Simple Stochastic Model Research Articles

Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps

Monitored quantum many-body systems display a rich pattern of entanglement dynamics, which is unique to this nonunitary setting. This work studies the effect of quantum jumps on the entanglement dynamics beyond the no-click limit corresponding to a deterministic non-Hermitian evolution. To this aim, we introduce a new tool that looks at the statistics of entanglement-entropy gain and loss after and in between quantum jumps. This insight allows us to build a simple stochastic model of a random walk with partial resetting, which reproduces the entanglement dynamics, and to dissect the mutual role of jumps and non-Hermitian evolution on the entanglement scaling. We apply these ideas to the study of measurement-induced transitions in monitored fermions. We demonstrate that significant deviations from the no-click limit arise whenever quantum jumps strongly renormalize the non-Hermitian dynamics, as in the case of models with U(1) symmetry at weak monitoring. On the other hand, we show that the weak-monitoring phase of the Ising chain leads to a robust subvolume logarithmic phase due to weakly renormalized non-Hermitian dynamics. Published by the American Physical Society 2024

Synaptic reorganization of synchronized neuronal networks with synaptic weight and structural plasticity.

Abnormally strong neural synchronization may impair brain function, as observed in several brain disorders. We computationally study how neuronal dynamics, synaptic weights, and network structure co-emerge, in particular, during (de)synchronization processes and how they are affected by external perturbation. To investigate the impact of different types of plasticity mechanisms, we combine a network of excitatory integrate-and-fire neurons with different synaptic weight and/or structural plasticity mechanisms: (i) only spike-timing-dependent plasticity (STDP), (ii) only homeostatic structural plasticity (hSP), i.e., without weight-dependent pruning and without STDP, (iii) a combination of STDP and hSP, i.e., without weight-dependent pruning, and (iv) a combination of STDP and structural plasticity (SP) that includes hSP and weight-dependent pruning. To accommodate the diverse time scales of neuronal firing, STDP, and SP, we introduce a simple stochastic SP model, enabling detailed numerical analyses. With tools from network theory, we reveal that structural reorganization may remarkably enhance the network's level of synchrony. When weaker contacts are preferentially eliminated by weight-dependent pruning, synchrony is achieved with significantly sparser connections than in randomly structured networks in the STDP-only model. In particular, the strengthening of contacts from neurons with higher natural firing rates to those with lower rates and the weakening of contacts in the opposite direction, followed by selective removal of weak contacts, allows for strong synchrony with fewer connections. This activity-led network reorganization results in the emergence of degree-frequency, degree-degree correlations, and a mixture of degree assortativity. We compare the stimulation-induced desynchronization of synchronized states in the STDP-only model (i) with the desynchronization of models (iii) and (iv). The latter require stimuli of significantly higher intensity to achieve long-term desynchronization. These findings may inform future pre-clinical and clinical studies with invasive or non-invasive stimulus modalities aiming at inducing long-lasting relief of symptoms, e.g., in Parkinson's disease.

The Feasibility of Coordinating International Monetary Policy Strategies in the Context of Asymmetric Demand Shocks

In the context of the increasing interdependence of countries due to the development of international trade, a relevant question arises as to whether it is necessary to conduct independent monetary policies for each country or whether it is advisable to coordinate these policies. This question becomes a key in the debate on optimal monetary policy strategies in open economies. The aim of this study is to analyze the impact of asymmetric aggregate demand shocks on the appropriateness of monetary policy coordination in a simple stochastic model of two interacting countries. The analysis of equilibrium states of the monetary authorities’ interaction strategies under study was carried out analytically by minimizing the loss function and solving one-period static optimization problems. The equilibrium states of macroeconomics of interacting countries under coordination of monetary policy and in cases of lack of coordination (Nash and Stackelberg equilibrium) in the presence of asymmetric, serially uncorrelated demand shocks have been analyzed. It is proven that the response of inflation to asymmetric demand shocks is smaller in the case of coordinated policy than in the case of non-cooperative policy. The loss function analysis shows that the compensation of demand shocks is found to be more costly in Nash equilibrium than in the case of monetary authority coordination policy. The analysis of the monetary authorities’ interaction strategies showed that the real exchange rate plays an important role in balancing supply and demand in the two economies.

