Modelling is a tool used to decipher the biochemical mechanisms involved in transcriptional control. Experimental evidence in genetics is usually supported by theoretical models in order to evaluate the effects of all the possible interactions that can occur in these complicated processes. Models derived from the thermodynamic method are critical in this labour because they are able to take into account multiple mechanisms operating simultaneously at the molecular micro-scale and relate them to transcriptional initiation at the tissular macro-scale. This work is devoted to adapting computational techniques to this context in order to theoretically evaluate the role played by several biochemical mechanisms. The interest of this theoretical analysis relies on the fact that it can be contrasted against those biological experiments where the response to perturbations in the transcriptional machinery environment is evaluated in terms of genetically activated/repressed regions. The theoretical reproduction of these experiments leads to a sensitivity analysis whose results are expressed in terms of the elasticity of a threshold function determining those activated/repressed regions. The study of this elasticity function in thermodynamic models already proposed in the literature reveals that certain modelling approaches can alter the balance between the biochemical mechanisms considered, and this can cause false/misleading outcomes. The reevaluation of classical thermodynamic models gives us a more accurate and complete picture of the interactions involved in gene regulation and transcriptional control, which enables more specific predictions. This sensitivity approach provides a definite advantage in the interpretation of a wide range of genetic experimental results.

This work provides theoretical tools to analyse the transcriptional effects of certain biochemical mechanisms (i.e. affinity and cooperativity) that have been proposed in previous literature to explain the proper spatial expression of Hedgehog target genes involved in Drosophila development. Specifically we have focused on the expression of decapentaplegic, wingless, stripe and patched. The transcription of these genes is believed to be controlled by enhancer modules able to interpret opposing gradients of the activator and repressor forms of the transcription factor Cubitus interruptus (Ci). This study is based on a thermodynamic approach, which provides expression rates for these genes. These expression rates are controlled by transcription factors which are competing and cooperating for common binding sites. We have made mathematical representations of the different expression rates which depend on multiple factors and variables. The expressions obtained with the model have been refined to produce simpler equivalent formulae which allow for their mathematical analysis. Thanks to this, we can evaluate the correlation between the different interactions involved in transcription and the biological features observed at tissular level. These mathematical models can be applied to other morphogenes to help understand the complex transcriptional logic of opposing activator and repressor gradients.

This paper is devoted to the analysis of qualitative properties of flux-saturated type operators in dimension one. Specifically, we study regularity properties and smoothing effects, discontinuous interfaces, the existence of traveling wave profiles, sub- and super-solutions and waiting time features. The aim of the paper is to better understand these kind of phenomena throughout two prototypic operators: The relativistic heat equation and the porous media flux-limited equation. As an important consequence of our results we deduce that solutions to the one-dimensional relativistic heat equation become smooth inside their support on the long time run.

A non-linear PDE featuring flux limitation effects together with those of the porous media equation (non-linear Fokker–Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and qualitative behavior of some admissible patterns, namely traveling wave solutions, to this singular reaction–diffusion equation. We show the existence and qualitative behavior of different types of traveling waves: classical profiles for wave speeds high enough, and discontinuous waves that are reminiscent of hyperbolic shock waves when the wave speed lowers below a certain threshold. Some of these solutions are of particular relevance as they provide models by which the whole solution (and not just the bulk of it, as it is the case with classical traveling waves) spreads through the medium with finite speed.

