Analyzing the competition of gamma rhythms with delayed pulse-coupled oscillators in phase representation

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Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation

Copyright © 2011 Springer. The final publication is available at www.springerlink.comWe consider the dynamics of small networks of coupled cells. We usually assume asymmetric inputs and no global or local symmetries in the network and consider equivalence of networks in this setting; that is, when two networks with different architectures give rise to the same set of possible dynamics. Focussing on transitive (strongly connected) networks that have only one type of cell (identical cell networks) we address three questions relating the network structure to dynamics. The first question is how the structure of the network may force the existence of invariant subspaces (synchrony subspaces). The second question is how these invariant subspaces can support robust heteroclinic attractors. Finally, we investigate how the dynamics of coupled cell networks with different structures and numbers of cells can be related; in particular we consider the sets of possible “inflations” of a coupled cell network that are obtained by replacing one cell by many of the same type, in such a way that the original network dynamics is still present within a synchrony subspace. We illustrate the results with a number of examples of networks of up to six cells

Stable and unstable periodic orbits in complex networks of spiking neurons with delays

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Pleasure and Desire in Moral Theory

Increasingly, moral philosophers are seeking to combine (1) An objectivist or value-based theory of reasons for action, on which one’s reasons are provided, not by one’s desires, but by “facts about what is relevantly good, or worth achieving” (Parfit, 2001), with (2) Subjectivist theories of some of the key elements of the good – chiefly, pleasure and well-being – on which one’s desires (or other subjective states such as likings) help to constitute these good things. This picture, which I call The New Standard View, is proving attractive to so many largely because it offers the possibility of explaining the widespread intuition that subjective states have a significant role to play in shaping what we have a reason to do, without giving these states full reign over our reasons and so entailing (counterintuitively) that a person who cares nothing about others (and who still would not care even if she were fully informed and vividly imagining relevant facts) has no reason to treat them well. I accept that there is an important sense in which our reasons are provided by good things. If nothing were good or bad, then nobody would have a reason to do anything. But I disagree with just about everything else in The New Standard View. Indeed, I think this view has things back to front. We should be objectivists about the good, and subjectivists about reasons. On the picture I favour, which I call The New Rival View, the good consists just in whatever makes people better off in some way (welfarism), what makes people better off is just anything that increases the pleasurableness (or decreases the unpleasurableness) of their lives (hedonism about well-being), and for an experience to be pleasurable (or unpleasurable) is just for it to have a certain phenomenology. Reasons, in turn, are provided by desires (subjectivism about reasons). But, of necessity, there is only one thing each of us intrinsically desires: that the good be done (the guise of the good). It follows that each of us has a reason to do just whatever is good in some way

Hub-activated signal transmission in complex networks

A wide range of networked systems exhibit highly connected nodes (hubs) as prominent structural elements. The functional roles of hubs in the collective nonlinear dynamics of many such networks, however, are not well understood. Here, we propose that hubs in neural circuits may activate local signal transmission along sequences of specific subnetworks. Intriguingly, in contrast to previous suggestions of the functional roles of hubs, here, not the hubs themselves, but nonhub subnetworks transfer the signals. The core mechanism relies on hubs and nonhubs providing activating feedback to each other. It may, thus, induce the propagation of specific pulse and rate signals in neuronal and other communication network

Building functional networks of spiking model neurons

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Cooperation and competition of gamma oscillation mechanisms

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Numbers and age standardized rates of in situ cervix uteri by year of diagnosis, and histologic type, Korea, 1993–2009.

1<p>ASR: Age-standardized rates.</p>2<p>EAPC: Estimated annual percent change.</p