Assessing Climate Forcing From the Sea Surface Temperature‐Surface Heat Flux Relation for SST‐Coupled Oscillatory Variability

AbstractThe interaction between sea surface temperatures (SST) and surface heat flux (SHF) is vital for atmospheric and oceanic variabilities. This study investigates SST‐SHF relationship in the framework of a coupled oscillatory model, extending beyond previous research that predominantly used AR‐1 type simple stochastic climate models. In contrast to the AR‐1 type model, we reveal distinct features of SST‐SHF relationships in the oscillatory model: sign reversals occur in the imaginary part of SST‐SHF coherence and the low‐pass SST tendency‐SHF correlation. However, these sign reversals are absent in the real part of SST‐SHF coherence and in the low‐pass SST‐SHF correlation. We find these features are robust across both the twentieth Century Reanalysis and GFDL SPEAR model for El Niño‐Southern Oscillation (ENSO) variability. Furthermore, we develop a new scheme to assess ENSO's climate forcing magnitude and natural frequency. Our findings thus provide novel insights into understanding ENSO dynamics from the perspective of heat flux.

The Fractional MacroEvolution Model: a simple quantitative scaling macroevolution model

AbstractScaling fluctuation analyses of marine animal diversity and extinction and origination rates based on the Paleobiology Database occurrence data have opened new perspectives on macroevolution, supporting the hypothesis that the environment (climate proxies) and life (extinction and origination rates) are scaling over the “megaclimate” biogeological regime (from ≈1 Myr to at least 400 Myr). In the emerging picture, biodiversity is a scaling “crossover” phenomenon being dominated by the environment at short timescales and by life at long timescales with a crossover at ≈40 Myr. These findings provide the empirical basis for constructing the Fractional MacroEvolution Model (FMEM), a simple stochastic model combining destabilizing and stabilizing tendencies in macroevolutionary dynamics, driven by two scaling processes: temperature and turnover rates.Macroevolution models are typically deterministic (albeit sometimes perturbed by random noises) and are based on integer-ordered differential equations. In contrast, the FMEM is stochastic and based on fractional-ordered equations. Stochastic models are natural for systems with large numbers of degrees of freedom, and fractional equations naturally give rise to scaling processes.The basic FMEM drivers are fractional Brownian motions (temperature, T) and fractional Gaussian noises (turnover rates, E+) and the responses (solutions), are fractionally integrated fractional relaxation noises (diversity [D], extinction [E], origination [O], and E− = O − E). We discuss the impulse response (itself representing the model response to a bolide impact) and derive the model's full statistical properties. By numerically solving the model, we verified the mathematical analysis and compared both uniformly and irregularly sampled model outputs with paleobiology series.

From Brownian to Deterministic Motor Movement in a DNA-Based Molecular Rotor.

Molecular devices that have an anisotropic periodic potential landscape can be operated as Brownian motors. When the potential landscape is cyclically switched with an external force, such devices can harness random Brownian fluctuations to generate a directed motion. Recently, directed Brownian motor-like rotatory movement was demonstrated with an electrically switched DNA origami rotor with designed ratchet-like obstacles. Here, we demonstrate that the intrinsic anisotropy of DNA origami rotors is also sufficient to result in motor movement. We show that for low amplitudes of an external switching field, such devices operate as Brownian motors, while at higher amplitudes, they behave deterministically as overdamped electrical motors. We characterize the amplitude and frequency dependence of the movements, showing that after an initial steep rise, the angular speed peaks and drops for excessive driving amplitudes and frequencies. The rotor movement can be well described by a simple stochastic model of the system.

