Les TIC a l'ensenyament de la modelització matemàtica en Ciències Econòmiques i en Ciències Experimentals

Aquest projecte proposa materials didàctics per a un nou plantejament de les assignatures de Matemàtiques dels primers cursos de Ciències Empresarials i d'Enginyeria Tècnica, més acord amb el procés de convergència europea, basat en la realització de projectes que anomenem “Tallers de Modelització Matemàtica” (TMM) en els quals: (1) Els alumnes parteixen de situacions i problemes reals per als quals han de construir per sí mateixos els models matemàtics més adients i, a partir de la manipulació adequada d’aquests models, poden obtenir la informació necessària per donar-los resposta. (2) El treball de construcció, experimentació i avaluació dels models es realitza amb el suport de la calculadora simbòlica Wiris i del full de càlcul Excel com a instruments “normalitzats” del treball matemàtic d’estudiants i professors. (3) S’adapten els programes de les assignatures de matemàtiques de primer curs per tal de poder-les associar a un petit nombre de Tallers que parteixen de situacions adaptades a cada titulació. L’assignatura de Matemàtiques per a les Ciències Empresarials s’articula entorn de dos tallers independents: “Matrius de transició” pel que fa a l’àlgebra lineal i “Previsió de vendes” per a la modelització funcional en una variable. L’assignatura de Matemàtiques per a l’Enginyeria s’articula entorn d’un únic taller, “Models de poblacions”, que abasta la majoria de continguts del curs: successions i models funcionals en una variable, àlgebra lineal i equacions diferencials. Un conjunt d’exercicis interactius basats en la calculadora simbòlica WIRIS (Wiris-player) serveix de suport per al treball tècnic imprescindible per al desenvolupament de les dues assignatures. L’experimentació d’aquests tallers durant 2 cursos consecutius (2006/07 i 2007/08) en dues universitats catalanes (URL i UAB) ha posat en evidència tant els innegables avantatges del nou dispositiu docent per a l’aprenentatge dels estudiants, així com les restriccions institucionals que actualment dificulten la seva gestió i difusió.

Factors de creixement autòlegs aplicats a les ferides cròniques amb evolució tòrpida

Les ferides cròniques, especialment les de lenta curació, suposen una carga important pels pacients i pels sistemes de salut. És imprescindible investigar en nous tractaments que redueixin el temps de curació d‟aquestes ferides. L‟objectiu d‟aquest projecte, és avaluar l‟eficàcia dels factors de creixement, obtinguts de plasma ric en plaquetes, en la curació o millora de les ferides cròniques. El projecte s‟ha dissenyat com un estudi d‟una sèrie de casos que compara el tractament convencional amb el tractament amb factors de creixement. La variable resultats és la curació o la disminució del àrea de l‟úlcera. El projecte pretén avaluar uns quants pacients consecutius atesos en l‟ unitat de ferides cròniques del nostre hospital. Els subjectes del estudi han de presentar una ferida de més de 3 mesos d‟evolució nul·la o escassa resposta als tractaments habituals. La tècnica de obtenció dels factors de creixement plaquetar no és complexa i es pot realitzar en l‟entorn d‟un hospital de dia. No s‟han comunicat en la literatura efectes secundaris majors de l‟aplicació dels factors de creixement en ferides cròniques.

Pathway databases and tools for their exploitation: benefits, current limitations and challenges

In past years, comprehensive representations of cell signalling pathways have been developed by manual curation from literature, which requires huge effort and would benefit from information stored in databases and from automatic retrieval and integration methods. Once a reconstruction of the network of interactions is achieved, analysis of its structural features and its dynamic behaviour can take place. Mathematical modelling techniques are used to simulate the complex behaviour of cell signalling networks, which ultimately sheds light on the mechanisms leading to complex diseases or helps in the identification of drug targets. A variety of databases containing information on cell signalling pathways have been developed in conjunction with methodologies to access and analyse the data. In principle, the scenario is prepared to make the most of this information for the analysis of the dynamics of signalling pathways. However, are the knowledge repositories of signalling pathways ready to realize the systems biology promise? In this article we aim to initiate this discussion and to provide some insights on this issue.

