Random Processes - Science topic

This paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the...

Power consumption management is crucial to maintaining the reliable operation of power grids, especially in the context of the decarbonization of the electric power industry. Managing power consumption of industrial enterprises by personnel proved ineffective, which required the development and implementation of automatic energy consumption managem...

Assessing the performance of earthquake-resistant structural and geotechnical systems is crucial for achieving a desired reliability level and enhancing the resilience of the built environment in seismic-prone regions. Nonlinear dynamic analyses are widely used to quantify structural and geotechnical performance. Still, they require an accurate rep...

Context: Wound healing and associated tissue regeneration process are significant to successful outcomes during periodontal therapy. Hyaluronic acid (HA) is one of the important promoting factors that facilitate cell migration and differentiation during this process. Aim: The aim of the present study was to evaluate the efficacy of HA as a therapeu...

Amid concerns of intensified water cycle during global warming, the scientific attention on rainfall dynamics and its extremes is increasing. Global trends in rainfall totals and extremes are investigated using long-term rainfall station data-spanning more than 150 years for rainfall maxima and more than 200 years for total annual totals, as well a...

Stochastic resetting, a method for accelerating target search in random processes, often incurs temporal and energetic costs. For a diffusing particle, a lower bound exists for the energetic cost of reaching the target, which is attained at low resetting rates and equals the direct linear transportation cost against fluid drag. Here, we study smart...

The gambler’s fallacy is a prevalent cognitive bias in betting behaviors, characterized by the mistaken belief that an independent and identically distributed random process exhibits negative serial correlation. This misconception often arises when individuals observe a series of realized outcomes from the process. We study how varying the quantity...

The primary objective of this study is to investigate the stochastic plasma-mechanical-elastic wave propagation at the boundary of an elastic half-space in a semiconductor material using photo-thermoelasticity theory. The novelty of this work lies in the combination of stochastic simulation with temperature-dependent electrical conductivity and var...

Mendelian randomization (MR), i.e. instrumental variable analysis using genetic instruments, is an approach that incorporates population genetics to improve causal inference. Given that genetics are randomly allocated at conception, this resembles the randomization process in randomized controlled trials and hence is more resistant to unobserved co...

We study the Riesz and logarithmic energies on the Grassmannian $\operatorname{Gr}_{2,4}$ of $2$-dimensional subspaces of $\mathbb{R}^4$. We prove that the continuous Riesz and logarithmic energies are uniquely minimized by the uniform measure, and we obtain asymptotic upper and lower bounds for the minimal discrete energies, with matching orders f...

A huge literature in statistics and machine learning is devoted to parametric families of correlation functions, where the correlation parameters are used to understand the properties of an associated spatial random process in terms of smoothness and global or compact support. However, most of current parametric correlation functions attain only no...

Let $\bF=\left(\cF(t), \:t\in \bR_+\right)$ be a filtration on some probability space, and $X$ be the strong solution of the equation $X(t)=\X+\int_0^tQ(s,X(s))\rd\iota(s)+\int_0^t\sigma(s,X(s-)) \rd Y(s),$ where $\X$ is an $\cF(0)$-measurable $\bR^d$-valued random variable, $\iota$ is a continuous increasing process with $\cF(0)$-measurable values...

Anxiety is a psychological phenomenon that is commonly felt by everyone, especially people who frequently interact with crowds. Anxiety can happen to anyone, including students. students who are indicated to experience anxiety do not have a clear picture of their future. Coloring can be used as an alternative as an effort to reduce anxiety. Doing c...

We consider the estimation of gradient of density function of positive associated random process $(X_{i})_{i}$ from noisy observations. We establish asymptotic expressions for the variance of the gradient of estimator of density of probability. We consider the case of algebraic decay of the tail of the noise characteristic function of ${\epsilon }_...

