An O(M(n) log n) algorithm for the Jacobi symbol

The best known algorithm to compute the Jacobi symbol of two n-bit integers runs in time O(M(n) log n), using Sch\"onhage's fast continued fraction algorithm combined with an identity due to Gauss. We give a different O(M(n) log n) algorithm based on the binary recursive gcd algorithm of Stehl\'e and Zimmermann. Our implementation - which to our knowledge is the first to run in time O(M(n) log n) - is faster than GMP's quadratic implementation for inputs larger than about 10000 decimal digits.Comment: Submitted to ANTS IX (Nancy, July 2010

Is 0716+714 a superluminal blazar?

We present an analysis of new and old high frequency VLBI data collected during the last 10 years at 5--22 GHz. For the jet components in the mas-VLBI jet, two component identifications are possible. One of them with quasi-stationary components oscillating about their mean positions. Another identification scheme, which formally gives the better expansion fit, yields motion with $\sim 9$ $c$ for $H_0=65$ km s$^{-1}$ Mpc$^{-1}$ and $q_0=0.5$. This model would be in better agreement with the observed rapid IDV and the expected high Lorentz-factor, deduced from IDV.Comment: 2 pages, 3 figures, appears in: Proceedings of the 6th European VLBI Network Symposium held on June 25th-28th in Bonn, Germany. Edited by: E. Ros, R.W. Porcas, A.P. Lobanov, and J.A. Zensu

Similarity Measure Development for Case-Based Reasoning- A Data-driven Approach

In this paper, we demonstrate a data-driven methodology for modelling the local similarity measures of various attributes in a dataset. We analyse the spread in the numerical attributes and estimate their distribution using polynomial function to showcase an approach for deriving strong initial value ranges of numerical attributes and use a non-overlapping distribution for categorical attributes such that the entire similarity range [0,1] is utilized. We use an open source dataset for demonstrating modelling and development of the similarity measures and will present a case-based reasoning (CBR) system that can be used to search for the most relevant similar cases

Analysis of severe atmospheric disturbances from airline flight records

Advanced methods were developed to determine time varying winds and turbulence from digital flight data recorders carried aboard modern airliners. Analysis of several cases involving severe clear air turbulence encounters at cruise altitudes has shown that the aircraft encountered vortex arrays generated by destabilized wind shear layers above mountains or thunderstorms. A model was developed to identify the strength, size, and spacing of vortex arrays. This model is used to study the effects of severe wind hazards on operational safety for different types of aircraft. The study demonstrates that small remotely piloted vehicles and executive aircraft exhibit more violent behavior than do large airliners during encounters with high-altitude vortices. Analysis of digital flight data from the accident at Dallas/Ft. Worth in 1985 indicates that the aircraft encountered a microburst with rapidly changing winds embedded in a strong outflow near the ground. A multiple-vortex-ring model was developed to represent the microburst wind pattern. This model can be used in flight simulators to better understand the control problems in severe microburst encounters

Reliable solid-state circuits Semiannual report no. 2, Jun. 1 - Nov. 30, 1965

Pulse width modulator and other microminiaturized electronic equipment for space age application

Analyzing and Predicting Verification of Data-Aware Process Models – a Case Study with Spectrum Auctions

Verification techniques play an essential role in detecting undesirable behaviors in many applications like spectrum auctions. By verifying an auction design, one can detect the least favorable outcomes, e.g., the lowest revenue of an auctioneer. However, verification may be infeasible in practice, given the vast size of the state space on the one hand and the large number of properties to be verified on the other hand. To overcome this challenge, we leverage machine-learning techniques. In particular, we create a dataset by verifying properties of a spectrum auction first. Second, we use this dataset to analyze and predict outcomes of the auction and characteristics of the verification procedure. To evaluate the usefulness of machine learning in the given scenario, we consider prediction quality and feature importance. In our experiments, we observe that prediction models can capture relationships in our dataset well, though one needs to be careful to obtain a representative and sufficiently large training dataset. While the focus of this article is on a specific verification scenario, our analysis approach is general and can be adapted to other domains

There are No Unfilled Shells in Hartree-Fock Theory

Hartree-Fock theory is supposed to yield a picture of atomic shells which may or may not be filled according to the atom's position in the periodic table. We prove that shells are always completely filled in an exact Hartree-Fock calculation. Our theorem generalizes to any system having a two-body interaction that, like the Coulomb potential, is repulsive.Comment: 5 pages, VBEHLMLJPS--16/July/9

Partially gapped fermions in 2D

We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.Comment: v1: 36 pages, 10 figures, v2: minor corrections; equation references to arXiv:0903.0055 updated

Spectral Properties of the Core and the VLBI-Jets of Cygnus A

We present a detailed VLBI study of the spectral properties of the inner core region of the radio galaxy Cygnus A at 5 GHz, 15 GHz, 22 GHz, 43 GHz and 86 GHz. Our observations include an epoch using phase-referencing at 15 GHz and 22 GHz and the first successful VLBI observations of Cygnus A at 86 GHz. We find a pronounced two-sided jet structure, with a steep spectrum along the jet and an inverted spectrum towards the counter-jet. The inverted spectrum and the frequency-dependent jet-to-counter-jet ratio suggest that the inner counter-jet is covered by a circum-nuclear absorber as it is proposed by the unified scheme.Comment: 2 pages, 2 figures, Proceedings of the 7th EVN Symposium held in Toledo, Spain in October 2004, needs evn2004.cl

TSAFE Interface Control Document v 2.0

This document specifies the data interface for TSAFE, the Tactical Separation-Assured Flight Environment. TSAFE is a research prototype of a software application program for alerting air traffic controllers to imminent conflicts in enroute airspace. It is intended for Air Route Traffic Control Centers ("Centers") in the U.S. National Airspace System. It predicts trajectories for approximately 3 minutes into the future, searches for conflicts, and sends data about predicted conflicts to the client, which uses the data to alert an air traffic controller of conflicts. TSAFE itself does not provide a graphical user interface