Noncommutative waves have infinite propagation speed

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.Comment: 15 pages, references adde

Spiders fluoresce variably across many taxa

The evolution of fluorescence is largely unexplored, despite the newfound occurrence of this phenomenon in a variety of organisms. We document that spiders fluoresce under ultraviolet illumination, and find that the expression of this trait varies greatly among taxa in this species-rich group. All spiders we examined possess fluorophores in their haemolymph, but bright fluorescence appears to result when a spider sequesters fluorophores in its setae or cuticle. By sampling widely across spider taxa, we determine that fluorescent expression is labile and has evolved multiple times. Moreover, examination of the excitation and emission properties of extracted fluorophores reveals that spiders possess multiple fluorophores and that these differ among some families, indicating that novel fluorophores have evolved during spider diversification. Because many spiders fluoresce in wavelengths visible to their predators and prey (birds and insects), we propose that natural selection imposed by predator–prey interactions may drive the evolution of fluorescence in spiders

Electron-Phonon Interacation in Quantum Dots: A Solvable Model

The relaxation of electrons in quantum dots via phonon emission is hindered by the discrete nature of the dot levels (phonon bottleneck). In order to clarify the issue theoretically we consider a system of $N$ discrete fermionic states (dot levels) coupled to an unlimited number of bosonic modes with the same energy (dispersionless phonons). In analogy to the Gram-Schmidt orthogonalization procedure, we perform a unitary transformation into new bosonic modes. Since only $N(N+1)/2$ of them couple to the fermions, a numerically exact treatment is possible. The formalism is applied to a GaAs quantum dot with only two electronic levels. If close to resonance with the phonon energy, the electronic transition shows a splitting due to quantum mechanical level repulsion. This is driven mainly by one bosonic mode, whereas the other two provide further polaronic renormalizations. The numerically exact results for the electron spectral function compare favourably with an analytic solution based on degenerate perturbation theory in the basis of shifted oscillator states. In contrast, the widely used selfconsistent first-order Born approximation proves insufficient in describing the rich spectral features.Comment: 8 pages, 4 figure

Open String Star as a Continuous Moyal Product

We establish that the open string star product in the zero momentum sector can be described as a continuous tensor product of mutually commuting two dimensional Moyal star products. Let the continuous variable $\kappa \in [~0,\infty)$ parametrize the eigenvalues of the Neumann matrices; then the noncommutativity parameter is given by $\theta(\kappa) =2\tanh(\pi\kappa/4)$. For each $\kappa$, the Moyal coordinates are a linear combination of even position modes, and the Fourier transform of a linear combination of odd position modes. The commuting coordinate at $\kappa=0$ is identified as the momentum carried by half the string. We discuss the relation to Bars' work, and attempt to write the string field action as a noncommutative field theory.Comment: 30 pages, LaTeX. One reference adde

A hybrid ARIMA and artificial neural networks model to forecast particulate matter in urban areas: The case of Temuco, Chile

Air quality time series consists of complex linear and non-linear patterns and are difficult to forecast. Box-Jenkins Time Series (ARIMA) and multilinear regression (MLR) models have been applied to air quality forecasting in urban areas, but they have limited accuracy owing to their inability to predict extreme events. Artificial neural networks (ANN) can recognize non-linear patterns that include extremes. A novel hybrid model combining ARIMA and ANN to improve forecast accuracy for an area with limited air quality and meteorological data was applied to Temuco, Chile, where residential wood burning is a major pollution source during cold winters, using surface meteorological and PM10 measurements. Experimental results indicated that the hybrid model can be an effective tool to improve the PM10 forecasting accuracy obtained by either of the models used separately, and compared with a deterministic MLR. The hybrid model was able to capture 100% and 80% of alert and pre-emergency episodes, respectively. This approach demonstrates the potential to be applied to air quality forecasting in other cities and countries

Uniqueness of diffeomorphism invariant states on holonomy-flux algebras

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space. In a second step, one implements the constraints. The main result of the paper concerns the representation theory of the kinematical algebra: We show that there is only one cyclic representation invariant under spatial diffeomorphisms. While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory.Comment: 38 pages, one figure. v2: Minor changes, final version, as published in CM

Hearing loss and satisfaction with healthcare: An unexplored relationship

Patient healthcare satisfaction has become increasingly important since Medicare’s introduction of the Hospital Care Quality Information from the Consumer Perspective (HCAHPS) survey. Greater satisfaction is associated with important healthcare outcomes including lower risk of 30-day readmission

Electron correlation resonances in the transport through a single quantum level

Correlation effects in the transport properties of a single quantum level coupled to electron reservoirs are discussed theoretically using a non-equilibrium Green functions approach. Our method is based on the introduction of a second-order self-energy associated with the Coulomb interaction that consistently eliminates the pathologies found in previous perturbative calculations. We present results for the current-voltage characteristic illustrating the different correlation effects that may be found in this system, including the Kondo anomaly and Coulomb blockade. We finally discuss the experimental conditions for the simultaneous observation of these effects in an ultrasmall quantum dot.Comment: 4 pages (two columns), 3 figures under reques

Dynamical aspects of mean field plane rotators and the Kuramoto model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur