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.
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…
The study derives generalization bounds for neural oscillators, improving their performance with regularization.
problem Quantifying the generalization capacities of neural oscillators.
method Using Rademacher complexity and squared Wasserstein-1 distances, the study derives theoretical upper PAC generalization bounds for neural oscillators.
result Theoretical bounds show polynomial growth in estimation errors with MLP size and time length, and regularization improves performance.
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.
FCOC framework improves financial volatility forecasting.
problem Tackles dual challenges of feature fidelity and model responsiveness in financial volatility forecasting.
method Synergizes fractal feature extraction and dynamic chaotic oscillation processing.
result Demonstrates profound and generalizable impact on S\&P 500 and DJI datasets.
The Duffing oscillator's parameters are identified online using variational message passing.
problem Estimating parameters of a nonlinear Duffing oscillator in real-time.
method Variational message passing on a factor graph of the Duffing oscillator's generative model.
result The online inference procedure performs as well as offline methods.
Enhanced Gaussian process regression for multi-fidelity data fusion.
problem Combining data of varying fidelity levels for accurate predictions.
method Gradient-enhanced Cokriging method (GE-Cokriging) for QoI and its gradients.
result GE-Cokriging outperforms conventional multi-fidelity Cokriging in predicting QoI and gradients.
We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of convex estimators that adapt to the structure of the problem depending on the avail…
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.
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the one real parameter is vanished.
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…
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
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.
We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be described by the Mittag-Leffler function superposed with various types of oscil…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…
Conductor galloping is the high-amplitude, low-frequency oscillation of overhead power lines due to wind. Such movements may lead to severe damages to transmission lines, and hence pose significant risks to the power system operation. In this paper, we target to design a prediction framework for conductor galloping. Th…
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 …
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of n-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of the harmonic oscillator. The set of abovementioned mechanical systems are realized…
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 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…
It is shown that a lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any ''visible cause''. In such a jump the system changes instantaneously its coordinates as well as its momenta. The mathematical dscription of the phenome…
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 …
Novel method for solving ODEs on k-polysymplectic manifolds.
problem Solving ordinary differential equations on k-polysymplectic manifolds.
method k-polysymplectic energy-momentum method.
result Novel stability analysis techniques applied to Hamiltonian 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.
SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.
problem SGDm with fixed step-size diverges under covariate shift.
method Approximated learning system as a time-varying system of ODEs and characterized divergence/convergence modes.
result SGDm with fixed step-size can diverge under covariate shift, similar to resonance in oscillators.
We show that a simple model of a spatially resolved evolving economic system, which has a steady state under simultaneous updating, shows stable oscillations in price when updated asynchronously. The oscillations arise from a gradual decline of the mean price due to competition among sellers competing for the same reso…
We prove a global smooth isometric immersion for negatively curved surfaces with finite total curvature.
problem Finding a sufficient condition for a complete negatively curved surface to be isometrically embedded in R^3.
method Developed new techniques to overcome slow decay and oscillations of Gauss curvature, reformulating the Gauss-Codazzi equations as a symmetric hyperbolic system.
result Proved the global existence of a smooth solution to the Gauss-Codazzi system, achieving a global smooth isometric immersion of the surface into R^3.
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we e…
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.
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising meaningful models out of such observations in an automated fashion still remains an op…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this algorithm cannot function in real time. Thus, we propose a new method that can be…
Market strategies minimize Fisher information to minimize risk.
problem Applying minimum Fisher information principle to market dynamics.
method Analytical extension to quantum harmonic oscillator eigenstates and Gibbs distribution.
result Minimizing Fisher information reduces information and risk.
Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor λ≈2, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so called commodity currencies expressed in terms of the US dollar appears to take place w…
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.
The paper adapts results for Reeb flows and Hamiltonian flows, showing all orbits are closed have identical periods.
problem Adapting results for Reeb flows and Hamiltonian flows with closed orbits.
method Adapting results from Geodesic circle foliations to Reeb and Hamiltonian flows.
result All orbits on connected contact manifolds with closed orbits have identical periods.
Traditional energy-based learning models associate a single energy metric to each configuration of variables involved in the underlying optimization process. Such models associate the lowest energy state to the optimal configuration of variables under consideration, and are thus inherently dissipative. In this paper we…
Study growth of systoles in arithmetic manifolds, focusing on k-dimensional cases.
problem Growth of systoles in arithmetic n-manifolds along congruence coverings. method Analyzes growth of k-dimensional systoles in arithmetic n-manifolds, proving polylogarithmic and constant power bounds. result Growth of systoles for k=r oscillates between a power of a logarithm and a power function of the degree of the covering. 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.
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…
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harm…
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.
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…
Unified approach to deform Lie-Hamilton systems using Poisson-Hopf algebra.
problem Deforming Lie systems with quantum algebras.
method Poisson-Hopf algebra deformations applied to Lie-Hamilton systems.
result Unified approach to deformations of Lie-Hamilton systems on the real plane.
A new RNN model tackles long-time dependencies with fast, invertible, and memory-efficient hidden states.
problem Challenges in processing sequential inputs with long-time dependencies in RNNs.
method A novel RNN architecture based on a Hamiltonian system of oscillators.
result The proposed RNN mitigates exploding and vanishing gradient problems, providing state-of-the-art performance.
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.
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.
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.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.