arXiv research

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 …

Improves training GANs by escaping limit cycles.

Endogenous business cycles explain higher comovement across countries.

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…

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

Study asymptotic expansion of graph Laplacian on discretized surfaces, relating spanning trees and cycle-rooted forests.

AdaBoost cycles in probability simplex dynamics.

Study on synchronization in financial markets with time delays.

Originally, the Carnot cycle is a theoretical thermodynamic cycle that provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of…

This paper proposes an alternative to the classical price-adjustment mechanism (called "tâtonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic equilibration process that depends only on local information. We show how such a proc…

We prove that tangent cones to 2-dimensional calibrated cycles are unique. Using this result we prove a rate of convergence for the mass of the blow-up of a calibrated integral 2-cycle towards the limiting density. With the same techniques, we can also prove such a rate for J-holomorphic maps between almost complex man…

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…

Paper speeds up topological signal identification and cycle matching.

Paper introduces Cycles Protocol to integrate trade credit into market clearing.

In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension $n$ in terms of differential forms. In the case $n=1$ such computations have many applications in differential equations and…

CycleMorph improves image registration by preserving topology with cycle consistency.

We have analyzed the Indices of Industrial Production (Seasonal Adjustment Index) for a long period of 240 months (January 1988 to December 2007) to develop a deeper understanding of the economic shocks. The angular frequencies estimated using the Hilbert transformation, are almost identical for the 16 industrial secto…

We consider any pseudo holomorphic integral 2-cycle in an arbitrary almost complex manifold and perform a blow up analysis at an arbitrary point. Building upon a pseudo algebraic blow up (previously introduced by the author) we prove a geometric rate of decay for the mass ratio towards the limiting density, with an exp…

Agent-based market shows herding cycles with square-root price impact.

The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C^* algebra. We construct nontrivial K-cycles for the cross-product algebra, thereby extending some results of Connes and Sullivan to higher dimensions. We also show how the Patterson-Sullivan measure on the limit set c…

Let N be a manifold (with boundary) of dimension at least 3, such that its interior admits a hyperbolic metric of finite volume. We discuss the possible limits arising from sequences of relative fundamental cycles approximating the simplicial volume. As applications, we extend results of Jungreis and Calegari from clos…

Constructs unbounded KK-cycles for Riemannian embeddings in codimension one.

CDLF predicts product life-cycles in cold-start phases with high accuracy.

Develop a variational framework for statistical inference on cyclic interactions.

We develop a method to summarize causal models with cycles in cubic time.

We present a simple agent-based model of a financial system composed of leveraged investors such as banks that invest in stocks and manage their risk using a Value-at-Risk constraint, based on historical observations of asset prices. The Value-at-Risk constraint implies that when perceived risk is low, leverage is high…

We address the issue of limit cycling behavior in training Generative Adversarial Networks and propose the use of Optimistic Mirror Decent (OMD) for training Wasserstein GANs. Recent theoretical results have shown that optimistic mirror decent (OMD) can enjoy faster regret rates in the context of zero-sum games. WGANs …

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

We describe an algorithm that associates to each positive real number $r$ and each finite collection $C_r$ of planar pixels of size $r$ a planar piecewise linear set $S_r$ with the following additional property: if $C_r$ is the collection of pixels of size $r$ that touch a given compact semialgebraic set $S$, then the …

Service-induced congestion in memory-constrained LLM serving

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

The paper analyzes profitable bidding strategies for BESS in day-ahead and intraday markets.

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…

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 …

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-match…

Maps with a single face converge to hyperbolic surfaces in large genus.

Study Agol cycles for pseudo-Anosov 3-braids.

Method detects lithium-ion battery knee onset for early warning.

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.

Study of large mass limits of G2 and Calabi-Yau monopoles on specific manifolds.

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

Let $G$ be a complex simple direct limit group, specifically $SL(\infty;\mathbb{C})$, $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$. Let $\mathcal{F}$ be a (generalized) flag in $\mathbb{C}^\infty$. If $G$ is $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$ we suppose further that $\mathcal{F}$ is isotropic. Let…