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.

Nets: Network estimation for time series

This work proposes novel network analysis techniques for multivariate time series.We define the network of a multivariate time series as a graph where verticesdenote the components of the process and edges denote non zero long run partialcorrelations. We then introduce a two step LASSO procedure, called NETS, toestimate high dimensional sparse Long Run Partial Correlation networks. This approachis based on a VAR approximation of the process and allows to decomposethe long run linkages into the contribution of the dynamic and contemporaneousdependence relations of the system. The large sample properties of the estimatorare analysed and we establish conditions for consistent selection and estimation ofthe non zero long run partial correlations. The methodology is illustrated with anapplication to a panel of U.S. bluechips.

Using gene-network landscape to dissect genotype effects of TCF7L2 genetic variant on diabetes and cardiovascular risk

Vaquero AR, Ferreira NE, Omae SV, Rodrigues MV, Teixeira SK, Krieger JE, Pereira AC. Using gene-network landscape to dissect genotype effects of TCF7L2 genetic variant on diabetes and cardiovascular risk. Physiol Genomics 44: 903-914, 2012. First published August 7, 2012; doi:10.1152/physiolgenomics.00030.2012.-The single nucleotide polymorphism (SNP) within the TCF7L2 gene, rs7903146, is, to date, the most significant genetic marker associated with Type 2 diabetes mellitus (T2DM) risk. Nonetheless, its functional role in disease pathology is poorly understood. The aim of the present study was to investigate, in vascular smooth muscle cells from 92 patients undergoing aortocoronary bypass surgery, the contribution of this SNP in T2DM using expression levels and expression correlation comparison approaches, which were visually represented as gene interaction networks. Initially, the expression levels of 41 genes (seven TCF7L2 splice forms and 40 other T2DM relevant genes) were compared between rs7903146 wild-type (CC) and T2DM-risk (CT + TT) genotype groups. Next, we compared the expression correlation patterns of these 41 genes between groups to observe if the relationships between genes were different. Five TCF7L2 splice forms and nine genes showed significant expression differences between groups. RXR alpha gene was pinpointed as showing the most different expression correlation pattern with other genes. Therefore, T2DM risk alleles appear to be influencing TCF7L2 splice form's expression in vascular smooth muscle cells, and RXR alpha gene is pointed out as a treatment target candidate for risk reduction in individuals with high risk of developing T2DM, especially individuals harboring TCF7L2 risk genotypes.

Characterisation of the sewage microbiome in four European cities throughout the COVID-19 pandemic by means of ecological and network modelling

The purpose of this work was to investigate possible patterns occurring in the sewage bacterial content of four cities (Bologna, Budapest, Rome, Rotterdam) over time (March 2020 - November 2021), also considering the possible effects of the lockdown periods due to the COVID-19 pandemic. The sewage metagenomics data were provided within VEO (Versatile Emerging infectious disease Observatory) project. The first analysis was the evaluation of the between samples diversity, looking for (dis)similarities among the cities, as well as among different time periods (seasonality). To this aim, we computed both similarity networks and Principal Coordinate Analysis (PCoA) plots based on the Bray-Curtis metric. Then, the alpha-biodiversity of the samples was estimated by means of different diversity indices. By looking at the temporal behaviour of the biodiversity in the four cities, we noticed an abrupt decrease in both Rome and Budapest in the Summer of 2020, that is related to: the prevalence of some species when the minimum occurred, and the change in correlations among species (studied via correlation networks), which is enriched in the period of minimum biodiversity. Rotterdam samples seem to be very different with respect to those from the other cities, as confirmed by PCoA. Moreover, the Rotterdam time series is proved to be stable and stationary also in terms of biodiversity. The low variability in the Rotterdam samples seems to be related to the species of Pseudomonas genus, which are highly variable and plentiful in the other cities, but are not among the most abundant in Rotterdam. Also, we observed that no seasonality effect emerged from the time series of the four cities. Regarding the impact of lockdown periods due to the COVID-19 pandemic, from the limited data available no effect on the time series considered emerges. More samples will be soon available and these analyses will be performed also on them, so that the possible effects of lockdowns may be studied.

