arXiv research

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

Algorithm constructs JSJ decomposition for hyperbolic groups.

Study finds lower bounds on flat cycles in congruence covers of symmetric spaces.

The simplest patterns of qualitative changes on the configurations of lines of principal curvature} around umbilic points on surfaces whose immersions into $\mathbb R^3$ depend smoothly on a real parameter (codimension one umbilic bifurcations) are described in this paper. Global effects, due to umbilic bifurcations, o…

We extend Schwartzman theory beyond dimension 1 and provide a unified treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoff's ergodic theorem for the class of immersions of solenoids with a trapping region.

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of imbeddings obtained by blowing up transversal double points in immersions. These cohomol…

Paper detects non-trivial cycles in embedding spaces using graph integrals.

Constructs unbounded Kasparov product for sphere embeddings into Euclidean space.

In classical surface theory there are but few known examples of surfaces admitting nontrivial isometric deformations and fewer still non-simply-connected ones. We consider the isometric deformability question for an immersion x: M \to R^3 of an oriented non-simply-connected surface with constant mean curvature H. We pr…

This paper sets a lower bound for the Gauss map area of surfaces in S^3.

Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature $\mathcal K$ is positive) of an oriented surface immersed in $\mathbb R^3$. The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given …

Consider oriented surfaces immersed in $\mathbb R^3.$ Associated to them, here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature $\mathcal K$, given by the product of the principal curvatures $k_1, k_2$ is positive. The leaves of the foliations …

Associated to oriented surfaces immersed in R^3 here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k_1, k_2 of the immersion, is positive. The leaves of the foliations are the lines of M- m…

We prove a freeness theorem for low-rank subgroups of one-relator groups. Let $F$ be a free group, and let $w\in F$ be a non-primitive element. The primitivity rank of $w$, $π(w)$, is the smallest rank of a subgroup of $F$ containing $w$ as an imprimitive element. Then any subgroup of the one-relator group $G=F/\langle…

We study the moduli space of torsion-free G2-structures on a fixed compact manifold, and define its associated universal intermediate Jacobian J. We define the Yukawa coupling and relate it to a natural pseudo-Kahler structure on J. We consider natural Chern-Simons type functionals, whose critical points give associati…

Divides help construct fibered links from singularities.

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.

Unified framework designs LK structures using integer twists on non-manifold meshes.

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

Study on inflection points of plane curve shadows with fixed embedded shapes.

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 …

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.

Paper introduces economic Carnot cycles in Roegenian economics.

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 …

Approximates cycles in planar and bounded-genus graphs.

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 [$…

We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an alg…

Endogenous business cycles explain higher comovement across countries.

Study Agol cycles in pseudo-Anosov 3-braids.

Study of height jumps in Ceresa cycle using asymptotic Hodge theory.

Smooth approximation of integral cycles in manifolds.

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to intr…

Proves the Weyl law for 1-cycles in manifolds.

The current article studies certain problems related to complex cycles of holomorphic foliations with singularities in the complex plane. We focus on the case when polynomial differential one-form gives rise to a foliation by Riemann surfaces. In this setting, a complex cycle is defined as a nontrivial element of the f…