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.

Applications of stochastic analysis in finance and statistical inference

First: A continuous-time version of Kyle's model (Kyle 1985), known as the Back's model (Back 1992), of asset pricing with asymmetric information, is studied. A larger class of price processes and of noise traders' processes are studied. The price process, as in Kyle's model, is allowed to depend on the path of the market order. The process of the noise traders' is an inhomogeneous Lévy process. Solutions are found by the Hamilton-Jacobi-Bellman equations. With the insider being risk-neutral, the price pressure is constant, and there is no equilibirium in the presence of jumps. If the insider is risk-averse, there is no equilibirium in the presence of either jumps or drifts. Also, it is analised when the release time is unknown. A general relation is established between the problem of finding an equilibrium and of enlargement of filtrations. Random announcement time is random is also considered. In such a case the market is not fully efficient and there exists equilibrium if the sensitivity of prices with respect to the global demand is time decreasing according with the distribution of the random time. Second: Power variations. it is considered, the asymptotic behavior of the power variation of processes of the form _integral_0^t u(s-)dS(s), where S_ is an alpha-stable process with index of stability 0&alpha&2 and the integral is an Itô integral. Stable convergence of corresponding fluctuations is established. These results provide statistical tools to infer the process u from discrete observations. Third: A bond market is studied where short rates r(t) evolve as an integral of g(t-s)sigma(s) with respect to W(ds), where g and sigma are deterministic and W is the stochastic Wiener measure. Processes of this type are particular cases of ambit processes. These processes are in general not of the semimartingale kind.

Mathematical modeling and analysis of the interaction of populations of bacteria and bacteriophages within chicken intestine

Vegeu el resum a l'inici del document de l'arxiu adjunt

Statistical modeling of bowing control applied to violin sound synthesis

Excitation-continuous music instrument control patterns are often not explicitly represented in current sound synthesis techniques when applied to automatic performance. Both physical model-based and sample-based synthesis paradigmswould benefit from a flexible and accurate instrument control model, enabling the improvement of naturalness and realism. Wepresent a framework for modeling bowing control parameters inviolin performance. Nearly non-intrusive sensing techniques allow for accurate acquisition of relevant timbre-related bowing control parameter signals.We model the temporal contour of bow velocity, bow pressing force, and bow-bridge distance as sequences of short Bézier cubic curve segments. Considering different articulations, dynamics, and performance contexts, a number of note classes are defined. Contours of bowing parameters in a performance database are analyzed at note-level by following a predefined grammar that dictates characteristics of curve segment sequences for each of the classes in consideration. As a result, contour analysis of bowing parameters of each note yields an optimal representation vector that is sufficient for reconstructing original contours with significant fidelity. From the resulting representation vectors, we construct a statistical model based on Gaussian mixtures suitable for both the analysis and synthesis of bowing parameter contours. By using the estimated models, synthetic contours can be generated through a bow planning algorithm able to reproduce possible constraints caused by the finite length of the bow. Rendered contours are successfully used in two preliminary synthesis frameworks: digital waveguide-based bowed stringphysical modeling and sample-based spectral-domain synthesis.

Statistical modeling of violin bowing parameter contours

We present a framework for modeling right-hand gestures in bowed-string instrument playing, applied to violin. Nearly non-intrusive sensing techniques allow for accurate acquisition of relevant timbre-related bowing gesture parameter cues. We model the temporal contour of bow transversal velocity, bow pressing force, and bow-bridge distance as sequences of short segments, in particular B´ezier cubic curve segments. Considering different articulations, dynamics, andcontexts, a number of note classes is defined. Gesture parameter contours of a performance database are analyzed at note-level by following a predefined grammar that dictatescharacteristics of curve segment sequences for each of the classes into consideration. Based on dynamic programming, gesture parameter contour analysis provides an optimal curve parameter vector for each note. The informationpresent in such parameter vector is enough for reconstructing original gesture parameter contours with significant fidelity. From the resulting representation vectors, weconstruct a statistical model based on Gaussian mixtures, suitable for both analysis and synthesis of bowing gesture parameter contours. We show the potential of the modelby synthesizing bowing gesture parameter contours from an annotated input score. Finally, we point out promising applicationsand developments.

