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.

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.

The first SEPServer event catalogue 68-MeV solar proton events observed at 1 AU in 1996-2010

SEPServer is a three-year collaborative project funded by the seventh framework programme (FP7-SPACE) of the European Union. The objective of the project is to provide access to state-of-the-art observations and analysis tools for the scientific community on solar energetic particle (SEP) events and related electromagnetic (EM) emissions. The project will eventually lead to better understanding of the particle acceleration and transport processes at the Sun and in the inner heliosphere. These processes lead to SEP events that form one of the key elements of space weather. In this paper we present the first results from the systematic analysis work performed on the following datasets: SOHO/ERNE, SOHO/EPHIN, ACE/EPAM, Wind/WAVES and GOES X-rays. A catalogue of SEP events at 1 AU, with complete coverage over solar cycle 23, based on high-energy (~68-MeV) protons from SOHO/ERNE and electron recordings of the events by SOHO/EPHIN and ACE/EPAM are presented. A total of 115 energetic particle events have been identified and analysed using velocity dispersion analysis (VDA) for protons and time-shifting analysis (TSA) for electrons and protons in order to infer the SEP release times at the Sun. EM observations during the times of the SEP event onset have been gathered and compared to the release time estimates of particles. Data from those events that occurred during the European day-time, i.e., those that also have observations from ground-based observatories included in SEPServer, are listed and a preliminary analysis of their associations is presented. We find that VDA results for protons can be a useful tool for the analysis of proton release times, but if the derived proton path length is out of a range of 1 AU < s[3 AU, the result of the analysis may be compromised, as indicated by the anti-correlation of the derived path length and release time delay from the asso ciated X-ray flare. The average path length derived from VDA is about 1.9 times the nominal length of the spiral magnetic field line. This implies that the path length of first-arriving MeV to deka-MeV protons is affected by interplanetary scattering. TSA of near-relativistic electrons results in a release time that shows significant scatter with respect to the EM emissions but with a trend of being delayed more with increasing distance between the flare and the nominal footpoint of the Earth-connected field line.

Electron tunneling in heavily In-doped polycrystalline CdS films

The electrical properties of heavily In‐doped polycrystalline CdS films have been studied as a function of the doping level. The films were prepared by vacuum coevaporation of CdS and In. Conductivity and Hall measurements were performed over the temperature range 77-400 K. The conductivity decreases weakly with the temperature and shows a tendency towards saturation at low temperatures. A simple relationship σ=σ0(1+βT2) is found in the low‐temperature range. The temperature dependence of the mobility is similar to that of the conductivity since the Hall coefficient is found to be a constant in the whole temperature range. We interpret the experimental results in terms of a modified version of grain‐boundary trapping Seto"s model, taking into account thermionic emission and tunneling of carriers through the potential barriers. The barriers are found to be high and narrow, and tunneling becomes the predominating transport mechanism.

A Database of >20 keV Electron Green's Functions of Interplanetary Transport at 1 AU

We use interplanetary transport simulations to compute a database of electron Green's functions, i.e., differential intensities resulting at the spacecraft position from an impulsive injection of energetic (>20 keV) electrons close to the Sun, for a large number of values of two standard interplanetary transport parameters: the scattering mean free path and the solar wind speed. The nominal energy channels of the ACE, STEREO, and Wind spacecraft have been used in the interplanetary transport simulations to conceive a unique tool for the study of near-relativistic electron events observed at 1 AU. In this paper, we quantify the characteristic times of the Green's functions (onset and peak time, rise and decay phase duration) as a function of the interplanetary transport conditions. We use the database to calculate the FWHM of the pitch-angle distributions at different times of the event and under different scattering conditions. This allows us to provide a first quantitative result that can be compared with observations, and to assess the validity of the frequently used term beam-like pitch-angle distribution.

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.

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.

Current Sheet Regulation of Solar Near-relativistic Electron Injection Histories

We present a sample of three large near-relativistic (>50 keV) electron events observed in 2001 by both the ACE and the Ulysses spacecraft, when Ulysses was at high-northern latitudes (>60◦) and close to 2 AU. Despite the large latitudinal distance between the two spacecraft, electrons injected near the Sun reached both heliospheric locations. All three events were associated with large solar flares, strong decametric type II radio bursts and accompanied by wide (>212◦) and fast (>1400 km s−1) coronal mass ejections (CMEs). We use advanced interplanetary transport simulations and make use of the directional intensities observed in situ by the spacecraft to infer the electron injection profile close to the Sun and the interplanetary transport conditions at both low and high latitudes. For the three selected events, we find similar interplanetary transport conditions at different heliolatitudes for a given event, with values of the mean free path ranging from 0.04 AU to 0.27 AU. We find differences in the injection profiles inferred for each spacecraft. We investigate the role that sector boundaries of the heliospheric current sheet (HCS) have on determining the characteristics of the electron injection profiles. Extended injection profiles, associated with coronal shocks, are found if the magnetic footpoints of the spacecraft lay in the same magnetic sector as the associated flare, while intermittent sparse injection episodes appear when the spacecraft footpoints are in the opposite sector or a wrap in the HCS bounded the CME structure.

Buccal dental microwear and stable isotopes of El Collado: A mesolithic site from Spain,

This study examines the correlation between buccal dental microwear and stable isotopes. The buccal surface of post-canine teeth casts from El Collado, the largest Mesolithic site in Spain, were examined under Scanning Electron Microscope; photomicrographs were taken from the middle third of the buccal surface with magnification 100X. Only six individuals passed the criteria for buccal dental microwear analysis. The photomicrographs were treated by adobe Photoshop 8.01 to cover an area 0.56 mm² of middle third of buccal surface, the output photomicrographs were digitized using Sigmascan Pro 5 by SPSS. Then the correlation between buccal microwear pattern and stable isotopes of the same individuals, of the previous study of Guixe et al., 2006, was examined using a Pearson test. Statistical analysis revealed that there is no significant correlation between stable isotopes and buccal dental microwear of the people of the Mesolithic site of El Collado. The historical and archaeological documentation suggest that the Mesolithic people tended to consume marine food. Fish-drying techniques were used during the Mesolithic period which allowed the introduction of dust and sand to the fish. These abrasive particles affected the buccal dental microwear pattern, so that no correlation between the isotopes and microwear may be expected. This also suggests that the buccal dental microwear pattern exceeds dietary reconstruction to reconstruct food processing techniques.

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.

Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment

A precise determination of the neutron skin thickness of a heavy nucleus sets a basic constraint on the nuclear symmetry energy (the neutron skin thickness is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on 208Pb. We investigate PVES in nuclear mean field approach to allow the accurate extraction of the neutron skin thickness of 208Pb from the parity-violating asymmetry probed in the experiment. We demonstrate a high linear correlation between the parity-violating asymmetry and the neutron skin thickness in successful mean field forces as the best means to constrain the neutron skin of 208Pb from PREX, without assumptions on the neutron density shape. Continuation of the experiment with higher precision in the parity-violating asymmetry is motivated since the present method can support it to constrain the density slope of the nuclear symmetry energy to new accuracy.