This paper classifies expanding attractors and non-transitive Anosov flows on specific knot and manifold spaces.
problem Classifying expanding attractors and non-transitive Anosov flows on specific knot and manifold spaces.
method Using the derived Anosov (DA) expanding attractor and the Franks-Williams manifold, the paper proves the uniqueness of these structures.
result The DA expanding attractor and the Franks-Williams non-transitive Anosov flow are the unique structures supported by N0 and M0 respectively. Combines ML and DA to infer unresolved scale parametrisation from noisy data.
problem Training ML-based parametrisations from realistic, noisy and sparse observations.
method Two-step process: DA for state estimation, ML for model error prediction.
result Hybrid model produces better forecasts and attractor representation.
Paper analyzes coexisting hidden and self-excited attractors in an economic system.
problem Existence of coexisting hidden and self-excited attractors in economic systems.
method Integer and fractional order analysis of an economic system.
result Integer-order system exhibits multiple combinations of coexisting hidden and self-excited attractors.
Characterizes knotted toroidal sets as attractors in 3D.
problem Characterizing knotted toroidal sets as attractors in R3. method Global and local dynamical systems analysis, homeomorphisms and flows.
result Sufficient conditions for incompressible surfaces as attractors.
CAD-DA controls anomaly detection under domain adaptation.
problem Valid statistical inference after domain adaptation.
method Conditional Selective Inference to handle domain adaptation effects.
result Valid statistical inference under domain adaptation achieved.
The paper is focused on the existence problem of attractors for foliations. Since the existence of an attractor is a transversal property of the foliation, it is natural to consider foliations admitting transversal geometric structures. As transversal structures are chosen Cartan geometries due to their universality. T…
SFS-DA method statistically tests FS reliability under domain adaptation.
problem Feature selection reliability under domain adaptation with limited target data.
method Selective Inference framework to control false positive rate and enhance true positive rate.
result SFS-DA method controls FPR below a pre-specified level α (e.g., 0.05) while maximizing true positive rate. New DA method CIRM outperforms existing methods under structural causal model assumptions.
problem Improving prediction performance in domain adaptation with perturbed source and target data.
method Theoretical framework based on structural causal models to analyze and compare DA methods.
result CIRM method outperforms existing methods when covariates and label distributions are perturbed in target data.
We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is chaos in the demand-supply dynamics. Our numerical simulation shows that such a cha…
The paper studies dimensions of attractors for modified Leray-alpha equation on various surfaces.
problem Investigate attractor dimensions of the modified Leray-alpha equation.
method Existence and uniqueness of weak solutions, global attractor existence, estimates for vorticity scalar equations, Kolmogorov flows.
result Established upper and lower bounds for Hausdorff and fractal dimensions of global attractors on S2 and T2. Study bounds topological entropy of toroidal attractors.
problem Bounding entropy of toroidal attractors.
method Analyzing topological properties of toroidal sets to bound entropy.
result Entropy of toroidal attractors is bounded from below.
There are a variety of Domain Adaptation (DA) scenarios subject to label sets and domain configurations, including closed-set and partial-set DA, as well as multi-source and multi-target DA. It is notable that existing DA methods are generally designed only for a specific scenario, and may underperform for scenarios th…
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…
Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial perturbations to the input data. Although DA is widely used, its capacity to provably impr…
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…
A central challenge faced by memory systems is the robust retrieval of a stored pattern in the presence of interference due to other stored patterns and noise. A theoretically well-founded solution to robust retrieval is given by attractor dynamics, which iteratively clean up patterns during recall. However, incorporat…
Domain adaptation (DA) is an important and emerging field of machine learning that tackles the problem occurring when the distributions of training (source domain) and test (target domain) data are similar but different. Current theoretical results show that the efficiency of DA algorithms depends on their capacity of …
ADDA framework speeds up data augmentation in massive data settings.
problem Slow data augmentation in massive data settings.
method Develops asynchronous and distributed data augmentation (ADDA) framework.
result ADDA significantly speeds up data augmentation compared to parent DA algorithms.
TransCal calibrates DA models with lower bias and variance.
problem Calibrating DA models to estimate accurate predictive uncertainty.
method Transferable Calibration (TransCal) in a unified hyperparameter-free optimization framework.
result TransCal achieves more accurate calibration with lower bias and variance.
OMD and DA perform similarly in static settings but OMD is inferior under dynamic learning rates.
problem Proving and understanding the performance difference between OMD and DA under dynamic learning rates.
method Introducing stabilization to OMD and modifying its convergence analysis.
result OMD with stabilization and DA have the same performance guarantees under dynamic learning rates.
The article contains a construction of a self-similar dendryte which cannot be the attractor of any self-similar zipper.
EnFF uses flows to speed up DA in high dimensions.
problem Efficiently assimilating noisy data in high-dimensional systems.
method Flow Matching (FM) for training-free, scalable data assimilation.
result EnFF accelerates DA with improved cost-accuracy tradeoffs and scalability.
For machine learning task, lacking sufficient samples mean the trained model has low confidence to approach the ground truth function. Until recently, after the generative adversarial networks (GAN) had been proposed, we see the hope of small samples data augmentation (DA) with realistic fake data, and many works valid…
GGDA simplifies DA for large models, speeding up attribution by up to 50x.
problem Computational intensity of existing DA methods limits their applicability to large-scale models.
method Generalized Group Data Attribution (GGDA) framework attributing to groups of training points.
result GGDA achieves up to 50x speedups over standard DA methods while maintaining effectiveness.
This review article surveys data augmentation MCMC algorithms.
problem Sampling from intractable probability distributions.
method Comprehensive study of DA MCMC algorithms, their convergence properties, and acceleration strategies.
result Synthesizes recent developments and provides insights for researchers.
