Queues with inter- ruption in Random/ Markovian Environment

In many situations probability models are more realistic than deterministic models. Several phenomena occurring in physics are studied as random phenomena changing with time and space. Stochastic processes originated from the needs of physicists.Let X(t) be a random variable where t is a parameter assuming values from the set T. Then the collection of random variables {X(t), t ∈ T} is called a stochastic process. We denote the state of the process at time t by X(t) and the collection of all possible values X(t) can assume, is called state space

Effect of low-level laser therapy on the healing process after tooth replantation: a histomorphometrical and immunohistochemical analysis

Success of tooth replantation is limited because part of the replanted tooth is lost because of progressive root resorption. This study used histomorphometry and immunohistochemistry to evaluate the effect of low-level laser therapy (LLLT) on the healing process of rat teeth replanted after different extra-oral periods, simulating immediate and delayed replantation. Sixty Wistar rats (Rattus norvegicus albinus) had their maxillary right incisors extracted and randomly assigned to six groups (n = 10): C4, C30 and C45, in which the teeth were replanted 4 min (immediate), 30 min (delayed) and 45 min (delayed) after extraction, respectively, and L4, L30 and L45, in which the teeth were replanted after the same extra-alveolar times, but the root surfaces and the alveolar wounds were irradiated with a gallium-aluminum-arsenate (GaAlAs) diode laser before replantation. The animals were sacrificed after 60 days. The anatomic pieces containing the replanted teeth were obtained and processed for either histomorphometrical analysis under optical microscopy or immunohistochemical expression of receptor activator of nuclear factor Kappa-B (RANK), and its ligand (RANKL), osteoprotegerin (OPG) and tartrate-resistant acid phosphatase (TRAP) proteins. Areas of external replacement and inflammatory root resorption were observed in all groups, without statistically significant differences (P > 0.05). Ankylosis was more frequent in L30 than in C30 (P < 0.05). RANKL immunostaining predominated over RANK and OPG immunostaining in both groups with immediate tooth replantation (P < 0.05). For the 45-min extra-alveolar time, however, there was greater evidence of RANK immunostaining compared to RANKL for both control and laser-treated groups (P < 0.05). Positive TRAP immunostaining predominated in L4 and L30 (P < 0.05). In conclusion, under the tested conditions, the treatment of the root surface and the alveolar wound with LLLT did not improve the healing process after immediate and delayed tooth replantation in rats.

Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Spectral gap for Glauber type dynamics for a special class of potentials

We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on Rd. These Glauber type dynamics are Markov processes constructed for pre-given reversible measures. A representation for the ``carré du champ'' and ``second carré du champ'' for the associate infinitesimal generators L are calculated in infinite volume and for a large class of functions in a generalized sense. The corresponding coercivity identity is derived and explicit sufficient conditions for the appearance and bounds for the size of the spectral gap of L are given. These techniques are applied to Glauber dynamics associated to Gibbs measure and conditions are derived extending all previous known results and, in particular, potentials with negative parts can now be treated. The high temperature regime is extended essentially and potentials with non-trivial negative part can be included. Furthermore, a special class of potentials is defined for which the size of the spectral gap is as least as large as for the free system and, surprisingly, the spectral gap is independent of the activity. This type of potentials should not show any phase transition for a given temperature at any activity.

Degenerative process and cell death in salivary glands of Rhipicephalus sanguineus (Latreille, 1806) (Acari: Ixodidae) semi-engorged female exposed to the acaricide permethrin

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Young ovine death during hyperimmunization: crotalic envenomation or copper toxicosis?

The unfavorable evolution of a young ovine during hyperimmunization process with Crotalus durissus terrificus venom was investigated in order to differentiate its origin between ophidic envenomation and copper toxicosis. Clinical, laboratory, necroscopic and histological exams as well as evaluation and measurement of heavy metals (copper) in the kidneys and in the liver were carried out. Blood counts revealed anemia and serological tests showed high levels of blood urea nitrogen, creatinine, aspartate aminotransferase, creatine phosphokinase, total bilirubin and indirect bilirubin; which indicates liver, kidney and skeletal muscle damages. At necropsy, the animal presented hepatopathy and nephropathy. Histological examination revealed renal and hepatic features that may imply copper intoxication. Copper levels were 237.8 mu g/g in the liver and 51.2 mu g/g in the kidneys. Although the amount of metal found in both organs was below the level that can cause death, according to the literature, anatomopathological signs were suggestive of copper intoxication. Therefore, the hypothesis of metal toxicosis during the hyperimmunization process became more consistent than the crotalic envenomation one.

Gibbs point process approximation: Total variation bounds using Stein's method

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.

AN ILLNESS-DEATH PROCESS WITH TIME-DEPENDENT COVARIATES

A general model for the illness-death stochastic process with covariates has been developed for the analysis of survival data. This model incorporates important baseline and time-dependent covariates to make proper adjustment for the transition probabilities and survival probabilities. The follow-up period is subdivided into small intervals and a constant hazard is assumed for each interval. An approximation formula is derived to estimate the transition parameters when the exact transition time is unknown.^ The method developed is illustrated by using data from a study on the prevention of the recurrence of a myocardial infarction and subsequent mortality, the Beta-Blocker Heart Attack Trial (BHAT). This method provides an analytical approach which simultaneously includes provision for both fatal and nonfatal events in the model. According to this analysis, the effectiveness of the treatment can be compared between the Placebo and Propranolol treatment groups with respect to fatal and nonfatal events. ^

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

On Multi- Server Queues With Consultation With Main Server

Queueing Theory is the mathematical study of queues or waiting lines. Queues abound in every day life - in computer networks, in tra c islands, in communication of electro-magnetic signals, in telephone exchange, in bank counters, in super market checkouts, in doctor's clinics, in petrol pumps, in o ces where paper works to be processed and many other places. Originated with the published work of A. K. Erlang in 1909 [16] on congestion in telephone tra c, Queueing Theory has grown tremendously in a century. Its wide range applications includes Operations Research, Computer Science, Telecommunications, Tra c Engineering, Reliability Theory, etc.