Application of a new discreet form of Gauss’ theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss’ theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference ± one standard deviation were 1.2 ± 2.3, 5.5 ± 4.7, 3.0 ± 3.2 and −1.2 ± 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

The Past is the Past? The Impossibility of Erasure of Historical LGBTIQ Policing

This paper considers the impossibility of erasing historical policing of LGBTIQ people. Significant events of LGBTIQ policing may appear to fade into the past and we perhaps assume they literally disappear – not discussed, not thought about, and erased from cultural memory. At times we see evidence of an almost nostalgic contemplation about LGBTIQ policing of the past embedded in the notion that we have moved beyond that point to the future, never to return to those histories. If we draw on the work of Foucault, an impossibility becomes apparent. Foucault suggests that discursive traces circulate in discourse and they emerge and re-emerge to shape future discourses. This paper ruminates on a case example, particularly the policing of the Gay and Lesbian Mardi Gras in Sydney, Australia, in 2013. We argue this case demonstrates Foucault’s understanding of discursive history in action: it shows how the remnant traces of historical LGBTIQ policing can re-emerge to profoundly shape LGBTIQ-police relations in the present. In addition to the case, we draw on qualitative data showing how ideas about historical LGBTIQ policing are rehearsed in a consistent cycle of iteration and reiteration through the musings of research participants across three different projects on LGBTIQ policing. We conclude therefore that LGBTIQ policing in the past may never be erased because moments reminiscent of historical LGBTIQ policing are always already circulating and undermining the governmental work of policing organisations in the present.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Shakedown stress analysis of insulated rail joint (IRJ)

A finite element numerical simulation is carried out to examine stress distributions on railhead in the cicinity of the endpost of an insulated rail joint. The contact patch and pressure distribution are considered using modified Hertzian simulation. A combined elasto-plastic material modelling available in Abaqus is employed in the simulation. A dynamic load factor of 1.21 is considered in modelling for the wheel load based on a previous study as part of this on going research. Shakedown theorem is employed in this study. A peak pressure load which is above the shakedown limit is determined as input load. As a result, a progressive damage in the railhead has been captured as depicted in the equivalent plastic strain plot.

(Dia)logics of difference : disability, performance & spectatorship

In this paper I examine the way artists with disabilities use performances in public spaces to encourage people to reflect on their own contribution to the construction of publics, or counter-publics, during and after the moment of encounter. I focus on Liz Crow’s Resistance on the Plinth. This is the title Crow gave her performance on the Forth Plinth in Trafalgar Square as part of Antony Gormley’s One and Other project in 2009. Described as a public art project presenting a portrait of the U.K., Gormley’s One and Other gave 2400 people selected at random via a lottery the chance to do whatever they chose for an hour on the vacant Forth Plinth in Trafalgar Square. In her hour, Crow chose to present herself in a Nazi uniform, in her wheelchair. In this paper, I discuss how Crow’s performance used a counterposition of images – the Nazi uniform, associated with eugenics and a desire to eliminate people who do not accord with the Arayan ‘norm’, counterposed with her wheelchair – to encourage passersby to “stop, look, think.” I examine how Crow used this counterposition to prevent passersby from attributing a single, stable, monologic meaning to the image – forestalling the risk that passersby would read the image as a Nazi on the Plinth – and instead draw passersby into a dialogue in which the impossibility of reconciling the contradictory images, ideologies and cultural logics Crow embodied encouraged people to continue thinking and talking about these cultural logics during and after the encounter.

Re-framing fashion : from original and copy to adaptation

This article discusses the interaction between original and adaptation in the fashion system; the study also analyses, at a micro level, practices of adaptation adopted by consumers when making and re-making fashionable clothes. The article shows that the distinction between original and copy is historically determined as it grew out of the romantic notion of the authentic work of art. This article suggests that, in the impossibility to determine copyright in fashion, adaptation is a better descriptor of practices that transform garments; the concept of adaptation also abolishes trite notions of fashion as pastiche or bricolage, arguing for as a way to look at the many variations and re-contextualisations of garments historically and cross-culturally.

A kiss is just...

This paper proposes that a survey of representations of men not-kissing men in recent television drama series makes clear a particularly hysterical fascination. While the Australian program GP has managed to produce a banal representation of two men kissing, American equivalents have resorted to a series of strategies which make insistently clear that not only can men not kiss-but that the act of not-kissing must be repeatedly displayed. By refusing to have lovers kiss; by having lovers kiss but refusing to show the act; by having gay lovers, but having one played by a woman; by having men kiss but rendering the act ridiculous; in these ways, American television programs make clear the importance of this act by consistently pointing towards it and declaring its impossibility. This paper calls for the justice of equal access to public images of kissing.

Elasto-plastic stress analysis of an insulated rail joint (IRJ) with a loading below shakedown limit

A finite element numerical simulation is carried out to examine stress distributions on railhead in the vicinity of the endpost of a insulated rail joint. The contact patch and pressure distribution are considered using modified Hertzian formulation. A combined elasto-plastic material modelling available in Abaqus is employed in the simulation. A dynamic load factor of 1.21 is considered in modelling for the wheel load based on a previous study as part of this on going research. Shakedown theorem is employed in this study. A peak pressure load which is above the shakedown limit is determined as input load. As a result, a progressive damage in the railhead has been captured as depicted in the equivalent plastic strain plot.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin