网范文：“Extending the mathematical formalism” 在当前的背景下了解表观遗传,基于广群结构的认知基因表达，可能适用于人类思维的发展及其障碍,众所周知尤其受到嵌入文化的作用。这篇范文中，探讨表观遗传如何催化结构?如何与自发对称性相关联,使用适当的随机微分方程,定义结构的完整等。特别是随机扩展的结果，英语论文，第一个问题看起来相当直接的和有趣的。
文化结构的社会心理压力,可以编写自己的图像在人类本体论,而且如果足够强大,通过各种机制,消除身体功能障碍。这发生在一个轮廓的方式，类似于作用强调生态系统,逆转或减轻可能是非常困难的。下面的范文进行详述。
We have, in the context of the tunable epigenetic catalysis of Wallace and Wallace (2017), developed three separate phase transition/branching models of cognitive gene expression based on groupoid structures that may be applied to the development of the human mind and its dysfunctions, as known to be particularly influenced by embedding culture. The first used Landau’s spontaneous symmetry breaking to explore phase transitions in a groupoid free energy FD[K]. The second examined a holonomy groupoid in phenotype space generated by disjoint developmental homotopy equivalence classes, and ‘loops’ constructed by pairing one-way development paths. The third introduced a metric on a manifold of different information sources dual to cognitive gene expression, leading to a more conventional picture of parallel transport around a loop leading to holonomy.
The dynamical groupoid of Wallace and Fullilove (2017, Sec. 3.8) is seen as involving a disjoint union across underlying manifolds that produces a holonomy groupoid in a natural manner. There are a number of evident mathematical questions. The first is the relation between the Landau formalism and the structures of phenotype space S and those of the associated manifold of dual information sources, the manifold M having metric M. How does epigenetic catalysis in M-space imposes structure on S-space? How is this related to spontaneous symmetry breaking? What would a stochastic version of the theory, in the sense of Emery (1989), look like? It is quite possible, using appropriate averages of the stochastic differential equations that arise naturally, to define parallel transport, holonomy, and the like for these structures.
In particular a stochastic extension of the results of the first question would seem both fairly direct and interesting from a real-world perspective, as development is always ‘noisy’. The construction of loops from directed homotopy arcs in figure 1 is complicated by the necessity of imposing a consistent piecewise patching rule for parallel translation at the end of each arc, say from Si to Sn. This can probably be done by some standard fiat, but the details will likely be messy. One extension of theory would be of great interest: We have imposed metrics on S and M space, making possible a fairly standard manifold analysis of complex cognitive processes of gene expression and development. While this is no small thing, an important ‘natural’ generalization, given the ubiquity of groupoids across our formalism, would be to a groupoid atlas, in the sense of Bak et al., (2017) and Glazebrook and Wallace (2017b, Section 7.4). The groupoid atlas permits a weaker structure compared with that of a conventional manifold since no condition of compatibility between arbitrary overlaps of the patches is necessary.
It is possible that the groupoid atlas will become, to complicated problems in biological cognitive process, something of what the Riemannian manifold has been to physics. The groupoid atlas, unlike the Riemannian manifold, is quite new and under active study. With regard to questions of ‘smoothness’, we are assuming that the cognitive landscape of gene expression is sufficiently rich that discrete paths can be well approximated as continuous where necessary, the usual physicist’s hack. Finally, sections 5 and 6 are based on existence of more-or-less conventional metrics, and this may not be a good approximation to many real systems. Extending topological phase transition theory to ‘weaker’ topologies, e.g., Finsler geometries and the like, is not a trivial task.
Discussion
Culturally structured psychosocial stress, and similar noxious exposures, can write distorted images of themselves onto human ontology – both child growth, and, if sufficiently powerful, adult development as well – by a variety of mechanisms, initiating a punctuated trajectory to characteristic forms of comorbid mind/body dysfunction. This occurs in a manner recognizably analogous to resilience domain shifts affecting stressed ecosystems (e.g., Wallace, 2017; Holling, 1973; Gunderson, 2017). Consequently, like ecosystem restoration, reversal or palliation may often be exceedingly difficult once a generalized domain shift has taken place.
