A central limit theorem for the zeroes of the zeta function

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.Comment: 22 pages. Incorporates referees suggestions. Contains minor corrections to published versio

Transient Thermo-Mechanical Analysis of the TPSG4 Beam Diluter

A new extraction channel is being built in the Super Proton Synchrotron (SPS) Long Straight Section 4 (LSS4) to transfer proton beams to the Large Hadron Collider (LHC) and also to the CERN Neutrino to Gran Sasso (CNGS) target. The beam is extracted in a fast mode during a single turn. For this purpose a protection of the MSE copper septum coil, in the form of a beam diluting element placed upstream, will be required to cope with the new failure modes associated with the fast extraction operation. The present analysis focuses on the thermo-mechanical behavior of the proposed TPSG4 diluter element irradiated by a fast extracted beam (up to 4.9 x 10^13 protons per 7.2 mus pulse) from the SPS. The deposited energy densities, estimated from primary and secondary particle simulations using the high-energy particle transport code FLUKA, were converted to internal heat generation rates taken as a thermal load input for the finite-element engineering analyses code ANSYS. According to the time dependence of the extracted beam, the transient solutions were obtained for coupled heat transfer, structural deformation, and shock wave problems. The results are given for the space distribution and the time evolution of temperatures and stresses in the most critical parts of the TPSG4 beam diluting element followed by the MSE copper septum coil. In the worst case of impact of the full LHC ultimate beam, the maximum temperatures remain safely below the melting point. However, the maximum equivalent stresses may slightly exceed the elastic limit in the aluminium section of the diluter. Also, the predicted maximum temperature rise in the MSE septum coil exceeds the design value

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Reducing the SPS Machine Impedance

The SPS as LHC Injector project has been working for some time to prepare the SPS for its role as final injector for the LHC. This included major work related to injection, acceleration, extraction and beam instrumentation for the LHC beams [1]. Measurements carried out with the high brightness LHC beam showed that a major improvement of the machine impedance would also be necessary [2]. In addition to removing all lepton related components (once LEP operation ended in 2000), the decision was made to shield the vacuum system pumping port cavities. These accidental cavities had been identified as having characteristic frequencies in the 1-1.5GHz range. Since the SPS vacuum system contains roughly 1000 of these cavities, they constitute a major fraction of the machine impedance. As removal of the ports and associated bellows is not possible, transition shields (PPS) had to be designed to insert within the pumping port cavities

Trusted Spanning Tree for Delay Tolerant MANETs

Quality of service is an important issue in Delay Tole-rant Mobile Ad-Hoc Networks (DTMs). This work attempts to improve the Quality of service (QoS) in DTMs by re-lying on spanning forests algorithms. The existing algo-rithms are improved by introducing the notion of trust and choosing the most robust (trustable) spanning trees among existing opportunities. The robustness/quality of the tree can be assessed based on two cost functions. In order to im-prove QoS in a DTM, a greedy-based heuristic is proposed to the existing algorithms and becomes G-TRUST. To aid efficient break away of low-trust node, another heuristic, BREAK heuristic, is further incorporated to G-TRUST (G-TRUST BREAK). Simulation on realistic mobility models were carried out on both G-TRUST and G-TRUST BREAK. Their results verified the advantages of incorporating these heuristics. 1

On the key expansion of D(n, K)-based cryptographical algorithm

The family of algebraic graphs D(n, K) defined over finite commutative ring K have been used in different cryptographical algorithms (private and public keys, key exchange protocols). The encryption maps correspond to special walks on this graph. We expand the class of encryption maps via the use of edge transitive automorphism group G(n, K) of D(n, K). The graph D(n, K) and related directed graphs are disconnected. So private keys corresponding to walks preserve each connected component. The group G(n, K) of transformations generated by an expanded set of encryption maps acts transitively on the plainspace. Thus we have a great difference with block ciphers, any plaintexts can be transformed to an arbitrarily chosen ciphertex by an encryption map. The plainspace for the D(n, K) graph based encryption is a free module P over the ring K. The group G(n, K) is a subgroup of Cremona group of all polynomial automorphisms. The maximal degree for a polynomial from G(n, K) is 3. We discuss the Diffie-Hellman algorithm based on the discrete logarithm problem for the group τ-1Gτ, where τ is invertible affine transformation of free module P i.e. polynomial automorphism of degree 1. We consider some relations for the discrete logarithm problem for G(n, K) and public key algorithm based on the D(n, K) graphs

