Reconstructing a manifold from internal scattering data.
problem Reconstructing a compact Riemannian manifold from internal scattering data.
method Generic assumption of the metric allows reconstruction from boundary measurements of geodesic exit directions.
result Isometric reconstruction of the manifold from boundary scattering data.
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary r…
Deep RL model optimizes pedestrian evacuation in multi-exit scenarios.
problem Optimizing pedestrian evacuation in multi-exit indoor environments.
method MultiExit-DRL using Deep Reinforcement Learning with DQN and DNN.
result MultiExit-DRL reduces evacuation frames and optimizes exit utilization.
In this note we give a construction of a smooth Riemannian metric on R^n which is standard Euclidean outside a compact set K and such that it has N = n(n + 1)=2 invisible directions, meaning that all geodesics lines passing through the set K in these directions remain the same straight lines on exit. For example in the…
We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…
For a Riemannian manifold (M,g) with strictly convex boundary ∂M, the lens data consists in the set of lengths of geodesics γ with endpoints on ∂M, together with their endpoints (x−,x+)∈∂M×∂M and tangent exit vectors (v−,v+)∈Tx−M×Tx+M. We show …
Study geodesics on neck-degenerate manifolds, focusing and winding behavior observed.
problem Geodesics behavior on neck-degenerate manifolds with cuspidal singularities.
method Detailed multiscale analysis, blow-up techniques.
result Geodesics exhibit focussing and winding behavior as the neck degenerates.
Holomorphic curves exiting bounded symmetric domains are asymptotically totally geodesic.
problem Understanding the asymptotic behavior of holomorphic curves in bounded symmetric domains.
method Proof by contradiction and rescaling, using the Poincaré-Lelong equation.
result Holomorphic curves exiting a bounded symmetric domain are asymptotically totally geodesic.
We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in these rotationally symm…
Mean exit times concentrate near equators and minimal hypersurfaces in high dimensions.
problem Understanding mean exit times on spheres and manifolds.
method Analyzing Brownian motion on spheres and manifolds with minimal hypersurfaces.
result Mean exit times concentrate near equators and minimal hypersurfaces in high dimensions.
Investors optimize liquid staking decisions in LSP and AMM protocols.
problem Optimal timing and allocation in liquid staking protocols.
method Derive optimal allocation strategy and model optimal exit timing using Laplace transforms and free-boundary techniques.
result Optimal stop-loss strategy maximizes expected payoff, influenced by fees and opportunity gains.
Extends Paulin's result to relatively hyperbolic groups.
problem Proving quasi-isometric equivalence between relatively hyperbolic groups.
method Introducing relative quasi-Mobius maps and using coarsely cusp-preserving quasi-isometries.
result Establishes a homeomorphism between Bowditch boundaries inducing quasi-Mobius maps.
Study of a generalized geometric Brownian motion with varying entry and exit rates.
problem Understanding the long-run behavior of economic systems with growth, volatility, entry, and exit.
method Generalized geometric Brownian motion framework with varying entry and exit rates, analyzing moments and survival probability.
result Optimal exit rate minimizes mean first-passage time, influencing system outcome.
Analyzes first exit times in a modified Barndorff-Nielsen and Shephard model.
problem Analyzing first exit times in a modified Barndorff-Nielsen and Shephard model.
method Formulated an approximate model driven by Brownian motion and Lévy subordinator, analyzed first exit times of log-return process.
result First exit time process decomposes into Brownian motion and Lévy subordinator components.
Study uses LLMs to optimize VC exit timing after IPO.
problem Optimal exit timing after IPO is crucial but not well studied.
method Uses LLMs to analyze financial data and market signals.
result LLMs can improve VC exit timing and generate better returns.
Study examines strategic exit timing in uncertain competition.
problem Timing of strategic exit decisions in competitive markets with uncertainty.
method Constructs a stochastic game equilibrium for exit strategies involving state variable and posterior belief process.
result Unique equilibrium found for symmetric Bayesian players.
In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary (M,g). We show that the boundary distance function, i.e., dg∣∂M×∂M, known near a point p∈∂M at which ∂M is strictly convex, determines g in a suita…
Mannheim curves are defined for immersed curves in 3-dimensional sphere S^3 . The definition is given by considering the geodesics of S^3. First, two special geodesics, called principal normal geodesic and binormal geodesic, of S^3 are defined by using Frenet vectors of a curve immersed in S^3. Later, the curve alpha i…
Enhances KANs for accuracy and interpretability with multi-exit architecture.
problem Unclear optimal depth for KANs and difficulty in optimization and interpretation.
method Introduces multi-exit KANs with each layer having its own prediction branch.
result Multi-exit KANs outperform single-exit versions on various datasets.
We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence 1→H→G→Q→1 of hyperbolic groups. These laminations arise in different contexts: existence of Cannon-Thurston maps; closed geodesics exiting ends of manifolds; dual to …
We show that a small perturbation of the boundary distance function of a simple Finsler metric on the n-disc is also the boundary distance function of some Finsler metric. (Simple metric form an open class containing all flat metrics.) The lens map is map that sends the exit vector to the entry vector as a geodesic c…
The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. In this Letter, we propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on…
Risk control improves EENNs to make faster predictions without sacrificing accuracy.
problem Determining safe times for EENNs to exit early without degrading performance.
method Adapting risk control frameworks to EENNs to tune their exiting mechanism.
result Risk control enables EENNs to make faster predictions while maintaining user-specified performance goals.
The problem of which Gauss diagram can be realized by knots is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that the needed conditions for realizability of a Gauss diagram can be interpreted as follows "the number of exits = the number of entrances…
This work optimizes DNN inference for energy-harvesting devices by compressing and selectively executing neural network exits.
problem Inference delays and energy inefficiency in energy-harvesting devices.
method Developed a power trace-aware and exit-guided network compression algorithm for multi-exit neural networks.
result Superior accuracy and reduced latency compared to state-of-the-art techniques.
Paper uses EXIT analysis for community detection with side information.
problem Community detection in the presence of side information.
method Imported EXIT method from iterative decoding of error control codes.
result Predicts asymptotic phase transition and residual errors for community detection.
New method controls mean exit time in stochastic systems using machine learning and quasipotential.
problem Controlling mean exit time in stochastic dynamical systems with white noise.
method Developed a neural network to compute the quasipotential function and designed an algorithm to calculate the controller.
result Effective and accurate control strategy demonstrated through numerical experiments.
Previous work in hierarchical reinforcement learning has faced a dilemma: either ignore the values of different possible exit states from a subroutine, thereby risking suboptimal behavior, or represent those values explicitly thereby incurring a possibly large representation cost because exit values refer to nonlocal a…
Unified ML approach for SDEs in bounded domains.
problem Challenges in simulating SDEs with particle exit phenomena.
method Hybrid approach combining diffusion model and exit prediction network.
result Accurate modeling of interior dynamics and boundary interactions.
Paper analyzes venture capital exit decisions under inconsistent preferences.
problem Time-inconsistent preferences in venture capital exit timing.
method Modeling four types of venture capitalists with varying levels of inconsistency.
result Time-inconsistent venture capitalists exit earlier than consistent ones.
Paper solves a Dirichlet problem using exit operator continuity.
problem Solving Dirichlet problems with fractional Laplacian.
method Continuity of exit operator under Skorokhod topology.
result Established sub and supersolutions for HJB equations.
E2CM uses class means for efficient early exits in neural networks.
problem Efficient early exits in neural networks with low computational cost.
method Early Exit Class Means (E2CM) based on class means of samples, without gradient-based training. result E2CM achieves higher accuracy with fixed training time budget and boosts existing early exit schemes. EENNs improve inference efficiency but need nested prediction sets for reliable uncertainty estimates.
problem Non-nested prediction sets from standard uncertainty quantification methods in EENNs.
method Introduced anytime-valid confidence sequences (AVCSs) tailored for EENNs.
result AVCSs generate nested prediction sets across EENN exits, addressing the issue of non-nested sets.
