arXiv research

The paper proves index theorems for graph-based optimal control problems.

New graph invariant measures embeddability in 3D.

This study applies EMD to MSCI World index and converts IMFs into graphs for GNN modeling.

Study shows surfaces without certain curves have infinite orbit graph.

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions…

We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure, an integral flow. We…

Researchers prove an index formula for spinors on 3-manifolds branching along graphs.

Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. In this paper, we extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index $α(G)$ of any spatial graph $G$ as $α(G) \leq c(G)+e+b,$ where $c(G)$ is the minimal cro…

If a graph is in bridge position in a 3-manifold so that the graph complement is irreducible and boundary irreducible, we generalize a result of Bachman and Schleimer to prove that the complexity of a surface properly embedded in the complement of the graph bounds the graph distance of the bridge surface. We use this r…

The paper calculates indices for families of Fredholm operators and their extensions.

In this paper, we introduce a bisected vertex leveling of a plane graph. Using this planar embedding, we present elementary proofs of the well-known upper bounds in terms of the minimal crossing number on braid index $b(L)$ and arc index $α(L)$ for any knot or non-split link $L$, which are $b(L) \leq \frac{1}{2} c(L) +…

We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index $\ge 5$. In order to have the necessity part, graphs are organized into small classes so that one of homological or cohomological characteristics of right-angled Artin groups can be applied. Fi…

Unified framework predicts S&P500 index direction using transfer learning and causal graph.

Improved linear upper bound for ribbonlength of knots.

We prove that the expectation value of the index function i(x) over a probability space of injective function f on any finite simple graph G=(V,E) is equal to the curvature K(x) at the vertex x. This result complements and links Gauss-Bonnet sum K(x) = chi(G) and Poincare-Hopf sum i(x) = chi(G) which both hold for arbi…

Unified framework for AMP iterations using graph indexing.

The abstract proves the non-existence of certain real algebraic surfaces.

Gauss-Bonnet for simple graphs G assures that the sum of curvatures K(x) over the vertex set V of G is the Euler characteristic X(G). Poincare-Hopf tells that for any injective function f on V the sum of i(f,x) is X(G). We also know that averaging the indices E[i(f,x)] over all functions gives curvature K(x). We explor…

New method calculates bridge indices of spatial graphs using diagram colorings and Wirtinger number.

Graph continuous operators become Riesz continuous after multiplication by unitary operators.

Graphs can model interactions between vertices, but how well depends on graph structure.

We define braid presentation of edge-oriented spatial graphs as a natural generalization of braid presentation of oriented links. We show that every spatial graph has a braid presentation. For an oriented link it is known that the braid index is equal to the minimal number of Seifert circles. We show that an analogy do…

NETpred uses graph models to predict multiple market indices.

We derive a generating series for the number of free subgroups of finite index in $Δ^+ = \mathbb{Z}_p*\mathbb{Z}_q$ by using a connection between free subgroups of $Δ^+$ and certain hypermaps (also known as ribbon graphs or "fat" graphs), and show that this generating series is transcendental. We provide non-linear rec…

We introduce GraSPy, a Python library devoted to statistical inference, machine learning, and visualization of random graphs and graph populations. This package provides flexible and easy-to-use algorithms for analyzing and understanding graphs with a scikit-learn compliant API. GraSPy can be downloaded from Python Pac…

Paper presents voxel graph operators for vector data models.

Sparse molecular representations improve interpretability in graph neural networks.

A blockchain protocol uses bandit algorithms to dynamically price transactions.

We determine the factorial growth rate of the number of finite index subgroups of right-angled Artin groups as a function of the index. This turns out to depend solely on the independence number of the defining graph. We also make a conjecture for right-angled Coxeter groups and prove that it holds in a limited setting…

In this paper, the first of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity, then the coarse Baum-Connes assembly map is injective, but not surjective, for the associated metric space $X$. Exp…

The paper challenges the validity of cluster validity measures in unsupervised learning.

New theorem bounds group quotient size to subgroups index.

Enhances knot counting using mosaic diagrams.

In this paper it is shown that a complete graph with $n$ vertices has an optimal diagram, i.e., a diagram whose crossing number equals the value of Guy's formula, with a free maximal linear tree and without free hamiltonian cycles for any odd integer $n \ge 7$.

Study fixed point indices and words at infinity for graph selfmaps.

Estimates graph curvature and diameter using Laplacian eigenvalues.

This study compares Markowitz and Single-Index models for Malaysian stocks.

Disease classification is a crucial element of biomedical research. Recent studies have demonstrated that machine learning techniques, such as Support Vector Machine (SVM) modeling, produce similar or improved predictive capabilities in comparison to the traditional method of Logistic Regression. In addition, it has be…

Agents cooperate to make decisions in multi-armed bandits over a graph.

There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence subgroups in terms of the corresponding graphs. We show some elementary criteria…

Bayesian methods estimate regression functions on submanifolds using graph Laplacian eigenbasis.

The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the…

Graph Ricci flow reveals hidden hierarchies in stock market correlations.

A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed …

In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse Baum-Connes assembly map is an isomorphism for the associated metric space $X$. As discussed in the first paper in this s…

By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie determined a Teichmüller flow invariant stratification of the space of quadratic differentials. In this final paper of a three-paper series, we give a first step to…

H. Masur and J. Smillie proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher ask: Is each connected, simplicial, (2r-1)-vertex graph the ideal Whitehead graph of a fully irreducible outer auto…

The purpose this article is to try to understand the mysterious coincidence between the asymptotic behavior of the volumes of the Moduli Space of closed hyperbolic surfaces of genus $g$ with respect to the Weil-Petersson metric and the asymptotic behavior of the number of arithmetic closed hyperbolic surfaces of genus …