The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a "limited offer" game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing

Density dependent strong coupling constant of QCD derived from compact star data

The present work is an endeavour to connect the properties of tiny nearly massless objects with those of some of the most massive ones, the compact stars. Since 1996 there is major influx of X-ray and $\gamma$ ray data from binary stars, one or both of which are compact objects that are difficult to explain as neutron stars since they contain a mass M in too small a radius R . The suggestion has been put forward that these are strange quark stars (SS) explainable in a simple model with chiral symmetry restoration (CSR) for the quarks and the M, R and other properties like QPOs (quasi periodic oscillations) in their X-ray power spectrum. It would be nice if this astrophysical data could shed some light on fundamental properties of quarks obeying QCD. One can relate the strong coupling constant of QCD, $\alpha_s$ to the quark mass through the Dyson-Schwinger gap equation using the real time formalism of Dolan and Jackiw. This enables us to obtain the density dependence of $\alpha_s$ from the simple CSR referred to above. This way fundamental physics, difficult to extract from other models like for example lattice QCD, can be constrained from present-day compact star data and may be put back to modelling the dense quark phase of early universe.Comment: 7 pages, 4 figure

Sustained Magnetic Responses in Temporal Cortex Reflect Instantaneous Significance of Approaching and Receding Sounds

Rising sound intensity often signals an approaching sound source and can serve as a powerful warning cue, eliciting phasic attention, perception biases and emotional responses. How the evaluation of approaching sounds unfolds over time remains elusive. Here, we capitalised on the temporal resolution of magnetoencephalograpy (MEG) to investigate in humans a dynamic encoding of perceiving approaching and receding sounds. We compared magnetic responses to intensity envelopes of complex sounds to those of white noise sounds, in which intensity change is not perceived as approaching. Sustained magnetic fields over temporal sensors tracked intensity change in complex sounds in an approximately linear fashion, an effect not seen for intensity change in white noise sounds, or for overall intensity. Hence, these fields are likely to track approach/recession, but not the apparent (instantaneous) distance of the sound source, or its intensity as such. As a likely source of this activity, the bilateral inferior temporal gyrus and right temporo-parietal junction emerged. Our results indicate that discrete temporal cortical areas parametrically encode behavioural significance in moving sound sources where the signal unfolded in a manner reminiscent of evidence accumulation. This may help an understanding of how acoustic percepts are evaluated as behaviourally relevant, where our results highlight a crucial role of cortical areas

Distinct and Convergent Visual Processing of High and Low Spatial Frequency Information in Faces

We tested for differential brain response to distinct spatial frequency (SF) components in faces. During a functional magnetic resonance imaging experiment, participants were presented with "hybrid” faces containing superimposed low and high SF information from different identities. We used a repetition paradigm where faces at either SF range were independently repeated or changed across consecutive trials. In addition, we manipulated which SF band was attended. Our results suggest that repetition and attention affected partly overlapping occipitotemporal regions but did not interact. Changes of high SF faces increased responses of the right inferior occipital gyrus (IOG) and left inferior temporal gyrus (ITG), with the latter response being also modulated additively by attention. In contrast, the bilateral middle occipital gyrus (MOG) responded to repetition and attention manipulations of low SF. A common effect of high and low SF repetition was observed in the right fusiform gyrus (FFG). Follow-up connectivity analyses suggested direct influence of the MOG (low SF), IOG, and ITG (high SF) on the FFG responses. Our results reveal that different regions within occipitotemporal cortex extract distinct visual cues at different SF ranges in faces and that the outputs from these separate processes project forward to the right FFG, where the different visual cues may converg

Optimal inference with suboptimal models:Addiction and active Bayesian inference

When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent's beliefs - based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment - as opposed to the agent's beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less 'optimally' than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject's generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described 'limited offer' task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work

Game theory of mind

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution

Altruistic Learning

The origin of altruism remains one of the most enduring puzzles of human behaviour. Indeed, true altruism is often thought either not to exist, or to arise merely as a miscalculation of otherwise selfish behaviour. In this paper, we argue that altruism emerges directly from the way in which distinct human decision-making systems learn about rewards. Using insights provided by neurobiological accounts of human decision-making, we suggest that reinforcement learning in game-theoretic social interactions (habitisation over either individuals or games) and observational learning (either imitative of inference based) lead to altruistic behaviour. This arises not only as a result of computational efficiency in the face of processing complexity, but as a direct consequence of optimal inference in the face of uncertainty. Critically, we argue that the fact that evolutionary pressure acts not over the object of learning (‘what’ is learned), but over the learning systems themselves (‘how’ things are learned), enables the evolution of altruism despite the direct threat posed by free-riders

Accretion Disks Around Black Holes: Twenty Five Years Later

We study the progress of the theory of accretion disks around black holes in last twenty five years and explain why advective disks are the best bet in explaining varied stationary and non-stationary observations from black hole candidates. We show also that the recently proposed advection dominated flows are incorrect.Comment: 30 Latex pages including figures. Kluwer Style files included. Appearing in `Observational Evidence for Black Holes in the Universe', ed. Sandip K. Chakrabarti, Kluwer Academic Publishers (DORDRECHT: Holland