Differential analysis of biological networks

In cancer research, the comparison of gene expression or DNA methylation networks inferred from healthy controls and patients can lead to the discovery of biological pathways associated to the disease. As a cancer progresses, its signalling and control networks are subject to some degree of localised re-wiring. Being able to detect disrupted interaction patterns induced by the presence or progression of the disease can lead to the discovery of novel molecular diagnostic and prognostic signatures. Currently there is a lack of scalable statistical procedures for two-network comparisons aimed at detecting localised topological differences. We propose the dGHD algorithm, a methodology for detecting differential interaction patterns in two-network comparisons. The algorithm relies on a statistic, the Generalised Hamming Distance (GHD), for assessing the degree of topological difference between networks and evaluating its statistical significance. dGHD builds on a non-parametric permutation testing framework but achieves computationally efficiency through an asymptotic normal approximation. We show that the GHD is able to detect more subtle topological differences compared to a standard Hamming distance between networks. This results in the dGHD algorithm achieving high performance in simulation studies as measured by sensitivity and specificity. An application to the problem of detecting differential DNA co-methylation subnetworks associated to ovarian cancer demonstrates the potential benefits of the proposed methodology for discovering network-derived biomarkers associated with a trait of interest

Statistical methods for comparing labelled graphs

Due to the availability of the vast amount of graph-structured data generated in various experiment settings (e.g., biological processes, social connections), the need to rapidly identify network structural differences is becoming increasingly prevalent. In many fields, such as bioinformatics, social network analysis and neuroscience, graphs estimated from the same experimental settings are always defined on a fixed set of objects. We formalize such a problem as a labelled graph comparison problem. The main issue in this area, i.e. measuring the distance between graphs, has been extensively studied over the past few decades. Although a large distance value constitutes evidence of difference between graphs, we are more interested in the issue of inferentially justifying whether a distance value as large or larger than the observed distance could have been obtained simply by chance. However, little work has been done to provide the procedures of statistical inference necessary to formally answer this question. Permutation-based inference has been proposed as a theoretically sound approach and a natural way of tackling such a problem. However, the common permutation procedure is computationally expensive, especially for large graphs. This thesis contributes to the labelled graph comparison problem by addressing three different topics. Firstly, we analyse two labelled graphs by inferentially justifying their independence. A permutation-based testing procedure based on Generalized Hamming Distance (GHD) is proposed. We show rigorously that the permutation distribution is approximately normal for a large network, under three graph models with two different types of edge weights. The statistical significance can be evaluated without the need to resort to computationally expensive permutation procedures. Numerical results suggest the validity of this approximation. With the Topological Overlap edge weight, we suggest that the GHD test is a more powerful test to identify network differences. Secondly, we tackle the problem of comparing two large complex networks in which only localized topological differences are assumed. By applying the normal approximation for the GHD test, we propose an algorithm that can effectively detect localised changes in the network structure from two large complex networks. This algorithm is quickly and easily implemented. Simulations and applications suggest that it is a useful tool to detect subtle differences in complex network structures. Finally, we address the problem of comparing multiple graphs. For this topic, we analyse two different problems that can be interpreted as corresponding to two distinct null hypotheses: (i) a set of graphs are mutually independent; (ii) graphs in one set are independent of graphs in another set. Applications for the multiple graphs problem are commonly found in social network analysis (i) or neuroscience (ii). However, little work has been done to inferentially address the problem of comparing multiple networks. We propose two different statistical testing procedures for (i) and (ii), by again using a normality approximation for GHD. We extend the normality of GHD for the two graphs case to multiple cases, for hypotheses (i) and (ii), with two different permutation strategies. We further build a link between the test of group independence to an existing method, namely the Multivariate Exponential Random Graph Permutation model (MERGP). We show that by applying asymptotic normality, the maximum likelihood estimate of MERGP can be analytically derived. Therefore, the original, computationally expensive, inferential procedure of MERGP can be abandoned.Open Acces