New energy vehicles have emerged as a prominent focus in the automotive industry. This study develops a comprehensive modeling specification for fuel cell systems in new energy vehicles and establishes a framework for fatigue life analysis in the frequency domain. First, a finite element model of the fuel cell system was created in accordance with...

The study of open-end fund is conducted in this paper in terms of the theory of Random process and the theory ofSequential Decision, which based on the benefit of investors and the cost of transaction (commission occurred in thetransaction). In addition the thesis introduces the method of factor of random discounting, by which investors can chooset...

Although artificial intelligence (AI) is often perceived as the field of computer science that experienced the greatest development, without the wide scope of mathematical fields and methods, AI would not be possible. Mathematical areas in AI include standard methods of analysis (continuous or discrete), set theory and various logic’s (propositiona...

In this paper, we examine a stochastic linear-quadratic control problem characterized by regime switching and Poisson jumps. All the coefficients in the problem are random processes adapted to the filtration generated by Brownian motion and the Poisson random measure for each given regime. The model incorporates two distinct types of controls: the...

The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance a particle moving along a straight-line trajectory travels through a specific material zone within the random...

Randomized control trials (RCTs) are regarded as the gold standard for intervention research. The randomization process is intended to establish comparability between groups, so that the study outcomes can be attributable to the intervention, rather than group differences. The purpose of this paper is to emphasize the inherent risks of conducting m...

This study aims to analyze the effect of financial ratios such as PER, PBV, and ROE on stock returns in companies that have just conducted an IPO in the 2022-2023 period. The research population consists of companies that conducted IPOs on the Indonesia Stock Exchange (IDX) in the period July 2022 to July 2023. The study population was taken using...

Low libido is a common and potentially distressing problem among midlife and older women. We recently reported results from a pilot randomized controlled trial of a mindfulness intervention for midlife and older cisgender women with low libido; the purpose of this qualitative investigation is to illustrate women’s experiences with being recruited f...

Let an $\bR^d$-valued random process $\xi$ be the solution of an equation of the kind $\xi(t)=\xi(0)+\int_0^tA(u)\xi(u)\rd\iota(u)+S(t),$ where $\xi(0)$ is a random variable measurable w.\,r.\,t. some $\sigma$-algebra $\cF(0)$, $S$ is a random process with $\cF(0)$-conditionally independent increments, $\iota$ is a continuous numeral random process...

Server resource allocation and traffic management is a large area of research and business concern in order to ensure proper functionality and maintenance procedures. As a result, good server reliability models that can incorporate workload and traffic stress are necessary. This paper generalizes previous dynamic server reliability models for parti...

Developing robust and secure image encryption methods for transmitting multiple images in batches over unprotected networks has become imperative. This necessity arises from the limitations of single-image encryption techniques in managing the escalating volume of extensive data. This paper introduces a novel three-layer multiple-image encryption (...

The significance and impact of Accrual-based Public Sector Accounting Standards (APSAS) in financial reporting has in recent times gained traction and has prompted debates which are aligned towards APSAS reporting. This implies that reforms in the government’s management systems are becoming critical towards examination of actions and steps taken t...

Let $k\geq 2$ and fix a $k$-uniform hypergraph $\mathcal{F}$. Consider the random process that, starting from a $k$-uniform hypergraph $\mathcal{H}$ on $n$ vertices, repeatedly deletes the edges of a copy of $\mathcal{F}$ chosen uniformly at random and terminates when no copies of $\mathcal{F}$ remain. Let $R(\mathcal{H},\mathcal{F})$ denote the nu...

Social insects, such as ants and bees, are known for their highly efficient and structured colonies. Division of labour, in which each member of the colony has a specific role, is considered to be one major driver of their ecological success. However, empirical evidence has accumulated showing that many workers, sometimes more than half, remain idl...

The importance of physical activity has grown in recent years, as seen by a rise in physical activity. High-intensity exercise can be harmful to bone health if not done correctly. This study investigates the effect of high-intensity exercise mixed with vitamin C and supplementation on bone cellular plasticity, with the goal of discovering new techn...

