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 “controlled coupled oscillators”
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.
Graph-Coupled Oscillator Networks (GraphCON) tackles graph-based learning problems.
problem The oversmoothing problem in Graph Neural Networks (GNNs).
method GraphCON is a novel framework based on discretizations of ODEs modeling oscillators coupled via graph adjacency.
result GraphCON mitigates the oversmoothing problem and exploding/vanishing gradients issues.
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.
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.
Neural ODEs control graph dynamics with low energy feedback.
problem Controlling complex dynamical systems on graphs.
method Neural Ordinary Differential Equation Control (NODEC) framework.
result NODEC learns low-energy control signals for graph dynamical systems.
Robotics: Rolling robots on a moving platform can be controlled.
problem Controlling the motion of rolling robots atop a moving platform.
method Developed a mathematical model and demonstrated simulations.
result Platform acceleration can control robot's heading and motion.
KuramotoGNN uses Kuramoto model to prevent over-smoothing in graph neural networks.
problem Over-smoothing in graph neural networks where node features become indistinguishable.
method Integrates Kuramoto model to prevent phase synchronization and instead achieve frequency synchronization.
result KuramotoGNN reduces over-smoothing on various graph deep learning tasks.
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific …
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic syste…
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…
PINNs struggle with increasingly complex ODEs, especially when parameters control their complexity.
problem Evaluating physics-informed neural networks on complex coupled ODEs.
method Tuned benchmarks of partial differential equations and harmonic oscillators; varying network architecture and training method.
result PINNs fail to solve complex ODEs, revealing issues like insufficient capacity, poor conditioning, and high local curvature.
Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Marketsq-fin.CP
Agent-based market shows herding cycles with square-root price impact.
problem Understanding herding cycles in agent-based markets.
method Agent-based model with 20,000 retail traders interacting with a single institutional agent.
result Agent discovers multi-cycle predatory strategy with 8-11 complete cycles over 2000 trading days.
To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we start by …
Quantifies fractional isoperimetric inequality with strong control over boundary oscillation.
problem Fractional isoperimetric inequality and its quantitative aspects.
method Regularization process with a new spirit.
result Stability estimates for fractional Cheeger inequality.
DiffObs predicts global precipitation with realistic wave modes and low frequency variations.
problem Predicting global precipitation evolution using satellite observations.
method Autoregressive generative diffusion model trained on satellite data.
result Model generates realistic wave modes and low frequency variations, validating its potential for climate prediction.
Modeling financial chaos with market makers' risk appetite.
problem Unpredictable price changes in financial markets.
method Using Hamiltonian approach with anharmonic oscillators and nonlinear coupling.
result Market makers' risk appetite determines chaotic dynamics in financial markets.
We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of minimal graphs that are almost flat but have small oscillations whose geometry we c…
Witten deformation connects manifold spectra to Morse functions.
problem Understanding spectral properties of Riemannian manifolds.
method Rellich-Kato theorem applied to Witten deformation.
result Relates spectral package to Morse complex and harmonic oscillators.
Study on black hole interiors with matter fields, showing oscillation condition impacts blow-up.
problem Examining Strong Cosmic Censorship in the presence of matter fields.
method Einstein equations coupled with charged/massive scalar fields, spherically symmetric data, relaxation rate analysis.
result Oscillation condition on event horizon determines whether matter fields blow up or not.
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.
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.
Paper proposes a coupling-based diagnostic for SGD stepsize optimization.
problem Optimizing stepsize for SGD convergence.
method Coupling-based convergence diagnostic for monitoring stationarity.
result Proposed stepsize scheme achieves superior performance across convex and non-convex problems.
Dynamical thermalization and turbulence in social stratification modelscond-mat.stat-mech
Study chaotic dynamics in social stratification models leading to thermalization and turbulence.
problem Understanding social stratification dynamics through chaotic nonlinear systems.
method Modeling social network links with oscillators and energies, studying Hamiltonian evolution and nonlinear interactions.
result Chaotic dynamics leads to dynamical thermalization and Kolmogorov-Zakharov turbulence, with implications for wealth inequality.
Financial markets have been extensively studied as highly complex evolving systems. In this paper, we quantify financial price fluctuations through a coupled dynamical system composed of phase oscillators. We find a Financial Coherence and Incoherence (FCI) coexistence collective behavior emerges as the system evolves …
We use principle component analysis (PCA) of cross correlations in European government bonds and European stocks to investigate the systemic risk contained in the European economy. We tackle the task to visualize the evolution of risk, introducing the conditional average rolling sum (CARS). Using this tool we see that …
In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the lite…
The paper proposes a method to identify power system oscillation modes using blind source separation.
problem Accurately identifying oscillation modes in power systems with renewable energy sources.
method A high-order blind source identification (HOBI) algorithm based on copula statistic combined with Hilbert transform and iteration procedure.
result The method can identify all oscillation modes and model order from a single channel of observation signals, outperforming state-of-the-art methods.
