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Introduction:Contrary to Diagnostic and Statistical Manual of Mental Disorders (DSM-5), fifth edition, some studies indicate that ADHD-inattentive presentation (ADHD-I) is a distinct diagnostic disorder and not an ADHD presentation.Methods:In this study, 12 ADHD-combined presentation (ADHD-C), 10 ADHD-I, and 13 controls were enrolled and their resting state EEG recorded. Following this, a graph theoretical analysis was performed and functional integration and segregation of brain network was calculated.Results:The results show that clustering coefficient of theta band was significantly different among three groups and significant differences were observed in theta global efficiency between controls and ADHD-C. Regarding the alpha band, a lower clustering coefficient was observed in control subjects. In the beta band, clustering coefficient was significantly different between the control and children with ADHD-C and also between ADHD-I and ADHD-C. The clustering coefficient, in the subjects with ADHD-C, demonstrated a rapid decline and was significantly lower than the subjects with ADHD-I and control.Conclusion:Decreased clustering, in high thresholds, may be associated with hyperactivity while increased segregation in low thresholds with inattentiveness. A different functional network occurs in the ADHD-C brain that is consistent with several studies that have reported ADHD-I as a distinct disorder.

Fixation probability, the probability that the frequency of a newly arising mutation in a population will eventually reach unity, is a fundamental quantity in evolutionary genetics. Here we use a number of models (several versions of the Moran model and the haploid Wright-Fisher model) to examine fixation probabilities for a constant size population where the fitness is a random function of both allelic state and spatial position, despite neither allele being favored on average. The concept of fitness varying with respect to both genotype and environment is important in models of cancer initiation and progression, bacterial dynamics, and drug resistance. Under our model spatial heterogeneity redefines the notion of neutrality for a newly arising mutation, as such mutations fix at a higher rate than that predicted under neutrality. The increased fixation probability appears to be due to rare alleles having an advantage. The magnitude of this effect can be large, and is an increasing function of the spatial variance and skew in fitness. The effect is largest when the fitness values of the mutants and wild types are anti-correlated across environments. We discuss results for both a spatial ring geometry of cells (such as that of a colonic crypt), a 2D lattice and a mass-action (complete graph) arrangement.

The mean conditional fixation time of a mutant is an important measure of stochastic population dynamics, widely studied in ecology and evolution. Here, we investigate the effect of spatial randomness on the mean conditional fixation time of mutants in a constant population of cells, N. Specifically, we assume that fitness values of wild type cells and mutants at different locations come from given probability distributions and do not change in time. We study spatial arrangements of cells on regular graphs with different degrees, from the circle to the complete graph, and vary assumptions on the fitness probability distributions. Some examples include: identical probability distributions for wild types and mutants; cases when only one of the cell types has random fitness values while the other has deterministic fitness; and cases where the mutants are advantaged or disadvantaged. Using analytical calculations and stochastic numerical simulations, we find that randomness has a strong impact on fixation time. In the case of complete graphs, randomness accelerates mutant fixation for all population sizes, and in the case of circular graphs, randomness delays mutant fixation for N larger than a threshold value (for small values of N, different behaviors are observed depending on the fitness distribution functions). These results emphasize fundamental differences in population dynamics under different assumptions on cell connectedness. They are explained by the existence of randomly occurring “dead zones” that can significantly delay fixation on networks with low connectivity; and by the existence of randomly occurring “lucky zones” that can facilitate fixation on networks of high connectivity. Results for death-birth and birth-death formulations of the Moran process, as well as for the (haploid) Wright Fisher model are presented.

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