Optical variability of the blazar 3C 371: From minute to year timescales

The BL Lac object 3C 371 was observed by the Transiting Exoplanet Survey Satellite (TESS) for approximately a year, between July 2019 and July 2020, with an unmatched two-minute imaging cadence. In parallel, the Whole Earth Blazar Telescope (WEBT) Collaboration organized an extensive observing campaign, providing three years of continuous optical monitoring between 2018 and 2020. These datasets allow for a thorough investigation of the variability of the source. The goal of this study is to evaluate the optical variability of 3C 371. Taking advantage of the remarkable cadence of TESS data, we aim to characterize the intra-day variability (IDV) displayed by the source and identify its shortest variability timescale. With this estimate, constraints on the size of the emitting region and black hole mass can be calculated. Moreover, WEBT data are used to investigate long-term variability (LTV), including in terms of the spectral behavior of the source and the polarization variability. Based on the derived characteristics, we aim to extract information on the origin of the variability on different timescales. We evaluated the variability of 3C 371 by applying the variability amplitude tool, which quantifies variability of the emission. Moreover, we employed common tools, such as ANOVA (ANalysis Of VAariance) tests, wavelet and power spectral density (PSD) analyses to characterize the shortest variability timescales present in the emission and the underlying noise affecting the data. We evaluated the short- and long-term color behavior to understand to understand its spectral behavior. The polarized emission was analyzed, studying its variability and possible rotation patterns of the electric vector position angle (EVPA). Flux distributions of the IDV and LTV were also studied with the aim being to link the flux variations to turbulent and/or accretion-disk-related processes. Our ANOVA and wavelet analyses reveal several entangled variability timescales. We observe a clear increase in the variability amplitude with increasing width of the time intervals evaluated. We are also able to resolve significant variations on timescales of as little as sim 0.5 hours. The PSD analysis reveals a red-noise spectrum with a break at IDV timescales. The spectral analysis shows a mild bluer-when-brighter (BWB) trend on long timescales. On short timescales, mixed BWB, achromatic and redder-when-brighter (RWB) signatures can be observed. The polarized emission shows an interesting slow EVPA rotation during the flaring period where a simple stochastic model can be excluded as the origin with a 3sigma significance . The flux distributions show a preference for a Gaussian model for the IDV, and suggest it may be linked to turbulent processes, while the LTV is better represented by a log-normal distribution and may have a disk-related.

Scheduling jobs using queries to interactively learn human availability times

The solution to a job scheduling problem that involves humans as well some other shared resource has to consider the humans’ availability times. For practical acceptance of a scheduling tool, it is crucial that the interaction with the humans is kept simple and to a minimum. It is rarely practical to ask users to fully specify their availability times or to let them enumerate all possible starting times for their jobs. In the scenario we are considering, users initially only propose a single starting time for each of their jobs and a feasible and optimized schedule shall then be found within a small number of interaction rounds. In each such interaction round, our scheduling approach may propose each user a small number of alternative time intervals for scheduling the user’s jobs, and then the user may accept or reject these. To make the best out of these limited interaction possibilities, we propose an approach that utilizes integer linear programming and an exact and computationally efficient probability calculation for the users’ availabilities assuming two different stochastic models. In this way, educated proposals of alternative time intervals for performing the jobs are determined based on the computed availability probabilities and the improvements these time intervals would enable. The approach is experimentally evaluated on a variety of artificial benchmark scenarios, and different variants are compared with each other and to diverse baselines. Results show that an initial schedule can usually be quickly improved over few interaction rounds even when assuming a quite simple stochastic model, and the final schedule may come close to the solution of the full-knowledge case despite the strongly limited interaction.

Bid-ask spread dynamics: large upward jump with geometric catastrophes

We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by [D. Farmer, L. Gillemot, F. Lillo, S. Mike and A. Sen, Quant. Finance 4 (2004) 383–397.], we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical study of the model’s properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.

Simple stochastic model with safe speed using Exchange approach to recognizing synchronized flow as speed-synchronized phase

