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Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converges to a Gaussian, and the individual measures on gaps between summands for $m \in [F_n, F_{n+1})$ converge to geometric decay for almost all $m$ as $n\to\infty$. While similar results are known for many other recurrences, previous work focused on proving Gaussianity for the number of summands or the average gap measure. We derive general conditions which are easily checked yield geometric decay in the individual gap measures of generalized Zeckendorf decompositions attached to many linear recurrence relations., Comment: Version 1.0, 6 pages

Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers, where the Fibonacci numbers satisfy $F_n=F_{n-1}+F_{n-2}$ for $n\geq 3$, $F_1=1$ and $F_2=2$. The distribution of the number of summands in such decomposition converges to a Gaussian, the gaps between summands converges to geometric decay, and the distribution of the longest gap is similar to that of the longest run of heads in a biased coin; these results also hold more generally, though for technical reasons previous work needed to assume the coefficients in the recurrence relation are non-negative and the first term is positive. We extend these results by creating an infinite family of integer sequences called the $m$-gonal sequences arising from a geometric construction using circumscribed $m$-gons. They satisfy a recurrence where the first $m+1$ leading terms vanish, and thus cannot be handled by existing techniques. We provide a notion of a legal decomposition, and prove that the decompositions exist and are unique. We then examine the distribution of the number of summands used in the decompositions and prove that it displays Gaussian behavior. There is geometric decay in the distribution of gaps, both for gaps taken from all integers in an interval and almost surely in distribution for the individual gap measures associated to each integer in the interval. We end by proving that the distribution of the longest gap between summands is strongly concentrated about its mean, behaving similarly as in the longest run of heads in tosses of a coin., Comment: Version 1.1, 22 pages

The two particle interferometry method to determine the size of the emitting source after a heavy ion collision is extended. Following the extension of the method to spherical expansion dynamics, here we extend the method to rotating systems. It is shown that rotation of a cylindrically symmetric system leads to modifications, which can be perceived as spatial asymmetry by the "azimuthal HBT" method. We study an exact rotating and expanding solution of the fluid dynamical model of heavy ion reactions. We consider a source that is azimuthally symmetric in space around the axis of rotation, and discuss the features of the resulting two particle correlation function. This shows the azimuthal asymmetry arising from the rotation. We show that this asymmetry leads to results similar to those given by spatially asymmetric sources., Comment: 3 pages, 3 figures, submitted to PLB. arXiv admin note: text overlap with arXiv:1508.01884

The "Iterative Laplace Transform Method" is used to solve the Fokker-Planck equation for finding the time evolution of the heavy quarks distribution functions such as charm and bottom in quark gluon plasma. These solutions will lead us to calculation of nuclear suppression factor RAA. The results have good agreement with available experiment data from the PHENIX collaboration., Comment: 13 pages, 4 figures

The technology of scintillating bolometers based on zinc molybdate (ZnMoO$_4$) crystals is under development within the LUMINEU project to search for 0$\nu$2$\beta$ decay of $^{100}$Mo with the goal to set the basis for large scale experiments capable to explore the inverted hierarchy region of the neutrino mass pattern. Advanced ZnMoO$_4$ crystal scintillators with mass of $\sim$~0.3 kg were developed and Zn$^{100}$MoO$_4$ crystal from enriched $^{100}$Mo was produced for the first time by using the low-thermal-gradient Czochralski technique. One ZnMoO$_4$ scintillator and two samples (59 g and 63 g) cut from the enriched boule were tested aboveground at milli-Kelvin temperature as scintillating bolometers showing a high detection performance. The first results of the low background measurements with three ZnMoO$_4$ and two enriched detectors installed in the EDELWEISS set-up at the Modane Underground Laboratory (France) are presented., Comment: 7 pages, 5 figures, Contribution to the proceedings of the 37th International Conference on High Energy Physics (ICHEP 2014), Valencia, Spain, 2-9 July 2014

