A new algorithm identifies features in non-stationary time series data.
problem Detecting features in non-stationary time series data.
method Hierarchical feature extraction using switching observable Markov chain models.
result The algorithm identifies features with high accuracy even under noisy conditions.
Researchers extend pseudodifferential calculus on filtered manifolds using fixed point algebras.
problem Defining operators with varying orders on filtered manifolds.
method Using generalized fixed point algebras and nilpotent Lie groups, they construct a new calculus.
result They establish a new calculus that reflects the behavior of differential operators on filtered manifolds.
A new approach to symbol calculus on filtered manifolds using C∗-algebras.
problem Symbol calculus on filtered manifolds with local isomorphism to stratified Lie groups.
method Establishing a surjective ∗-homomorphism between a C∗-algebra bundle and the algebra of bounded continuous sections. result Existence of a surjective ∗-homomorphism sym_M: Π_M → C_b(E_hom) with specific kernel properties. Improves music composition with user-defined constraints using continuous time models.
problem Combining sequence models with user-defined constraints in continuous time.
method Introduces a novel particle filter scheme for continuous time point processes.
result The particle filter scheme yields superior results in a human listening test.
Isomorphism found between filtered calculus and crossed products.
problem Tackles isomorphism in filtered calculus and crossed products.
method Uses natural R-action and structure result for C*-algebra of graded nilpotent Lie groups.
result Found isomorphism between kernel of tangent groupoid and crossed product.
Study explains Zipf's law using geometric mechanisms from a finite alphabet.
problem Explains Zipf's law in language without relying on linguistic elements.
method Uses the Full Combinatorial Word Model (FCWM) to generate geometric distributions of word lengths.
result Supports predictions of power-law rank-frequency curves, matching various languages.
Defines transverse symbols for foliated manifolds and proves their K-homology class.
problem Transverse index theory for foliated manifolds.
method Using filtrations of tangent bundles, defining transverse symbols, and constructing equivariant KK-classes.
result Transversally Rockland operators yield a K-homology class and there is a Poincare duality result.
Study recovers C*-algebra from fields of Toeplitz algebras on specific groups.
problem Recovering C*-algebra from fields of Toeplitz algebras on specific groups.
method Using continuous fields of Toeplitz algebras and a crossed product.
result Algebra of principal symbols can be recovered from fields of Toeplitz algebras.
Symbolic dynamics applied to share prices reveals complex, non-Markovian patterns.
problem Analyzing complex systems like share prices using symbolic dynamics.
method Symbolic dynamics applied to time series of share price returns.
result Nontrivial spectrum of Renyi entropies found, indicating non-Markovian behavior.
This paper presents a ML-based receiver for SDR that outperforms conventional methods.
problem Complexity and performance issues in multiuser detection.
method Supervised learning for direct symbol detection without parameter estimation.
result The ML-based receiver achieves similar or better performance than SIC and MMSE receivers.
Unified framework integrates symbolic planning and HRL for robust decision-making.
problem Combining reinforcement learning and symbolic planning for robust decision-making in dynamic environments.
method Integrates symbolic planning with hierarchical reinforcement learning to guide task execution and improve planning.
result Unified framework leads to rapid policy search and robust symbolic plans in complex domains.
Characterizes polyhomogeneous symbols and applies to Heisenberg calculus.
problem Understanding polyhomogeneous symbols and their applications.
method Simple characterisation and generalization of A.~Connes' tangent groupoid.
result Heisenberg calculus on contact manifolds coincides with groupoid calculus.
PySR method automates discovering equations from data in chaotic dynamics and epidemics.
problem Discovering equations from complex data in dynamical systems.
method Symbolic regression methods, focusing on PySR.
result PySR method efficiently infers equations from chaotic dynamics and epidemic models, matching original forms.
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.
Characterizes how the shape of a polygon affects billiard dynamics.
problem Understanding how the shape of a billiard table influences its dynamics.
method New theorem linking Liouville current support to flat cone metrics.
result Only right-angled tables with affine differences have identical bounce spectra.
Examines predictability and complexity of economic time series using symbolic dynamics and entropy.
problem Understanding the predictability and complexity of economic time series.
method Symbolic dynamics and Information theory (entropy and uncertainty).
result Economic time series are complex and can be expressed in terms of information production.
