Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering ofcompositional data in situations where observations are constituted by trajectories ofcompositional data, that is, by sequences of composition measurements along a domain.Observed trajectories are known as “functional data” and several methods have beenproposed for their analysis.In particular, methods for clustering functional data, known as Functional ClusterAnalysis (FCA), have been applied by practitioners and scientists in many fields. To ourknowledge, FCA techniques have not been extended to cope with the problem ofclustering compositional data trajectories. In order to extend FCA techniques to theanalysis of compositional data, FCA clustering techniques have to be adapted by using asuitable compositional algebra.The present work centres on the following question: given a sample of compositionaldata trajectories, how can we formulate a segmentation procedure giving homogeneousclasses? To address this problem we follow the steps described below.First of all we adapt the well-known spline smoothing techniques in order to cope withthe smoothing of compositional data trajectories. In fact, an observed curve can bethought of as the sum of a smooth part plus some noise due to measurement errors.Spline smoothing techniques are used to isolate the smooth part of the trajectory:clustering algorithms are then applied to these smooth curves.The second step consists in building suitable metrics for measuring the dissimilaritybetween trajectories: we propose a metric that accounts for difference in both shape andlevel, and a metric accounting for differences in shape only.A simulation study is performed in order to evaluate the proposed methodologies, usingboth hierarchical and partitional clustering algorithm. The quality of the obtained resultsis assessed by means of several indices

Anonymizing Graphs: Measuring Quality for Clustering

Peer-reviewed

Clustering in complex networks. I. General formalism

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two¿and not just one¿vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests different metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of this formalism and the metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the weak and the strong transitivity classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties.

Efficiency and quality in local government management: the case of Spanish local authorities

This study analyses efficiency levels in Spanish local governments and their determining factors through the application of DEA (Data Envelopment Analysis) methodology. It aims to find out to what extent inefficiency arises from external factors beyond the control of the entity, or on the other hand, how much it is due to inadequate management of productive resources. The results show that on the whole, there is still a wide margin within which managers could increase local government efficiency levels, although it is revealed that a great deal of inefficiency is due to exogenous factors. It is specifically found that the size of the entity, per capita tax revenue, the per capita grants or the amount of commercial activity are some of the factors determining local government inefficiency.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Metrics on diagram groups and uniform embeddings in a Hilbert space

"Vegeu el resum a l'inici del document del fitxer adjunt".

Spatial competition between two candidates of different quality: the effects of candidate ideology and private information

This paper examines competition in a spatial model of two-candidate elections, where one candidate enjoys a quality advantage over the other candidate. The candidates care about winning and also have policy preferences. There is two-dimensional private information. Candidate ideal points as well as their tradeoffs between policy preferences and winning are private information. The distribution of this two-dimensional type is common knowledge. The location of the median voter's ideal point is uncertain, with a distribution that is commonly known by both candidates. Pure strategy equilibria always exist in this model. We characterize the effects of increased uncertainty about the median voter, the effect of candidate policy preferences, and the effects of changes in the distribution of private information. We prove that the distribution of candidate policies approaches the mixed equilibrium of Aragones and Palfrey (2002a), when both candidates' weights on policy preferences go to zero.

Human capital in growth regressions: how much difference does data quality make? An update and further results

We construct estimates of educational attainment for a sample of OECD countries using previously unexploited sources. We follow a heuristic approach to obtain plausible time profiles for attainment levels by removing sharp breaks in the data that seem to reflect changes in classification criteria. We then construct indicators of the information content of our series and a number of previously available data sets and examine their performance in several growth specifications. We find a clear positive correlation between data quality and the size and significance of human capital coefficients in growth regressions. Using an extension of the classical errors in variables model, we construct a set of meta-estimates of the coefficient of years of schooling in an aggregate Cobb-Douglas production function. Our results suggest that, after correcting for measurement error bias, the value of this parameter is well above 0.50.