Correlation of Modified Natural Rubber Properties by Artificial Neural Networks

Natural rubber (NR) is a raw material largely used by the modern industry; however, it is common that chemical modifications must be made to NR in order to improve properties such as hydrophobicity or mechanical resistance. This work deals with the correlation of properties of NR modified with dimethylaminoethylmethacrylate or methylmethacrylate as grafting agents. Dynamic-mechanical behavior and stress/strain relations are very important properties because they furnish essential characteristics of the material such as glass transition temperature and rupture point. These properties are concerned with different physical principles; for this reason, normally they are not related to each other. This work showed that they can be correlated by artificial neural networks (ANN). So, from one type of assay, the properties that as a rule only could be obtained from the other can be extracted by ANN correlation. POLYM. ENG. SCI., 49:499-505, 2009. (c) 2009 Society of Plastics Engineers

Correlation between Clinical/Radiographic Features and Inflammatory Cytokine Networks Produced by Macrophages Stimulated with Endodontic Content

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Complex tracer mobilities in polymer networks revealed by fluorescence correlation spectroscopy

Gels are elastic porous polymer networks that are accompanied by pronounced mechanical properties. Due to their biocompatibility, ‘responsive hydrogels’ (HG) have many biomedical applications ranging from biosensors and drug delivery to tissue engineering. They respond to external stimuli such as temperature and salt by changing their dimensions. Of paramount importance is the ability to engineer penetrability and diffusion of interacting molecules in the crowded HG environment, as this would enable one to optimize a specific functionality. Even though the conditions under which biomedical devices operate are rather complex, a bottom-up approach could reduce the complexity of mutually coupled parameters influencing tracer mobility. The present thesis focuses on the interaction-induced tracer diffusion in polymer solutions and their homologous gels, probed by means of Fluorescence Correlation Spectroscopy (FCS). This is a single-molecule-sensitive technique having the advantage of optimal performance under ultralow tracer concentrations, typically employed in biosensors. Two different types of hydrogels have been investigated, a conventional one with broad polydispersity in the distance between crosslink points and a so-called ‘ideal’, with uniform mesh size distribution. The former is based on a thermoresponsive polymer, exhibiting phase separation in water at temperatures close to the human body temperature. The latter represents an optimal platform to study tracer diffusion. Mobilities of different tracers have been investigated in each network, varying in size, geometry and in terms of tracer-polymer attractive strength, as perturbed by different stimuli. The thesis constitutes a systematic effort towards elucidating the role of the strength and nature of different tracer-polymer interactions, on tracer mobilities; it outlines that interactions can still be very important even in the simplified case of dilute polymer solutions; it also demonstrates that the presence of permanent crosslinks exerts distinct tracer slowdown, depending on the tracer type and the nature of the tracer-polymer interactions, expressed differently by each tracer with regard to the selected stimulus. In aqueous polymer solutions, the tracer slowdown is found to be system-dependent and no universal trend seems to hold, in contrast to predictions from scaling theory for non-interacting nanoparticle mobility and empirical relations concerning the mesh size in polymer solutions. Complex tracer dynamics in polymer networks may be distinctly expressed by FCS, depending on the specific synergy among-at least some of - the following parameters: nature of interactions, external stimuli employed, tracer size and type, crosslink density and swelling ratio.

Correlation Dimension of Complex Networks

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.

A comparison of sound localisation techniques using cross-correlation and spiking neural networks for mobile robotics

This paper outlines the development of a crosscorrelation algorithm and a spiking neural network (SNN) for sound localisation based on real sound recorded in a noisy and dynamic environment by a mobile robot. The SNN architecture aims to simulate the sound localisation ability of the mammalian auditory pathways by exploiting the binaural cue of interaural time difference (ITD). The medial superior olive was the inspiration for the SNN architecture which required the integration of an encoding layer which produced biologically realistic spike trains, a model of the bushy cells found in the cochlear nucleus and a supervised learning algorithm. The experimental results demonstrate that biologically inspired sound localisation achieved using a SNN can compare favourably to the more classical technique of cross-correlation.

A correlation aware algorithm for energy efficiency improvement in FiWi networks

Dissertação de Mestrado, Engenharia Informática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2014

Explosive Synchronization With Partial Degree-frequency Correlation.

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of their corresponding vertices exhibit so-called explosive synchronization behavior, which is now under intensive investigation. Here we study and discuss explosive synchronization in a situation that has not yet been considered, namely when only a part, typically a small part, of the vertices is subjected to a degree-frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform a mean-field analysis and our conclusions were corroborated by exhaustive numerical experiments for synthetic networks and also for the undirected and unweighed version of a typical benchmark biological network, namely the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed.