Una de las ultimas tendencias en el area de las TIC (Tecnologias de la Informacion y Comunicacion) es la adopcion del paradigma de Computacion en la Nube (Cloud Computing). Cloud Computing aboga por el uso de recursos computacionales (redes, servidores, almacenamiento, asi como aplicaciones y servicios software) de terceros prestados como servicios, evitando el despliegue y mantenimiento de una infraestructura propia. Las Smart Cities no pueden permanecer ajenas a este nuevo modelo de prestacion de servicios. Contar con una plataforma flexible y escalable puede dar solucion a momentos de aumento de la demanda de determinados servicios. Las ciudades modernas pugnan por un espacio de relevancia en este ambito, buscando implementar politicas de desarrollo sostenible que respondan a las necesidades basicas de instituciones, empresas y de los propios habitantes, tanto en lo economico, como en los aspectos operativos, sociales y medioambientales. Por ello, las ciudades modernas deben orientarse a mejorar el confort (servicio) de los ciudadanos, siendo cada vez mas eficaces y brindando una mayor calidad en el servicio, mientras respetan al maximo los aspectos medioambientales y el uso prudente de los recursos naturales no renovables. El concepto de ciudad inteligente implica maximizar el uso de las TIC para mejorar la calidad de vida poniendo a disposicion del usuario multitud de servicios y aplicaciones a traves de Internet. Por ello, hay una tendencia en el desarrollo software para Smart Cities bajo el paradigma de Cloud Computing. Este Proyecto de Fin de Grado (PFG) aborda el estudio y uso de Cloud Computing como paradigma de desarrollo en proyectos TIC. El PFG describe nociones basicas del cambio de modelo que introduce Cloud, asi como los diferentes modelos de servicio que ofrece: infraestructura, plataforma de desarrollo y software (IaaS, PaaS y SaaS, respectivamente). Ademas, se presentan los principales proveedores que se encuentran en el mercado, incidiendo de manera especial en Microsoft y su PaaS Azure, pormenorizando sus caracteristicas mas relevantes: suscripciones, planes de servicios y recursos, asi como los servicios de desarrollo que ofrece. El objetivo principal de este Proyecto Final de Grado (PFG) es el estudio y uso de la plataforma de desarrollo en la nube Microsoft Azure, mediante el desarrollo y posterior despliegue de un servicio del dominio de las Smart Cities que soporte interoperabilidad entre sistemas heterogeneos, identificacion y autenticacion, gestion de bases de datos y ejecucion de procesos en segundo plano de forma transparente al usuario. La utilizacion del Service Bus de Azure para la comunicacion entre sistemas y el uso de WebJobs para implementar procesos de segundo plano son los elementos centrales y mas significativos de este desarrollo que se han utilizado de la PaaS (Platform as a Service) de Microsoft, ya que representan soluciones efectivas a problemas que se presentan en numerosas ocasiones. Concretamente, el servicio disenado, desarrollado y desplegado en la nube para poner en practica estos conceptos es un Sistema de Control de Estacionamientos para la Policia Municipal de Mostoles. De esta manera, a traves de este caso practico y su descripcion detallada, se demuestra el como usar de un conjunto de servicios avanzados proporcionados por la PaaS de Microsoft y su utilidad para las necesidades actuales de los proyectos TIC. ABSTRACT Cloud Computing is one of the latest trends in the area of ICT (Information and Communications Technology). Cloud Computing advocates the use of computer resources (networks, servers, storage and software applications and services) provided as third-party services, avoiding the deployment and maintenance of in-house infrastructure. Smart Cities cannot remain outside this new model of service provisioning. Modern cities compete to implement sustainable development policies that provide the basic needs of institutions, companies, and citizens regarding with economic, operational, social, and environmental aspects. Therefore, modern cities should aim at improving the comfort (service) of citizens, becoming more efficient and providing better quality of service, while respecting environmental aspects and the prudent use of nonrenewable natural resources. The smart city concept involves maximizing the use of ICT to improve the quality of life by providing the user with a multitude of services and applications over the Internet. Flexible and scalable platforms on cloud can deal with times of increased demand for certain ‘smart city services’. Therefore, the adoption of the Cloud Computing paradigm in the development of Smart Cities services is becoming a trend for the last years. This Final Degree Project (FDP) deals with the study and use of Cloud Computing as a paradigm for developing ICT projects, specifically in the domain of Smart Cities. The FDP describes the basics of model change that Cloud introduces, as well as different service models that Cloud offers: infrastructure, development platform and software (IaaS, PaaS and SaaS, respectively). Cloud vendors are also briefly presented, with special attention to Microsoft and its Azure PaaS, by describing its most important features: subscriptions, service plans and resources, as well as development services. The main goal of this Final Degree Project (FDP) is the study and use of the cloud development platform of Microsoft Azure by developing and then deploying a service for the Smart Cities domain. This service is characterized by supporting interoperability among hetereogeneous systems, identification and authentication, database management, and execution of background processes. The use of Azure Service Bus for communication among systems and the use of WebJobs to implement background processes are the central and most significant elements of this development that has been used of the Microsoft PaaS (Platform as a Service), as they represent effective solutions to representative problems of smart cities. Specifically, to put these concepts into practice, it has been designed, developed and deployed a service for a Parking Management System of the Municipal Police of Mostoles. As a result, this case study demonstrates the use advanced services of the Microsoft PaaS and their utility in the current needs of ICT projects.

