Cash transfer program and education investment: A model for social evolution

Assume that the households of a country are socially classified according to the monthly total income, and that they can be part of a lower, a middle or an upper class. By using multi-agent systems, here we model and simulate the economic evolution of households which earn a wage, pay taxes and invest in education. The return of the education investment is monthly added to the salary of the family, and it is function of the corresponding grand total put in education along the time. When a family is unemployed, we consider that it receives cash due to a social program made by the government. The time evolution of the percentages of households belonging to each class is investigated by varying the government investment in such a program of cash transfer and the proportion of employed households in the population. We show that the government should invest in the unemployed lower class if it intends a growth of the middle class. We also propose and analyze a mean-field approximation written in terms of ordinary differential equations. In addition, we verify that our model fits real data from Brazil, in the period between 2003 (when the cash transfer program Bolsa Família was launched) and 2011.     

Asymmetric exclusion processes with site sharing in a one-channel transport system

This Letter investigates two-species totally asymmetric simple exclusion process (TASEP) with site sharing in a one-channel transport system. In the model, different species of particles may share the same sites, while particles of the same species may not (hard-core exclusion). The site-sharing mechanism is applied to the bulk as well as the boundaries. Such sharing mechanism within the framework of the TASEP has been largely ignored so far. The steady-state phase diagrams, currents and bulk densities are obtained using a mean-field approximation and computer simulations. The presence of three stationary phases (low-density, high-density, and maximal current) are identified. A comparison on the stationary current with the Bridge model [M.R. Evans, et al., Phys. Rev. Lett. 74 (1995) 208] has shown that our model can enhance the current. The theoretical calculations are well supported by Monte Carlo simulations.     

The evolutionary dynamics of a spatial multi-strain host-pathogen system with cross-immunity

We considered a Susceptible-Infective-Recovered-Susceptible (SIRS) model with strain mutation and cross-immunity in a non-spatial model and a lattice-structured model, where all individuals can reproduce if the space/resources allow. In the lattice-structured model, both the host reproduction and pathogen transmission processes are assumed to interact with next nearest neighbors, and the model was analyzed by an improved pair approximation (IPA). A family of correlated equations of pair approximation and mean-field were presented. We show the phase diagram of the coexistence and extinction which were obtained from parameterization by measuring the basic reproduction numbers of the strains during their infection processes. The qualitative results of the pair approximation model are similar to that of the corresponding non-spatial model. Furthermore, the spatial model predicts coexistence over a wider range of parameters than the non-spatial model. In particular, when the strain evolution tends to a larger basic reproduction number, the correlated spatial approximation could predict better than the mean-field approximation.     

Mean-field bounds on the magnetization for ferromagnetic spin models

The mean-field approximation is shown to give an upper bound on the magnetization for a large class of one-component models with arbitrary ferromagnetic pair interactions. Specific examples include discrete and continuous spin Ising models. In addition, a new comparison inequality for multicomponent rotators is proven which allows this result to be extended to the plane rotator and classical Heisenberg ferromagnets.     

Large deviation for mean-field stochastic differential equations with subdifferential operator

In this article, we prove the existence and uniqueness of a solution for a class of mean-field stochastic differential equations with subdifferential operator (i.e., mean-field MSDEs) by means of the Moreau–Yosida type penalization method. Moreover, we prove a large deviation principle of its path solution via the weak convergence method.     

Parallel Variational Bayes for Large Datasets With an Application to Generalized Linear Mixed Models

The article develops a hybrid variational Bayes (VB) algorithm that combines the mean-field and stochastic linear regression fixed-form VB methods. The new estimation algorithm can be used to approximate any posterior without relying on conjugate priors. We propose a divide and recombine strategy for the analysis of large datasets, which partitions a large dataset into smaller subsets and then combines the variational distributions that have been learned in parallel on each separate subset using the hybrid VB algorithm. We also describe an efficient model selection strategy using cross-validation, which is straightforward to implement as a by-product of the parallel run. The proposed method is applied to fitting generalized linear mixed models. The computational efficiency of the parallel and hybrid VB algorithm is demonstrated on several simulated and real datasets. Supplementary material for this article is available online.     

An Explicit Multistep Scheme for Mean-Field Forward-Backward Stochastic Differential Equations

This is one of our series works on numerical methods for mean-field forward backward stochastic differential equations (MFBSDEs). In this work, we propose an explicit multistep scheme for MFBSDEs which is easy to implement, and is of high order rate of convergence. Rigorous error estimates of the proposed multistep scheme are presented. Numerical experiments are carried out to show the efficiency and accuracy of the proposed scheme.     

Modulated phases and the mean-field theory of magnetism with competing interactions

The mean-field theory of an Ising magnet with infinitely weak, infinitely long-range potentials of arbitrary sign is presented in terms of a variational principle for the magnetization. Previous studies of the theory have revealed paramagnetic, ferromagnetic, and modulated phases. For a particular choice of potential, which is an obvious continuous version of the between-plane ANNNI model interaction, exact solutions of the stationary condition implied by the variational principle are obtained. This leads us to formulate a trial magnetization to well describe the modulated phase in general. To illustrate the utility of the trial magnetization, both analytic and numerical calculations are performed, which determine the wavenumber in certain portions of the modulated phase for the above-mentioned potential.     

Mean-field limit of generalized Hawkes processes

We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point.Within this class, we investigate the limit behaviour, when $n$ goes to infinity, of a system of $n$ mean-field interacting age-dependent Hawkes processes. We prove that such a system can be approximated by independent and identically distributed age dependent point processes interacting with their own mean intensity. This result generalizes the study performed by Delattre et al. (2016).In continuity with Chevallier et al. (2015), the second goal of this paper is to give a proper link between these generalized Hawkes processes as microscopic models of individual neurons and the age-structured system of partial differential equations introduced by Pakdaman et al. (2010) as macroscopic model of neurons.