Partial correlation : Network analysis

The final year project came to us as an opportunity to get involved in a topic which has appeared to be attractive during the learning process of majoring in economics: statistics and its application to the analysis of economic data, i.e. econometrics.Moreover, the combination of econometrics and computer science is a very hot topic nowadays, given the Information Technologies boom in the last decades and the consequent exponential increase in the amount of data collected and stored day by day. Data analysts able to deal with Big Data and to find useful results from it are verydemanded in these days and, according to our understanding, the work they do, although sometimes controversial in terms of ethics, is a clear source of value added both for private corporations and the public sector. For these reasons, the essence of this project is the study of a statistical instrument valid for the analysis of large datasets which is directly related to computer science: Partial Correlation Networks.The structure of the project has been determined by our objectives through the development of it. At first, the characteristics of the studied instrument are explained, from the basic ideas up to the features of the model behind it, with the final goal of presenting SPACE model as a tool for estimating interconnections in between elements in large data sets. Afterwards, an illustrated simulation is performed in order to show the power and efficiency of the model presented. And at last, the model is put into practice by analyzing a relatively large data set of real world data, with the objective of assessing whether the proposed statistical instrument is valid and useful when applied to a real multivariate time series. In short, our main goals are to present the model and evaluate if Partial Correlation Network Analysis is an effective, useful instrument and allows finding valuable results from Big Data.As a result, the findings all along this project suggest the Partial Correlation Estimation by Joint Sparse Regression Models approach presented by Peng et al. (2009) to work well under the assumption of sparsity of data. Moreover, partial correlation networks are shown to be a very valid tool to represent cross-sectional interconnections in between elements in large data sets.The scope of this project is however limited, as there are some sections in which deeper analysis would have been appropriate. Considering intertemporal connections in between elements, the choice of the tuning parameter lambda, or a deeper analysis of the results in the real data application are examples of aspects in which this project could be completed.To sum up, the analyzed statistical tool has been proved to be a very useful instrument to find relationships that connect the elements present in a large data set. And after all, partial correlation networks allow the owner of this set to observe and analyze the existing linkages that could have been omitted otherwise.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

A two-dimensional doppler-radiometer for earth observation

Compared to synthetic aperture radars (SARs), the angular resolution of microwave radiometers is quite poor. Traditionally, it has been limited by the physical size of the antenna. However, the angular resolution can be improved by means of aperture synthesis interferometric techniques. A narrow beam is synthesized during the image formation processing of the cross-correlations measured at zero-lag between pairs of signals collected by an array of antennas. The angular resolution is then determined by the maximum antenna spacing normalized to the wavelength (baseline). The next step in improving the angular resolution is the Doppler-Radiometer, somehow related to the super-synthesis radiometers and the Radiometer-SAR. This paper presents the concept of a three-antenna Doppler-Radiometer for 2D imaging. The performance of this instrument is evaluated in terms of angular/spatial resolution and radiometric sensitivity, and an L-band illustrative example is presented.

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.

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Spectral analysis of the angular distribution function of back reflectors for thin film silicon solar cells

Nowadays, one of the most important challenges to enhance the efficiency of thin film silicon solar cells is to increase the short circuit intensity by means of optical confinement methods, such as textured back-reflector structures. In this work, two possible textured structures to be used as back reflectors for n-i-p solar cells have been optically analyzed and compared to a smooth one by using a system which is able to measure the angular distribution function (ADF) of the scattered light in a wide spectral range (350-1000 nm). The accurate analysis of the ADF data corresponding to the reflector structures and to the μc-Si:H films deposited onto them allows the optical losses due to the reflector absorption and its effectiveness in increasing light absorption in the μc-Si:H layer, mainly at long wavelengths, to be quantified.

Angular distributions of leptons from J/ ψ's produced in 920 GeV fixed-target proton-nucleus collisions

A study of the angular distributions of leptons from decays of J/ψ"s produced in p-C and p-W collisions at s√=41.6~GeV has been performed in the J/ψ Feynman-x region −0.341 GeV/c a significant dependence on the reference frame is found: the polar anisotropy is more pronounced in the Collins-Soper frame and almost vanishes in the helicity frame, where, instead, a significant azimuthal anisotropy arises.

Genotypic classification of patients with Wolfram syndrome: insights into the natural history of the disease and correlation with phenotype

Purpose: Wolfram syndrome is a degenerative, recessive rare disease with an onset in childhood. It is caused by mutations in WFS1 or CISD2 genes. More than 200 different variations in WFS1 have been described in patients with Wolfram syndrome, which complicates the establishment of clear genotype-phenotype correlation. The purpose of this study was to elucidate the role of WFS1 mutations and update the natural history of the disease. Methods: This study analyzed clinical and genetic data of 412 patients with Wolfram syndrome published in the last 15 years. Results: (i) 15% of published patients do not fulfill the current ­inclusion criterion; (ii) genotypic prevalence differences may exist among countries; (iii) diabetes mellitus and optic atrophy might not be the first two clinical features in some patients; (iv) mutations are nonuniformly distributed in WFS1; (v) age at onset of diabetes mellitus, hearing defects, and diabetes insipidus may depend on the patient"s genotypic class; and (vi) disease progression rate might depend on genotypic class. Conclusion: New genotype-phenotype correlations were established, disease progression rate for the general population and for the genotypic classes has been calculated, and new diagnostic criteria have been proposed. The conclusions raised could be important for patient management and counseling as well as for the development of treatments for Wolfram syndrome.

