The 𝑀-Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey by Francesco Mainardi, Antonio Mura, Gianni Pagnini

“…In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as 𝑀-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we generally refer to as time-fractional diffusion processes. …”
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The role of multiple modeling perspectives in students' learning of exponential growth by Carlos Castillo-Garsow

“…The exponential is among the most important family functions in mathematics; the foundation for the solution of linear differential equations, linear difference equations, and stochastic processes. However there is little research and superficial agreement on how the concepts of exponential growth are learned and/or should be taught initially. …”
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Lyapunov Stability of the Generalized Stochastic Pantograph Equation by Ramazan Kadiev, Arcady Ponosov

“…To prove stability, we check that the solutions of the equation belong to a suitable space of stochastic processes, instead of searching for an appropriate Lyapunov functional. …”
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Successive spike times predicted by a stochastic neuronal model with a variable input signal by Giuseppe D'Onofrio, Enrica Pirozzi

“…Two different stochastic processes are used to model the evolution of the membrane voltage of a neuron exposed to a time-varying input signal. …”
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Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion by Yuling Wang, Jing Wang

“…In conclusion, since mfBm is a well-developed mathematical model of strongly correlated stochastic processes, this model will be an efficient model for pricing carbon financial derivative.…”
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Long Memory of Pathfinding Aesthetics by Ron Coleman

“…., long memory) in stochastic processes and provides a novel well-defined mathematical classification for pathfinding. …”
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Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos by Yao Wang, Shengkui Zeng, Jianbin Guo

“…According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. …”
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On the mathematical modelling of tumor-induced angiogenesis by Luis L. Bonilla, Vincenzo Capasso, Mariano Alvaro, Manuel Carretero, Filippo Terragni

“…An angiogenic system is taken as an example of extremely complex ones in the field of Life Sciences, from both analytical and computational points of view, due to the strong coupling between the kinetic parameters of the relevant branching -growth -anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. …”
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Heavy metal contamination and eutrophication effects on bacterial communities in the Han River basin by Fei Xiong, Cejia Yao, Dongdong Zhai, Hongyan Liu, Wang Dong, Yuanyuan Chen

“…Analysis of β-nearest taxon index (βNTI) indicated that stochastic processes primarily shaped community assembly. …”
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Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models by Luca Faes, Alberto Porta, Michal Javorka, Giandomenico Nollo

“…To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state-space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the complexity of the process. …”
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Dynamic Prediction for Accuracy Maintaining Reliability of Superprecision Rolling Bearing in Service by Liang Ye, Xintao Xia, Zhen Chang

“…A dynamic prediction method for accuracy maintaining reliability (AMR) of superprecision rolling bearings (SPRBs) in service is proposed by effectively fusing chaos theory and grey system theory and applying stochastic processes. In this paper, the time series of a vibration signal is used to characterize the state information for SPRB, and four runtime data points can be predicted in the future, which depends on four chaotic forecasting models to preprocess the time series. …”
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Estimation of High Structural Reliability Involving Nonlinear Dependencies Based on Linear Correlations by Liulin Kong, Heng Li, Bo Zhang, Hanbin Luo

“…A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. …”
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Microscopic origin of the spatial and temporal precision in biological systems by Anupam Mondal, Anatoly B. Kolomeisky

“…Although the underlying molecular mechanisms of surprisingly high precision in biology remain not well understood, a novel theoretical picture that relies on the coupling of relevant stochastic processes has recently been proposed and applied to explain different phenomena. …”
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Minimizing Delay and Power Consumption at the Edge by Erol Gelenbe

“…These results are obtained with a mathematical model of a multiple-server edge system that is managed by a task distribution platform, whose equations are derived and solved using methods from stochastic processes. This approach has low computational cost and provides simple linear complexity formulas to compute the fraction of tasks that should be assigned to the different servers to achieve minimum latency and minimum energy consumption.…”
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Differences in Biogeographic Patterns and Mechanisms of Assembly in Estuarine Bacterial and Protist Communities by Weiyue Zhang, Yunlei Zhang, Zhizhuo Shao, Yi Sun, Hongjun Li

“…In addition, the two community assemblages were shown to be dominated by deterministic and stochastic processes, respectively. Furthermore, our results emphasized the influence of the local species pool on microbial communities and the fact that, at larger scales, geographic factors played a more significant role than environmental factors in driving microbial community variation. …”
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Crab bioturbation alters the community assemblies of abundant and rare bacteria on an intertidal wetland in the Yellow River estuary by Zhikang Wang, Yongqi Wang, Jisong Yang, Jisong Yang, Junfen Yan, Kaixin Yang, Zhonghua Ren, Wei Wang, Yang He, Min Li, Junfei Zhan, Bo Guan, Xuehong Wang, Yunzhao Li, Di Zhou, Buli Cui, Junbao Yu

“…Furthermore, we discovered that the assembly processes of abundant subcommunities were primarily influenced by stochastic processes, while rare subcommunity assemblies were collectively shaped by both stochastic and deterministic processes. …”
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An examination of changes in autumn Eurasian snow cover and its relationship with the winter Arctic Oscillation using 20th Century Reanalysis version 3 by G. J. Marshall

“…Novel aspects are (i) analysis back to 1836, (ii) adjusting the reanalysis SC through comparison with observations, and (iii) analysing the statistical significance of the frequency of periods of significant SC–AO relationships to determine whether these connections can be distinguished from stochastic processes. Across the full span of 20CRv3, there is a small increase in mean September Eurasian SC. …”
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The landscape of nucleotide diversity in Drosophila melanogaster is shaped by mutation rate variation by Barroso, Gustavo V, Dutheil, Julien Y

“…Attempts to answer this question have sparked debate about the roles of neutral stochastic processes and natural selection in molecular evolution. …”
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Host selection is not a universal driver of phyllosphere community assembly among ecologically similar native New Zealand plant species by Anya S. Noble, Jaber Abbaszadeh, Charles K. Lee

“…In contrast, the phyllosphere community compositions of neighbouring, ecologically similar native plants were highly variable, suggesting that stochastic processes, such as dispersal, had a stronger influence on the phyllosphere microbiomes of those non-mānuka plants compared to the phyllosphere microbiome of mānuka. …”
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Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense by Md. Nur Alam

“…The results offer significant insights into understanding and modeling intricate behaviors across various scientific and engineering fields, showcasing the versatility and applicability of the MG'/GE scheme for addressing complex nonlinear evolution equations (NLEEs) influenced by stochastic processes. The dynamic properties and features of these solutions are extensively examined through 3-dimensional, 2-dimensional and contour plots. …”
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