Paper analyzes learning dynamics in quasi-periodic environments, showing consistent solutions.
problem Challenges in stochastic gradient learning for complex environments.
method Uses energy balance equations derived from Caldirola-Kanai Hamiltonian to model learning.
result In quasi-periodic environments, learning yields consistent solutions for similar patterns.
we construct a properly embedded minimal surface in the flat product R^2*S^1 which is quasi-periodic but is not periodic.
In this article we consider the motion of relativistic strings in the Minkowski space R1+n. Those surfaces are known as a timelike minimal surface, and described by a system with n nonlinear wave equations of Born-Infeld type. By constructing a suitable Nash-Moser iteration scheme, we prove that the n…
New method detects change points in quasi-periodic signals without supervision.
problem Detecting change points in complex, non-harmonic signals.
method Optimal transport theory, topological analysis, bootstrap procedure.
result Successfully detects abnormal cardiac cycles in various arrhythmias.
Paper proposes TBSD for efficient anomaly detection in textured images.
problem Challenges in anomaly detection for textured images, especially in manufacturing systems.
method Texture basis integrated smooth decomposition (TBSD) approach.
result TBSD surpasses benchmarks with less misidentification and superior performance.
The M and A transactions represent a wide range of unique business optimization opportunities in the corporate transformation deals, which are usually characterized by the high level of total risk. The M and A transactions can be successfully implemented by taking to an account the size of investments, purchase price, …
The study examines two types of fractals and their topological properties.
problem Analyzing the topological properties of self-similar fractals with a shifting parameter.
method Detailed discussion and proof for disk-likeness and connectivity.
result Conditions for Tε to be quasi-periodic and connected. In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (including Riemannian) manifold of dimension not less than 2.
We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic examples of infinite genus.
This work uses QPGPs to improve ILC performance in repetitive tasks.
problem Performance degradation in repetitive motion tasks due to environmental changes and robot wear.
method Incorporates Quasi-Periodic Gaussian Processes into a predictive ILC framework.
result The proposed approach achieves faster convergence and robustness under disturbances.
New financial models explain market phenomena like boom-bust cycles.
problem Financial markets behavior not well captured by current models.
method Agent-based modeling, physical ideas, stochastic differential equations.
result Second order models better explain market phenomena.
The paper explores the geometry of level lines of quasiperiodic functions with many periods.
problem Describing the geometry of level lines of quasi-periodic functions with a large number of periods.
method Generalizes the Novikov problem to the multidimensional case of quasiperiodic functions.
result Arises of open or closed level lines of arbitrarily large sizes.
Consider a Riemannian metric on two-torus. We prove that the question of existence of polynomial first integrals leads naturally to a remarkable system of quasi-linear equations which turns out to be a Rich system of conservation laws. This reduces the question of integrability to the question of existence of smooth (q…
For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such a…
Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichmüller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the…
Study shows invariant curves in tubular origami dynamics, revealing geometric barriers to folding transitions.
problem Understanding the dynamics and geometric barriers in tubular origami structures.
method Kolmogorov--Arnold--Moser (KAM) theory and numerical simulations.
result Invariant curves persist in large module limits, providing phase-space interpretation of folding modes.
The celebrated KAM Theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws a lot of attention. …
In this paper we consider Monge-Ampère equations on compact Hessian manifolds, or equivalently Monge-Ampère equations on certain unbounded convex domains Ω⊆Rn, with a periodicity constraint given by the action of an affine group. In the case where the affine group action is volume-preserving, i.e.,…
Study of stellar activity cycles using probabilistic methods.
problem Debate over the existence of stellar activity branches and the effects of linear trends and harmonicity assumptions.
method Application of Gaussian processes to study mean cycle periods in chromospheric activity index.
result Confirmation of two activity branches and finding only one trend in inactive population.
In this paper we present a continuous time dynamical model of heterogeneous agents interacting in a financial market where transactions are cleared by a market maker. The market is composed of fundamentalist, trend following and contrarian agents who process information from the market with different time delays. Each …
Let G be a connected Lie group, LG its loop group, and PG->G the principal LG-bundle defined by quasi-periodic paths in G. This paper is devoted to differential geometry of the Atiyah algebroid A=T(PG)/LG of this bundle. Given a symmetric bilinear form on the Lie algebra g and the corresponding central extension of Lg,…
Develops finite-gap solutions for Pohlmeyer--Lund--Regge equation and Lund--Regge curve evolution.
problem Solving the Pohlmeyer--Lund--Regge equation and understanding Lund--Regge curve evolution.
method Finite-gap construction using hyperelliptic spectral data, Baker--Akhiezer function, and SU(2)-frame. result Explicit theta-quotient formula for PLR solutions and criteria for Lund--Regge curve evolution.
The paper constructs a symplectic groupoid for a specific Poisson structure.
problem Integrating the Adler-Gelfand-Dikii Poisson structure on Lie groups.
method Constructing a symplectic groupoid Morita equivalent to the quasi-symplectic groupoid.
result The constructed symplectic groupoid is Morita equivalent to the quasi-symplectic groupoid.
Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.
problem Automatically dating ice cores with high accuracy and capturing uncertainty.
method Probabilistic models and probabilistic programming for automatic inference.
result Demonstrated the use of probabilistic programming for ice core dating, showcasing its benefits and limitations.
We compute the chains associated to the left-invariant CR structures on the three-sphere. These structures are characterized by a single real modulus a. For the standard structure a=1, the chains are well-known and are closed curves. We show that for almost all other values of the modulus a either two or three ty…
Zero-energy orbits in the Kepler-Heisenberg problem are self-similar and stratify into three families.
problem Determining the motion of a planet around a sun in the Heisenberg group.
method Analysis of the sub-Riemannian Hamiltonian and sub-Laplacian dynamics.
result Zero-energy orbits are self-similar and stratify into future collision, past collision, and quasi-periodic families.
