Renewal Process Research Articles

Generalised Ornstein–Uhlenbeck process: memory effects and resetting

Abstract In this work we consider a generalised Ornstein-Uhlenbeck process for a stochastically driven particle in an harmonic potential which is governed by a Fokker-Planck equation in the presence of a memory kernel. We analyse the probability density function, the mean and the mean squared displacement by employing the subordination approach connecting the operational time of the process with the (generalised) laboratory time. We provide analytical results for the mean and the mean squared displacement in case of a power-law memory kernel which corresponds to the fractional Ornstein-Uhlenbeck process. The generalised Ornstein-Uhlenbeck process in the presence of Poissonian resetting is also investigated by using the renewal equation approach, and the nonequilibrium stationary state approached in the long time limit is obtained. The analytical results are confirmed by numerical simulations based on the coupled Langevin equations.

Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models

Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided for the SVIS (Susceptible-Vaccinated-Infected-Susceptible) disease epidemic model to investigate the impacts of hazard rate functions (HRFs) on disease control. The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. Key statistical properties and the basic reproduction number () are derived, and conditions for the system’s asymptotic autonomy are established for specific lifetime distributions. Four HRF behaviors—monotonic, bathtub, reverse bathtub, and constant—are analyzed to determine conditions for disease eradication and the asymptotic population under these scenarios. Sensitivity analysis examines how HRF behaviors shape system trajectories. Numerical simulations illustrate the influence of diverse lifetime models on vaccine efficacy and immunity, offering insights for effective disease management.

Research on the Urban Village Renewal Mechanism Based on Rent Gap Theory: A Case Study in Xi’an, China

Urban renewal is a critical approach to address issues such as the scarcity of urban spatial resources and infrastructure aging in the later stages of urbanization. Urban village renewal is one of the typical practices of urban renewal. Based on China’s unique dual urban–rural land system and urbanization process, this study localizes the rent gap theory. It applies the modified rent gap theory to conduct a case study on Wangjiapeng Village in Xi’an using the process-tracing method. It explores the internal mechanisms of urban village renewal and the key factors influencing the progress of renewal projects. The findings reveal that the size of the rent gap directly determines the attractiveness and timing of urban village renewal. However, issues such as interest conflicts, administrative redundancy, and government supervision during the renewal process significantly increase transaction costs, raising the rent gap threshold and thereby affecting the progress and outcomes of the renewal. This paper proposes a rent gap theory that is more suited to China’s context and further expands its applicability through case study research. The practical experience of Wangjiapeng Village provides important policy implications for other major cities in China and cities currently in the late stages of urbanization.

Random walks with stochastic resetting in complex networks: A discrete-time approach.

We consider a discrete-time Markovian random walk with resets on a connected undirected network. The resets, in which the walker is relocated to randomly chosen nodes, are governed by an independent discrete-time renewal process. Some nodes of the network are target nodes, and we focus on the statistics of first hitting of these nodes. In the non-Markov case of the renewal process, we consider both light- and fat-tailed inter-reset distributions. We derive the propagator matrix in terms of discrete backward recurrence time probability density functions, and in the light-tailed case, we show the existence of a non-equilibrium steady state. In order to tackle the non-Markov scenario, we derive a defective propagator matrix, which describes an auxiliary walk characterized by killing the walker as soon as it hits target nodes. This propagator provides the information on the mean first passage statistics to the target nodes. We establish sufficient conditions for ergodicity of the walk under resetting. Furthermore, we discuss a generic resetting mechanism for which the walk is non-ergodic. Finally, we analyze inter-reset time distributions with infinite mean where we focus on the Sibuya case. We apply these results to study the mean first passage times for Markovian and non-Markovian (Sibuya) renewal resetting protocols in realizations of Watts-Strogatz and Barabási-Albert random graphs. We show nontrivial behavior of the dependence of the mean first passage time on the proportions of the relocation nodes, target nodes, and of the resetting rates. It turns out that, in the large-world case of the Watts-Strogatz graph, the efficiency of a random searcher particularly benefits from the presence of resets.

The influence of perceived landscape value on tourists' behavioral intentions in historical and cultural blocks.

