Mathematics in Internet Traffic Data Analysis

The Internet traffic data have been found to possess extreme variability and bursty structures in a wide range of time-scales, so that there is no definite duration of busy or silent periods. But there is a self-similarity for which it is possible to characterize the data. The self-similar nature was first proposed by Leland et a1 [l] and subsequently established by others in a flood of research works on the subject [2]-[5]. It was then a new concept against the long believed idea of Poisson traffic. The traditional Poison model, a short ranged process, assumed the variation of data flow to be finite but the observations on Internet traffic proved otherwise. It is this large variance that leads to the self-similar nature of the data almost at all scales of resolution. Such a feature is always associated with a fractal structure of the data. The fractal characteristics can exist both in temporal and spatial scales. This was indicated by Willinger and Paxson [6], as due to the extreme variability and long range dependence in the process. Presently, one of the main research interests in the field of Internet traffic is that of prediction of data which will help a network manager to render a satisfactory quality of service. Before preparing a model of prediction, one of the important tasks is to determine its statistics. Any model to predict the future values will have to preserve these characteristics

"Rural-Urban Migration and Urban Poverty: Socio-Economic Profiles of Rickshaw Pullers and Owner-Contractors in North-East Delhi"

In December 2005 and January 2006, we conducted a pilot survey to collect detailed information on eighty rickshaw pullers and twenty-six rickshaw owner-contractors in north-east Delhi. This is a preliminary report based on the data thus collected.

Crossing and weighted crossing number of near-planar graphs

A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from different combinatorial viewpoints. On the one hand, we develop min-max formulas involving efficiently computable lower and upper bounds. These min-max results are the first of their kind in the study of crossing numbers and improve the approximation factor for the approximation algorithm given by Hliněny and Salazar (Graph Drawing GD’06). On the other hand, we show that it is NP-hard to compute a weighted version of the crossing number for near-planar graphs

Singular Scaling Functions in Clustering Phenomena

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling function is singular for small argument -- it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.Comment: 8 pages, 3 figures, Invited talk delivered at Statphys 23, Genova, July 200

Search for heavy neutrinos mixing with tau neutrinos

We report on a search for heavy neutrinos (\nus) produced in the decay D_s\to \tau \nus at the SPS proton target followed by the decay \nudecay in the NOMAD detector. Both decays are expected to occur if \nus is a component of $\nu_{\tau}$.\ From the analysis of the data collected during the 1996-1998 runs with $4.1\times10^{19}$ protons on target, a single candidate event consistent with background expectations was found. This allows to derive an upper limit on the mixing strength between the heavy neutrino and the tau neutrino in the \nus mass range from 10 to 190 $\rm MeV$. Windows between the SN1987a and Big Bang Nucleosynthesis lower limits and our result are still open for future experimental searches. The results obtained are used to constrain an interpretation of the time anomaly observed in the KARMEN1 detector.\Comment: 20 pages, 7 figures, a few comments adde

Final NOMAD results on nu_mu->nu_tau and nu_e->nu_tau oscillations including a new search for nu_tau appearance using hadronic tau decays

Results from the nu_tau appearance search in a neutrino beam using the full NOMAD data sample are reported. A new analysis unifies all the hadronic tau decays, significantly improving the overall sensitivity of the experiment to oscillations. The "blind analysis" of all topologies yields no evidence for an oscillation signal. In the two-family oscillation scenario, this sets a 90% C.L. allowed region in the sin^2(2theta)-Delta m^2 plane which includes sin^2(2theta)<3.3 x 10^{-4} at large Delta m^2 and Delta m^2 < 0.7 eV^2/c^4 at sin^2(2theta)=1. The corresponding contour in the nu_e->nu_tau oscillation hypothesis results in sin^2(2theta)<1.5 x 10^{-2} at large Delta m^2 and Delta m^2 < 5.9 eV^2/c^4 at sin^2(2theta)=1. We also derive limits on effective couplings of the tau lepton to nu_mu or nu_e.Comment: 46 pages, 16 figures, Latex, to appear on Nucl. Phys.

Search for the exotic Θ+\Theta^+ resonance in the NOMAD experiment

A search for exotic Theta baryon via Theta -> proton +Ks decay mode in the NOMAD muon neutrino DIS data is reported. The special background generation procedure was developed. The proton identification criteria are tuned to maximize the sensitivity to the Theta signal as a function of xF which allows to study the Theta production mechanism. We do not observe any evidence for the Theta state in the NOMAD data. We provide an upper limit on Theta production rate at 90% CL as 2.13 per 1000 of neutrino interactions.Comment: Accepted to European Physics Journal

Search for nu(mu)-->nu(e) Oscillations in the NOMAD Experiment

We present the results of a search for nu(mu)-->nu(e) oscillations in the NOMAD experiment at CERN. The experiment looked for the appearance of nu(e) in a predominantly nu(mu) wide-band neutrino beam at the CERN SPS. No evidence for oscillations was found. The 90% confidence limits obtained are delta m^2 < 0.4 eV^2 for maximal mixing and sin^2(2theta) < 1.4x10^{-3} for large delta m^2. This result excludes the LSND allowed region of oscillation parameters with delta m^2 > 10 eV^2.Comment: 19 pages, 8 figures. Submitted to Phys. Lett.