Dilated Floor Functions That Commute

We determine all pairs of real numbers $(\alpha, \beta)$ such that the dilated floor functions $\lfloor \alpha x\rfloor$ and $\lfloor \beta x\rfloor$ commute under composition, i.e., such that $\lfloor \alpha \lfloor \beta x\rfloor\rfloor = \lfloor \beta \lfloor \alpha x\rfloor\rfloor$ holds for all real $x$.Comment: 6 pages, to appear in Amer. Math. Monthl

Field Quantization in 5D Space-Time with Z2_2-parity and Position/Momentum Propagator

Field quantization in 5D flat and warped space-times with Z$_2$-parity is comparatively examined. We carefully and closely derive 5D position/momentum(P/M) propagators. Their characteristic behaviours depend on the 4D (real world) momentum in relation to the boundary parameter ($l$) and the bulk curvature (\om). They also depend on whether the 4D momentum is space-like or time-like. Their behaviours are graphically presented and the Z$_2$ symmetry, the "brane" formation and the singularities are examined. It is shown that the use of absolute functions is important for properly treating the singular behaviour. The extra coordinate appears as a {\it directed} one like the temperature. The $\delta(0)$ problem, which is an important consistency check of the bulk-boundary system, is solved {\it without} the use of KK-expansion. The relation between P/M propagator (a closed expression which takes into account {\it all} KK-modes) and the KK-expansion-series propagator is clarified. In this process of comparison, two views on the extra space naturally come up: orbifold picture and interval (boundary) picture. Sturm-Liouville expansion (a generalized Fourier expansion) is essential there. Both 5D flat and warped quantum systems are formulated by the Dirac's bra and ket vector formalism, which shows the warped model can be regarded as a {\it deformation} of the flat one with the {\it deformation parameter} \om. We examine the meaning of the position-dependent cut-off proposed by Randall-Schwartz.Comment: 44 figures, 22(fig.)+41 pages, to be published in Phys.Rev.D, Fig.4 is improve

Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information

Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording LFPs and spikes from the primary visual cortex of anesthetized macaques while presenting a color movie.Wethen determined how the power of LFPs and spikes at different frequencies represents the visual features in the movie.Wefound that the most informative LFP frequency ranges were 1– 8 and 60 –100 Hz. LFPs in the range of 12– 40 Hz carried little information about the stimulus, and may primarily reflect neuromodulatory inputs. Spike power was informative only at frequencies <12 Hz. We further quantified “signal correlations” (correlations in the trial-averaged power response to different stimuli) and “noise correlations” (trial-by-trial correlations in the fluctuations around the average) of LFPs and spikes recorded from the same electrode. We found positive signal correlation between high-gamma LFPs (60 –100 Hz) and spikes, as well as strong positive signal correlation within high-gamma LFPs, suggesting that high-gamma LFPs and spikes are generated within the same network. LFPs<24 Hz shared strong positive noise correlations, indicating that they are influenced by a common source, such as a diffuse neuromodulatory input. LFPs<40 Hz showed very little signal and noise correlations with LFPs>40Hzand with spikes, suggesting that low-frequency LFPs reflect neural processes that in natural conditions are fully decoupled from those giving rise to spikes and to high-gamma LFPs

Complete recovery from anxiety disorders following Cognitive Behavioural Therapy in children and adolescents: a meta analysis

Cognitive Behavior Therapy (CBT) is a well-established treatment for childhood anxiety disorders. Meta-analyses have concluded that approximately 60% of children recover following treatment, however these include studies using a broad range of diagnostic indices to assess outcomes including whether children are free of the one anxiety disorder that causes most interference (i.e. the primary anxiety disorder) or whether children are free of all anxiety disorders. We conducted a meta-analysis to establish the efficacy of CBT in terms of absence of all anxiety disorders. Where available we compared this rate to outcomes based on absence of primary disorder. Of 56 published randomized controlled trials, 19 provided data on recovery from all anxiety disorders (n = 635 CBT, n = 450 control participants). There was significant heterogeneity across those studies with available data and full recovery rates varied from 47.6 to 66.4% among children without autistic spectrum conditions (ASC) and 12.2 to 36.7% for children with ASC following treatment, compared to up to 20.6% and 21.3% recovery in waitlist and active treatment comparisons. The lack of consistency in diagnostic outcomes highlights the urgent need for consensus on reporting in future RCTs of childhood anxiety disorders for the meaningful synthesis of data going forwards

