Stochastic Regime Research Articles

Threshold of stochastic self-focusing from the Poisson property of extreme-event statistics.

Statistics of self-focusing induced by a stochastic laser driver is shown to converge, in the large-sample-size limit, to a generalized Poisson distribution whose mean is given by the exponent of the respective extreme-value statistics. For a given ratio of the laser peak power to the self-focusing threshold Pcr, the mean number of self-focusing counts in a large sample of laser pulses is shown to depend on the number of pulses in the sample, N, and the signal-to-noise ratio of laser pulses, a. We derive a closed-form solution for the threshold of stochastic self-focusing, which, unlike its deterministic counterpart, Pcr, is a function of the sample size N and the signal-to-noise ratio a. The parameter Na = exp (a2/2) is shown to set a borderline between the deterministic and stochastic regimes of self-focusing. When the number of laser pulses in a sample becomes comparable to Na, self-focusing can no longer be viewed as deterministic even for high signal-to-noise laser beams.

The thermal dependent biology of cultured lumpfish (Cyclopterus lumpus Linnaeus 1758): Differences due to temperatures during early life and how tolerance is measured

The use of lumpfish as a “cleaner fish” in Atlantic salmon aquaculture is increasing. However, during the summer months, there have been large-scale mortalities of lumpfish at some North Atlantic salmon sea-cage sites. There is evidence that manipulating temperatures during early life can improve the thermal tolerance of fishes. Thus, we reared lumpfish embryos (eggs), larvae and juveniles under different temperature regimes, and measured their metabolic physiology and upper thermal limits, with the goal of better understanding their physiology and mitigating the effects of high summer water temperatures on their welfare. The specific incubation (egg) / rearing temperature combinations were 6 °C / 9 °C (normal production temperatures), 8.5 °C / 9 °C, 6–11 °C / 9 °C, 8.5 °C / 9–11 °C and 6–11 °C / 9–11 °C; with a range of temperatures indicating that fish were exposed to stochastic temperature changes.Hatching success was 61 % in the control (6 °C) group, as compared to ~47 % and 26.5 % in the groups exposed to 8.5 °C and the stochastic temperature regime (6–11 °C), respectively. Groups exposed to stochastic incubation and rearing temperatures also had the lowest survival rate (33.7 %) as opposed to those incubated and reared at constant temperatures (66.1 and 50.7 %) when unexpectedly exposed to high, and variable, ambient water temperatures that were experienced for roughly 7 weeks during rearing (due to abnormal water temperatures in the bay supplying our aquaculture facility). Interestingly, the critical thermal maximum (CTMax), incremental temperature maximum (ITMax) and metabolic capacity (i.e., aerobic scope) of 30-40 g lumpfish did not differ between the groups, and the first two parameters on average were 22.85 ± 0.12 °C and 20.63 ± 0.02 °C, respectively.

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

A probabilistic approach for the valuation of variance swaps under stochastic volatility with jump clustering and regime switching

The effects of stochastic volatility, jump clustering, and regime switching are considered when pricing variance swaps. This study established a two-stage procedure that simplifies the derivation by first isolating the regime switching from other stochastic sources. Based on this, a novel probabilistic approach was employed, leading to pricing formulas with time-dependent and regime-switching parameters. The formulated solutions were easy to implement and differed from most existing results of variance swap pricing, where Fourier inversion or fast Fourier transform must be performed to obtain the final results, since they are completely analytical without involving integrations. The numerical results indicate that jump clustering and regime switching have a significant influence on variance swap prices.

Stochastic circular persistent currents of exciton polaritons

We monitor the orbital degree of freedom of exciton-polariton condensates confined within an optical trap and unveil the stochastic switching of persistent annular polariton currents under pulse-periodic excitation. Within an elliptical trap, the low-lying in energy polariton current states manifest as a two-petaled density distribution with a swirling phase. In the stochastic regime, the density distribution, averaged over multiple excitation pulses, becomes homogenized in the azimuthal direction. Meanwhile, the weighted phase, extracted from interference experiments, exhibits two compensatory jumps when varied around the center of the trap. Introducing a supplemental control optical pulse to break the reciprocity of the system enables the transition from a stochastic to a deterministic regime, allowing for controlled polariton circulation direction.

