Geometric Stability Switch Criteria in Delay Differential Systems with Delay-dependent Parameters
- Edoardo Beretta; Yang Kuang
In most applications of delay di#erential equations in population dynamics, the need of incorporation of time delays is often the result of the existence of some stage structure. Since the through-stage survival rate is often a function of time delays, it is thus easy to conceive that these models may involve some delay dependent parameters. The presence of such parameters often greatly complicates the task of an analytical study of such models. The main objective of this paper is to provide practical guidelines that combine graphical information with analytical work to e#ectively study the local stability of some models involving...
Solving gap metabolites and blocked reactions in genome-scale models: application to the metabolic network of Blattabacterium cuenoti
- Ponce-de-Leon, Miguel; Montero, Francisco J; Peretó, Juli
Background:Metabolic reconstruction is the computational-based process that aims to elucidate the network of metabolites interconnected through reactions catalyzed by activities assigned to one or more genes. Reconstructed models may contain inconsistencies that appear as gap metabolites and blocked reactions. Although automatic methods for solving this problem have been previously developed, there are many situations where manual
curation is still needed.
Results:We introduce a general definition of gap metabolite that allows its detection in a straightforward manner.
Moreover, a method for the detection of Unconnected Modules, defined as isolated sets of blocked reactions
connected through gap metabolites, is proposed. The method has been successfully applied...
Métodos en Biomatemática I: Cálculo Integral y Álgebra Lineal con wxMaxima
- Lahoz Beltrá, Rafael
Perfil paleodemográfico Muisca: el caso del cementerio de Soacha, Cundinamarca
- Rodríguez Cuenca, José Vicente
En las dos últimas décadas los bioantropólogos y arqueólogos han aunado un gran interés por documentar y explicar los cambios en la estructura poblacional de las comunidades prehistóricas, tanto en el plano evolutivo como en el tránsito de las sociedades cazadoras recolectoras y horticultoras a la agricultura. La medición e interpretación de las diferencias en el nivel de salud, en las expectativas de vida, en las tasas de mortalidad, fecundidad y crecimiento poblacional es uno de los objetivos principales de la paleodemografía y paleopatología (Milner et al., 1989). Mientras que la demografía se considera objetiva en cuanto se basa en...
Efectos de la estimulación artificial de un nervio periférico seccionado sobre la vía somatosensorial desaferentizada de la rata
- Herrera Rincón, Celia
Métodos en Biomatemática II: Ecuaciones Diferenciales con wxMaxima
- Lahoz Beltra, Rafael
En este manual, y haciendo uso del sistema de álgebra computacional wxMaxima, se describen técnicas y métodos fundamentales en Biología Matemática, en particular algunos modelos clásicos de ecuaciones diferenciales ordinarias(EDOs) así como la metodología para resolver con wxMaxima sistemas de dos y tres ecuaciones diferenciales lineales de primer orden.
Un vistazo a la Biomatemática
- Lombardero Ozores, Antón
Mathematical Biology, or the use of mathematical tools to deal with aspects of Biology,
Medicine, Ecology or Environmental Sciences, is an active branch of Science with a
major predictable projection in the coming decades. The positive impact of the
introduction of mathematical concepts and techniques in the field of Life Sciences are
already noticeable. This article is a brief introduction to this discipline, dealing with both
historical aspects and application examples.
A model for acid-mediated tumour growth with nonlinear acid production term
- Holder, Andrew B.; Rodrigo, Marianito R.; Herrero, Miguel A.
This article considers a mathematical model for tumour growth based on an acid-mediated hypothesis, i.e. the assumption that tumour progression is facilitated by acidification of the region around the tumour-host interface. The resulting destruction of the normal tissue environment promotes tumour growth. We will derive and analyse a reaction–diffusion model for tumour progression that includes different aspects of pathological and healthy cell metabolism to check tumour growth. Our results can provide insights into the governing dynamics of invasive processes that may suggest possible intervention strategies, leading to the design of new and better experiments or treatments.
Comparison of Modal Variables Using Multivariate Analysis
- Doria, Isabel; Sousa, Áurea; Bacelar-Nicolau, Helena; Le Calvé, Georges
Domiciliary palliative care satisfaction and quality were estimated by caregivers via ﬁve perception scales with partly ordered answering modalities. The perception scales were codiﬁed as symbolic modal variables and analyzed using two multivariate approaches based on complex (symbolic) data to compare modal variables. This study compares the outcomes of previous work by Doria (Representações euclidianas de dados: Uma abordagem para variáveis heterogéneas. Tese de doutoramento, Universidade de Lisboa, Lisboa, 2008), Doria et al. (Livro de Resumos da XI Conferencia Española de Biometria e Primer Encuentro Iberoamericano de Biometria (CEIB2007)101–102,2007) and Bacelar-Nicolau et al. (Revista Portuguesa de Filosoﬁa 66(2):427–460,2010). In particular,...
