This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
New Lie systems derived from Goursat distributions with applications to differential equations.
problem Analyzing Lie systems associated with Goursat distributions and their applications.
method Analyzing bracket-generating distributions and their relation to Lie systems, focusing on reductions and reconstructions.
result Lie systems associated with Goursat distributions can be reduced and solutions reconstructed from reduced systems.
Study new k-contact distributions and Lie systems.
problem Characterizing and understanding k-contact distributions. method Analyzing Goursat distributions and Lie systems.
result Characterized new types of k-contact distributions. Theory explains power-law distributions without complex models.
problem Understanding power-law distributions in geometrically growing systems.
method Developed a theory of geometrically growing systems and applied it to explain various distributions.
result The geometrically growing system's distribution flattens over time, increasing relative size ratios.
This paper uses multivariate probability models to assess financial system risks.
problem Assessing systemic risk in financial systems.
method Computes multivariate conditional probability distributions for elliptical distributions, focusing on Student-t and Normal models.
result Proposes measures of stress impact and systemic risk.
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus can not be used as a standard distribution. Normally professionals in the area …
Asynchronous SGD generalizes well with enough data, improving stability and reducing error.
problem Generalization performance of asynchronous distributed SGD systems.
method Algorithm stability framework, adaptive learning rate strategy.
result Distributed asynchronous SGD generalizes well with enough data samples.
Study curvature and torsion in Gaussian distribution's dual coordinate system.
problem Characterize geometric invariants of Gaussian distribution.
method Investigate Riemannian curvature and torsion in a dual coordinate system of Gaussian distribution.
result Explicitly give Amari formulas in the new coordinate system.
A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly, we derive precisely the geometric constraint conditions of the induced distribu…
Efficiently designs distributed controllers for sparse systems with sub-linear sample complexity.
problem Designing robust distributed controllers for unknown-but-sparse linear systems.
method Combining distributed controller synthesis and structured linear inverse problems for system identification.
result Near-optimal distributed controllers can be learned with sub-linear sample complexity and near-linear time complexity.
Ray is a distributed system for AI applications that learn from continuous interactions.
problem Demanding systems requirements for next-gen AI applications.
method Unified interface for task-parallel and actor-based computations, distributed scheduler, fault-tolerant store.
result Demonstrated scaling beyond 1.8 million tasks per second and better performance for reinforcement learning.
Develops a method to predict system behavior under disruptions.
problem Predicting changes in system behavior due to external perturbations.
method Counterfactual distribution regression for structured inference.
result Generalizes behavior predictions from natural to disrupted states.
Bayesian inference models failure distributions in autonomous systems.
problem Estimating the distribution of failures in complex systems.
method Bayesian inference using system dynamics rollouts and gradient computation.
result Improves sample efficiency and parameter space coverage in autonomous systems.
The paper describes conformal structures and Pfaffian systems for rolling surfaces.
problem Maximally symmetric rolling distributions and their conformal structures.
method Analyzes Nurowski's conformal structure and complexifies rolling distributions.
result Changes of coordinates map conformal structures to flat metrics.
New method improves predictive systems with better theoretical guarantees.
problem Constructing predictive systems with out-of-sample calibration guarantees.
method Residual Distribution Predictive Systems (RDPs) that nest conformal predictive systems and offer flexibility.
result Empirically, RDPs perform competitively with conformal predictive systems and can be implemented with various regression methods.
RMCSE improves voltage estimation in low-observability distribution systems.
problem Insufficient measurements in distribution system state estimation.
method Combines matrix completion and power system model, minimizes rank and residual with different weights.
result Robust voltage estimation in low-observability systems without bad data detection.
Two new methods improve efficiency of conformal predictive systems.
problem Efficiency of conformal predictive systems in regression problems.
method Split conformal predictive systems and cross-conformal predictive systems.
result Cross-conformal predictive systems are more efficient but not guaranteed valid.
New approach for large-scale distributed learning systems that improve generalization performance.
problem Transitioning from centralized to distributed AI systems for complex learning tasks.
method Self-organizing hierarchical structuring mechanism based on agglomerative clustering, hierarchical generalization, and personalized learning.
result Demonstrates better generalization performance compared to conventional federated learning algorithms.
The paper studies distributions and controllability in quantum mechanical systems.
problem Controlling quantum mechanical systems and their evolution.
method Analysis of distributions, controllability, and geodesics on sub-Finsler manifolds.
result Proves the Lie group decomposition and geodesics equivalence for quantum system steering.
New tools for uncertainty in dynamical systems without distribution assumptions.
problem Uncertainty representation in dynamical systems without distributional assumptions.
method Kernel mean embedding and kernel probabilistic programming.
result Distribution-free representation, comparison, and propagation of uncertainties.
Metaoptimization improves deep reinforcement learning on distributed systems.
problem Stability and hyperparameter tuning issues in deep reinforcement learning.
method Introducing HyperTrick, a metaoptimization algorithm.
result HyperTrick effectively tunes hyperparameters in deep reinforcement learning.
We describe financial systems as condensates, similar to Bose-Einstein condensates, and calculate statistical distributions following from the model. The calculated distributions of investments into speculated financial assets are found equivalent to a Pareto distribution, and the calculated distributions of the price …
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety…
Transferable Boltzmann Generators learn to sample unseen molecules efficiently.
problem Generating equilibrium samples of molecular systems.
method Boltzmann Generators using normalizing flows to learn transformations.
result Transferable Boltzmann Generators can predict zero-shot Boltzmann distributions for unseen molecules.