Factors de creixement autòlegs aplicats a les ferides cròniques amb evolució tòrpida

Les ferides cròniques, especialment les de lenta curació, suposen una carga important pels pacients i pels sistemes de salut. És imprescindible investigar en nous tractaments que redueixin el temps de curació d‟aquestes ferides. L‟objectiu d‟aquest projecte, és avaluar l‟eficàcia dels factors de creixement, obtinguts de plasma ric en plaquetes, en la curació o millora de les ferides cròniques. El projecte s‟ha dissenyat com un estudi d‟una sèrie de casos que compara el tractament convencional amb el tractament amb factors de creixement. La variable resultats és la curació o la disminució del àrea de l‟úlcera. El projecte pretén avaluar uns quants pacients consecutius atesos en l‟ unitat de ferides cròniques del nostre hospital. Els subjectes del estudi han de presentar una ferida de més de 3 mesos d‟evolució nul·la o escassa resposta als tractaments habituals. La tècnica de obtenció dels factors de creixement plaquetar no és complexa i es pot realitzar en l‟entorn d‟un hospital de dia. No s‟han comunicat en la literatura efectes secundaris majors de l‟aplicació dels factors de creixement en ferides cròniques.

Determinació de diferents compostos bioactius en ingredients naturals per a l'elaboració de bombons funcionals amb beneficis cardiovasculars

Durant les darreres dècades, i degut, principalment, a un canvi en els hàbits alimentaris, hi ha hagut un augment a nivell mundial de malalties cròniques (l’obesitat, malalties cardiovasculars, etc.). En els països mediterranis hi ha menys incidència d’aquestes malalties i sembla ser que això es deu a l’anomenada dieta mediterrània. La dieta mediterrània es caracteritza per una combinació d’oli d’oliva com a grassa principal, verdures, hortalisses i fruites en abundància, lleguminoses, fruits secs, formatges i iogurt, peix, pa, pasta, cereals i els seus derivats i un consum moderat de vi i carns. Aquest model alimentari, ric en tocoferols, fitosterols i fitoestanols que ajuden a reduir el contingut de colesterol en sang, fa que en les poblacions mediterrànies hi hagi menys incidència de malalties cardiovasculars. Aquests compostos inhibeixen el deteriorament oxidatiu dels olis, actuen com agent antipolimerització per olis de fregir. Tenen capacitat de reduir els nivells de colesterol, evitant la incidència de malalties cardiovasculars. Els fitoesterols y fitoestanols es poden trobar en forma lliure o esterificada amb àcids grassos, àcids fenòlics i glucosa. Els objectius d’ aquest treball han estat, primer en el desenvolupament de mètodes d'anàlisi ràpids, fiables i robusts dels tocoferols, fitoesterols i fitoestanols i la seva aplicació en fruits sec, oli de segó, oli de pinyol de raïm i productes que els continguin. El primer mètode va estar basat en la cromatografía líquida (HPLC-DAD) amb extracció en fase sòlida (SPE) com tècnica alternativa a la saponificació para la determinació de fitoesterols lliures. Aquest mètode va estar aplicada a mostres de bombons que contenia fitoesterols. El segon mètode va estar basat en la cromatografia de gasos (GCFID) amb aponificació i SPE per quantificar fitoesterols i fitoestanols lliures, esterificats i totals. En els documents annexos es descriuen a profunditat els mètodes desenvolupats.

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.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Effects of erythropoietin on muscle O2 transport during exercise in patients with chronic renal failure.

Erythropoietin (rHuEPO) has proven to be effective in the treatment of anemia of chronic renal failure (CRF). Despite improving the quality of life, peak oxygen uptake after rHuEPO therapy is not improved as much as the increase in hemoglobin concentration ([Hb)] would predict. We hypothesized that this discrepancy is due to failure of O2 transport rates to rise in a manner proportional to [Hb]. To test this, eight patients with CRF undergoing regular hemodialysis were studied pre- and post-rHuEPO ([Hb] = 7.5 +/- 1.0 vs. 12.5 +/- 1.0 g x dl-1) using a standard incremental cycle exercise protocol. A group of 12 healthy sedentary subjects of similar age and anthropometric characteristics served as controls. Arterial and femoral venous blood gas data were obtained and coupled with simultaneous measurements of femoral venous blood flow (Qleg) by thermodilution to obtain O2 delivery and oxygen uptake (VO2). Despite a 68% increase in [Hb], peak VO2 increased by only 33%. This could be explained largely by reduced peak leg blood flow, limiting the gain in O2 delivery to 37%. At peak VO2, after rHuEPO, O2 supply limitation of maximal VO2 was found to occur, permitting the calculation of a value for muscle O2 conductance from capillary to mitochondria (DO2). While DO2 was slightly improved after rHuEPO, it was only 67% of that of sedentary control subjects. This kept maximal oxygen extraction at only 70%. Two important conclusions can be reached from this study. First, the increase in [Hb] produced by rHuEPO is accompanied by a significant reduction in peak blood flow to exercising muscle, which limits the gain in oxygen transport. Second, even after restoration of [Hb], O2 conductance from the muscle capillary to the mitochondria remains considerably below normal.

