Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Models of collective cell behaviour with crowding effects : comparing lattice-based and lattice-free approaches

Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice based model is that a proliferative population will always eventually fill the lattice. Here we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental setups. Lattice-free simulation results are compared to these mean-field descriptions and to a corresponding lattice-based model. Data from a proliferation experiment is used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.

Mean-field descriptions of collective migration with strong adhesion

Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

An inhomogeneous multispecies TASEP on a ring

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove Lam and Williams' conjectures in two special cases by generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species. (C) 2014 Elsevier Inc. All rights reserved.

Emancipação social e exclusão no cotidiano escolar: a homofobia e sua influência nas tessituras identitárias

Esta pesquisa teve como objetivo entender como os processos de exclusão ocorridos nos/dos/com os cotidianos de uma escola pública influenciam nos processos de tessituras identitárias das alunas e dos alunos com orientação homossexual e dos demais alunos que praticam ou assistem aos procedimentos de exclusão. A pesquisa nos/dos/com os cotidianos possibilitou a compreensão sobre os processos cotidianos de produção de exclusões em sua complexidade e o modo como esses interferem nas formações identitárias dos sujeitos. A partir de histórias narradas, podemos perceber algumas práticas emancipatórias que influenciaram tais tessituras de todas as alunas e alunos ao lado de práticas excludentes e homofóbicas que igualmente interferiram nas constituições das identidades de todos os estudantes. Todos esses discentes teceram aprendizagens, a partir das ações e discursos proferidos por suas professoras e professores, em relação à sexualidade e aos modos de suas manifestações. Assim, foi necessário darmos visibilidade a algumas dessas práticas para percebermos que na tessitura das identidades de todos os estudantes estão presentes aprendizagens emancipatórias e processos de subjetivações que podem ser entendidos como aprendizagens regulatórias. Verificamos que o sofrimento foi um alinhavo permanente das tessituras identitárias de alguns estudantes, tendo se transformado, para alguns, em potência e para outros, em apenas dor.

Disability and Identity Processes

This article presents a reflection about the Disability like a human phenomenon, which needs not only new definitions if not a criticism point of view as a Concept, with the end of indicate representations forms not only for people with disabilities if not for the citizens in general. Considers discourses that identify arguments from social sciences, appearing the Disability like a differentiate condition between human beings, mainly for an exclusion process that announce social behaviors in relations with the persons with disabilities.

A Hopping Mechanism for Cargo Transport by Molecular Motors on Crowded Microtubules

Most models designed to study the bidirectional movement of cargos as they are driven by molecular motors rely on the idea that motors of different polarities can be coordinated by external agents if arranged into a motor-cargo complex to perform the necessary work Gross, Hither and yon: a review of bidirectional microtubule-based transport (Gross in Phys. Biol. 1:R1-R11, 2004). Although these models have provided us with important insights into these phenomena, there are still many unanswered questions regarding the mechanisms through which the movement of the complex takes place on crowded microtubules. For example (i) how does cargo-binding affect motor motility? and in connection with that-(ii) how does the presence of other motors (and also other cargos) on the microtubule affect the motility of the motor-cargo complex? We discuss these questions from a different perspective. The movement of a cargo is conceived here as a hopping process resulting from the transference of cargo between neighboring motors. In the light of this, we examine the conditions under which cargo might display bidirectional movement even if directed by motors of a single polarity. The global properties of the model in the long-time regime are obtained by mapping the dynamics of the collection of interacting motors and cargos into an asymmetric simple exclusion process (ASEP) which can be resolved using the matrix ansatz introduced by Derrida (Derrida and Evans in Nonequilibrium Statistical Mechanics in One Dimension, pp. 277-304, 1997; Derrida et al. in J. Phys. A 26: 1493-1517, 1993).

