An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture

Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.

Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

A continuous strain-space model of viral evolution within a host

Viruses rapidly evolve, and HIV in particular is known to be one of the fastest evolving human viruses. It is now commonly accepted that viral evolution is the cause of the intriguing dynamics exhibited during HIV infections and the ultimate success of the virus in its struggle with the immune system. To study viral evolution, we use a simple mathematical model of the within-host dynamics of HIV which incorporates random mutations. In this model, we assume a continuous distribution of viral strains in a one-dimensional phenotype space where random mutations are modelled by di ffusion. Numerical simulations show that random mutations combined with competition result in evolution towards higher Darwinian fitness: a stable traveling wave of evolution, moving towards higher levels of fi tness, is formed in the phenoty space.

Neutralizing antibodies in Multiple Sclerosis a model-based analysis of Interferon beta signaling pathway in macrophages

Multiple Sclerosis is the most common non-traumatic cause of neurologicaldisability in young people. There is no cure yet, and until recently, few long-termtherapies existed. Interferon beta (IFNβ) was the first treatment, and remains the mostcommonly prescribed. One of the most significant problems of IFNβ therapy is theproduction of drug specific antibodies. Up to 45% of patients develop neutralizingantibodies (NAbs) to IFNβ products. The neutralizing antibody binds to the biologicalagent preventing its interaction with its receptor, inhibiting the biological action of theprotein, which abrogates the clinical efficacy of IFNβ treatment. Interferon-betamediates its response by binding to its high affinity cell surface receptor and initiatingthe JAK/STAT signalling cascade. In this project we have analyzed the IFNβ signalingpathway in macrophages when neutralizing antibodies are present. The response tothis pathway after IFNβ stimulation shows a transient oscillatory rhythm of STAT1phosphorylation, which varies as NAbs concentration increases. To improve ourunderstanding of that behavior, we extended an existing mathematical model based onnonlinear ordinary differential equations of JAK/STAT pathway by including IFN-NAbassociation and IFN-activation receptor. Combining our theoretical model withexperimental data we could study the role of neutralizing antibodies on the molecularresponse and determine its lifetime after cytokine stimulation.

Why are slip lengths so large in carbon nanotubes?

The enhanced flow in carbon nanotubes is explained using a mathematical model that includes a depletion layer with reduced viscosity near the wall. In the limit of large tubes the model predicts no noticeable enhancement. For smaller tubes the model predicts enhancement that increases as the radius decreases. An analogy between the reduced viscosity and slip-length models shows that the term slip-length is misleading and that on surfaces which are smooth at the nanoscale it may be thought of as a length-scale associated with the size of the depletion region and viscosity ratio. The model therefore provides a physical interpretation of the classical Navier slip condition and explains why `slip-lengths' may be greater than the tube radius.

Stochastic optimal bid to electricity markets with environmental risk constraints

There are many factors that influence the day-ahead market bidding strategies of a generation company (GenCo) in the current energy market framework. Environmental policy issues have become more and more important for fossil-fuelled power plants and they have to be considered in their management, giving rise to emission limitations. This work allows to investigate the influence of both the allowances and emission reduction plan, and the incorporation of the derivatives medium-term commitments in the optimal generation bidding strategy to the day-ahead electricity market. Two different technologies have been considered: the coal thermal units, high-emission technology, and the combined cycle gas turbine units, low-emission technology. The Iberian Electricity Market and the Spanish National Emissions and Allocation Plans are the framework to deal with the environmental issues in the day-ahead market bidding strategies. To address emission limitations, some of the standard risk management methodologies developed for financial markets, such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), have been extended. This study offers to electricity generation utilities a mathematical model to determinate the individual optimal generation bid to the wholesale electricity market, for each one of their generation units that maximizes the long-run profits of the utility abiding by the Iberian Electricity Market rules, the environmental restrictions set by the EU Emission Trading Scheme, as well as the restrictions set by the Spanish National Emissions Reduction Plan. The economic implications for a GenCo of including the environmental restrictions of these National Plans are analyzed and the most remarkable results will be presented.

Identificació i caracterització funcional dels complexes proteics dels receptors BRL1 i BRL3 en el teixit vascular d’Arabidopsis Thaliana

