Invariants of motion with stochastic resetting and space-time coupled returns

Pal, A.; Kuśmierz, Łukasz; Reuveni, Shlomi

doi:10.1088/1367-2630/ab5201

Cited by 83 publications

(85 citation statements)

References 80 publications

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“…Case p = 1. As we have recently highlighted elsewhere [5], when p = 1 (zero probability of failure) the above model can be mapped onto a stochastic resetting process for a particle with a refractory (nucleation) period [10] and a finite return time [21,22]. This is illustrated in Fig.…”

Section: 2mentioning

confidence: 97%

Search-and-capture model of cytoneme-mediated morphogen gradient formation

Bressloff

Kim

2019

Phys. Rev. E

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In this paper we develop a directional search-and-capture model of cytoneme-based morphogenesis. We consider a single cytoneme nucleating from a source cell and searching for a set of N target cells Ω k ⊂ R d , k = 1,. .. , N , with d ≥ 2. We assume that each time the cytoneme nucleates, it grows in a random direction so that the probability of being oriented towards the k-th target is p k with N k=1 p k < 1. Hence, there is a non-zero probability of failure to find a target unless there is some mechanism for returning to the nucleation site and subsequently nucleating in a new direction. We model the latter as a one-dimensional search process with stochastic resetting, finite returns times and refractory periods. We use a renewal method to calculate the splitting probabilities and conditional mean first passage times (MFPTs) for the cytoneme to be captured by a given target cell. We then determine the steady-state accumulation of morphogen over the set of target cells following multiple rounds of search-and-capture events and morphogen degradation. This then yields the corresponding morphogen gradient across the set of target cells, whose steepness depends on the resetting rate. We illustrate the theory by considering a single layer of target cells, and discuss the extension to multiple cytonemes.

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Section: 2mentioning

confidence: 97%

Search-and-capture model of cytoneme-mediated morphogen gradient formation

Bressloff

Kim

2019

Phys. Rev. E

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“…An extension of the idea of a refractory period following a reset is to have a different dynamics, which commences on resetting and returns the process to the origin over some finite time. Such two-phase, reset-return processes have been studied in [115][116][117].…”

Section: Effects Of Refractory Periodmentioning

confidence: 99%

Stochastic resetting and applications

Evans

Majumdar

Schehr

2020

J. Phys. A: Math. Theor.

506

600

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In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.

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“…What does this mean? is requires a detailed discussion on the decision-making unit of urban development and what the technical aspects of urban development are, followed by making the corresponding result judgment in combination with the actual situation [25][26][27][28].…”

Section: Evaluation and Analysis Methods Of Efficiency In Financing O...mentioning

confidence: 99%

Research on Efficiency in Financing of Small and Medium Companies Based on DEA Method

Pang

Gai

2022

Discrete Dynamics in Nature and Society

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At this stage, SMEs cannot survive and grow without the support of large amounts of capital, and the issue of financing efficiency has always been a bottleneck for different types of SMEs. This paper studies the financial data of relevant enterprises by constructing variable index evaluation systems such as anti-risk ability, internal management, financial system, market competitiveness, short-term debt, long-term debt, paid-in capital to property right ratio, comprehensive efficiency, pure technical efficiency, and scale efficiency and takes manufacturing, service, high-tech, and community-based small-sized and medium-sized enterprises as the research points. The DEA model is used to analyze the financing efficiency of enterprises. The results show that small-sized and medium-sized enterprises in high-tech and manufacturing industries are in the stage of increasing returns to scale. In a homogeneous environment, internal financing environment variables, total assets, asset liability ratio, debt service ratio, current ratio, and other variables have an impact on liquidity efficiency. External financing environment variables, science and technology investment, and economic level have a good and significant impact on enterprise financing.

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Invariants of motion with stochastic resetting and space-time coupled returns

Cited by 83 publications

References 80 publications

Search-and-capture model of cytoneme-mediated morphogen gradient formation

Search-and-capture model of cytoneme-mediated morphogen gradient formation

Stochastic resetting and applications

Research on Efficiency in Financing of Small and Medium Companies Based on DEA Method

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