Enhances early-exit neural networks for anytime classification.
problem Lack of guaranteed prediction quality improvement with longer computation time.
method Post-hoc modification based on Product-of-Experts to enforce conditional monotonicity.
result Achieves conditional monotonicity in prediction quality, enabling anytime classification.
New method estimates mean exit times for diffusions and PDEs.
problem Estimating mean exit times and related functionals of stopped diffusions.
method Multilevel Monte Carlo method for mean exit times and PDE solutions.
result Complexity of O(ε−2∣logε∣3) for ε error. EERO optimizes resource usage for efficient classification.
problem Managing computational resources in complex machine learning models.
method EERO uses multiple classifiers with a reject option to adaptively shorten processing paths.
result EERO effectively manages budget allocation and enhances accuracy in complex scenarios.
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal submanifolds of N×R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fund…
Geodesic flow averages to half-dimensional directions.
problem Understanding divergent directions in Teichmüller flow.
method Analysis of quadratic differentials and geodesic flow.
result Hausdorff dimension of divergent directions is 0.5.
Developed policy gradient methods for stochastic control with exit time, outperforming traditional techniques in share repurchase pricing.
problem Optimal control with exit time in stochastic models.
method Two types of algorithms: direct policy learning and alternately learning value function and control.
result Policy gradient methods outperform PDE or neural networks in share repurchase pricing.
The purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane.
Study compares eigenvalues and moment spectra of geodesic balls in Riemannian manifolds.
problem Comparing eigenvalues and moment spectra of geodesic balls in Riemannian manifolds.
method Explicit upper and lower bounds for Poisson hierarchy and torsional rigidity.
result Equality of eigenvalues and moment spectra characterizes the model space.
Study geodesic trees and exceptional directions in FPP on hyperbolic groups.
problem Understanding the geometry and uniqueness of geodesics in FPP on hyperbolic groups.
method Analyzing random geodesic trees and exceptional directions in the context of FPP on hyperbolic groups.
result The set of exceptional directions has strictly smaller Hausdorff dimension than the boundary, and hence has measure zero.
A framework combining HSMM and survival analysis for lifecycle-oriented mobility analysis.
problem Understanding individual metro usage dynamics over multi-year horizons.
method A state-based lifecycle modeling framework integrating HSMM and discrete-time survival analysis.
result Identification of interpretable mobility states, transition dynamics, and state-dependent exit and re-entry processes.
Study on market entry timing in stock liquidation with trading constraints.
problem Optimal timing of market entry and exit in portfolio liquidation with trading restrictions.
method Mean-field game approach to model N-player and mean-field games of optimal portfolio liquidation. result Existence of unique equilibrium in both mean-field and N-player games. Eigenfunctions constructed via Brownian motion exit times on curved spaces.
problem Constructing eigenfunctions of Laplacian on curved spaces.
method Using exit times of Brownian motion on a Riemannian manifold.
result Eigenfunctions can be constructed for a wide range of Laplacian eigenvalues.
Survey on geodesic flows in 2-surfaces with changing signatures.
problem Generic singularities of geodesic flows in pseudo-Riemannian metrics.
method Analyzing the behavior of geodesics over different domains and near signature-changing curves.
result Geodesics have limited admissible directions near signature-changing points.
Biotech startups are found to be similar to tech startups overall.
problem The uniqueness of biotech startups was previously overemphasized.
method Extensive research from new databases analyzed similarities and differences.
result Biotech startups share similarities in venture capital, exit time, and geography with tech startups.
Study shows submanifolds can't be immersed in certain spaces.
problem Non-immersibility of submanifolds with infinite mean exit time.
method Not based on the weak maximum principle at infinity, generalizes previous results.
result Estimates for complete tower of moments for submanifolds with small mean curvature.