Search

In this paper, we look at higher-order nonlinear Schrö dinger equation (HONLSE) through stochastic sense. This equation is examined in the presence of Brownian motion and noise term. Using the robust solver, we generate several new crucial stochastic solutions for the HONLSE. During fibre transmissions, the HONLSE coefficients, such as nonlinearity, dispersion and noise term, influenced the solitonic picture. The solitary properties of communication fibers were altered by higher-order features. To illustrate how these optical solutions behave physically, certain representations of the acquired solutions as super and shock-like shapes are introduced. The presented research can be extended to other nonlinear equations with comparable properties. [ABSTRACT FROM AUTHOR]

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020. [ABSTRACT FROM AUTHOR]

This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research. [ABSTRACT FROM AUTHOR]

In the last decades, the production of fuel ethanol from corn has spread as a valid renewable alternative to pursue sustainability goals. However the uncertain nature of both input (corn) and output (gasoline) prices, together with price dependent operational decisions, combine to make this difficult plant valuation require a real options approach. Moreover, this project is characterized by various sequential stages that contribute to increase its valuation difficulties. The purpose of this paper is to provide a reliable valuation methodology of a corn ethanol plant project able to consider the characteristics of the project. We apply the compound Real Options Approach to price a corn ethanol plant project considering that the corn and gasoline prices both follow a skew-geometric Brownian motion. We also propose a case study to show a real implementation of our theoretical model. The results show that the corn ethanol plant is financially attractive as renewable investment since the uncertainties inherent in the project add value, via managerial flexibility, to the real option valuation. [ABSTRACT FROM AUTHOR]

The use of renewable energy sources to achieve carbon neutrality is increasing. However, the uncertainty and volatility of renewable resources are causing problems in power systems. Flexible and low-carbon resources such as Energy Storage Systems (ESSs) are essential for solving the problems of power systems and achieving greenhouse gas reduction goals. However, ESSs are not being installed because of Korea's fuel-based electricity market. To address this issue, this paper presents a method for determining the optimal investment timing of Battery Energy Storage Systems (BESSs) using the Least Squares Monte Carlo (LSMC) method. A case study is conducted considering the System Marginal Price (SMP) and Capacity Payment (CP), which are electricity rates in Korea. Revenue is calculated through the arbitrage of a 10 MW/40 MWh lithium-ion BESS, and linear programming optimization is performed for ESS scheduling to maximize revenue. The ESS revenue with uncertainty is modeled as a stochastic process using Geometric Brownian Motion (GBM), and the optimal time to invest in an ESS is determined using an LSMC simulation considering investment costs. The proposed method can be used as a decision-making tool for ESS investors to provide information on facility investments in arbitrage situations. [ABSTRACT FROM AUTHOR]

The theory of nanoliquids has revealed several fundamental properties, including a significant increase in thermal conductivity over the base fluid. In this study, we analyzed the nanoliquids two-dimensional laminar boundary layer flow over an exponentially stretching surface. Suitable variables are applied to simplify the nonlinear partial differential equations (𝑷𝑫𝑬𝒔) into ordinary differential equations (𝑶𝑫𝑬𝒔). The resulting equations are analytically solved by using the variational homotopy perturbation method (𝑽𝑷𝑯𝑴), and the graphical representation obtained with the help of the expressions for momentum, temperature, and concentration are evaluated for specific estimates of the dimensionless parameters, specifically the Lewis number(𝑳𝒆), Brownian motion parameter (𝑵𝒃), thermophoresis parameter (𝑵𝒕), Prandtl number (𝑷𝒓), of suction and injection parameters. [ABSTRACT FROM AUTHOR]

Compartmental models that describe infectious disease transmission across subpopulations are central for assessing the impact of non-pharmaceutical interventions, behavioral changes and seasonal effects on the spread of respiratory infections. We present a Bayesian workflow for such models, including four features: (1) an adjustment for incomplete case ascertainment, (2) an adequate sampling distribution of laboratory-confirmed cases, (3) a flexible, time-varying transmission rate, and (4) a stratification by age group. Within the workflow, we benchmarked the performance of various implementations of two of these features (2 and 3). For the second feature, we used SARS-CoV-2 data from the canton of Geneva (Switzerland) and found that a quasi-Poisson distribution is the most suitable sampling distribution for describing the overdispersion in the observed laboratory-confirmed cases. For the third feature, we implemented three methods: Brownian motion, B-splines, and approximate Gaussian processes (aGP). We compared their performance in terms of the number of effective samples per second, and the error and sharpness in estimating the time-varying transmission rate over a selection of ordinary differential equation solvers and tuning parameters, using simulated seroprevalence and laboratory-confirmed case data. Even though all methods could recover the time-varying dynamics in the transmission rate accurately, we found that B-splines perform up to four and ten times faster than Brownian motion and aGPs, respectively. We validated the B-spline model with simulated age-stratified data. We applied this model to 2020 laboratory-confirmed SARS-CoV-2 cases and two seroprevalence studies from the canton of Geneva. This resulted in detailed estimates of the transmission rate over time and the case ascertainment. Our results illustrate the potential of the presented workflow including stratified transmission to estimate age-specific epidemiological parameters. The workflow is freely available in the R package HETTMO, and can be easily adapted and applied to other infectious diseases. Author summary: Mathematical models are a central tool for understanding the spread of infectious diseases. These models can frequently be fitted to surveillance data such as the number of laboratory-confirmed cases and seroprevalence over time. We identified that in these situations, four crucial features are required for a model to provide insightful information for managing an epidemic. These features relate to the adjustment for incomplete case ascertainment, to the choice of sampling distribution, to the variation of transmission over time and to the stratification by age. For each feature, we identify and compare several implementation options on simulated data. This structural comparison of methods results in a Bayesian workflow that is optimized for modeling the transmission of SARS-CoV-2 over a short period. We highlight the advantages and limitations of our approach in a real situation, using real-world SARS-CoV-2 data from the canton of Geneva. In addition to providing validated solutions to important technical points, such a comprehensive workflow helps to improve the reliability and the transparency of epidemic models. [ABSTRACT FROM AUTHOR]