Els esteroids juguen papers clau en el creixement I el desenvolupament d’eucariotes multicel•lulars. En plantes, aquestes hormones, anomenades Brassinosteroides (BRs), estan involucrades en una gran varietat de processos biològics essencials per a les plantes. S’han descrit anteriorment dos receptors de BRs del tipus Leucine Rich Repeat Receptor Like Kinase LRR-RLK, BRASSINOSTEROID RECEPTOR LIKE 1 i 3 (BRL1 i BRL3 respectivalemt) que són homòlegs al receptor principal BRI1 i són necessaris pel desenvolupament vascular. Tot i que els principals components de la senyal ja han estat identificats pel seu homòleg més pròxim, el receptor BRI1, els complexes de BRL1 i BRL3 juntament amb els candidats co-receptors així com els components de la ruta de senyalització encara no han sigut identificats. Per tal d’entendre millor la funció molecular d’aquests receptors de BRs en la planta aquesta tesis doctoral planteja dues aproximacions: com a primera aproximació, vaig realitzar un estudi fenotípic del desenvolupament del teixit vascular a la planta model Arabidopsis thaliana (Arabidopsis). Disposant d'una amplia bateria de mutants de síntesis de la hormona i senyalització del receptor BRI1, vam analitzar quantitativament el seu patró vascular a la tija d'Arabidopsis. Vam establir els paràmetres en les plantes silvestres [Col-0 wild type, (WT)] i els vam analitzar a tots i cadascun dels mutants. Això conjuntament amb una col•laboració amb la Dr. Marta Ibañes, física de la Universitat de Barcelona que va construir un model matemàtic per simular la formació del patró vascular ens va permetre el•laborar una hipòtesis que vam demostrar experimentalment i va ser publicada a la revista PNAS. Posteriorment vam observar que les plantes knock-out d'aquests dos receptors BRL1 y BRL3 a diferència de BRI1, no tenien cap fenotip obvi en el teixit vascular de la planta adulta. Així, a continuació, per entendre quina necessitat té la planta de disposar de tres receptors tant altament homòlegs que poden percebre la mateixa hormona, vam utilitzar una aproximació bioquímica en col•laboració amb el Prof. de Vries de la Universitat de Wageningen (Holanda) per tal de purificar els complexes dels receptors in vivo i els seus interactors. Això ens ha permès entendre millor el paper funcional d'aquests receptors en la planta. Els resultats d’aquests experiments estan resumits en un article en preparació que aviat estarà en revisió.

N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Beyond GDP: Methodological and measurement issues in redefining “wealth”

In the last decades; a growing stock of literature has been devoted to the criticism of GDP as an indicator of societal wealth. A relevant question is: what are the perspectives to build, on the existing knowledge and consensus, alternative measures of prosperity? A starting point may be to connect well-being research agenda with the sustainability one. However, there is no doubt that there is a lot of complexity and fuzziness inherent in multidimensional concepts such as sustainability and well-being. This article analyses the theoretical foundations and the empirical validity of some multidimensional technical tools that can be used for well-being evaluation and assessment. Of course one should not forget that policy conclusions derived through any mathematical model depend also on the conceptual framework used, i.e. which representation of reality (and thus which societal values and interests) has been considered.

Minimizing recombinations in consensus networks for phylogeographic studies

Background: We address the problem of studying recombinational variations in (human) populations. In this paper, our focus is on one computational aspect of the general task: Given two networks G1 and G2, with both mutation and recombination events, defined on overlapping sets of extant units the objective is to compute a consensus network G3 with minimum number of additional recombinations. We describe a polynomial time algorithm with a guarantee that the number of computed new recombination events is within ϵ = sz(G1, G2) (function sz is a well-behaved function of the sizes and topologies of G1 and G2) of the optimal number of recombinations. To date, this is the best known result for a network consensus problem.Results: Although the network consensus problem can be applied to a variety of domains, here we focus on structure of human populations. With our preliminary analysis on a segment of the human Chromosome X data we are able to infer ancient recombinations, population-specific recombinations and more, which also support the widely accepted 'Out of Africa' model. These results have been verified independently using traditional manual procedures. To the best of our knowledge, this is the first recombinations-based characterization of human populations. Conclusion: We show that our mathematical model identifies recombination spots in the individual haplotypes; the aggregate of these spots over a set of haplotypes defines a recombinational landscape that has enough signal to detect continental as well as population divide based on a short segment of Chromosome X. In particular, we are able to infer ancient recombinations, population-specific recombinations and more, which also support the widely accepted 'Out of Africa' model. The agreement with mutation-based analysis can be viewed as an indirect validation of our results and the model. Since the model in principle gives us more information embedded in the networks, in our future work, we plan to investigate more non-traditional questions via these structures computed by our methodology.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Diffraction theory of Fresnel lenses encoded in low-resolution devices

A mathematical model that describes the behavior of low-resolution Fresnel lenses encoded in any low-resolution device (e.g., a spatial light modulator) is developed. The effects of low-resolution codification, such the appearance of new secondary lenses, are studied for a general case. General expressions for the phase of these lenses are developed, showing that each lens behaves as if it were encoded through all pixels of the low-resolution device. Simple expressions for the light distribution in the focal plane and its dependence on the encoded focal length are developed and commented on in detail. For a given codification device an optimum focal length is found for best lens performance. An optimization method for codification of a single lens with a short focal length is proposed.

Diffraction theory of optimized low-resolution Fresnel encoded lenses

A mathematical model describing the behavior of low-resolution Fresnel encoded lenses (LRFEL's) encoded in any low-resolution device (e.g., a spatial light modulator) has recently been developed. From this model, an LRFEL with a short focal length was optimized by our imposing the maximum intensity of light onto the optical axis. With this model, analytical expressions for the light-amplitude distribution, the diffraction efficiency, and the frequency response of the optimized LRFEL's are derived.

El comportament de l'inversor: incertesa i risc

A new conceptualization of the investments is defended in accordance with the nature of the uncertainty. The results of this conceptualization offer a theory of the investment compatible with the concept of intrinsec value that is been able expressed in mathematical model. This model is an alternative to the named 'pricing models'.