Avaluació d’un nou protocol MAC per IEEE 802.11 en un entorn multicel·lular exterior

Estudi realitzat a partir d’una estada al laboratori LSR (Logiciels, Systèmes, Réseaux) – IMAG a Grenoble, França, entre els mesos de setembre del 2005 i febrer del 2006. El grup de recerca Drakkar d’aquest laboratori va desenvolupar un nou mecanisme d’accés al medi per a xarxes d’àrea local sense fils (WLAN) anomenat Idle Sense. S’ha avaluat aquest mecanisme en entorns cel·lulars i s’ha comparat del seu comportament amb l’estàndard IEEE 802.11 DCF mitjançant la implementació en un simulador. En els entorns cel·lulars es troben condicions de transmissió molt allunyades de les ideals, i de les analitzades fins al moment, que consisteixen en escenaris formats per una única cel·la aïllada. Per aquest motiu, primer s’ha estudiat els mecanismes d’accés al medi d’Idle Sense en una cel·la i en condicions de transmissió adverses. Després, s’ha estudiat en entorns multicel·lulars, on les comunicacions entre estacions es veuen influenciades pel problema de solapament de cel·les i per les interferències provocades per les transmissions d’estacions d’altres cel·les. També s’ha comparat els resultats obtinguts amb el comportament d’IEEE 802.11 DCF i d’altres propostes de millora: Asymptotically Optimal Backoff (AOB) i Slow Decrease. Finalment, s’ha realitzat una modificació sobre Idle Sense, que s’ha anomenat Weighted Idle Sense, que resulta més adecuat per a treballar en xarxes d’àrea local sense fils en mode infraestructura.

Disseny i aplicació del protocol d'instal·lació d'energia fotovoltaica en edificis aïllats de la xarxa elèctrica al PNAP

En el perímetre del parc es troben gran nombre d’edificacions amb mancances de subministrament elèctric per la gran dispersió de la població de la comarca. L’objectiu d’aquest estudi és desenvolupar un protocol per determinar la viabilitat de l’energia fotovoltaica en edificis aïllats i aplicar-la de forma pilot a dos edificis gestionats pels responsables del Parc Natural de l’Alt Pirineu: el Centre de Logística i Manteniment (CLM) i el Refugi del Fornet. Aquests han estat escollits per la seva representativitat com a edificis aïllats de la xarxa elèctrica convencional. S’ha elaborat una metodologia pròpia, el Protocol d’instal·lació d’energia fotovoltaica en edificis aïllats de la xarxa elèctrica. S’ha realitzat una anàlisi de sensibilitats del dimensionat fotovoltaic davant la modificació de diversos paràmetres rellevants. Això ha permès determinar les característiques òptimes de viabilitat per als dos edificis en estudi i el cost de la instal·lació fotovoltaica (17.183€ el CLM i 164.815 € el Refugi del Fornet). Els resultats obtinguts en els dos edificis pilot han mostrat el gran cost relatiu entre l’energia fotovoltaica i l’energia elèctrica produïda a partir de combustibles fòssils.

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.

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of householdexpenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that tryto add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spendingexcluding alcohol/tobacco similar for teetotal and non-teetotal households?In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than onecomponent, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durableswithin the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small.While this analysis is based on around economic data, the ideas carry over tomany other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

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.

Modelling of Mercury’s surface composition and remote detection from the orbit with the BepiColombo Mercury Planetary Orbiter

It can be assumed that the composition of Mercury’s thin gas envelope (exosphere) is related to thecomposition of the planets crustal materials. If this relationship is true, then inferences regarding the bulkchemistry of the planet might be made from a thorough exospheric study. The most vexing of allunsolved problems is the uncertainty in the source of each component. Historically, it has been believedthat H and He come primarily from the solar wind, while Na and K originate from volatilized materialspartitioned between Mercury’s crust and meteoritic impactors. The processes that eject atoms andmolecules into the exosphere of Mercury are generally considered to be thermal vaporization, photonstimulateddesorption (PSD), impact vaporization, and ion sputtering. Each of these processes has its owntemporal and spatial dependence. The exosphere is strongly influenced by Mercury’s highly ellipticalorbit and rapid orbital speed. As a consequence the surface undergoes large fluctuations in temperatureand experiences differences of insolation with longitude. We will discuss these processes but focus moreon the expected surface composition and solar wind particle sputtering which releases material like Caand other elements from the surface minerals and discuss the relevance of composition modelling