On the effects of firing memory in the dynamics of conjunctive networks

Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel or \emph{synchronous} to \emph{asynchronous.} However, studying each possible dynamics defined by different update schemes might not be efficient. In this context, considering some type of temporal delay in the dynamics of Boolean networks emerges as an alternative approach. In this paper, we focus in studying the effect of a particular type of delay called \emph{firing memory} in the dynamics of Boolean networks. Particularly, we focus in symmetric (non-directed) conjunctive networks and we show that there exist examples that exhibit attractors of non-polynomial period. In addition, we study the prediction problem consisting in determinate if some vertex will eventually change its state, given an initial condition. We prove that this problem is {\bf PSPACE}-complete

The cultural epigenetics of psychopathology: The missing heritability of complex diseases found?

We extend a cognitive paradigm for gene expression based on the asymptotic limit theorems of information theory to the epigenetic epidemiology of mental disorders. In particular, we recognize the fundamental role culture plays in human biology, another heritage mechanism parallel to, and interacting with, the more familiar genetic and epigenetic systems. We do this via a model through which culture acts as another tunable epigenetic catalyst that both directs developmental trajectories, and becomes convoluted with individual ontology, via a mutually-interacting crosstalk mediated by a social interaction that is itself culturally driven. We call for the incorporation of embedding culture as an essential component of the epigenetic regulation of human mental development and its dysfunctions, bringing what is perhaps the central reality of human biology into the center of biological psychiatry. Current US work on gene-environment interactions in psychiatry must be extended to a model of gene-environment-culture interaction to avoid becoming victim of an extreme American individualism that threatens to create paradigms particular to that culture and that are, indeed, peculiar in the context of the world's cultures. The cultural and epigenetic systems of heritage may well provide the 'missing' heritability of complex diseases now under so much intense discussion

Networks of Gene Regulation, Neural Development and the Evolution of General Capabilities, Such as Human Empathy

A network of gene regulation organized in a hierarchical and combinatorial manner is crucially involved in the development of the neural network, and has to be considered one of the main substrates of genetic change in its evolution. Though qualitative features may emerge by way of the accumulation of rather unspecific quantitative changes, it is reasonable to assume that at least in some cases specific combinations of regulatory parts of the genome initiated new directions of evolution, leading to novel capabilities of the brain. These notions are applied, in this paper, to the evolution of the capability of cognition-based human empa­thy. It is suggested that it has evolved as a secondary effect of the evolution of strategic thought. Development of strategies depends on abstract representations of one’s own pos­sible future states in one’s own brain to allow assessment of their emotional desirability, but also on the representation and emotional evaluation of possible states of others, allowing anticipation of their behaviour. This is best achieved if representations of others are con­nected to one’s own emotional centres in a manner similar to self-representations. For this reason, the evolution of the human brain is assumed to have established representations with such linkages. No group selection is involved, because the quality of strategic thought affects the fitness of the individual. A secondary effect of this linkage is that both the actual states and the future perspectives of others elicit vicarious emotions, which may contribute to the motivations of altruistic behaviour

Gene Expression and its Discontents: Developmental disorders as dysfunctions of epigenetic cognition

Systems biology presently suffers the same mereological and sufficiency fallacies that haunt neural network models of high order cognition. Shifting perspective from the massively parallel space of gene matrix interactions to the grammar/syntax of the time series of expressed phenotypes using a cognitive paradigm permits import of techniques from statistical physics via the homology between information source uncertainty and free energy density. This produces a broad spectrum of possible statistical models of development and its pathologies in which epigenetic regulation and the effects of embedding environment are analogous to a tunable enzyme catalyst. A cognitive paradigm naturally incorporates memory, leading directly to models of epigenetic inheritance, as affected by environmental exposures, in the largest sense. Understanding gene expression, development, and their dysfunctions will require data analysis tools considerably more sophisticated than the present crop of simplistic models abducted from neural network studies or stochastic chemical reaction theory