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.
The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzi…
Paper proposes a new method to optimize robot body structure and control policy.
problem Optimizing robot body structure and control policy in a coupled manner.
method Revisits co-design problem as a Stackelberg game, incorporating control adaptation dynamics.
result Stackelberg PPO outperforms standard PPO in stability and performance.
The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capill…
We introduce tools to capture the dynamics of three different pathways, in which the synchronization of human decision-making could lead to turbulent periods and contagion phenomena in financial markets. The first pathway is caused when stock market indices, seen as a set of coupled integrate-and-fire oscillators, sync…
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Researchers develop a method to control nonlinear systems with Koopman operator regression.
problem Controlling nonlinear systems with finite action spaces.
method Koopman operator regression for dynamics estimation and model predictive control for control.
result The method yields a linear switching predictive model for control.
This paper extends SLS controllers to two stocks, proving the RPE property with cross-coupling.
problem Extending SLS controllers to two stocks without exploiting correlations.
method Developed a novel architecture for cross-coupling two SLS controllers, derived a closed-form expected value, and proved the RPE property.
result Guaranteed RPE property with cross-coupling for a large class of stock dynamics.
Study tests five popular trading signal families and finds four refuted, one inconclusive, and one not refuted.
problem Testing the viability of five popular trading signal families for generating a positive edge.
method Statistical edge testing, economic viability assessment, and finite-bankroll survival under leverage using exposure-matched benchmarks, stationary-bootstrap confidence intervals, and hierarchical Benjamini-Yekutieli control.
result Four out of five signal families are refuted, one is inconclusive, and one is not refuted.
CAP-BM learns complex-valued data's amplitude and phase distributions.
problem Learning from complex-valued data with amplitude variation.
method Complex Amplitude-Phase Boltzmann machine (CAP-BM) with Gibbs sampling.
result Necessity of amplitude-amplitude coupling term in CAP-BM.
A new oscillator measures trending behavior of financial instruments.
problem Detecting underlying deterministic components in financial market prices.
method Financial market geometry and tube oscillator derived from past history.
result Simple trading strategy based on tube oscillator leads to consistent positive returns.
Study on convergence of SDEs using entropy methods.
problem Analyzing convergence of stochastic differential equations.
method Applied Lyapunov method to Fokker-Planck equation with weighted relative Fisher information.
result Exponential convergence of probability density function to invariant distribution in distance.
Develops a control framework for systemic risk under uncertainty.
problem Systemic risk under model uncertainty.
method Linear-quadratic mean-field control framework with viscosity solutions and verification theorems.
result Explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability.
Minimal vector fields on oscillator groups studied, with specific conditions for minimality.
problem Characterizing minimal left-invariant unit vector fields on oscillator groups.
method Analyzing structure constants and harmonic maps into the unit tangent bundle.
result Minimal vector fields defined by specific conditions on oscillator groups.
Study examines boundedness of oscillating singular integrals on specific Lie groups.
problem Investigating boundedness of oscillating singular integrals on Lie groups of polynomial growth.
method Presented kernel criteria in terms of sub-Riemannian structure and Fourier analysis.
result Extended classical oscillating conditions for boundedness of oscillating convolution operators.
Another type of log-periodic oscillations on Polish stock market?cond-mat.stat-mech
Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "an…
Estimates box dimension of fractal interpolation surfaces using oscillation vectors.
problem Estimating the complexity of fractal interpolation surfaces.
method Defined vertical scaling matrices and used them to relate oscillation vectors of different levels.
result Obtained the box dimension of generalized affine fractal interpolation surfaces.
This paper explores the capability of deep neural networks to capture key characteristics of vehicle dynamics, and their ability to perform coupled longitudinal and lateral control of a vehicle. To this extent, two different artificial neural networks are trained to compute vehicle controls corresponding to a reference…
Researchers classify lattices in a specific four-dimensional group.
problem Classifying lattices in the split oscillator group.
method Parametrizing and classifying lattices up to automorphisms of the ambient group.
result Commensurability classes of lattices correspond to real quadratic fields.
This study compares direct and indirect methods for estimating own funds in life insurance, finding indirect methods more effective under realistic asset-liability coupling.
problem Computing own funds for life insurers using direct and indirect methods in a risk-neutral pricing framework.
method Introduced a novel family of mixed estimators including both direct and indirect methods, integrated into a control variate framework for variance reduction.
result The indirect method is more effective under realistic asset-liability coupling, but neither method is universally superior.