Deep neural network generates symbolic equations from data.
problem Lack of insight into underlying mappings from traditional deep learning.
method Combines deep learning flexibility with symbolic solutions.
result Accurately generates governing equations for dynamical systems.
S2KAN integrates symbolic primitives into neural network activations for improved interpretability.
problem Training activations in KANs often lack symbolic fidelity, leading to unintelligible models.
method Softly Symbolified Kolmogorov-Arnold Networks (S2KAN) integrates symbolic primitives into training with learnable gates and a Minimum Description Length objective.
result S2KAN discovers interpretable forms when symbolic terms suffice, gracefully degrading to dense splines when necessary.
Neuro-symbolic traders suppress market prices, highlighting risks to stability.
problem Understanding and quantifying the influence of AI-generated financial models on markets.
method Developed virtual neuro-symbolic traders using deep generative models and tested them in a virtual market.
result Neuro-symbolic traders suppress market prices compared to historical data, indicating potential market instability.
The study explores highly supersymmetric backgrounds in 11D supergravity.
problem Understanding and constructing highly supersymmetric backgrounds in 11D supergravity.
method Definition of abstract symbols and a strong version of the Reconstruction Theorem, proposing a strategy to construct backgrounds, and providing an example with detailed computation.
result Bijective correspondence between highly supersymmetric backgrounds and abstract symbols, and a classical supersymmetry gap result.
Isomorphic algebra connects Toeplitz to Heisenberg group.
problem Connecting Toeplitz algebra to Heisenberg group.
method Isomorphism between Toeplitz algebra and Heisenberg group ideal.
result Found isomorphism between algebra and Heisenberg group ideal.
Paper analyzes symbolic-dynamics inspired Markov modeling for time-series data.
problem Capturing temporal patterns in sequential data for statistical learning.
method Two-step process: discretization of continuous attributes and estimation of temporal memory.
result Effective Markov modeling depends on accurate discretization and memory estimation.
Develops new approach to recover CR structures from their Levi foliations.
problem Recovering CR structures from their Levi foliations for nonregular symbols.
method Reduction to dynamical Legendrian contact structure on leaf space.
result New geometric interpretation of CR prolongation conditions.
The paper learns an autoregressive filter for unknown dynamical systems with robust guarantees.
problem Learning optimal predictions in an unknown dynamical system.
method Directly learns an autoregressive filter using an L∞-based objective, regressing on both inputs and outputs. result The algorithm has optimal sample complexity in terms of the rollout length.
This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.
problem Ensuring long-term accuracy of ensemble Kalman filters for complex dynamical systems.
method Established conditions for long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems.
result Ensemble Kalman filters maintain small estimation error over long time horizons for chaotic and machine-learned systems.
Proposes a new filtering method for dynamical systems that relaxes Gaussian and affine assumptions.
problem Inferring states of dynamical systems from observations with Gaussian and affine assumptions.
method Relaxes Gaussian and affine assumptions using deep, nonlinear, non-Gaussian models.
result Significant advantage over Gaussian Filtering and nonlinear fixed kernels.
The paper introduces invariants to describe period-doubling routes to chaos in dynamical systems.
problem Understanding the dynamics of period-doubling routes to chaos in complex systems.
method Introducing three topological invariants to describe the topology of period-doubling routes to chaos.
result Ascribed symbolic dynamics to perturbations of the Shilnikov homoclinic scenario and dynamics of the Henon map.
HKF uses neural networks to adapt Kalman filters for dynamic channel tracking.
problem Tracking channels with varying dynamics and Doppler values.
method Combines Kalman filters with hypernetworks for dynamic adaptation.
result HKF achieves up to 2dB gain over Kalman filters at high Doppler values.
We construct symbolic dynamics on sets of full measure (w.r.t. an ergodic measure of positive entropy) for C1+ε flows on compact smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent bundle of a compact C∞ surface has at least const ×(ehT/T) simple clos…
A new method for efficient variational inference in dynamic models.
problem Performing variational inference in dynamical latent variable models efficiently.
method Amortized variational filtering algorithm derived from the filtering setting.
result Improves performance across various deep dynamical latent variable models.
