Modelling legacy telecommunications switching systems for interaction analysis

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Properties of the Lindemann Mechanism in Phase Space

We study the planar and scalar reductions of the nonlinear Lindemann mechanism of unimolecular decay. First, we establish that the origin, a degenerate critical point, is globally asymptotically stable. Second, we prove there is a unique scalar solution (the slow manifold) between the horizontal and vertical isoclines. Third, we determine the concavity of all scalar solutions in the nonnegative quadrant. Fourth, we establish that each scalar solution is a centre manifold at the origin given by a Taylor series. Moreover, we develop the leading-order behaviour of all planar solutions as time tends to infinity. Finally, we determine the asymptotic behaviour of the slow manifold at infinity by showing that it is a unique centre manifold for a fixed point at infinity.Comment: 27 pages, 6 figure

Analysis of Superoscillatory Wave Functions

Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory functions was presented and it was shown that superoscillatory quantum mechanical wave functions should exhibit a number of counter-intuitive physical effects. Following up on this work, we here present more general methods which allow the calculation of superoscillatory wave functions with custom-designed physical properties. We give concrete examples and we prove results about the limits to superoscillatory behavior. We also give a simple and intuitive new explanation for the exponential computational cost of superoscillations.Comment: 20 pages, several figure

An adequate logic for full LOTOS

We present a novel result for a logic for symbolic transition systems based on LOTOS processes. The logic is adequate with respect to bisimulation defined on symbolic transition systems

White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.Comment: Accepted for publication in the Astrophysical Journa

Multi-criteria Anomaly Detection using Pareto Depth Analysis

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria using a linear combination of them. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria and is provably better than linear combinations of the criteria.Comment: Removed an unnecessary line from Algorithm