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.

From SNPs to pathways: integration of functional effect of sequence variations on models of cell signalling pathways

Background: Single nucleotide polymorphisms (SNPs) are the most frequent type of sequence variation between individuals, and represent a promising tool for finding genetic determinants of complex diseases and understanding the differences in drug response. In this regard, it is of particular interest to study the effect of non-synonymous SNPs in the context of biological networks such as cell signalling pathways. UniProt provides curated information about the functional and phenotypic effects of sequence variation, including SNPs, as well as on mutations of protein sequences. However, no strategy has been developed to integrate this information with biological networks, with the ultimate goal of studying the impact of the functional effect of SNPs in the structure and dynamics of biological networks. Results: First, we identified the different challenges posed by the integration of the phenotypic effect of sequence variants and mutations with biological networks. Second, we developed a strategy for the combination of data extracted from public resources, such as UniProt, NCBI dbSNP, Reactome and BioModels. We generated attribute files containing phenotypic and genotypic annotations to the nodes of biological networks, which can be imported into network visualization tools such as Cytoscape. These resources allow the mapping and visualization of mutations and natural variations of human proteins and their phenotypic effect on biological networks (e.g. signalling pathways, protein-protein interaction networks, dynamic models). Finally, an example on the use of the sequence variation data in the dynamics of a network model is presented. Conclusion: In this paper we present a general strategy for the integration of pathway and sequence variation data for visualization, analysis and modelling purposes, including the study of the functional impact of protein sequence variations on the dynamics of signalling pathways. This is of particular interest when the SNP or mutation is known to be associated to disease. We expect that this approach will help in the study of the functional impact of disease-associated SNPs on the behaviour of cell signalling pathways, which ultimately will lead to a better understanding of the mechanisms underlying complex diseases.

A Multi-state model for the analysis of functional decline and mortality of frail elderly patients

L’objectiu d’aquest estudi, que correspon a un projecte de recerca sobre la pèrdua funcional i la mortalitat de persones grans fràgils, és construir un procés de supervivència predictiu que tingui en compte l’evolució funcional i nutricional dels pacients al llarg del temps. En aquest estudi ens enfrontem a l’anàlisi de dades de supervivència i mesures repetides però els mètodes estadístics habituals per al tractament conjunt d’aquest tipus de dades no són apropiats en aquest cas. Com a alternativa utilitzem els models de supervivència multi-estats per avaluar l’associació entre mortalitat i recuperació, o no, dels nivells funcionals i nutricionals considerats normals. Després d’estimar el model i d’identificar els factors pronòstics de mortalitat és possible obtenir un procés predictiu que permet fer prediccions de la supervivència dels pacients en funció de la seva història concreta fins a un determinat moment. Això permet realitzar un pronòstic més precís de cada grup de pacients, la qual cosa pot ser molt útil per als professionals sanitaris a l’hora de prendre decisions clíniques.

Local Distance-Based Generalized Linear Models using the dbstats package for R

This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models firstly with the generalized linear model concept, then by localizing. Distances between individuals are the only predictor information needed to fit these models. Therefore they are applicable to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. Models can be fitted and analysed with the R package dbstats, which implements several distancebased prediction methods.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Brain functional abnormality in schizo-affective disorder: an fMRI study.

Background.Schizo-affective disorder has not been studied to any significant extent using functional imaging. The aim of this study was to examine patterns of brain activation and deactivation in patients meeting strict diagnostic criteria for the disorder. METHOD: Thirty-two patients meeting research diagnostic criteria (RDC) for schizo-affective disorder (16 schizomanic and 16 schizodepressive) and 32 matched healthy controls underwent functional magnetic resonance imaging (fMRI) during performance of the n-back task. Linear models were used to obtain maps of activations and deactivations in the groups. RESULTS: Controls showed activation in a network of frontal and other areas and also deactivation in the medial frontal cortex, the precuneus and the parietal cortex. Schizo-affective patients activated significantly less in prefrontal, parietal and temporal regions than the controls, and also showed failure of deactivation in the medial frontal cortex. When task performance was controlled for, the reduced activation in the dorsolateral prefrontal cortex (DLPFC) and the failure of deactivation of the medial frontal cortex remained significant. CONCLUSIONS: Schizo-affective disorder shows a similar pattern of reduced frontal activation to schizophrenia. The disorder is also characterized by failure of deactivation suggestive of default mode network dysfunction.

Brain functional abnormality in schizo-affective disorder: an fMRI study.

Background.Schizo-affective disorder has not been studied to any significant extent using functional imaging. The aim of this study was to examine patterns of brain activation and deactivation in patients meeting strict diagnostic criteria for the disorder. METHOD: Thirty-two patients meeting research diagnostic criteria (RDC) for schizo-affective disorder (16 schizomanic and 16 schizodepressive) and 32 matched healthy controls underwent functional magnetic resonance imaging (fMRI) during performance of the n-back task. Linear models were used to obtain maps of activations and deactivations in the groups. RESULTS: Controls showed activation in a network of frontal and other areas and also deactivation in the medial frontal cortex, the precuneus and the parietal cortex. Schizo-affective patients activated significantly less in prefrontal, parietal and temporal regions than the controls, and also showed failure of deactivation in the medial frontal cortex. When task performance was controlled for, the reduced activation in the dorsolateral prefrontal cortex (DLPFC) and the failure of deactivation of the medial frontal cortex remained significant. CONCLUSIONS: Schizo-affective disorder shows a similar pattern of reduced frontal activation to schizophrenia. The disorder is also characterized by failure of deactivation suggestive of default mode network dysfunction.

