Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks.

In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.

An Information Theoretical Multilayer Network Approach to Breast Cancer Transcriptional Regulation.

Breast cancer is a complex, highly heterogeneous disease at multiple levels ranging from its genetic origins and molecular processes to clinical manifestations. This heterogeneity has given rise to the so-called intrinsic or molecular breast cancer subtypes. Aside from classification, these subtypes have set a basis for differential prognosis and treatment. Multiple regulatory mechanisms-involving a variety of biomolecular entities-suffer from alterations leading to the diseased phenotypes. Information theoretical approaches have been found to be useful in the description of these complex regulatory programs. In this work, we identified the interactions occurring between three main mechanisms of regulation of the gene expression program: transcription factor regulation, regulation via noncoding RNA, and epigenetic regulation through DNA methylation. Using data from The Cancer Genome Atlas, we inferred probabilistic multilayer networks, identifying key regulatory circuits able to (partially) explain the alterations that lead from a healthy phenotype to different manifestations of breast cancer, as captured by its molecular subtype classification. We also found some general trends in the topology of the multi-omic regulatory networks: Tumor subtype networks present longer shortest paths than their normal tissue counterpart; epigenomic regulation has frequently focused on genes enriched for certain biological processes; CpG methylation and miRNA interactions are often part of a regulatory core of conserved interactions. The use of probabilistic measures to infer information regarding theoretical-derived multilayer networks based on multi-omic high-throughput data is hence presented as a useful methodological approach to capture some of the molecular heterogeneity behind regulatory phenomena in breast cancer, and potentially other diseases.

Gene-Microbiome Co-expression Networks in Colon Cancer.

It is known that cancer onset and development arise from complex, multi-factorial phenomena spanning from the molecular, functional, micro-environmental, and cellular up to the tissular and organismal levels. Important advances have been made in the systematic analysis of the molecular (mostly genomic and transcriptomic) within large studies of high throughput data such as The Cancer Genome Atlas collaboration. However, the role of the microbiome in the induction of biological changes needed to reach these pathological states remains to be explored, largely because of scarce experimental data. In recent work a non-standard bioinformatics strategy was used to indirectly quantify microbial abundance from TCGA RNA-seq data, allowing the evaluation of the microbiome in well-characterized cancer patients, thus opening the way to studies incorporating the molecular and microbiome dimensions altogether. In this work, we used such recently described approaches for the quantification of microbial species alongside with gene expression. With this, we will reconstruct bipartite networks linking microbial abundance and gene expression in the context of colon cancer, by resorting to network reconstruction based on measures from information theory. The rationale is that microbial communities may induce biological changes important for the cancerous state. We analyzed changes in microbiome-gene interactions in the context of early (stages I and II) and late (stages III and IV) colon cancer, studied changes in network descriptors, and identify key discriminating features for early and late stage colon cancer. We found that early stage bipartite network is associated with the establishment of structural features in the tumor cells, whereas late stage is related to more advance signaling and metabolic features. This functional divergence thus arise as a consequence of changes in the organization of the corresponding gene-microorganism co-expression networks.

On a Class of Tensor Markov Fields.

Here, we introduce a class of Tensor Markov Fields intended as probabilistic graphical models from random variables spanned over multiplexed contexts. These fields are an extension of Markov Random Fields for tensor-valued random variables. By extending the results of Dobruschin, Hammersley and Clifford to such tensor valued fields, we proved that tensor Markov fields are indeed Gibbs fields, whenever strictly positive probability measures are considered. Hence, there is a direct relationship with many results from theoretical statistical mechanics. We showed how this class of Markov fields it can be built based on a statistical dependency structures inferred on information theoretical grounds over empirical data. Thus, aside from purely theoretical interest, the Tensor Markov Fields described here may be useful for mathematical modeling and data analysis due to their intrinsic simplicity and generality.

BrainWave Nets: Are Sparse Dynamic Models Susceptible to Brain Manipulation Experimentation?

Sparse time series models have shown promise in estimating contemporaneous and ongoing brain connectivity. This paper was motivated by a neuroscience experiment using EEG signals as the outcome of our established interventional protocol, a new method in neurorehabilitation toward developing a treatment for visual verticality disorder in post-stroke patients. To analyze the [complex outcome measure (EEG)] that reflects neural-network functioning and processing in more specific ways regarding traditional analyses, we make a comparison among sparse time series models (classic VAR, GLASSO, TSCGM, and TSCGM-modified with non-linear and iterative optimizations) combined with a graphical approach, such as a Dynamic Chain Graph Model (DCGM). These dynamic graphical models were useful in assessing the role of estimating the brain network structure and describing its causal relationship. In addition, the class of DCGM was able to visualize and compare experimental conditions and brain frequency domains [using finite impulse response (FIR) filter]. Moreover, using multilayer networks, the results corroborate with the susceptibility of sparse dynamic models, bypassing the false positives problem in estimation algorithms. We conclude that applying sparse dynamic models to EEG data may be useful for describing intervention-relocated changes in brain connectivity.

Using multiplex networks to capture the multidimensional nature of social structure.

Network analysis has increasingly expanded our understanding of social structure in primates and other animal species. However, most studies use networks representing only one interaction type, when social relationships (and the emerging social structure) are the result of many types of interactions and their interplay through time. The recent development of tools facilitating the integrated analysis of multiple interaction types using multiplex networks has opened the possibility of extending the insight provided by social network analysis. We use a multiplex representation of interactions among the members of a group of wild Geoffroy's spider monkeys (Ateles geoffroyi), to study their social structure. We constructed a six-layered multiplex network based on three indices of overt social interactions (aggression, embraces, grooming) and three distance-based indices (contact, proximity, and association). With tools provided by the MuxViz software, we assessed the relevance of including all six indices in our analysis, the role of individuals in the network (through node versatility), and the presence of modules and non-random triadic structures or motifs. The multiplex provided information which was not equivalent to any individual layer or to the simple aggregation of layers. Network patterns based on associations did not correspond with those observed for overt-interactions or for the multiplex structure. Males were the most versatile individuals, while multiplex modularity and motifs highlighted the relevance of different interaction types for the overall connectivity of the network. We conclude that the multiplex approach improves on previous methods by retaining valuable information from each interaction type and how it is patterned among individuals.