By Zeckendorf's theorem, an equivalent definition of the Fibonacci sequence (appropriately normalized) is that it is the unique sequence of increasing integers such that every positive number can be written uniquely as a sum of non-adjacent elements; this is called a legal decomposition. Previous work examined the distribution of the number of summands and the spacings between them, in legal decompositions arising from the Fibonacci numbers and other linear recurrence relations with non-negative integral coefficients. Many of these results were restricted to the case where the first term in the defining recurrence was positive. We study a generalization of the Fibonacci numbers with a simple notion of legality which leads to a recurrence where the first term vanishes. We again have unique legal decompositions, Gaussian behavior in the number of summands, and geometric decay in the distribution of gaps., Comment: Version 1.0, 22 pages, 2 figures

Agent-Based Modeling and Simulation (ABMS) is a simple and yet powerful method for simulation of interactions among individual agents. Using ABMS, different phenomena can be modeled and simulated without spending additional time on unnecessary complexities. Although ABMS is well-matured in many different fields such as economic, social, and natural phenomena, it has not received much attention in the context of mobile ad-hoc networks (MANETs). In this paper, we present ABMQ, a powerful Agent-Based platform suitable for modeling and simulation of self-organization in wireless networks, and particularly MANETs. By utilizing the unique potentials of Qt Application Framework, ABMQ provides the ability to easily model and simulate self-organizing algorithms, and then reuse the codes and models developed during simulation process for building real third-party applications for several desktop and mobile platforms, which substantially decreases the development time and cost, and prevents probable bugs that can happen as a result of rewriting codes., Comment: 6 pages, 8 figures, conference paper

We present new constraints on the couplings of axions and more generic axion-like particles using data from the EDELWEISS-II experiment. The EDELWEISS experiment, located at the Underground Laboratory of Modane, primarily aims at the direct detection of WIMPs using germanium bolometers. It is also sensitive to the low-energy electron recoils that would be induced by solar or dark matter axions. Using a total exposure of up to 448 kg.d, we searched for axion-induced electron recoils down to 2.5 keV within four scenarios involving different hypotheses on the origin and couplings of axions. We set a 95% CL limit on the coupling to photons $g_{A\gamma}<2.13\times 10^{-9}$ GeV$^{-1}$ in a mass range not fully covered by axion helioscopes. We also constrain the coupling to electrons, $g_{Ae} < 2.56\times 10^{-11}$, similar to the more indirect solar neutrino bound. Finally we place a limit on $g_{Ae}\times g_{AN}^{\rm eff}<4.70 \times 10^{-17}$, where $g_{AN}^{\rm eff}$ is the effective axion-nucleon coupling for $^{57}$Fe. Combining these results we fully exclude the mass range $0.91\,{\rm eV}

The EDELWEISS-II collaboration has completed a direct search for WIMP dark matter using cryogenic Ge detectors (400 g each) and 384 kg$\times$days of effective exposure. A cross-section of $4.4 \times 10^{-8}$ pb is excluded at 90% C.L. for a WIMP mass of 85 GeV. The next phase, EDELWEISS-III, aims to probe spin-independent WIMP-nucleon cross-sections down to a few $\times10^{-9}$ pb. We present here the study of gamma and neutron background coming from radioactive decays in the set-up and shielding materials. We have carried out Monte Carlo simulations for the completed EDELWEISS-II setup with GEANT4 and normalised the expected background rates to the measured radioactivity levels (or their upper limits) of all materials and components. The expected gamma-ray event rate in EDELWEISS-II at 20-200 keV agrees with the observed rate of 82 events/kg/day within the uncertainties in the measured concentrations. The calculated neutron rate from radioactivity of 1.0-3.1 events (90% C.L.) at 20-200 keV in the EDELWEISS-II data together with the expected upper limit on the misidentified gamma-ray events ($\le0.9$), surface betas ($\le0.3$), and muon-induced neutrons ($\le0.7$), do not contradict 5 observed events in nuclear recoil band. We have then extended the simulation framework to the EDELWEISS-III configuration with 800 g crystals, better material purity and additional neutron shielding inside the cryostat. The gamma-ray and neutron backgrounds in 24 kg fiducial mass of EDELWEISS-III have been calculated as 14-44 events/kg/day and 0.7-1.4 events per year, respectively. The results of the background studies performed in the present work have helped to select better purity components and improve shielding in EDELWEISS-III to further reduce the expected rate of background events in the next phase of the experiment., Comment: 15 pages, 9 figures, to be published in Astroparticle Physics

