An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal

The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable, quantitatively-accurate, individual-level model. However, important problems in areas ranging from ecology to medicine involve large collections of individuals, and a further intellectual challenge is to model population-level behavior based on a detailed individual-level model. Because of the large number of interacting individuals and because the individual-level model is complex, classical direct Monte Carlo simulations can be very slow, and often of little practical use. In this case, an equation-free approach may provide effective methods for the analysis and simulation of individual-based models. In this paper we analyze equation-free coarse projective integration. For analytical purposes, we start with known partial differential equations describing biological random walks and we study the projective integration of these equations. In particular, we illustrate how to accelerate explicit numerical methods for solving these equations. Then we present illustrative kinetic Monte Carlo simulations of these random walks and show a decrease in computational time by as much as a factor of a thousand can be obtained by exploiting the ideas developed by analysis of the closed form PDEs. The illustrative biological example here is chemotaxis, but it could be any random walker which biases its movement in response to environmental cues.Comment: 30 pages, submitted to Physica

Physical Surveys of Over 300 Buildings in Hot and Humid Climates Indicate Material/Design Performance Flaws Exist in Comparison to Expected Results Using Nationally Accepted Standards

Surveys conducted by the State of Florida Energy Offices Energy Conservation Assistance Program (ECAP) at the University of South Florida and other participating centers, over a 10 year period, have consistently shown that construction materials including windows, skylighting, insulation, and major HVAC systems components do not perform as well as expected in installed / finished product state. The end result is buildings designed with calculations taken from standard ASTM and ASHRAE formulas do not deliver the comfort levels expected by the design engineers or the facility occupants

Coupling geometric PDEs with physics, cell morphology, motility and pattern formation

Annual report on the 6-months research programme held at the Isaac Newton Institute for Mathematical Sciences on Coupling geometric PDEs with physics for cell morphology, motility and pattern formation from July 13th - December 18th 201

From microscopic to macroscopic descriptions of cell\ud migration on growing domains

Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs

A case study of a radially polarized Pc4 event observed by the Equator-S satellite

International audienceA 16 mHz Pc4 pulsation was recorded on March 17, 1998, in the prenoon sector of the Earth's magnetosphere by the Equator-S satellite. The event is strongly localized in radial direction at approximately L = 5 and exhibits properties of a field line resonance such as an ellipticity change as seen by applying the method of the analytical signal to the magnetic field data. The azimuthal wave number was estimated as m \approx 150. We discuss whether this event can be explained by the FLR mechanism and find out that the change in ellipticity is more a general feature of a localized Alfvén wave than indicative of a resonant process

Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source

This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Wild edible fruits as a potential source of phytochemicals with capacity to inhibit lipid peroxidation

The edible fruits of four wild small trees or shrubs (Arbutus unedo, Crataegus monogyna, Prunus spinosa and Rubus ulmifolius) traditionally consumed in the Iberian Peninsula were studied to evaluate their potential for human nutrition, considering their content in bioactive compounds. Lipophilic phytochemicals, such as fatty acids and tocopherols, as well as some hydrophilic antioxidants, such as vitamin C (ascorbic and dehydroascorbic acids), and organic acids, were analysed. In addition, the antioxidant activity, measured as lipid peroxidation inhibition (β-carotene/linoleate and TBARS assays), was evaluated in each fruit. As far as we know, this is the first report relating to bioactive compounds in wild fruits with relation to the lipid peroxidation inhibition. Data revealed that these wild edible fruits are good sources of bioactive compounds such as ascorbic acid, tocopherols and polyunsaturated fatty acids. They could be considered as functional foods or potential sources of lipidic bioactive compounds to be included as antioxidant food ingredients or in dietary supplements, mainly Rubus ulmifolius, due to its high content in tocopherols. This study provides useful and relevant information that justify tocopherols influence in the prevention of lipid peroxidation, due to the strong correlation observed (r > 0.95) between these lipophilic bioactive compounds and the antioxidant activity.ERDF and the Spanish Ministry of Education and Science (CGL2006-09546/BOS). The authors are also grateful to Fundação para a Ciência e a Tecnologia (FCT, Portugal) and COMPETE/QREN/EU for financial support to CIMO (strategic project PEst-OE/AGR/UI0690/2011). We also thank to María Molina, Laura Aceituno, Susana González, and Manuel Pardo de Santayana for their collaboration in the gathering and preparation of the samples