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Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
We investigate using direct numerical simulations with grids up to 1536^3 points, the rate at which small scales develop in a decaying three-dimensional MHD flow both for deterministic and random initial conditions. Parallel current and…
We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest…
In this paper, to cope with the shortage of sufficient theoretical support resulted from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their…
This paper investigates the dynamics of risk transmission in cryptocurrency markets and proposes a novel framework for volatility forecasting. The framework uncovers two key empirical facts: the asymmetric amplification of volatility…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
Using a time-varying approach, this paper examines the dynamics of volatility in the REIT sector. The results highlight the attractiveness and suitability of using GARCH based approaches in the modeling of daily REIT volatility. The paper…
We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily…
This paper is a supplement to our recent paper ``Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models". We introduce the class of regime-switching L\'evy models with memory,…
Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
Fidelity serves as a benchmark for the relieability in quantum information processes, and has recently atracted much interest as a measure of the susceptibility of dynamics to perturbations. A rich variety of regimes for fidelity decay have…
Our article considers a regression model with observed factors. The observed factors have a flexible stochastic volatility structure that has separate dynamics for the volatilities and the correlation matrix. The correlation matrix of the…
We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this…
Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
Despite their importance in turbulence theory, a unifying and predictive rule determining the direction of the cascades of conserved quantities is lacking. In this work, we show that the direction of the cascades in two-dimensional…
Large models based on the Transformer architecture are susceptible to extreme-token phenomena, such as attention sinks and value-state drains. These issues, which degrade model performance, quantization fidelity, and interpretability, arise…
A methodology is developed to quantify the transfer and transport of kinetic energy of specific scales associated with coherent structures. Coherent motions are characterized by the triple decomposition of a multi-scale flow and used to…