On the first place antitonicity in QL-implications

To obtain a demanded fuzzy implication in fuzzy systems, a number of desired properties have been proposed, among which the first place antitonicity, the second place isotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, R- and QL-implications all satisfy the second place isotonicity and the boundary conditions. However, not all the QL-implications satisfy the first place antitonicity as S- and R-implications do. In this paper we study the QL-implications satisfying the first place antitonicity. First we establish the relationship between the first place antitonicity and other required properties of QL-implications. Second we work on the conditions under which a QL-implication generated by different combinations of a t-conorm S, a t-norm T and a strong fuzzy negation N satisfy the first place antitonicity, especially in the cases that both S and T are continuous. We further investigate the interrelationships between S- and R-implications generated by left-continuous t-norms on one hand and QL-implications satisfying the first place antitonicity on the other

A relação entre o desempenho e a forma legal das instituições de microcrédito

This paper investigates the relationship between the legal forms adopted by microfinance institutions (MFIs) and their performance within three scopes: financial performance, social performance, and efficiency in resource allocation. The MFIs studied are classified into four groups: banks, non-governmental organizations, cooperatives, and a fourth group formed of for-profit institutions not characterized as banks, made up of non-bank financial institutions (NBFIs) and rural banks. The data used are annual and cover the six years from 2007 to 2012. The quantitative regression model with panel data was used together with dummy variables to compare between the four groups of legal forms, except for the group made up of NBFIs and rural banks, which was not represented by any dummy variable. 304 MFIs from 59 countries made up the sample. In the study it was observed that larger MFIs have higher profits, higher returns, and higher operational self-sufficiency rates than smaller MFIs, indicating that MFI growth could enable consolidation in the microfinance market. The results also indicate that for smaller MFIs the way to consolidate and improve the indicators could be through assimilating or merging with other MFIs. It was also noted that non-bank financial institutions and rural banks are able to serve more customers and that cooperatives provide smaller loans, causing a bigger social impact, and that they obtain higher returns and profits. The results indicate that these legal forms may be the most appropriate for the microfinance market.Este trabalho observa a relação entre as formas legais adotadas por instituições de microcrédito (IMCs) e o desempenho das instituições sob três escopos: o desempenho financeiro, o desempenho social e a eficiência na alocação de recursos. As IMCs estudadas classificaram-se em quatro grupos, de acordo com as formas legais adotadas: bancos, organizações não governamentais, cooperativas e um quarto grupo formado pelas instituições com fins lucrativos não caracterizadas como bancos; esse grupo formou-se por instituições financeiras não bancárias (IFNBs) e bancos rurais. Os dados utilizados compreendem o período de seis anos, de 2007 a 2012, com periodicidade anual. Empregou-se o modelo quantitativo de regressão com dados em painel no qual se utilizaram variáveis dummies para comparação entre os quatro grupos de formas legais, excetuando-se o grupo formado por IFNBs e bancos rurais, não representados por uma variável dummy. Formaram a amostra 304 IMCs de 59 países. No trabalho, observou-se que IMCs maiores conseguem lucros maiores, retornos maiores e índices de autossuficiência operacional maiores, indicando que o crescimento das IMCs pode permitir a consolidação no mercado de microfinanças. O resultado também indica que, para as IMCs menores, o caminho para consolidação e melhora nos indicadores pode ser a assimilação ou fusão com outras IMCs. Também se observou que as IFNBs e os bancos rurais conseguem atender mais clientes; já as cooperativas fornecem empréstimos menores, causando maior impacto social, obtêm maiores lucros e maiores retornos. Tais resultados são indicativos que essas formas legais podem ser as mais adequadas para o mercado de microfinanças

Some views on information fusion and logic based approaches in decision making under uncertainty

Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches. The aim of this paper is to show noteworthy theoretical and applicational issues in the area of decision making under uncertainty that have been already done and raise new open research related to these topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty