The braiding for representations of q-deformed affine sl2sl_2

We compute the braiding for the `principal gradation' of $U_q(\hat{{\it sl}_2})$ for $|q|=1$ from first principles, starting from the idea of a rigid braided tensor category. It is not necessary to assume either the crossing or the unitarity condition from S-matrix theory. We demonstrate the uniqueness of the normalisation of the braiding under certain analyticity assumptions, and show that its convergence is critically dependent on the number-theoretic properties of the number $\tau$ in the deformation parameter $q=e^{2\pi i\tau}$. We also examine the convergence using probability, assuming a uniform distribution for $q$ on the unit circle.Comment: LaTeX, 10 pages with 2 figs, uses epsfi

Radiation testing of composite materials, in situ versus ex situ effects

The effect of post irradiation test environments on tensile properties of representative advanced composite materials (T300/5208, T300/934, C6000/P1700) was investigated. Four ply (+ or - 45 deg/+ or - 45 deg) laminate tensile specimens were exposed in vacuum up to a bulk dose of 1 x 10 to the 10th power rads using a mono-energetic fluence of 700 keV electrons from a Van de Graaff accelerator. Post irradiation testing was performed while specimens were being irradiated (in situ data), in vacuum after cessation of irradiation (in vacuo data), and after exposure to air (ex situ data). Room temperature and elevated temperature effects were evaluated. The radiation induced changes to the tensile properties were small. Since the absolute changes in tensile properties were small, the existance of a post irradiation test environment effect was indeterminate

Inverse scattering and solitons in An−1A_{n-1} affine Toda field theories II

New single soliton solutions to the affine Toda field theories are constructed, exhibiting previously unobserved topological charges. This goes some of the way in filling the weights of the fundamental representations, but nevertheless holes in the representations remain. We use the group doublecross product form of the inverse scattering method, and restrict ourselves to the rank one solutions.Comment: 19 pages, latex, 12 fig

Gravity induced from quantum spacetime

We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a single real parameter which we interpret as a time in the past from which all timelike geodesics emerge and a corresponding time in the future at which they all converge. Our analysis also implies a reduction of moduli in n-dimensions and we study the suggested spherically symmetric classical geometry in n=4 in detail, identifying two 1-parameter subcases where the Einstein tensor matches that of a perfect fluid for (a) positive pressure, zero density and (b) negative pressure and positive density with ratio w_Q=-{1\over 2}. The classical geometry is conformally flat and its geodesics motivate new coordinates which we extend to the quantum case as a new description of the quantum spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for $n=2$ and includes the quantum Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as \lambda\to 0. We also propose a `quantum Einstein tensor' which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the quantum Ricci tensor and metric are viewed as deformations of their classical counterparts there would be an O(\lambda^2) correction to the classical Einstein tensor and an O(\lambda) correction to the classical metric.Comment: 42 pages LATEX, 4 figures; expanded on the physical significanc

Signal integration enhances the dynamic range in neuronal systems

The dynamic range measures the capacity of a system to discriminate the intensity of an external stimulus. Such an ability is fundamental for living beings to survive: to leverage resources and to avoid danger. Consequently, the larger is the dynamic range, the greater is the probability of survival. We investigate how the integration of different input signals affects the dynamic range, and in general the collective behavior of a network of excitable units. By means of numerical simulations and a mean-field approach, we explore the nonequilibrium phase transition in the presence of integration. We show that the firing rate in random and scale-free networks undergoes a discontinuous phase transition depending on both the integration time and the density of integrator units. Moreover, in the presence of external stimuli, we find that a system of excitable integrator units operating in a bistable regime largely enhances its dynamic range.Comment: 5 pages, 4 figure

Predicting criticality and dynamic range in complex networks: effects of topology

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure

Beyond the Death of Linear Response: 1/f optimal information transport

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.Comment: 4 pages, 2 figures, 1 table, in press on Phys. Rev. Let