Intrinsically disordered regions (IDRs) are segments of proteins without stable three-dimensional structures. As this flexibility allows them to interact with diverse binding partners, IDRs play key roles in cell signaling and gene expression. Despite the prevalence and importance of IDRs in eukaryotic proteomes and various biological processes, associating them with specific molecular functions remains a significant challenge due to their high rates of sequence evolution. However, by comparing the observed values of various IDR-associated properties against those generated under a simulated model of evolution, a recent study found most IDRs across the entire yeast proteome contain conserved features. Furthermore, it showed clusters of IDRs with common "evolutionary signatures," i.e. patterns of conserved features, were associated with specific biological functions. To determine if similar patterns of conservation are found in the IDRs of other systems, in this work we applied a series of phylogenetic models to over 7,500 orthologous IDRs identified in the Drosophila genome to dissect the forces driving their evolution. By comparing models of constrained and unconstrained continuous trait evolution using the Brownian motion and Ornstein-Uhlenbeck models, respectively, we identified signals of widespread constraint, indicating conservation of distributed features is mechanism of IDR evolution common to multiple biological systems. In contrast to the previous study in yeast, however, we observed limited evidence of IDR clusters with specific biological functions, which suggests a more complex relationship between evolutionary constraints and function in the IDRs of multicellular organisms. Author summary: Proteins are the molecular machines that carry out many processes required for life at an atomic level. Though many proteins use fixed structures to perform their functions, proteins with flexible segments are widespread, especially in multicellular organisms. Furthermore, these intrinsically disordered regions (IDRs) are often involved in essential cellular functions. However, the sequences of IDRs evolve quickly, which challenges traditional bioinformatics methods that depend on sequence conservation to predict function. Several studies have demonstrated that distributed biophysical features of IDRs are constrained rather than their exact sequences, and a recent study in yeast found that IDRs with common patterns of conserved features were associated with specific functions. Therefore, in this work we ask if IDRs in fruit flies, another common laboratory organism, also have patterns of conservation with associated functions. We build on the previous study by integrating their approach into a fully statistical framework based on mathematical models of trait evolution. Though we identify widespread signals of conservation in the IDRs of fruit flies, we find less evidence of a simple relationship between features and function. These methods and results will provide a valuable resource that can guide future experimental analyses of IDRs in fruit flies and other organisms. [ABSTRACT FROM AUTHOR]

This manuscript focuses on a class of stochastic functional differential equations driven by time-changed Brownian motion. By utilizing the Lyapunov method, we capture some sufficient conditions to ensure that the solution for the considered equation is η-stable in the pth moment sense. Subsequently, we present some new criteria of the η-stability in mean square by using time-changed Itô formula and proof by contradiction. Finally, we provide some examples to demonstrate the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

The motor neuroscience literature suggests that the central nervous system may encode some motor commands in terms of velocity. In this work, we tackle the question: what consequences would velocity commands produce at the behavioral level? Considering the ubiquitous presence of noise in the neuromusculoskeletal system, we predict that velocity commands affected by stationary noise would produce "random walks", also known as Brownian processes, in position. Brownian motions are distinctively characterized by a linearly growing variance and a power spectral density that declines in inverse proportion to frequency. This work first shows that these Brownian processes are indeed observed in unbounded motion tasks e.g., rotating a crank. We further predict that such growing variance would still be present, but bounded, in tasks requiring a constant posture e.g., maintaining a static hand position or quietly standing. This hypothesis was also confirmed by experimental observations. A series of descriptive models are investigated to justify the observed behavior. Interestingly, one of the models capable of accounting for all the experimental results must feature forward-path velocity commands corrupted by stationary noise. The results of this work provide behavioral support for the hypothesis that humans plan the motion components of their actions in terms of velocity. [ABSTRACT FROM AUTHOR]

The Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless real scalar field in Einstein's universe is studied. By assuming the small displacement condition, the dispersion in the momentum and position of a point particle coupled to the massless scalar field are obtained. As a consequence of the homogeneity and isotropy properties of the Einstein's Universe, we find that all components of these physical observables are identical. We also examine divergent behaviors associated with the physical momentum and position dispersions, which we attribute to the IR 1 × S 3 compact topology of Einstein's universe. Finally, based on the small displacement condition assumed, we analyze the limit of validity of our investigation. [ABSTRACT FROM AUTHOR]

