A Riemann hypothesis analogue for invariant rings

AbstractA Riemann hypothesis analogue for coding theory was introduced by I.M. Duursma [A Riemann hypothesis analogue for self-dual codes, in: A. Barg, S. Litsyn (Eds.), Codes and Association Schemes (Piscataway, NJ, 1999), American Mathematical Society, Providence, RI, 2001, pp. 115–124]. In this paper, we extend zeta polynomials for linear codes to ones for invariant rings, and we investigate whether a Riemann hypothesis analogue holds for some concrete invariant rings. Also we shall show that there is some subring of an invariant ring such that the subring is not an invariant ring but extremal polynomials all satisfy the Riemann hypothesis analogue

Analysis of human mitochondrial genome co-occurrence networks of Asian population at varying altitudes

Networks have been established as an extremely powerful framework to understand and predict the behavior of many large-scale complex systems. We studied network motifs, the basic structural elements of networks, to describe the possible role of co-occurrence of genomic variations behind high altitude adaptation in the Asian human population. Mitochondrial DNA (mtDNA) variations have been acclaimed as one of the key players in understanding the biological mechanisms behind adaptation to extreme conditions. To explore the cumulative effects of variations in the mitochondrial genome with the variation in the altitude, we investigated human mt-DNA sequences from the NCBI database at different altitudes under the co-occurrence motifs framework. Analysis of the co-occurrence motifs using similarity clustering revealed a clear distinction between lower and higher altitude regions. In addition, the previously known high altitude markers 3394 and 7697 (which are definitive sites of haplogroup M9a1a1c1b) were found to co-occur within their own gene complexes indicating the impact of intra-genic constraint on co-evolution of nucleotides. Furthermore, an ancestral ‘RSRS50’ variant 10,398 was found to co-occur only at higher altitudes supporting the fact that a separate route of colonization at these altitudes might have taken place. Overall, our analysis revealed the presence of co-occurrence interactions specific to high altitude at a whole mitochondrial genome level. This study, combined with the classical haplogroups analysis is useful in understanding the role of co-occurrence of mitochondrial variations in high altitude adaptation

Investigating Mitonuclear Genetic Interactions Through Machine Learning: A Case Study on Cold Adaptation Genes in Human Populations From Different European Climate Regions

Cold climates represent one of the major environmental challenges that anatomically modern humans faced during their dispersal out of Africa. The related adaptive traits have been achieved by modulation of thermogenesis and thermoregulation processes where nuclear (nuc) and mitochondrial (mt) genes play a major role. In human populations, mitonuclear genetic interactions are the result of both the peculiar genetic history of each human group and the different environments they have long occupied. This study aims to investigate mitonuclear genetic interactions by considering all the mitochondrial genes and 28 nuclear genes involved in brown adipose tissue metabolism, which have been previously hypothesized to be crucial for cold adaptation. For this purpose, we focused on three human populations (i.e., Finnish, British, and Central Italian people) of European ancestry from different biogeographical and climatic areas, and we used a machine learning approach to identify relevant nucDNA–mtDNA interactions that characterized each population. The obtained results are twofold: (i) at the methodological level, we demonstrated that a machine learning approach is able to detect patterns of genetic structure among human groups from different latitudes both at single genes and by considering combinations of mtDNA and nucDNA loci; (ii) at the biological level, the analysis identified population-specific nuclear genes and variants that likely play a relevant biological role in association with a mitochondrial gene (such as the “obesity gene” FTO in Finnish people). Further studies are needed to fully elucidate the evolutionary dynamics (e.g., migration, admixture, and/or local adaptation) that shaped these nucDNA–mtDNA interactions and their functional role