The paper shows singularities in geometric flows can wander off.
problem Understanding the dynamics and behavior of singularities in geometric flows.
method Combining dynamical properties with smoothing effects for long time behavior.
result Singularities in certain geometric flows are shown to wander off, not returning to a dilated or translated copy of themselves.
Study shows non-wandering, partially hyperbolic systems are ergodic.
problem Ergodicity of partially hyperbolic systems.
method Analysis of partially hyperbolic diffeomorphisms, focusing on non-wandering systems.
result These systems are ergodic when they preserve volume, confirming a conjecture.
Deep CNN detects mind wandering from EEG data.
problem Detecting mind wandering to reorient attention.
method Channel-wise deep convolutional neural network (CNN) model.
result 91.78% accuracy in detecting mind wandering.
Surveying Ricci flow and its applications to Ricci limit spaces.
problem Understanding Ricci flows with unbounded curvature.
method Analyzing Ricci flows that can have infinite curvature at infinity and singular times.
result Developed insights into Ricci limit spaces.
We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface are not dense in the set of probability measures invariant by the geodesic flow. F…
Simulates patient pathways to detect delayed rare disease diagnoses.
problem Delayed rare disease diagnoses in France, causing health system and patient harm.
method Probabilistic modelling of patient pathways to create an alert system.
result Alert system detects and refers wandering patients to CRMRs.
Study partially hyperbolic dynamics on 3-manifolds with quasi-isometric center.
problem Characterize dynamics on 3-manifolds with specific center properties.
method Analyzes partially hyperbolic diffeomorphisms with quasi-isometric center under non-wandering conditions.
result Volume-preserving diffeomorphisms are ergodic without su-tori, confirming a conjecture. New method improves combinatorial optimization by overcoming inefficient sampling.
problem Wandering in contours: sampling similar solutions for long periods.
method Reheated Gradient-based Discrete Sampling with a novel mechanism.
result Superior performance across various combinatorial optimization problems.
Paper characterizes early-stage dementia signatures from sensor data.
problem Detecting early-stage dementia from sensor data.
method Developed bespoke behavioural models from longitudinal sensor data.
result Found subtle differences in sleep quality and wandering between dementia patients and controls.
The paper studies 3-manifolds with specific Morse-Smale diffeomorphisms and finds they are homeomorphic to lens spaces.
problem Understanding the topology of 3-manifolds with certain Morse-Smale diffeomorphisms.
method Analyzing the structure of fixed points and separatrices of diffeomorphisms in 3-manifolds.
result All supporting manifolds of these diffeomorphisms are homeomorphic to lens spaces.
In this paper we describe the stable and unstable leaves for the geodesic flow on the space of non-wandering spacelike geodesics of a Margulis Space Time and prove contraction properties of the leaves under the flow. We also show that monodromy of Margulis Space Times are "Anosov representations in non semi-simple Lie …
If there exists a diffeomorphism f on a closed, orientable n-manifold M such that the non-wandering set Ω(f) consists of finitely many orientable (±) attractors derived from expanding maps, then M must be a rational homology sphere; moreover all those attractors are of topological dimension n−2. Expandi…
New online few-shot learning model for context-aware recognition.
problem Few-shot learning in online, continuous settings with spatiotemporal context.
method Proposed new dataset and online versions of existing few-shot learning approaches.
result Contextual prototypical memory model improves performance.
Let Σ be a complete finite-area orientable hyperbolic surface with one cusp, and let R be the space of complete geodesic rays in Σ emanating from the puncture. Then there is a natural action of the mapping class group of Σ on R. We show that this action is "almost everywhere" wandering.
Motivated by the study in Morse theory and Smale's work in dynamics, the following questions are studied and answered: (1) When does a 3-manifold admit an automorphism having a knotted Smale solenoid as an attractor? (2) When does a 3-manifold admit an automorphism whose non-wandering set consists of Smale solenoids? T…
Using alternating Heegaard diagrams, we construct some 3-manifolds which admit diffeomorphisms such that the non-wandering sets of the diffeomorphisms are composed of Smale-Williams solenoid attractors and repellers, an interesting example is the truncated-cube space. In addition, we prove that if the nonwandering set …
Geodesic flow mixing on convex projective manifolds proven.
problem Understanding mixing properties of geodesic flow on convex projective manifolds.
method Introduced biproximal unit tangent bundle and proved mixing properties.
result Geodesic flow is topologically mixing on biproximal unit tangent bundle.
