Study of Moncrief lines' behavior in curved space-times.
problem Understanding the asymptotic behavior of Moncrief lines in curved space-times.
method Analysis of geodesic laminations and convergence to Thurston boundary.
result Moncrief lines converge to a unique point in the Thurston boundary.
Study on manifolds with kinks and Gaussian kernel behavior.
problem Understanding the asymptotic behavior of graph Laplacian on manifolds with singularities.
method Introduced manifolds with kinks, derived asymptotic behavior of Graph Laplacian with Gaussian kernel, and validated results numerically.
result Asymptotic behavior of the Graph Laplacian is determined by the inward sector of the tangent space.
The paper studies heat kernel behavior on symmetric spaces.
problem Large-time behavior of heat operator traces on symmetric spaces.
method Uses representation theory and Carmona's proof of Vogan's lambda map.
result Provides an asymptotic formula for heat kernel behavior.
Study on harmonic functions in spaces with collapsing behaviors.
problem Harmonic functions on spaces with inhomogeneous collapsing behaviors at infinity.
method Analysis of complete and incomplete spaces with nonnegative Ricci curvature.
result Any nonconstant harmonic function yields a definite exponential growth rate.
Study precise asymptotic behavior of functions in singular metric spaces.
problem Singular metric spaces with incomplete geometry.
method Expansions of quasi-harmonic and eigenfunctions.
result More precise description of asymptotic behavior at infinity.
Study chaotic behavior in homeomorphism groups of countable products of spaces.
problem Investigate chaotic behavior in homeomorphism groups of countable products of various metrizable topological spaces.
method Construct numerous examples of chaotic groups of homeomorphisms of countable products of spaces.
result New chaotic groups of homeomorphisms of countable products of various metrizable topological spaces are discovered.
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 Lp heat semigroups (p>2) on a symmetric space of non-compact type is very different from the dynamics of the Lp heat semigroups if p≤2. To see this, it is shown that certain shifts of the Lp 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.
problem Determining the global meromorphic connection based on specified local behavior at singular points.
method Expository discussion of various problems related to meromorphic connections with specified local behavior, including Deligne-Simpson and rigidity problems.
result The existence and nonemptiness of moduli spaces of meromorphic connections with specified local behavior.
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.
problem High variance in off-policy evaluation for ranking policies.
method GMIPS estimator with user behavior model on ranking embedding spaces.
result GMIPS achieves lowest MSE and balances bias-variance trade-off.
The method approximates stationary distributions of Markov models by truncating irrelevant states.
problem Computing the stationary distribution of complex Markov models is computationally challenging.
method A state-space lumping scheme that aggregates states in a grid structure, iteratively refining the state-space.
result The method provides a well-justified finite-state projection tailored to the stationary behavior of Markov models.
FOCOPS optimizes agent's behavior while adhering to constraints.
problem Optimizing agent's behavior while respecting safety constraints.
method FOCOPS solves a constrained optimization problem in policy space, then projects the solution back into the parametric space.
result FOCOPS achieves better performance on constrained robotics tasks.
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 C∗-family of flat SL(2,C)-connections ∇λ. In this paper we consider the asymptotic behavior (for λ→0) of the gauge equivalence classes of ∇λ for compact CMC surfaces of genus g≥2. We …
MLDS dataset reveals hidden model behavior via weight-space analysis.
problem Neural networks' opacity makes them hard to evaluate.
method Presented MLDS dataset of trained neural networks.
result Weight-space analysis reveals meaningful divergence with small changes in training data.
The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.
problem Analyzing the behavior of harmonic map heat flow to moduli space of flat tori.
method Investigates stability and ergodic behavior of harmonic map heat flow using hyperbolic structure and relative entropy.
result The flow converges weak--∗ to the normalized hyperbolic measure on the moduli space. 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.
problem Investigate differential geometric properties of lightcone framed surfaces.
method Introduced modified frame to study the properties of lightcone framed surfaces.
result Showed behavior of Gaussian and mean curvatures at lightlike and singular points.
Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.
problem Investigating long-time dynamics of Yang-Mills heat flow with specific initial data.
method Analysis of SO(4)-equivariant Yang-Mills heat flow with SU(2) group in 4D space. result Global solutions can exhibit oscillatory behavior at time infinity.
Paper models market dynamics using bull and bear forces.
problem Complex market dynamics influenced by biases and narratives.
method Bias to Behavior from Bull-Bear Dynamics (B4) model.
result Model predicts market trends with superior performance and interpretable insights.
