Study of height jumps in Ceresa cycle using asymptotic Hodge theory.
problem Understanding height jumps in the Ceresa cycle.
method Analysis of asymptotic behavior of Hain-Reed beta-invariant in degenerating families of curves.
result Height jump of Ceresa cycle is equal to the slope of the dual graph of the curve.
Proves homological inequality for cycles in Hadamard spaces of asymptotic rank 2.
problem Establishing isoperimetric inequalities in Hadamard spaces of asymptotic rank two.
method Homological inequality for cycles in dimensions at least 2, assuming finite linearly controlled asymptotic dimension.
result Homological inequality for general cycles in Hadamard 3-manifolds and finite-dimensional CAT(0) cube complexes.
Study asymptotic expansion of graph Laplacian on discretized surfaces, relating spanning trees and cycle-rooted forests.
problem Asymptotic expansion of graph Laplacian on discretized surfaces.
method Relate spanning trees and cycle-rooted spanning forests to zeta-regularized determinants.
result Explicit formula for limit of cycle-rooted spanning forest probability and topological observables.
The paper proves a new theorem about paths on nilmanifolds.
problem Understanding the asymptotic behavior of paths on nilmanifolds.
method Analytic mechanism involving uniform convergence and layer-by-layer convergence of nilpotent developments.
result Recovering and extending previous theories to arbitrary nilpotent steps.
We prove that every one-dimensional real Ambrosio-Kirchheim normal current in a Polish (i.e. complete separable metric) space can be naturally represented as an integral of simpler currents associated to Lipschitz curves. As a consequence a representation of every such current with zero boundary (i.e. a cycle) as an in…
We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd, we show that the expectation of the corresponding current of integration equidi…
Let (X,L) be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of X along a 0-dimensional cycle are closely related to Chow stability of the cycle itself, for polarizations making the exceptional divisors small. This can be used to give (almost) a converse to a result of Arezzo …
We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of correspondin…
Mathematical counterparts to effective degrees of freedom inspired by Guth's results.
problem Understanding effective degrees of freedom in mathematical contexts.
method Formulating specific questions inspired by Guth's results and Weyl asymptotics.
result New mathematical counterparts to effective degrees of freedom.
Constructs unbounded KK-cycles for Riemannian embeddings in codimension one.
problem Understanding Riemannian embeddings in codimension one.
method Constructs unbounded KK-cycles from C(X) to C0(Y), each with a connection, representing the shriek class. result The unbounded product of !ε with the Dirac operator DY represents the KK-theoretic factorization of the fundamental class [X]=!⊗[Y]. Constructs new coassociative fibrations for G2 manifolds.
problem Tackles the construction of new coassociative fibrations for G2 manifolds.
method Constructs fibrations by coassociative 4-folds, relates to hypersymplectic geometry and Donaldson's work.
result Shows natural generalizations of known coassociative fibrations.
Study of random multicurves and square-tiled surfaces on large genus surfaces.
problem Understanding the geometry and combinatorial properties of random multicurves and square-tiled surfaces on surfaces of large genus.
method Combination of combinatorial and geometric analysis, including large genus asymptotic analysis of moduli space volumes and intersection numbers.
result Random multicurves and square-tiled surfaces have well-approximated properties by random permutations, with specific expected values.
New filling functions for groups with coefficients show different asymptotic behavior.
problem Difficulty in filling loops with surfaces in Cayley graphs.
method Defining homological filling functions with coefficients and proving their differences.
result Filling functions for n-cycles with coefficients in different groups have distinct asymptotic behavior. Study of WKB asymptotics of Stokes matrices and spectral curves, proving rhombus inequalities.
problem Analyzing WKB asymptotics of Stokes matrices and spectral curves.
method Using spectral network theory, Poisson geometry, and cluster structures.
result Real parts of leading WKB exponents satisfy rhombus inequalities.
We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We unveil the presence of limit cycles and scrutinize the features of the asymptotic sta…
Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; b…
We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a half-translation surface with a flat unitary vector bundle and the spectrum of the Friedrichs extension of the Laplacian with von Neumann boundary conditions. As an interesting byproduct of our study, w…
Lyapunov 1-forms on orbifolds help understand flows on compact spaces.
problem Understanding flows on orbifolds using Lyapunov 1-forms.
method Introducing Lyapunov 1-forms, using asymptotic cycles and chain-recurrent sets.
result Existence of a Lyapunov 1-form in a prescribed cohomology class for compact orbifolds.
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
problem Analyzing crossing and rotation numbers of cycles in plane immersions of graphs.
method Generic immersions and Legendrian embeddings of graphs, focusing on cycles of specific lengths.
result Sum of rotation numbers of all 5-cycles is even, and sum of crossing numbers is odd.
The paper introduces vortex cycles and nerves, inspired by Thomson's vortex atoms.
problem Understanding vortex structures and their homology.
method Introducing and analyzing non-concentric, nesting vortex cycles and nerves.
result Whitehead CW topology and Leader uniform topology outcomes of vortex cycles.
Study of M5-brane flows leading to Kähler-Einstein metrics.
problem Understanding Kähler uniformization in M-theory.
method Holographic renormalization group flows in seven-dimensional gauged supergravity.
result Reach a Kähler-Einstein metric at the infrared fixed point.
Study uses Gaussian processes to model female hormonal cycles.
problem Personalized modeling of the female hormonal cycle.
method Used a mechanistic model and Gaussian process regression.
result Gaussian processes can help model the female menstrual cycle.
