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This paper introduces a variational formulation of natural selection, paying special attention to the nature of 'things' and the way that different 'kinds' of 'things' are individuated from-and influence-each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain-and are constrained by-fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (Bayesian model) selection. The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations of distinct natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses-and identify points of contact with related mathematical formulations of evolution.
Rapid imaging techniques are increasingly used in functional MRI studies because they allow a greater number of samples to be acquired per unit time, thereby increasing statistical power. However, temporal correlations limit the increase in functional sensitivity and must be accurately accounted for to control the false-positive rate. A common approach to accounting for temporal correlations is to whiten the data prior to estimating fMRI model parameters. Models of white noise plus a first-order autoregressive process have proven sufficient for conventional imaging studies, but more elaborate models are required for rapidly sampled data. Here we show that when the "FAST" model implemented in SPM is used with a well-controlled number of parameters, it can successfully prewhiten 80% of grey matter voxels even with volume repetition times as short as 0.35 s. We further show that the temporal signal-to-noise ratio (tSNR), which has conventionally been used to assess the relative functional sensitivity of competing imaging approaches, can be augmented to account for the temporal correlations in the time series. This amounts to computing the t-score testing for the mean signal. We show in a visual perception task that unlike the tSNR weighted by the number of samples, the t-score measure is directly related to the t-score testing for activation when the temporal correlations are correctly modeled. This score affords a more accurate means of evaluating the functional sensitivity of different data acquisition options.
Abstract This work addresses the complexity of neuronal interactions, the nature of this complexity and how it can be characterised in real neurophysiological processes. A measure of complexity has been introduced recently (Tononi et al. [1994]: Proc Natl Acad Sci USA 91:5033–5037) that is sensitive to the joint constraints imposed by two principles of brain organisation: functional segregation and functional integration. Functional segregation implies that the dynamics of a cortical area should reflect the multidimensional attributes for which that area is specialised (in other words, regional dynamics should show a relatively high entropy). Conversely, functional integration implies a distributed and divergent influence of every cortical area on the remaining areas (i.e., the overall dynamics should show a low entropy). Our measure is based on the profile of entropies of different sized regions of the brain. Complexity is high when smaller regions have (on average) a relatively high entropy with respect to the entropy of the whole system. This measure is equivalent to the (average) mutual information between all small regions and the rest of the system in question. We have applied this measure to nonlinear simulations and to neurophysiological data obtained with fMRI during photic stimulation. Because patterns of activity in the brain are intermediate between a state of incoherence, with regionally specific dynamics and a state of global coherence, we predicted that simulated nonlinear processes with similar characteristics would have a high complexity. In the language of nonlinear dynamics we hypothesised that the greatest complexity would be found somewhere between high‐dimensional, chaotic behaviour and low‐dimensional, orderly behaviour. Equivalently, using the metaphor of loosely coupled oscillators, we predicted that complexity would be highest in the domain between asynchronous oscillations and global synchrony. This hypothesis was confirmed using nonlinear neuronal simulations. In addition, we demonstrate that the complexity of neurophysiological data is easily measured and can show a significant complexity when compared to suitable control processes. © 1996 Wiley‐Liss, Inc.