arXiv research

Study of Moncrief lines' behavior in curved space-times.

Study on manifolds with kinks and Gaussian kernel behavior.

The paper studies heat kernel behavior on symmetric spaces.

Study on harmonic functions in spaces with collapsing behaviors.

Study chaotic behavior in homeomorphism groups of countable products of spaces.

Most animals possess the ability to actuate a vast diversity of movements, ostensibly constrained only by morphology and physics. In practice, however, a frequent assumption in behavioral science is that most of an animal's activities can be described in terms of a small set of stereotyped motifs. Here we introduce a m…

The aim of this paper is to show that the dynamics of $L^p$ heat semigroups ($p>2$) on a symmetric space of non-compact type is very different from the dynamics of the $L^p$ heat semigroups if $p\leq 2$. To see this, it is shown that certain shifts of the $L^p$ heat semigroups have a chaotic behavior if $p>2$ and that …

We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson-Walker space-time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the …

In this paper, we study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solitons of the mean curvature flow in Minkowski space. We also study the asymptotic behavior and the strict convexity of general solitons of such flows.

This paper explores how local behavior of meromorphic connections on the projective line determines the global connection.

This paper aims to describe the behavior of diffeological differential forms under the operation of gluing of diffeological spaces along a smooth map. In the diffeological context, two ways of looking at diffeological forms are available, that of the vector space of all diffeological forms on a given space, and that of…

In this paper, we prove pointwise convergence of heat kernels for mGH-convergent sequences of $RCD^*(K,N)$-spaces. We obtain as a corollary results on the short-time behavior of the heat kernel in $RCD^*(K,N)$-spaces. We use then these results to initiate the study of Weyl's law in the $RCD$ setting

In this paper, we propose a new feature extraction technique for program execution logs. First, we automatically extract complex patterns from a program's behavior graph. Then, we embed these patterns into a continuous space by training an autoencoder. We evaluate the proposed features on a real-world malicious softwar…

New estimator GMIPS reduces variance in ranking policy evaluation.

The method approximates stationary distributions of Markov models by truncating irrelevant states.

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions over policy behaviors that can in turn be used to lead policy optimization towar…

Constant mean curvature (CMC) surfaces in space forms can be described by their associated $\mathbb C^*$-family of flat $SL(2,\mathbb C)$-connections $\nabla^λ$. In this paper we consider the asymptotic behavior (for $λ\to0$) of the gauge equivalence classes of $\nabla^λ$ for compact CMC surfaces of genus $g\geq2.$ We …

MLDS dataset reveals hidden model behavior via weight-space analysis.

The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.

In this paper, we introduce the pseudo-torsion functions along spacelike curves whose curvature vector field has isolated lightlike points in Lorentz-Minkowski 3-space, and prove the fundamental theorem. Moreover, we analyze the behavior of the torsion function at such points. As a corollary, we obtain a necessary and …

Study of lightcone framed surfaces in Lorentz-Minkowski 3-space, focusing on curvature behavior.

Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.

Paper models market dynamics using bull and bear forces.

A new framework optimizes fMRI and behavioral data for better understanding of Autism.

Study shows twist tori equidistribute in moduli space, with other families having singular distributions.

In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmuller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmuller geodesics and lines of minima. We also sho…

Study on high-codimensional minimal surfaces in hyperbolic space.

We consider the problem of off-policy evaluation in Markov decision processes. Off-policy evaluation is the task of evaluating the expected return of one policy with data generated by a different, behavior policy. Importance sampling is a technique for off-policy evaluation that re-weights off-policy returns to account…

We study the asymptotic behavior of convex Cauchy hypersurfaces on maximal globally hyperbolic spatially compact space-times of constant curvature. We generalise the result of [11] to the (2+1) de Sitter and anti de Sitter cases. We prove that in these cases the level sets of quasi-concave times converge in the Gromov …

The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.

New method learns behavioral representations from mobility data.

In this article, associated with each lattice $T\subseteq \mathbb{Z}^n$ the concept of a harmonic-counting measure $ν_T$ on a sphere $S^{n-1}$ is introduced and it is applied to determine the asymptotic behavior of the eigenfunctions of the Laplace-Beltrami operator on a lens space. In fact, the asymptotic behavior of …

The aim of this paper is to study the spectrum of the $L^p$ Laplacian and the dynamics of the $L^p$ heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in t…

In reinforcement learning, an agent attempts to learn high-performing behaviors through interacting with the environment, such behaviors are often quantified in the form of a reward function. However some aspects of behavior-such as ones which are deemed unsafe and to be avoided-are best captured through constraints. W…

Quality-Diversity algorithms explore multiple high-performing solutions in a search space.

In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original strategy, by blowing down the metric, using Cheeger and Colding's theory about l…

The study examines the asymptotic behavior of extremal length in Teichmüller space.

Study intersection numbers, lengths, and shortest geodesics on hyperbolic surfaces.

Study Goeritz groups of link decompositions, focusing on their asymptotic behavior.

BEACON optimizes discovery by efficiently finding novel behaviors.

Study explores quantum spaces on toric varieties and their limiting behavior.

We develop a theory of "minimal $θ$-graphs" and characterize the behavior of limit laminations of such surfaces, including an understanding of their limit leaves and their curvature blow-up sets. We use this to prove that it is possible to realize families of catenoids in euclidean space as limit leaves of sequences of…

Study continuity of phi-invariant for degenerating graphs.

Survey on geodesics on tetrahedra in curved spaces.

DETECT clusters mobility behaviors from trajectories using deep learning.

Agent-based modeling is a paradigm of modeling dynamic systems of interacting agents that are individually governed by specified behavioral rules. Training a model of such agents to produce an emergent behavior by specification of the emergent (as opposed to agent) behavior is easier from a demonstration perspective. W…

In \cite{CM5}, Colding and Minicozzi describe a type of compactness property possessed by sequences of embedded minimal surfaces in $\Real^3$ with finite genus and with boundaries going to $\infty$. They show that any such sequence either contains a sub-sequence with uniformly bounded curvature or the sub-sequence has …

The paper studies the asymptotic behavior of HCMA equations on ALE Kahler manifolds.