N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice

The N-tree approximation scheme, introduced in the context of random directed polymers, is here applied to the computation of the maximum Lyapunov exponent in a coupled map lattice. We discuss both an exact implementation for small tree-depth $n$ and a numerical implementation for larger $n$s. We find that the phase-transition predicted by the mean field approach shifts towards larger values of the coupling parameter when the depth $n$ is increased. We conjecture that the transition eventually disappears.Comment: RevTeX, 15 pages,5 figure

A Search for Stellar Obscuration Events due to Dark Clouds

The recent detections of a large population of faint submillimetre sources, an excess halo gamma-ray background, and the extreme scattering events observed for extragalactic radio sources have been explained as being due to baryonic dark matter in the form of small, dark, gas clouds. In this paper we present the results of a search for the transient stellar obscurations such clouds are expected to cause. We examine the Macho project light curves of 48 x 10^6 stars toward the Galactic bulge, LMC and SMC for the presence of dark cloud extinction events. We find no evidence for the existence of a population of dark gas clouds with Av > 0.2 and masses between ~ 10^-4 and 10^-2 M_solar in the Galactic disk or halo. However, it is possible that such dark cloud populations could exist if they are clustered in regions away from the observed lines of sight.Comment: 13 pages, 9 figures, submitted to Ap

Libraries Respond to Mobile Ubiquity: Research and Assessment of Mobile Device Usage Trends for Academic and Medical Libraries

The authors consider trends in mobile device usage for the Internet as a whole, for EBSCO Discovery Service across all client libraries, and at two specific libraries: Preston Medical Library, serving the University of Tennessee (UT) Graduate School of Medicine and UT Medical Center, and the Joyner Library at East Carolina University, serving students and faculty on the main campus. Librarians at Preston Medical Library conducted a survey to determine which mobile devices, platforms, and apps were used by their patrons in 2012. East Carolina University piloted an iPad and e-reader lending program in 2010–2011. The results of each are being used to guide service planning related to mobile applications, education, and support

Directed paths on hierarchical lattices with random sign weights

We study sums of directed paths on a hierarchical lattice where each bond has either a positive or negative sign with a probability $p$. Such path sums $J$ have been used to model interference effects by hopping electrons in the strongly localized regime. The advantage of hierarchical lattices is that they include path crossings, ignored by mean field approaches, while still permitting analytical treatment. Here, we perform a scaling analysis of the controversial ``sign transition'' using Monte Carlo sampling, and conclude that the transition exists and is second order. Furthermore, we make use of exact moment recursion relations to find that the moments always determine, uniquely, the probability distribution $P(J)$. We also derive, exactly, the moment behavior as a function of $p$ in the thermodynamic limit. Extrapolations ($n\to 0$) to obtain for odd and even moments yield a new signal for the transition that coincides with Monte Carlo simulations. Analysis of high moments yield interesting ``solitonic'' structures that propagate as a function of $p$. Finally, we derive the exact probability distribution for path sums $J$ up to length L=64 for all sign probabilities.Comment: 20 pages, 12 figure

Quantum Revivals in Periodically Driven Systems close to nonlinear resonance

We calculate the quantum revival time for a wave-packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven system is shown analytically. As an example of application of our approach, we compare the analytically obtained values of the revival time for various modulation strengths with the numerically computed ones in the case of a driven gravitational cavity. We show that they are in very good agreement.Comment: 14 pages, 1 figur

Sparsity of integer solutions in the average case

We examine how sparse feasible solutions of integer programs are, on average. Average case here means that we fix the constraint matrix and vary the right-hand side vectors. For a problem in standard form with m equations, there exist LP feasible solutions with at most m many nonzero entries. We show that under relatively mild assumptions, integer programs in standard form have feasible solutions with O(m) many nonzero entries, on average. Our proof uses ideas from the theory of groups, lattices, and Ehrhart polynomials. From our main theorem we obtain the best known upper bounds on the integer Carathéodory number provided that the determinants in the data are small