Finite dimesional Hamiltonian formalism for gauge and field theories

We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the generalized Poisson $\mathfrak{p}$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\mathfrak{p}$-brackets. As illustration of our formalism we present three examples: the interacting scalar fields, conformal string theory and the electromagnetic field.Comment: 52 pages. In this paper we give a more general hamiltonian formulation for a gauge and field theories, it's an extension of our previous paper math-ph/000402

Attention-dependent modulation of cortical taste circuits revealed by granger causality with signal-dependent noise

We show, for the first time, that in cortical areas, for example the insular, orbitofrontal, and lateral prefrontal cortex, there is signal-dependent noise in the fMRI blood-oxygen level dependent (BOLD) time series, with the variance of the noise increasing approximately linearly with the square of the signal. Classical Granger causal models are based on autoregressive models with time invariant covariance structure, and thus do not take this signal-dependent noise into account. To address this limitation, here we describe a Granger causal model with signal-dependent noise, and a novel, likelihood ratio test for causal inferences. We apply this approach to the data from an fMRI study to investigate the source of the top-down attentional control of taste intensity and taste pleasantness processing. The Granger causality with signal-dependent noise analysis reveals effects not identified by classical Granger causal analysis. In particular, there is a top-down effect from the posterior lateral prefrontal cortex to the insular taste cortex during attention to intensity but not to pleasantness, and there is a top-down effect from the anterior and posterior lateral prefrontal cortex to the orbitofrontal cortex during attention to pleasantness but not to intensity. In addition, there is stronger forward effective connectivity from the insular taste cortex to the orbitofrontal cortex during attention to pleasantness than during attention to intensity. These findings indicate the importance of explicitly modeling signal-dependent noise in functional neuroimaging, and reveal some of the processes involved in a biased activation theory of selective attention

Neural mechanisms of economic commitment in the human medial prefrontal cortex

Neurobiologists have studied decisions by offering successive, independent choices between goods or gambles. However, choices often have lasting consequences, as when investing in a house or choosing a partner. Here, humans decided whether to commit (by acceptance or rejection) to prospects that provided sustained financial return. BOLD signals in the rostral medial prefrontal cortex (rmPFC) encoded stimulus value only when acceptance or rejection was deferred into the future, suggesting a role in integrating value signals over time. By contrast, the dorsal anterior cingulate cortex (dACC) encoded stimulus value only when participants rejected (or deferred accepting) a prospect. dACC BOLD signals reflected two decision biases–to defer commitments to later, and to weight potential losses more heavily than gains–that (paradoxically) maximised reward in this task. These findings offer fresh insights into the pressures that shape economic decisions, and the computation of value in the medial prefrontal cortex. - See more at: http://elifesciences.org/content/3/e03701#sthash.rpmo51q5.dpu

Dissociation of Subjectively Reported and Behaviorally Indexed Mind Wandering by EEG Rhythmic Activity

Inattention to current activity is ubiquitous in everyday situations. Mind wandering is an example of such a state, and its related brain areas have been examined in the literature. However, there is no clear evidence regarding neural rhythmic activities linked to mind wandering. Using a vigilance task with thought sampling and electroencephalography recording, the current study simultaneously examined neural oscillatory activities related to subjectively reported and behaviorally indexed mind wandering. By implementing time-frequency analysis, we found that subjectively reported mind wandering, relative to behaviorally indexed, showed increased gamma band activity at bilateral frontal-central areas. By means of beamformer source imaging, we found subjectively reported mind wandering within the gamma band to be characterized by increased activation in bilateral frontal cortices, supplemental motor area, paracentral cortex and right inferior temporal cortex in comparison to behaviorally indexed mind wandering. These findings dissociate subjectively reported and behaviorally indexed mind wandering and suggest that a higher degree of executive control processes are engaged in subjectively reported mind wandering