Introducing the DizzyQuest: an app-based diary for vestibular disorders

BACKGROUND Most questionnaires currently used for assessing symptomatology of vestibular disorders are retrospective, inducing recall bias and lowering ecological validity. An app-based diary, administered multiple times in daily life, could increase the accuracy and ecological validity of symptom measurement. The objective of this study was to introduce a new experience sampling method (ESM) based vestibular diary app (DizzyQuest), evaluate response rates, and to provide examples of DizzyQuest outcome measures which can be used in future research. METHODS Sixty-three patients diagnosed with a vestibular disorder were included. The DizzyQuest consisted of four questionnaires. The morning- and evening-questionnaires were administered once each day, the within-day-questionnaire 10 times a day using a semi-random time schedule, and the attack questionnaire could be completed after the occurrence of a vertigo or dizziness attack. Data were collected for 4~weeks. Response rates and loss-to-follow-up were determined. Reported symptoms in the within-day-questionnaire were compared within and between patients and subgroups of patients with different vestibular disorders. RESULTS Fifty-one patients completed the study period. Average response rates were significantly higher than the desired response rate of \textgreater 50% (p \textless 0.001). The attack-questionnaire was used 159 times. A variety of neuro-otological symptoms and different disease profiles were demonstrated between patients and subgroups of patients with different vestibular disorders. CONCLUSION The DizzyQuest is able to capture vestibular symptoms within their psychosocial context in daily life, with little recall bias and high ecological validity. The DizzyQuest reached the desired response rates and showed different disease profiles between subgroups of patients with different vestibular disorders. This is the first time ESM was used to assess daily symptoms and quality of life in vestibular disorders, showing that it might be a useful tool in this population

Preliminary Report on the Consequences of LHC Civil Engineering for the SPS and LEP

The excavation of the shafts and caverns for the ATLAS and CMS experiments of the LHC will start whilst LEP and the SPS are running. This will be at a period when LEP should be at its peak performance and the SPS will be providing beams for LEP, fixed target physics and LHC test beams. Simulations show that movements of the machine tunnels can be expected during the excavation and it is essential that this does not affect the performance of the SPS and LEP. These movements are of sufficient amplitude to prevent machine operation if no precautions are taken. This preliminary report outlines the problems and suggests what actions should be taken to ensure efficient operation of the SPS and LEP during the critical period

Steel septum magnets for the LHC beam injection and extraction

The Large Hadron Collider (LHC) will be a superconducting accelerator and collider to be installed in the existing underground LEP ring tunnel at CERN. It will provide proton-proton collisions with a centre of mass energy of 14 TeV. The proton beams coming from the SPS will be injected into the LHC at 450 GeV by vertically deflecting kicker magnets and horizontally deflecting steel septum magnets (MSI). The proton beams will be dumped from the LHC with the help of two extraction systems comprising horizontally deflecting kicker magnets and vertically deflecting steel septum magnets (MSD). The MSI and MSD septa are laminated iron-dominated magnets using an all welded construction. The yokes are constructed from two different half cores, called coil core and septum core. The septum cores comprise circular holes for the circulating beams. This avoids the need for careful alignment of the usually wedge-shaped septum blades used in classical Lambertson magnets. The MSI and MSD septum magnets were designed and built in a collaboration between IHEP (Protvino) and CERN (Geneva). This paper presents the magnet design, the experience gathered during the preseries construction, and gives the results of detailed magnetic measurements of the MSIB and MSDC preseries magnets