Paper develops a method for compact Markov modeling of time series data.
problem Compact representation of time-series data with reduced memory.
method Symbolic dynamics for partitioning, hierarchical clustering for state representation, Bayesian inference for parameter identification.
result Reduced-order Markov models capture system dynamics with minimal memory.
Paper uses STPN for energy/power prediction in complex systems.
problem Predicting energy in complex dynamical systems.
method Spatiotemporal pattern network (STPN) framework with mutual information metric.
result Improved energy prediction accuracy in wind and residential energy contexts.
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of volatility dynamics of denoised series are noticeably different…
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
GP-SUM filters complex non-Gaussian states using Gaussian Processes.
problem Stochastic dynamic filtering and state propagation with complex beliefs.
method GP-SUM combines sampling and probabilistic Bayes filters, using Gaussian Processes for dynamic and observation models.
result GP-SUM outperforms other filters on benchmarks and predicts non-Gaussian states accurately.
In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More precisely, we first show that for any modular subgroup the geodesic forward dynami…
This research explores canonical Cartan connections for filtered G-structures.
problem Determining canonical Cartan connections for filtered G-structures.
method Generalization of parabolic geometries, Lie algebra valued forms, and explicit characterization.
result Existence of canonical Cartan connections for filtered G-structures, with specific features.
The study proves the uniqueness of entropy-maximizing measures for geodesic flows on specific manifolds.
problem Uniqueness of entropy-maximizing measures for geodesic flows on rank 1 manifolds.
method Symbolic dynamics applied to countable topological Markov flows.
result Proof of the uniqueness of the measure of maximal entropy.
This paper learns state, dynamics, and filtering algorithms together for data assimilation.
problem Costly parameter tuning and inaccurate dynamics models hinder data assimilation algorithms.
method Auto-differentiable data assimilation framework that learns state, dynamics, and parameters via gradient-based optimization.
result Several data assimilation methods can be learned or tuned within this framework.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
The paper explores states of financial markets using correlation matrices and their dynamics.
problem Understanding the states of financial markets based on correlations.
method Revisits previous work and introduces recent developments in practical applications.
result Analysis of trajectories and symbolic dynamics in correlation matrix space.
New algorithms improve time series classification accuracy and efficiency while enhancing interpretability.
problem Lack of interpretability in time series classification algorithms.
method Combining multiple resolutions and domains, using SEQL with greedy feature selection.
result SAX-SFA-SEQL achieves similar accuracy to state-of-the-art methods but with lower computational time.
Develops an online learning framework for Bayesian joint filtering.
problem Streaming inference of nonlinear state-space models.
method Variational inference and sequential Monte Carlo.
result Efficient approximation of filtering posterior for a wide class of models.
Discovering quasipotential equations from data using machine learning.
problem Understanding escape mechanisms from metastable states in nonlinear systems.
method Combining neural networks and sparse regression to symbolically reconstruct quasipotential equations.
result Model-unbiased analytical forms of quasipotential discovered directly from data.
Symbolic grounding in causal dynamics achieves near-infinite temporal consistency.
problem Achieving linear identifiability in non-Gaussian physical systems.
method Physics-Grounded Symbolic Architecture (PGSA)
result PGSA achieves exact linear identifiability for all physical regimes.
AD-EnKFs use machine learning to improve data assimilation in high-dimensional systems.
problem Data assimilation in high-dimensional, unknown dynamics systems.
method Auto-differentiable ensemble Kalman filters blending machine learning and ensemble Kalman filters.
result AD-EnKFs outperform existing methods in the Lorenz-96 model.
Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.
problem Extracting symbolic information from signals, especially in music, is challenging and non-generic.
method Turned into a density estimation task, using two variational auto-encoders with additive constraint.
result Bijective signal/symbol translation achieved, allowing both signal-to-symbol and symbol-to-signal inference.
The paper studies how geometric transformations affect semi-classical operators on specific Lie groups.
problem Analyzing the effects of diffeomorphisms on semi-classical pseudodifferential operators.
method Examined the pull-back of semi-classical pseudodifferential operators by diffeomorphisms preserving the filtration.
result The pull-back of a semi-classical pseudodifferential operator by a Pansu differentiable diffeomorphism has a semi-classical symbol that is expressed in terms of the Pansu differential.