The classical theory of univalent functions and quasistatic crack propagation

We study the propagation of a crack in critical equilibrium for a brittle material in a Mode III field. The energy variations for small virtual extensions of the crack are handled in a novel way: the amount of energy released is written as a functional over a family of univalent functions on the upper half plane. Classical techniques developed in connection to the Bieberbach Conjecture are used to quantify the energy-shape relationship. By means of a special family of trial paths generated by the so-called Löwner equation we impose a stability condition on the field which derives in a local crack propagation criterion. We called this the anti-symmetry principle, being closely related to the well known symmetry principle for the in-plane fields

Arbitrage conditions with no short selling

A key assumption to prove the Fundamental Theorem of Mathematical Finance is the possibility of short selling the risky assets of the market. In this article we exhibit a simple geometric condition to handle the arbitrage opportunities when short selling is not possible. Moreover, this approach provides a pedagogical tool to visualize the consistency of the model when shorting is allowed for only some of the assets. Some examples are presented, both in analytical and graphical ways

Serosurvey for selected pathogens in Iberian roe deer

<p>Abstract</p> <p>Background</p> <p>The roe deer is the most abundant and widespread wild Eurasian cervid. Its populations are expanding and increasingly in contact with livestock. This may affect the distribution of infectious diseases shared with other wild and domestic ungulates.</p> <p>Methods</p> <p>We investigated the antibody seroprevalence against Pestivirus, Herpesvirus, Bluetongue (BT) virus, <it>M. avium paratuberculosis </it>(MAP), and <it>Brucella </it>sp. in 519 roe deer from different regions in Spain, south-western Europe.</p> <p>Results</p> <p>No antibodies were detected against BT and <it>Brucella </it>sp. However, antibodies were detected against Pestivirus (1.5%), Herpesvirus (0.2%) and MAP (9.2%). MAP antibodies were detected in seven of the eight populations (range 5-16.4%).</p> <p>Conclusions</p> <p>The detection of MAP antibodies in samples from most roe deer populations suggests that contact with MAP is widespread in this wildlife species. The highest prevalence was detected in sites with abundant dairy cattle and frequent use of liquid manure on pastures. Considering the results obtained regarding exposure to different pathogens, we suggest that antibody prevalences in this non-gregarious browser are largely determined by environmental factors, potentially modulating vector populations or pathogen survival in the environment.</p

Bone remodeling: A tissue-level process emerging from cell-level molecular algorithms

<div><p>The human skeleton undergoes constant remodeling throughout the lifetime. Processes occurring on microscopic and molecular scales degrade bone and replace it with new, fully functional tissue. Multiple bone remodeling events occur simultaneously, continuously and independently throughout the body, so that the entire skeleton is completely renewed about every ten years.Bone remodeling is performed by groups of cells called Bone Multicellular Units (BMU). BMUs consist of different cell types, some specialized in the resorption of old bone, others encharged with producing new bone to replace the former. These processes are tightly regulated so that the amount of new bone produced is in perfect equilibrium with that of old bone removed, thus maintaining bone microscopic structure.To date, many regulatory molecules involved in bone remodeling have been identified, but the precise mechanism of BMU operation remains to be fully elucidated. Given the complexity of the signaling pathways already known, one may question whether such complexity is an inherent requirement of the process or whether some subset of the multiple constituents could fulfill the essential role, leaving functional redundancy to serve an alternative safety role. We propose in this work a minimal model of BMU function that involves a limited number of signals able to account for fully functional BMU operation. Our main assumptions were i) at any given time, any cell within a BMU can select only one among a limited choice of decisions, i.e. divide, die, migrate or differentiate, ii) this decision is irreversibly determined by depletion of an appropriate internal inhibitor and iii) the dynamics of any such inhibitor are coupled to that of specific external mediators, such as hormones, cytokines, growth factors. It was thus shown that efficient BMU operation manifests as an emergent process, which results from the individual and collective decisions taken by cells within the BMU unit in the absence of any external planning.</p></div

Curvature tensor and collective behavior in a population of bacteria

In this work, from a geometric point of view, we analyze the SET model (Schweitzer, Ebeling and Tilch) of the mobility of a bacterium. Biological systems are out of thermodynamic equilibrium and they are subject to complex external or internal influences that can be modeled in the form of noise or fluctuations. In this sense, due to the stochasticity of the variables, we study the probability of finding a bacteria with a speed v in the interval (v; v +dv) or, from a population point of view, we can interpret the probability density function as associated with finding a bacterium with a speed v in the interval (v; v +dv). We carry out this study from the stationary probability density solution of the Fokker-Planck equation and using the structure of the statistical manifold related with the stationary probability density, we study the curvature tensor in terms of two coordinates associated with the state of mobility of the bacteria and the environmental conditions. Taking as reference the geometric interpretations found in the framework of equilibrium thermodynamics, our results suggest that bacteria have an effective repulsive interaction that increases with mobility. These results are compatible with the behavior of populations of bacteria that form biofilms when their mobility decreases

Internacionalización de los estudios de másteres en Matemáticas: un paso adelante

Fac. de Ciencias MatemáticasFALSEsubmitte

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure

Sobre la ecuación de black-scholes

Exploramos la deducción de la ecuación de Black-Scholes de tres maneras distintas y explicamos por qué la ecuación es necesaria en un contexto de precios estocásticos. Despues de introducir las herramientas básicas aplicamos las siguientes estrategias para su deducción: la primera utilizala idea de replicación con una cartera autofinanciada, la segunda utiliza la eliminación local del riesgo y el concepto de precio del riesgo en el mercado, y la tercera considera la replicación para el precio forward de la opción en función del precio forward del activo. Cuando el precio del subyacente es estocástico concluimos que, para obtener el precio de unaopción, es necesario disponer de un modelo de evolución del precio del activo, pues otras estrategias ingenuas de valoración no son aplicables