A dedicated analysis of the muon-induced background in the EDELWEISS dark matter search has been performed on a data set acquired in 2009 and 2010. The total muon flux underground in the Laboratoire Souterrain de Modane (LSM) was measured to be $\Phi_{\mu}=(5.4\pm 0.2 ^{+0.5}_{-0.9})$\,muons/m$^2$/d. The modular design of the muon-veto system allows the reconstruction of the muon trajectory and hence the determination of the angular dependent muon flux in LSM. The results are in good agreement with both MC simulations and earlier measurements. Synchronization of the muon-veto system with the phonon and ionization signals of the Ge detector array allowed identification of muon-induced events. Rates for all muon-induced events $\Gamma^{\mu}=(0.172 \pm 0.012)\, \rm{evts}/(\rm{kg \cdot d})$ and of WIMP-like events $\Gamma^{\mu-n} = 0.008^{+0.005}_{-0.004}\, \rm{evts}/(\rm{kg \cdot d})$ were extracted. After vetoing, the remaining rate of accepted muon-induced neutrons in the EDELWEISS-II dark matter search was determined to be $\Gamma^{\mu-n}_{\rm irred} < 6\cdot 10^{-4} \, \rm{evts}/(\rm{kg \cdot d})$ at 90%\,C.L. Based on these results, the muon-induced background expectation for an anticipated exposure of 3000\,\kgd\ for EDELWEISS-3 is $N^{\mu-n}_{3000 kg\cdot d} < 0.6$ events., Comment: 21 pages, 16 figures, Accepted for publication in Astropart. Phys

We report on a search for low-energy (E < 20 keV) WIMP-induced nuclear recoils using data collected in 2009 - 2010 by EDELWEISS from four germanium detectors equipped with thermal sensors and an electrode design (ID) which allows to efficiently reject several sources of background. The data indicate no evidence for an exponential distribution of low-energy nuclear recoils that could be attributed to WIMP elastic scattering after an exposure of 113 kg.d. For WIMPs of mass 10 GeV, the observation of one event in the WIMP search region results in a 90% CL limit of 1.0x10^-5 pb on the spin-independent WIMP-nucleon scattering cross-section, which constrains the parameter space associated with the findings reported by the CoGeNT, DAMA and CRESST experiments., Comment: PRD rapid communication accepted

The CDMS and EDELWEISS collaborations have combined the results of their direct searches for dark matter using cryogenic germanium detectors. The total data set represents 614 kg.d equivalent exposure. A straightforward method of combination was chosen for its simplicity before data were exchanged between experiments. The results are interpreted in terms of limits on spin-independent WIMP-nucleon cross-section. For a WIMP mass of 90 GeV/c^2, where this analysis is most sensitive, a cross-section of 3.3 x 10^{-44} cm^2 is excluded at 90% CL. At higher WIMP masses, the combination improves the individual limits, by a factor 1.6 above 700 GeV/c^2. Alternative methods of combining the data provide stronger constraints for some ranges of WIMP masses and weaker constraints for others., Comment: Events, efficiencies, and main limit are available in text format (see README.txt)

The EDELWEISS-II collaboration has completed a direct search for WIMP dark matter with an array of ten 400-g cryogenic germanium detectors in operation at the Laboratoire Souterrain de Modane. The combined use of thermal phonon sensors and charge collection electrodes with an interleaved geometry enables the efficient rejection of gamma-induced radioactivity as well as near-surface interactions. A total effective exposure of 384 kg.d has been achieved, mostly coming from fourteen months of continuous operation. Five nuclear recoil candidates are observed above 20 keV, while the estimated background is 3.0 events. The result is interpreted in terms of limits on the cross-section of spin-independent interactions of WIMPs and nucleons. A cross-section of 4.4x10^-8 pb is excluded at 90%CL for a WIMP mass of 85 GeV. New constraints are also set on models where the WIMP-nucleon scattering is inelastic., Comment: 23 pages, 5 figures; matches published version

