The advantage of being slow: The quasi-neutral contact process.

According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which mechanisms confer an advantage to a given species against the other(s)? In general, it is expected that the species with the higher reproductive/death ratio will win the competition, but other mechanisms, such as asymmetry in interspecific competition or unequal diffusion rates, have been found to change this scenario dramatically. In this work, we examine competitive advantage in the context of quasi-neutral population models, including stochastic models with spatial structure as well as macroscopic (mean-field) descriptions. We employ a two-species contact process in which the "biological clock" of one species is a factor of α slower than that of the other species. Our results provide new insights into how stochasticity and competition interact to determine extinction in finite spatial systems. We find that a species with a slower biological clock has an advantage if resources are limited, winning the competition against a species with a faster clock, in relatively small systems. Periodic or stochastic environmental variations also favor the slower species, even in much larger systems.

A 61-year-old woman with adult T-cell leukemia÷lymphoma.

Adult T-cell leukemia÷lymphoma (ATL) is caused by human T-cell lymphotropic virus type-1 (HTLV-1) infection. Classification of ATL includes acute, chronic, lymphomatous and smoldering, and main features are hypercalcemia, organomegaly, bone, brain, lung, and skin changes. Elevated mortality rates of ATL may be due to the advanced age at diagnosis, because this malignancy can evolve unsuspected for decades before the first clinical manifestations. Palliative therapy, chemotherapy and stem cell transplantation are often utilized, but response to treatment is poor. The patient herein reported presented diffuse abdominal pain with duration of eight months in addition to ascites. The diagnosis of the acute leukemia type of ATL was done with base on clinical, laboratory and imaging findings. Gastrointestinal symptoms and ascites are uncommon first manifestations of ATL, and pose challenging diagnosis.

Phase diagram of the symbiotic two-species contact process.

We study the two-species symbiotic contact process, recently proposed by de Oliveira, Santos, and Dickman [Phys. Rev. E 86, 011121 (2012)]. In this model, each site of a lattice may be vacant or host single individuals of species A and/or B. Individuals at sites with both species present interact in a symbiotic manner, having a reduced death rate µ<1. Otherwise, the dynamics follows the rules of the basic contact process, with individuals reproducing to vacant neighbor sites at rate λ and dying at a rate of unity. We determine the full phase diagram in the λ-µ plane in one and two dimensions by means of exact numerical quasistationary distributions, cluster approximations, and Monte Carlo simulations. We also study the effects of asymmetric creation rates and diffusion of individuals. In two dimensions, for sufficiently strong symbiosis (i.e., small µ), the absorbing-state phase transition becomes discontinuous for diffusion rates D within a certain range. We report preliminary results on the critical surface and tricritical line in the λ-µ-D space. Our results raise the possibility that strongly symbiotic associations of mobile species may be vulnerable to sudden extinction under increasingly adverse conditions.

Symbiotic two-species contact process.

We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited. Symbiosis is represented by a reduced death rate µ<1 for individuals at sites with both species present. Otherwise, the dynamics is that of the basic CP, with creation (at vacant neighbor sites) at rate λ and death of (isolated) individuals at a rate of unity. Mean-field theory and Monte Carlo simulation show that the critical creation rate λ(c)(µ) is a decreasing function of µ, even though a single-species population must go extinct for λ<λ(c) (1), the critical point of the basic CP. Extensive simulations yield results for critical behavior that are compatible with the directed percolation (DP) universality class, but with unusually strong corrections to scaling. A field-theoretic argument supports the conclusion of DP critical behavior. We obtain similar results for a CP with creation at second-neighbor sites and enhanced survival at first neighbors in the form of an annihilation rate that decreases with the number of occupied first neighbors.

Orthodontic treatment of a patient with Lowe syndrome.

This article describes the orthodontic treatment of a patient with Lowe syndrome. The objective of the treatment was to improve the patient's dental relationships and consequently his quality of life. This was achieved by maxillary expansion and extraction of the mandibular central incisors and maxillary deciduous canines. The teeth were aligned and leveled with a fixed orthodontic appliance. Satisfactory results were obtained at the end of treatment, with substantial improvement in dental esthetics, occlusal function, and facial profile.

Contact process with sublattice symmetry breaking.

We study a contact process with creation at first- and second-neighbor sites and inhibition at first neighbors, in the form of an annihilation rate that increases with the number of occupied first neighbors. Mean-field theory predicts three phases: inactive (absorbing), active symmetric, and active asymmetric, the latter exhibiting distinct sublattice densities on a bipartite lattice. These phases are separated by continuous transitions; the phase diagram is re-entrant. Monte Carlo simulations in two dimensions verify these predictions qualitatively, except for a first-neighbor creation rate of zero. (In the latter case one of the phase transitions is discontinuous.) Our numerical results confirm that the symmetric-asymmetric transition belongs to the Ising universality class, and that the active-absorbing transition belongs to the directed percolation class, as expected from symmetry considerations.

How to simulate the quasistationary state.

For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasistationary (QS) regime. We propose a practical simulation method for studying quasistationary properties, based on the equation of motion governing the QS distribution. In applications to the contact process, the method is shown to reproduce exact results (for the process on a complete graph) and known scaling behavior to high precision. At the critical point, our method is about an order of magnitude more efficient than conventional simulation.