Metabolic sensing in AgRP neurons integrates homeostatic state with dopamine signalling in the striatum

Agouti-related peptide (AgRP) neurons increase motivation for food, however, whether metabolic sensing of homeostatic state in AgRP neurons potentiates motivation by interacting with dopamine reward systems is unexplored. As a model of impaired metabolic-sensing, we used the AgRP-specific deletion of carnitine acetyltransferase

Traffic jams induced by rare switching events in two-lane transport

We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular traffic. Introducing a coupling between the internal states by allowing particles to switch from one to another induces an intriguing polarization phenomenon. In a mesoscopic scaling, a rich stationary regime for the density profiles is discovered, with localized domain walls in the density profile of one of the internal states being feasible. We derive the shape of the density profiles as well as resulting phase diagrams analytically by a mean-field approximation and a continuum limit. Continuous as well as discontinuous lines of phase transition emerge, their intersections induce multi-critical behaviour

Constraints, gauge symmetries, and noncommutative gravity in two dimensions

After an introduction into the subject we show how one constructs a canonical formalism in space-time noncommutative theories which allows to define the notion of first-class constraints and to analyse gauge symmetries. We use this formalism to perform a noncommutative deformation of two-dimensional string gravity (also known as Witten black hole).Comment: Based on lectures given at IFSAP-2004 (St.Petersburg), to be submitted to Theor. Math. Phys., dedicated to Yu.V.Novozhilov on the occasion of his 80th birthda

Generalized quantum tomographic maps

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of "thick" quantum tomography. Applications for quantum state measurements of photons and matter waves are discussed.Comment: 8 page

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

Phase diagram of two-lane driven diffusive systems

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail

Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf 428}, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely the `rock-paper-scissors' or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a \emph{finite number of agents} drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.Comment: 12 pages, 9 figures, minor correction

Pauli problem for a spin of arbitrary length: A simple method to determine its wave function

The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems