New 3-manifolds created from 4-regular graphs with unique Eulerian cycles.
problem Creating compact 3-manifolds from specific graph structures. method Defining 3-manifolds via compatible Eulerian cycles in 4-regular graphs. result Each manifold in the class has a unique minimal ideal triangulation with n tetrahedra. The study constructs links from polytope subgraphs and proves their hyperbolic properties.
problem Proving hyperbolic structures for links from polytope subgraphs.
method Construction of 3-manifolds from polytope subgraphs and analysis of their topology.
result Hyperbolic links are parametrized by specific subgraphs in hyperbolic polytopes.
Study on linking numbers in random book embeddings of complete graphs.
problem Distribution and mean of linking numbers in random book embeddings of complete graphs.
method Analyzes a family of two-component links arising from random embeddings of complete graphs, using Eulerian numbers and linear growth in mean linking number.
result Mean of squared linking number over all random embeddings is $ rac{i}{6}$, where i is the number of interior edges. Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
problem Unknottability of spatial graphs by region crossing changes.
method Region crossing changes to switch over/under relations within regions of spatial graph diagrams.
result Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
Smartfluidnet accelerates Eulerian fluid simulation with neural networks.
problem Current neural network methods for Eulerian fluid simulation lack flexibility and generalization.
method Smartfluidnet automates model generation and dynamic switching to meet user requirements.
result Smartfluidnet achieves 1.46x and 590x speedup compared to state-of-the-art models, with better simulation quality.
A graph (digraph) G=(V,E) with a set T⊆V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint T-paths in an inner Eulerian graph $G…
Study controls bifurcations in Eulerian flows with multiple Hopf singularities.
problem Bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularities.
method Analysis of CW complex bifurcations of flow-invariant Clifford hypertori, using leaf-bifurcation varieties.
result Tertiary toral CW complex bifurcates from and persists outside a secondary toral CW complex.
We consider generalized linear transient convection-diffusion problems for differential forms on bounded domains in Rn. These involve Lie derivatives with respect to a prescribed smooth vector field. We construct both new Eulerian and semi-Lagrangian approaches to the discretization of the Lie derivatives…
New method preserves topology in Hodge decomposition for scalar and vector fields.
problem Topology-preserving Hodge decomposition on manifolds with boundaries.
method Comprehensive 5-component decomposition in Eulerian representation.
result Effective numerical experiments validate the method's accuracy and orthogonality.
In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is base…
We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine h-vector of balanced semi-Eulerian complexes and the toric h-vector of semi-Eulerian posets. The lower bounds on simplicial h…
The action principle by Low [Proc. R. Soc. Lond. A 248, 282--287] for the classic Vlasov-Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the syst…
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexi…
Study on stability in discretized hydrodynamics model.
problem Stability analysis of discretized hydrodynamics model.
method Geometric structure of Euler equations, convergence of sectional curvature and Jacobi equations.
result Geometric insights from discretized model transfer to Euler equations.
A new method solves high-dimensional MFGs using particle-based flow matching.
problem Solving high-dimensional Mean-Field Games (MFGs) is computationally challenging.
method Proposes a particle-based deep Flow Matching (FM) method to update particles and train a flow neural network.
result Proves convergence of the scheme to a stationary point sublinearly and linearly under convexity assumptions.
New method uses dynamic sampling to improve PINNs efficiency.
problem Improving sample efficiency and performance of PINNs.
method pdPINN, inspired by Eulerian formulation, uses dynamic Monte Carlo sampling from particle positions.
result Higher sample efficiency and improved performance of PINNs.
We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series…
New method for manifold topological learning avoids remeshing issues.
problem Persistent homology on manifolds is numerically inconsistent.
method Persistent de Rham-Hodge Laplacians in Eulerian representation.
result Avoids numerical inconsistency over multiscale manifolds.
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha > alpha_0, where 0 < alpha_0 < 1 is of the order 1/k. This suggests that the flow…
Study Alexander polynomials of special alternating links and generalize Fox's conjecture.
problem Distinguish special alternating links up to isotopy using polynomial invariants.
method Combinatorial and discrete geometric properties of Alexander polynomials of special alternating links.
result Generalized Alexander polynomials of special alternating links can be expressed in terms of volumes of root polytopes of unimodular matrices.
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational, and directional. The covaria…
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.
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 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.
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 …
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.
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.
The Multinomial Logit (MNL) model and the axiom it satisfies, the Independence of Irrelevant Alternatives (IIA), are together the most widely used tools of discrete choice. The MNL model serves as the workhorse model for a variety of fields, but is also widely criticized, with a large body of experimental literature cl…
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…
Develops a real-analytic embedding for diffeomorphisms of the line, linking to Fisher-Rao geometry.
problem Embedding diffeomorphisms of the line in a geometric framework.
method Real-analytic embedding, Lp Fisher-Rao geometry, Schwarzian curvature. result Establishes a connection between diffeomorphisms and Fisher-Rao geometry, providing explicit geodesics and connections.
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.