Biometria florestal: modelos de crescimento e produção: anais.
- REUNIÃO TÉCNICA, 2013, Colombo.
Crescimento e produção florestal; Crescimento e produção das variáveis dendrométricas; Variáveis fundamentais nos modelos de produção; Métodos para estimativa da altura por meio da análise de tronco; Métodos para classificação de sítios florestais; Técnicas de predição e projeção do crescimento e produção como suporte para o manejo florestal; Modelos biomatemáticos e modelos implícitos de produção e crescimento; Modelos para povoamentos desbastados; Modelos para árvores individuais; Modelagem em florestas nativas; Taxa de corte sustentada em Floresta Ombrófila Densa.
The mathematics of chemotaxis
- Herrero, Miguel A.
This chapter provides a description of some of the mathematical approaches that have been developed to account for quantitative and qualitative aspects of chemotaxis. This last is an important biological property, consisting in motion of cells induced by chemical substances, which is known to occur in a large number of situations, both homeostatic and pathological. Particular attention will be paid to the limits on a cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slime mold Dictyostelium discoideum on the other.
Reaction-diffusion systems: a mathematical biology approach
- Herrero, Miguel A.
This book is addressed at curricula in applied mathematics, bio-physics, bio-mathematics, and theoretical biology and medicine. It is proposed as an advanced textbook for graduate interdisciplinary courses having as a common point the interest in modelling and simulation of tumoural systems. The aim of this volume is to give both types of readers a common starting block, and complete knowledge of the mathematical and biological aspects of tumor growth. In the chapters contributed by an interdisciplinary team of leading researchers, this book addresses the entire modelling process, from phenomenological observations to simulation and validation, through the development of mathematical models...
Bone formation: biological aspects and modelling problems
- Herrero, Miguel A.; López, J. M.
In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and desirable. In this way, a number of open questions are formulated whose study seems to require interaction among mathematical analysis and biological
Lines and nets: models of filamentary structures
- Herrero, Miguel A.
We shall recall some reaction-difussion models which have been used to describe the growth of net-like structures, mainly in a biological context. In particular, a modified activator-inhibitor system proposed by Hans Meinhardt in 1976 will be considered, and some properties of their solutions will be analyzed
A blow-up mechanism for a chemotaxis model
- Herrero, Miguel A.; Velázquez, J.J. L.
We consider the following nonlinear system of parabolic equations: (1) ut =Δu−χ∇(u∇v), Γvt =Δv+u−av for x∈B R, t>0. Here Γ,χ and a are positive constants and BR is a ball of radius R>0 in R2. At the boundary of BR, we impose homogeneous Neumann conditions, namely: (2) ∂u/∂n=∂v/∂n=0 for |x|=R, t>0.
Problem (1),(2) is a classical model to describe chemotaxis, i.e., the motion of organisms induced by high concentrations of a chemical that they secrete. In this paper we prove that there exist radial solutions of (1),(2) that develop a Dirac-delta type singularity in finite time, a feature known in...
Asymptotic properties of reaction-diffusion systems modeling chemotaxis
- Herrero, Miguel A.
This paper examines a system first introduced by Keller and Segel in 1970 to model the tendency of slime molds to move towards higher concentrations of a chemical which they themselves secrete. The paper particularly addresses the question of blow-up or chemotactic collapse, i.e., the formation of single point aggregations of the cells. Results are discussed for 2 and 3 space dimensions. Asymptotic computations yield information on the manner of the blow-up.
A mathematical model for the growth of elongated bones
- Fasano, A.; Herrero, Miguel A.; López, J. M.; Medina Reus, Elena
A mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling molecules. These molecules characterize the dynamics of the transition zone between the cartilage and the bone tissue. Some experimental data are needed to estimate some model parameters. We discuss
how our results are essentially unaffected by small variations, and in a particular case, not necessarily small variations in the experimental values.
Modelo não isotérmico de um biorreator experimental
- Luvizetto, Débora Jung; Ferreira, Luciane da Silveira; Longhi, Luís Gustavo Soares; Rech, Rosane; Ayub, Marco Antônio Záchia; Secchi, Argimiro Resende
Linear stability analysis and metastable solutions for a phase-field model
- Jiménez Casas, Ángela; Rodríguez Bernal, Aníbal
We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable solutions that evolve very slowly in time.
Models of aggregation in Dictyostelium discoideum: On the track of spiral waves
- Herrero, Miguel A.; Sastre, Leandro
This work is concerned with some aspects of the social life of the amoebae Dictyostelium discoideum (Dd). In particular, we shall focus on the early stages of the starvation-induced aggregation of Dd cells. Under such circumstances, amoebae are known to exchange a chemical messenger (cAMP) which acts as a signal to mediate their individual behaviour. This molecule is released from aggregation centres and advances through aggregation fields, first as circular waves and later on as spiral patterns. We shall recall below some of the basic features of this process, paying attention to the mathematical models that have been derived to...