Rewiring of molecular interactions under different conditions causes different phenotypic responses. Differential Network Analysis (also indicated as DNA) aims to investigate the rewiring of gene and protein networks. DNA algorithms combine statistical learning and graph theory to explore the changes in the interaction patterns starting from experimental observation. Despite there exist many methods to model rewiring in networks, we propose to use age and gender factors to guide rewiring algorithms. We present a novel differential network analysis method that consider the differential expression of genes by means of sex and gender attributes. We hypothesise that the expression of genes may be represented by using a non-gaussian process. We quantify changes in nonparametric correlations between gene pairs and changes in expression levels for individual genes. We apply our method to identify the differential networks between males and females in public expression datasets related to mellitus diabetes in liver tissue. Results show that this method can find biologically relevant differential networks.
Networks provide an understandable and, in the case of small size, visualizable representation of data, which allows us to obtain essential information about the relationships between pairs of nodes, e.g., their distances. In visualization, networks have an alternative two-dimensional vector representation to which various machine-learning methods can be applied. More generally, networks can be transformed into a low-dimensional space using so-called embedding methods, which bridge the gap between network analysis and traditional machine learning by creating numerical representations that capture the essence of the network structure. In this article, we present a new embedding method that uses non-symmetric dependency to find the distance between nodes and applies an iterative procedure to find a satisfactory distribution of nodes in space. For dimension 2 and the visualization of the result, we demonstrate the method’s effectiveness on small networks. For higher dimensions and several larger networks, we present the results of two experiments comparing our results with two well-established methods in the research community, namely node2vec and DeepWalk. The first experiment focuses on a qualitative comparison of the methods, while the second focuses on applying and comparing the classification results to embeddings in a higher dimension. Although the presented method does not outperform the two chosen methods, its results are still comparable. Therefore, we also explain the limitations of our method and a possible way to overcome them.
People who inject drugs (PWID) are often members of HIV/AIDS risk networks, where individuals engage in sexual and injection risk behavior. Engagement in HIV care is important for this population. Low socioeconomic status, stigmatization, and lack of access to medical care often complicate successful engagement in the HIV cascade of care for PWID. This study investigates how individual's attitudes about how much control they have over HIV/AIDS risk in their life (i.e., locus of control and self-blame) affect health-seeking behavior in PWID participants and their community members. We applied causal inference methodology to PWID HIV risk networks ascertained from the Social Factors and HIV Risk Study (SFHR) conducted between 1991 and 1993 in Bushwick, Brooklyn, New York. We estimated protective disseminated effects of attitudes toward HIV/AIDS on the health-seeking behaviors of others in the PWID community. In other words, a positive attitude toward controlling HIV/AIDS can improve the health-seeking behavior of other members of the community who report a pessimistic attitude toward HIV/AIDS control. Given this finding, we also discuss potential network interventions to improve health-seeking behavior among both PWID individuals who receive the intervention and others in the PWID network informed by our analysis of disseminated effects.
Topological Data Analysis is a field of great interest in many applications such as finance or neuroscience. The goal of the present paper is to propose a novel approach to building simplicial complexes that capture the multiway ordered interactions in the components of high-dimensional time series using the theory of Signatures. Signatures represent one of the most powerful transforms for extracting group-wise structural features and we put them to work in the task of discovering statistically meaningful simplices from a complex that we estimate sequentially. Numerical experiments on an fMRI dataset illustrates the efficiency and relevance of our approach.
Uniform sampling from the set $\mathcal{G}(\mathbf{d})$ of graphs with a given degree-sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ is a classical problem in the study of random graphs. We consider an analogue for temporal graphs in which the edges are labeled with integer timestamps. The input to this generation problem is a tuple $\mathbf{D} = (\mathbf{d}, T) \in \mathbb N^n \times \mathbb N_{>0}$ and the task is to output a uniform random sample from the set $\mathcal{G}(\mathbf{D})$ of temporal graphs with degree-sequence $\mathbf{d}$ and timestamps in the interval $[1, T]$. By allowing repeated edges with distinct timestamps, $\mathcal{G}(\mathbf{D})$ can be non-empty even if $\mathcal{G}(\mathbf{d})$ is, and as a consequence, existing algorithms are difficult to apply. We describe an algorithm for this generation problem which runs in expected time $O(M)$ if $\Delta^{2+\epsilon} = O(M)$ for some constant $\epsilon > 0$ and $T - \Delta = \Omega(T)$ where $M = \sum_i d_i$ and $\Delta = \max_i d_i$. Our algorithm applies the switching method of McKay and Wormald $[1]$ to temporal graphs: we first generate a random temporal multigraph and then remove self-loops and duplicated edges with switching operations which rewire the edges in a degree-preserving manner.
