The Role of Stochastic Models in Interpreting the Origins of Biological Chirality

Gábor Lente

doi:10.3390/sym2020767

Stochastic models in cell kinetics

Journal of Applied Probability ◽

10.2307/3214149 ◽

1988 ◽

Vol 25 (A) ◽

pp. 91-111

Author(s):

Peter J. Brockwell

Keyword(s):

Life Cycle ◽

Stochastic Models ◽

Death Rate ◽

Cell Kinetics ◽

Branching Processes ◽

Experimental Studies ◽

Renewal Theory ◽

Biological Cell ◽

Age Dependent

We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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Mathematical Modeling of Supply Chain Management Systems

Enterprise Information Systems and Implementing IT Infrastructures ◽

10.4018/978-1-61520-625-4.ch022 ◽

2010 ◽

pp. 344-357

Author(s):

N. Anbazhagan

Keyword(s):

Mathematical Modeling ◽

Supply Chain ◽

Supply Chain Management ◽

Mathematical Models ◽

Stochastic Models ◽

Management System ◽

Raw Materials ◽

Chain Management ◽

Supply Chain Management System

Supply Chain Management (SCM) is the practice of coordinating the flow of goods, services, information and finances as they move from raw materials to parts supplier to manufacturer to wholesaler to retailer to consumer. Different supply chains have been designed for a variety of firms and this chapter discusses some issues in this regard. This chapter attempts to find why we require different supply chain for different companies. In this chapter we discuss the role of stochastic models in supply chain management system, and also discuss other mathematical models for SCM.

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Stochastic Models for Studying the Role of Cellular Noise and Heterogeneity

Systems Medicine ◽

10.1016/b978-0-12-801238-3.11466-7 ◽

2021 ◽

pp. 34-44

Author(s):

Sayuri K. Hortsch ◽

Andreas Kremling

Keyword(s):

Stochastic Models

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Stochastic models in cell kinetics

Journal of Applied Probability ◽

10.1017/s0021900200040286 ◽

1988 ◽

Vol 25 (A) ◽

pp. 91-111

Author(s):

Peter J. Brockwell

Keyword(s):

Life Cycle ◽

Stochastic Models ◽

Death Rate ◽

Cell Kinetics ◽

Branching Processes ◽

Experimental Studies ◽

Renewal Theory ◽

Biological Cell ◽

Age Dependent

We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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Culture without copying or selection

Evolutionary Human Sciences ◽

10.1017/ehs.2021.47 ◽

2021 ◽

pp. 1-31

Author(s):

Alberto Acerbi ◽

Mathieu Charbonneau ◽

Helena Miton ◽

Thom Scott-Phillips

Keyword(s):

Cultural Evolution ◽

Stochastic Models ◽

Selection Process ◽

Population Level ◽

Fundamental Question ◽

High Fidelity ◽

Formal Support ◽

Random Transformation ◽

Degree Of Similarity

Abstract Typical examples of cultural phenomena all exhibit a degree of similarity across time and space at the level of the population. As such, a fundamental question for any science of culture is, what ensures this stability in the first place? Here we focus on the evolutionary and stabilizing role of ‘convergent transformation’, in which one item causes the production of another item whose form tends to deviate from the original in a directed, non-random way. We present a series of stochastic models of cultural evolution investigating its effects. Results show that cultural stability can emerge and be maintained by virtue of convergent transformation alone, in the absence of any form of copying or selection process. We show how high-fidelity copying and convergent transformation need not be opposing forces, and can jointly contribute to cultural stability. We finally analyse how non-random transformation and high-fidelity copying can have different evolutionary signatures at population level, and hence how their distinct effects can be distinguished in empirical records. Collectively, these results supplement existing approaches to cultural evolution based on the Darwinian analogy, while also providing formal support for other frameworks — such as Cultural Attraction Theory — that entail its further loosening.