Brain functional abnormality in schizo-affective disorder: an fMRI study.

Background.Schizo-affective disorder has not been studied to any significant extent using functional imaging. The aim of this study was to examine patterns of brain activation and deactivation in patients meeting strict diagnostic criteria for the disorder. METHOD: Thirty-two patients meeting research diagnostic criteria (RDC) for schizo-affective disorder (16 schizomanic and 16 schizodepressive) and 32 matched healthy controls underwent functional magnetic resonance imaging (fMRI) during performance of the n-back task. Linear models were used to obtain maps of activations and deactivations in the groups. RESULTS: Controls showed activation in a network of frontal and other areas and also deactivation in the medial frontal cortex, the precuneus and the parietal cortex. Schizo-affective patients activated significantly less in prefrontal, parietal and temporal regions than the controls, and also showed failure of deactivation in the medial frontal cortex. When task performance was controlled for, the reduced activation in the dorsolateral prefrontal cortex (DLPFC) and the failure of deactivation of the medial frontal cortex remained significant. CONCLUSIONS: Schizo-affective disorder shows a similar pattern of reduced frontal activation to schizophrenia. The disorder is also characterized by failure of deactivation suggestive of default mode network dysfunction.

A priori parameterisation of the CERES soil-crop models and tests against several European data sets

Mechanistic soil-crop models have become indispensable tools to investigate the effect of management practices on the productivity or environmental impacts of arable crops. Ideally these models may claim to be universally applicable because they simulate the major processes governing the fate of inputs such as fertiliser nitrogen or pesticides. However, because they deal with complex systems and uncertain phenomena, site-specific calibration is usually a prerequisite to ensure their predictions are realistic. This statement implies that some experimental knowledge on the system to be simulated should be available prior to any modelling attempt, and raises a tremendous limitation to practical applications of models. Because the demand for more general simulation results is high, modellers have nevertheless taken the bold step of extrapolating a model tested within a limited sample of real conditions to a much larger domain. While methodological questions are often disregarded in this extrapolation process, they are specifically addressed in this paper, and in particular the issue of models a priori parameterisation. We thus implemented and tested a standard procedure to parameterize the soil components of a modified version of the CERES models. The procedure converts routinely-available soil properties into functional characteristics by means of pedo-transfer functions. The resulting predictions of soil water and nitrogen dynamics, as well as crop biomass, nitrogen content and leaf area index were compared to observations from trials conducted in five locations across Europe (southern Italy, northern Spain, northern France and northern Germany). In three cases, the model’s performance was judged acceptable when compared to experimental errors on the measurements, based on a test of the model’s root mean squared error (RMSE). Significant deviations between observations and model outputs were however noted in all sites, and could be ascribed to various model routines. In decreasing importance, these were: water balance, the turnover of soil organic matter, and crop N uptake. A better match to field observations could therefore be achieved by visually adjusting related parameters, such as field-capacity water content or the size of soil microbial biomass. As a result, model predictions fell within the measurement errors in all sites for most variables, and the model’s RMSE was within the range of published values for similar tests. We conclude that the proposed a priori method yields acceptable simulations with only a 50% probability, a figure which may be greatly increased through a posteriori calibration. Modellers should thus exercise caution when extrapolating their models to a large sample of pedo-climatic conditions for which they have only limited information.

Brain functional abnormality in schizo-affective disorder: an fMRI study.

Background.Schizo-affective disorder has not been studied to any significant extent using functional imaging. The aim of this study was to examine patterns of brain activation and deactivation in patients meeting strict diagnostic criteria for the disorder. METHOD: Thirty-two patients meeting research diagnostic criteria (RDC) for schizo-affective disorder (16 schizomanic and 16 schizodepressive) and 32 matched healthy controls underwent functional magnetic resonance imaging (fMRI) during performance of the n-back task. Linear models were used to obtain maps of activations and deactivations in the groups. RESULTS: Controls showed activation in a network of frontal and other areas and also deactivation in the medial frontal cortex, the precuneus and the parietal cortex. Schizo-affective patients activated significantly less in prefrontal, parietal and temporal regions than the controls, and also showed failure of deactivation in the medial frontal cortex. When task performance was controlled for, the reduced activation in the dorsolateral prefrontal cortex (DLPFC) and the failure of deactivation of the medial frontal cortex remained significant. CONCLUSIONS: Schizo-affective disorder shows a similar pattern of reduced frontal activation to schizophrenia. The disorder is also characterized by failure of deactivation suggestive of default mode network dysfunction.