The aim of this paper is to review the main recent results about the dynamics of nonlinear partial differential equations describing flux-saturated transport mechanisms, eventually in combination with porous media flow and/or reactions terms. The result is a system characterized by the presence of wave fronts which move defining an interface. This can be used to model different process in applications in a variety of areas as Developmental Biology or Astrophysics. The concept of solution and its properties (well-posedness in a Bounded Variation scenario, Rankine–Hugoniot and geometric conditions for jumps, regularity results, finite speed of propagation, …), qualitative study of these fronts (traveling waves in particular) and application in morphogenesis cover the panorama of this review.

Hedgehog (Hh) molecules act as morphogens directing cell fate during development by activating various target genes in a concentration dependent manner. Hitherto, modeling morphogen gradient formation in multicellular systems has employed linear diffusion, which is very far from physical reality and needs to be replaced by a deeper understanding of nonlinearities. We have developed a novel mathematical approach by applying flux-limited spreading (FLS) to Hh morphogenetic actions. In the new model, the characteristic velocity of propagation of each morphogen is a new key biological parameter. Unlike in linear diffusion models, FLS modeling predicts concentration fronts and correct patterns and cellular responses over time. In addition, FLS considers not only extracellular binding partners influence, but also channels or bridges of information transfer, such as specialized filopodia or cytonemes as a mechanism of Hh transport. We detect and measure morphogen particle velocity in cytonemes in the Drosophila wing imaginal disc. Indeed, this novel approach to morphogen gradient formation can contribute to future research in the field.

This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell–Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration–compactness method.

Spanish MINECO; Marie Curie FP6 (RTN035528-2); FP7(ITN238186); Fundacion Areces; Juntad e Andalucia (Project P08-FQM-4267); Swiss National Science Foundation; the University of Geneva; European Research Council; Leenaards foundation; European Molecular Biology Organization (younginvestigatorprogram); Cantonet Republique de Geneveto

In this paper we study the existence and qualitative properties of traveling waves associated with a nonlinear flux limited partial differential equation coupled to a Fisher–Kolmogorov–Petrovskii–Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C2 classical regularity, but also the existence of discontinuous entropy traveling wave solutions.

A central question in biology is how secreted morphogens act to induce different cellular responses within a group of cells in a concentration-dependent manner. Modeling morphogenetic output in multicellular systems has so far employed linear diffusion, which is the normal type of diffusion associated with Brownian processes. However, there is evidence that at least some morphogens, such as Hedgehog (Hh) molecules, may not freely diffuse. Moreover, the mathematical analysis of such models necessarily implies unrealistic instantaneous spreading of morphogen molecules, which are derived from the assumptions of Brownian motion in its continuous formulation. A strict mathematical model considering Fick's diffusion law predicts morphogen exposure of the whole tissue at the same time. Such a strict model thus does not describe true biological patterns, even if similar and attractive patterns appear as results of applying such simple model. To eliminate non-biological behaviors from diffusion models we introduce flux-limited spreading (FLS), which implies a restricted velocity for morphogen propagation and a nonlinear mechanism of transport. Using FLS and focusing on intercellular Hh-Gli signaling, we model a morphogen gradient and highlight the propagation velocity of morphogen particles as a new key biological parameter. This model is then applied to the formation and action of the Sonic Hh (Shh) gradient in the vertebrate embryonic neural tube using our experimental data on Hh spreading in heterologous systems together with published data. Unlike linear diffusion models, FLS modeling predicts concentration fronts and the evolution of gradient dynamics and responses over time. In addition to spreading restrictions by extracellular binding partners, we suggest that the constraints imposed by direct bridges of information transfer such as nanotubes or cytonemes underlie FLS. Indeed, we detect and measure morphogen particle velocity in such cell extensions in different systems.

