Data size sufficiency analyses of haplotype inference algortihms

We present experimental and theoretical analyses of data requirements for haplotype inference algorithms. Our experiments include a broad range of problem sizes under two standard models of tree distribution and were designed to yield statistically robust results despite the size of the sample space. Our results validate Gusfield's conjecture that a population size of n log n is required to give (with high probability) sufficient information to deduce the n haplotypes and their complete evolutionary history. The experimental results inspired our experimental finding with theoretical bounds on the population size. We also analyze the population size required to deduce some fixed fraction of the evolutionary history of a set of n haplotypes and establish linear bounds on the required sample size. These linear bounds are also shown theoretically.

Orthogonal systems in finite grahps

To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Why are offspring born larger when it is colder? Phenotypic plasticity for offspring size in the cladoceran Simocephalus vetulus (Müller)

It has been predicted on theorerical grounds (Sibly & Calow, 1983; Taylor & Williams, 1984) that optimal offspring size should be highly sensitive to juvenile growth and survival rates. To test such models, genetically-identical individuals of Simicephalus vetulus were reared at different temperatures and monitored for offspring size and juvenile growth rate. As adult size correlates negatively with temperature, an analysis of covariance was performed to separate the effects of temperature and maternal size. The result is that offspring size indeed correlates negatively with juvenile growth rate. Comparisons are made with field observation of several authors on seasonal variation of offspring size and alternative explanations are discussed. It is concluded that present experiments support the prediction of the theoretical models.

Sexual dimorphism in resource acquisition and deployment: both size and timing matter.

Background and Aims The males and females of many dioecious plant species differ from one another in important life-history traits, such as their size. If male and female reproductive functions draw on different resources, for example, one should expect males and females to display different allocation strategies as they grow. Importantly, these strategies may differ not only between the two sexes, but also between plants of different age and therefore size. Results are presented from an experiment that asks whether males and females of Mercurialis annua, an annual plant with indeterminate growth, differ over time in their allocation of two potentially limiting resources (carbon and nitrogen) to vegetative (below-and above-ground) and reproductive tissues.Methods Comparisons were made of the temporal patterns of biomass allocation to shoots, roots and reproduction and the nitrogen content in the leaves between the sexes of M. annua by harvesting plants of each sex after growth over different periods of time.Key Results and Conclusions Males and females differed in their temporal patterns of allocation. Males allocated more to reproduction than females at early stages, but this trend was reversed at later stages. Importantly, males allocated proportionally more of their biomass towards roots at later stages, but the roots of females were larger in absolute terms. The study points to the important role played by both the timing of resource deployment and the relative versus absolute sizes of the sinks and sources in sexual dimorphism of an annual plant.

Caracteritació de models funcionals d'àmfores romanes mitjançant Finite Element Analysis

Projecte de recerca elaborat a partir d’una estada al Laboratory of Archaeometry del National Centre of Scientific Research “Demokritos” d’Atenes, Grècia, entre juny i setembre 2006. Aquest estudi s’emmarca dins d’un context més ampli d’estudi del canvi tecnològic que es documenta en la producció d’àmfores de tipologia romana durant els segles I aC i I dC en els territoris costaners de Catalunya. Una part d’aquest estudi contempla el càlcul de les propietats mecàniques d’aquestes àmfores i la seva avaluació en funció de la tipologia amforal, a partir de l’Anàlisi d’Elements Finits (AEF). L’AEF és una aproximació numèrica que té el seu origen en les ciències d’enginyeria i que ha estat emprada per estimar el comportament mecànic d’un model en termes, per exemple, de deformació i estrès. Així, un objecte, o millor dit el seu model, es dividit en sub-dominis anomenats elements finits, als quals se’ls atribueixen les propietats mecàniques del material en estudi. Aquests elements finits estan connectats formant una xarxa amb constriccions que pot ser definida. En el cas d’aplicar una força determinada a un model, el comportament de l’objecte pot ser estimat mitjançant el conjunt d’equacions lineals que defineixen el rendiment dels elements finits, proporcionant una bona aproximació per a la descripció de la deformació estructural. Així, aquesta simulació per ordinador suposa una important eina per entendre la funcionalitat de ceràmiques arqueològiques. Aquest procediment representa un model quantitatiu per predir el trencament de l’objecte ceràmic quan aquest és sotmès a diferents condicions de pressió. Aquest model ha estat aplicat a diferents tipologies amforals. Els resultats preliminars mostren diferències significatives entre la tipologia pre-romana i les tipologies romanes, així com entre els mateixos dissenys amforals romans, d’importants implicacions arqueològiques.

On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

Decomposing differences in total factor productivity across firm size

This paper investigates the extent to which the gap in total factor productivity between small and large firms is due to differences in the endowment of factors determining productivity and to the returns associated with these factors. We place particular emphasis on the contribution of differences in the propensity to innovate and in the use of skilled labor across firms of different size. Empirical evidence from a representative sample of Spanish manufacturing firms corroborates that both differences in endowments and returns to innovation and skilled labor significantly contribute to the productivity gap between small and large firms. In addition, it is observed that the contribution of innovation to this gap is caused only by differences in quantity, while differences in returns have no effect; in the case of human capital, however, most of the effect can be attributed to increasing differences in returns between small and large firms.