The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the n...

While there are many works on the applications of machine learning, not so many of them are trying to understand the theoretical justifications to explain their efficiency. In this work, overfitting control (or generalization property) in machine learning is explained using analogies from physics and biology. For stochastic gradient Langevin dynami...

The actomyosin cortex is an active material that provides animal cells with a strong but flexible exterior whose mechanics, including non-Gaussian fluctuations and occasional large displacements or cytoquakes, have defied explanation. We study the active fluctuations of the cortex using nanoscale tracking of arrays of flexible microposts adhered to...

This study aims to investigate the impact of momentum in tennis matches and develop methods for its prediction. Momentum is defined as the deviation of an athlete's scoring trend from a random process, representing a critical non-technical factor in competition. We employed a fuzzy comprehensive evaluation model to assess athlete performance during...

Introduction: While social science research has ignored the religious space and religion-based services for almost a century (Bielfeld and Cleveland, 2014: 443), the last three decades have seen the emergence of a new class of actors in the field of community development. They organize volunteers and provide services to citizens and even government...

An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli experiment is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementa...

Pantograph-based electrical current transmission systems are used in electric traction vehicles. The contact surface between the pantograph and the catenary wire experiences mechanical and thermal effects during the train’s movement. Typically, this contact surface on the pantograph is covered by a segmented carbon or copper rod, attached to an alu...

By replacing the Euler gamma function by the Barnes double gamma function in the definition of the Meijer G-function, we introduce a new family of special functions, which we call K-functions. This is a very general class of functions, which includes as special cases Meijer G-functions (thus also all hypergeometric functions \documentclass[12pt]{mi...

Nowadays, the functional integration of digital twin (DT) technology and artificial intelligence (AI) methodologies has enabled reliable predictions of many random processes, supporting efficient control and optimization procedures. In line with this trend, this paper explores the joint use of these technologies in an AI-empowered DT framework for...

Lévy processes with increasing sample paths or subordinators are widely used in Operations Research and Engineering. The main areas of applications of these stochastic processes are insurance mathematics, inventory control, maintenance and reliability theory. Special and well-known instances of these increasing processes are stationary Poisson and...

Background In an effort to combat burnout, a study investigates Mindfulness-Based Stress Reduction (MBSR) training for nurses. The goal is to reduce stress and improve job satisfaction, ultimately enhancing patient care. These findings may inspire the development of mindfulness-based support systems for healthcare professionals to promote overall w...

A probabilistic approach to predicting the properties of identified software vulnerabilities has been developed. The approach is based on representing the process of changing the values of the basic metrics of detected software vulnerabilities CVSS v3.0 as a random Markov process with discrete states and continuous time. When constructing systems o...

The modeling and analysis of sea clutter are of great significance in radar target detection studies in marine environments. Sea clutter typically exhibits non-Gaussian characteristics and spatiotemporal correlations, posing challenges for modeling, especially when generating simulation data of continuous correlated non-Gaussian random processes. T...

Understanding the evolution of pathogen resistance genes (nucleotide‐binding site‐leucine‐rich repeats, NLRs) within a species requires a comprehensive examination of factors that affect gene loss and gain. We present a new reference genome of Solanum chilense, which leads to an increased number and more accurate annotation of NLRs. Using a target...

Research background and purpose Soil microorganisms that are closely related to plants are important factors affecting plant health. Therefore, elucidating the abundant and rare bacterial species in soil associated with plant diseases is crucial for understanding ecological processes, maintaining the stability of microecological environments, and f...

Purpose This study aimed to construct a prediction model regarding risk factors and prognostic factors for distant metastasis of T1-T3 stage rectal cancer. For this purpose, a population-based retrospective cohort study was conducted. Methods Data on 7872 patients diagnosed with rectal cancer between 2004 and 2020 were obtained from the Surveillan...

p dir="ltr">Spatial patterns of species’ distributions are often biased with respect to environmental variables, including discrete habitats. Patterns alone, however, cannot uniquely identify the combinations of processes that produced them. Many alternative processes could give rise to positive and negative habitat associations, including a popula...