Thus a public health approach to the prevention of mental disorders may be paramount: rather than seeking to understand why half a population does not respond to the LD50 of a teratogenic environmental exposure, one seeks policies and social reforms that limit the exposure. Both socio-cultural and epigenetic environmental influences – like gene methylation – are heritable, in addition to genetic mechanisms. The missing heritability of complex diseases that Manolio et al. (2017) seek to find in more and better gene studies is most likely dispersed within the ‘dark matter’ of these two other systems of heritage that together constitute the larger, and likely highly synergistic, regulatory machinery for gene expression.
More and more purely genetic studies would, under such circumstances, be akin to using increasingly powerful microscopes to look for cosmic membranes of strewn galaxies. A crucial matter for future work is the conversion of the probability models we present here into statistical tools suitable for analyzing real data. This requires not only programming the models for use, but identifying appropriate real-world problems, assembling available data sets, transforming the data as needed for the models, and actually applying the programs.
Indeed, the environmental health literature contains numerous examples of developmental deviations due to either chemical exposures or interaction between chemical and socioeconomic exposures, and these could serve as sources of data for direct analysis (e.g., Needleman et al., 1996; Fullilove, 2017; Dietrich et al., 2017; Miranda et al., 2017; Glass et al., 2017; Jacobson and Jacobson, 2017; Shankardass et al., 2017; Clougherty et al., 2017; Ben Jonathan et al., 2017; Karp et al., 2017; Sarlio-Lahteenkorva and Lahelma, 2017; Wallace and Wallace, 2017; Wallace, Wallace and Rauh, 2017). Thus, quite a number of data sets exist in the environmental health and socioeconomic epidemiological literature that could be subjected to meta-analysis and other review for model verification and fitting.
Our topological models, when converted to statistical tools for data analysis, hold great potential for understanding developmental trajectories and interfer- ing factors (teratogens) through the life course. Sets of cross cultural variants of these data focusing specifically on mental disorders, would be needed to address the particular concerns of this . Nonetheless, what we have done is of no small interest for understanding the ontology of the human mind and its pathologies. West-Eberhard (2017, 2017) argues that any new input, whether it comes from the genome, like a mutation, or from the external environment, like a temperature change, a pathogen, or a parental opinion, has a developmental effect only if the preexisting phenotype is responsive to it.
A new input causes a reorganization of the phenotype, or ‘developmental recombination’. In developmental recombination, phenotypic traits are expressed in new or distinctive combinations during ontogeny, or undergo correlated quantitative change in dimensions. Developmental recombination can result in evolutionary divergence at all levels of organization. According to West-Eberhard, individual development can be visualized as a series of branching pathways. Each branch point is a developmental decision, or switch point, governed by some regulatory apparatus, and each switch point defines a modular trait.
Developmental recombination implies the origin or deletion of a branch and a new or lost modular trait. The novel regulatory response and the novel trait originate simultaneously. Their origins are, in fact, inseparable events: There cannot, West-Eberhard concludes, be a change in the phenotype, a novel phenotypic state, without an altered developmental pathway. Our analysis provides a new formal picture of this process as it applies to the human mind: The normal branching of developmental trajectories, and the disruptive impacts of teratogeneic events of various kinds, can be described in terms of a growing sequence of holonomy groupoids, each associated with a set of dual information sources representing patterns of cognitive gene expression catalyzed by epigenetic information sources that, for humans, must include culture and culturally-modulated social interaction as well as more direct mechanisms like gene methylation.
This is a novel way of looking at human mental development and its disorders that may prove to be of some use. The most important innovation of this work, however, seems to be the natural incorporation of embedding culture as an essential component of the epigenetic regulation of human mental development, and in the effects of environment on the expression of mental disorders, bringing what is perhaps the central reality of human biology into the center of contemporary biological psychiatry. In sum, we have outlined a broad class of probability models of gene-cultureenvironment interaction that might help current studies of gene-environment interaction in American psychiatry avoid Heine’s (2017) trap of developing an understanding of the self, and its disorders, that is peculiar in the context of the world’s cultures.()
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