Genome-wide association studies (GWAS) have become a common method for discovery of gene-disease relationships, in particular for complex diseases like Type 2 Diabetes Mellitus (T2DM). The experience with GWAS analysis has revealed that the genetic risk for complex diseases involves cumulative, small effects of many genes and only some genes with a moderate effect. In order to explore the complexity of the relationships between T2DM genes and their potential function at the process level as effected by polymorphism effects, a secondary analysis of a GWAS meta-analysis is presented. Network analysis, pathway information and integration of different types of biological information such as eQTLs and gene-environment interactions are used to elucidate the biological context of the genetic variants and to perform an analysis based on data visualization. We selected a T2DM dataset from a GWAS meta-analysis, and extracted 1,971 SNPs associated with T2DM. We mapped 580 SNPs to 360 genes, and then selected 460 pathways containing these genes from the curated collection of WikiPathways. We then created and analyzed SNP-gene and SNP-gene-pathway network modules in Cytoscape. A focus on genes with robust connections to pathways permitted identification of many T2DM pertinent pathways. However, numerous genes lack literature evidence of association with T2DM. We also speculate on the genes in specific network structures obtained in the SNP-gene network, such as gene-SNP-gene modules. Finally, we selected genes relevant to T2DM from our SNP-gene-pathway network, using different sources that reveal gene-environment interactions and eQTLs. We confirmed functions relevant to T2DM for many genes and have identified some—LPL and APOB—that require further validation to clarify their involvement in T2DM.

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In this paper, we consider systems with one resource, which can be in several states. The states differ significantly in their processes of mortality, reproduction and mutual influence. For instance, infected elements can have a higher mortality rate than healthy and recovered ones. For cyclic models, in which the initial state of the system coincides with the final state, balance relations are found. They represent a system with functional operators with shift and integrals with degenerate kernels. Modified Fredholm method, proposed in previous works to solve the integral equations of the second type with degenerate kernels and shifts, is applied. Equilibrium position of a system with a three-state resource is found.

This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

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