Differential entropy estimation with a Paretian kernel: Tail heaviness and smoothing

Differential entropy extends the concept of entropy to continuous probability distributions, measuring the uncertainty associated with a continuous random variable. In financial data analysis, accurately estimating differential entropy is pivotal for understanding market dynamics and assessing risk. Traditional methods often fall short when dealing with the heavy-tailed distributions characteristic of financial returns. This paper introduces a novel approach to differential entropy estimation employing a Paretian kernel function adept at handling tail heaviness’s intricacies. By incorporating an additional smoothing parameter, the Pareto exponent, our method offers flexibility in adjusting to light and heavy-tailed distributions. We compare our approach against established estimators through a comprehensive Monte Carlo simulation, demonstrating its superior performance in various scenarios. Applying our method to foreign exchange market data further illustrates its practical utility in identifying stochastic regimes and enhancing financial analysis. Our findings advocate for integrating the Paretian kernel estimator into the toolkit of financial analysts and researchers for a more nuanced understanding of market behavior.

Three-dimensional Modeling of the Solar Wind and Local Interstellar Medium Interaction with Pickup Ions in the Presence of Heliospheric Current Sheet

Our three-dimensional, time-dependent, multi-fluid model has been used to investigate the solar wind (SW)–local interstellar medium (LISM) interaction with pickup ions (PUIs) treated as a separate fluid. A non-zero, but fixed, angle between the Sun’s magnetic and rotation axis is adopted. The flow of the plasma mixture (thermal SW protons, PUIs, and electrons), is described by the system of ideal magnetohydrodynamic equations with the source terms responsible for charge exchange between ions and neutral atoms. Different populations of neutral atoms are governed by the individual sets of the Euler equations. As the standard Rankine–Hugoniot relations are not appropriate to describe the anisotropic behavior of PUIs at the termination shock, we use a kinetically-derived set of boundary conditions at it. We extend our previous work [1] and perform these new simulations on a Cartesian grid. This approach allows us to maintain a uniform grid resolution in all directions, without compromising resolution, at large distances from the Sun. The possibility of transition of the SW flow to a stochastic regime in the region between the termination shock and heliopause is further investigated.

Nonlinear stochastic behavior of soft-core sandwich panels

The nonlinear stochastic behavior of soft-core sandwich panels and the evolution of uncertainty along the nonlinear path are investigated. The paper focuses on the way the geometrically nonlinear and unstable behavior is affected by uncertainty and considers, for the first time, the evolution of uncertainty along the unstable structural response. The structural modeling relies on the EHSAPT and its integration into the geometrically nonlinear stochastic regime. A tailored nonlinear FE model that is based on a variational formulation and an arc-length solution scheme are developed. The stochastic analysis adopts the Perturbation-based SFEM and its generalization for the evolution of uncertainty along the process axis. A numerical study demonstrates the stochastic methodology and explores the impact of uncertainty on the nonlinear structural behavior. The evolution of the stochastic stress resultants at the displaced end is studied along the two axes of evolution. The differences between the two representations and their physical and engineering significance are highlighted revealing significant changes to the uncertainty evolution pattern with the shift from global buckling to localized wrinkling instabilities. The representation of the stochastic results along the process axis also quantifies the level of uncertainty near critical and singular points where conventional analyses diverge.

Analytical formulae for variance and volatility swaps with stochastic volatility, stochastic equilibrium level and regime switching

<p>The CIR stochastic volatility model is modified to introduce nonlinear mean reversion, with the long-run volatility average as a random variable controlled by two parts being modeled through a Brownian motion and a Markov chain, respectively. This model still possesses an analytical formulation of the forward characteristic function, from which we establish variance swap prices as well as volatility swap ones with a nonlinear payoff in closed form. The numerical implementation of the two formulae demonstrates the significant impact of regime switching.</p>

Correlated spectral and recurrence variations of Cygnus X-1

ABSTRACT We present results of recurrence analysis of the black hole X-ray binary Cygnus X-1 using combined observations from the Rossi X-ray Timing Explorer All-sky Monitor and the Japanese Monitor of All-sky X-ray Image aboard the International Space Station. From the time-dependent windowed recurrence plot (RP), we compute 10 recurrence quantities that describe the dynamical behaviour of the source and compare them to the spectral state at each point in time. We identify epochs of state changes corresponding to transitions into highly deterministic or highly stochastic dynamical regimes and their correlation to specific spectral states. We compare k-Nearest Neighbors and Random Forest models for various sizes of the time-dependent RP. The spectral state in Cygnus X-1 can be predicted with greater than 95 per cent accuracy for both types of models explored across a range of RP sizes based solely on the recurrence properties. The primary features from the RP that distinguish between spectral states are the determinism, Shannon entropy, and average line length, all of which are systematically higher in the hard state compared to the soft state. Our results suggest that the hard and soft states of Cygnus X-1 exhibit distinct dynamical variability and the time domain alone can be used for spectral state classification.