Border detection in complex networks

One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded on the recently introduced concept of node diversity. It is shown that this feature does not exhibit any relevant correlation with several well-established complex networks measurements. A methodology for the identification of the borders of complex networks is described and illustrated with respect to theoretical (geographical and knitted networks) as well as real-world networks (urban and word association networks), yielding interesting results and insights in both cases.

Optimization of the AZO dyes decoloration process through neural networks: Determination of the H2O2 addition critical point

The concentration of hydrogen peroxide is an important parameter in the azo dyes decoloration process through the utilization of advanced oxidizing processes, particularly by oxidizing via UV/H2O2. It is pointed out that, from a specific concentration, the hydrogen peroxide works as a hydroxyl radical self-consumer and thus a decrease of the system`s oxidizing power happens. The determination of the process critical point (maximum amount of hydrogen peroxide to be added) was performed through a ""thorough mapping"" or discretization of the target region, founded on the maximization of an objective function objective (constant of reaction kinetics of pseudo-first order). The discretization of the operational region occurred through a feedforward backpropagation neural model. The neural model obtained presented remarkable coefficient of correlation between real and predicted values for the absorbance variable, above 0.98. In the present work, the neural model had, as phenomenological basis the Acid Brown 75 dye decoloration process. The hydrogen peroxide addition critical point, represented by a value of mass relation (F) between the hydrogen peroxide mass and the dye mass, was established in the interval 50 < F < 60. (C) 2007 Elsevier B.V. All rights reserved.

An fMRI Normative Database for Connectivity Networks Using One-Class Support Vector Machines

The application of functional magnetic resonance imaging (fMRI) in neuroscience studies has increased enormously in the last decade. Although primarily used to map brain regions activated by specific stimuli, many studies have shown that fMRI can also be useful in identifying interactions between brain regions (functional and effective connectivity). Despite the widespread use of fMRI as a research tool, clinical applications of brain connectivity as studied by fMRI are not well established. One possible explanation is the lack of normal pattern, and intersubject variability-two variables that are still largely uncharacterized in most patient populations of interest. In the current study, we combine the identification of functional connectivity networks extracted by using Spearman partial correlation with the use of a one-class support vector machine in order construct a normative database. An application of this approach is illustrated using an fMRI dataset of 43 healthy Subjects performing a visual working memory task. In addition, the relationships between the results obtained and behavioral data are explored. Hum Brain Mapp 30:1068-1076, 2009. (C) 2008 Wiley-Liss. Inc.

Characterization of dimethacrylate polymeric networks: A study of the crosslinked structure formed by monomers used in dental composites

The resin phase of dental composites is mainly composed of combinations of dimethacrylate comonomers, with final polymeric network structure defined by monomer type/reactivity and degree of conversion. This fundamental study evaluates how increasing concentrations of the flexible triethylene glycol dimethacrylate (TEGDMA) influences void formation in bisphenol A diglycidyl dimethacrylate (BisGMA) co-polymerizations and correlates this aspect of network structure with reaction kinetic parameters and macroscopic volumetric shrinkage. Photopolymerization kinetics was followed in real-time by a near-infrared (NIR) spectroscopic technique, viscosity was assessed with a viscometer, volumetric shrinkage was followed with a linometer, free volume formation was determined by positron annihilation lifetime spectroscopy (PALS) and the sol-gel composition was determined by extraction with dichloromethane followed by (1)H NMR analysis. Results show that, as expected, volumetric shrinkage increases with TEGDMA concentration and monomer conversion. Extraction/(1)H NMR studies show increasing participation of the more flexible TEGDMA towards the limiting stages of conversion/crosslinking development. As the conversion progresses, either based on longer irradiation times or greater TEGDMA concentrations, the network becomes more dense, which is evidenced by the decrease in free volume and weight loss after extraction in these situations. For the same composition (BisGMA/TEGDMA 60-40 mol%) light-cured for increasing periods of time (from 10 to 600 s), free volume decreased and volumetric shrinkage increased, in a linear relationship with conversion. However, the correlation between free volume and macroscopic volumetric shrinkage was shown to be rather complex for variable compositions exposed for the same time (600 s). The addition of TEGDMA decreases free-volume up to 40 mol% (due to increased conversion), but above that concentration, in spite of the increase in conversion/crosslinking, free volume pore size increases due to the high concentration of the more flexible monomer. In those cases, the increase in volumetric shrinkage was due to higher functional group concentration, in spite of the greater free volume. Therefore, through the application of the PALS model, this study elucidates the network formation in dimethacrylates commonly used in dental materials. (C) 2010 Elsevier Ltd. All rights reserved.