When writing down a Langevin equation for the time evolution of a "system" in contact with a thermal bath, one typically makes the implicit (and often tacit) assumption that the thermal environment is in equilibrium at all times. Here, we take this assumption as a starting point to formulate the problem of a system evolving in contact with a thermal bath from the perspective of the bath, which, since it is in equilibrium, can be described by the microcanonical ensemble. We show that the microcanonical ensemble of the bath, together with the Hamiltonian equations of motion for all the constituents of the bath and system together, give rise to a Langevin equation for the system evolution alone. The friction coefficient turns out to be given in terms of auto-correlation functions of the interaction forces between the bath particles and the system, and the Einstein relation is recovered. Moreover, the connection to the Fokker–Planck equation is established. [ABSTRACT FROM AUTHOR]

Roller bearing degradation features fractal characteristics such as self-similarity and long-range dependence (LRD). However, the existing remaining useful life (RUL) prediction models are memoryless or short-range dependent. To this end, we propose a RUL prediction model based on fractional Brownian motion (FBM). Bearing faults can happen in different places, and thus their degradation features are difficult to extract accurately. Through variational mode decomposition (VMD), the original degradation feature is decomposed into several components of different frequencies. The monotonicity, robustness and trends of the different components are calculated. The frequency component with the best metric values is selected as the training data. In this way, the performance of the prediction model is hugely improved. The unknown parameters in the degradation model are estimated by the maximum likelihood algorithm. The Monte Carlo method is applied to predict the RUL. A case study of a bearing is presented and the prediction performance is evaluated using multiple indicators. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the evolutionary dynamic model for signed edges as observed in online signed social networks. We introduce the incremental mechanism of signed edges behind a simple random walk and explain how this relates to Brownian motion and the diffusive process. We prove how a one-dimensional thermal diffusion equation can be obtained to describe such edge-generating mechanism, and moreover obtain a macroscopic probability distribution of positive and negative edges. The result reveals that the signed edge growth dynamics process can be regarded as a thermodynamic diffusion process. Both empirically and theoretically, we validate that signed network links follow the classic statistic mechanism, i.e., local Brownian motion gives rise to the global emergence pattern of the Gaussian process. The investigation might discover a new and universal characteristic for signed networks, and shed light on some potential applications, such as information spreading, evolutionary games, trust transmission, and dynamic structural balance. [ABSTRACT FROM AUTHOR]

We investigate a class of statistical arbitrage strategies under the assumption that stock prices are driven by fractional Brownian motions. Specifically, the buy-and-hold with a stop-profit threshold strategies are analysed to demonstrate the existence of statistical arbitrage opportunities. Our analysis establishes the conditions for the considered strategy class to yield statistical arbitrage. The Hurst parameter in the fractional Brownian motion-based asset price model is shown to be a determining factor. The analysis is confirmed by a Monte Carlo simulation study. Furthermore, a modified Thompson sampling method is proposed for optimizing the strategy parameters of the selling-threshold and its growth rate to maximize investment performance. [ABSTRACT FROM AUTHOR]

The trapping potential induced by the interaction of a highly focused laser light with a spherical dielectric particle can be accurately approximated by a parabolic potential. In this work, we revisit experimental and numerical methodologies used to characterize the Brownian motion of a colloidal particle under the influence of a simple harmonic potential produced by optical tweezers. A classic Brownian dynamics simulation is used to model the experimental results, focusing on statistical properties that can be measured by direct visualization of the system using videomicroscopy. This work represents a useful insight into the underlying physics behind the optical tweezers technique, also giving guidelines regarding programming protocols and experimental analysis methodologies, that may be of help for students working with such techniques, as well as for professors teaching undergraduate advanced optics courses. Editor's Note: Optical tweezers are fascinating tools to manipulate micrometer-size particles, such as cells or colloids, via the confining potential of a laser. This paper shows how this external potential hinders the Brownian motion of a colloid. It presents several usual theoretical approaches, including the Langevin equation, that one could use in class, as well as the Brownian dynamics simulations one can run to predict the trajectories of the confined colloid. It also details some experiments that would allow undergraduate students in a statistical physics course to measure such an effect. [ABSTRACT FROM AUTHOR]

Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing some of the underlying ideas of stochastic processes through direct experimentation. Students analyze stochastic trajectories of beads in a bouncing bed of smaller beads subjected to an external periodic drive. The analysis of the trajectories involves the application of a vast toolkit of statistical estimators that are useful in many fields of physics. Editor's Note: This paper shows how colliding beads can be used to demonstrate stochastic trajectories. While the experiment is simple, students can analyze the trajectories using techniques with a range of sophistication, making the experiment appropriate for students at a wide range of levels. [ABSTRACT FROM AUTHOR]

We analyze the multiscale behaviors of high-frequency intraday prices, with a focus on how asset prices are correlated over different timescales. The multiscale approach proposed in this paper is designed for the analysis of high-frequency intraday prices. It incorporates microstructure noise into the stochastic price process. We consider a noisy fractional Brownian motion model and illustrate its various statistical properties. This leads us to introduce new latent correlation and noise estimators. New numerical algorithms are developed for model estimation using empirical high-frequency data. For a collection of stocks and exchange-traded funds, examples are provided to illustrate the relationship between multiscale correlation and sampling frequency as well as the evolution of multiscale correlation over time. [ABSTRACT FROM AUTHOR]

Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this paper, we study a class of BSDEs with time-delay generators driven by Caputo fractional derivatives. In contrast to conventional BSDEs, in this class of equations, the generator is also affected by the past values of solutions. Under the Lipschitz condition and some new assumptions, we present a theorem on the existence and uniqueness of solutions. [ABSTRACT FROM AUTHOR]

