We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We note that the operation used in knot-theoretic flocks has its non-associative version in extra loops. We use a group action on the set of f…
The paper proposes a GP-based method for discovering second-order particle dynamics models.
problem Discovering a general second-order particle-based model for agent interactions.
method Gaussian Process-based approach integrating two independent GP priors on latent interaction kernels.
result The method learns effective nonlinear dynamics representations from small data sets.
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic dynamics of each individual in a flock, and use a fractional PDE to model the evo…
Model assesses systemic risk in crude oil and gasoline futures markets.
problem Systemic risk in high-frequency crude oil and gasoline futures markets.
method Hawkes flocking model examining endogeneity and interactivity.
result Significantly higher endogenous systemic risk in WTI crude oil compared to gasoline, with gasoline having a higher influence on WTI.
The goal of this paper is to study organized flocking behavior and systemic risk in heterogeneous mean-field interacting diffusions. We illustrate in a number of case studies the effect of heterogeneity in the behavior of systemic risk in the system, i.e., the risk that several agents default simultaneously as a result…
Learning the activities of animals is important for the purpose of monitoring their welfare vis a vis their behaviour with respect to their environment and conspecifics. While previous works have largely focused on activity recognition in a single animal, little or no work has been done in learning the collective behav…
Graph neural networks learn decentralized controllers from data.
problem Finding optimal decentralized controllers for autonomous agents is challenging.
method Adapting graph neural networks to handle delayed communications and ensure scalability and transferability.
result Graph neural networks can learn decentralized controllers from data, addressing the scalability and practical implementation issues of centralized controllers.
Enhances particle filters with neural augmentation for multi-sub-state tracking.
problem Particle filters struggle with complex or approximated models and low latency requirements.
method Learning Flock (LF) uses a neural network to correct particle weights based on sub-particle relationships.
result LF improves performance, robustness, and latency in radar multi-target tracking.
New method learns SDEs with structured noise from data.
problem Learning SDEs with structured noise from data.
method Nonparametric framework for drift and diffusion terms.
result Accurately infers low-dimensional interaction kernels.
Transformers approximate mean-field dynamics of indistinguishable particles.
problem Approximating the dynamics of indistinguishable particles in complex systems.
method Using transformers to model the mean-field dynamics of interacting particle systems.
result Theoretical bounds on the distance between true and transformer-obtained mean-field dynamics.
We propose a simple model of the banking system incorporating a game feature where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The Markov Nash equilibrium generated through minimizing the linear quadratic cost subject to Cox-Ingersoll-Ross type processes creates liquidity and …
Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or a…
JAX MD enables differentiable physics simulations for molecular dynamics.
problem Performing efficient and differentiable physics simulations for molecular dynamics.
method Differentiable physics simulation environments, interaction potentials, neural networks, flexible primitives.
result Differentiable physics simulations can be used for meta-optimization and scaling to large particle systems.
We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data) subject to a network regularization term that penalizes a local model that differs fr…
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
New tool for summarizing time-varying data shapes.
problem Understanding dynamic data shapes.
method Introducing crocker stacks for time-varying metric spaces.
result Demonstrated utility in parameter identification task.
New method for online learning in interacting particle systems.
problem Parameter estimation in stochastic interacting particle systems.
method Stochastic approximation of gradient of asymptotic log likelihood using continuous observations.
result Convergence to stationary points of asymptotic log-likelihood under suitable assumptions.
Wide and Deep GNN learns from distributed graphs and retrain online.
problem Decentralized graph support changes over time, causing mismatch between training and testing graphs.
method Wide and Deep GNN architecture with distributed online learning.
result Convergence guarantees for online retraining of the wide part of the GNN.
Safe Pattern Pruning reduces pattern explosion in predictive pattern mining.
problem Exponential growth of patterns in structured data.
method Safe Pattern Pruning (SPP) method.
result Effective model building in practical data analysis.
BN^2MF identifies unknown exposure patterns in environmental mixtures.
problem Identifying unknown exposure patterns in environmental mixtures.
method Bayesian non-parametric non-negative matrix factorization (BN^2MF) with non-negative continuous priors and a non-parametric sparse prior.
result Estimates patterns of chemical exposures without specifying the number of patterns.
RestoreAI predicts landmine risk from patterns, improving clearance efficiency.
problem Predicting landmine risk from spatial patterns to enhance clearance efficiency.
method RestoreAI uses landmine patterns for risk prediction, implementing three deminers: linear, curved, and Bayesian.
result RestoreAI significantly boosts clearance efficiency, achieving a 14.37 percentage point increase in cleared landmines per timestep.
Study of knots with generalized Mazur patterns and their invariants.
problem Understanding the invariants and properties of knots with generalized Mazur patterns.
method Computational analysis of τ and ε invariants for n-twisted satellites. result None of the n-twisted patterns from the family act surjectively on the smooth or rational concordance group. Two approaches detect EV charging patterns at stations.
problem Identify charging patterns at electric vehicle charging stations.
method Two approaches: rule-based and hierarchical clustering.
result Hierarchical clustering revealed unexpected charging patterns.
Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern of learning machine. In [2,4], we discussed subjective spatial pattern, and estab…
Proves existence of circle patterns on surfaces with cusps.
problem Existence of circle patterns with prescribed angles on surfaces with cusps.
method Introduced combinatorial Ricci and Calabi flows to prove longtime existence and convergence.
result Existence of generalized circle patterns with prescribed angles on surfaces with cusps.