This paper is concerned with the analysis of asymptotic problems from discrete drift-diffusion models describing charge transport in semiconductor superlattices. The regimes we are interested in lead to balance laws. However, the nonconservative structure of the discrete system might produce defect measure terms in the limit process. These defect terms, concentrated on the shock discontinuities, can be related to nonstandard jump relations (in contrast with the usual Rankine–Hugoniot law) when considering discontinuous solutions and wave fronts.

It is well known that steady states of the Vlasov-Poisson system, a widely used model in non-relativistic galactic dynamics, have negative energy. In this paper we derive the analogous property for two relativistic generalizations of the Vlasov-Poisson system: The Nordstr\"om-Vlasov system and the Einstein-Vlasov system. In the first case we show that the energy of steady states is bounded by their total rest mass; in the second case, where we also assume spherical symmetry, we prove an inequality which involves not only the energy and the rest mass, but also the central redshift. In both cases the proof makes use of integral inequalities satisfied by time depedent solutions and which are derived using the vector fields multipliers method.

The aim of this work is to give some insight into the controversy between N-body simulations and observations of cold dark matter (CDM) halos by considering polytropic DM spheres associated to a collisionless gravitational Boltzmann–Poisson (BP) system. Our resulting polytrope model is used to make predictions on the behavior of the CDM halos in those regions in which the numerical models cannot produce detailed results, i.e. near the center < 1 kpc (due to resolution limitations), and at the rim (as halos cannot have infinite extent). These provides a complementary information where other models present difficulties to make predictions.

The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally dispersive solutions and a sufficient condition for the occurence of statistical dispersion. These conditions take the form of inequalities involving the energy, the mass and the momentum of the solution. Examples of dispersive and non-dispersive solutions-steady states, periodic solutions and virialized solutions-are also considered.

Collisionless particles in dark matter halos constitute ideal systems for applying the theory of collisionless Boltzmann–Poisson (BP) polytropes. This analysis provides a powerful complementary method for studying galactic halos. A comparison of the results obtained here and the Navarro, Frenk and White (NFW), Isothermal and Burkert profiles is shown. We obtain very good agreement with NFW profiles with errors of the order of 3%. The best polytropic profile for a finite mass halo is close to the Plummer/Schuster profile. We can explore in detail the central region and find the inner profile that complements the NFW profile. A simple formula for the inner region to which the NFW should converge for R→0 could be ρ=ρ0(1−(R/C)2)4.7, ρ0 and C being constants. Boltzmann–Poisson polytropes provide a theoretical approach fully compatible with the universal NFW profiles at intermediate radii and complementing them at low radii: they permit the determination of the density profile in the inner kiloparsec inaccessible to N-body simulations because of resolution limits.

In this paper, motivated by the Galilean invariance of the solutions, we use the concept of orbital stability for the Vlasov–Poisson system. We prove that a family of stationary solutions, called polytropic gas spheres, are orbitally L 1 stable in the gravitational case by considering direct variational arguments.

This paper1 is intended to constitute a review of some mathematical theories incorporating quantum corrections to the Schrödinger-Poisson (SP) system. More precisely we shall focus our attention in the electrostatic Poisson potential with corrections of power type.

In this paper, motivated by the Galilean invariance of the solutions, we use the concept of orbital stability for the Vlasov-Poisson system. We prove that a family of stationary solutions, called polytropic gas spheres, are orbitally L-1 stable in the gravitational case by considering direct variational arguments. (C) 2006 Elsevier Masson SAS. All rights reserved.