To investigate the consequence of thermophoresis and Brownian diffusion on convective boundary layer micropolar fluid flow over a stretching wedge-shaped surface. The effects of non-dimensional parameters namely coupling constant parameter (0.01 ≤ B1 ≤ 0.05), magnetic parameter (1.0 ≤ M ≤ 15.0), Grashof number (0.3 ≤ Gr ≤ 0.9), modified Grashof number (0.3 ≤ Gm ≤ 0.8), micropolar parameter (2.0 ≤ G2 ≤ 7.5), vortex viscosity constraint (0.02 ≤ G1 ≤ 0.2), Prandtl number (7.0 ≤ Pr ≤ 15.0), thermal radiation parameter (0.25 ≤ R ≤ 0.50), Brownian motion parameter (0.2 ≤ Nb ≤ 0.62), thermophoresis parameter (0.04 ≤ Nt ≤ 0.10), heat generation parameter (0.1 ≤ Q ≤ 0.5), Biot number (0.65 ≤ Bi ≤ 1.0), stretching parameter (0.2 ≤ A ≤ 0.5), Lewis number (3.0 ≤ Le ≤ 7.0), and chemical reaction parameter (0.2 ≤ K ≤ 0.7) on the steady MHD heat and mass transfer is investigated in the present study. The coupled non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations employing similarity transformation. Furthermore, by using the Runge-Kutta method followed by the shooting technique, the transformed equations are solved. The main goal of this study is to investigate the numerical analysis of nanofluid flow within the boundary layer region with the effects of the microrotation parameter and velocity ratio parameter. The novelty of this paper is to propose a numerical method for solving third-order ordinary differential equations that include both linear and nonlinear terms. To understand the physical significance of this work, numerical analyses and tabular displays of the skin friction coefficient, Nusselt number, and Sherwood number are shown. The new approach of the present study contributes significantly to the understanding of numerical solutions to nonlinear differential equations in fluid mechanics and micropolar fluid flow. Micropolar fluids are becoming even more of a focus due to the desire for engineering applications in various fields of medical, mechanical engineering, and chemical processing. [ABSTRACT FROM AUTHOR]

This paper is devoted to the synchronization of stochastic differential equations driven by the linear multiplicative fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1). We use equivalent transformations to prove that the differential equation has a unique stationary solution, which generates a random dynamical system. Moreover, the system has the pathwise singleton set random attractor. We then establish the synchronization of the coupled differential equations and provide numerical simulation results. At the end, we discuss two specific noise forms and present the corresponding synchronization results. [ABSTRACT FROM AUTHOR]

Adams and Collyer argue that contemporary multivariate (Gaussian) phylogenetic comparative methods are prone to favouring more complex models of evolution and sometimes rotation invariance can be an issue. Here we dissect the concept of rotation invariance and point out that, depending on the understanding, this can be an issue with any method that relies on numerical instead of analytical estimation approaches. We relate this to the ongoing discussion concerning phylogenetic principal component analysis. Contrary to what Adams and Collyer found, we do not observe a bias against the simpler Brownian motion process in simulations when we use the new, improved, likelihood evaluation algorithm employed by mvSLOUCH, which allows for studying much larger phylogenies and more complex model setups. [ABSTRACT FROM AUTHOR]

Monte-Carlo based valuation in life insurance involves the simulation of various components of the balance sheet: portfolios, guarantees, assets mix, market conditions and many other specific risk factors; which can be time-consuming. In view of the time needed to achieve this task, insurers are then facing a trade-off of balancing the number of simulations against the uncertainty surrounding the estimated quantity. In the current paper, we propose a variance-reduction methodology using a machine learning technique. It roots from the unsupervised learning literature in conjunction with the quantization of random processes. The goal is to reduce the number of simulated Brownian paths, using auxiliary scenarios that can be seen as path clusters, which efficiently and accurately approximate the initial ones with regards to an adequate measure of distance. Moreover, we introduce penalty to accommodate for various inputs of the initial conditions of risk factors. By doing so, we implicitly assign labels to the scenarios and thus advocate using a semi-supervised learning to enhance the performance of the scenarios reduction by imposing an additional impurity condition on the clusters based on these labels. This is made possible thanks to a decomposition property of the insurers cash-flows, which allows to disentangle the initial conditions of risk factors from the Brownian motions driving their dynamics. The training of the proposed learning algorithm is based on an adaptation of the well-known k-means algorithm. An intensive numerical study is carried out over a range of simulation setups to compare the performances of the proposed methodology. We show, numerically, that the proposed methodology outperforms some classical variance reduction approach. Also, using a real-life dataset, we show that our methodology outperforms some conventional variance reduction used by life insurance practitioners. [ABSTRACT FROM AUTHOR]

