Stochastic Processes - Science topic

Après un master en Fonctionnement des écosystèmes à l’université de Montpellier (2008-2010), j’ai fait ma thèse à l’université de Lorraine ( soutenue en 2014) entre le laboratoire agronomie et environnement et l’Agroscope ( Zurich, Suisse). Par la suite j’ai travaillé au sein de l’institut Norvégien de Bioéconomie( NIBIO) avant d’être recruté au CI...

Neutron fluctuations, also coined zero power noise, is concerned with the study of the random fluctuations observed in the neutron population evolving in a fissile medium, due to the fundamentally intrinsic stochastic nature of the neutrons' interactions in matter. The canonical theoretical modeling of such fluctuations rely on the establishment of...

Life, in all its forms, is a complex interplay of adaptation, evolution, and resilience. From the intricate dynamics of Earth's ecosystems to the tantalizing possibility of life beyond our planet, understanding the mathematical foundations of life's complexity is one of the most profound challenges of our time. This book bridges the gap between app...

This study presents analyses of the optical variability of the 1ES 1215+303 on diverse timescales using multiband observations, including observations in the optical BVRI bands carried out with the 0.6 and 1.0 m telescopes located at the Tübitak National Observatory (TUG) from 2022 to 2024 and Zwicky Transient Facility (ZTF) gri data from 2018 to 2...

The boundary stabilization of a class of reaction-diffusion systems perturbed by second-order processes is investigated in this work. It extends the results from random ordinary differential equations to random reaction-diffusion systems (RRDSs). First, the stability analysis of RRDSs with boundary function is presented. Using the Lyapunov method a...

Stochastic processes are foundational tools in many scientific disciplines, including biology, operational research, social sciences, and stochastic finance, among others [...]

A closure model is presented for large-eddy simulation (LES) based on the three-dimensional variational data assimilation algorithm. The approach aims at reconstructing high-fidelity kinetic energy spectra in coarse numerical simulations by including feedback control to represent unresolved dynamics interactions in the flow as stochastic processes....

A machine learning tasks from observations must encounter and process uncertainty and novelty, especially when it is expected to maintain performance when observing new information and to choose the best fitting hypothesis to the currently observed information. In this context, some key questions arise: what is information, how much information did...

This work considers a stochastic form of an extended version of the Kairat-II equation by adding Browning motion into the deterministic equation. Two analytical approaches are utilized to derive analytical solutions of the modified equation. The first method is the modified Tanh technique linked with the Riccati equation, which is implemented to ex...

Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the “state of the art” in many applied fields. However, while the asymptotic theory supporting the use of max-stable pr...

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming tha...

In this study, the Enhanced RAO-based Translation Process (ERTP) method, which is an enhanced version of the RAO-based Translation Process (RTP) method proposed in the previous study, is newly proposed. The RTP method approximates the Extreme Value Distribution (EVD) in arbitrary irregular waves from the nonlinear response in regular waves based on...

We consider when there is absolute or unconditional convergence of series of various types of stochastic processes. These processes include differences of averages in ergodic theory and harmonic analysis, like the classical Cesaro average in ergodic theory and Lebesgue derivatives in harmonic analysis.

Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which is a quantum stochastic process that interpolates between quantum and classical walk dynamics. Surprisingly,...

Scientific theory largely neglects linkage between organic phosphorus (Po) mineralization rate and dispersal potential of alkaline phosphatase‐encoding bacteria (PEB) containing the phoD gene. Different densities of substrates (i.e. compacted soils, culture media, and soil aggregates) were prepared and molecular tools were used to unveil relationsh...

Stochastic processes are crucial in financial mathematics, providing a framework to model the inherent uncertainties of financial markets. This paper explores stochastic process application across various financial domains, such as option pricing, risk management, and financial engineering. Through case studies, literature review, and case analysis...

In the context of data security, this work aims to present a novel solution that, rather than addressing the topic of endpoint security—which has already garnered significant attention within the international scientific community—offers a different perspective on the subject. In other words, the focus is not on device security but rather on the pr...

The main focus of this article is the study of ergodicity of Interacting Particle Systems (IPS). We present a simple lemma showing that scaling time is equivalent to taking the convex combination of the transition matrix of the IPS with the identity. As a consequence, the ergodic properties of IPS are invariant under this transformation. Surprising...