Cellular automaton model for molecular traffic jams

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally asymmetric simple exclusion process with sublattice parallel update and thus may serve as a model for studying traffic jams in systems of self-driven particles. We study the emergence of shocks from the microscopic dynamics of the model. In particular, we introduce shock measures whose time evolution we can compute explicitly, both in the thermodynamic limit and for open boundaries where a boundary-induced phase transition driven by the motion of a shock occurs. The motion of the shock, which results from the collective dynamics of the exclusion particles, is a random walk with an internal degree of freedom that determines the jump direction. This type of hopping dynamics is reminiscent of some transport phenomena in biological systems.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

O pedagogo como agente de transformação social para além dos muros escolares

This thesis concerns the problem about the pedagogue actuation in the social education into no scholars places. It search to understand the context and the social pedagogue role to his praxis and formation that enlarger the possibilities of the social educative practices into no scholars places. In this direction, we developed an investigation about the actuation of the pedagogues-educators in Natal city, in the 2007-2010 periods, into Municipal Secretary of the Labor and Social Assistance (SEMTAS). Considering that pedagogues are regularly attached in social educators profession as municipals public employees, we re the objective to evaluate their role into the social executed in the no scholars places, with the focus in the environmental dimensions of theirs work s places, pedagogical organization, institutional management and the professional formation. It privileged in this research the Specialized Reference Center of Social Assistance II (CREAS II), the Passages Houses I, II and III, the Social-Educative Measures in Open Environment Execution Program of Natal city (PENSEMA) and the Pitimbú Educational Center (CEDUC-Pitimbú). To realize this study it developed a research with qualitative nature by critic ethnography approach privileging those information collected with the social pedagogue-educators of the mentioned places. Through the methodological procedures adopted; beyond the bibliographical review we remarked the documental research, the semi-structured interview, the questionnaires-routes and the field observations. The analytical results revealed that the politics to the social education in Brazil historically came been dimensioned by the fight of social movements demanding the fundamental rights to the excluded people; that the SEMTAS politics of social education present a relative basic social protection to the excluded children and young people specially into law view; that the politics of social education in Natal city it s close of the logic of sanitarian attention about the disadvantaged groups; that the conceptual, methodological and formatives fragilities needs to the social pedagogues-educators praxis into non scholars places made difficult the operation capacity of a educative proposition anchored in a institutional action guided by the idea of emancipator education; that the SEMTAS take face several difficulties to developed a web assistance as preview in the reception proposition elaborated by the social pedagogues-educators. However in despite the tensions we remarked the value of this potentiality to the non scholar social education in her attempt to constitute herself in a legitimate space to the pedagogue professional actuation. In despite the obstacles to work and formation quotidian, across those non scholar spaces in the municipalities institutes to the social politics, it demonstrated personal sensibility and professional creativity in learning mediations and educative action to the children and younger derived from exclusion process and the social iniquities

Famílias privadas de liberdade: a saga da violência vivenciada por adolescentes que trilham os áridos caminhos da criminalidade

This paper has as its main focus the relation between the infringement act and the adolescents families social economical problematic, who obey the social educational deprivation of freedom at CEDUC in the district of Pitimbu RN, establishing in the theme Children and Adolescents, with the objective of showing how these families breed in the social economical and cultural political aspect. It also seizes who those adolescents are and their family members in their social aspect and as those families face their daily activities. The focus on the social matter, family, adolescent, infringement act, exclusion, inclusion formed the analysis categories which made myths and reality possible, taking into consideration the infringement act in our society. The data collection showed that those families conditions of life are of poverty. Families originated from low social classes, 62.5 % coming from the countryside and living with a daily income ranging from R$ 0,31 to R$ 8,31. Their level of education is low; there is lack of human and citizenship rights and no professional qualification whatsoever. It questions the degrading social exclusion suffered by millions of Brazilian people due to social, political and infringement economical problems. Has this favored the infringement practice? How to confirm the families lack of competence having the social vulnerability? Are the Public Political Institutions really performing the way they should? Are they really carrying out their role as they should? We have noticed that from then on, the necessity of understanding the exclusion/inclusion suffered not only in an imprecise and empty way, but understood as processes of integrative exclusion or ways of delinquency, where the excluding is not only the only one who has lack of material care but the one who is seen or recognized as a person, is not being treated as one. The effort of this paper provided an approach to our object, and the seizing of a close relation between the infringement act and the exclusion process or inclusion suffered, which are submitted to families of those adolescents who deprive of freedom