Spatio-Temporal Urban Land Use/Cover Change Analysis in a Hill Station: The Case of Baguio City, Philippines

AbstractThis study explores the spatial and temporal characteristics of land use/cover (LUC) changes in Baguio city, the only American hill station in Asia and the summer capital of the Philippines. Remote sensing (RS) satellite images were used to develop the 1988, 1998, and 2009 LUC maps of the city in a Geographic Information Systems (GIS) platform. Results reveal that the city has undergone a major physical landscape transformation for the last 21 years as indicated by a rapid built-up area expansion and substantial changes in its other land uses/covers. This study also analyzes the spatial pattern of urban growth in Baguio city. Furthermore, it presents insights in planning for the future sustainable urbanization of this highly valued city

Physics at e^- e^-: a Case for Multi-channel Studies

I argue that it would be crucial to have as many channels as possible to understand the physics of electroweak symmetry breaking (EWSB) in next-generation collider experiments. A historic example of the parity violation and the $V-A$ interaction is used to make this point. An e^- e^- option offers us a new channel in this respect. The usefulness of this channel is exemplified for the case of supersymmetry and of the strongly coupled EWSB sector.Comment: 8 pages, 3 figures, uses psfig, to appear in the proceedings of the the Second International Workshop on Electron-Electron Interactions at TeV Energies, references correcte

High-Energy Neutrino Signatures of Dark Matter Decaying into Leptons

Decaying dark matter has previously been proposed as a possible explanation for the excess high energy cosmic ray electrons and positrons seen by PAMELA and the Fermi Gamma-Ray Space Telescope (FGST). To accommodate these signals however, the decays must be predominantly leptonic, to muons or taus, and therefore produce neutrinos, potentially detectable with the IceCube neutrino observatory. We find that, with five years of data, IceCube (supplemented by DeepCore) will be able to significantly constrain the relevant parameter space of decaying dark matter, and may even be capable of discovering dark matter decaying in the halo of the Milky Way.Comment: 4 pages, 1 figur

Discriminating spin through quantum interference

Many of the proposed solutions to the hierarchy and naturalness problems postulate new `partner' fields to the standard model particles. Determining the spins of these new particles will be critical in distinguishing among the various possible SM extensions, yet proposed methods rely on the underlying models. We propose a new model-independent method for spin measurements which takes advantage of quantum interference among helicity states. We demonstrate that this method will be able to discriminate scalar particles from higher spin states at the ILC, and discuss application to higher spins and possible uses at the LHC.Comment: 11 pages, 11 figure

Transport properties of a quantum wire: the role of extended time-dependent impurities

We study the transport properties of a quantum wire, described by the Tomonaga-Luttinger model, in the presence of a backscattering potential provided by several extended time-dependent impurities (barriers). Employing the B\" uttiker-Landauer approach, we first consider the scattering of noninteracting electrons ($g=1$) by a rectangular-like barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons ($g=1$), coincides with the result obtained using the B\" uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions $0<g<1$ already in the case of a single oscillating extended impurity, in contrast %contrary to the case of a point-like impurity, where this phenomenon occurs only for $0<g<1/2$.Comment: 9 pages, 5 figure

Cosmological Higgs fields

We present a time-dependent solution to the coupled Einstein-Higgs equations for general Higgs-type potentials in the context of flat FRW cosmological models. Possible implications are discussed.Comment: 5 pages, no figures. Version to be published in Phys. Rev. Lett. Changes: references and citations added; introduction partly modified; expanded discussion of relations between parameters in the Higgs potentia