In this article we study the topology of a family of real analytic germs F:(C3,0)→(C,0) with isolated critical point at 0, given by F(x,y,z)=f(x,y)g(x,y)ˉ+zr, where f and g are holomorphic, r∈Z+ and r≥2. We describe the link LF as a graph manifold us…
Spectral methods predict long-term signals from linear and nonlinear systems.
problem Forecasting temporal signals from linear and nonlinear systems with arbitrary sampling.
method Introduces a spectral algorithm for linear signals and extends it to nonlinear systems using Koopman theory.
result The spectral methods achieve high accuracy in forecasting and uncertainty quantification.
Mechanical devices such as engines, vehicles, aircrafts, etc., are typically instrumented with numerous sensors to capture the behavior and health of the machine. However, there are often external factors or variables which are not captured by sensors leading to time-series which are inherently unpredictable. For insta…
Classifies minimal surfaces of finite genus in 3D space.
problem Classifying minimal surfaces of finite genus in 3D space.
method Four-step classification, lamination techniques, dynamics theorem, and topology bounds.
result Classification of minimal surfaces of genus zero and infinite topology.
Unified framework for intermittent demand forecasting using renewal processes.
problem Intermittency in demand forecasting.
method Unified framework based on extensions of discrete-time renewal processes.
result Efficacy demonstrated in forecasting practice with favorable predictive accuracy.
The study improves pitch detection in polyphonic music by learning harmonic priors.
problem Challenges in transcribing polyphonic music due to overlapping harmonics.
method Introduced Gaussian process priors and used variational Bayes for inference.
result Learning priors that fit the frequency content of sound events improves pitch detection.
Two algorithms improve Federated RL in diverse environments.
problem Collaborative learning in environments with varying dynamics.
method Proposed two federated RL algorithms, QAvg and PAvg, and a personalization heuristic.
result Achieved better performance and generalization in diverse environments.
OBSER framework infers sub-environments from objects, outperforming scene-based methods.
problem Zero-shot recognition of environments from object distributions.
method Bayesian framework using metric and self-supervised learning models to estimate object distributions in latent space.
result OBSER framework reliably performs inference in open-world and photorealistic environments, outperforming scene-based methods.
UAED discovers adaptive environments for robust learning.
problem Avoiding spurious correlations in data.
method Unified framework that learns a distribution over data transformations.
result Improves worst-case accuracy on standard benchmarks.
New approach handles stochastic and partially-observable environments using discrete autoencoders and Monte Carlo tree search.
problem Challenges in planning for stochastic and partially-observable environments.
method Uses discrete autoencoders and a stochastic variant of Monte Carlo tree search.
result Significantly outperforms MuZero on stochastic chess and scales to DeepMind Lab.
Self-supervised policy adapts after deployment without rewards.
problem Generalizing reinforcement learning policies across different environments.
method Uses self-supervision to train policies in new environments without reward signals.
result Significant improvements in generalization across diverse environments.
Bayesian model for multi-environment prediction with latent variable changes.
problem Prediction in environments with changing latent variable distributions.
method Bayesian model with empirical Bayes prior and amortized variational algorithm.
result Method outperforms previous approaches in new environments.
This paper introduces CENIE to quantify environment novelty for better UED.
problem Challenges in measuring environment novelty for effective UED.
method CENIE framework using state-action space coverage and Gaussian Mixture Models.
result CENIE improves UED performance across multiple benchmarks.
A new method learns to prioritize and use multiple views of an environment for better decision-making.
problem Learning from multiple views of an environment to improve decision-making.
method Attention-based deep reinforcement learning to dynamically attend to views of the environment.
result The method improves performance in complex 3D environments with obstacles.
Proposes a Kalman Filter modifier to improve neural network performance in changing environments.
problem Maintaining performance of neural networks in non-stationary environments.
method Kalman Filter based modifier to adapt to changes.
result The proposed model adapts better to changes with a 0.4% accuracy drop compared to 90% for conventional models.
Infinite hierarchical contrastive clustering identifies personal environments linked to health outcomes.
problem Identifying meaningful relationships between environmental features and health outcomes on an individual level.
method Contrastive clustering framework with stick-breaking prior and participant-specific prediction loss.
result Model effectively identifies distinct personal environments and groups them into meaningful types linked to health outcomes.
Dex improves reinforcement learning by solving complex environments incrementally.
problem Training reinforcement learning agents for complex, ever-changing environments.
method Incremental learning approach, using optimal weights from simpler environments.
result Incremental learning yields superior performance across multiple Dex environments.
We consider apprenticeship learning, i.e., having an agent learn a task by observing an expert demonstrating the task in a partially observable environment when the model of the environment is uncertain. This setting is useful in applications where the explicit modeling of the environment is difficult, such as a dialog…
Improved model predicts future environment changes efficiently.
problem Efficiently predicting future changes in environments for agents.
method Recurrent neural networks for high-dimensional pixel observations, reducing computational load.
result Model can predict hundreds of time-steps into the future, improving exploration and adaptability.
This paper tackles RL in non-stationary environments, improving decision-making.
problem Develop optimal RL decisions in non-stationary environments.
method Adapted change point algorithm for detecting model changes and developed an RL algorithm.
result RL algorithm maximizes long-run reward in changing environments.
Research shows collective learning across diverse environments is hard due to privacy and security concerns.
problem Privacy, security, and equity concerns restrict information sharing in diverse AI environments.
method Characterized learning algorithms as choice correspondences, provided minimum requirements for rational learning algorithms.
result The only rational learning algorithm in heterogeneous environments is unilaterally learning from a single environment without information sharing.
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …