Using Spectral Radius Ratio for Node Degree to Analyze the Evolution of Scale Free Networks and Small World Networks

In this paper, we show the evaluation of the spectral radius for node degree as the basis to analyze the variation in the node degrees during the evolution of scale-free networks and small-world networks. Spectral radius is the principal eigenvalue of the adjacency matrix of a network graph and spectral radius ratio for node degree is the ratio of the spectral radius and the average node degree. We observe a very high positive correlation between the spectral radius ratio for node degree and the coefficient of variation of node degree (ratio of the standard deviation of node degree and average node degree). We show how the spectral radius ratio for node degree can be used as the basis to tune the operating parameters of the evolution models for scale-free networks and small-world networks as well as evaluate the impact of the number of links added per node introduced during the evolution of a scale-free network and evaluate the impact of the probability of rewiring during the evolution of a small-world network from a regular network.Comment: 8 pages, 8 figures, Second International Conference on Computer Science and Information Technology, (COSIT-2015), Geneva, Switzerland, March 21-22, 201

DAMA and the self similar infall halo model

The annual modulation in the rate of WIMP recoils observed by the DAMA collaboration at high significance is often analyzed in the context of an isothermal Maxwell-Boltzmann velocity distribution. While this is the simplest model, there is a need to consider other well motivated theories of halo formation. In this paper, we study a different halo model, that of self similar infall which is characterized by the presence of a number of cold streams and caustics, not seen in simulations. It is shown that the self similar infall model is consistent with the DAMA result both in amplitude and in phase, for WIMP masses exceeding $\approx$ 250 GeV at the 99.7% confidence level. Adding a small thermal component makes the parameter space near $m_\chi$ = 12 GeV consistent with the self similar model. The minimum $\chi^2$ per degree of freedom is found to be 0.92(1.03) with(without) channeling taken into account, indicating an acceptable fit. For WIMP masses much greater than the mass of the target nucleus, the recoil rate depends only on the ratio $\sigma_{\rm p}/m_\chi$ which is found to be $\approx$ 0.06 femtobarn/TeV. However as in the case of the isothermal halo, the allowed parameter space is inconsistent with the null result obtained by the CDMS and Xenon experiments for spin-independent elastic scattering. Future experiments with directional sensitivity and mass bounds from accelerator experiments will help to distinguish between different halo models and/or constrain the contribution from cold flows.Comment: Main conclusions unchanged. Text is expanded, figures and references added. Accepted for publication in Physical Review D, and this replacement reflects the final versio

Proposed search for an electric-dipole moment using laser-cooled 171^{171}Yb atoms

We propose an experiment to search for a permanent atomic electric-dipole moment (EDM) using laser-cooled $^{171}$Yb atoms launched in an atomic fountain. A uniform B field sets the quantization axis, and the Ramsey separated-oscillatory-fields method is used to measure the Zeeman precession frequency of the atoms. Laser beams of appropriate polarization are used for preparation and detection in a given magnetic sublevel. The signature of an EDM is a shift in the Ramsey resonance correlated with application of a large E field. The precision is expected to be at least 20 times better than current limits because the use of a cold atomic beam allows application of E field 10 times larger than in a vapor cell, and the interaction time with the E field is 200 times larger compared to a thermal beam. The leading source of systematic error in beam experiments, the (E x v/c) motional magnetic field, is reduced considerably because of the near-perfect reversal of velocity between up and down trajectories through the E-field region.Comment: 7 pages, 3 figure

Caustics, cold flows, and annual modulation

We discuss the formation of dark matter caustics, and their possible detection by future dark matter experiments. The annual modulation expected in the recoil rate measured by a dark matter detector is discussed. We consider the example of dark matter particles with a Maxwell-Boltzmann velocity distribution modified by a cold stream due to a nearby caustic. It is shown that the effect of the caustic flow is potentially detectable, even when the density enhancement due to the caustic is small. This makes the annual modulation effect an excellent probe of inner caustics. We also show that the phase of the annual modulation at low recoil energies does not constrain the particle mass unless the velocity distribution of particles in the solar neighborhood is known.Comment: Minor corrections made, replaced to reflect the published versio