Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization…
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48 results for “Coupled Systems”
Coupled entropy corrects flaws in Tsallis entropy for complex systems.
problem Misinterpretation of generalized temperature and entropy.
method Derived from generalized Pareto and Student's t distributions.
result Provides balanced measure of uncertainty for complex systems.
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…
MUSIC learns coupled systems with sparse data and incomplete physics.
problem Learning coupled systems with incomplete physical constraints and missing data.
method Sparsity induced multitask neural network framework integrating partial physical constraints with data-driven learning.
result MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions.
The coupled KdV-mKdV system arises as the classical part of one of superextensions of the KdV equation. For this system, we prove its complete integrability, i.e., existence of a recursion operator and of infinite series of symmetries.
Global solutions found for a wave-Klein-Gordon system with strong couplings in divergence form.
problem Global well-posedness of a wave-Klein-Gordon system with strong couplings in divergence form.
method Constructed an auxiliary system with shifted primitives to handle the strong couplings.
result Established global well-posedness theorem for the wave-Klein-Gordon system.
Novel framework detects lead-lag relationships in Chinese A-share market.
problem Detecting lead-lag relationships in the Chinese A-share market.
method Two-stage framework: long-term coupling via correlation, dynamic time warping, and rank-based metrics; high-frequency data analysis via cross-correlation, Granger causality, and regression models.
result Strongly coupled stock pairs often exhibit lead-lag effects, especially at finer time scales.
Anticorrelations, subbrownian stochastic drift, and 1/f-like spectra in stable financial systemscond-mat.dis-nn
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
New integrable systems derived from Nijenhuis geometry.
problem Developing new integrable systems from Nijenhuis geometry.
method Constructing a new series of multicomponent integrable PDE systems.
result Many famous integrable systems are contained within the new series.
New insights connect strong coupling SYM amplitudes to hyperkähler geometry.
problem Understanding strong coupling SYM amplitudes.
method Integrable systems, pseudo-hyperkähler geometry, twistor theory.
result Remainder function is a pseudo-Kähler scalar in hyperkähler geometry.
New integrable systems are created using matrix operations and Lie algebra elements.
problem Generating coupled nonlinear integrable systems from zero curvature equation.
method Constructing Maurer-Cartan forms using Kronecker product and specific matrices (nilpotent, Hadamard, idempotent, k-idempotent).
result Found a closure property among chosen matrices crucial for coupling and nonlinearity.
New equations derived for Kähler metrics, linking stability and curvature.
problem Finding metrics with constant scalar curvature in Kähler geometry.
method Introduced coupled cscK equations and defined K-polystability.
result Proved existence of coupled cscK metrics for small perturbations.
LR and L+R Systemsmath-ph
We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study -dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrizat…
Agents learn and control complex mechanical systems through shared memories.
problem Controlling multi-joint dynamical systems.
method Coupled autoregressive active inference agents using Bayesian filtering and minimizing expected free energy.
result Demonstrated learning and control of a double mass-spring-damper system.
Synchronization in a market model with time delaysphysics.soc-ph
Study on synchronization in financial markets with time delays.
problem Understanding market dynamics and synchronization in financial systems with time delays.
method Examined a system of coupled non-linear delay-differential equations, linearized for small delays, and analyzed collective dynamics using bifurcation diagrams and numerical solutions.
result Demonstrated that limit cycles can be maintained in coupled N-asset models with appropriate parameterization, leading to market synchronization.
Researchers analyze wave equations for spacetime perturbations with electromagnetic and gravitational effects.
problem Analyzing perturbations in Reissner-Nordström spacetime.
method Deriving and analyzing a system of coupled wave equations for the Weyl and Ricci curvatures.
result Combined energy-Morawetz and -estimates for the system of wave equations in the case of small charge.
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysisphysics.comp-ph
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis
problem Multidisciplinary design analysis of coupled engineering systems requires solving equilibrium states where all disciplinary coupling variables are consistent.
method Residual manifold surrogate modeling framework for coupled systems.
result REMAL learns a surrogate model of the joint residual manifold via multitask Gaussian process models.
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 …
Study finds Stäckel equivalence for superintegrable systems via invariant quadrics.
problem Understanding Stäckel equivalence in superintegrable systems.
method Using invariant quadrics to determine Stäckel classes of superintegrable systems.
result Stäckel classes of superintegrable systems can be derived from associated invariant quadrics.
A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending o…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise senses of convergence and links with the long time behaviour of the systems to be con…
We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with…
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
New equations reveal moduli space rigidity in geometric deformations.
problem Understanding moduli space rigidity in geometric deformations.
method Coupled Hitchin-He equations, Lax pair, nonlinear embedding.
result Moduli space is analytically isomorphic to the classical case for small deformations.
Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
problem Proving convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
method Differentiation-based approach to handle Z process, uniformly controlling Lipschitz continuity of decoupling fields.
result Proves convergence of Markovian iteration method for FBSDEs with fully coupled drift and Z process.
We survey systemic risks to financial markets and present a high-level description of an algorithm that measures systemic risk in terms of coupled networks.
New method improves neural network classification accuracy and confidence.
problem Improving neural network classification accuracy and confidence.
method Pairwise coupling of convolutional neural networks.
result Bayes covariant method provides higher accuracy and better sureness predictions.
