Neural Correlates of Instrumental Contingency Learning: Differential Effects of Action–Reward Conjunction and Disjunction

Contingency theories of goal-directed action propose that experienced disjunctions between an action and its specific consequences, as well as conjunctions between these events, contribute to encoding the action–outcome association. Although considerable behavioral research in rats and humans has provided evidence for this proposal, relatively little is known about the neural processes that contribute to the two components of the contingency calculation. Specifically, while recent findings suggest that the influence of action–outcome conjunctions on goal-directed learning is mediated by a circuit involving ventromedial prefrontal, medial orbitofrontal cortex, and dorsomedial striatum, the neural processes that mediate the influence of experienced disjunctions between these events are unknown. Here we show differential responses to probabilities of conjunctive and disjunctive reward deliveries in the ventromedial prefrontal cortex, the dorsomedial striatum, and the inferior frontal gyrus. Importantly, activity in the inferior parietal lobule and the left middle frontal gyrus varied with a formal integration of the two reward probabilities, ΔP, as did response rates and explicit judgments of the causal efficacy of the action

A specific role for posterior dorsolateral striatum in human habit learning

Habits are characterized by an insensitivity to their consequences and, as such, can be distinguished from goal-directed actions. The neural basis of the development of demonstrably outcome-insensitive habitual actions in humans has not been previously characterized. In this experiment, we show that extensive training on a free-operant task reduces the sensitivity of participants' behavior to a reduction in outcome value. Analysis of functional magnetic resonance imaging data acquired during training revealed a significant increase in task-related cue sensitivity in a right posterior putamen–globus pallidus region as training progressed. These results provide evidence for a shift from goal-directed to habit-based control of instrumental actions in humans, and suggest that cue-driven activation in a specific region of dorsolateral posterior putamen may contribute to the habitual control of behavior in humans

Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases

We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of the integral representation method, classifying the independent solutions as equivalence classes of homotopic paths in the complex plane. We discuss the structure of the bound states as function of the height U_0 of the step and we study the propagation of a sharp-peaked wave packet reflected by the barrier. For both the linear and the exponential barrier we provide an explicit formula for the delay time \tau(E) as a function of the peak energy E. We display the resonant behavior of \tau(E) at energies close to U_0. By analyzing the asymptotic behavior for large energies of the eigenfunctions of the continuous spectrum we also show that, as expected, \tau(E) approaches the classical value for E -> \infty, thus diverging for the step-linear case and vanishing for the step-exponential one.Comment: 14 pages, 10 figure

Neural evidence for inequality-averse social preferences

A popular hypothesis in the social sciences is that humans have social preferences to reduce inequality in outcome distributions because it has a negative impact on their experienced reward. Although there is a large body of behavioural and anthropological evidence consistent with the predictions of these theories, there is no direct neural evidence for the existence of inequality-averse preferences. Such evidence would be especially useful because some behaviours that are consistent with a dislike for unequal outcomes could also be explained by concerns for social image or reciprocity, which do not require a direct aversion towards inequality. Here we use functional MRI to test directly for the existence of inequality-averse social preferences in the human brain. Inequality was created by recruiting pairs of subjects and giving one of them a large monetary endowment. While both subjects evaluated further monetary transfers from the experimenter to themselves and to the other participant, we measured neural responses in the ventral striatum and ventromedial prefrontal cortex, two areas that have been shown to be involved in the valuation of monetary and primary rewards in both social and non-social contexts. Consistent with inequality-averse models of social preferences, we find that activity in these areas was more responsive to transfers to others than to self in the ‘high-pay’ subject, whereas the activity of the ‘low-pay’ subject showed the opposite pattern. These results provide direct evidence for the validity of this class of models, and also show that the brain’s reward circuitry is sensitive to both advantageous and disadvantageous inequality

Radiation from perfect mirrors starting from rest and the black body spectrum

We address the question of radiation emission from a perfect mirror that starts from rest and follows the trajectory z=-ln(cosht) till t->Infinity. We show that a correct derivation of the black body spectrum via the calculation of the Bogolubov amplitudes requires consideration of the whole trajectory and not just of its asymptotic part.Comment: Typos correcte

Integration through transients for Brownian particles under steady shear

Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are obtained, which take the form of generalized Green-Kubo relations. They require integration of transient dynamics. Equations of motion with memory effects for transient density fluctuation functions are derived from the same microscopic starting point. We argue that the derived formal expressions provide useful starting points for approximations in order to describe the stationary non-equilibrium state of steadily sheared dense colloidal dispersions.Comment: 17 pages, Submitted to J. Phys.: Condens. Matter; revised version with minor correction

Testing Supersymmetry in the Associated Production of CP-odd and Charged Higgs Bosons

In the Minimal Supersymmetric Standard Model (MSSM), the masses of the charged Higgs boson ($H^\pm$) and the CP-odd scalar ($A$) are related by $M_{H^+}^2=M_A^2+m_W^2$. Furthermore, because the coupling of $W^-$-$A$-$H^+$ is fixed by gauge interaction, the tree level production rate of $q \bar q' \to W^{\pm \ast} \to A H^\pm$ depends only on one supersymmetry parameter --the mass ($M_A$) of $A$. We show that to a good approximation this conclusion also holds at the one-loop level. Consequently, this process can be used to distinguish MSSM from its alternatives (such as a general two-Higgs-doublet model) by verifying the above mass relation, and to test the prediction of the MSSM on the product of the decay branching ratios of $A$ and $H^\pm$ in terms of only one single parameter -- $M_A$.Comment: 8 pages, 2 figures, RevTe

Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated to very entangled states, and one at a negative temperature, signalling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to 2-D quantum gravity) and study the finite size corrections to the saddle point solution.Comment: 23 pages, 32 figures. More details added about the metastable branch and the first-order phase transitio

Spectral density of generalized Wishart matrices and free multiplicative convolution

We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix. In particular, making use of the Cauchy transform, we study free multiplicative powers of the Marchenko-Pastur (MP) distribution, ${\rm MP}^{\boxtimes s}$, which for an integer $s$ yield Fuss-Catalan distributions corresponding to a product of $s$ independent square random matrices, $X=X_1\cdots X_s$. New formulae for the level densities are derived for $s=3$ and $s=1/3$. Moreover, the level density corresponding to the generalized Bures distribution, given by the free convolution of arcsine and MP distributions is obtained. We also explain the reason of such a curious convolution. The technique proposed here allows for the derivation of the level densities for several other cases.Comment: 10 latex pages including 4 figures, Ver 4, minor improvements and references updat

A unified fluctuation formula for one-cut β\beta-ensembles of random matrices

Using a Coulomb gas approach, we compute the generating function of the covariances of power traces for one-cut $\beta$-ensembles of random matrices in the limit of large matrix size. This formula depends only on the support of the spectral density, and is therefore universal for a large class of models. This allows us to derive a closed-form expression for the limiting covariances of an arbitrary one-cut $\beta$-ensemble. As particular cases of the main result we consider the classical $\beta$-Gaussian, $\beta$-Wishart and $\beta$-Jacobi ensembles, for which we derive previously available results as well as new ones within a unified simple framework. We also discuss the connections between the problem of trace fluctuations for the Gaussian Unitary Ensemble and the enumeration of planar maps.Comment: 16 pages, 4 figures, 3 tables. Revised version where references have been added and typos correcte