Using Canonical Forms for Isomorphism Reduction in Graph-based Model Checking

Graph isomorphism checking can be used in graph-based model checking to achieve symmetry reduction. Instead of one-to-one comparing the graph representations of states, canonical forms of state graphs can be computed. These canonical forms can be used to store and compare states. However, computing a canonical form for a graph is computationally expensive. Whether computing a canonical representation for states and reducing the state space is more efficient than using canonical hashcodes for states and comparing states one-to-one is not a priori clear. In this paper these approaches to isomorphism reduction are described and a preliminary comparison is presented for checking isomorphism of pairs of graphs. An existing algorithm that does not compute a canonical form performs better that tools that do for graphs that are used in graph-based model checking. Computing canonical forms seems to scale better for larger graphs

Development of an amperometric biosensor for the detection of alcohol: a thesis presented in partial fulfilment of the requirements for the degree of Masters in Science in Biochemistry at Massey University

The aim of the following work was to design a biosensor for the detection of ethanol. A biosensor is an analytical device in which a biological sensing element is connected to or integrated with a physical transducing element. Amperometric enzyme biosensors utilise one or more enzymes to convert a substance which cannot be measured electrochemically to one which can be. In the case of an alcohol biosensor one of two enzymes (alcohol dehydrogenase and alcohol oxidase) can be used to convert electrochemically stable alcohol to either hydrogen peroxide or NADH which can be oxidised. In the design of an alcohol biosensor there are three major variables to consider, these are; enzyme type, electrode material, and immobilisation technique. The goal was to select optimum conditions for the formulation of the desired sensor. In the present work the electrode materials used were platinum, carbon (foil and paste) and the conducting organic salt N-methyl phenazinium.Tetracyanoquinodimethane (NMP.TCNQ). The immobilisation techniques used were; adsorption, cross-linking to a protein matrix and covalent binding. Of the biosensors produced from a selected combination or these variables each was tested by one or more of the following; cyclic voltammetry, enzyme assay, and amperometry. The most promising approach appears to be that of conjugating enzyme to haemin and allowing the conjugate to bind irreversibly to platinum via the haemin group. An electrode made with the organic salt NMP.TCNQ looked promising also but because the salt is readily oxidised it is unstable and therefore not an ideal electrode material

Investigating the memory requirements for publish/subscribe filtering algorithms

Various filtering algorithms for publish/subscribe systems have been proposed. One distinguishing characteristic is their internal representation of Boolean subscriptions: They either require conversions to disjunctive normal forms (canonical approaches) or are directly exploited in event filtering (non-canonical approaches). In this paper, we present a detailed analysis and comparison of the memory requirements of canonical and non-canonical filtering algorithms. This includes a theoretical analysis of space usages as well as a verification of our theoretical results by an evaluation of a practical implementation. This practical analysis also considers time (filter) efficiency, which is the other important quality measure of filtering algorithms. By correlating the results of space and time efficiency, we conclude when to use non-canonical and canonical approaches

NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions

This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky & Chudnovsky. In some cases, our descriptions contain improvements over existing algorithms. We also provide references to relevant ideas not currently used in NumGfun

Converting between quadrilateral and standard solution sets in normal surface theory

The enumeration of normal surfaces is a crucial but very slow operation in algorithmic 3-manifold topology. At the heart of this operation is a polytope vertex enumeration in a high-dimensional space (standard coordinates). Tollefson's Q-theory speeds up this operation by using a much smaller space (quadrilateral coordinates), at the cost of a reduced solution set that might not always be sufficient for our needs. In this paper we present algorithms for converting between solution sets in quadrilateral and standard coordinates. As a consequence we obtain a new algorithm for enumerating all standard vertex normal surfaces, yielding both the speed of quadrilateral coordinates and the wider applicability of standard coordinates. Experimentation with the software package Regina shows this new algorithm to be extremely fast in practice, improving speed for large cases by factors from thousands up to millions.Comment: 55 pages, 10 figures; v2: minor fixes only, plus a reformat for the journal styl

Resonant Absorption as Mode Conversion?

Resonant absorption and mode conversion are both extensively studied mechanisms for wave "absorption" in solar magnetohydrodynamics (MHD). But are they really distinct? We re-examine a well-known simple resonant absorption model in a cold MHD plasma that places the resonance inside an evanescent region. The normal mode solutions display the standard singular resonant features. However, these same normal modes may be used to construct a ray bundle which very clearly undergoes mode conversion to an Alfv\'en wave with no singularities. We therefore conclude that resonant absorption and mode conversion are in fact the same thing, at least for this model problem. The prime distinguishing characteristic that determines which of the two descriptions is most natural in a given circumstance is whether the converted wave can provide a net escape of energy from the conversion/absorption region of physical space. If it cannot, it is forced to run away in wavenumber space instead, thereby generating the arbitrarily small scales in situ that we recognize as fundamental to resonant absorption and phase mixing. On the other hand, if the converted wave takes net energy way, singularities do not develop, though phase mixing may still develop with distance as the wave recedes.Comment: 23 pages, 8 figures, 2 tables; accepted by Solar Phys (July 9 2010

Slow Learners are Fast

Online learning algorithms have impressive convergence properties when it comes to risk minimization and convex games on very large problems. However, they are inherently sequential in their design which prevents them from taking advantage of modern multi-core architectures. In this paper we prove that online learning with delayed updates converges well, thereby facilitating parallel online learning.Comment: Extended version of conference paper - NIPS 200