We consider the Cauchy problem for a first-order linear inhomogeneous system of partial differential equations with random processes as coefficients. Explicit formulas for the mathematical expectation of the solution are obtained. Examples of systems with Gaussian and uniformly distributed random coefficients are considered. An example of calculati...

One of the key objectives of statistics is to provide a model compatible with the data generated by an unknown random process. Often, it happens that the unknown process is intractable, and no prior data or information associated with the unknown process is available. Under such circumstances, well-known techniques like regression modelling techniq...

Problem: the city absorbs the natural and historical and cultural resources of the territory, due to which it is growing. The technical and economic growth of the city does not coincide with the preservation and prosperity of nature and culture. The quality of life with the growth of the city is deteriorating as a result of the predominance of the...

We use the theory of Bernstein functions, completely monotonic functions, and Levy processes to define a positive random process $\tau(t)$. For radar clutter one may think of $\tau(t)$ as the instantaneous power of the scattered radar signal that is described by a compound-Gaussian model. Thus the results herein give a mechanism for defining and si...

The study explores the use of Artificial Intelligence (AI) to assess the efficiency of random walkers in high-dimensional spaces, focusing on the application of reinforcement learning algorithms and machine learning techniques to optimize their behaviour. Random walks are widely studied in statistical mechanics, physics, biology, and finance, with...

Record high temperatures and heatwaves are increasingly being reported worldwide, sparking significant public concern. In a stable climate, occurrences of record‐breaking events (RBEs) should naturally decrease over time. Therefore, the increasing occurrence of record high temperatures signifies significant instability in the current climate change...

The interspecific associations among tree species in natural forest stands help to reveal mechanisms for maintaining species diversity and provide theoretical foundations for vegetation restoration and regeneration. This study focused on woody species within a 4-ha study plot established in an evergreen broadleaved forest in Con Dao National Park,...

Kluvánek extended the Whittaker-Kotel’nikov-Shannon theorem to the abstract harmonic analysis setting over a LCA group G. In this context, the classical condition for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl...

We consider a synchronous process of particles moving on the vertices of a graph G$$ G $$, introduced by Cooper et al. Initially, M$$ M $$ particles are placed on a vertex of G$$ G $$. At the beginning of each time step, for every vertex inhabited by at least two particles, each of these particles moves independently to a neighbor chosen uniformly...

Real-world data (RWD) are rapidly emerging sources of information for patients, clinicians and regulators. While randomized controlled trials (RCTs) reduce bias and confounding through the randomization process and provide the highest quality of evidence regarding drug efficacy, RCTs may be impractical or unfeasible for rare diseases or disease sub...

The varying wealth of an agent betting on the results of tossing a fair coin is a classic example of a random process with martingale property. In such a game, there is no strategy that yields a positive expectation of profit. However, the problem of whether one can rationally choose a strategy other than inaction remains meaningful and nontrivial:...

Exact solution of finite-dimensional linear stochastic differential system with control is derived. Its uniqueness up to stochastic modification is proved. In order to achieve this, detailed grounding of existence for stochastic integral over a process with orthogonal increments is provided. Particularly, density of step-functions set in the set of...

Background: Topical applications have long been regarded as precise methods for delivering drugs to soft tissues, such as the periodontal ligament, as well as hard structures, including the alveolar bone and cementum. Recently, the combination of hyaluronic acid (HA) and ozone therapy has gained popularity as a supportive treatment for chronic infl...

Context. We investigate a method to signal processing based on the Kolmogorov-Wiener filter weight function calculation for the prediction of a continuous stationary heavy-tail process in the MFSD (multifractal fractional sum-difference) model. Such a process may describe telecommunication traffic in some systems with data packet transfer, the cons...