We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics f is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which f acts bijectively. The…
The study shows conditions for thermostats to have no conjugate points.
problem Conditions for thermostats to have no conjugate points.
method Analyzes smooth functions and properties of thermostats.
result Proves conditions for thermostats to be projectively Anosov and have no conjugate points.
The paper classifies 3D contact partially hyperbolic diffeomorphisms.
problem Classifying contact partially hyperbolic diffeomorphisms in 3D.
method Smooth classification, conjugation to known flows or automorphisms, use of invariant distributions.
result Classification up to finite quotient or power, conjugation to known structures.
Explains the Borromean rings, icosahedron, and Poincaré homology sphere.
problem Exploring the relationship between Borromean rings, icosahedron, and Poincaré homology sphere.
method Introduction of topological concepts and geometric construction of icosahedral compound of octahedra.
result Proofs about the orientation-preserving symmetry group of an icosahedron and the linked nature of Borromean rings.
If X is a proper CAT(-1)-space and Γ a non-elementary discrete group of isometries acting properly discontinuously on X, it is shown that the geodesic flow on the quotient space Y=X/Γ is topologically mixing, provided that the generalized Busemann function has zeros on the boundary ∂X and the non-wanderin…
This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which fits well dynamics of diffeomorphism. The paper is devoted to finding…
Study of transitivity in partially hyperbolic maps with expanding linear part.
problem Transitivity of partially hyperbolic endomorphisms with expanding linear part.
method Use of Blichfedt's theorem to analyze dynamical information from homology action.
result Robust transitivity condition and complete dichotomy for special cases.
Gradient-like flows on certain manifolds restrict saddle Morse indices to 1 or n-1.
problem Restricting Morse indices of saddles in gradient-like flows.
method Analyzing invariant manifolds and their intersections for gradient-like flows.
result Morse indices of saddles are either 1 or n-1, no other indices possible.
Constructs flows on quotients of Lie groups for Anosov subgroups.
problem Understanding dynamics on quotients of Lie groups by Anosov subgroups.
method Utilizes geometric structures and Lie group theory to construct and analyze flows.
result Establishes that all refraction flows arise from this construction.
Time and Sales of corn futures traded electronically on the CME Group Globex are studied. Theories of continuous prices turn upside down reality of intra-day trading. Prices and their increments are discrete and obey lattice probability distributions. A function for systematic evolution of futures trading volume is pro…
LionForests interprets random forests for better understanding of predictions.
problem Interpreting black-box tree ensemble models like random forests.
method Combining unsupervised learning and a similarity metric to explain tree ensembles.
result LionForests provides transparent rules for interpreting random forest predictions.
Paper unifies off-policy learning algorithms and introduces C-trace for better trade-offs.
problem Improving efficiency and scalability in off-policy learning.
method Unified view of off-policy algorithms, considering update variance, fixed-point bias, and contraction rate trade-offs.
result C-trace algorithm demonstrates better trade-offs and state-of-the-art performance.
Study off-policy evaluation in partially observable environments, reducing bias and errors.
problem Bias and large errors in off-policy evaluation for partially observable environments.
method Defined and solved off-policy evaluation for POMDPs, introduced Decoupled POMDP model.
result Demonstrated and compared off-policy evaluation methods, showing benefits of new approach.
Adapts GRPO for off-policy RL, improving reward.
problem Improving training stability and efficiency in RL.
method Adapts GRPO to off-policy setting, uses clipped surrogate objectives.
result Off-policy GRPO outperforms on-policy GRPO in empirical tests.
We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson's group F. The resulting class of groups exhibits a combination of uniformity and diversity. On the one hand, a chain group either has a simple commutator subgroup or the action of the…
New method improves off-policy critic evaluation in reinforcement learning.
problem High variance and instability in off-policy policy evaluation.
method Doubly robust estimators applied to actor-critic algorithms.
result Doubly robust estimation significantly improves performance in continuous control tasks.