The provision of quality in a bilateral search market

We accomplish two goals. First, we provide a non-cooperative foundation for the use of the Nash bargaining solution in search markets. This finding should help to close the rift between the search and the matching-and-bargaining literature. Second, we establish that the diversity of quality offered (at an increasing price-quality ratio) in a decentralized market is an equilibrium phenomenon - even in the limit as search frictions disappear.

The effect of candidate quality on electoral equilibrium: an experimental study

When two candidates of different quality compete in a one dimensional policy space, the equilibrium outcomes are asymmetric and do not correspond to the median. There are three main effects. First, the better candidate adopts more centrist policies than the worse candidate. Second, the equilibrium is statistical, in the sense that it predicts a probability distribution of outcomes rather than a single degenerate outcome. Third, the equilibrium varies systematically with the level of uncertainty about the location of the median voter. We test these three predictions using laboratory experiments, and find strong support for all three. We also observe some biases and show that they canbe explained by quantal response equilibrium.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Microbial spoilage and quality of marinated dark, firm, dry meat

Estudi elaborat a partir d’una estada al Royal Veterinary and Agricultural University of Denmark entre els mesos de Març a Juny del 2006. S’ha investigat l’efecte dels envasats amb atmosferes modificades (MAP), així com la marinació amb vi tint, sobre l’evolució de la contaminació bacteriològica de carns fosques, dures i seques (DFD). Les carns DFD es troben a les canals d’animals que, abans del sacrifici, han estat exposades a activitats musculars prolongades o estrès. Les carns DFD impliquen importants pèrdues econòmiques degut a la contaminació bacteriològica i als problemes tecnològics relacionats amb la alta capacitat de retenció d’aigua. A més a més, és crític per la indústria investigar la diversitat de la contaminació bacteriana, identificar les espècies bacterianes i controlar-les. Però és difícil degut a la inhabilitat per detectar algunes bactèries en medis coneguts, les interaccions entre elles, la complexitat dels tipus de contaminació com són aigua, terra, femtes i l’ambient. La Polymerasa chain reaction- Denaturating Electrophoresis Gel (PCR-DGEE ) pot sobrepassar aquests problemes reflectint la diversitat microbial i les espècies bacterianes. Els resultants han indicat que la varietat bacteriana de la carn incrementava amb els dies d’envasat independentment del mètode d’envasat, però decreixia significativament amb el tractament de marinació amb vi tint. La DGEE ha mostrat diferències en les espècies trobades, indicant canvis en la contaminació bacteriana i les seves característiques en la carn DFD sota els diferents tractaments. Tot i que la marinació és una bona alternativa i solució a la comercialització de carn DFD , estudis de seqüenciació són necessaris per identificar les diferents tipus de bactèries.

Production and carcass quality of ten beef cattle breeds of the southwest of Europe

A sample of about 70 young bulls of each of ten beef cattle breeds reared in their typical production systems has been studied regarding growth and carcass quality traits. Breeds included were Asturiana de los Valles (AV), Asturiana de la Montaña (AM), Avileña-Negra Ibérica (A-NI), Bruna dels Pirineus (BP), Morucha (Mo), Pirenaica (Pi) and Retinta (Re) from Spain, and Aubrac (Au), Gasconne (Ga) and Salers (Sal) from France. There existed large differences between breeds and also within breeds. AV and Pi were the breeds with more muscle and less fat, whereas A-NI, Mo and Re were in the opposite side. BP and AM occupied an intermediate position. This allows to classify the Spanish breeds in three groups: AV and Pi would belong to the group of late maturity, A-NI, Mo and Re, would be early maturing breeds, whereas BP and AM, despite the small size of the last, will be of intermediate maturity. In the French populations, Au was the breed with the highest carcass weight and Ga exhibited the lowest. Sal occupied an intermediate position, showing the longer and thinner thigh. In a wide range of carcass weight, the general relationships among carcass traits have been confirmed. Animals with the better conformation were also the leaner and longer carcasses tended to be lowly associated with a poorer conformation and fatter carcasses. Bone content was clearly opposed to carcass conformation and muscle content and was associated with longer carcasses