In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces,…
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48 results for “Dynamic Extension”
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
The paper connects rational maps to limiting dynamical systems on R-trees.
problem Understanding the dynamics of degenerating rational maps.
method Barycentric extension and limit on rescalings of hyperbolic space.
result The limiting dynamical system records the limiting length spectra of rational maps.
Financial Market Dynamicscond-mat.stat-mech
Distributions derived from non-extensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S&P500…
The paper explores relationships between quandle cohomology, extensions, and automorphisms.
problem Understanding the structure of quandle extensions and automorphisms.
method Establishes a four-term exact sequence and proves relationships involving cohomology, extensions, and automorphisms of quandles.
result Derives new relationships between quandle cohomology, extensions, and automorphisms.
The paper studies dynamics of rational maps using barycentric extensions and Berkovich spaces.
problem Classifying rational maps with bounded length spectra.
method Geometric and algebraic constructions on R-trees.
result Two constructions for limiting dynamics on R-trees are equivalent.
We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our extensions to Bayesian optimization use the information learnt from this model to guide…
Abstract: Connections between Lie algebras and symplectic nilmanifolds explored.
problem Understanding the relationship between Lie algebras and symplectic nilmanifolds.
method Central extensions of Lie algebras, dynamical systems, and symplectic nilmanifolds constructed.
result Covering Lie groups for symplectic nilmanifolds can have any rank as solvable Lie groups.
The study examines how model predictions hold up under model extensions.
problem Model predictions may not be robust under model extensions, limiting their applicability.
method The study uses causal ordering to assess robustness of qualitative model predictions and characterizes model extensions that preserve predictions.
result Conditions and techniques are provided to assess robustness of model predictions under model extensions.
SINDy-PI robustly identifies implicit dynamics from noisy data.
problem Accurately modeling nonlinear dynamics from noisy data.
method Parallel, implicit SINDy algorithm with multiple optimization algorithms and model selection.
result Significantly more noise robust than previous SINDy approaches.
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.
Extends DeTEcT framework for token economies with dynamic and probabilistic parameters.
problem Modeling wealth distribution in token economies with dynamic and probabilistic parameters.
method Introduces four parametrization techniques: dynamic vs static, probabilistic vs non-probabilistic.
result Derives existing wealth distribution models from DeTEcT framework with added restrictions.
In an -framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures…
Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk Sharingq-fin.RM
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…
Derives stochastic and dissipative dynamics preserving Gibbs measure.
problem Understanding and deriving structure-preserving stochastic systems.
method Extension of Hamilton-Pontryagin principle, symmetry reduction, and inclusion of dissipation.
result New derivation of double-bracket dissipation.
Dynamic factor analysis reveals insights into Philippine stock market dynamics.
problem Understanding complex stock market dynamics.
method Dynamic factor model using Kalman method and maximum likelihood estimation.
result Common factors extracted from the model represent market trends and volatility.
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative …
New obstruction found for embedding Riemannian manifolds into Euclidean spaces.
problem Embedding Riemannian manifolds into Euclidean spaces with specific conditions.
method Motivated by incompressible Euler equations, a dynamical-topological obstruction is derived.
result Nontrivial first real homology and trivial center of fundamental group imply embedding violation.
Extends pricing methods for index options under rough volatility.
problem Pricing and hedging of index options under non-Markovian dynamics.
method Extension of large deviations methods to non-local volatility dynamics, specifically rough volatility.
result Validates the approach for pricing index options under rough volatility.
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this perspective to nonsmooth and constrained problems by obtaining differential inclusi…
New connection found between complex polynomials and surface homeomorphisms.
problem Investigating the existence of generalized pseudo-Anosov maps from quadratic polynomials.
method Developed a new connection between dynamics of quadratic polynomials and surface homeomorphisms, focusing on Hubbard trees.
result Identified conditions for constructing generalized pseudo-Anosov maps from quadratic polynomials.
New exact sequence links cohomology, automorphisms, and extensions of symmetric quandles.
problem Understanding the structure of extensions and automorphisms in symmetric quandles.
method Derived a four-term exact sequence relating 1-cocycles, second cohomology, and automorphisms.
result Obstruction to automorphisms lies in the second cohomology of symmetric quandles.
Derives equations for interacting Lie-Poisson systems using 2-cocycle extensions.
problem Understanding collective motion of interacting Lie-Poisson systems.
method Derives equations on dual space of extended structure, including 2-cocycle terms.
result Provides most general realization of Lie-Poisson system coupling.
This paper improves forecast stability without sacrificing accuracy using dynamic loss weighting.
problem Rolling origin forecast instability in time series forecasting.
method Dynamic loss weighting algorithms applied to the N-BEATS model.
result Dynamic loss weighting can further improve forecast stability without compromising accuracy.
Study calculates curvature for fluid dynamics group, proving positivity.
problem Analyzing curvature in fluid dynamics groups with Coriolis force.
method Calculates Misiolek curvature of central extension group.
result Positivity of sectional curvature implies existence of conjugate points.
New method learns dynamical systems efficiently using active learning.
problem Efficiently learning dynamical systems from data.
method Active learning strategies leveraging Gaussian process regression.
result Data-efficient training of the model through exploratory sampling.