A critical need in Mobile Wireless Sensor Network (MWSN) is to achieve energy efficiency during routing as the sensor nodes have scarce energy resource. The nodes' mobility in MWSN poses a challenge to design an energy efficient routing protocol. Clustering helps to achieve energy efficiency by reducing the organization complexity overhead of the network which is proportional to the number of nodes in the network. This paper proposes a novel hybrid multipath routing algorithm with an efficient clustering technique. A node is selected as cluster head if it has high surplus energy, better transmission range and least mobility. The Energy Aware (EA) selection mechanism and the Maximal Nodal Surplus Energy estimation technique incorporated in this algorithm improves the energy performance during routing. Simulation results can show that the proposed clustering and routing algorithm can scale well in dynamic and energy deficient mobile sensor network., Comment: 9 pages, 4 figures

Mobile Ad Hoc Network (MANET) is a collection of nodes that can be rapidly deployed as a multi-hop network without the aid of any centralized administration. Misbehavior is challenged by bandwidth and energy efficient medium access control and fair share of throughput. Node misbehavior plays an important role in MANET. In this survey, few of the contention window misbehavior is reviewed and compared. The contention window cheating either minimizes the active communication of the network or reduces bandwidth utilization of a particular node. The classification presented is in no case unique but summarizes the chief characteristics of many published proposals for contention window cheating. After getting insight into the different contention window misbehavior, few of the enhancements that can be done to improve the existing contention window are suggested. The purpose of this paper is to facilitate the research efforts in combining the existing solutions to offer more efficient methods to reduce contention window cheating mechanisms., Comment: 12 pages,4 figures, 1 table

Muon-induced neutrons constitute a prominent background component in a number of low count rate experiments, namely direct searches for Dark Matter. In this work we describe a neutron detector to measure this background in an underground laboratory, the Laboratoire Souterrain de Modane. The system is based on 1 m3 of Gd-loaded scintillator and it is linked with the muon veto of the EDELWEISS-II experiment for coincident muon detection. The system was installed in autumn 2008 and passed since then a number of commissioning tests proving its full functionality. The data-taking is continuously ongoing and a count rate of the order of 1 muon-induced neutron per day has been achieved., Comment: Accepted for publication in Astroparticle Physics; 14 pages, 10 figures

This paper describes precise measurements of the thermal neutron flux in the LSM underground laboratory in proximity of the EDELWEISS-II dark matter search experiment together with short measurements at various other locations. Monitoring of the flux of thermal neutrons is accomplished using a mobile detection system with low background proportional counter filled with $^3$He. On average 75 neutrons per day are detected with a background level below 1 count per day (cpd). This provides a unique possibility of a day by day study of variations of the neutron field in a deep underground site. The measured average 4$\pi$ neutron flux per cm$^{2}$ in the proximity of EDELWEISS-II is $\Phi_{MB}=3.57\pm0.05^{stat}\pm0.27^{syst}\times 10^{-6}$ neutrons/sec. We report the first experimental observation that the point-to-point thermal neutron flux at LSM varies by more than a factor two., Comment: submitted to Journal of Physics G: Nuclear and Particle Physics, 8 pages, 4 figures

The EDELWEISS-II collaboration has performed a direct search for WIMP dark matter with an array of ten 400 g heat-and-ionization cryogenic detectors equipped with interleaved electrodes for the rejection of near-surface events. Six months of continuous operation at the Laboratoire Souterrain de Modane have been achieved. The observation of one nuclear recoil candidate above 20 keV in an effective exposure of 144 kgd is interpreted in terms of limits on the cross-section of spin-independent interactions of WIMPs and nucleons. A cross-section of 1.0x10^-7 pb is excluded at 90%CL for a WIMP mass of 80 GeV/c2. This result demonstrates for the first time the very high background rejection capabilities of these simple and robust detectors in an actual WIMP search experiment., Comment: 14 pages, 3 figures. Submitted to Phys Lett. B

A new design of a cryogenic germanium detector for dark matter search is presented, taking advantage of the coplanar grid technique of event localisation for improved background discrimination. Experiments performed with prototype devices in the EDELWEISS II setup at the Modane underground facility demonstrate the remarkably high efficiency of these devices for the rejection of low-energy $\beta$, approaching 10$^5$ . This opens the road to investigate the range beyond 10$^{-8}$ pb in the WIMP-nucleon collision cross-sections, as proposed in the EURECA project of a one-ton cryogenic detector mass., Comment: submitted to Physical Review Letters