Phylogenetic signal (PS) is the propensity of closely related species to resemble each other. PS has been tested across clades of terrestrial plants; however, insight for seagrasses is still lacking. Signatures of PS and models of niche (trait) evolution can help to detect phylogenetic niche conservatism (PNC), that is, close relatives live in comparable niches.The initial goal of this study was to assess the pattern of PS for the world's seagrasses, by testing the non‐independence of phylogenetic relatedness and seagrass species traits. A phylogeny of 49 seagrasses was constructed, together with a matrix of nine traits covering morphological, life‐history and reproductive attributes. PS of traits was tested through complementary indices (Pagel's λ, Blomberg's K, Moran's I and Abouheif's Cmean). Three models of niche evolution (Brownian Motion, BM; Ornstein–Uhlenbeck, OU; Early Burst, EB) were then fitted to each trait and the multivariate trait matrix.Results supported the existence of strong PS for seagrasses, with a particularly large effect size for seagrass reproductive traits, which followed an EB evolution model. Local Indicators of Phylogenetic Association (local autocorrelation metrics that can help to identify areas of large autocorrelation) supported the presence of PS across seagrass lineages/clades, supported by the dominance of OU as the most parsimonious trait evolution model.The pattern of strong PS seems to be a consequence of long‐term PNC of seagrass traits after initial radiation.Synthesis: Our study highlights the relevance of evolution from common ancestors and shared history underpinning large seagrass phylogenetic structuring. [ABSTRACT FROM AUTHOR]

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media. [ABSTRACT FROM AUTHOR]

A collection of smaller, less expensive sensor nodes called wireless sensor networks (WSNs) use their sensing range to gather environmental data. Data are sent in a multi-hop manner from the sensing node to the base station (BS). The bulk of these sensor nodes run on batteries, which makes replacement and maintenance somewhat difficult. Preserving the network's energy efficiency is essential to its longevity. In this study, we propose an energy-efficient multi-hop routing protocol called ESO-GJO, which combines the enhanced Snake Optimizer (SO) and Golden Jackal Optimization (GJO). The ESO-GJO method first applies the traditional SO algorithm and then integrates the Brownian motion function in the exploitation stage. The process then integrates multiple parameters, including the energy consumption of the cluster head (CH), node degree of CH, and distance between node and BS to create a fitness function that is used to choose a group of appropriate CHs. Lastly, a multi-hop routing path between CH and BS is created using the GJO optimization technique. According to simulation results, the suggested scheme outperforms LSA, LEACH-IACA, and LEACH-ANT in terms of lowering network energy consumption and extending network lifetime. [ABSTRACT FROM AUTHOR]

In an equilibrium thermal environment, random elastic collisions between background particles and a tracer establish the picture of Brownian motion fulfilling the celebrated Einstein relation between diffusivity and mobility. However, extensions of the Einstein relation to link dissipation, fluctuations, and nonequilibrium dynamical mechanisms in active matter systems are still debated. Here, we investigate experimentally the impact of an active background on a passive tracer using vibrationally excited active particles, that result in multiple correlated tapping collisions with the tracer, for which a persistent memory emerges in the dynamics. The system is described by a generalized active Einstein relation that constrains fluctuations, dissipation, and effective activity, by taking the emerging tracer memory into account. Since the resulting persistence can largely be tuned by the environmental density and motility, our findings can be useful to engineer properties of various active systems in biomedical applications, microfluidics, chemical engineering, or swarm robotics. Einstein relations in non-equilibrium active matter systems break upon increase of fluctuations and changes in the system's dissipative properties. By observing the tapping collisions of a tracer in a bath of vibrationally excited active granular particles, the authors propose a generalized active Einstein relation accounting for memory effects. [ABSTRACT FROM AUTHOR]

The uncertainty relation is considered to be one of key features of quantum mechanics which distinguishes quantum and classical systems. Recently, we developed a new formulation of the uncertainty relation based on the generalized scheme of variational principle, the stochastic variational method (SVM). In this method, the uncertainty relation is related to the nondifferentiability of observables and thus can be obtained even in classical stochastic systems. This new formulation resolves the famous paradox in quantum mechanics, the angular uncertainty relation without introducing artificial assumptions. In this paper, we show that the fluctuations of position and momentum for a nonrelativistic viscous fluid element satisfies the uncertainty relation analogous to the corresponding quantum mechanical one. Such a fluctuation is sensitive to the temperature gradient at the freezeout surface and can affect the collective flow anisotropy in relativistic heavy‐ion collisions. [ABSTRACT FROM AUTHOR]

This article introduces a new class of diffusive processes with rough mutually exciting jumps for modeling financial asset returns. The novel feature is that the memory of positive and negative jump processes is defined by the product of a dampening factor and a kernel involved in the construction of the rough Brownian motion. The jump processes are nearly unstable because their intensity diverges to + ∞ for a brief duration after a shock. We first infer the stability conditions and explore the features of the dampened rough (DR) kernel, which defines a fractional operator, similar to the Riemann-Liouville integral. We next reformulate intensities as infinite-dimensional Markov processes. Approximating these processes by discretization and then considering the limit allows us to retrieve the Laplace transform of asset log-return. We show that this transform depends on the solution of a particular fractional integro-differential equation. We also define a family of changes of measure that preserves the features of the process under a risk-neutral measure. We next develop an econometric estimation procedure based on the peak over threshold (POT) method. To illustrate this work, we fit the mutually exciting rough jump-diffusion to time series of Bitcoin log-returns and compare the goodness of fit to its non-rough equivalent. Finally, we analyze the influence of roughness on option prices. [ABSTRACT FROM AUTHOR]