Many techniques originally developed in the context of deterministic control theory have been recently applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask what is the best way to change in time its controllable parameters in order to maximize, on average, a certain re...

Even in a simple stochastic process, the study of the full distribution of time integrated observables can be a difficult task. This is the case of a much-studied process such as the Ornstein-Uhlenbeck process where, recently, anomalous dynamical scaling of large deviations of time integrated functionals has been highlighted. Using the mapping of a...

This study develops a comprehensive framework to model the dynamics of happiness as an interconnected system of stochastic differential equations (SDEs). Happiness is conceptualized as a multifaceted, time-dependent phenomenon influenced by key variables, including income, mental health, physical health, stress, coping strategies, relationships, vo...

This manuscript proposes one possible solution for intrusion detection (IDS) based on stochastic modeling of the threshold value, which is defined as a random variable (RV) obtained using the so-called General Split-BREAK (GSB) stochastic process. Applying such a model to previously recorded traffic values and using this type of stochastic modeling...

The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the values of a given portion of the data using the values from the remaining parts? Unlike the classical task of...

Soil biodiversity underpins multiple ecosystem functions and services essential for human well-being. Understanding the determinants of biodiversity-ecosystem function relationships (BEFr) is critical for the conservation and management of soil ecosystems. Community assembly processes determine community diversity and structure. However, there rema...

Detecting directional couplings from time series is crucial in understanding complex dynamical systems. Various approaches based on reconstructed state-spaces have been developed for this purpose, including a cross-distance vector measure, which we introduced in our recent work. Here, we devise two new cross-vector measures that utilize ranks and t...

Accurately predicting the remaining useful life (RUL) of critical mechanical components is a central challenge in reliability engineering. Stochastic processes, which are capable of modeling uncertainties, are widely used in RUL prediction. However, conventional stochastic process models face two major limitations: (1) the reliance on strict assump...

In this study, we present a monitoring scheme with a group of agents, that is considered a practical challenge in operations management. In particular, mobile multi-agents, such as drones, can facilitate the implementation of monitoring tasks in more efficient and flexible manners. However, comparing to a monitoring system with stationary agents, a...

Life has existed on Earth for most of the planet’s history, yet major gaps and unresolved questions remain about how it first arose and persisted. Early Earth posed numerous challenges for life, including harsh and fluctuating environments. Today, many organisms cope with such conditions by entering a reversible state of reduced metabolic activity,...

Physical unclonable functions (PUFs) are considered the most promising approach to address the global issue of counterfeiting. Current PUF devices are often based on a single stochastic process, which can be broken, especially since their practical encoding capacities can be significantly lower than the theoretical value. Here we present stochastic...

This paper presents a predictive methodology based on an uncertainty-corrected fractional generalized Pareto motion (fGPM) to address challenges in self-capacity regeneration and stochastic fluctuations in lithium-ion batteries. The approach uses probabilistic adjustments via Wasserstein distance and transitional Markov chain Monte Carlo methods to...

The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as li...

Alpine areas are host to diverse plant communities that support ecosystems through structural and floral resources and persist through specialized adaptations to harsh high-elevation conditions. An ongoing question in these plant communities is whether composition is shaped by stochastic processes (e.g., dispersal limitations) or by deterministic p...

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable fu...

This paper studies two related stochastic processes driven by Brownian motion: the Cox–Ingersoll–Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates, distance between the processes in integral norms, and parameter estimation. The squared Bessel process is shown to...

We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued stochastic processes (MVSPs), which describe the evolution of the singular, stochastic concentration fields of each che...

Background The regional species pool and local community assembly processes shape the biogeographic patterns of soil bacterial community diversity. However, how community assembly mechanisms regulate biogeographic patterns in rare and abundant bacterial communities remains unclear. Methods Soil samples of 16 grassland habitats across the Inner Mon...

Continuous cropping obstacles are significant factors that limit the yield and quality of tobacco. Thus, the selection and breeding of varieties is a crucial strategy for mitigating these challenges. However, the effects and mechanisms by which different tobacco varieties influence the structural composition of soil microbial remain unclear. To add...

