Multitype Case Research Articles

Cultura y planeación del desarrollo en comunidades indígenas de la Sierra Sur, Oaxaca

Indigenous communities are characterized by particular ways of exercising and organizing internal life. The union of these forms builds a sociocultural identity, as well as a life expectancy and development objectives. The objective was to analyze how municipal development planning fits into the sociocultural context of the indigenous communities of the Southern Sierra under the theoretical dimensions of ethnodevelopment and good living. The latter are alternative models that arise as a critique of the hegemonic conception of Western development and demonstrate the construction of multiple ways of living in harmony with nature, community and individual itself. The study was conducted in the municipalities of San Francisco Logueche, San José Lachiguirí, San Cristobal Amatlán, San Miguel Suchixtepec and San Andrés Paxtlán, located in the Sierra Sur region. The methodology corresponded to a multi-type case study with a qualitative approach. The techniques of gathering information were the analysis of content and the semi-structured interview. The results show that indigenous communities face a rigid system of planning that is subject to development guidelines, national and international guidelines and agreements. They define technical solutions that try to respond to the problems of the population, from a reduced approach to human and sustainable development; a situation that violates the customs and good lives that are always local and specific to each context.

Asymptotic degree distribution in preferential attachment graph models with multiple type edges

We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the N-type case, we define the (generalized) degree of a given vertex as where is the number of type k edges connected to it. We prove the existence of an a.s. asymptotic degree distribution for a general family of preferential attachment random graph models with multi-type edges. More precisely, we show that the proportion of vertices with (generalized) degree d tends to some random variable as the number of steps goes to infinity. We also provide recurrence equations for the asymptotic degree distribution. Finally, we generalize the scale-free property of random graphs to the multi-type case.

Analysis and numerical simulation of an inverse problem for a structured cell population dynamics model.

In this work, we study a multiscale inverse problem associated with a multi-type model for age structured cell populations. In the single type case, the model is a McKendrick-VonFoerster like equation with a mitosis-dependent death rate and potential migration at birth. In the multi-type case, the migration term results in an unidirectional motion from one type to the next, so that the boundary condition at age 0 contains an additional extrinsic contribution from the previous type. We consider the inverse problem of retrieving microscopic information (the division rates and migration proportions) from the knowledge of macroscopic information (total number of cells per layer), given the initial condition. We first show the well-posedness of the inverse problem in the single type case using a Fredholm integral equation derived from the characteristic curves, and we use a constructive approach to obtain the lattice division rate, considering either a synchronized or non-synchronized initial condition. We take advantage of the unidirectional motion to decompose the whole model into nested submodels corresponding to self-renewal equations with an additional extrinstic contribution. We again derive a Fredholm integral equation for each submodel and deduce the well-posedness of the multi-type inverse problem. In each situation, we illustrate numerically our theoretical results.

Fitness potentials and qualitative properties of the Wright-Fisher dynamics

We present a mechanistic formalism for the study of evolutionary dynamics models based on the diffusion approximation described by the Kimura Equation. In this formalism, the central component is the fitness potential, from which we obtain an expression for the amount of work necessary for a given type to reach fixation. In particular, within this interpretation, we develop a graphical analysis — similar to the one used in classical mechanics — providing the basic tool for a simple heuristic that describes both the short and long term dynamics. As a by-product, we provide a new definition of an evolutionary stable state in finite populations that includes the case of mixed populations. We finish by showing that our theory – rigorous for two types evolution without mutations– is also consistent with the multi-type case, and with the inclusion of rare mutations.

The asymptotic relative generation distribution of the closest common ancestor of the multitype Galton–Watson tree conditioned on non-extinction

We extend Geiger’s size-biased tree method to the multitype case to give another proof of Zubkov’s result that the asymptotic relative generation distribution of the closest common ancestor of the multitype Galton–Watson branching process conditioned on non-extinction is uniform.

Adversarial queuing theory with setups

We look at routing and scheduling problems on Kelly type networks where the injection process is under the control of an adversary. The novelty of the model we consider is that the adversary injects requests of distinct types. Resources are subject to switch-over delays or setups when they begin servicing a new request class. In this new setting, we study the behavior of sensible policies as introduced by Dai and Jennings [J. Dai, O. Jennings, Stabilizing queueing networks with setups, Math. Oper. Res. (2004) 891–922]. We first show that the model is robust in the sense that under some mild conditions universal stability of work conserving packet routing protocols is preserved for natural variants of the underlying model. Also, the model’s equivalence to so called token networks is established. We adapt to the multi-type request and setup setting, standard arguments for proving stability. Nevertheless, we provide counterexamples that show that for several reasonable adaptations of contention resolution protocols to the multi-type case, stability results do not carry over from the single-type scenario. This motivates us to explore fluid model based arguments that could be used for proving stability for a given network. Specifically we show analogues of results obtained by Gamarnik [D. Gamarnik, Stability of adversarial queues via fluid model, in: Proc. of the 39th Annual Symposium on Foundations of Computer Science, 1998, pp. 60–70] but in the multi-type request with setups scenario.

Poisson point process limits in size-biased Galton-Watson trees

Consider a critical binary continuous-time Galton-Watson tree size-biased according to the number of particles at time $t$. Decompose the population at $t$ according to the particles' degree of relationship with a distinguished particle picked purely at random from those alive at $t$. Keeping track of the times when the different families grow out of the distinguished line of descent and the related family sizes at $t$, we represent this relationship structure as a point process in a time-size plane. We study limits of these point processes in the single- and some multitype case.

Rates of decay for the survival probability of a mutant gene II The multitype case

This paper extends the results of [1] to the multitype case. For a multitype branching process that is slightly supercritical, approximations for the survival probability in terms of the maximal eigenvalue ϱ of the mean matrix and a generalized variance σ2 are developed. Our results improve upon those of Hoppe [5] and Eshel [3] that seek to validate a conjecture of Ewens [4].

A multitype random sequential process

A random sequential process (RSP) can be formulated in two different ways: (I) A linear array of n identical compartments is ceaselessly bombarded by particles which occupy β( β≥2) contiguous lattice sites. These so-called β-bell particles are assumed to make contact in a spatially random manner and to stick only if striking β (adjacent) vacant compartments. (II) A linear array of n identical compartments is sequentially filled by β-bell particles, the occupation process being ‘‘selective,’’ i.e., always being directed to vacant sequences of compartments of lengths at least β. Dynamics of RSP’s has always been formulated in either way and in the case of lattice spaces all the efforts have been addressed so far to allow in the space filling process just one kind of particle. The aim of this paper is to remove that restriction and to consider a lattice space filling problem with various kinds of particles involved. The situations of the two above-described models, making no difference in the one-type case, become distinct in the multitype case. In this paper we will be concerned with the generalization of model II.