Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

Anàlisi de la qualitat de l'aigua: estudi dels impactes humans sobre la qualitat de l'aigua en pous i basses del Parc del Garraf i rodalies

Amb la finalitat de conèixer l’estat de qualitat de les aigües de les basses i pous del Parc del Garraf, s’analitzen una sèrie de paràmetres fisico-químics en 17 estacions de mostreig prèviament seleccionades, distribuïdes en zones amb diferents tipologies d’ús del sòl. La base de l’anàlisi ha estat la integració d’informació provinent de diferents fonts. Mitjançant l’elaboració de taules i gràfics, la generació de cartografia i el tractament estadístic de les dades, s’ha procedit a la tria de punts de mostreig i s’ha obtingut un inventari que ha permès la interpretació global dels resultats, facilitant la diagnosi. El procés de tractament de dades inclou la confecció d’un índex de qualitat de les aigües (ICA) propi, no vinculant, a partir de fórmules genèriques de normalització i ponderació de valors. Durant la realització de la diagnosi s’han detectat pertorbacions puntuals en determinats paràmetres corresponents a contaminacions locals, en diferents estacions de mostreig. Aquestes pertorbacions s’han relacionat amb la situació dels pous i les basses al Garraf i les tipologies d’ús del sòl de cada zona. El diagnòstic de pertorbacions ha orientat les propostes de millora aplicables que s’han dividit en tres classes segons el nivell d’actuació. Aquestes incideixen principalment, en la millora de la informació disponible, l’aplicació de l’agricultura ecològica, l’explotació sostenible dels aqüífers i la realització d’estudis globals i/o locals, més complets i exhaustius.

The glasses of the transept's rosette of the Cathedral of Tarragona: characterization, classification and decay.

The glasses of the rosette forming the main window of the transept of the Gothic Cathedral of Tarragona have been characterised by means of SEM/EDS, XRD, FTIR and electronic microprobe. The multivariate statistical treatment of these data allow to establish a classification of the samples forming groups having an historical significance and reflecting ancient restorations. Furthermore, the decay patterns and mechanisms have been determined and the weathering by-products characterised. It has been demonstrated a clear influence of the bioactivity in the decay of these glasses, which activity is partially controlled by the chemical composition of the glasses.

The glasses of the transept's rosette of the Cathedral of Tarragona: characterization, classification and decay.

The glasses of the rosette forming the main window of the transept of the Gothic Cathedral of Tarragona have been characterised by means of SEM/EDS, XRD, FTIR and electronic microprobe. The multivariate statistical treatment of these data allow to establish a classification of the samples forming groups having an historical significance and reflecting ancient restorations. Furthermore, the decay patterns and mechanisms have been determined and the weathering by-products characterised. It has been demonstrated a clear influence of the bioactivity in the decay of these glasses, which activity is partially controlled by the chemical composition of the glasses.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Anàlisi i proposta de millora del bloc de continguts d'activitats en el medi natural de la ESO

En aquet TFG1 és presenta un estudi on el seu objectiu és l’anàlisi de les dificultats que és troben els professors a l’hora d’impartir les activitats al medi natural, per tal de poder entendré com és que és el bloc de continguts menys treballat. Per això, s’ha utilitzat com a instrument un qüestionari que s’ha aplicat a 49 professors d’educació física de 26 comarques de Catalunya. Aquests docents han estat escollit aleatòriament i han respòs el qüestionari per voluntat pròpia. El tractament estadístic del qüestionari s’ha dut a terme amb Google Drive. Entre les conclusions cal destacar la diferència entre el currículum proposat per la LOE (2006) i el proposat per la LOE (2007), i la clara aposta del professorat per realitzar les activitats al medi natural fora del centre, amb el cost afegit que això suposa. Aquest últim fet, a més, sembla comportar, per una banda, la dificultat afegida que suposa pels professors el fet de sortir fora de l’escola i, per altra banda, la responsabilitat que requereix dur a terme aquestes activitats.

Lattice-gas model of particles with orientational and positional degrees of freedom: Mean-field treatment

We consider a lattice-gas model of particles with internal orientational degrees of freedom. In addition to antiferromagnetic nearest-neighbor (NN) and next-nearest-neighbor (NNN) positional interactions we also consider NN and NNN interactions arising from the internal state of the particles. The system then shows positional and orientational ordering modes with associated phase transitions at Tp and To temperatures at which long-range positional and orientational ordering are, respectively, lost. We use mean-field techniques to obtain a general approach to the study of these systems. By considering particular forms of the orientational interaction function we study coupling effects between both phase transitions arising from the interplay between orientational and positional degrees of freedom. In mean-field approximation coupling effects appear only for the phase transition taking place at lower temperatures. The strength of the coupling depends on the value of the long-range order parameter that remains finite at that temperature.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Hardness of FRHC-Cu determined by statistical analysis

A statistical indentation method has been employed to study the hardness value of fire-refined high conductivity copper, using nanoindentation technique. The Joslin and Oliver approach was used with the aim to separate the hardness (H) influence of copper matrix, from that of inclusions and grain boundaries. This approach relies on a large array of imprints (around 400 indentations), performed at 150 nm of indentation depth. A statistical study using a cumulative distribution function fit and Gaussian simulated distributions, exhibits that H for each phase can be extracted when the indentation depth is much lower than the size of the secondary phases. It is found that the thermal treatment produces a hardness increase, due to the partly re-dissolution of the inclusions (mainly Pb and Sn) in the matrix.

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.