Historic cultural blocks are areas where a city's material cultural heritage and humanistic characteristics converge, showcasing the city's unique features and preserving rich and complete urban memories. Research on historic blocks primarily involves strategies related to protection, renewal, planning, and enhancement. However, there is a paucity of studies that explore the relationship between landscape value perception and tourist behavioral intentions from the perspective of recreation participants during the development and renewal of historic cultural blocks. This study uses the Zhongshan Road and Sifang Road historic cultural blocks in Qingdao as a case example. By collecting multi-source data such as online texts, tourist questionnaires, and interviews, and employing qualitative analysis and structural equation modeling as quantitative analysis methods, the study reveals the structural relationship between landscape value perception, place identity, and tourist behavioral intentions: (1) Landscape value perception has a significant positive effect on tourist behavioral intentions; (2) Landscape value perception has a significant positive effect on place identity; (3) Place identity, as a mediating variable, does not mediate the relationship between ecological landscape value perception and skill education value perception, but partially mediates the relationship between historical cultural value perception and recreational value perception. Based on the research results, feedback on the development effectiveness of historic cultural blocks from the perspective of recreation participants can be visually obtained. This helps identify the pain points in the renewal and development process, pinpoint the perceptual dimensions of landscape value that need improvement, and effectively enhance the multiple dimensions of landscape value perception in the blocks. This, in turn, activates the tourism vitality of historic cultural blocks and forms a virtuous cycle model for their development.

Bayesian Analysis of Accelerated Trend Renewal Processes With Application to Lithium-Ion Battery Data

Bayesian Analysis of Accelerated Trend Renewal Processes With Application to Lithium-Ion Battery Data

Procrastination on production of energy using renewable sources retard settlement of congenial society: Evidence of Bangladesh

A better flow of resources to total package of energy production can ensure sustainable development of a nation. Bangladesh is a country which cannot yet make available all resources of energy required for sustainable development. Production of energy from renewable sources are not yet been accounted nationally. Sustainable Development Goals (Goal–7) demands creation of energy through resources like: water, air, sunlight and joint effect of another environmental resources. The task of production of energy through renewable sources has already been started but in a discrete manner. As a result, energy from conventional resources are used heavily for completing the production cycles in Bangladesh. The sources of energy at persisting process are mentioned as: natural gas (54.67%), fossil fuel (21.72%), coal (6.97%) wind, solar etc. (0.085%) and hydro (0.12%) and bio-fuels (15.90%). It can be pointed that the sources of energy through renewable resources is observing very negligible picture even after nine years of adopting UN convention and ratification for SDG (Goal 7). The absent of energy through renewable sources and burning of coal, fossil fuels, and natural gas for energy warming the atmosphere and affecting human health and environment. Considering this, the study attempts to find relationship of per capita generation of electricity with economic growth and other energy resources. Besides this, the study attempts to know how the changes of resources quantity influence the per capita generation of energy. Moreover, the research required to find out the turning point of the individual series contributing to the amount final product. The values of the parameters and the analysis are shown significant results, which support that the atmosphere getting more heat, polluting the environment and affecting the human health. As a result, more strong steps are to be taken to get rid of many unacceptable issues which is degrading atmospheric environment, human health and retarding the development of congenial process of living. On this situation, the study suggests that the generation of electricity observing renewal process should be started in full swing reducing the persisting long traditional process. This may lead to achieving targeted indicators for sustainable development goals (SDG 7) and help creating a pleasant and congenial society.

Thermoelectric Performance of YSZ Additions to ZnO Ceramics: Processing and Investigation

The increasing global demand for alternative energy sources and the environmental consequences of climate change necessitate research into renewable energy sources and energy conversion processes. Thermoelectric technology, which converts heat directly to electricity, can solve the energy issue and provide greener energy sources. The effects of yttria-stabilized zirconia (YSZ) on thermoelectric properties, such as electrical resistivity and Seebeck coefficients, of YSZ/ZnO composite have been investigated in this research. The study investigates the influence of sintering ZnO ceramics in an argon atmosphere at 1450°C with various quantities of YSZ addition to the microstructure and thermoelectric properties. The solid-state reaction method was used to synthesize all ZnO ceramic samples without YSZ and with YSZ of 0.5, 2 and 3 wt%. The Seebeck coefficient of the sintered samples increased 44-92% with YSZ additions at 800°C. At 800°C, the nominal composition of 0.5 wt% YSZ had power factor 1505 μW.m−1.K−2

Chondrocyte-targeted bilirubin/rapamycin carrier-free nanoparticles alleviate oxidative stress and modulate autophagy for osteoarthritis therapy.