In order to unravel the physical and mathematical mystery of synchronized-flow mechanism and to reveal the fundamental mechanism and origin of synchronized flow produced by nonlinear stochastic processes, we have produced simple stochastic traffic flow models (the gradual-NaSch, Phoenix and mPhoenix models) with nonlinear safe speeds. In the mNaSch model and our gradual-NaSch model, the [Formula: see text]th vehicle’s speed is the same as or different from the [Formula: see text]th vehicle’s speed because they are discrete values. In the mNaSch and gradual-NaSch models, the same discrete values of the [Formula: see text]th and [Formula: see text]th states make it easy to identify synchronized flow with speed-synchronized phase of the [Formula: see text]th and [Formula: see text]th states. On the other hand, when we deal with synchronized flow in continuous traffic flow models, we face a problem. Continuous values cause the difficulty in identification of synchronization. In order to definitely clarify whether or not synchronized flow occurs in continuous models, we have established a novel idea of Exchange approach to recognizing synchronized flow as speed-synchronized phase. Our idea is generated from the analogical image that the whole system of synchronized metronomes does not change even if the [Formula: see text]th and [Formula: see text]th synchronized metronomes are exchanged. The Exchange approach (exchanging the [Formula: see text]th vehicle’s state for any [Formula: see text]th vehicle’s state in the whole system of traffic flow), which causes distortion such as a collision if non-synchronized vehicle’s states are exchanged and makes it possible to definitely clarify whether or not synchronized flow occurs in continuous models, is applied to our simple stochastic continuous model (the mPhoenix model). On the basis of the Exchange approach, we can recognize that the mPhoenix model surely reproduces synchronized flow. In addition, we have proposed mathematical approach to deriving nonlinear safe speeds which guarantee collision free driving and reproduce synchronized flow.

Ideal Observer Computation by Use of Markov-Chain Monte Carlo With Generative Adversarial Networks.

Medical imaging systems are often evaluated and optimized via objective, or task-specific, measures of image quality (IQ) that quantify the performance of an observer on a specific clinically-relevant task. The performance of the Bayesian Ideal Observer (IO) sets an upper limit among all observers, numerical or human, and has been advocated for use as a figure-of-merit (FOM) for evaluating and optimizing medical imaging systems. However, the IO test statistic corresponds to the likelihood ratio that is intractable to compute in the majority of cases. A sampling-based method that employs Markov-chain Monte Carlo (MCMC) techniques was previously proposed to estimate the IO performance. However, current applications of MCMC methods for IO approximation have been limited to a small number of situations where the considered distribution of to-be-imaged objects can be described by a relatively simple stochastic object model (SOM). As such, there remains an important need to extend the domain of applicability of MCMC methods to address a large variety of scenarios where IO-based assessments are needed but the associated SOMs have not been available. In this study, a novel MCMC method that employs a generative adversarial network (GAN)-based SOM, referred to as MCMC-GAN, is described and evaluated. The MCMC-GAN method was quantitatively validated by use of test-cases for which reference solutions were available. The results demonstrate that the MCMC-GAN method can extend the domain of applicability of MCMC methods for conducting IO analyses of medical imaging systems.

Kinetic modeling of fluid-induced interactions in compressible, rarefied gas flows for aerodynamically interacting particles

In the study of gas-particulate multiphase systems, the flow of high-speed gas through a distribution of solid particulates is of utmost importance. While these aerodynamically interacting systems have been extensively studied for low-speed gas flows in the gas continuum regime, less attention has been given to high-speed systems where non-continuum effects are significant due to the high flow gradients. To address this, the flow of rarefied gas through an aerodynamically interacting monodisperse spherical particle system is studied using the Direct Simulation Monte Carlo (DSMC) gas-kinetic approach. Since the method provides the best resolution of shocks at supersonic Mach numbers it is used to classify the weak separated shocks and strong collective shocks in these systems based on particle spacing in a two-particulate system at different orientation angles. The study used the two-particle system to help analyze more complex particle distributions of volume fractions, 1%, 5%, and 15%, exposed to gas flows in the slip and transitional gas regime for a free-stream Mach number range of 0.2<Ma∞<2.0. We observe that the weak separated shocks in the 1% distribution allow a higher degree of gas penetration and shock-particle interactions or “hypersonic-surfing”, exposing a major fraction of the particulates to higher force magnitudes. In contrast, the strong collective shock in the 5% and 15% distributions only generates high particulate forces on the flow-facing particles. Finally, a simple stochastic model is proposed for use in large-scale Eulerian–Lagrangian simulations that captures the non-monotonic behavior of average drag and force variability generated by the complicated gas particulate interactions in the compressible gas regime.