Study of combinatorial Calabi flow on ideal circle patterns.
problem Finding ideal circle patterns with prescribed curvatures.
method Combinatorial Calabi flow in hyperbolic and Euclidean geometry.
result Flow converges exponentially to ideal circle patterns.
CDPA identifies common and distinctive patterns in high-dimensional datasets.
problem Existing methods fail to capture the common pattern between coefficient matrices of shared latent factors.
method Proposes CDPA, an unsupervised learning method that incorporates both common and distinctive patterns of coefficient matrices.
result CDPA provides better characterization of common and distinctive patterns in high-dimensional datasets.
Study circle patterns on tori, linking symplectic forms and homeomorphisms.
problem Understanding circle patterns on tori and their symplectic properties.
method Investigates the space of circle patterns on closed tori with complex projective structures, embedding it into Teichmüller spaces and analyzing symplectic forms.
result Non-degeneracy of the pulled-back Weil-Petersson symplectic form and homeomorphism between circle patterns and Teichmüller spaces.
FSR efficiently discovers significant patterns with few resampled datasets.
problem Mining significant patterns in transactional data, especially subgroups.
method FSR uses resampling to bound the supremum deviation of quality statistics, providing rigorous guarantees on false discoveries.
result FSR effectively discovers significant subgroups with a small number of resampled datasets.
In this paper we study predictive pattern mining problems where the goal is to construct a predictive model based on a subset of predictive patterns in the database. Our main contribution is to introduce a novel method called safe pattern pruning (SPP) for a class of predictive pattern mining problems. The SPP method a…
TFPS improves time series forecasting by learning pattern-specific experts.
problem Challenges in forecasting time series data with varying patterns across segments.
method Dual-domain encoder, subspace clustering, pattern-specific experts.
result Significantly improved forecasting accuracy, especially in long-term forecasting.
Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations wh…
While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning using point process theory. Likelihood functions for point pattern data derived …
Generative model attacks CNN on MNIST by subtly replacing input patterns.
problem Adversarial attacks on neural networks.
method Generative model that replaces input patterns with generated ones.
result Demonstrated effectiveness on MNIST dataset.
The paper integrates statistical significance and discriminative power in pattern discovery.
problem Discovering actionable patterns that meet rigorous statistical significance and discriminative power criteria.
method Integrates statistical significance and discriminative power criteria into state-of-the-art algorithms.
result Improves discriminative power and statistical significance of discovered patterns without quality deterioration.
Paper extends circle pattern theory to obtuse angles.
problem Circle patterns with obtuse angles not previously covered.
method Using topological degree theory, extends Koebe-Andreev-Thurston Theorem.
result Generalized Andreev's Theorem for obtuse dihedral angles.
This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences,…
Pattern sampling reduces time series classification complexity.
problem High computational complexity of exhaustive search for shapelets.
method Pattern sampling using a weighted trie to extract discriminative patterns.
result Significant reduction in computational and memory resources.
Symplectic forms match on circle pattern space.
problem Matching symplectic forms on circle pattern space.
method Pullback of symplectic forms to circle pattern space.
result Symplectic forms on circle pattern space coincide.
Study identifies clusters of EU countries with similar young mortality patterns.
problem Identify clusters of EU countries with similar mortality patterns in young population.
method Symbolic data analysis (SDA) with age, gender, and main causes of death dimensions.
result Identified clusters of EU countries with similar mortality patterns in young population.
This research improves LSTM for monthly electricity demand forecasting using pattern-based methods.
problem Forecasting mid-term monthly electricity demand with high accuracy.
method Developed a hybrid LSTM model using x-patterns and exponential smoothing.
result The hybrid model outperformed standard LSTM and classical models.
Proposes SCR-Apriori for efficient mining of SCR-patterns.
problem Mining high-quality `Set of Contrasting Rules'-pattern (SCR-pattern) efficiently.
method Integrates SCR-pattern structure into Apriori algorithm to prune search space.
result Significantly reduces computational cost compared to state-of-the-art.
For using neural networks in safety critical domains, it is important to know if a decision made by a neural network is supported by prior similarities in training. We propose runtime neuron activation pattern monitoring - after the standard training process, one creates a monitor by feeding the training data to the ne…
In this paper, we investigate the multi-variate sequence classification problem from a multi-instance learning perspective. Real-world sequential data commonly show discriminative patterns only at specific time periods. For instance, we can identify a cropland during its growing season, but it looks similar to a barren…
The paper proposes a method to identify high-quality financial patterns using entropy.
problem Extracting reliable short-term patterns from noisy financial data.
method Entropy-assisted framework for clustering and pruning patterns.
result High-quality patterns with low local entropy and historical profitability.
We consider ``hyperideal'' circle patterns, i.e. patterns of disks appearing in the definition of the Delaunay decomposition associated to a set of disjoint disks, possibly with cone singularities at the center of those disks. Hyperideal circle patterns are associated to hyperideal hyperbolic polyhedra. We describe the…
Thurston's Circle Pattern Theorem studies existence and rigidity of circle patterns of a given combinatorial type and the given non-obtuse exterior intersection angles. Using topological degree theory, variational principle, Teichmuller theory, and Sard's Theorem, this paper generalizes Circle Pattern Theorem to the ca…
Discriminative pattern mining is an essential task of data mining. This task aims to discover patterns which occur more frequently in a class than other classes in a class-labeled dataset. This type of patterns is valuable in various domains such as bioinformatics, data classification. In this paper, we propose a novel…