An important specific feature of the functioning of machines and equipment in the technologies of post-harvest processing of grain and seeds is the probabilistic variability of external conditions that negatively affect the efficiency of their work. The drying process is also characterized by non-stationarity in its probabilistic and statistical ch...

The object of research is a complex system of three subsystems, which function independently of each other and are in a working or failed state. There is a need to analytically model and manage the Markov random process in the system, varying the intensity of their development-restoration and degradation-destruction flows. In the study, an analytic...

The definition of generalized random processes in Gel'fand sense allows to extend well-known stochastic models, such as the fractional Brownian motion, and study the related fractional pde's, as well as stochastic differential equations in distributional sense. By analogy with the construction (in the infinite-dimensional white-noise space) of the...

This paper explores the concept of the "Law of Averages" through the lens of artificial intelligence (AI) and statistical modelling. While the Law of Averages is an informal expectation of "averaging out" in random processes, the paper analyses its basis within the framework of probability and the Law of Large Numbers. Through mathematical modellin...

In order to investigate the effects of fertilizer application on functional traits, gut bacterial co-occurrence network, and assembly mechanism in collembolan. Entomobrya proxima Folsom—an abundant soil-dwelling species in North China—was selected as the study species. Dietary exposure was employed to simulate scenarios of fertilizer application. M...

This work devoted to construct a probabilistic model for solving boundary value problems for the semi-linear Helmholtz equation. Probabilistic representations of problem solving in the form of the mathematical expectation of some random variable are obtained. In accordance with probabilistic representation, branching processes are constructed and m...

This paper delves into the concepts of persistence and long-term memory within random processes, primarily through simulation. Often, the distinctions between persistence and memory in time series analysis are con-flated. The Hurst (H) exponent is commonly used to measure both; however, its application is typically restricted to fractional Brownian...

We investigate whether transformers can learn to track a random process when given observations of a related process and parameters of the dynamical system that relates them as context. More specifically, we consider a finite-dimensional state-space model described by the state transition matrix $F$, measurement matrices $h_1, \dots, h_N$, and the...

This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the antigen-driven immune repertoire synthesis. The processes of formati...

Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov semigroup. The unbounded nature of IGs complicates traditional methods such as vector-valued regression and Hilber...

In the Hall-Héroult process for extracting aluminum, the generation of anodic bubbles is an inherent phenomenon in the electrolysis process. In this study, the bubble dynamics beneath the anode during aluminum electrolysis were studied using the bottom-observation transparent electrolysis cell. The bubble formation, growth and release processes und...

Background and Aims Nurses are highly susceptible to developing low back pain (LBP), which is considered a common occupational hazard. The present study investigated the efficacy of flexible learning methods on the nurses' awareness, perspectives, and practice regarding the prevention of LBP. Methods In pre‐test posttest quasi‐experimental study c...

Meandering designates the main manifestation of unsteady vortex dynamics observed in experiments. This study has the twofold objective to (i) develop a theoretical model describing vortex meandering and (ii) conduct a quantitative and objective evaluation of the model against experimental data. Based on an analogy with Brownian motion, we derive th...

This paper presents a sensitivity analysis to assess the impact of random rail unevenness profiles on the generation of ground-borne vibrations. The random profiles are generated from a power spectral density function, assuming that the uneven rail surface is governed by a stationary Gaussian random process in space. Different proposals are employe...

Background The quality of reporting in randomized controlled trials (RCTs) is crucial for accurate interpretation and synthesis of evidence. The Consolidated Standards of Reporting Trials (CONSORT) guidelines provide a standardized framework for reporting RCT abstracts. This study aimed to evaluate the adherence of RCT abstracts published in three...

Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random d-regular graph mixes fast beyond the tree uniqueness threshold when d is large enough (and conjecture that it...

Background False confessions are often the product of an interrogation process, and the method by which an interrogation is conducted likely affects both the rate of truthful confessions and false confessio