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A Stochastic Compartmental Model for COVID-19

10.1101/2020.12.03.20243584 ◽

2020 ◽

Author(s):

Giorgio Sonnino ◽

Fernando Mora ◽

Pasquale Nardone

Keyword(s):

Health Care ◽

Probability Density Function ◽

Stochastic Models ◽

Compartmental Model ◽

Real Data ◽

Third Wave ◽

Theoretical Predictions ◽

Massive Distribution ◽

Hospital Capacities

AbstractWe propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density function, have duly been computed. Our models, which generalises a model previously proposed and published in a specialised journal, take into account the adoption of the lockdown measures as well as the crucial role of the hospitals and Health Care Institutes. To accomplish this work we have analysed two scenarios: the SIS-model (Susceptible ⇒ Infectious ⇒ Susceptible) in presence of the lockdown measures and the SIS-model integrated with the action of the hospitals (always in presence of the lockdown measures). We show that in the case of the pure SIS-model, once the lockdown measures are removed, the Coronavirus will start growing again. However, in the second scenario, beyond a certain threshold of the hospital capacities, the Coronavirus is not only kept under control, but its capacity to spread tends to diminish in time. Therefore, the combined effect of the lockdown measures with the action of the hospitals and health Institutes is able to contain and dampen the spread of the SARS-CoV-2 epidemic. This result can be used during a period of time when the massive distribution of delivery of a limited number of vaccines in a given population is not yet feasible. By way of example, we analysed the data for USA and France where the intensities of the noise have been estimated by Statistical Mechanics. In particular, for USA we have analysed two possible hypotheses: USA is still subject to the first wave of infection by and USA is in the second (or third) wave of SARS-CoV-2 infection.The agreement between theoretical predictions and real data confirms the validity of our approach.

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Stochastic models of receptor oligomerization by bivalent ligand

Journal of The Royal Society Interface ◽

10.1098/rsif.2006.0116 ◽

2006 ◽

Vol 3 (9) ◽

pp. 545-559 ◽

Cited By ~ 17

Author(s):

Tomás Alarcón ◽

Karen M Page

Keyword(s):

Stochastic Models ◽

Cellular Response ◽

Cell Activation ◽

Design Principle ◽

Ligand Concentration ◽

Bivalent Ligand ◽

Oligomer Formation ◽

Receptor Oligomerization ◽

Stochastic Fluctuations

In this paper, we develop stochastic models of receptor binding by a bivalent ligand. A detailed kinetic study allows us to analyse the role of cross-linking in cell activation by receptor oligomerization. We show how oligomer formation could act to buffer intracellular signalling against stochastic fluctuations. In addition, we put forward the hypothesis that formation of long linear oligomers increases the range of ligand concentration to which the cell is responsive, whereas formation of closed oligomers increases ligand concentration specificity. Thus, different physiological functions requiring different degrees of specificity to ligand concentration would favour formation of oligomers with different lengths and geometries. Furthermore, provided that ligand concentration specificity is taken as a design principle, our model enables us to estimate parameters, such as the minimum proportion of receptors, that must engage in oligomer formation in order to trigger a cellular response.

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Modelling Extreme Market Events. A Report of the Benchmarking Stochastic Models Working Party

British Actuarial Journal ◽

10.1017/s1357321700005468 ◽

2009 ◽

Vol 15 (1) ◽

pp. 99-201 ◽

Cited By ~ 10

Author(s):

R. Frankland ◽

A. D. Smith ◽

T. Wilkins ◽

E. Varnell ◽

A. Holtham ◽

...

Keyword(s):

Interest Rate ◽

Stochastic Models ◽

Financial Services ◽

Working Party ◽

Prior Beliefs

ABSTRACTThis paper focusses on some practical issues that can arise when developing methodologies for calculating benchmark figures for extreme market events, particularly in the context of the Financial Services Authority's ICAS regime. The paper limits discussion to equity and interest rate risks. Whilst not intended to constitute formal guidance, it is hoped that the material contained within the paper will be useful to practitioners. The paper acknowledges the role of prior beliefs in the choice of data to be used for modelling and its influence upon the ensuing results.

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