Optimal phenotypic adaptation in fluctuating environments

Phenotypic adaptation is a universal feature of biological systems navigating highly variable environments. Recent empirical data support the role of memory-driven decision making in cellular systems navigating uncertain future nutrient landscapes, wherein a distinct growth phenotype emerges in fluctuating conditions. We develop a simple stochastic mathematical model to describe memory-driven cellular adaptation required for systems to optimally navigate such uncertainty. In this framework, adaptive populations traverse dynamic environments by inferring future variation from a memory of prior states, and memory capacity imposes a fundamental trade-off between the speed and accuracy of adaptation to new fluctuating environments. Our results suggest that the observed growth reductions that occur in fluctuating environments are a direct consequence of optimal decision making and result from bet hedging and occasional phenotypic-environmental mismatch. We anticipate that this modeling framework will be useful for studying the role of memory in phenotypic adaptation, including in the design of temporally varying therapies against adaptive systems.

Stochastic modeling of Dalbulus maidis, vector of maize diseases

We developed a simple linear stochastic model for Dalbulus maidis dependent exclusively on temperature, whose parameters were determined from published field and laboratory studies performed at different temperatures. This model takes into account the principal stages and events of the life cycle of this pest, which is vector of maize diseases. We implemented the effect of distributed delays or Linear Chain Trick (LCT) considering a fixed number of sub-stages for egg and nymph stages of Dalbulus maidis in order to accurately represent what is observed in nature. A sensitivity analysis allows us to observe that the speed of the dynamics is sensitive to changes in the development rates, but not to the longevity of each stage or the fecundity, which almost exclusively affect insect abundance. We used our model to study its predictive and explanatory capacity considering a published experiment as a case study. Although the simulation results show a behavior qualitatively equivalent to that observed in the experimental results it is not possible to explain accurately the magnitude, nor the times in which the maximum abundances of second-generation nymphs and adults are reached. Therefore, we evaluated three possible scenarios for the insect that allow us to glimpse some of the advantages of having a computational model in order to find out what processes, taken into account in the model, may explain the differences observed between published experimental results and model results. The three proposed scenarios, based on variations in the parameterized rates of the model, can satisfactorily explain the experimental observations. We observed that in order to better simulate the experimental results it is not necessary to modify fecundity or mortality rates. However, it is necessary to accelerate the average development rates of our model by 20 to 40 %, compatible with extreme values of the rates close to the upper edges of the confidence bands of our parameterization rate curves, according to insects with faster development rates already reported in literature.

Generative abstraction of Markov population processes

Markov population models are a widespread formalism used to model the dynamics of complex systems, with applications in systems biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when a massive number of simulations has to be performed, e.g. in a multi-scale model. A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, exploring and comparing state-of-the-art generative models, which are flexible enough to automatically learn distributions over entire trajectories, rather than single simulation steps, from observed realizations of the system. In particular, we compare a Generative Adversarial setting with a Score-based Diffusion approach and show how the latter outperforms the former both in terms of accuracy and stability at the cost of slightly higher simulation times. To improve the accuracy of abstract samples, we develop an active learning framework to enrich our dataset with observations whose expected satisfaction of a temporal requirement differs significantly from the abstract one. We experimentally show how the proposed abstractions are well suited to work on multi-scale and data-driven scenarios, meaning that we can infer a (black-box) dynamical model from a pool of real data.

More Accurate Climate Trend Attribution by Using Cointegrating Vector Time Series Models

