We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dyn…
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168,742 papers · 148 categories
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48 results for “dynamical classes”
Analyzes how class imbalance and heterogeneity affect diffusion model learning dynamics.
problem Understanding how class imbalance and heterogeneity impact the learning dynamics of diffusion models.
method Developed a high-dimensional analytical framework to study class-dependent learning in score-based diffusion models.
result Class variance is the primary determinant of learning order, favoring higher-variance classes; centroid geometry plays a secondary role.
Class-imbalance refers to classification problems in which many more instances are available for certain classes than for others. Such imbalanced datasets require special attention because traditional classifiers generally favor the majority class which has a large number of instances. Ensemble of classifiers have been…
Class-imbalance refers to classification problems in which many more instances are available for certain classes than for others. Such imbalanced datasets require special attention because traditional classifiers generally favor the majority class which has a large number of instances. Ensemble of classifiers have been…
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
problem Function theory on Teichmüller space and dynamics of mapping class groups.
method Utilizes Thurston's theory and Sullivan's theory on discrete subgroups of hyperbolic space.
result Establishes connections between function theory, dynamics, and ergodic theory.
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit …
Links and dynamicsmath.DS
This paper classifies links in 3D dynamical systems.
problem Classifying links in 3D dynamical systems.
method Analyzing diffeomorphisms and link complements in .
result Countable number of equivalence classes of tame links in .
Study dynamic risk measures and performance indices using distortion functions.
problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.
method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.
result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.
This paper discusses online algorithms for inverse dynamics modelling in robotics. Several model classes including rigid body dynamics (RBD) models, data-driven models and semiparametric models (which are a combination of the previous two classes) are placed in a common framework. While model classes used in the litera…
Symbolic dynamics for flows in high dimensions, extending previous work.
problem Coding flows with positive speed in high dimensions.
method Construct symbolic dynamics for flows with positive speed in any dimension.
result Extended symbolic dynamics to flows in high dimensions, including homoclinic classes.
This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied. The existence of a dynamically minimal representative with respect to these relat…
Classifying foliationsmath.DS
We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …
The paper explores the dynamics of composite symplectic Dehn twists with nonuniform hyperbolicity.
problem Understanding the dynamics and properties of composite symplectic Dehn twists.
method Analyzing the form of nonuniform hyperbolicity, growth of Floer cohomology, and classification of symplectic mapping classes.
result Composite symplectic Dehn twists exhibit positive topological entropy and exponential growth in Floer cohomology.
New study on guidance in masked diffusion models, showing how it shapes sampling dynamics.
problem Understanding how guidance influences the sampling behavior of masked diffusion models.
method Derived explicit solution to guided reverse dynamics, analyzing effects in 1D and 2D.
result Guidance amplifies class-specific regions and suppresses shared regions, affecting covariance structures.
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of compl…
The study analyzes the performance of a nonparametric estimator for dynamical systems.
problem Analyzing the performance of a nonparametric estimator for dynamical systems.
method Nonparametric least squares estimator (LSE) and information-theoretic methods.
result Rate-optimal error bounds for nonparametric hypotheses classes.
Analyzes SGD dynamics on multi-class problems with exact expressions.
problem Analyzing SGD dynamics on multi-class problems.
method Developed a framework for analyzing training and learning rate dynamics using exact expressions.
result Exact expressions for risk and overlap with true signal in terms of ODEs.
A new classifier improves one-class predictions on unevenly sampled data.
problem Non-uniformly sampled data affects one-class classifier performance.
method Dynamic decision boundary based on minimum spanning tree.
result Proves effectiveness and robustness compared to state-of-the-art classifiers.
In this paper we propose a new class of Dynamic Mixture Models (DAMMs) being able to sequentially adapt the mixture components as well as the mixture composition using information coming from the data. The information driven nature of the proposed class of models allows to exactly compute the full likelihood and to avo…
Study shows certain diffeomorphisms cannot be dynamically coherent.
problem Dynamically coherent behavior in partially hyperbolic diffeomorphisms.
method Analyzes pseudo-Anosov components and Nielsen-Thurston classification.
result Extends previous work to larger class of diffeomorphisms.
As we enter into the big data age and an avalanche of images have become readily available, recognition systems face the need to move from close, lab settings where the number of classes and training data are fixed, to dynamic scenarios where the number of categories to be recognized grows continuously over time, as we…
Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies are considered. An algorithm for the reconstruction of the topology of interacti…
Class Balanced Dynamic Acquisition for Domain Adaptive Semantic Segmentation using Active Learningcs.CV
CBDA improves active learning for semantic segmentation, especially with imbalanced classes.
problem Class imbalance degrades performance in domain adaptive active learning.
method Class Balanced Dynamic Acquisition (CBDA) selects more balanced labels for active learning.
result CBDA increases minority class performance and outperforms baselines by 0.6-2.4 mIoU.
Class of Newtonian dynamical systems admitting normal blow-up of points in Riemannian manifolds is considered. Geometric interpretation for weak normality condition, which arose earlier in the theory of dynamical systems admitting the normal shift of hypersurfaces, is found.
