bipartite graph, whose vertices are conjugacy classes of nontrivial ele…
We provide the details for Gromov's proof of Stallings' theorem on groups with infinitely many ends using harmonic functions. The main technical result of the paper is a compactness theorem for a certain family of harmonic functions.
A new algorithm reduces graph complexity for better dense subgraph analysis.
New algorithm detects cores in graphs with community structure, improving vertex selection for better clustering.
Proves a theorem about groups and 3-manifolds.
KCoreMotif clusters large networks efficiently by exploiting k-core decomposition and motifs.
``What aspects of a group are unchanged, or stable, under homology equivalences''? The model theorem in this regard is the 1963 result of J. Stallings that the lower central series is preserved under any integral homological equivalence of groups. Various other theorems of this nature have since appeared. Stallings him…
A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the core. Interactions between pairs of nodes in the fringe, however, are not recor…
In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair where each of is either a vertex or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any net…
Corrects a flawed proof of the Kropholler Conjecture.
New method constructs non-quasiconvex subgroups in hyperbolic groups.
CTGCN learns dynamic graph embeddings preserving both local and global graph structure.
The sizes of Markov equivalence classes of directed acyclic graphs play important roles in measuring the uncertainty and complexity in causal learning. A Markov equivalence class can be represented by an essential graph and its undirected subgraphs determine the size of the class. In this paper, we develop a method to …
In this article we construct a family of knot surgery -manifolds admitting arbitrarily many nonisomorphic Lefschetz fibration structures with the same genus fiber. We obtain such families by performing knot surgery on an elliptic surface using connected sums of fibered knots obtained by Stallings twist from a…
We observe that Whitehead's lemma is an immediate consequence of Stallings folds.
New -manifolds without - and -handles are created from knots.
The paper proves an ascending chain condition for subgroups in hyperbolic and graph 3-manifolds.
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called ``twisting loop''. We show that the existence of a twisting loop on the fiber surface of an open book is e…
The thesis shows how automorphisms of hyperbolic groups can be represented by train track maps.
We show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most 2. From this it follows that the Hausdorff distance between any two surgery paths with the same initial sphere system and same target sphere system is at most 4. Our proof relies on understanding how su…
New perspective on Heegaard splittings using square complexes and combinatorial measurements.
In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, t…
The paper tackles scalability issues in Graph Representation Learning.
We introduce GSimCNN (Graph Similarity Computation via Convolutional Neural Networks) for predicting the similarity score between two graphs. As the core operation of graph similarity search, pairwise graph similarity computation is a challenging problem due to the NP-hard nature of computing many graph distance/simila…
By proving graph theoretical versions of Green-Stokes, Gauss-Bonnet and Poincare-Hopf, core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting. In this pedagogical exposition we present the main proofs on a single page and add illustrations. While discrete Stokes is is old, the …
The paper extends end concepts to arbitrary groups and spaces.
We give new information about the relationship between the low-dimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group. Applications are given to detecting when a set of elements of a group generates a…
The paper studies graph products of groups and recovers graph and vertex groups under certain conditions.
A labeled oriented tree is called injective if each generator occurs at most once as an edge label. We show that injective labeled oriented trees are aspherical. The proof relies on a new relative asphericity test based on a lemma of Stallings.
We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors , we say a set is an -spectral spanner if for all there is a probability distribution supported on such that $$vv^\intercal \preceq α\cdot\m…
Method learns software resource usage from snapshots.
A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives information about the structure of the Sageev cubing.
The paper establishes analogs of Stallings' theorem for group homomorphisms and their nilpotent quotients.
A new method for neural network initialization using graph degeneracy.
We give a general treatment of the somewhat unfamiliar operation on manifolds called Connected Sum at Infinity, or CSI for short. A driving ambition has been to make the geometry behind the well definition and basic properties of CSI as clear and elementary as possible. CSI then yields a very natural and elementary pro…
Study filling links in 3-manifolds to understand their topological properties.
This paper classifies fibered links in 3-sphere using open book decompositions.
The stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We show that families of fibre surfaces related by iterated Stallings twists have unbounded stabilisation height.
The aim of this note is to take benefit of the foam nature of the Khovanov-Kuperberg algebras to compute the Grothendieck groups of their categories of finitely generated projective modules. The computation relies on the Hattori-Stallings trace and some geometrical properties of foams in a solid torus.
Despite the recent successes in robotic locomotion control, the design of robot relies heavily on human engineering. Automatic robot design has been a long studied subject, but the recent progress has been slowed due to the large combinatorial search space and the difficulty in evaluating the found candidates. To addre…
Summarization of long sequences into a concise statement is a core problem in natural language processing, requiring non-trivial understanding of the input. Based on the promising results of graph neural networks on highly structured data, we develop a framework to extend existing sequence encoders with a graph compone…
A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two propertie…
In this paper, we present a new R package COREclust dedicated to the detection of representative variables in high dimensional spaces with a potentially limited number of observations. Variable sets detection is based on an original graph clustering strategy denoted CORE-clustering algorithm that detects CORE-clusters,…
Searching new molecules in areas like drug discovery often starts from the core structures of candidate molecules to optimize the properties of interest. The way as such has called for a strategy of designing molecules retaining a particular scaffold as a substructure. On this account, our present work proposes a scaff…
A general graph-structured neural network architecture operates on graphs through two core components: (1) complex enough message functions; (2) a fixed information aggregation process. In this paper, we present the Policy Message Passing algorithm, which takes a probabilistic perspective and reformulates the whole inf…