An elliptic curve test of the L-Functions Ratios Conjecture

We compare the L-Function Ratios Conjecture's prediction with number theory for the family of quadratic twists of a fixed elliptic curve with prime conductor, and show agreement in the 1-level density up to an error term of size X^{-(1-sigma)/2} for test functions supported in (-sigma, sigma); this gives us a power-savings for \sigma<1. This test of the Ratios Conjecture introduces complications not seen in previous cases (due to the level of the elliptic curve). Further, the results here are one of the key ingredients in the companion paper [DHKMS2], where they are used to determine the effective matrix size for modeling zeros near the central point for this family. The resulting model beautifully describes the behavior of these low lying zeros for finite conductors, explaining the data observed by Miller in [Mil3]. A key ingredient in our analysis is a generalization of Jutila's bound for sums of quadratic characters with the additional restriction that the fundamental discriminant be congruent to a non-zero square modulo a square-free integer M. This bound is needed for two purposes. The first is to analyze the terms in the explicit formula corresponding to characters raised to an odd power. The second is to determine the main term in the 1-level density of quadratic twists of a fixed form on GL_n. Such an analysis was performed by Rubinstein [Rub], who implicitly assumed that Jutila's bound held with the additional restriction on the fundamental discriminants; in this paper we show that assumption is justified.Comment: 35 pages, version 1.2. To appear in the Journal of Number Theor

Independent Orbiter Assessment (IOA): Assessment of the manned maneuvering unit

The results of the Independent Orbiter Assessment (IOA) of the Failure Modes and Effects Analysis (FMEA) and Critical Items List (CIL) are presented. The IOA effort first completed an analysis of the Manned Maneuvering Unit (MMU) hardware, generating draft failure modes and potential critical items. To preserve independence, this analysis was accomplished without reliance upon the results contain within the NASA FMEA/CIL documentation. The IOA results were then compared to the proposed Martin Marietta FMEA/CIL Post 51-L updates. A discussion of each discrepancy from the comparison is provided through additional analysis as required. These discrepancies were flagged as issues, and recommendations were made based on the FMEA data available at the time. The results of this comparison for the Orbiter MMU hardware are documented. The IOA product for the MMU analysis consisted of 204 failure mode worksheets that resulted in 95 potential critical items being identified. Comparison was made to the NASA baseline which consisted of 179 FMEAs and 110 CIL items. This comparison produced agreement on all 121 FMEAs which caused differences in 92 CIL items

Tour-based Travel Mode Choice Estimation based on Data Mining and Fuzzy Techniques

This paper extends tour-based mode choice model, which mainly includes individual trip level interactions, to include linked travel modes of consecutive trips of an individual. Travel modes of consecutive trip made by an individual in a household have strong dependency or co-relation because individuals try to maintain their travel modes or use a few combinations of modes for current and subsequent trips. Traditionally, tour based mode choice models involved nested logit models derived from expert knowledge. There are limitations associated with this approach. Logit models assumes i) specific model structure (linear utility model) in advance; and, ii) it holds across an entire historical observations. These assumptions about the predefined model may be representative of reality, however these rules or heuristics for tour based mode choice should ideally be derived from the survey data rather than based on expert knowledge/ judgment. Therefore, in this paper, we propose a novel data-driven methodology to address the issues identified in tour based mode choice. The proposed methodology is tested using the Household Travel Survey (HTS) data of Sydney metropolitan area and its performances are compared with the state-of-the-art approaches in this area

Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

An Agent Based Model for the Simulation of Transport Demand and Land Use

Agent based modelling has emerged as a promising tool to provide planners with insights on social behaviour and the interdependencies characterising urban system, particularly with respect to transport and infrastructure planning. This paper presents an agent based model for the simulation of land use and transport demand of an urban area of Sydney, Australia. Each individual in the model has a travel diary which comprises a sequence of trips the person makes in a representative day as well as trip attributes such as travel mode, trip purpose, and departure time. Individuals are associated with each other by their household relationship, which helps define the interdependencies of their travel diary and constrains their mode choice. This allows the model to not only realistically reproduce how the current population uses existing transport infrastructure but more importantly provide comprehensive insight into future transport demands. The router of the traffic micro-simulator TRANSIMS is incorporated in the model to inform the actual travel time of each trip and changes of traffic density on the road network. Simulation results show very good agreement with survey data in terms of the distribution of trips done by transport modes and by trip purposes, as well as the traffic density along the main road in the study area

New results from H.E.S.S. observations of galaxy clusters

Clusters of galaxies are believed to contain a significant population of cosmic rays. From the radio and probably hard X-ray bands it is known that clusters are the spatially most extended emitters of non-thermal radiation in the Universe. Due to their content of cosmic rays, galaxy clusters are also potential sources of VHE (>100 GeV) gamma rays. Recently, the massive, nearby cluster Abell 85 has been observed with the H.E.S.S. experiment in VHE gamma rays with a very deep exposure as part of an ongoing campaign. No significant gamma-ray signal has been found at the position of the cluster. The non-detection of this object with H.E.S.S. constrains the total energy of cosmic rays in this system. For a hard spectral index of the cosmic rays of -2.1 and if the cosmic-ray energy density follows the large scale gas density profile, the limit on the fraction of energy in these non-thermal particles with respect to the total thermal energy of the intra-cluster medium is 8% for this particular cluster. This value is at the lower bounds of model predictions.Comment: 4 pages, one figure, invited talk at the 2nd Heidelberg workshop: "High-Energy Gamma-rays and Neutrinos from Extra-Galactic Sources", January 13 - 16, 2009, to be published in Int. J. Mod. Phys.