arXiv research

This paper extends the Good Covering Theorem and Jordan Curve Theorem for proximal Alexandrov spaces.

Approximates cycles in planar and bounded-genus graphs.

The paper defines a path metric on a stable component of polynomial families.

This article introduces vortex nerve complexes in CW (Closure finite Weak) topological spaces, which first appeared in works by P. Alexandroff, H. Hopf and J.H.C. Whitehead during the 1930s. A vortex nerve is a CW complex containing one or more intersecting path-connected cycles. Each vortex nerve has its own distincti…

This article introduces proximal cell complexes in a hyperconnected space. Hyperconnectedness encodes how collections of path-connected sub-complexes in a Alexandroff-Hopf-Whitehead CW space are near to or far from each other. Several main results are given, namely, a hyper-connectedness form of CW (Closure Finite Weak…

Study the landscape of Lipschitz functions between manifolds using persistent homology.

We extend the edge version of the classical Menger's Theorem for undirected graphs to $n$-dimensional simplicial complexes with chains over the field $\mathbb{F}_2$. The classical Menger's Theorem states that two different vertices in an undirected graph can be connected by $k$ pairwise edge-disjoint paths if, and only…

This paper proposes a TL method for SOH estimation of lithium-ion batteries.

New Lie algebras from quivers lead to rigid Ricci solitons.

This paper suggests that business cycles may be a manifestation of coupled real economy and stock market dynamics and describes a mechanism that can generate economic fluctuations consistent with observed business cycles. To this end, we seek to incorporate into the macroeconomic framework a dynamic stock market model …

This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive proximity. A 1-cycle is a closed, connected path with a zero boundary in a simplicial c…

For a finite simplicial graph $Γ$, let $G(Γ)$ denote the right-angled Artin group on the complement graph of $Γ$. In this article, we introduce the notions of "induced path lifting property" and "semi-induced path lifting property" for immersions between graphs, and obtain graph theoretical criteria for the embedabilit…

Paper studies simplified trisections and their equivalence classes.

The study finds conditions on graph complements for positive curvature.

We use a control framework to analyze the digital vendor's profit maximization problem. The vendor captures market share by focusing costly effort on post-launch product maintenance, which influences user perception of the product and drives a revenue stream associated with product use. Our theoretical results show nec…

Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…

DAGMA learns DAGs faster and more accurately using log-determinant acyclicity.

We examine the action of the fundamental group $Γ$ of a Riemann surface with $m$ punctures on the middle dimensional homology of a regular fiber in a Lefschetz fibration, and describe to what extent this action can be recovered from the intersection numbers of vanishing cycles. Basis changes for the vanishing cycles re…

Subsurface projection has become indispensable in studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called relative twisting. We give two alternate versions of relative twisting for the outer automorphism group of a free …

This research integrates human interaction into reinforcement learning to improve sample efficiency and real-time learning.

For a connected locally path-connected topological space $X$ and a continuous function $f$ on it such that its Reeb graph $R_f$ is a finite topological graph, we show that the cycle rank of $R_f$, i.e., the first Betti number $b_1(R_f)$, in computational geometry called \emph{number of loops}, is bounded from above by …

In this paper, we focus on graph representation learning of heterogeneous information network (HIN), in which various types of vertices are connected by various types of relations. Most of the existing methods conducted on HIN revise homogeneous graph embedding models via meta-paths to learn low-dimensional vector spac…

We give an equivalent description of taut submanifolds of complete Riemannian manifolds as exactly those submanifolds whose normal exponential map has the property that every preimage of a point is a union of submanifolds. It turns out that every taut submanifold is also $\mathbb Z_2$-taut. We explicitely construct gen…

Odd crossing numbers and even rotation numbers for cycles in plane immersions.

We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and interpolate between holomorphic gauge and the Wu-Mandelstam-Liebran…

Proves inequality for 1-dimensional cycles.

This work introduces novel methods to identify and compare cycles across topological objects.

This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …

This paper identifies the unique efficient cycle for most hyperbolic manifolds but not for the figure-8 knot complement.

Study Agol cycles for pseudo-Anosov 3-braids.

Study shows credit expansion in mortgage markets influenced U.S. business cycle.

Researchers compute Connes-Chamseddine cycle on 6D manifolds using noncommutative integral.

Gauss diagrams' properties can change with Hamiltonian cycle choice.

Proximal algorithms applied to current deformation into cycles.

New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.

Credit expansion led to stronger household leverage cycles during the U.S. business cycle.

In the current article we study complex cycles of higher multiplicity in a specific polynomial family of holomorphic foliations in the complex plane. The family in question is a perturbation of an exact polynomial one-form giving rise to a foliation by Riemann surfaces. In this setting, a complex cycle is defined as a …

We use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslov index in the case of a real-analytic path having possibly non transversal intersections. We discuss some applications of the theory, with special emphasis o…

We start by studying the distribution of (cyclically reduced) elements of the free groups Fn with respect to their abelianization (or equivalently, their integer homology class. We derive an explicit generating function, and a limiting distribution, by means of certain results (of independent interest) on Chebyshev pol…

In this paper, we introduce a novel task for machine learning in healthcare, namely personalized modeling of the female hormonal cycle. The motivation for this work is to model the hormonal cycle and predict its phases in time, both for healthy individuals and for those with disorders of the reproductive system. Becaus…

AdaBoost cycles in probability simplex dynamics.

Smooth approximation of integral cycles mod 2 in Riemannian manifolds.

Constructs an explicit cycle in arithmetic group cohomology.

Using Kontsevich's identification of the homology of the Lie algebra l_infty with the cohomology of Out(F_r), Morita defined a sequence of 4k-dimensional classes mu_k in the unstable rational homology of Out(F_{2k+2}). He showed by a computer calculation that the first of these is non-trivial, so coincides with the uni…

We introduce a notion of vanishing Maslov index for lagrangian varifolds and lagrangian integral cycles in a Calabi-Yau manifold. We construct mass-decreasing flows of lagrangian varifolds and lagrangian cycles which satisfy this condition. The flow of cycles converges, at infinite time, to a sum of special lagrangian …

Study examines cash conversion cycle in manufacturing firms, finding negative relationships with profitability and size.

By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [$y$], inflation [$π$] and nominal interest rate [$…

This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces the standard optimization approach by a probabilistic description of both the enti…