Born-Regulated Gravity in Four Dimensions

Previous work involving Born-regulated gravity theories in two dimensions is extended to four dimensions. The action we consider has two dimensionful parameters. Black hole solutions are studied for typical values of these parameters. For masses above a critical value determined in terms of these parameters, the event horizon persists. For masses below this critical value, the event horizon disappears, leaving a ``bare mass'', though of course no singularity.Comment: LaTeX, 15 pages, 2 figure

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

Bifurcations and Chaos in the Six-Dimensional Turbulence Model of Gledzer

The cascade-shell model of turbulence with six real variables originated by Gledzer is studied numerically using Mathematica 5.1. Periodic, doubly-periodic and chaotic solutions and the routes to chaos via both frequency-locking and period-doubling are found by the Poincar\'e plot of the first mode $v_1$. The circle map on the torus is well approximated by the summation of several sinusoidal functions. The dependence of the rotation number on the viscosity parameter is in accordance with that of the sine-circle map. The complicated bifurcation structure and the revival of a stable periodic solution at the smaller viscosity parameter in the present model indicates that the turbulent state may be very sensitive to the Reynolds number.Comment: 19 pages, 12 figures submitted to JPS

Unconditionally verifiable blind computation

Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's input, output and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the server has followed the instructions of the protocol, or if there has been some deviation resulting in a corrupted output state. A verifiable BQC protocol can be viewed as an interactive proof system leading to consequences for complexity theory. The authors, together with Broadbent, previously proposed a universal and unconditionally secure BQC scheme where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. In this paper we extend that protocol with new functionality allowing blind computational basis measurements, which we use to construct a new verifiable BQC protocol based on a new class of resource states. We rigorously prove that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter. The new resource state allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead. This is a significant improvement on the original scheme, which required that all computations to be performed must first be put into a nearest neighbour form, incurring linear overhead in the number of qubits. Such an improvement has important consequences for efficiency and fault-tolerance thresholds.Comment: 46 pages, 10 figures. Additional protocol added which allows arbitrary circuits to be verified with polynomial securit

Resonant guided wave networks

A resonant guided wave network (RGWN) is an approach to optical materials design in which power propagation in guided wave circuits enables material dispersion. The RGWN design, which consists of power-splitting elements arranged at the nodes of a waveguide network, results in wave dispersion which depends on network layout due to localized resonances at several length scales in the network. These structures exhibit both localized resonances with Q ~ 80 at 1550 nm wavelength as well as photonic bands and band-gaps in large periodic networks at infrared wavelengths.Comment: 9 pages, 5 figure

Gravity a la Born-Infeld

A simple technique for the construction of gravity theories in Born-Infeld style is presented, and the properties of some of these novel theories are investigated. They regularize the positive energy Schwarzschild singularity, and a large class of models allows for the cancellation of ghosts. The possible correspondence to low energy string theory is discussed. By including curvature corrections to all orders in alpha', the new theories nicely illustrate a mechanism that string theory might use to regularize gravitational singularities.Comment: 21 pages, 2 figures, new appendix B with corrigendum: Class. Quantum Grav. 21 (2004) 529

Roundoff-induced Coalescence of Chaotic Trajectories

Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of precision of calculations. Two generic behaviors of the average coalescence time are identified: exponential or linear. In both cases no synchronization occurs if iterations are done with {\em infinite} precision.Comment: 6 pages, 3 postscript figures, to be published in Phys. Rev.

Multifractality in Time Series

We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous" specific heat of the S&P500 discrete price index displays a shoulder to the right of the main peak for low values of time lags. On decreasing T, the presence of the shoulder is a consequence of the peaked, temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80), we have found that C_{q} displays typical features of a classical phase transition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describing scaling measures.Comment: 22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000

Nonextensivity and multifractality in low-dimensional dissipative systems

Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently introduced by one of us (C.T.) and characterized by the entropic index $q$. We show that general scaling arguments imply that $1/(1-q) = 1/\alpha_{min}-1/\alpha_{max}$, where $\alpha_{min}$ and $\alpha_{max}$ are the extremes of the multifractal singularity spectrum $f(\alpha)$ of the attractor. This relation is numerically checked to hold in standard one-dimensional dissipative maps. The above result sheds light on a long-standing puzzle concerning the relation between the entropic index $q$ and the underlying microscopic dynamics.Comment: 12 pages, TeX, 4 ps figure

Vulnerable warriors: the atmospheric marketing of military and policing equipment before and after 9/11

In this article, we analyse changes in the circulation of advertisements of policing products at security expos between 1995 and 2013. While the initial aim of the research was to evidence shifts in terrorist frames in the marketing of policing equipment before and after 9/11, our findings instead suggested that what we are seeing is the rise of marketing to police as “vulnerable warriors”, law enforcement officers in need of military weapons both for their offensive capabilities and for the protection they can offer to a police force that is always under threat