STAND-DA improves AD in DA target domains with limited data.
problem Statistical validity of AD after DA with limited data.
method Selective Inference framework for GPU-accelerated p-value computation. result Valid p-values and controlled false positive rate. DA improves solar wind forecasts by updating model boundary conditions.
problem Improving solar wind forecasting accuracy.
method Variational Data Assimilation with solar wind model and in-situ observations.
result DA forecasts are more accurate than non-DA forecasts, especially when STEREO-B's latitude is offset from Earth.
The paper studies geometric properties of soliton surfaces using an extended Darboux frame field.
problem Geometric analysis of soliton surfaces associated with the Betchov-Da Rios equation.
method Derivative formulas of an extended Darboux frame field, geometric invariants, curvature calculations.
result Construction of curvature ellipse and Wintgen ideal soliton surfaces.
Paper tackles multi-source domain adaptation for regression.
problem Predicting HDL cholesterol levels using gut microbiome data.
method Two-step procedure: 1) Extend a flexible single-source DA algorithm for classification to regression. 2) Augment with ensemble learning for multi-source DA.
result Consistent improvement in HDL cholesterol level prediction performance over existing methods.
In human perception and cognition, a fundamental operation that brains perform is interpretation: constructing coherent neural states from noisy, incomplete, and intrinsically ambiguous evidence. The problem of interpretation is well matched to an early and often overlooked architecture, the attractor network---a recur…
In dialogues, an utterance is a chain of consecutive sentences produced by one speaker which ranges from a short sentence to a thousand-word post. When studying dialogues at the utterance level, it is not uncommon that an utterance would serve multiple functions. For instance, "Thank you. It works great." expresses bot…
In this paper we focus on compacta K⊆R3 which possess a neighbourhood basis that consists of nested solid tori Ti. We call these sets toroidal. In \cite{hecyo1} we defined the genus of a toroidal set as a generalization of the classical notion of genus from knot theory. Here we introduce the se…
We study few-shot supervised domain adaptation (DA) for regression problems, where only a few labeled target domain data and many labeled source domain data are available. Many of the current DA methods base their transfer assumptions on either parametrized distribution shift or apparent distribution similarities, e.g.…
Study analyzes Echo State Network parameters for Rossler attractor dynamics.
problem Understanding the influence of network type on Echo State Network performance.
method Experimental analysis of Echo State Network parameters using Rossler attractor.
result Exploration of how network type affects Echo State Network performance.
There are few papers about the consumption pattern of the Portuguese wine, using econometrics techniques. This work, pretend to analyze the consumers behavior of the wine produced in Portugal, determining the demand equation with panel data methods. There were used statistical data available in the Alentejo Regional Wi…
This work extends ME-RL using diffusion models to sample optimal policies.
problem Sampling from the optimal policy trajectory distribution in ME-RL.
method Introducing Diffusion-Augmented Markov Decision Processes (DA-MDPs) to minimize reverse KL divergence.
result DA-MDPs enable seamless integration into various ME-RL methods and outperform baselines.
New risk models use chaotic attractors to predict extreme events.
problem Predicting Black Swan events in financial markets.
method Combining heavy-tailed priors with chaotic dynamics (Lorenz and Rossler systems).
result Models generate volatility clustering, fat tails, and extreme events.
Paper analyzes gradient descent with noisy data copies for linear regression, showing regularization and acceleration effects.
problem Improving generalization in machine learning through data augmentation with noise.
method Gradient descent with on-line noisy copies for linear regression analysis.
result Training with on-line noisy copies is equivalent to ridge regularization with a specific regularization parameter.
This paper studies closed 3-manifolds which are the attractors of a system of finitely many affine contractions that tile R3. Such attractors are called self-affine tiles. Effective characterization and recognition theorems for these 3-manifolds as well as theoretical generalizations of these results to hig…
New method uses data augmentation to improve causal effect estimation.
problem Improving causal effect estimation in the presence of hidden confounders.
method Introduces IV-like regression and data augmentation techniques.
result Data augmentation can simulate worst-case scenarios for causal estimation.
Voice activity detection (VAD), which classifies frames as speech or non-speech, is an important module in many speech applications including speaker verification. In this paper, we propose a novel method, called self-adaptive soft VAD, to incorporate a deep neural network (DNN)-based VAD into a deep speaker embedding …
In this paper we consider the realization of DE attractors by self-diffeomorphisms of manifolds. For any expanding self-map φ:M→M of a connected, closed p-dimensional manifold M, one can always realize a (p,q)-type attractor derived from φ by a compactly-supported self-diffeomorphsm of $\RR^{p+q}$, as long…
Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and that give predictions without explicit knowledge of the rules governing a syste…
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from experimental data implicitly assume that the measurements have higher intrinsic …
As a first step to understand how complicated attractors for dynamical systems can be, one may consider the following realizability problem: given a continuum K⊆R3, decide when K can be realized as an attractor for a homeomorphism of R3. In this paper we introduce toroidal sets as th…
Deep Neural Networks (DNNs) have recently been achieving state-of-the-art performance on a variety of computer vision related tasks. However, their computational cost limits their ability to be implemented in embedded systems with restricted resources or strict latency constraints. Model compression has therefore been …
Deep learning improves chaotic dynamics filtering without ensemble.
problem Discovering efficient DA schemes for chaotic dynamics.
method Residual Convolutional Neural Network for the analysis step.
result Deep learning achieves ensemble filtering accuracy without an ensemble.
Bayesian model selection optimizes data augmentation for improved machine learning robustness.
problem Choosing optimal data augmentation parameters is challenging and often done through trial and error.
method Interprets augmentation parameters as model hyperparameters and uses Bayesian model selection to optimize them.
result Our approach improves calibration and robust performance on various tasks.