Value encoding in the globus pallidus: fMRI reveals an interaction effect between reward and dopamine drive

The external part of the globus pallidus (GPe) is a core nucleus of the basal ganglia (BG) whose activity is disrupted under conditions of low dopamine release, as in Parkinson's disease. Current models assume decreased dopamine release in the dorsal striatum results in deactivation of dorsal GPe, which in turn affects motor expression via a regulatory effect on other nuclei of the BG. However, recent studies in healthy and pathological animal models have reported neural dynamics that do not match with this view of the GPe as a relay in the BG circuit. Thus, the computational role of the GPe in the BG is still to be determined. We previously proposed a neural model that revisits the functions of the nuclei of the BG, and this model predicts that GPe encodes values which are amplified under a condition of low striatal dopaminergic drive. To test this prediction, we used an fMRI paradigm involving a within-subject placebo-controlled design, using the dopamine antagonist risperidone, wherein healthy volunteers performed a motor selection and maintenance task under low and high reward conditions. ROI-based fMRI analysis revealed an interaction between reward and dopamine drive manipulations, with increased BOLD activity in GPe in a high compared to low reward condition, and under risperidone compared to placebo. These results confirm the core prediction of our computational model, and provide a new perspective on neural dynamics in the BG and their effects on motor selection and cognitive disorders

QFT with Twisted Poincar\'e Invariance and the Moyal Product

We study the consequences of twisting the Poincare invariance in a quantum field theory. First, we construct a Fock space compatible with the twisting and the corresponding creation and annihilation operators. Then, we show that a covariant field linear in creation and annihilation operators does not exist. Relaxing the linearity condition, a covariant field can be determined. We show that it is related to the untwisted field by a unitary transformation and the resulting n-point functions coincide with the untwisted ones. We also show that invariance under the twisted symmetry can be realized using the covariant field with the usual product or by a non-covariant field with a Moyal product. The resulting S-matrix elements are shown to coincide with the untwisted ones up to a momenta dependent phase.Comment: 11 pages, references adde

Realization of Uq(so(N))U_q(so(N)) within the differntial algebra on RqN{\bf R}_q^N

We realize the Hopf algebra $U_{q^{-1}}(so(N))$ as an algebra of differential operators on the quantum Euclidean space ${\bf R}_q^N$. The generators are suitable q-deformed analogs of the angular momentum components on ordinary ${\bf R}^N$. The algebra $Fun({\bf R}_q^N)$ of functions on ${\bf R}_q^N$ splits into a direct sum of irreducible vector representations of $U_{q^{-1}}(so(N))$; the latter are explicitly constructed as highest weight representations.Comment: 26 pages, 1 figur

Testing hypotheses about the harm that capitalism causes to the mind and brain: a theoretical framework for neuroscience research

In this paper, we will attempt to outline the key ideas of a theoretical framework for neuroscience research that reflects critically on the neoliberal capitalist context. We argue that neuroscience can and should illuminate the effects of neoliberal capitalism on the brains and minds of the population living under such socioeconomic systems. Firstly, we review the available empirical research indicating that the socio-economic environment is harmful to minds and brains. We, then, describe the effects of the capitalist context on neuroscience itself by presenting how it has been influenced historically. In order to set out a theoretical framework that can generate neuroscientific hypotheses with regard to the effects of the capitalist context on brains and minds, we suggest a categorization of the effects, namely deprivation, isolation and intersectional effects. We also argue in favor of a neurodiversity perspective [as opposed to the dominant model of conceptualizing neural (mal-)functioning] and for a perspective that takes into account brain plasticity and potential for change and adaptation. Lastly, we discuss the specific needs for future research as well as a frame for post-capitalist research

Impaired belief updating and devaluation in adult women with bulimia nervosa

Recent models of bulimia nervosa (BN) propose that binge-purge episodes ultimately become automatic in response to cues and insensitive to negative outcomes. Here, we examined whether women with BN show alterations in instrumental learning and devaluation sensitivity using traditional and computational modeling analyses of behavioral data. Adult women with BN (n = 30) and group-matched healthy controls (n = 31) completed a task in which they first learned stimulus-response-outcome associations. Then, participants were required to repeatedly adjust their responses in a “baseline test”, when different sets of stimuli were explicitly devalued, and in a “slips-of-action test”, when outcomes instead of stimuli were devalued. The BN group showed intact behavioral sensitivity to outcome devaluation during the slips-of-action test, but showed difficulty overriding previously learned stimulus-response associations on the baseline test. Results from a Bayesian learner model indicated that this impaired performance could be accounted for by a slower pace of belief updating when a new set of previously learned responses had to be inhibited (p = 0.036). Worse performance and a slower belief update in the baseline test were each associated with more frequent binge eating (p = 0.012) and purging (p = 0.002). Our findings suggest that BN diagnosis and severity are associated with deficits in flexibly updating beliefs to withhold previously learned responses to cues. Additional research is needed to determine whether this impaired ability to adjust behavior is responsible for maintaining automatic and persistent binge eating and purging in response to internal and environmental cues