IDESS: a toolbox for identification and automated design of stochastic gene circuits.

One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation. In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks. IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Stochastic generation in a Josephson-like antiferromagnetic spin Hall oscillator driven by a pure AC current

We numerically demonstrate that a pure time-harmonic bias AC current of a specific amplitude τf and angular frequency ωf can excite the chaotic magnetization dynamics in a Josephson-like antiferromagnetic (AFM) spin Hall oscillator (SHO) with biaxial magnetic anisotropy of an AFM layer. The nature of such a stochastic generation regime in a Josephson-like AFM SHO could be explained by the random hopping of the working point of the SHO between several quasi-stable states under the action of an applied AC current. We reveal that depending on the ωf/τf ratio several stochastic generation regimes interspersed with regular generation regimes can be achieved in an AFM SHO, which can be used in spintronic random signal sources and various nano-scale random signal devices, including the spintronic p-bit device considered in this work. The obtained results are important for the development and optimization of spintronic devices capable of generating and processing (sub-)THz-frequency random signals, which are promising for ultra-fast probabilistic computing, cryptography, secure communication, etc.

Stochastic transition in synchronized spiking nanooscillators

This work reports that synchronization of Mott material-based nanoscale coupled spiking oscillators can be drastically different from that in conventional harmonic oscillators. We investigated the synchronization of spiking nanooscillators mediated by thermal interactions due to the close physical proximity of the devices. Controlling the driving voltage enables in-phase 1:1 and 2:1 integer synchronization modes between neighboring oscillators. Transition between these two integer modes occurs through an unusual stochastic synchronization regime instead of the loss of spiking coherence. In the stochastic synchronization regime, random length spiking sequences belonging to the 1:1 and 2:1 integer modes are intermixed. The occurrence of this stochasticity is an important factor that must be taken into account in the design of large-scale spiking networks for hardware-level implementation of novel computational paradigms such as neuromorphic and stochastic computing.

Optimal transport of active particles induced by substrate concentration oscillations.

We show the existence of a stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport in cell membranes and tissues for medical treatments and soil remediation.

Infrastructure to factorially manipulate the mean and variance of precipitation in the field

AbstractExtensive ecological research has investigated extreme climate events or long‐term changes in average climate variables, but changes in year‐to‐year (interannual) variability may also cause important biological responses, even if the mean climate is stable. The environmental stochasticity that is a hallmark of climate variability can trigger unexpected biological responses that include tipping points and state transitions, and large differences in weather between consecutive years can also propagate antecedent effects, in which current biological responses depend on responsiveness to past perturbations. However, most studies to date cannot predict ecological responses to rising variance because the study of interannual variance requires empirical platforms that generate long time series. Furthermore, the ecological consequences of increases in climate variance could depend on the mean climate in complex ways; therefore, effective ecological predictions will require determining responses to both nonstationary components of climate distributions: the mean and the variance. We introduce a new design to resolve the relative importance of, and interactions between, a drier mean climate and greater climate variance, which are dual components of ongoing climate change in the southwestern United States. The Mean × Variance Experiment (MVE) adds two novel elements to prior field infrastructure methods: (1) factorial manipulation of variance together with the climate mean and (2) the creation of realistic, stochastic precipitation regimes. Here, we demonstrate the efficacy of the experimental design, including sensor networks and PhenoCams to automate monitoring. We replicated MVE across ecosystem types at the northern edge of the Chihuahuan Desert biome as a central component of the Sevilleta Long‐Term Ecological Research Program. Soil sensors detected significant treatment effects on both the mean and interannual variability in soil moisture, and PhenoCam imagery captured change in vegetation cover. Our design advances field methods to newly compare the sensitivities of populations, communities, and ecosystem processes to climate mean × variance interactions.

