Optimization in task--completion networks

We discuss the collective behavior of a network of individuals that receive, process and forward to each other tasks. Given costs they store those tasks in buffers, choosing optimally the frequency at which to check and process the buffer. The individual optimizing strategy of each node determines the aggregate behavior of the network. We find that, under general assumptions, the whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA

Exact results for the Barabasi model of human dynamics

Human activity patterns display a bursty dynamics, with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the Barabasi model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.Comment: 4 pages, 4 figures, revte

Poincare recurrences of Schwarzschild black holes

We discuss massive scalar perturbations of a Schwarzschild black hole. We argue that quantum effects alter the effective potential near the horizon resulting in Poincare recurrences in Green functions. Results at the semi-classical level are independent of the details of the modification of the potential provided its minimum near the horizon is inversely proportional to the square of the Poincare time. This modification may be viewed as a change in the near-horizon geometry. We consider explicitly the examples of a brick wall, a smooth cutoff and a wormhole-like modification showing that they all lead to the same results at leading order.Comment: 15 page

A status report on the observability of cosmic bubble collisions

In the picture of eternal inflation as driven by a scalar potential with multiple minima, our observable universe resides inside one of many bubbles formed from transitions out of a false vacuum. These bubbles necessarily collide, upsetting the homogeneity and isotropy of our bubble interior, and possibly leading to detectable signatures in the observable portion of our bubble, potentially in the Cosmic Microwave Background or other precision cosmological probes. This constitutes a direct experimental test of eternal inflation and the landscape of string theory vacua. Assessing this possibility roughly splits into answering three questions: What happens in a generic bubble collision? What observational effects might be expected? How likely are we to observe a collision? In this review we report the current progress on each of these questions, improve upon a few of the existing results, and attempt to lay out directions for future work.Comment: Review article; comments very welcome. 24 pages + 4 appendices; 19 color figures. (Revised version adds two figures, minor edits.

Semi-classical stability of AdS NUT instantons

The semi-classical stability of several AdS NUT instantons is studied. Throughout, the notion of stability is that of stability at the one-loop level of Euclidean Quantum Gravity. Instabilities manifest themselves as negative eigenmodes of a modified Lichnerowicz Laplacian acting on the transverse traceless perturbations. An instability is found for one branch of the AdS-Taub-Bolt family of metrics and it is argued that the other branch is stable. It is also argued that the AdS-Taub-NUT family of metrics are stable. A component of the continuous spectrum of the modified Lichnerowicz operator on all three families of metrics is found.Comment: 18 pages, 3 figures; references adde

IKE: An interactive klystron evaluation program for SLAC linear collider klystron performance

When the new 65 MW klystrons for the SLC were planned, a computer based interlock and data recording system was implemented in the general electronics upgrade. Significant klystron operating parameters are interlocked and displayed in the SLC central control room through the VAX control computer. A program titled ''IKE'' has been written to record klystron operating data each day, store the data in a database, and provide various sorted operating and statistical information to klystron engineers, and maintenance personnel in the form of terminal listings, bar graphs, and special printed reports. This paper gives an overview of the IKE system, describes its use as a klystron maintenance tool, and explains why it is valuable to klystron engineers

Unitarity, quasi-normal modes and the AdS_3/CFT_2 correspondence

In general, black-hole perturbations are governed by a discrete spectrum of complex eigen-frequencies (quasi-normal modes). This signals the breakdown of unitarity. In asymptotically AdS spaces, this is puzzling because the corresponding CFT is unitary. To address this issue in three dimensions, we replace the BTZ black hole by a wormhole, following a suggestion by Solodukhin [hep-th/0406130]. We solve the wave equation for a massive scalar field and find an equation for the poles of the propagator. This equation yields a rich spectrum of {\em real} eigen-frequencies. We show that the throat of the wormhole is $o(e^{-1/G})$, where $G$ is Newton's constant. Thus, the quantum effects which might produce the wormhole are non-perturbative.Comment: 9 page

Factorization of correlations in two-dimensional percolation on the plane and torus

Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, in agreement with the numerical value 1.022 found previously in a study of R on the conformally equivalent cylinder. In this paper we confirm the factorization on the plane numerically using periodic lattices (tori) of very large size, which locally approximate a plane. We also investigate the general behavior of R on the torus, and find a minimum value of R approx. 1.0132 when the three points are maximally separated. In addition, we present a simplified expression for R on the plane as a function of the SLE parameter kappa.Comment: Small corrections (final version). In press, J. Phys.

Flux Discharge Cascades in Various Dimensions

We study the dynamics of electric flux discharge by charged particle pair or spherical string or membrane production in various dimensions. When electric flux wraps at least one compact cycle, we find that a single "pair" production event can initiate a cascading decay in real time that "shorts out" the flux and discharges many units of it. This process arises from local dynamics in the compact space, and so is invisible in the dimensionally-reduced truncation. It occurs in theories as simple as the Schwinger model on a circle, and has implications for any theory with compact dimensions and electric flux, including string theories and the string landscape.Comment: 19+8 pages, 3 figures, 3 appendice

Cosmic 21-cm Fluctuations as a Probe of Fundamental Physics

Fluctuations in high-redshift cosmic 21-cm radiation provide a new window for observing unconventional effects of high-energy physics in the primordial spectrum of density perturbations. In scenarios for which the initial state prior to inflation is modified at short distances, or for which deviations from scale invariance arise during the course of inflation, the cosmic 21-cm power spectrum can in principle provide more precise measurements of exotic effects on fundamentally different scales than corresponding observations of cosmic microwave background anisotropies.Comment: 8 pages, 2 figure