On quantum mechanics with a magnetic field on R^n and on a torus T^n, and their relation

We show in elementary terms the equivalence in a general gauge of a U(1)-gauge theory of a scalar charged particle on a torus T^n = R^n/L to the analogous theory on R^n constrained by quasiperiodicity under translations in the lattice L. The latter theory provides a global description of the former: the quasiperiodic wavefunctions defined on R^n play the role of sections of the associated hermitean line bundle E on T^n, since also E admits a global description as a quotient. The components of the covariant derivatives corresponding to a constant (necessarily integral) magnetic field B = dA generate a Lie algebra g_Q and together with the periodic functions the algebra of observables O_Q . The non-abelian part of g_Q is a Heisenberg Lie algebra with the electric charge operator Q as the central generator; the corresponding Lie group G_Q acts on the Hilbert space as the translation group up to phase factors. Also the space of sections of E is mapped into itself by g in G_Q . We identify the socalled magnetic translation group as a subgroup of the observables' group Y_Q . We determine the unitary irreducible representations of O_Q, Y_Q corresponding to integer charges and for each of them an associated orthonormal basis explicitly in configuration space. We also clarify how in the n = 2m case a holomorphic structure and Theta functions arise on the associated complex torus. These results apply equally well to the physics of charged scalar particles on R^n and on T^n in the presence of periodic magnetic field B and scalar potential. They are also necessary preliminary steps for the application to these theories of the deformation procedure induced by Drinfel'd twists.Comment: Latex2e file, 22 pages. Final version appeared in IJT

Dynamics of a Dirac Fermion in the presence of spin noncommutativity

Recently, it has been proposed a spacetime noncommutativity that involves spin degrees of freedom, here called "spin noncommutativity". One of the motivations for such a construction is that it preserves Lorentz invariance, which is deformed or simply broken in other approaches to spacetime noncommutativity. In this work, we gain further insight in the physical aspects of the spin noncommutativity. The noncommutative Dirac equation is derived from an action principle, and it is found to lead to the conservation of a modified current, which involves the background electromagnetic field. Finally, we study the Landau problem in the presence of spin noncommutativity. For this scenario of a constant magnetic field, we are able to derive a simple Hermitean non-commutative correction to the Hamiltonian operator, and show that the degeneracy of the excited states is lifted by the noncommutativity at the second order or perturbation theory.Comment: 18 pages, revtex

On the deformability of Heisenberg algebras

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum mechanics. For the case of a q-oscillator there exists a deforming map to the classical algebra. It is shown that the differential calculus on quantum planes with involution, i.e. if one works in position-momentum realization, can be mapped on a q-difference calculus on a commutative real space. Although this calculus leads to an interesting discretization it is proved that it can be realized by generators of the undeformed algebra and does not posess a proper group of global transformations.Comment: 16 pages, latex, no figure

Braided algebras and the kappa-deformed oscillators

Recently there were presented several proposals how to formulate the binary relations describing kappa-deformed oscillator algebras. In this paper we shall consider multilinear products of kappa-deformed oscillators consistent with the axioms of braided algebras. In general case the braided triple products are quasi-associative and satisfy the hexagon condition depending on the coassociator $Phi \in A\otimes A\otimes A$. We shall consider only the products of kappa-oscillators consistent with co-associative braided algebra, with Phi =1. We shall consider three explicite examples of binary kappa-deformed oscillator algebra relations and describe briefly their multilinear coassociative extensions satisfying the postulates of braided algebras. The third example, describing kappa-deformed oscillators in group manifold approach to kappa-deformed fourmomenta, is a new result.Comment: v2, 13 pages; Proc. of 2-nd Corfu School on Quantum Gravity and Quantum Geometry, September 2009, Corfu; Gen. Rel. Grav. (2011),special Proceedings issue; version in pres

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compute the corresponding equation of motion operators. The Green's operators and the fundamental solution of the deformed equation of motion are obtained in terms of formal power series. It is shown that, using the deformed fundamental solution, we can define deformed *-algebras of field observables, which in general depend on the spacetime deformation parameter. This dependence is absent in the special case of Killing deformations, which include in particular the Moyal-Weyl deformation of the Minkowski spacetime.Comment: LaTeX 14 pages, no figures, svjour3.cls style; v2: clarifications and references added, compatible with published versio