Abstract: Necessary conditions for stabilizing subsets in systems are found.
problem Stabilizing subsets in dynamical and control systems.
method Homotopical and homological conditions are derived to rule out certain extensions.
result Certain extensions to asymptotic stabilization are ruled out.
In this paper we introduce a generalized extension of the Eisenberg-Noe model of financial contagion to allow for time dynamics of the interbank liabilities, including a dynamic examination of default risk. This framework separates the cash account and long-term capital account to more accurately model the health of a …
Introduces new info-geometric structure for dynamics on graphs and hypergraphs.
problem Modeling dynamics on discrete structures like graphs and hypergraphs.
method Introduces two dually flat structures: one on vertex space and another on edge space.
result Extends gradient flows to include nonequilibrium dynamics.
Study on neural network dynamics in high dimensions with quadratic activation.
problem Understanding training dynamics in overparameterized neural networks.
method Derivation of gradient flow equations and analysis under l2-regularization.
result Characterization of estimator performance and spectral properties in the high-dimensional limit.
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition,…
Algorithm adapts to non-stationary rewards without prior knowledge.
problem Optimizing decisions in non-stationary environments without prior knowledge of changes.
method Optimization-based algorithm that restarts when non-stationarity is detected.
result Achieves tighter dynamic regret bound and is nearly minimax optimal.
We prove that all atoroidal automorphisms of act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of non virtually cyclic, free and purely atoroidal subgroups of such that the corresponding free group extension is hyp…
DRNets dynamically route instances to efficient transformations.
problem High inference costs due to static model capacity.
method Dynamic Routing Networks (DRNets) with RouterNets for branch selection.
result DRNets reduce inference costs with comparable performance.
Paper extends knowledge tracing algorithms to infer student knowledge and predict posttest performance.
problem Lack of algorithms that directly infer student knowledge and predict posttest performance.
method Extended DKT and DKVMN to infer knowledge, and applied to BKT and PFA for comparison.
result Knowledge estimates from the extended algorithms correlate better with posttest performance than existing methods.
We study the homeomorphic extension of biholomorphisms between convex domains in without boundary regularity and boundedness assumptions. Our approach relies on methods from coarse geometry, namely the correspondence between the Gromov boundary and the topological boundaries of the domains and the dynamic…
This work extends locally conformal analysis to multi-Hamiltonian settings, providing new geometric structures and Hamiltonian dynamics.
problem Globalization problem in multi-Hamiltonian formalisms due to incompatibilities on chart overlaps.
method Investigation of locally conformally Nambu--Poisson and locally conformally generalized Poisson manifolds, constructing Hamiltonian-type evolution equations.
result Unified framework for classical, Nambu--Poisson, and generalized Poisson manifolds within a locally conformal context.
Study Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds.
problem Analyzing the Schrödinger evolution on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Relating self-adjointness of the Schrödinger operator to geometric invariants of the foliation.
result Classification of self-adjoint extensions yielding disjoint dynamics.
Crossing penalised CAViaRq-fin.ST
Paper proposes a method to estimate multiple dynamic quantiles jointly.
problem Limited joint estimation of multiple dynamic quantiles.
method Introduces a crossing penalty objective function for joint estimation.
result Validation through Monte Carlo experiments and empirical application on FTSE100 shows effectiveness.
The theory of quandle (co)homology and cocycle knot invariants is rapidly being developed. We begin with a summary of these recent advances. One such advance is the notion of a dynamical cocycle. We show how dynamical cocycles can be used to color knotted surfaces that are obtained from classical knots by twist-spinnin…
This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equa- tion, while the latter exploits a suitable kernel function. We provide an extensive comparison …
Dual pairs in fluid dynamicsmath.SG
This paper is a rigorous study of the dual pair structure of the ideal fluid and the dual pair structure for the -dimensional Camassa-Holm (EPDiff) equation, including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition of the momentum maps leads natura…
Theory of point vortices extended to closed surfaces.
problem Extending point vortex dynamics to closed surfaces.
method Unified theory of point vortex dynamics on the plane, sphere, and closed surfaces.
result Comprehensive guide to point vortex dynamics on closed surfaces with genus zero and vanishing total vorticity.
SINN combines social science and deep learning for predicting opinion dynamics.
problem Predicting opinion dynamics in social networks using traditional models requires extensive calibration with real data.
method SINN integrates theoretical models and social media data using physics-informed neural networks (PINNs) and matrix factorization.
result SINN outperforms six baseline methods in predicting opinion dynamics on real-world and synthetic datasets.
Classifies quantum particle behavior on a special cylinder.
problem Quantum confinement and transmission on a Grushin cylinder.
method Characterizes self-adjoint realizations of the Laplace-Beltrami operator.
result Identifies physically meaningful extensions of the Hamiltonian.
Motion Code models time series dynamics with sparse approximations.
problem Challenges in time series classification and forecasting on noisy data.
method Motion Code views time series as stochastic processes, assigning unique signatures to distinct dynamics.
result Motion Code outperforms benchmarks in noisy datasets, including real-world Parkinson's disease tracking.
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…
Study on learning quantum dynamics without direct interaction.
problem Learning quantum dynamics incoherently without direct interaction.
method Analyze sample complexity and prove bounds for incoherent learning.
result Prove that arbitrary measurements allow efficient learning of unitary processes incoherently.