Adapting to human-induced climate change is becoming an increasingly important aspect of sustainable development. To be able to do this effectively, it is important to know how much human influence has contributed to observed climate trends. Climate detection and attribution (D&amp;A) studies achieve this by estimating scaling factors usually obtained by performing a least squares regression of the observed trending climate variable on the equivalent variable simulated by a climate model. This study proposed instead to estimate scaling factors by using the econometric approach of dynamically modelling the time series as a cointegrating Vector Auto-Regressive (VAR) time series process. It is shown that a 2nd-order cointegrating VAR(2) model is theoretically justified if the observed and simulated variables can be represented as a one-box AR(1) response to a common integrated forcing. The VAR(2) model can be expressed as a Vector Error-Correction Model (VECM) and then fitted to the data to obtain the cointegration relationship, the stationary linear combination of the two variables, from which the scaling factor is then easily obtained. Estimates of the scaling factor from the VAR(2) model are critically compared to those from Ordinary Least Squares (OLS) and Total Least Squares (TLS) for annual Global Mean Surface Temperature (GMST) data simulated by a simple stochastic model of the carbon–climate system and for historical simulations from 16 climate models in the Coupled Model Intercomparison Project 5 (CMIP5) experiment. Results from the toy model simulations show that the slope estimates from OLS are negatively biased, TLS estimates are less biased but have high variance, and the VAR(2) estimates are unbiased and have lower variance and provide the most accurate estimates with smallest mean squared error. Similar behaviour is noted in the CMIP5 data. Hypothesis tests on the VAR(2) fits found strong evidence of a cointegrating relationship with the observations for all the CMIP5 simulations.

A stochastic model leading to various particle mass distributions including the RRSB distribution

Modern particle size statistics uses many different statistical distributions, but these distributions are empirical approximations for theoretically unknown relationships. This also holds true for the famous RRSB (Rosin-Rammler-Sperling-Bennett) distribution. Based on the compound Poisson process, this paper introduces a simple stochastic model that leads to a general product form of particle mass distributions. The beauty of this product form is that its two factors characterize separately the two main components of samples of particles, namely, individual particle masses and total particle number. The RRSB distribution belongs to the class of distributions following the new model. Its simple product form can be a starting point for developing new particle mass distributions. The model is applied to the statistical analysis of samples of blast-produced fragments measured by hand, which enables a precise investigation of the mass-size relationship. This model-based analysis leads to plausible estimates of the mass and size factors and helps to understand the influence of blasting conditions on fragment-mass distributions.

Continuous-time Markov-chain models for reaction systems: fast and slow processes

It is sometimes of interest to identify the fast and slow processes in a reaction system. We present here an approach to this problem which is based on a simple stochastic model, a continuous-time Markov chain on a small number of states. We show how it is possible to use such a stochastic model to find and plot the time-courses of concentrations, and to find simple short-time and long-time approximations to these time-courses; that is, to separate the fast and the slow processes. The most significant computation involved is the exponentiation of many small matrices, which is easily accomplished in the computing environment R.

Design of restricted normalizing flow towards arbitrary stochastic policy with computational efficiency

This paper proposes a new design method for a stochastic control policy using a normalizing flow (NF). In reinforcement learning (RL), the policy is usually modeled as a distribution model with trainable parameters. When this parameterization has less expressiveness, it would fail to acquiring the optimal policy. A mixture model has capability of a universal approximation, but it with too much redundancy increases the computational cost, which can become a bottleneck when considering the use of real-time robot control. As another approach, NF, which is with additional parameters for invertible transformation from a simple stochastic model as a base, is expected to exert high expressiveness and lower computational cost. However, NF cannot compute its mean analytically due to complexity of the invertible transformation, and it lacks reliability because it retains stochastic behaviors after deployment for robot controller. This paper therefore designs a restricted NF (RNF) that achieves an analytic mean by appropriately restricting the invertible transformation. In addition, the expressiveness impaired by this restriction is regained using bimodal student-t distribution as its base, so-called Bit-RNF. In RL benchmarks, Bit-RNF policy outperformed the previous models. Finally, a real robot experiment demonstrated the applicability of Bit-RNF policy to real world.

Modeling the Breakdown of Dielectrics Loaded With Conducting Particles

This study addresses the electrical breakdown of dielectrics loaded with randomly dispersed conducting particles. A simple stochastic breakdown model is proposed and used to provide information on the tree structure and dielectric breakdown strength. Parametric simulations suggest an important role of the particle fraction and microstructure (regular versus aggregated) on the breakdown strength while the particle size and size dispersity have limited effects. The obtained results have been recast in terms of geometrical parameters describing the particle structure and the minimum-gap path (path having the shortest length of dielectrics) is found to correlate quite well with numerical results. This suggests that simple geometrical quantities are relevant to provide quantitative predictions of breakdown strength for such materials.