Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Multi-Agent Rendezvous Algorithm with Rectilinear Decision Domain

The aim of this paper is to develop a computationally efficient decentralized rendezvous algorithm for a group of autonomous agents. The algorithm generalizes the notion of sensor domain and decision domain of agents to enable implementation of simple computational algorithms. Specifically, the algorithm proposed in this paper uses a rectilinear decision domain (RDD) as against the circular decision domain assumed in earlier work. Because of this, the computational complexity of the algorithm reduces considerably and, when compared to the standard Ando's algorithm available in the literature, the RDD algorithm shows very significant improvement in convergence time performance. Analytical results to prove convergence and supporting simulation results are presented in the paper.

Rectilinear Path Following in 3D Space

This paper addresses the problem of determining an optimal (shortest) path in three dimensional space for a constant speed and turn-rate constrained aerial vehicle, that would enable the vehicle to converge to a rectilinear path, starting from any arbitrary initial position and orientation. Based on 3D geometry, we propose an optimal and also a suboptimal path planning approach. Unlike the existing numerical methods which are computationally intensive, this optimal geometrical method generates an optimal solution in lesser time. The suboptimal solution approach is comparatively more efficient and gives a solution that is very close to the optimal one. Due to its simplicity and low computational requirements this approach can be implemented on an aerial vehicle with constrained turn radius to reach a straight line with a prescribed orientation as required in several applications. But, if the distance between the initial point and the straight line to be followed along the vertical axis is high, then the generated path may not be flyable for an aerial vehicle with limited range of flight path angle and we resort to a numerical method for obtaining the optimal solution. The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

Larval Fish Recruitment and Research in the Americas: Proceedings of the Thirteenth Annual Larval Fish Conference Merida, Mexico, 21-26 May 1989

The 13th Annual Larval Fish Conference and Annual Meeting of the American Fisheries Society Early Life History Section cohosted by Mote Marine Laboratory, United States, and the Instituto Nacional de la Pesca, Mexico, were held 21-26 May 1989, in Merida, Yucatan, Mexico. The purpose of holding the meeting in Mexico was to encourage the participation of our Latin American and Caribbean colleagues and to provide a forum for the exchange of ideas and information among researchers working in the Americas. More than 150 participants represented 24 U.S. states, the District of Columbia, and 13 foreign countries including Mexico, Canada, Puerto Rico, Costa Rico, Panama, Cuba, Columbia, Chile, Peru, Brazil, Argentina, South Africa, and West Germany. The Conference began with registration and a social in the courtyard patio of the Merida Holiday Inn. Fresh red grouper, the most important commercial finfish species of the State of Yucatan, was prepared and served by the hotel staff, courtesy of CPI, Itzamex, and the Terramar Trading Company. (PDF file contains 146 pages.)

Non-governmental organizations and multi-sited marine conservation science: A case study

Non-governmental organizations (NGOs) are now major players in the realm of environmental conservation. While many environmental NGOs started as national organizations focused around single-species protection, governmental advocacy, and preservation of wilderness, the largest now produce applied conservation science and work with national and international stakeholders to develop conservation solutions that work in tandem with local aspirations. Marine managed areas (MMAs) are increasingly being used as a tool to manage anthropogenic stressors on marine resources and protect marine biodiversity. However, the science of MMA is far from complete. Conservation International (CI) is concluding a 5 year, $12.5 million dollar Marine Management Area Science (MMAS) initiative. There are 45 scientific projects recently completed, with four main “nodes” of research and conservation work: Panama, Fiji, Brazil, and Belize. Research projects have included MMA ecological monitoring, socioeconomic monitoring, cultural roles monitoring, economic valuation studies, and others. MMAS has the goals of conducting marine management area research, building local capacity, and using the results of the research to promote marine conservation policy outcomes at project sites. How science is translated into policy action is a major area of interest for science and technology scholars (Cash and Clark 2001; Haas 2004; Jasanoff et al. 2002). For science to move policy there must be work across “boundaries” (Jasanoff 1987). Boundaries are defined as the “socially constructed and negotiated borders between science and policy, between disciplines, across nations, and across multiple levels” (Cash et al. 2001). Working across the science-policy boundary requires boundary organizations (Guston 1999) with accountability to both sides of the boundary, among other attributes. (Guston 1999; Clark et al. 2002). This paper provides a unique case study illustrating how there are clear advantages to collaborative science. Through the MMAS initiative, CI built accountability into both sides of the science-policy boundary primarily through having scientific projects fed through strong in-country partners and being folded into the work of ongoing conservation processes. This collaborative, boundary-spanning approach led to many advantages, including cost sharing, increased local responsiveness and input, better local capacity building, and laying a foundation for future conservation outcomes. As such, MMAS can provide strong lessons for other organizations planning to get involved in multi-site conservation science. (PDF contains 3 pages)

HIV/AIDS-related institutional mistrust among multiethnic men who have sex with men: effects on HIV testing and risk behaviors.

OBJECTIVE: To investigate relationships between institutional mistrust (systematic discrimination, organizational suspicion, and conspiracy beliefs), HIV risk behaviors, and HIV testing in a multiethnic sample of men who have sex with men (MSM), and to test whether perceived susceptibility to HIV mediates these relationships for White and ethnic minority MSM. METHOD: Participants were 394 MSM residing in Central Arizona (M age = 37 years). Three dimensions of mistrust were examined, including organizational suspicion, conspiracy beliefs, and systematic discrimination. Assessments of sexual risk behavior, HIV testing, and perceived susceptibility to HIV were made at study entry (T1) and again 6 months later (T2). RESULTS: There were no main effects of institutional mistrust dimensions or ethnic minority status on T2 risk behavior, but the interaction of systematic discrimination and conspiracy beliefs with minority status was significant such that higher levels of systematic discrimination and more conspiracy beliefs were associated with increased risk only among ethnic minority MSM. Higher levels of systematic discrimination were significantly related to lower likelihood for HIV testing, and the interaction of organizational suspicion with minority status was significant such that greater levels of organizational suspicion were related to less likelihood of having been tested for HIV among ethnic minority MSM. Perceived susceptibility did not mediate these relationships. CONCLUSION: Findings suggest that it is important to look further into the differential effects of institutional mistrust across marginalized groups, including sexual and ethnic minorities. Aspects of mistrust should be addressed in HIV prevention and counseling efforts.