A Sparse Bayesian Approach for Joint Feature Selection and Classifier Learning

Peer-reviewed

Modeling and Classifying Breast Tissue Density in Mammograms

We present a new approach to model and classify breast parenchymal tissue. Given a mammogram, first, we will discover the distribution of the different tissue densities in an unsupervised manner, and second, we will use this tissue distribution to perform the classification. We achieve this using a classifier based on local descriptors and probabilistic Latent Semantic Analysis (pLSA), a generative model from the statistical text literature. We studied the influence of different descriptors like texture and SIFT features at the classification stage showing that textons outperform SIFT in all cases. Moreover we demonstrate that pLSA automatically extracts meaningful latent aspects generating a compact tissue representation based on their densities, useful for discriminating on mammogram classification. We show the results of tissue classification over the MIAS and DDSM datasets. We compare our method with approaches that classified these same datasets showing a better performance of our proposal

A first attempt of geographically-distributed Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM): mapping human time and energy throughput in metropolitan Barcelona

This study presents a first attempt to extend the “Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM)” approach to a spatial dimension using GIS techniques in the Metropolitan area of Barcelona. We use a combination of census and commercial databases along with a detailed land cover map to create a layer of Common Geographic Units that we populate with the local values of human time spent in different activities according to MuSIASEM hierarchical typology. In this way, we mapped the hours of available human time, in regards to the working hours spent in different locations, putting in evidence the gradients in spatial density between the residential location of workers (generating the work supply) and the places where the working hours are actually taking place. We found a strong three-modal pattern of clumps of areas with different combinations of values of time spent on household activities and on paid work. We also measured and mapped spatial segregation between these two activities and put forward the conjecture that this segregation increases with higher energy throughput, as the size of the functional units must be able to cope with the flow of exosomatic energy. Finally, we discuss the effectiveness of the approach by comparing our geographic representation of exosomatic throughput to the one issued from conventional methods.

Statistical modeling on (α, +∞)

Observations in daily practice are sometimes registered as positive values larger then a given threshold α. The sample space is in this case the interval (α,+∞), α & 0, which can be structured as a real Euclidean space in different ways. This fact opens the door to alternative statistical models depending not only on the assumed distribution function, but also on the metric which is considered as appropriate, i.e. the way differences are measured, and thus variability

Statistical modeling on coordinates

This paper is a first draft of the principle of statistical modelling on coordinates. Several causes —which would be long to detail—have led to this situation close to the deadline for submitting papers to CODAWORK’03. The main of them is the fast development of the approach along thelast months, which let appear previous drafts as obsolete. The present paper contains the essential parts of the state of the art of this approach from my point of view. I would like to acknowledge many clarifying discussions with the group of people working in this field in Girona, Barcelona, Carrick Castle, Firenze, Berlin, G¨ottingen, and Freiberg. They have given a lot of suggestions and ideas. Nevertheless, there might be still errors or unclear aspects which are exclusively my fault. I hope this contribution serves as a basis for further discussions and new developments

Attention, memory and verbal learning and their relation to schizotypal traits in unaffected parents of schizophrenic patients

The main objective of this ex post facto study is to compare the differencesin cognitive functions and their relation to schizotypal personality traits between agroup of unaffected parents of schizophrenic patients and a control group. A total of 52unaffected biological parents of schizophrenic patients and 52 unaffected parents ofunaffected subjects were assessed in measures of attention (Continuous PerformanceTest- Identical Pairs Version, CPT-IP), memory and verbal learning (California VerbalLearning Test, CVLT) as well as schizotypal personality traits (Oxford-Liverpool Inventoryof Feelings and Experiences, O-LIFE). The parents of the patients with schizophreniadiffer from the parents of the control group in omission errors on the ContinuousPerformance Test- Identical Pairs, on a measure of recall and on two contrast measuresof the California Verbal Learning Test. The associations between neuropsychologicalvariables and schizotpyal traits are of a low magnitude. There is no defined pattern ofthe relationship between cognitive measures and schizotypal traits

CoDaPack. An Excel and Visual Basic based software of compositional data analysis. Current version and discussion form upcoming versions

In the eighties, John Aitchison (1986) developed a new methodological approach for the statistical analysis of compositional data. This new methodology was implemented in Basic routines grouped under the name CODA and later NEWCODA inMatlab (Aitchison, 1997). After that, several other authors have published extensions to this methodology: Marín-Fernández and others (2000), Barceló-Vidal and others (2001), Pawlowsky-Glahn and Egozcue (2001, 2002) and Egozcue and others (2003). (...)

