The Coherence Field in the Field Perturbation Theory of Superconductivity

We re-examine the Nambu-Gorkov perturbation theory of superconductivity on the basis of the Bogoliubov-Valatin quasi-particles. We show that two different fields (and two additional analogous fields) may be constructed, and that the Nambu field is only one of them. For the other field- the coherence field- the interaction is given by means of two interaction vertices that are based on the Pauli matrices tau1 and tau3. Consequently, the Hartree integral for the off-diagonal pairing self-energy may be finite, and in some cases large. We interpret the results in terms of conventional superconductivity, and also discuss briefly possible implications to HTSC

Monte Carlo Planning method estimates planning horizons during interactive social exchange

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent's preference for equity with their partner, beliefs about the partner's appetite for equity, beliefs about the partner's model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference

Monte Carlo Planning method estimates planning horizons during interactive social exchange

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent's preference for equity with their partner, beliefs about the partner's appetite for equity, beliefs about the partner's model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference

Nearly extensive sequential memory lifetime achieved by coupled nonlinear neurons

Many cognitive processes rely on the ability of the brain to hold sequences of events in short-term memory. Recent studies have revealed that such memory can be read out from the transient dynamics of a network of neurons. However, the memory performance of such a network in buffering past information has only been rigorously estimated in networks of linear neurons. When signal gain is kept low, so that neurons operate primarily in the linear part of their response nonlinearity, the memory lifetime is bounded by the square root of the network size. In this work, I demonstrate that it is possible to achieve a memory lifetime almost proportional to the network size, "an extensive memory lifetime", when the nonlinearity of neurons is appropriately utilized. The analysis of neural activity revealed that nonlinear dynamics prevented the accumulation of noise by partially removing noise in each time step. With this error-correcting mechanism, I demonstrate that a memory lifetime of order $N/\log N$ can be achieved.Comment: 21 pages, 5 figures, the manuscript has been accepted for publication in Neural Computatio

Learning Contextual Reward Expectations for Value Adaptation

Substantial evidence indicates that subjective value is adapted to the statistics of reward expected within a given temporal context. However, how these contextual expectations are learned is poorly understood. To examine such learning, we exploited a recent observation that participants performing a gambling task adjust their preferences as a function of context. We show that, in the absence of contextual cues providing reward information, an average reward expectation was learned from recent past experience. Learning dependent on contextual cues emerged when two contexts alternated at a fast rate, whereas both cue-independent and cue-dependent forms of learning were apparent when two contexts alternated at a slower rate. Motivated by these behavioral findings, we reanalyzed a previous fMRI data set to probe the neural substrates of learning contextual reward expectations. We observed a form of reward prediction error related to average reward such that, at option presentation, activity in ventral tegmental area/substantia nigra and ventral striatum correlated positively and negatively, respectively, with the actual and predicted value of options. Moreover, an inverse correlation between activity in ventral tegmental area/substantia nigra (but not striatum) and predicted option value was greater in participants showing enhanced choice adaptation to context. The findings help understanding the mechanisms underlying learning of contextual reward expectation

Neural Prediction Errors Reveal a Risk-Sensitive Reinforcement-Learning Process in the Human Brain

Humans and animals are exquisitely, though idiosyncratically, sensitive to risk or variance in the outcomes of their actions. Economic, psychological, and neural aspects of this are well studied when information about risk is provided explicitly. However, we must normally learn about outcomes from experience, through trial and error. Traditional models of such reinforcement learning focus on learning about the mean reward value of cues and ignore higher order moments such as variance. We used fMRI to test whether the neural correlates of human reinforcement learning are sensitive to experienced risk. Our analysis focused on anatomically delineated regions of a priori interest in the nucleus accumbens, where blood oxygenation level-dependent (BOLD) signals have been suggested as correlating with quantities derived from reinforcement learning. We first provide unbiased evidence that the raw BOLD signal in these regions corresponds closely to a reward prediction error. We then derive from this signal the learned values of cues that predict rewards of equal mean but different variance and show that these values are indeed modulated by experienced risk. Moreover, a close neurometric–psychometric coupling exists between the fluctuations of the experience-based evaluations of risky options that we measured neurally and the fluctuations in behavioral risk aversion. This suggests that risk sensitivity is integral to human learning, illuminating economic models of choice, neuroscientific models of affective learning, and the workings of the underlying neural mechanisms

Tamping Ramping: Algorithmic, Implementational, and Computational Explanations of Phasic Dopamine Signals in the Accumbens.

Substantial evidence suggests that the phasic activity of dopamine neurons represents reinforcement learning's temporal difference prediction error. However, recent reports of ramp-like increases in dopamine concentration in the striatum when animals are about to act, or are about to reach rewards, appear to pose a challenge to established thinking. This is because the implied activity is persistently predictable by preceding stimuli, and so cannot arise as this sort of prediction error. Here, we explore three possible accounts of such ramping signals: (a) the resolution of uncertainty about the timing of action; (b) the direct influence of dopamine over mechanisms associated with making choices; and (c) a new model of discounted vigour. Collectively, these suggest that dopamine ramps may be explained, with only minor disturbance, by standard theoretical ideas, though urgent questions remain regarding their proximal cause. We suggest experimental approaches to disentangling which of the proposed mechanisms are responsible for dopamine ramps