Study Kähler metrics with constant scalar curvature using coupled equations.
problem Finding Kähler metrics with constant scalar curvature.
method Solving a system of elliptic equations for a Kähler metric and a closed (1,1)-form, proving higher order estimates and smooth convergence.
result Smooth convergence to a cscK metric coupled to a harmonic (1,1)-form under uniform estimates.
New method linearizes nonlinear coupled oscillators on graphs.
problem Predicting global synchronization in nonlinear coupled oscillators on graphs.
method Latent dynamic filters learned through supervised matrix factorization.
result Latent dynamics filters enable effective prediction of global synchronization.
Study reveals geometric context of second-order superintegrable systems.
problem Understanding second-order superintegrable systems and their Weylian geometry.
method Re-examined second-order maximally conformally superintegrable Hamiltonian systems, revealing their Weyl structure.
result Extended conformal superintegrability to Weyl structures, interpreting systems as semi-Weyl structures.
Extracts intrinsic spatial coordinates for complex agent systems to learn PDEs.
problem Modeling collective dynamics of heterogeneous agents.
method Data-driven extraction of intrinsic spatial coordinates, learning PDEs in emergent space.
result Collective dynamics can be approximated through learned PDEs in emergent coordinates.
A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One parameter expresses the growth capacity of the agents and the other describes the local…
Modeling bank leverage dynamics to understand systemic risk in financial markets.
problem Understanding systemic risk in financial markets triggered by bank leverage dynamics.
method Developed a dynamical model of bank leverage, analyzing coupled dynamics in isolated and interconnected bank models.
result Identified a procyclical feedback loop between asset prices and leverage, leading to chaotic dynamics.
Boundedness and decay for the Teukolsky system of spin on Reissner-Nordström spacetime: the case gr-qc
Proves boundedness and decay for spin 2 Teukolsky system on Reissner-Nordström spacetime.
problem Analyzing stability of Reissner-Nordström spacetime for small charge.
method Derived quantities and generalized coupled Regge-Wheeler system.
result Proves boundedness and polynomial decay for spin 2 solutions.
Scaling Limits of Bivariate Nearly-Unstable Hawkes Processes and Applications to Rough Volatilitymath.PR
Study of coupled Hawkes processes with rough-volatility limits.
problem Understanding coupled Hawkes processes with rough-volatility limits.
method Proving weak convergence of rescaled intensity vector to stochastic Volterra equations.
result Limiting components exhibit different degrees of roughness and cross-decorrelation law.
We consider structures with torsion coupled with -instantons, on a compact -dimensional manifold. The coupling is via an equation for -forms which appears in supergravity and generalized geometry, known as the Bianchi identity. The resulting system of partial differential equations can be regarded as a…
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.
In this paper we show how a natural coupling of the Dirac equation with the generalized Jang equation, leads to a proof of the rigidity statement in the positive mass theorem with charge, without the maximal slicing condition, provided a solution to the coupled system exists.
Bayesian analysis uncovers flux couplings in metabolic networks.
problem Uncertainty and unrealistic assumptions in traditional flux analysis methods.
method Introduces Bayesian metabolic flux analysis to model reactions probabilistically and infer flux distributions.
result Reveals informative flux couplings and more unobserved fluxes in metabolic networks.
Theory for gravity coupled with fields on manifolds with null-boundary.
problem Formulating a theory for gravity coupled with scalar, SU(n), and spinor fields on manifolds with null-boundary.
method Symplectic reduction of boundary fields and constraints analysis.
result The set of constraints does not form a first class system for the three couplings.
Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger systemmath.AP
In this paper, we establish two new types of invariant sets for the coupled nonlinear Schrodinger system on , and derive two sharp thresholds of blow-up and global existence for its solution. Some analogous results for the nonlinear Schrodinger system posed on the hyperbolic space and on th…
Coupled uncertainty provided by a multifractal random walkerphysics.data-an
The aim here is to study the concept of pairing multifractality between time series possessing non-Gaussian distributions. The increasing number of rare events creates "criticality". We show how the pairing between two series is affected by rare events, which we call "coupled criticality". A method is proposed for stud…
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
Study reconstructs network interactions from oscillator dynamics data.
problem Reconstructing network interactions from observed oscillator dynamics.
method Machine learning methods applied to phase-oscillator networks.
result Reconstruction of network interactions and intrinsic dynamics parameters.
A new RNN model based on coupled oscillators mitigates gradient issues.
problem Gradient vanishing and exploding issues in RNNs.
method Time-discretization of a system of second-order ODEs modeling coupled oscillators.
result The model maintains bounded gradients, leading to stable learning of long-term dependencies.
The paper introduces new equations in Kähler geometry and proves their solutions and convexity.
problem Solving equations in Kähler geometry and understanding their geometric implications.
method Using moment map pictures to motivate and prove solutions for the equations.
result The Mabuchi functional for certain equations is shown to be convex.
The paper proposes a mechanism for business cycles using coupled real economy and stock market dynamics.
problem Understanding and predicting business cycles.
method Developed a dynamic stock market model based on opinion interactions and integrated it into a macroeconomic framework.
result The model generates quasiperiodic fluctuations (business cycles) through coupled real economy and stock market dynamics.
Research explores how interconnected systems synchronize and how to control their behavior.
problem Understanding and controlling the behavior of interconnected dynamical systems.
method Mean field games approach applied to controlled coupled oscillators.
result Developed methods to predict and influence emergent phenomena in interconnected systems.