As defaultable options are subject to default risks in over-the-counter (OTC) markets, vulnerable options are one of the financial securities closely linked with the risk caused by the situation that the option issuer may be unable to execute their contractual obligations. In this study, taking account of the changes in stock prices show different degrees of long-term correlation and autocorrelation at different times in the real-world situations of the financial market, contrary to the assumption of Black-Scholes settings, we propose the closed-form pricing formulas for the vulnerable options based on a fractional Brownian environment. First of all, from the model dynamics for the underlying asset under the fractional Brownian motions, we derive partial differential equations (PDEs) for vulnerable option prices, and subsequently derive the closed-form solutions for the options based on the issuer's credit risk via double Mellin transforms. In addition, we evaluate the accuracy of vulnerable option pricing by comparing the solutions obtained using the aforementioned closed formulas with those obtained via Monte Carlo simulations. Finally, we examine the price sensitivities of vulnerable options in fractional Brownian markets with respect to the model parameters. [ABSTRACT FROM AUTHOR]

The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings. [ABSTRACT FROM AUTHOR]

Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering. We construct least-square estimators for the unknown drift parameters within Vasicek models that are driven by these processes. To demonstrate their strong consistency, we establish asymptotic bounds with probability 1 for the rate of growth of trajectories of tempered fractional processes. [ABSTRACT FROM AUTHOR]

Brownian motion on manifolds with non-trivial diffusion coefficient can be constructed by stochastic development of Euclidean Brownian motions using the fiber bundle of linear frames. We provide a comprehensive study of paths for such processes that are most probable in the sense of Onsager–Machlup, however with path probability measured on the driving Euclidean processes. We obtain both a full characterization of the resulting family of most probable paths, reduced equation systems for the path dynamics where the effect of curvature is directly identifiable, and explicit equations in special cases, including constant curvature surfaces where the coupling between curvature and covariance can be explicitly identified in the dynamics. We show how the resulting systems can be integrated numerically and use this to provide examples of most probable paths on different geometries and new algorithms for estimation of mean and infinitesimal covariance. [ABSTRACT FROM AUTHOR]

We consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order  α ∈ (0 , 1) , and the non-linear terms satisfy the global Lipschitz conditions. We first approximate the noise with the piecewise constant function to obtain the regularized stochastic fractional differential equation. By applying Minkowski's inequality for double integrals, we establish that the error between the exact solution and the solution of the regularized problem has an order of  O (Δ t α)  in the mean square norm, where  Δ t  denotes the step size. To validate our theoretical conclusions, numerical examples are presented, demonstrating the consistency of the numerical results with the established theory. [ABSTRACT FROM AUTHOR]

Generally, stochastic functional differential equations (SFDEs) pose a challenge as they often lack explicit exact solutions. Consequently, it becomes necessary to seek certain favorable conditions under which numerical solutions can converge towards the exact solutions. This article aims to delve into the convergence analysis of solutions for stochastic functional differential equations by employing the framework of G-Brownian motion. To establish the goal, we find a set of useful monotone type conditions and work within the space C r ((− ∞ , 0 ] ; R n) . The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both L G 2 and exponential estimates. [ABSTRACT FROM AUTHOR]

The absorption of photons by atoms encompasses fundamental quantum mechanical aspects, particularly the emergence of randomness to account for the inherent unpredictability in absorption outcomes. We demonstrate that vacuum fluctuations can be the origin of this randomness. An illustrative example of this is the absorption of a single photon by two symmetrically arranged atoms. In the absence of a mechanism to introduce randomness, the Schrödinger equation alone can govern the time evolution of the process initially. Then, it becomes stuck, and an entangled state of the two atoms emerges. This entangled state consists of two components: in one, the first atom is excited by the photon while the second is in the ground state, and in the other, the second atom is excited while the first remains in the ground state. These components form a superposition state characterized by an unbreakable symmetry in the absence of external influences. Consequently, the absorption process remains incomplete. When vacuum fluctuations come into play, they can induce fluctuations in the weights of these components, akin to Brownian motion. Over time, one component diminishes, thereby breaking the entanglement between the two atoms and allowing the photon absorption process to conclude. The remaining component shows which atom completes the photon absorption. Vacuum fluctuations not only introduce randomness but also have the potential to give rise to the Born rule in this context. Furthermore, the Casimir effect, which is closely tied to vacuum fluctuations, presents a promising experimental avenue for validating this mechanism. Similar studies can also be conducted with varying numbers of atoms. [ABSTRACT FROM AUTHOR]

In this research, the effect of different models of thermal conductivity and dynamic viscosity has been investigated by considering the effect of Brownian motion of nanoparticles on the flow field and heat transfer of nanofluids. This study was performed numerically in a square cavity with water/aluminum-oxide nanofluid in three modes of natural, mixed and forced convection by changing the independent variable such as nanoparticle volume fraction, Rayleigh number, Richardson number, and Reynolds number. The governing equations with certain boundary conditions are solved using the finite volume method. Also, according to the obtained numerical results, Nusselt number has been investigated for different conditions with and without considering Brownian motion. The results showed that for all the studied models, in all three modes of natural, mixed and forced convection, the average Nusselt number when the effect of Brownian motion is considered, is more than the case that the effect of this motion is not considered. In all cases, the Koo & Kleinstreuer and Li & Kleinstreuer models show approximately the same values for the maximum mean Nusselt number. The similar results are obtained employing the Wajjha & Das and Xiao et al. models. For mixed convection, the highest and lowest increases of Nusselt number, considering Brownian motion are 17.68% and 14.84%, respectively. While referred values for forced convection are 30.46% and 17.94 %, respectively. [ABSTRACT FROM AUTHOR]