Study on loss probabilities for diversified financial systems with light-tailed claims.
problem Analyzing risks in systems of diversified financial agents with light-tailed claims.
method Assuming exponentially distributed claims, we derive conditional loss distributions and compare with heavy-tailed claims.
result Conditional loss distributions reveal different risk profiles for agents and systems compared to heavy-tailed claims.
Develops a neural framework for probabilistic forecasting of dynamical systems.
problem Uncertainty quantification in dynamical systems using trajectory-oriented approaches.
method D2D neural probabilistic forecasting framework using kernel mean embeddings and mixture density networks.
result The D2D model captures distributional evolution in chaotic systems and produces skillful probabilistic forecasts.
Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and luck and not of reason! 2. Data for property, automobile sales, marriages and job m…
The paper analyzes heavy-tailed multivariate distributions in non-stationary systems using random matrix theory.
problem Risk assessment for rare events in complex, non-stationary systems.
method Generalized scalar product between correlation matrices, model for non-stationary fluctuations.
result Formulae for multivariate distributions with reduced parameters, facilitating applications.
Bayesian state estimation improves accuracy for unobservable power distribution systems.
problem State estimation for unobservable distribution systems.
method Deep learning approach with distribution learning, Monte Carlo training, and Bayesian bad-data detection.
result Deep learning outperforms existing benchmarks in state estimation accuracy.
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
The paper optimizes learning Gaussian Processes in distributed systems with minimal communication.
problem Learning Gaussian Processes in distributed and communication-limited systems.
method Information-theoretic bounds and practical schemes like per-symbol quantization.
result The proposed methods outperform previous zero-rate distributed GP learning schemes.
Study magnetic Hamiltonian systems with constraints, deriving Hamilton-Jacobi equations.
problem Understanding dynamics of controlled magnetic Hamiltonian systems with constraints.
method Defined CMH system, derived Hamilton-Jacobi equations for different constraints.
result Invariant solutions of Hamilton-Jacobi equations under CMH-equivalence.
DES training speeds up large-scale recommender systems convergence.
problem Training large-scale recommender systems with dynamic sparse features.
method Distributed Equivalent Substitution (DES) framework for fully synchronous training.
result DES achieves higher AUC and up to 68.7% communication savings.
SharedMF uses secret sharing to protect privacy in distributed recommendation systems.
problem Privacy issues in multi-source data for recommendation systems.
method Federated learning and secret sharing technology.
result SharedMF achieves faster execution speed and better data adaptability compared to homomorphic encryption methods.
This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.
problem Understanding dynamics of magnetic systems with geometric constraints.
method Developed Hamilton-Jacobi equations for magnetic systems with nonholonomic constraints.
result Revealed relationships between magnetic structures, constraints, and dynamics.
DVK model infers uncertainty-aware dynamical models for better control.
problem Uncertainty in nonlinear dynamical systems makes prediction and control challenging.
method Deep Variational Koopman (DVK) model infers distributions over observations.
result DVK model provides a distribution over dynamical models for long-term prediction and control.
Real-time detection of out-of-distribution data in CPS control systems.
problem Detecting out-of-distribution data in CPS control systems for safety.
method Inductive conformal prediction and anomaly detection using variational autoencoders and deep support vector data description.
result Efficient real-time detection with low false alarm rates and comparable execution time.
Fair ML systems can be safe ML systems by considering uncertainty.
problem Safety of data-driven decision systems is often neglected.
method Viewing ML systems as socio-technical, uncertainty-aware modeling.
result Fair models should be uncertainty-aware, e.g. through distributional regression.
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical systems. Specifically, we study …
The paper presents the geometry of Lie algebroids and its applications to optimal control. The first part deals with the theory of Lie algebroids, connections on Lie algebroids and dynamical systems defined on Lie algebroids (mainly Lagrangian and Hamiltonian systems). In the second part we use the framework of Lie alg…
Generative adversarial network for probabilistic forecasting of random systems.
problem Forecasting random dynamical systems without distributional assumptions.
method Recurrent neural network and generative adversarial network (GAN) with regularization based on maximum mean discrepancy (MMD).
result The proposed model successfully forecasts complex stochastic processes with multiple-step predictions.
New methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.
Study analyzes stock market correlations using multivariate distributions.
problem Capturing the correlation structure of complex, non-stationary systems.
method Applied Random Matrix Model to empirical data of 479 US stocks.
result Described and quantified changes in empirical distributions due to non-stationarity.
New AI model improves grid planning efficiency and reliability.
problem Improving distribution grid planning with AI for energy sustainability.
method Hyperstructures Graph Convolutional Neural Networks (Hyper-GCNNs) with attention mechanism.
result Hyper-GCNNs outperforms existing models in computational efficiency and accuracy.
Paper studies IPG method's robustness in noisy distributed linear regression.
problem Distributed linear regression with noise.
method Iteratively Pre-conditioned Gradient-descent (IPG) method.
result IPG method's robustness against noise compared favorably to state-of-the-art algorithms.
A framework combines diverse power grid data for a unified view.
problem Unified view of complex power grids with distributed resources.
method Belief Propagation for probabilistic data fusion.
result Efficient distributed inference algorithm for grid state quantification.