Pseudogenes in the ENCODE regions: consensus annotation, analysis of transcription, and evolution

Arising from either retrotransposition or genomic duplication of functional genes, pseudogenes are “genomic fossils” valuable for exploring the dynamics and evolution of genes and genomes. Pseudogene identification is an important problem in computational genomics, and is also critical for obtaining an accurate picture of a genome’s structure and function. However, no consensus computational scheme for defining and detecting pseudogenes has been developed thus far. As part of the ENCyclopedia Of DNA Elements (ENCODE) project, we have compared several distinct pseudogene annotation strategies and found that different approaches and parameters often resulted in rather distinct sets of pseudogenes. We subsequently developed a consensus approach for annotating pseudogenes (derived from protein coding genes) in the ENCODE regions, resulting in 201 pseudogenes, two-thirds of which originated from retrotransposition. A survey of orthologs for these pseudogenes in 28 vertebrate genomes showed that a significant fraction (∼80%) of the processed pseudogenes are primate-specific sequences, highlighting the increasing retrotransposition activity in primates. Analysis of sequence conservation and variation also demonstrated that most pseudogenes evolve neutrally, and processed pseudogenes appear to have lost their coding potential immediately or soon after their emergence. In order to explore the functional implication of pseudogene prevalence, we have extensively examined the transcriptional activity of the ENCODE pseudogenes. We performed systematic series of pseudogene-specific RACE analyses. These, together with complementary evidence derived from tiling microarrays and high throughput sequencing, demonstrated that at least a fifth of the 201 pseudogenes are transcribed in one or more cell lines or tissues.

Impairment of mossy fiber long-term potentiation and associative learning in pituitary adenylate cyclase activating polypeptide type I receptor-deficient Mice

The pituitary adenylate cyclase activating polypeptide (PACAP) type I receptor (PAC1) is a G-protein-coupled receptor binding the strongly conserved neuropeptide PACAP with 1000-fold higher affinity than the related peptide vasoactive intestinal peptide. PAC1-mediated signaling has been implicated in neuronal differentiation and synaptic plasticity. To gain further insight into the biological significance of PAC1-mediated signaling in vivo, we generated two different mutant mouse strains, harboring either a complete or a forebrain-specific inactivation of PAC1. Mutants from both strains show a deficit in contextual fear conditioning, a hippocampus-dependent associative learning paradigm. In sharp contrast, amygdala-dependent cued fear conditioning remains intact. Interestingly, no deficits in other hippocampus-dependent tasks modeling declarative learning such as the Morris water maze or the social transmission of food preference are observed. At the cellular level, the deficit in hippocampus-dependent associative learning is accompanied by an impairment of mossy fiber long-term potentiation (LTP). Because the hippocampal expression of PAC1 is restricted to mossy fiber terminals, we conclude that presynaptic PAC1-mediated signaling at the mossy fiber synapse is involved in both LTP and hippocampus-dependent associative learning.

Asymptotic robust inferences in the analysis of mean and covariance structures

Structural equation models are widely used in economic, socialand behavioral studies to analyze linear interrelationships amongvariables, some of which may be unobservable or subject to measurementerror. Alternative estimation methods that exploit different distributionalassumptions are now available. The present paper deals with issues ofasymptotic statistical inferences, such as the evaluation of standarderrors of estimates and chi--square goodness--of--fit statistics,in the general context of mean and covariance structures. The emphasisis on drawing correct statistical inferences regardless of thedistribution of the data and the method of estimation employed. A(distribution--free) consistent estimate of $\Gamma$, the matrix ofasymptotic variances of the vector of sample second--order moments,will be used to compute robust standard errors and a robust chi--squaregoodness--of--fit squares. Simple modifications of the usual estimateof $\Gamma$ will also permit correct inferences in the case of multi--stage complex samples. We will also discuss the conditions under which,regardless of the distribution of the data, one can rely on the usual(non--robust) inferential statistics. Finally, a multivariate regressionmodel with errors--in--variables will be used to illustrate, by meansof simulated data, various theoretical aspects of the paper.