The fractal dimension (D) is a very useful indicator for recognizing images. The fractal dimension increases as the pattern of an image becomes rougher. Therefore, images are frequently described as certain models of fractal geometry. Among the models, two-dimensional fractional Brownian motion (2D FBM) is commonly used because it has specific physical meaning and only contains the finite-valued parameter (a real value from 0 to 1) of the Hurst exponent (H). More usefully, H and D possess the relation of D = 3 − H. The accuracy of the maximum likelihood estimator (MLE) is the best among estimators, but its efficiency is appreciably low. Lately, an efficient MLE for the Hurst exponent was produced to greatly improve its efficiency, but it still incurs much higher computational costs. Therefore, in the paper, we put forward a deep-learning estimator through classification models. The trained deep-learning models for images of 2D FBM not only incur smaller computational costs but also provide smaller mean-squared errors than the efficient MLE, except for size 32 × 32 × 1. In particular, the computational times of the efficient MLE are up to 129, 3090, and 156248 times those of our proposed simple model for sizes 32 × 32 × 1, 64 × 64 × 1, and 128 × 128 × 1. [ABSTRACT FROM AUTHOR]

In this paper, the approximate stationarity of the second-order moment increments of the sub-fractional Brownian motion is given. Based on this, the pricing model for European options under the sub-fractional Brownian regime in discrete time is established. Pricing formulas for European options are given under the delta and mixed hedging strategies, respectively. Furthermore, European call option pricing under delta hedging is shown to be larger than under mixed hedging. The hedging error ratio of mixed hedging is shown to be smaller than that of delta hedging via numerical experiments. [ABSTRACT FROM AUTHOR]

The birefringence response of aqueous cellulose nanocrystal (CNC) suspensions in a two-dimensional laminar flow is measured and studied. The suspensions have CNC concentrations of 1.0 wt% (weight percentage) and 1.2 wt%. Cellulose nanocrystals are optically anisotropic rod-like particles that align when subjected to local velocity gradients, whereas at rest, they remain randomly orientated by Brownian motion. The alignment causes birefringence, a phenomenon also known as flow-induced birefringence. We study the flow through an additively manufactured flow channel and measure the amount of birefringence as well as the position of the refractive index axes by using polarizers and a polarization camera. With the help of reference data published in a previous study (Lane, Rode, et al., 2022a), strain rates are derived from the birefringence measurements and compared with numerical simulations. Two flow situations are studied, a plane Poiseuille flow and the flow around a cosine-shaped constriction. The experimentally derived shear rates for the plane Poiseuille flow are consistent with theoretical and computational results. The derived strain rates for the flow around the cosine-shaped constriction show an unexpected asymmetric profile, with the strain rates in the contraction zone being larger than in the expansion zone. The averaged orientation of the CNCs in the flow is linked to the position of the refractive index axes. In the contraction zone, the CNCs tend to align parallel to the flow, whereas in the expansion zone, the CNCs tend to align perpendicular to the flow. The results of this study are discussed in the context of previous, similar studies. The asymmetric strain rate profile around the cosine-shaped constriction is thought to originate from history effects, and the alignment of the CNCs is influenced by extensional rates. [ABSTRACT FROM AUTHOR]

The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics. Specifically, the formula provides a solution to the partial differential equation, expressed as an expectation value for Brownian motion. This paper demonstrates that the Feynman–Kac formula does not produce a unique solution but instead carries infinitely many solutions to the corresponding partial differential equation. [ABSTRACT FROM AUTHOR]

We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes. [ABSTRACT FROM AUTHOR]

Conditions for the existence and uniqueness of mild solutions for a system of semilinear impulsive differential equations with infinite fractional Brownian movements and the Wiener process are established. Our approach is based on a novel application of Burton and Kirk's fixed point theorem in extended Banach spaces. This paper aims to extend current results to a differential-inclusions scenario. The motivation of this paper for impulsive neutral differential equations is to investigate the existence of solutions for impulsive neutral differential equations with fractional Brownian motion and a Wiener process (topics that have not been considered and are the main focus of this paper). [ABSTRACT FROM AUTHOR]

This paper reviews 17 studies addressing dynamic option hedging in frictional markets through Deep Reinforcement Learning (DRL). Specifically, this work analyzes the DRL models, state and action spaces, reward formulations, data generation processes and results for each study. It is found that policy methods such as DDPG are more commonly employed due to their suitability for continuous action spaces. Despite diverse state space definitions, a lack of consensus exists on variable inclusion, prompting a call for thorough sensitivity analyses. Mean-variance metrics prevail in reward formulations, with episodic return, VaR and CvaR also yielding comparable results. Geometric Brownian motion is the primary data generation process, supplemented by stochastic volatility models like SABR (stochastic alpha, beta, rho) and the Heston model. RL agents, particularly those monitoring transaction costs, consistently outperform the Black–Scholes Delta method in frictional environments. Although consistent results emerge under constant and stochastic volatility scenarios, variations arise when employing real data. The lack of a standardized testing dataset or universal benchmark in the RL hedging space makes it difficult to compare results across different studies. A recommended future direction for this work is an implementation of DRL for hedging American options and an investigation of how DRL performs compared to other numerical American option hedging methods. [ABSTRACT FROM AUTHOR]