New algorithm reduces bias in off-policy reinforcement learning.
problem Challenges in designing off-policy reinforcement learning algorithms.
method Doubly robust off-policy actor-critic (DR-Off-PAC) with a single timescale structure.
result Establishes the first overall sample complexity analysis for a single time-scale off-policy AC algorithm.
The paper introduces a new framework for off-policy reinforcement learning.
problem Improving off-policy reinforcement learning algorithms.
method Conceptual framework based on conditional importance sampling.
result Theoretical analysis and concrete algorithm investigation.
This work analyzes the gap between off-policy and on-policy policy gradient methods and provides conditions to reduce this gap.
problem The gap between off-policy and on-policy policy gradient methods and conditions to reduce it.
method Theoretical analysis and empirical evidence of conditions to reduce the on-off gap.
result Conditions to reduce the on-off gap between off-policy and on-policy policy gradient methods.
Evolutionary Strategies optimize hyper-parameters for off-policy learning.
problem Hyper-parameter sensitivity in off-policy learning.
method Application of Evolutionary Strategies for online hyper-parameter tuning.
result Our method outperforms state-of-the-art baselines.
New method reduces state distribution mismatch in off-policy RL.
problem State distribution mismatch in off-policy RL algorithms.
method Develops a novel constrained off-policy gradient objective to minimize state distribution shift.
result Minimizing state distribution shift improves performance in off-policy RL algorithms.
Framework for balancing accuracy and robustness in machine learning.
problem Balancing accuracy and robustness in machine learning models.
method Developed a framework and introduced quantities to characterize the trade-off, including a simple trade-off curve and an influence function.
result Theoretical insight and experimental demonstration of the trade-off between accuracy and robustness.
Memory-efficient algorithm reduces variance in off-policy RL.
problem High variance in off-policy policy optimization.
method Memory-efficient, stochastically variance-reduced algorithm using off-policy samples.
result Empirically validated effectiveness of the proposed algorithm.
Paper improves bootstrapping for off-policy reinforcement learning inference.
problem Improving bootstrapping for off-policy reinforcement learning inference.
method Proposes a bootstrapping FQE method for off-policy statistical inference and a subsampling procedure to improve runtime.
result Asymptotically efficient and distributionally consistent bootstrapping FQE method for off-policy inference.
We determine Kelly criterion for a game with variable pay-off. The Kelly fraction satisfies a fundamental integral equation and is smaller than the classical Kelly fraction for the same game with the constant average pay-off.
New method corrects state distribution mismatch for off-policy policy optimization.
problem Mismatch between behavior and evaluation policy state distributions.
method Off-policy policy gradient with state distribution correction.
result Significantly improved policy quality in simulations.
We propose and analyze an alternate approach to off-policy multi-step temporal difference learning, in which off-policy returns are corrected with the current Q-function in terms of rewards, rather than with the target policy in terms of transition probabilities. We prove that such approximate corrections are sufficien…
A new estimator improves off-policy evaluation in RL, outperforming existing methods.
problem Estimating performance of a new policy using historical data from a different policy.
method Doubly-robust estimator based on Targeted Maximum Likelihood Estimation, with variance reduction techniques.
result Our estimator uniformly outperforms existing methods across various RL environments and levels of model misspecification.
New algorithm BEAR reduces instability in off-policy Q-learning.
problem High sensitivity of off-policy Q-learning methods to data distribution.
method Identified and mitigated bootstrapping error through constrained action selection.
result BEAR algorithm learns robustly from various off-policy distributions.
A new framework enables real-time task trade-off control.
problem Conflict between multiple related tasks in a fixed model capacity.
method Formulates MTL as a preference-conditioned multiobjective optimization problem; uses a hypernetwork-based neural network.
result A single model can handle different trade-off preferences among multiple tasks.
Approximates measures on curved spaces using Dirac measures.
problem Topology of invariant measures on curved manifolds.
method Introducing weakly regular vectors and approximating measures by Dirac measures.
result Ergodicity is a generic property in the space of invariant measures supported on weakly regular vectors.