QDENSITY—A Mathematica Quantum Computer simulation

This Mathematica 5.2 package¹ is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, Tutorial.nb is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: QFT.nb, Teleportation.nb, Grover.nb and Shor.nb where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of “one way computing” ideas, are included as an additional tool in the notebook Cluster.nb. A Mathematica palette containing most commands in QDENSITY is also included: QDENSpalette.nb.

Program summary

Title of program: QDENSITYCatalogue identifier: ADXH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v1_0Program available from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating systems: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4Programming language used: Mathematica 5.2No. of bytes in distributed program, including test data, etc.: 180 581No. of lines in distributed program, including test data, etc.: 19 382Distribution format: tar.gzMethod of solution: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed.     

A theory of bunches

A bunch is a simple data structure, similar in many respects to a set. However, bunches differ from sets in that the data is not packaged up or encapsulated, and in particular in that a bunch consisting of one element is the same as that element. Bunches are attractive for handling nondeterminacy and underspecification, by which is meant that for any particular input to the program or specification, the associated output is not fully determined. The acceptable outputs for any given input can be described by a bunch. This approach nicely generalises traditional single-output programs and specifications. We present a formal theory of bunches. It includes an axiomatisations of boolean and function types whose behaviour is well-known to be complicated by the presence of nondeterminacy. The axiomatisation of the booleans preserves most of the laws of classical predicate calculus. The axiomatisation of functions accommodates higher-order functions in all their generality, while avoiding the dangers of inconsistency when functions and nondeterminacy intermix. Our theory is presented as a Hilbert-style system of axioms and inference rules for a small specification language. We prove consistency. Received: 23 December 1998 / 2 November 1999     

Bronchoalveolar lavage. Quantitation of intraalveolar fluid?

A precise calculation of the amount of intraalveolar fluid is the basis of a quantitative analysis of intraalveolar compounds. Different approaches have been made to cover this important problem. Here, we report a comparative study with five markers: 99mTc-DTPA, 51Cr-EDTA, inulin, urea, and methylene blue in animal experiments as well as in human experiments. The marker substances were added to the lavage fluid, and the "dilution" of the markers, i.e., the alveolar fluid, was calculated. The results showed that in animals with healthy lungs the tracer methods are able to calculate amounts of intraalveolar fluid that are comparable to morphologic findings. In animals as well as in humans, methylene blue and inulin were shown to be useless in determining alveolar fluid volume compared with the tracer methods. In humans, the calculations with the urea method and with Tc-DTPA were in the same magnitude, but there was no individual correlation. We conclude that, at present, the methods to quantitate alveolar fluid volume lack precision and add nothing to a deeper understanding of alveolar biology.     

Circular cross-polarization measurements on earth-space paths at 11,7 GHz

Rain and icecrystal depolarization measurements were made on earthspace paths at four locations across Canada using the circularlypolarized 11.7 GHz beacon transmission from the cts satellite. Results show that when rain is the dominant depolarization mechanism, crosspolarization discrimination (xpd)is statistically related to copolar attenuation (cpa)according to xpd =U?20 log cpa with U showing improvement with increasing elevation angle. Icecrystal depolarization events, with accompanying differential phase shifts as large as 20°, were also observed. An analysis separating these events from the data demonstrates that at 11.7 GHz icecrystal depolarization degrades xpd statistics by less than 1 dB at the small percentages of time.     

A new algorithm for shortest paths among obstacles in the plane

We introduce a new algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles. In particular, for a given start points, we build a planar subdivision (ashortest path map) that supports efficient queries for shortest paths froms to any destination pointt. The worst-case time complexity of our algorithm isO(kn log² n), wheren is the number of vertices describing the polygonal obstacles, andk is a parameter we call the illumination depth of the obstacle space. Our algorithm usesO(n) space, avoiding the possibly quadratic space complexity of methods that rely on visibility graphs. The quantityk is frequently significantly smaller thann, especially in some of the cases in which the visibility graph has quadratic size. In particular,k is bounded above by the number of different obstacles that touch any shortest path froms.Partially supported by NSF Grants IRI-8710858 and ECSE-8857642 and by a grant from Hughes Research Laboratories, Malibu, CA.     