Correlation of the EPR properties of perchlorotriphenylmethyl radical and their efficiency as DNP polarizers

Water soluble perchlorinated trityl (PTM) radicals were found to be effective 95 GHz DNP (dynamic nuclear polarization) polarizers in ex situ (dissolution) 13C DNP (Gabellieri et al., Angew Chem., Int. Ed. 2010, 49, 3360). The degree of the nuclear polarization obtained was reported to be dependent on the position of the chlorine substituents on the trityl skeleton. In addition, on the basis of the DNP frequency sweeps it was suggested that the 13C NMR signal enhancement is mediated by the Cl nuclei. To understand the DNP mechanism of the PTM radicals we have explored the 95 GHz EPR characteristics of these radicals that are relevant to their performance as DNP polarizers. The EPR spectra of the radicals revealed axially symmetric g-tensors. A comparison of the spectra with the 13C DNP frequency sweeps showed that although the solid effect mechanism is operational the DNP frequency sweeps reveal some extra width suggesting that contributions from EPR forbidden transitions involving 35,37Cl nuclear flips are likely. This was substantiated experimentally by ELDOR (electron-electron double resonance) detected NMR measurements, which map the EPR forbidden transitions, and ELDOR experiments that follow the depolarization of the electron spin upon irradiation of the forbidden EPR transitions. DFT (density functional theory) calculations helped to assign the observed transitions and provided the relevant spin Hamiltonian parameters. These results show that the 35,37Cl hyperfine and nuclear quadrupolar interactions cause a considerable nuclear state mixing at 95 GHz thus facilitating the polarization of the Cl nuclei upon microwave irradiation. Overlap of Cl nuclear frequencies and the 13C Larmor frequency further facilitates the polarization of the 13C nuclei by spin diffusion. Calculation of the 13C DNP frequency sweep based on the Cl nuclear polarization showed that it does lead to an increase in the width of the spectra, improving the agreement with the experimental sweeps, thus supporting the existence of a new heteronuclear assisted DNP mechanism.

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.

Correlation between charge transport and electroluminescence properties of Si-rich oxide/nitride/oxide-based light emitting capacitors.

The electrical and electroluminescence (EL) properties at room and high temperatures of oxide/ nitride/oxide (ONO)-based light emitting capacitors are studied. The ONO multidielectric layer is enriched with silicon by means of ion implantation. The exceeding silicon distribution follows a Gaussian profile with a maximum of 19%, centered close to the lower oxide/nitride interface. The electrical measurements performed at room and high temperatures allowed to unambiguously identify variable range hopping (VRH) as the dominant electrical conduction mechanism at low voltages, whereas at moderate and high voltages, a hybrid conduction formed by means of variable range hopping and space charge-limited current enhanced by Poole-Frenkel effect predominates. The EL spectra at different temperatures are also recorded, and the correlation between charge transport mechanisms and EL properties is discussed.

Approach to the Lower Pliocene marine-continental correlation from southern Spain. The micrommamal site of Alhaurín el Grande-1 (Málaga Basin, Betic Cordillera, Spain)

A new micromammal site at Alhaurín el Grande (Málaga, southern Spain) located above early Pliocene marine deposits allows an approach to the marine-continental correlation for this age. The early Pliocene marine filling throughout the Málaga Basin is developed in three transgressive-regressive sequences (Pl-1, Pl-2, and Pl-3 units) bounded by discontinuities. At the top of the intermediate sequence Pl-2, peaty sediments have yielded fossils of Rodentia, Lagomorpha, Insectivora, and Crocodylia. The presence of Cricetus barrieri Mein & Michaux, 1970 in combination with murids, both of primitive morphology, such as Apodemus gudrunae Van de Weerd, 1976, and more advanced forms (i.e. Occitanomys brailloni Michaux, 1969 and Stephanomys donnezani cordii Ruiz Bustos, 1986), points to an early Ruscinian age (MN 14 biozone). Based on the planktonic foraminifers, the biostratigraphic data indicate that marine sediments just below the micromammal beds belong to the MPl-2 biozone of the early Zanclean. Available paleomagnetic data from the marine sediments show that the micromammal bed must be located between the normal geomagnetic subchron C3n3n (4.89-4.80 Ma) and the subchron C3n2n (4.63-4.49 Ma), limiting the age of this site to the late part of the early Zanclean.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.