A new framework optimizes fMRI and behavioral data for better understanding of Autism.
problem Linking complex fMRI data to behavioral measures is challenging.
method Coupled manifold optimization framework projecting fMRI onto a shared manifold and mapping to behavioral measures.
result Framework outperforms traditional methods in predicting clinical severity of Autism.
Study shows twist tori equidistribute in moduli space, with other families having singular distributions.
problem Statistical behavior of twist tori in moduli space of hyperbolic surfaces.
method Analyzing expanding families of twist tori and their limiting distributions.
result Equidistribution of twist tori to a Lebesgue measure, 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.
problem Understanding high-codimensional minimal surfaces in hyperbolic space.
method Investigating asymptotic behavior and boundary regularity of area-minimizing currents.
result Established boundary regularity results for high-codimensional minimal surfaces near their asymptotic boundaries.
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.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
New method learns behavioral representations from mobility data.
problem Analyzing behavioral similarity of moving individuals from CDR trajectories.
method mob2vec framework combining segmentation, generalization, and unsupervised learning.
result Mob2vec generates low-dimensional vector representations preserving mobility behavior similarities.
Method constructs WP geodesics to study Teichmüller space behavior.
problem Understanding behavior of WP geodesics in Teichmüller space.
method Constructs WP geodesics with specific properties.
result Demonstrates disparity between geodesics and hyperbolic 3-manifold curves.
In this article, associated with each lattice T⊆Zn the concept of a harmonic-counting measure νT on a sphere Sn−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 Lp Laplacian and the dynamics of the Lp 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…
Quality-Diversity algorithms explore multiple high-performing solutions in a search space.
problem Finding multiple high-performing solutions in complex optimization problems.
method Evolutionary computation approach focusing on behavioral space and holistic solution distribution.
result Quality-Diversity algorithms provide a comprehensive view of 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.
problem Understanding the asymptotic behavior of extremal length along Teichmüller rays.
method Analyzing the limit of extremal length and deriving formulas for limiting Teichmüller distance and detour metric.
result An explicit formula for the limiting Teichmüller distance and a necessary and sufficient condition for Teichmüller rays to be asymptotic.
Study intersection numbers, lengths, and shortest geodesics on hyperbolic surfaces.
problem Understanding the relationship between intersection numbers, lengths, and shortest geodesics on hyperbolic surfaces.
method Analyzing the asymptotic behavior of interaction strength I(X) as X approaches infinity in the moduli space of compact hyperbolic surfaces.
result Determined the asymptotic behavior of interaction strength I(X) in terms of the length of the shortest geodesic sys(X).
Study Goeritz groups of link decompositions, focusing on their asymptotic behavior.
problem Understanding the asymptotic behavior of Goeritz groups for link decompositions.
method Defined Goeritz groups for link decompositions, analyzed their properties, and discussed their asymptotic behavior.
result Discussed the asymptotic behavior of minimal pseudo-Anosov entropies and related it to Goeritz groups of Heegaard splittings.
BEACON optimizes discovery by efficiently finding novel behaviors.
problem Discovering diverse system behaviors without a scalar objective.
method Bayesian optimization inspired strategy using multi-output Gaussian processes.
result BEACON discovers broader sets of distinct behaviors than competing methods.
Study explores quantum spaces on toric varieties and their limiting behavior.
problem Understanding quantum spaces on toric varieties and their limiting behavior.
method Established quantum spaces for mixed polarizations and examined one-parameter families of Kähler polarizations.
result Quantum spaces Hk,t converge to Hk as tightarrow∞. 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.
problem Continuity of phi-invariant for degenerating graphs.
method Use Yuan--Zhang's adelic divisors and follow Yuan's globalization of phi-invariants.
result Asymptotic expression of Zhang--Kawazumi's invariants for Riemann surfaces near the boundary of the moduli space.
DETECT clusters mobility behaviors from trajectories using deep learning.
problem Clustering similar mobility behaviors in large, complex trajectory data.
method DETECT uses deep learning to cluster mobility behaviors from trajectories, transforming and summarizing them to identify similar behaviors.
result DETECT effectively clusters mobility behaviors from real-world datasets.
Survey on geodesics on tetrahedra in curved spaces.
problem Understanding geodesics on tetrahedra in curved spaces.
method Analyzing geodesics on regular tetrahedra in spaces of constant curvature.
result Results on the behavior of simple closed geodesics.
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…