Proves inequality for 1-dimensional cycles.
problem Proving the Parametric Coarea Inequality for 1-cycles.
method Analytical proof based on conjecture by Guth and Liokumovich.
result Proved the Parametric Coarea Inequality for 1-cycles.
This work introduces novel methods to identify and compare cycles across topological objects.
problem Identifying and comparing topological features, particularly cycles, across different topological objects.
method Two complementary approaches: dendrogram-based merge-tree algorithms and Stratified Gradient Sampling.
result Transformed cycle matching into hierarchical clustering and topological optimization framework.
This paper identifies the unique efficient cycle for most hyperbolic manifolds but not for the figure-8 knot complement.
problem Identifying the unique efficient cycle for hyperbolic manifolds.
method Analyzing the limit of fundamental cycles and their ℓ1-norm convergence. result The uniqueness of the efficient cycle is proven for most hyperbolic manifolds but not for the figure-8 knot complement.
Study Agol cycles for pseudo-Anosov 3-braids.
problem Conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
method Investigate necessary and sufficient conditions.
result Necessary and sufficient conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
Study shows credit expansion in mortgage markets influenced U.S. business cycle.
problem Lack of causal evidence in cross-country business cycle studies.
method Unique research design combining cross-metropolitan U.S. data.
result Credit expansion caused stronger booms and busts in house-related industries.
Researchers compute Connes-Chamseddine cycle on 6D manifolds using noncommutative integral.
problem Computing the Connes-Chamseddine cycle for 6D manifolds.
method Using noncommutative integral on 6D manifolds, they compute the cycle.
result The Connes-Chamseddine cycle on 6D manifolds is computed.
Gauss diagrams' properties can change with Hamiltonian cycle choice.
problem The impact of Hamiltonian cycle choice on Gauss diagrams.
method Examined realizable and unrealizable Gauss diagrams, and proved preservation of realizability under certain Hamiltonian cycle changes.
result Properties of Gauss diagrams can vary with Hamiltonian cycle choice.
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.
problem Learning causal structures with cycles in linear non-Gaussian models.
method Characterizing when graphs determine the same model, using quadratic and cubic polynomial relations, and a strategy of decorrelating cycles and multivariate regression.
result Consistent and computationally efficient algorithm for learning causal structures with disjoint cycles.
Credit expansion led to stronger household leverage cycles during the U.S. business cycle.
problem Understanding the role of credit supply in the U.S. business cycle.
method Causal evidence from 1999-2010 U.S. business cycle data.
result Credit expansion, particularly in private-label mortgages, caused stronger household leverage cycles.
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 …
AdaBoost cycles in probability simplex dynamics.
problem Understanding cycling behavior in AdaBoost.
method Computational methods and dynamical systems analysis.
result Correspondence between AdaBoost cycling and continued fractions dynamics.
Smooth approximation of integral cycles mod 2 in Riemannian manifolds.
problem Approximating mod 2 integral cycles by smooth submanifolds.
method Approximation of mod 2 integral cycles by smooth submanifolds with controlled singularities.
result Every mod 2 integral cycle can be approximated by a smooth submanifold with a controlled singular set.
Constructs an explicit cycle in arithmetic group cohomology.
problem Cohomology of SLn(Z) at virtual cohomological dimension. method Geometric rigidity of Voronoi tessellations and abstract framework for polyhedral tessellations.
result Explicit canonical cycle in top-dimensional homology of Voronoi complex.
Paper introduces economic Carnot cycles in Roegenian economics.
problem Economic efficiency limits in Roegenian systems.
method Uses Carnot cycle principles to model economic systems.
result Validates 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.
problem Finding many disjoint cycles in planar and bounded-genus graphs.
method Constant-factor approximation algorithms for vertex-disjoint and edge-disjoint cycles.
result First algorithms for vertex-disjoint paths in fully planar and bounded-genus instances.
Study examines cash conversion cycle in manufacturing firms, finding negative relationships with profitability and size.
problem Understanding cash conversion cycle in manufacturing firms and its impact on profitability and size.
method Empirical study of 30 manufacturing firms in Dhaka Stock Exchanges, categorizing them into six industries, analyzing industry averages and relationships with size and profitability.
result Negative relationship between cash conversion cycle and profitability, especially ROE; negative relationship with firm size in terms of net sales.
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.
problem Standard models struggle to explain high comovement in business cycles across countries.
method Developed a demand-driven reduced-form model with strategic complementarities and international trade linkages.
result Combining endogenous business cycles with exogenous shocks matches empirical comovement levels.
Study Agol cycles in pseudo-Anosov 3-braids.
problem Understanding conjugacy invariants of pseudo-Anosov maps.
method Investigate train tracks associated with Farey intervals and describe Agol cycles.
result Complete description of Agol cycles in pseudo-Anosov 3-braids.
Smooth approximation of integral cycles in manifolds.
problem Approximating integral cycles in Riemannian manifolds.
method Approximation of integral cycles by smooth submanifolds with controlled area and singularities.
result Integral cycles can be approximated by smooth submanifolds with controlled area and singularities.
Researchers found a special basis for cycles on a K3 surface.
problem Understanding the structure of two-cycles on K3 surfaces.
method Constructed a canonical basis of two-cycles using formal sums of smooth submanifolds.
result The intersection form of the basis takes a specific canonical form.
New model for STSs with restricted horizontal gluings, focusing on maximal horizontal cylinders.
problem Modeling STSs with specific horizontal restrictions.
method Modified model with conjugacy classes of permutations to restrict horizontal gluings.
result Asymptotic analysis of components, genus distribution, and saddle connections.