Subdiffusive search with home returns via stochastic resetting: A subordination scheme approach

Stochastic resetting with home returns is widely found in various manifestations in life and nature. Using the solution to the home return problem in terms of the solution to the corresponding problem without home returns [Pal et al. Phys. Rev. Research 2, 043174 (2020)], we develop a theoretical framework for search with home returns in the case of subdiffusion. This makes a realistic description of restart by accounting for random walks with random stops. The model considers stochastic processes, arising from Brownian motion subordinated by an inverse infinitely divisible process (subordinator).

Using the Kriging Response Surface Method for the Estimation of Failure Values of Carbon-Fibre-Epoxy Subsea Composite Flowlines under the Influence of Stochastic Processes

This paper investigates the use of the Kriging response surface method to estimate failure values in carbon-fibre-epoxy composite flow-lines under the influence of stochastic processes. A case study of a 125 mm flow-line was investigated. The maximum stress, Tsai-Wu and Hashin failure criteria was used to assess the burst design under combined loading with axial forces, torsion and bending moments. An extensive set of measured values was generated using Monte Carlo simulation and used as the base case population to which the results from the response surfaces was compared. The response surfaces were evaluated in detail in their ability to reproduce the statistical moments, probability and cumulative distributions and failure values at low probabilities of failure. In addition, the optimisation of the response surface calculation was investigated in terms of reducing the number of input parameters and size of the response surface. Finally, a decision chart that can be used to build a response surface to calculate failures in a carbon fibre-epoxy-composite (CFEC) flow-line was proposed based on the findings obtained. The results show that the response surface method is suitable and can calculate failure values close to that calculated using a large set of measured values. The results from this paper provide an analytical framework for identifying the principal design parameters, response surface generation, and failure prediction for CFEC flow-lines.

Dynamic and Assembly of Benthic Bacterial Community in an Industrial-Scale In-Pond Raceway Recirculating Culture System

To reduce water utilization, limit environmental pollution, and guarantee aquatic production and quality, the in-pond raceway recirculating culture system (IPRS) has been developed and is widely used. The effectiveness and sustainability of IPRSs rely on a good understanding of the ecological processes related to bacterial communities in the purification area. In this study, we investigated the dynamics and assembly mechanisms of benthic bacterial communities in the purification area of an industrial-scale IRPS. We found significant temporal and spatial variations in the sediment characteristics and benthic bacterial communities of the IPRS, although correlation analyses revealed a very limited relationship between them. Among the different culture stages, we identified numerous benthic bacteria with different abundances. Abundances of the phyla Bacteroidota and Desulfobacterota decreased whereas those of Myxococcota and Gemmatimonadota increased as the culture cycle progressed. Co-occurrence networks revealed that the bacterial community was less complex but more stable in the IPRS at the final stage compared with the initial stage. The neutral community model (NCM) showed that stochastic processes were the dominant ecological processes shaping the assembly of the benthic bacterial community. The null model suggested that homogenizing dispersal was more powerful than dispersal limitation and drift in regulating the assembly of the community. These findings indicate that the benthic microbial communities in purification areas of the IPRS may not be affected by the deposited wastes, and a more stable benthic microbial communities were formed and mainly driven by stochastic processes. However, the benthic microbial communities in the purification area at the end of the culturing stage was characterized by potentially inhibited organic matter degradation and carbon and sulfur cycling abilities, which was not corresponding to the purification area’s function. From this point on, the IPRS, especially the purification area was needed to be further optimized and improved.

Worldwide clustering and infection cycles as universal features of multiscale stochastic processes in the SARS-CoV-2 pandemic

Predicting the evolution of the current epidemic depends significantly on understanding the nature of the underlying stochastic processes. To unravel the global features of these processes, we analyse the world data of SARS-CoV-2 infection events, scrutinising two eight-month periods associated with the epidemic's outbreak and initial immunisation phase. Based on the correlation-network mapping, K-means clustering, and multifractal time series analysis, our results reveal universal patterns, suggesting potential predominant drivers of the pandemic. More precisely, the Laplacian eigenvectors localisation has revealed robust communities of different countries and regions that then cluster according to similar shapes of infection fluctuations. Apart from quantitative measures, the immunisation phase differs significantly from the epidemic outbreak by the countries and regions constituting each cluster. While the similarity grouping possesses some regional components, the appearance of large clusters spanning different geographic locations is persevering. Furthermore, cyclic trends are characteristic of the identified clusters, dominating large temporal fluctuations of infection evolution, which are prominent in the immunisation phase. Meanwhile, persistent fluctuations around the local trend occur in intervals smaller than 14 days. These results provide a basis for further research into the interplay between biological and social factors as the primary cause of infection cycles and a better understanding of the impact of socio-economical and environmental factors at different phases of the pandemic.

Worldwide clustering and infection cycles as universal features of multiscale stochastic processes in the SARS-CoV-2 pandemic

Predicting the evolution of the current epidemic depends significantly on understanding the nature of the underlying stochastic processes. To unravel the global features of these processes, we analyse the world data of SARS-CoV-2 infection events, scrutinising two eight-month periods associated with the epidemic’s outbreak and initial immunisation phase. Based on the correlation-network mapping, K-means clustering, and multifractal time series analysis, our results reveal universal patterns, suggesting potential predominant drivers of the pandemic. More precisely, the Laplacian eigenvectors localisation has revealed robust communities of different countries and regions that then cluster according to similar shapes of infection fluctuations. Apart from quantitative measures, the immunisation phase differs significantly from the epidemic outbreak by the countries and regions constituting each cluster. While the similarity grouping possesses some regional components, the appearance of large clusters spanning different geographic locations is persevering. Furthermore, cyclic trends are characteristic of the identified clusters, dominating large temporal fluctuations of infection evolution, which are prominent in the immunisation phase. Meanwhile, persistent fluctuations around the local trend occur in intervals smaller than 14 days. These results provide a basis for further research into the interplay between biological and social factors as the primary cause of infection cycles and a better understanding of the impact of socio-economical and environmental factors at different phases of the pandemic.

A study on stochastic modelling of the repairable system

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible.When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

Estimating the true arrival, balking, and reneging processes from censored transactional data: a simulation-based approach

The transactional data typically collected/available on queueing systems are often subject to censoring as unsuccessful arrivals due to balking and/or unserved entities due to reneging are not recorded. In fact, in many situations, the true arrival, balking, and reneging events are unobservable, making it virtually impossible to collect data on these stochastic processes—information that is crucial for capacity planning and process improvement decisions. The objective of this paper is to estimate the true (latent) external arrival, balking, and reneging processes in queueing systems from such censored transactional data. The estimation problem is formulated as an optimization model and an iterative simulation-based inference approach is proposed to find appropriate input models for these stochastic processes. The proposed method is applicable in any complex queueing situation as long as it can be simulated. The problem is investigated under both known and unknown reneging distribution. Through extensive simulation experiments, general guidelines are provided for specifying the parameters of the proposed approach, namely, sample size and number of replications. The proposed approach is also validated through a real-world application in a call center, where it successfully estimates the underlying arrival, balking, and reneging distributions. Finally, to enable reproducibility and technology transfer, a working example, including all codes and sample data, are made available in an open online data repository associated with this paper.