[Display omitted] Measuring rotational and translational Brownian motion of single spherical particles reveals dissipations due to the interaction between the particle and the environment. In this article, we show experiments where the in-plane translational and the two rotational drag coefficients of a single spherical Brownian particle can be measured. These particle drags are functions of the particle size and of the particle–wall distance, and of the viscous dissipations at play. We measure drag coefficients for Janus particles close to a solid wall and close to a lipid bilayer membrane. For a particle close to a wall, we show that according to hydrodynamic models, particle–wall distance and particle size can be determined. For a particle partially wrapped by lipid membranes, in absence of strong binding interactions, translational and rotational drags are significantly larger than the ones of non-wrapped particles. Beside the effect of the membrane viscosity, we show that dissipations in the deformed membrane cap region strongly contribute to the drag coefficients. [ABSTRACT FROM AUTHOR]

The thin needle is viewed as a revolutionary object since it has a thinner thickness than a boundary layer. As a consequence, scientific and engineering applications for instance electrical equipment, hot wire anemometers and geothermal power generation are significantly impacted by the flow deformed by a thin moving needle. MHD Eyring–Powell fluid flow over a thin needle perceiving heat source, chemical reaction and nonlinear thermal radiation is the subject of the current investigation. In addition, the present study utilizes the Buongiorno model to examine the special effects of the fluid's Brownian and thermophoretic forces. The solution of the dimensionless form of ODEs is produced by applying exact renovations to the given problem, which is determined by the structure of PDEs. The bvp4c algorithm, based on the finite difference approach is utilized to numerically solve such modified ODEs. For validation, the results obtained indicate good agreement when compared to the literature. Finally, a detailed graphical analysis of key parameters is shown and explained while keeping in mind the physical significance of flow parameters. The results show that as magnetic and fluid parameter values improve, the velocity gradient falls. Increasing heat source and radiation parameters optimises heat transfer rate. The augmentation of the Lewis number and chemical reaction accelerates the rate of mass transfer on the surface. Brownian motion and thermophoresis provide enhanced thermal performance for the fluid temperature. Growing the thermophoresis parameter from 0.1 to 0.3 upsurges the Nusselt number by 5.47% and the Sherwood number by 12.26%. [ABSTRACT FROM AUTHOR]

Nanoparticle deposition in nanofluid boiling can significantly impact heat transfer efficiency. However, there is still much to be uncovered regarding the heterogeneity of micro-structures in nanoparticle deposition and how to quantitatively model variations in deposition layer thickness. To gain a deeper understanding, we conducted experiments where single boiling bubbles were grown from an artificial micro-cavity in SiO2 nanofluids with varying concentrations and durations under a constant heat flux. Our results reveal that the nanoparticle deposition region increases with concentration and boiling duration. Notably, while the deposition morphology is irregular near the bubble nucleation site, it becomes more uniform further away from the bubble nucleation site. We believe that the heterogeneity in the micro-structure of the deposition layer is due to differences in the evaporation time of the liquid microlayer at different positions, variations in its thickness beneath a single boiling bubble, and dependency of nanoparticles Brownian motion on temperature. Additionally, the thickness of the deposition layer decreases as the distance from the nucleation site increases. To accurately describe this variation in thickness, we have proposed a semi-empirical correlation based on the liquid microlayer evaporation theory and the conservation of mass of nanoparticles beneath a single boiling bubble. The thickness of the nanoparticle deposition layer is determined by the number of growing bubbles, liquid density, initial thickness of the liquid microlayer, local nanoparticle concentration, and local nanoparticle stacking density. This study provides valuable insights into optimizing micro-structures or thickness of the deposition layer, leading to improved nanofluid boiling heat transfer. [ABSTRACT FROM AUTHOR]

We discuss formal analogies between a nonlinear Schrödinger equation derived by the author from the theory of scale relativity and the equations of Brownian theory. By using the Madelung transformation, the nonlinear Schrödinger equation takes the form of hydrodynamic equations involving a friction force, an effective thermal pressure, a pressure due to the self-interaction, and a quantum potential. These hydrodynamic equations have a form similar to the damped Euler equations obtained for self-interacting Brownian particles in the theory of simple liquids. In that case, the temperature is due to thermal motion and the pressure arises from spatial correlations between the particles. More generally, the correlations can be accounted for by using the dynamical density functional theory. We determine the excess free energy of Brownian particles that reproduces the standard quantum potential. We then consider a more general form of excess free energy functionals and propose a new class of generalized Schrödinger equations. For a certain form of excess free energy, we recover the generalized Schrödinger equation associated with the Tsallis entropy considered in a previous paper. [ABSTRACT FROM AUTHOR]

This study investigates the pricing formula for European options when the underlying asset follows a fuzzy mixed weighted fractional Brownian motion within a jump environment. We construct a pricing model for European options driven by fuzzy mixed weighted fractional Brownian motion with jumps. By converting the partial differential equation (PDE) into a Cauchy problem, we derive explicit solutions for both European call options and European put options. The figures and tables demonstrating the effectiveness of the results highlight the suitability of the fuzzy mixed weighted fractional Brownian motion with jump model for option pricing. [ABSTRACT FROM AUTHOR]

We establish both the uniqueness and the existence of the solutions to a hidden-memory variable-order fractional stochastic partial differential equation, which models, e.g., the stochastic motion of a Brownian particle within a viscous liquid medium varied with fractal dimensions. We also investigate the inverse problem concerning the observations of the solutions, which eliminates the analytic assumptions on the variable orders in the literature of this topic and theoretically guarantees the reliability of the determination and experimental inference. [ABSTRACT FROM AUTHOR]