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Atlan and Cohen (1998) and Cohen (2017) argue that the essence of immune cognition is comparison of a perceived antigenic signal with an internal, learned picture of the world, and then, upon that comparison, the choice of one response from a large repertoire of possible responses. Following the approach of Wallace (2017, 2017a), we make a ‘weak’, and hence very general, model of that process. Pattern recognition-and-response, as we characterize it, proceeds by convoluting (i.e. comparing) an incoming external ‘sensory’ antigenic signal with an internal ‘ongoing activity’ – the ‘learned picture of the world’ – and, at some point, triggering an appropriate action based on a decision that the pattern of sensory activity requires a response. We need not model how the pattern recognition system is ‘trained’, and hence we adopt a weak model, regardless of learning paradigm, which can itself be more formally described by the Rate Distortion Theorem. We will, fulfilling Atlan and Cohen’s (1998) criterion of meaning-from-response, define a language’s contextual meaning entirely in terms of system output. Introduction Taking this formal description of immune cognition as a starting point, Wallace (2017a) has explored host response to sudden pathogenic challenge, using a mathematical model of the generalized ‘cognitive condensation’ that characterizes human biology. Suppose the pathogen avoids extirpation by that response, but, changing its coat or hiding within refugia, becomes an established invading population. The immune system is cognitive, the pathogen is adaptive. We and others argue at some length (Wallace and Wallace, 1998, 1999; Rojdestvensky and Cottam, 2017) that this is indeed a systematic mathematical homology which, we contend, permits importation of renormalization symmetry into information theory. Imposition of invariance under renormalization on the mutual information splitting criterion I(X, Y ) implies the existence of phase transitions analogous to learning plateaus or punctuated evolutionary equilibria in the relations between host and pathogen. An extensive mathematical development will be presented in the next section. The physiological details of mechanism, we speculate, will be particularly captured by the definitions of coupling parameter, renormalization symmetry, and, perhaps, the distribution of the renormalization across agency, a matter we treat below. Here, however, these changes are perhaps better described as ‘punctuated interpenetration’ between the challenged cognitive condensation of the host and the adaptive abilities of the pathogen. Even more elaborate developments are possible. For example, in the next section we explore canonical patterns of transition between disease stages that emerge quite naturally. We reiterate that the details are highly dependent on the choice of renormalization symmetry, which is likely to re- flect details of mechanism – the manner in which the dynamics of the forest are dependent on the detailed physiology of trees, albeit in a many-to-one manner. Renormalization properties are not likely to follow simple physical analogs, and may well be subject to characteristic distributions. The algebra is straightforward if complicated, and given later. Following Nesbitt et al. (2017), however, any ‘cognitive’ process is likely to show significant cultural variation, and even distribution of properties. Representations of the general argument Earlier work in this series addressed the problem of how a ‘language’, in a large sense, ‘spoken’ on a network structure responds as properties of the network change. The language might be spoken, pattern recognition, or cognition. The network might be social, chemical, or neural. The properties of interest were the magnitude of ‘strong’ or ‘weak’ ties which, respectively, either disjointly partitioned the network or linked it. These would be analogous to local and mean-field couplings in physical systems. We fix the magnitude of strong ties, but vary the index of weak ties between components, which we call P, taking K = 1/P. For neural networks P is just proportional to the number of training cycles, suggesting that, for interacting cognitive/adaptive systems, P may be proportional to the number of ‘challenge cycles’, likely indexed by human diurnal or other activity patterns, or perhaps even those of the parasite itself. We assume the piecewise, adiabatically memoryless ergodic information source (Wallace, 2017b) depends on three parameters, two explicit and one implicit. The explicit are K as above and an ‘external field strength’ analog J, which gives a ‘direction’ to the system. We will, in the limit, set J = 0. The implicit parameter, which we call r, is an inherent generalized ‘length’ characteristic of the phenomenon, on which J and K are defined. That is, we can write J and K as functions of averages of the parameter r, which may be quite complex, having nothing at all to do with conventional ideas of space: For example r may be defined by the degree of niche partitioning in ecosystems or separation in social structures. Thus the information dynamic phase transition properties of mixed systems will not in general be simply related to those of a single subcomponent, a matter of possible empirical importance: If sets of relevant parameters defining renormalization ‘universality classes’ are indeed distributed, experiments observing ‘pure’ phase changes may be very difficult. Tuning among different possible renormalization strategies in response to external pressures would result in even greater ambiguity in recognizing and classifying information dynamic phase transitions. We believe that important aspects of mechanism may be reflected in the combination of renormalization properties and the details of their distribution across subsystems. Elsewhere (Wallace, Wallace, Wallace, and Wallace, 2017) we examine the possible relation of the ‘tuning’ of renormalization parameters to the adaptive mutator. In sum, real biological, social, or ‘biopsychosocial’ systems are likely to have very rich patterns of phase transition which may not display the simplistic, indeed, literally elemental, purity familiar to physicists. Overall mechanisms will, we believe, still remain significantly constrained by our theory, in the general sense of probability limit theorems. Extending the general argument As we discuss elsewhere (Wallace and Wallace, 2017; Wallace, 2017a), structured psychosocial stress constitutes a determining context for immune cognition or, more generally, the immunocultural condensation. We wish to analyze the way structured stress affects the interaction between the cognitive ICC and an adaptive mutator, the principal line of defense against the ICC for a large class of highly successful pathogens. To do this we must extend our theory to three interacting information sources. The Rate Distortion and Joint Asymptotic Equipartition Theorems are generalizations of the Shannon-McMillan Theorem which examine the interaction of two information sources, with and without the constraint of a fixed average distortion. We conduct one more iteration, and require a generalization of the SMT in terms of the splitting criterion for triplets as opposed to single or double stranded patterns. The tool for this is at the core of what is termed network information theory [Cover and Thomas, 1991, Theorem 14.2.3]. Suppose we have three (piecewise adiabatically memoryless) ergodic information sources, Y1, Y2 and Y3. Discussion Evolution machines and magic bullets Scientific enterprise encompasses the interaction of facts, tools, and theories, all embedded in a path-dependent political economy which seems as natural to us as air to a bird, water to a fish, or an atomic matrix to a solid state electron. Molecular biology, Central Limit Theorem statistics, and 19th century mathematics, presently provide the reductionist tool kit most popular in the study of immune function and disease process. Many essential matters related to the embedding social, economic, and cultural matrix so fundamental to human biology are simply blindsided, and one is reminded, not very originally, of the joke about the drunk looking for his car keys under a street lamp, while having lost them down the block in a darkened parking lot, “because the light here is better”. The asymptotic limit theorems of probability beyond the Central Limit Theorem, in concert with related formalism adapted from statistical physics, would seem to provide new tools which can generate theoretical speculations of value in obtaining and interpreting empirical results about infection and immune process, particularly regarding the way in which culture is, for human populations, “as much a part of human biology as the enamel on our teeth” (Richerson and Boyd, 1995). We have, as yet, explored relatively few possibilities: While we can model the interaction of first and second order phenomena in the context of structured stress using network information theory, it is difficult to envision interaction between second order ‘tuning’ processes, or the mechanics of even higher order effects: can we continue to ‘tune the tuners’ in a kind of idiotypic hall of mirrors? The mathematics would be straightforward, but the corresponding molecular biology would have to be subtle indeed. While unlikely in general, higher order interpenetration – mutating the mutator – may be observable in certain isolated circumstances, for example the interplay between B-cell hypermutation and a high order parasitic coat of many colors.()，英语论文网站，英语论文范文 |