Global Optimization Approach for Parameter Estimation in Stochastic Dynamic Models of Biosystems.

Mechanistic dynamic models have become an essential tool for understanding biomolecular networks and other biological systems. Biochemical stochasticity can be extremely important in some situations, e.g., at the single-cell level where there is a low copy number of the species involved. In these scenarios, deterministic models are not suitable to characterize the dynamics, so stochastic dynamic models should be considered. Here, we address the challenging problem of parameter estimation in stochastic dynamic models. Despite recent advances, this area is considerably less mature than its deterministic counterpart. We present a novel strategy based on two components: (i) global optimization via a hybrid stochastic-deterministic approach, and (ii) stochastic simulation techniques tailored to the sparsity of the available experimental data. Regarding the latter, for cases of dense population data we make use of a novel approach using a Partial Integro-Differential Equation (PIDE) model solved using a semilagrangian method. In order to further speed up the simulations, we also present efficient parallel implementations for multi-core CPUs and also for graphical processing units (GPUs). Importantly, whereas SDE and Fokker Planck approximations of the Chemical Master Equation (CME) apply when the reactant populations are sufficiently large, the PIDE approximation to the CME is valid for very low copy numbers, and therefore they enable us to tackle parameter estimation for systems with large intrinsic molecular noise, (highly stochastic regimes far from the thermodynamic limit). We test our strategy with four challenging problems: a Lotka-Volterra system, a polarization system in S. cerevisiae, a genetic toggle switch, and a genetic circadian oscillator. Our method could successfully solve these problems in very reasonable computation times (often a few minutes for the first two problems) using standard low-cost hardware, showing very significant speedups with respect to recent alternative methods. The code used to obtain the results reported here is available at https://doi.org/10.5281/zenodo.5195408.

Stochastic growth and regime shift risk in renewable resource management

Renewable resources are affected by both environmental variability, which makes the year-to-year stock growth uncertain, and the risk of irreversible events (e.g., a stock collapse). Little is known about how a renewable resource harvester would optimally respond to the combined effects of both sources of risk. In this paper, we propose a simple dynamic resource model to investigate this issue. For some structures of the harvesting cost function, we find that anticipating a higher variability in biological growth induces a cautious management policy, but only when regime shift risk is accounted for. Accounting for the risk of regime shift may prescribe large changes in management responses to anticipated random changes in biological growth whereas ignoring such a risk prescribes small changes in management. Optimal escapement is not constant but varies across all periods when the planning horizon is finite and the regime shift risk is endogenous.

Time-dependent non-Abelian waves and their stochastic regimes for gauge fields coupled to external sources

In this paper we explore explicit exact solutions of the $SU(2)$ Yang-Mills (YM) and Yang-Mill-Higgs (YMH) equations with homogeneous and inhomogeneous external sources. Whereas in the case of YM we have confirmed our analytical findings with the numerical simulations, the numerical corroborations in the YMH case yielded the stochastic character of motion for the ensuing fields.

Analytically pricing exchange options with stochastic liquidity and regime switching

AbstractWe investigate the valuation of exchange options when the market is affected by changing economic conditions as well as liquidity risks. The volatility and expected returns of both stocks are assumed to be controlled by a continuous‐time Markov chain to reflect the effects of varying economic conditions, and a liquidity discounting factor is employed to capture the impact of market liquidity on stock prices. Once the model has been established, we construct a risk‐neutral measure with the use of regime‐switching Esscher transform, and the characteristic function is then derived in an analytical form, so that a closed‐form formula for exchange options can be presented. We further analyze the effects of the two considered factors on exchange option prices numerically.

On the interaction of stochastic forcing and regime dynamics

Abstract. Stochastic forcing can, sometimes, stabilise atmospheric regime dynamics, increasing their persistence. This counter-intuitive effect has been observed in geophysical models of varying complexity, and here we investigate the mechanisms underlying stochastic regime dynamics in a conceptual model. We use a six-mode truncation of a barotropic β-plane model, featuring transitions between analogues of zonal and blocked flow conditions, and identify mechanisms similar to those seen previously in work on low-dimensional random maps. Namely, we show that a geometric mechanism, here relating to monotonic instability growth, allows for asymmetric action of symmetric perturbations on regime lifetime and that random scattering can “trap” the flow in more stable regions of phase space. We comment on the implications for understanding more complex atmospheric systems.