Osteoarthritis (OA) is a prevalent chronic disease, characterized by the destruction of joint cartilage and synovitis, affects over 7 % of people worldwide. Disease-modifying treatments for OA still face significant challenges. Chondrocytes, as the exclusive cellular component of articular cartilage, play a pivotal role in synthesizing the intricate matrix of cartilage, thereby assuming a critical responsibility in facilitating its renewal and repair processes. However, oxidative stress within chondrocytes and subsequent apoptotic cell death plays significant roles in the progression of OA. Therefore, targeting apoptosis inhibition and mitigation of oxidative stress in chondrocytes represents a promising therapeutic strategy for OA. This study develops a type II collagen-targeting peptide (WYRGRLC) modified bilirubin/rapamycin carrier-free nanoparticle (PP/BRRP) and evaluate its therapeutic potential for OA. The PP/BRRP system exhibits remarkable chondrocyte-targeting ability, enabling the rupture of highly oxidized chondrocytes and subsequent release of bilirubin and rapamycin. This dual payload effectively scavenges reactive oxygen species, triggers autophagy, and suppresses the mTOR pathway, thereby augmenting anti-inflammatory and anti-apoptotic effects. The in vivo experiments further validate the retention and therapeutic efficacy of PP/BRRP in rat joints affected by OA. Overall, PP/BRRP exhibits significant potential for intervention and treatment of OA.

An integral renewal equation approach to behavioural epidemic models with information index.

We propose an integral model describing an epidemic of an infectious disease. The model is behavioural in the sense that the force of infection includes the information index that describes the opinion-driven human behavioural changes. The information index contains a memory kernel to mimic how the individuals maintain memory of the past values of the infection. We obtain sufficient conditions for the endemic equilibrium to be locally stable. In particular, we show that when the infectivity function is represented by an exponential distribution, stability is guaranteed by the weak Erlang memory kernel. However, through numerical simulations, we show that oscillations, possibly self-sustained, may arise when the memory is more focused in the disease's past history, as exemplified by the strong Erlang kernel. We also show the model solutions in cases of different infectivity functions taken from studies where specific diseases like Influenza and SARS are considered.

Continuous degradation modeling under random shocks and imperfect maintenance using generalized renewal process

Continuous degradation modeling under random shocks and imperfect maintenance using generalized renewal process

On Random Extrema with Applications to Renewal Processes

On Random Extrema with Applications to Renewal Processes

Analytical model of a computing system with software rejuvenation

The foundational basis of present technological advancements worldwide largely relies on computing systems. The integration of virtualisation amplifies the capabilities of these computing systems. The incorporation of virtualisation requires a virtual machine monitor (VMM) or hypervisor, host or server, and virtual machines (VMs). Over the time, as the system ages, the hypervisor requires rejuvenation, in order to ensure the system continues operating at its full capacity. Security of virtual system also compromises due to ageing. This article aims to examine the impact of software rejuvenation on the reliability, security and the performance of virtualised computing systems by comparing two probabilistic models. In Model-I, VMM quickly recovers from failure, restoring access to the robust state. Whereas, in Model-II, despite prompt repair, access shifts to the rejuvenation state before returning to the robust state. The models are built on the foundation of the theory of semi-Markov processes, employing the regenerative point approach from renewal theory to deduce results for diverse performance indicators. The findings from this research will contribute for making computing systems more resilient and long-lasting in different fields of applications.

Design of a Renewable Methanol Production Process from Biogas: Analysis of the Influence of the Operating Pressure in the Synthesis Loop

Design of a Renewable Methanol Production Process from Biogas: Analysis of the Influence of the Operating Pressure in the Synthesis Loop

Asymptotic estimation for statistical models of continuous-time discrete martingales

The paper deals with statistical experiments of the continuous-time discrete local martingales, including models of all types of point processes. The process of local density of the discrete local martingales is expressed by a stochastic exponent of the stochastic integral according to the compensated point measure. General conditions convenient for testing are determined to assure continuous validity of the maximum probability and Bayesian estimators, as well as the continuous asymptotic normality and the asymptotic minimaxity in each compact of the parametric set. The research applies the optimum Fréchet differentiation of random and parametric functions based on the probability in normed spaces in terms of a continuous compensator. It is demonstrated how the basic conditions become much simpler in the case of the renewal process with the continuous compensator.

