Posthumanist Education

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Complete synchronization in coupled Type-I neurons

For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of instantaneous frequency with the instantaneous phase of the stochastic inputs to each neuron matches exactly with that for the other in the event of CS of their outputs. Our observation can be exploited in practical situations to produce completely synchronized outputs in artificial devices. For excitatory-excitatory synaptic coupling, a functional dependence for the synchronization error on coupling and noise strengths is obtained. Finally we report an observation of noise-induced CS between non-identical neurons coupled bidirectionally through random non-zero couplings in an all-to- all way in a large neuronal ensemble.Comment: 24 pages, 9 figure

Efficient Dynamic Importance Sampling of Rare Events in One Dimension

Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of ``Dynamic Importance Sampling'' (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a $5 k_B T$ barrier height and 300 for $9 k_B T$, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instanton-like crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the ``Jacobian'' term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.Comment: version to be published in Phys. Rev.

Tagging the world : descrying consciousness in cognitive processes

Although having conscious experiences is a fundamental feature of our everyday life, our understanding of what consciousness is is very limited. According to one of the main conclusions of contemporary philosophy of mind, the qualitative aspect of consciousness seems to resist functionalisation, i.e. it cannot be adequately defined solely in terms of functional or causal roles, which leads to an epistemic gap between phenomenal and scientific knowledge. Phenomenal qualities, then, seem to be, in principle, unexplainable in scientific terms. As a reaction to this pessimistic conclusion it is a major trend in contemporary science of consciousness to turn away from subjective experiences and re-define the subject of investigations in neurological and behavioural terms. This move, however, creates a gap between scientific theories of consciousness, and the original phenomenon, which we are so intimately connected with. The thesis focuses on this gap. It is argued that it is possible to explain features of consciousness in scientific terms. The thesis argues for this claim from two directions. On the one hand, a specific identity theory is formulated connecting phenomenal qualities to certain intermediate level perceptual representations which are unstructured for central processes of the embedding cognitive system. This identity theory is hypothesised on the basis of certain similarities recognised between the phenomenal and the cognitive-representational domains, and then utilised in order to uncover further similarities between these two domains. The identity theory and the further similarities uncovered are then deployed in formulating explanations of the philosophically most important characteristics of the phenomenal domain—i.e. why phenomenal qualities resist functionalisation, and why the epistemic gap occurs. On the other hand, the thesis investigates and criticises existing models of reductive explanation. On the basis of a detailed analysis of how successful scientific explanations proceed a novel account of reductive explanation is proposed, which utilises so-called prior identities. Prior identities are prerequisites rather than outcomes of reductive explanations. They themselves are unexplained but are nevertheless necessary for mapping the features to be explained onto the features the explanation relies on. Prior identities are hypothesised in order to foster the formulation of explanatory claims accounting for target level phenomena in terms of base level processes—and they are justified if they help projecting base level explanations to new territories of the target level. The thesis concludes that the identity theory proposed is a prior identity, and the explanations of features of the phenomenal domain formulated with the aid of this identity are reductive explanations proper. In this sense, the thesis introduces the problem of phenomenal consciousness into scientific discourse, and therefore offers a bridge between the philosophy and the science of consciousness: it offers an approach to conscious experience which, on the one hand, tries to account for the philosophically most important features of consciousness, whereas, on the other hand, does it in a way which smoothly fits into the everyday practice of scientific research