As artificial intelligence advances rapidly, particularly with the advent of GANs and diffusion models, the accuracy of Image Inpainting Localization (IIL) has become increasingly challenging. Current IIL methods face two main challenges: a tendency towards overconfidence, leading to incorrect predictions; and difficulty in detecting subtle tamperi...

A class of stochastic parabolic equations with singular potentials is analysed in the chaos expansion setting where the Wick product is used to give sense to the product of generalized stochastic processes. For the analysis of such equations we combine the chaos expansion method from the white noise analysis and the concept of very weak solutions f...

This article explores the intersection of Artificial General Intelligence (AGI) development, ethics, and statistical physics, highlighting the challenges of bias, uncertainty, and fairness in AI systems. It discusses how AGI must be "tuned" like the cochlea of the human ear, aligning with human values and societal ethics to avoid reinforcing harmfu...

The valuation of financial derivatives often assumes risk neutrality with respect to the risk-neutral martingale measure, which prevents arbitrage opportunities. However, casual traders may still incur substantial losses when trading at this risk-neutral price, especially when the price has to be paid now and the payoff is only realized in the futu...

Continuous-time Markov processes are governed by the Chapman-Kolmogorov differential equation. We show that replacing the standard time derivative of the governing equation with a Caputo fractional derivative of order 0 < α < 1 , leads to a fractional differential equation whose solution can describe the state probabilities of a class of non-Markov...

We propose several new models in finance known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. We derive solutions of option Greeks and compare with those in the Black-Scholes...

Verifying the provenance of content is crucial to the function of many organizations, e.g., educational institutions, social media platforms, firms, etc. This problem is becoming increasingly difficult as text generated by Large Language Models (LLMs) becomes almost indistinguishable from human-generated content. In addition, many institutions util...

Leaf endospheres harbor diverse bacterial communities, comprising generalists and specialists, that profoundly affect ecosystem functions. However, the ecological dynamics of generalist and specialist leaf-endophytic bacteria and their responses to climate change remain poorly understood. We investigated the diversity and environmental responses of...

The human immune system can recognize, attack, and eliminate cancer cells, but cancers can escape this immune surveillance. Variants of ecological predator–prey models can capture the dynamics of such cancer control mechanisms by adaptive immune system cells. These dynamical systems describe, e.g., tumor cell-effector T cell conjugation, immune cel...

Jetted Active Galactic Nuclei (AGN) exhibit variability across a wide range of time scales. Traditionally, this variability can often be modeled well as a stochastic process. However, in certain cases, jetted AGN variability displays regular patterns, enabling us to conduct investigations aimed at understanding its origins. Additionally, a novel ty...

While stochastic resetting (or total resetting) is less young and more established concept in stochastic processes, partial stochastic resetting (PSR) is a relatively new field. PSR means that, at random moments in time, a stochastic process gets multiplied by a factor between 0 and 1, thus approaching but not reaching the resetting position. In th...

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...

In this paper Artificial Neural Style Transfer, Markov chain modelling and Kolmogorov's equation are used to detect the spread of infection in human lungs. The study aims to analyze the likelihood of state transitions in a discrete space, determine joint probability distributions of different sets of coordinates on a stochastic process, forecast th...

The development of models of the physicochemical and biochemical behavior of nanomaterials is useful for improving the evaluation and management of this material. Quasi-SMILES technology makes it possible to quite successfully cope with this kind of modeling task, accounting for various experimental conditions, where the use of other approaches is...

This article proposes a new mathematical model that accurately predicts statistical margin characteristics of bit-line sense amplifiers (BLSAs) with offset calibration (OC) and pre-sensing (PS), while providing techniques to improve sensing margins. In particular, threshold voltage mismatch caused by reduced transistor sizes introduces sensing offs...

Travel Time estimation is largely caused by the stochastic process of arrivals and departures of vehicles and its reliability measurements considering important issues for improving operational efficiency and safety for traffic road networks. The exploration of travel time variability and spatio-temporal analysis of urban streets using the Global P...

