Flexible servers in tandem lines with setup costs

We study the dynamic assignment of flexible servers to stations in the presence of setup costs that are incurred when servers move between stations. The goal is to maximize the long-run average profit. We provide a general problem formulation and some structural results, and then concentrate on tandem lines with two stations, two servers, and a finite buffer between the stations. We investigate how the optimal server assignment policy for such systems depends on the magnitude of the setup costs, as well as on the homogeneity of servers and tasks. More specifically, for systems with either homogeneous servers or homogeneous tasks, small buffer sizes, and constant setup cost, we prove the optimality of “multiple threshold” policies (where servers’ movement between stations depends on both the number of jobs in the system and the locations of the servers) and determine the values of the thresholds. For systems with heterogeneous servers and tasks, small buffers, and constant setup cost, we provide results that partially characterize the optimal server assignment policy. Finally, for systems with larger buffer sizes and various service rate and setup cost configurations, we present structural results for the optimal policy and provide numerical results that strongly support the optimality of multiple threshold policies.     

Maximum likelihood estimation in a partially observed stratified regression model with censored data

The stratified proportional intensity model generalizes Cox’s proportional intensity model by allowing different groups of the population under study to have distinct baseline intensity functions. In this article, we consider the problem of estimation in this model when the variable indicating the stratum is unobserved for some individuals in the studied sample. In this setting, we construct nonparametric maximum likelihood estimators for the parameters of the stratified model and we establish their consistency and asymptotic normality. Consistent estimators for the limiting variances are also obtained.     

Minimal Submanifolds in Sp+3 with Constant Scalar Curvature

Let M be a compact, minimal 3-dimensional submanifold with constant scalar curvature R immersed in the standard sphere S^3+p. In codimension 1, we know from the work that has been done on Chern’s conjecture that M is isoparametric and R = 3D0, R = 3D3 or R = 3D6. In this paper we extend this result from codimension one to compact submanifolds with a flat normal bundle and give a complete classification.     

Affine interval exchange transformation without an isometric model

Contrary to the case of interval exchange transformation, we show that generalized affine interval exchange transformation (affine GIET), with or without flips and admitting dense orbits, may not be conjugated to an isometric GIET. This result is proved by constructing explicitly one such affine GIET. The author was partially supported by FAPESP – Proj. Tematico No. 03/03107-9.     

Laplace Transform and Moments of Waiting Times in Poisson Driven (max,+) Linear Systems

(Max,+) linear systems can be used to represent stochastic Petri nets belonging to the class of event graphs. This class contains various instances of queueing networks like acyclic or cyclic fork-and-join queueing networks, finite or infinite capacity tandem queueing networks with various types of blocking, synchronized queueing networks and so on. It also contains some basic manufacturing models such as kanban networks, assembly systems and so forth.In their 1997 paper, Baccelli, Hasenfuss and Schmidt provide explicit expressions for the expected value of the waiting time of the nth customer in a given subarea of a (max,+) linear system. Using similar analysis, we present explicit expressions for the moments and the Laplace transform of transient waiting times in Poisson driven (max,+) linear systems. Furthermore, starting with these closed form expressions, we also derive explicit expressions for the moments and the Laplace transform of stationary waiting times in a class of (max,+) linear systems with deterministic service times. Examples pertaining to queueing theory are given to illustrate the results.     

Can males contribute to the genetic improvement of a species?

In the time evolution of finite populations, the accumulation of harmful mutations in further generations might have lead to a temporal decay in the mean fitness of the whole population. This, in turn, would reduce the population size and so lead to its extinction. The production of genetically diverse offspring, through recombination, is a powerful mechanism in order to avoid this catastrophic route. From a selfish point of view, meiotic parthenogenesis can ensure the maintenance of better genomes, while sexual reproduction presents the risk of genome dilution. In this paper, by using Monte Carlo simulations of age-structured populations, through the Penna model, I compare the evolution of populations with different repoductive regimes. It is shown that sexual reproduction with male competition can produce better results than meiotic parthenogenesis. This contradicts results recently published, but agrees with the strong evidence that nature chose sexual reproduction instead of partenogenesis for most of the higher species.     

Differential realizations of the two-mode bosonic and fermionic Hamiltonians: A unified approach

A method is developed to determine the eigenvalues and eigenfunction of two-boson 2 × 2 matrix Hamiltonians that include a wide class of quantum optical models. The quantum Hamiltonians are transformed in the form of the one variable differential equation and the conditions for their solvability are discussed. We present two different transformation procedures and we show our approach unify various approaches based on Lie algebraic technique. As an application, solutions of the modified Jaynes-Cummings and two-level Jahn-Teller Hamiltonians are studied.