Ignitable Liquid Classification and Identification Using the Summed-Ion Mass Spectrum

Abstract

The mass spectra calculated by summing the intensities of each nominal mass over all chromatographic times, the summed ion spectra, were calculated for a set of 440 commercially available ignitable liquids that had been analyzed by gas chromatography–mass spectrometry. Each ignitable liquid is generally comprised of a mixture of chemicals, and the mixtures may be very complex in some cases, e.g., petroleum distillates, gasoline, etc. The summed ion spectra were evaluated to determine if they contained sufficient information content to allow their use for rapid and accurate identification of the ignitable liquid in a database or library. The summed ion nominal mass spectra were encoded in one bit per channel at 1% transition intensity and a set of 96,580 unique pairwise comparisons were made between spectra, resulting in an average of approximately 50 differing channels per comparison. A subset of 62 summed ion spectra were further compared by a similarity metric and found by cluster analysis to group closely along the ASTM ignitable liquid classification scheme. Receiver operator characteristic analysis of the use of the similarity index in combination with the summed ion spectra was shown to provide 99% probability of correct liquid identification and 95% probability of correct ASTM classification by primary and sub-class. Interlaboratory tests found 95% probability of correct liquid identification and 85% probability of correct ASTM classification at the primary class level. These results demonstrate the use of the summed ion spectrum as a first step in the rapid identification of an ignitable liquid by database or library searching.     

The use of NDVI and its Derivatives for Monitoring Lake Victoria’s Water Level and Drought Conditions

Normalized Difference Vegetation Index (NDVI), which is a measure of vegetation vigour, and lake water levels respond variably to precipitation and its deficiency. For a given lake catchment, NDVI may have the ability to depict localized natural variability in water levels in response to weather patterns. This information may be used to decipher natural from unnatural variations of a given lake’s surface. This study evaluates the potential of using NDVI and its associated derivatives (VCI (vegetation condition index), SVI (standardised vegetation index), AINDVI (annually integrated NDVI), green vegetation function (F _g ), and NDVIA (NDVI anomaly)) to depict Lake Victoria’s water levels. Thirty years of monthly mean water levels and a portion of the Global Inventory Modelling and Mapping Studies (GIMMS) AVHRR (Advanced Very High Resolution Radiometer) NDVI datasets were used. Their aggregate data structures and temporal co-variabilities were analysed using GIS/spatial analysis tools. Locally, NDVI was found to be more sensitive to drought (i.e., responded more strongly to reduced precipitation) than to water levels. It showed a good ability to depict water levels one-month in advance, especially in moderate to low precipitation years. SVI and SWL (standardized water levels) used in association with AINDVI and AMWLA (annual mean water levels anomaly) readily identified high precipitation years, which are also when NDVI has a low ability to depict water levels. NDVI also appears to be able to highlight unnatural variations in water levels. We propose an iterative approach for the better use of NDVI, which may be useful in developing an early warning mechanisms for the management of lake Victoria and other Lakes with similar characteristics.     

2010 CAV award announcement

The 2010 CAV (Computer-Aided Verification) award was awarded to Kenneth L. McMillan of Cadence Research Laboratories for a series of fundamental contributions resulting in significant advances in scalability of model checking tools. The annual award recognizes a specific fundamental contribution or a series of outstanding contributions to the CAV field.     

Distributed pursuit-evasion without mapping or global localization via local frontiers

This paper addresses a visibility-based pursuit-evasion problem in which a team of mobile robots with limited sensing and communication capabilities must coordinate to detect any evaders in an unknown, multiply-connected planar environment. Our distributed algorithm to guarantee evader detection is built around maintaining complete coverage of the frontier between cleared and contaminated regions while expanding the cleared region. We detail a novel distributed method for storing and updating this frontier without building a map of the environment or requiring global localization. We demonstrate the functionality of the algorithm through simulations in realistic environments and through hardware experiments. We also compare Monte Carlo results for our algorithm to the theoretical optimum area cleared as a function of the number of robots available.