Processos de Renovação Generalizada (PRG’s) vêm sendo utilizados em Análise de Sobrevivência/Confiabilidade com bastante sucesso, particularmente para modelar tempos entre eventos indesejados de falhas em equipamentos eletromecânicos, falhas essas que acarretam enormes prejuízos para empresas. Assim, PRG’s são importante ferramenta na Engenharia de...

This paper explores the design of proportional-integral observer (PIO) for a type of time-varying stochastic nonlinear complex networks in which the network dynamics are corrupted by the unknown but bounded noises. With the aim to efficiently regulate the data exchange between network nodes, a transmitting scheme called FlexRay protocol (FRP) is ad...

This paper proposes and experimentally validates a grid-aware scheduling and control framework for Electric Vehicle Charging Stations (EVCSs) for dispatching the operation of active distribution networks (ADNs). The framework consists of two stages. In the first stage (day-ahead), we determine an optimal 24-hour power schedule at the grid connectio...

Autonomous vehicles need to continuously analyse the driving context and establish a comprehensive understanding of the dynamic traffic environment. To ensure the safety and efficiency of their operations, it would be beneficial to have accurate predictions of surrounding vehicles’ future trajectories. AVs can adjust their motions proactively to im...

Sinusoidal modeling (SM) has been studied for speech modeling, which aims at representing and flexibly resynthesizing the speech waveform by the frequency and complex amplitude of several components. However, SM methods model the speech frame by frame, which inevitably leads to a loss of information between individual frames. In addition, SM method...

Since the fractional $ G $-Brownian motion (fGBm) generalizes the concepts of the standard Brownian motion, fractional Brownian motion, and $ G $-Brownian motion, while it can exhibit long-range dependence or antipersistence and feature the volatility uncertainty simultaneously, it can be a better alternative stochastic process in the financial app...

In this paper, the unified approach is used in acquiring some new results to the coupled Maccari system (MS) in Itô sense with multiplicative noise. The MS is a nonlinear model used in hydrodynamics, plasma physics, and nonlinear optics to represent isolated waves in a restricted region. We provide new results with complicated structures to this mo...

Despite a lot of efforts devoted to construct efficient microbiomes, there are still major obstacles to moving from the lab to industrial applications due to the inapplicability of existing technologies or limited understanding of microbiome variation regularity. Here we show a domestication strategy to cultivate an effciient and resilient function...

We present an update on our studies on the restoration of the highly endangered Koelerion glaucae vegetation in the Upper Rhine valley (Hesse, Germany), a habitat type protected by the European Union Fauna-Flora-Habitat directive. Our three-step restoration approach (deep-sand deposition, inoculation with plant material, non-intensive donkey grazin...

Goal. Develop the methodology for assessing production risks at workplaces of mechanical engineering workers. Methodology. The methodology has been developed for assessing industrial risks during the operation of equipment, that can lead to dangerous situation with employee injury. Such a situation is characteristic of the complex argotic system, t...

Background and aims Plants influence soil microbial communities through aboveground litter and root inputs. However, studies on the effects of various plant carbon inputs on soil microbial communities in grassland ecosystems are limited. Methods We characterized bacteria, ammonia-oxidizing bacteria and ammonia-oxidizing archaea using 16S rRNA ampl...

Understanding the dynamics of atoms in glasses is crucial for unraveling the origin of relaxation and the glass transition as well as predicting transport properties. However, identifying the structural features controlling atom dynamics in glasses remains challenging. Recently, machine learning models based on graph neural networks (GNNs) have suc...

Background: The cerebral microvasculature forms a dense network of interconnected blood vessels where flow is modulated partly by astrocytes. Increased neuronal activity stimulates astrocytes to release vasoactive substances at the endfeet, altering the diameters of connected vessels. Methods: Our study simulated the coupling between blood flow var...

A charged colloidal (dust) particle immersed in a plasma with an ion flow creates a disturbed region behind it, known as a wake. The paper considers a system of two charged and strongly coupled microparticles aligned along the ion flow in a weakly ionized plasma (e.g., in the plasma sheath of a ground-based RF discharge) and confined vertically by...

In this paper the problem of the proper construction of the average rate of return (ARR) of pension (or investment) funds is considered, using a chain price index approach. Some known formulas of the ARR can be expressed by chain indices. The paper proposes and discusses a continuous-time formula. The prices and the number of the participating unit...