Revising the Motion Control Parameter Optimization Research of a Two-Wheel Differential Car

This paper proposes a solution based on the particle swarm optimization algorithm to address the issue of Proportional Integral Derivative parameter selection in the motion control of a two-wheel differential car. The mathematical motion model is established based on the driving principle of a two-wheel differential car. The transfer function of the DC motor is derived in detail, based on Kirchhoff’s law and the Laplace transform. The pose renewal equation and error renewal equation of the car are based on the mathematical motion model. Finally, a numerical simulation and experimental analysis were conducted using MATLAB R2022a, Simulink 9.1 (part of R2018a), VOFA 1.3.10 software, an STM32 microcontroller, an L298N driver chip, and other hardware components. The results indicate that the particle swarm optimization algorithm enables the rapid acquisition of optimal Proportional Integral Derivative parameters. The optimized parameter of the motor speed convergence time is set to 10 ms, with an overshoot of 1 r/min and an enhanced anti-interference ability. The optimized parameters effectively regulate the car’s motion, ensuring a maximum error control of approximately 0.003 m.

FAKTOR-FAKTOR YANG MENGHAMBAT MASYARAKAT UNTUK BERJALAN KAKI DAERAH PERKOTAAN

Walking is very important in cities as it helps people to travel from one place to another. Urban areas in Bali are experiencing rapid development as tourism normalises, gradually entering a process of urban renewal. Improving the quality of the pedestrian environment is an important issue. The purpose of this research is to study how a person's physical condition, concepts, and activities affect their physical character and interest in walking. A quantitative method was used using randomly distributed open-ended questionnaires. Pedestrian criteria and facilities will be the source of data categorised in inhibiting pedestrians. A person who wants to walk should have good access and well-maintained facilities so that urban areas can be specialised for pedestrian paths.

Distribution theory for dependent renewal–reward processes and their first-passage times using saddlepoint and residue expansions

Distribution theory for dependent renewal–reward processes and their first-passage times using saddlepoint and residue expansions

Sustainable biomaterials for pharmaceutical and medical applications

The utilization of sustainable biomaterials in pharmaceutical and medical applications has gained significant momentum in recent years due to their dual ability to address environmental concerns and meet the evolving demands of modern healthcare. As the need for greener alternatives in healthcare intensifies, this review presents a comprehensive overview of recent advancements and innovations in sustainable biomaterials for pharmaceutical and medical fields. The review begins by exploring sustainable sourcing methods and eco-friendly production techniques, which are crucial in reducing the environmental footprint of biomaterial development. Emphasis is placed on adopting renewable resources and processes that minimize waste and energy consumption, ensuring sustainability throughout the lifecycle of these materials. A diverse array of sustainable biomaterials is highlighted, including biopolymers, natural extracts, and biobased nanoparticles, with a focus on their unique properties and biomedical applications. These materials are increasingly utilized in critical areas such as drug delivery systems, tissue engineering, wound healing, and medical device fabrication. Their attributes, including biocompatibility, biodegradability, and therapeutic efficacy, make them valuable assets in advancing healthcare solutions while preserving environmental integrity. Additionally, this review delves into regulatory considerations and the commercialization prospects of sustainable biomaterials, discussing the challenges and opportunities in integrating these materials into mainstream medical and pharmaceutical practices. Issues such as cost-effectiveness, scalability, and adherence to stringent regulatory standards are critically examined to understand their implications for real-world applications. By elucidating the potential, challenges, and future directions of sustainable biomaterials, this article aims to inspire further research and innovation in developing environmentally friendly and effective healthcare solutions. It advocates for a transformative approach to material science that prioritizes sustainability without compromising therapeutic outcomes, paving the way for a greener and healthier future.

IBN SINA’S CONTRIBUTIONS TO MODERNITY: INTEGRATING MEDIEVAL PHILOSOPHY, NEUROPHILOSOPHY, AND EDUCATIONAL REFORM IN ISLAMIC THOUGHT AND CIVILISATION

This study explores the enduring legacy of Ibn Sina, a seminal figure in Islamic medieval philosophy, focusing on his theory of the soul and its implications for modern neurophilosophy, educational reform, and the renewal of Islamic thought and civilisation. By bridging the intellectual heritage of Ibn Sina with contemporary discussions in neurophilosophy, this paper highlights his contributions to understanding the nature of consciousness, perception, and the human mind. Furthermore, it examines how Ibn Sina's insights can inform modern educational practices, advocating for an integration of classical wisdom and scientific advancements within the curriculum of Islamic studies. This integration not only pays homage to the rich intellectual tradition of Islamic civilisation but also fosters a dialogue between the medieval and the modern, contributing to the ongoing process of renewal and reform in Islamic thought. By applying Ibn Sina’s philosophical principles to contemporary challenges in education and society, this research underscores the potential for medieval Islamic philosophy to contribute to modernity, offering innovative pathways for navigating the complexities of the 21st century.