New financial models use tempered stable subordination for better correlation dynamics.
problem Building financial models with better correlation dynamics.
method Introducing tempered stable Sato subordinators and additive inhomogeneous processes.
result The new process has time-dependent correlation, improving fit for financial data.
We consider dynamical stability for a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics. Our focus is on homogeneous metrics on non-compact manifolds. Following the program of Guenther, Isenberg, and Knopf, we define a class of weighted little Hölder spaces with certain …
Study classifies stock price jumps as exogenous or endogenous using news data.
problem Differentiating between exogenous and endogenous price jumps.
method Synchronized news data with order book data to analyze stock price movements.
result Exogenous jumps are abrupt and follow a decaying power-law, while endogenous jumps are progressively accelerating.
A novel one-class classifier fusion method for robust anomaly detection.
problem Fundamental challenges in ensemble-based anomaly detection.
method Locally adaptive learning with dynamic ℓp-norm constraints and interior-point optimization.
result Significantly improved computational efficiency and superior performance across diverse anomaly types.
At present, object recognition studies are mostly conducted in a closed lab setting with classes in test phase typically in training phase. However, real-world problem is far more challenging because: i) new classes unseen in the training phase can appear when predicting; ii) discriminative features need to evolve when…
In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how information-theoretic criterion functions can be used to induce sparse, discriminative, and c…
Analysis shows data imbalance slows learning curves for minority and majority classes.
problem Data imbalance impacts learning dynamics and model performance.
method Theoretical analysis of GD and SGD, including per-class normalization.
result Data imbalance causes sub-optimal learning trajectories for minority and majority classes.
We present a solution to an optimal stopping problem for a process with a wide-class of novel dynamics. The dynamics model the support/resistance line concept from financial technical analysis.
Paper tackles dynamic label shift in online learning, achieving optimal performance.
problem Adapting to changing class marginals in online supervised and unsupervised learning.
method Develops novel algorithms reducing adaptation to online regression, achieving optimal dynamic regret.
result Achieves superior performance in various online label shift scenarios.
In recent years, more machine learning algorithms have been applied to odor classification. These odor classification algorithms usually assume that the training datasets are static. However, for some odor recognition tasks, new odor classes continually emerge. That is, the odor datasets are dynamically growing while b…
Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality in terms of dynamical properties of generators of the holonomy groups are found. The non-triviality for…
We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an applications, we positively answer the Sard problem in some classes of Carnot groups.
We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we employ posterior distributions over models, thus taking into account in a princi…
A fast spectral algorithm detects community structure in evolving graphs.
problem Detecting community structure in time-evolving sparse graphs.
method Extension of the Bethe-Hessian matrix for spectral community detection.
result The algorithm reaches the optimal detectability threshold and outperforms other methods.
Study on order book dynamics with uniform catastrophes, explaining volatility and trends.
problem Understanding volatility and trends in financial markets with different types of liquidity.
method Stochastic models and population processes with uniform catastrophes.
result Law of large numbers, central limit theorem, and large deviations proved for the model.
Study mapping class group action on character varieties, proving Kronecker's Theorem.
problem Topological-dynamical action of mapping class group on character varieties.
method Analyzes -character variety and dense orbit conditions.
result Provides a dynamical proof of Kronecker's Theorem.
Slow north-south dynamics on math.GT
We consider the action of a pseudo-Anosov mapping class on . This action has north-south dynamics and so, under iteration, laminations converge exponentially to the stable lamination. We study the rate of this convergence and give examples of families of pseudo-Anosov mapping classes where the rate go…
This paper focuses on the interplay between the intersection theory and the Teichmueller dynamics on the moduli space of curves. As applications, we study the cycle class of strata of the Hodge bundle, present an algebraic method to calculate the class of the divisor parameterizing abelian differentials with a non-simp…
Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we propose \emph{variational integrator networks}, a class of neural network architecture…
We give a dynamical characterisation of odd-dimensional balls within the class of all contact manifolds whose boundary is a standard even-dimensional sphere. The characterisation is in terms of the non-existence of short periodic Reeb orbits.
High-dimensional diffusion models suffer from distorted samples due to CFG.
problem Distortions in high-dimensional guided diffusion models.
method Analytical tools from statistical physics, dynamic mean-field theory.
result Distortions arise in high-dimensional settings due to class separability issues.
New bounds on learning from multiple distributions for VC classes.
problem Understanding the sample complexity of learning from multiple data distributions.
method Analyzing the gap between known upper and lower bounds for PAC-learnable classes.
result Recent progress on sample complexity for VC dimension d classes on k distributions.
Develops a framework for robust RL with dynamic risk measures.
problem Optimal RL strategies depend on risk preferences and model dynamics.
method Dynamic robust distortion risk measures, Wasserstein ball, neural networks, strictly consistent scoring functions, policy gradient formulae, actor-critic algorithm.
result Demonstrates improved performance in portfolio allocation example.
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the Laplace spectrum. In particular, we prove dynamical stability of some classes of E…