Study of the influence of grain size and precipitates on the electromagnetic losses in different grades of non-oriented fully processed electrical steel

The study was performed in the installations of OCAS, a Steel Research Centre of ArcelorMittal. Taking M32 steel (3.25%Si+0.9%Al) as the basis chemical composition and three different thicknesses (0.35, 0.5 and 0.65mm), different annealing conditions (temperature and time) have been applied in the laboratory simulator at St. Chély, France. The aim was to link annealing parameters, grain size and energy loss. It was determined the optimum annealing parameters to reach the lowest power losses for three different grades of non-oriented fully processed electrical steel. In addition, M250-50 samples having different magnetic behaviour (high and low losses) but the same grain size and texture, have been analyzed in terms of TEM observations of their precipitates, in the University of Marseille. The results reveal that a high amount of medium and big precipitates (&10 nm) worsen the magnetic properties of the material. The small precipitates (&10nm) do not have a strong influence on the magnetic properties. The presence of precipitates can have a great influence on the power losses and further work is clearly necessary.

Firms in Scottish High Technology Clusters: software, life sciences, microelectronics, optoelectronics and digital media – preliminary evidence and analysis on firm size, growth and optimality

This paper reports on: (a) new primary source evidence on; and (b) statistical and econometric analysis of high technology clusters in Scotland. It focuses on the following sectors: software, life sciences, microelectronics, optoelectronics, and digital media. Evidence on a postal and e-mailed questionnaire is presented and discussed under the headings of: performance, resources, collaboration & cooperation, embeddedness, and innovation. The sampled firms are characterised as being small (viz. micro-firms and SMEs), knowledge intensive (largely graduate staff), research intensive (mean spend on R&D GBP 842k), and internationalised (mainly selling to markets beyond Europe). Preliminary statistical evidence is presented on Gibrat’s Law (independence of growth and size) and the Schumpeterian Hypothesis (scale economies in R&D). Estimates suggest a short-run equilibrium size of just 100 employees, but a long-run equilibrium size of 1000 employees. Further, to achieve the Schumpeterian effect (of marked scale economies in R&D), estimates suggest that firms have to grow to very much larger sizes of beyond 3,000 employees. We argue that the principal way of achieving the latter scale may need to be by takeovers and mergers, rather than by internally driven growth.

Simulación de fluidos inmiscibles con el Particle Finite Element Method (PFEM)

Proyecto de investigación realizado a partir de una estancia en el Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC), Argentina, entre febrero y abril del 2007. La simulación numérica de problemas de mezclas mediante el Particle Finite Element Method (PFEM) es el marco de estudio de una futura tesis doctoral. Éste es un método desarrollado conjuntamente por el CIMEC y el Centre Internacional de Mètodos Numèrics en l'Enginyeria (CIMNE-UPC), basado en la resolución de las ecuaciones de Navier-Stokes en formulación Lagrangiana. El mallador ha sido implementado y desarrollado por Dr. Nestor Calvo, investigador del CIMEC. El desarrollo del módulo de cálculo corresponde al trabajo de tesis de la beneficiaria. La correcta interacción entre ambas partes es fundamental para obtener resultados válidos. En esta memoria se explican los principales aspectos del mallador que fueron modificados (criterios de refinamiento geométrico) y los cambios introducidos en el módulo de cálculo (librería PETSc, algoritmo predictor-corrector) durante la estancia en el CIMEC. Por último, se muestran los resultados obtenidos en un problema de dos fluidos inmiscibles con transferencia de calor.

Entrance pupil size predicts retinal illumination in darkly pigmented eyes, but not lightly pigmented eyes.

PURPOSE: We determined the effect of entrance pupil size on retinal illumination. The influence of unilateral miosis on the magnitude of the pupil light reflex was studied to ascertain how a clinically significant anisocoria influences the relative afferent pupil defect (RAPD). METHODS: Miosis was induced by topical 1% pilocarpine in the right eye of 14 healthy subjects with normal eyes. The interocular difference in retinal illumination was assessed by computerized pupillometry from the stimulus response curve of the right and left eyes. The main outcome measure was the RAPD, determined by computerized pupillography, at baseline and after pilocarpine-induced anisocoria. RESULTS: Induced anisocoria produced a significant change in RAPD from baseline (mean = 1.60 dB in the miotic eye, P = 0.007). However, anisocoria correlated with RAPD only in subjects with darkly pigmented irides (Pearson correlation coefficient 0.793, P = 0.05). CONCLUSIONS: In darkly pigmented eyes, entrance pupil size significantly influenced the retinal illumination. However, retinal illumination of lightly pigmented eyes is relatively independent of entrance pupil size, presumably due to extrapupillary transmission of light through the iris and sclera. This has important implications in understanding the potential influence of anisocoria on the RAPD and also greater susceptibility of lightly pigmented eyes to light toxicity.

Finite Horizon Learning

Incorporating adaptive learning into macroeconomics requires assumptions about how agents incorporate their forecasts into their decision-making. We develop a theory of bounded rationality that we call finite-horizon learning. This approach generalizes the two existing benchmarks in the literature: Eulerequation learning, which assumes that consumption decisions are made to satisfy the one-step-ahead perceived Euler equation; and infinite-horizon learning, in which consumption today is determined optimally from an infinite-horizon optimization problem with given beliefs. In our approach, agents hold a finite forecasting/planning horizon. We find for the Ramsey model that the unique rational expectations equilibrium is E-stable at all horizons. However, transitional dynamics can differ significantly depending upon the horizon.