Converse Bergmann cline in a eucalyptus herbivore, paropsis atomaria olivier (coleoptera: chrysomelidae) : phenotypic plasticity or local adaptation?

Aim To measure latitude-related body size variation in field-collected Paropsis atomaria Olivier (Coleoptera: Chrysomelidae) individuals and to conduct common-garden experiments to determine whether such variation is due to phenotypic plasticity or local adaptation. Location Four collection sites from the east coast of Australia were selected for our present field collections: Canberra (latitude 35°19' S), Bangalow (latitude 28°43' S), Beerburrum (latitude 26°58' S) and Lowmead (latitude 24°29' S). Museum specimens collected over the past 100 years and covering the same geographical area as the present field collections came from one state, one national and one private collection. Methods Body size (pronotum width) was measured for 118 field-collected beetles and 302 specimens from collections. We then reared larvae from the latitudinal extremes (Canberra and Lowmead) to determine whether the size cline was the result of phenotypic plasticity or evolved differences (= local adaptation) between sites. Results Beetles decreased in size with increasing latitude, representing a converse Bergmann cline. A decrease in developmental temperature produced larger adults for both Lowmead (low latitude) and Canberra (high latitude) individuals, and those from Lowmead were larger than those from Canberra when reared under identical conditions. Main conclusions The converse Bergmann cline in P. atomaria is likely to be the result of local adaptation to season length.

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.

Balls up : the converse blank canvas project

Research background: For decades the Chuck Taylor All Star basketball shoe (first designed in 1921 by Converse, an American shoe company), has been an iconic item of fashion apparel, particularly for the youth oriented market - as a form of self expression and identify, adolescents have for generations been customising their Converse sneakers to create innovative and unique footwear. Although originally developed purely for sport, sneakers gradually crossed over into fashion and the majority of athletic shoes are now purchased for street fashion or leisure wear. Artisan Gallery (Brisbane), in conjunction with the exhibition Reboot: Function, Fashion and the Sneaker, a history of the sneaker, selected 20 designers to customise and re-design the classic Converse Chuck Taylor All Stars shoe and in doing so highlighted the diversity of forms possible for creative outcomes. As Artisan Gallery Curator Kirsten Fitzpatrick states “the ‘sports show’, designed to coincide with the Olympics, is also about exploring the sneaker as a platform for creativity... and (one) of the more bazaar creations was Dean Brough's deconstructed shoes to make men’s underwear.” The exhibition ran from 21 June – 16 August 2012: http://artisan-ideaskillproduct.blogspot.com.au/2012/06/converse-blank-canvas-project.html Research question: Even though the sneaker is a fashion item, it still is fundamentally used for foot protection and historically was aligned to ball sports, principally Basketball - as a fashion designers/practitioner how can I connect (in a whimsical manner) this history of usage for ball sports to the sneaker and re-design and re-use all the physical elements of the shoe to produce a unique wearable item of clothing - the selected medium for this challenge and experimentation was the classic archetypal men’s white boxer shorts. Artisan Statement BALLS UP - The Converse Sneaker, it’s almost impossible to imagine a better rounded item to maintain peak performance for all types of ball sports. Gentlemen, your other most precious balls also deserve this level of comfort and support to sustain the hard times – the Converse Boxer, balls up, bats out, get ready to play hard. Research contribution: The project highlighted some of the unique and diverse creative manifestations that are possible from the classic sneaker. From a fashion practitioners’ perspective, the design outcomes (men’s boxer short made from converse sneakers) demonstrated the strong association to iconic fashion apparel, and recognised the connection to wearability and comfort that is requisite in both footwear and men’s underwear. Research significance: The exhibition was viewed by in excess of 1000 people and generated exceptional media coverage and public exposure/impact. As Artisan Gallery Curator Kirsten Fitzpatrick states “20 of Brisbane's best designers were given the opportunity to customise their own Converse Sneakers, with The Converse Blank Canvas Project.” And to be selected in this category demonstrates the calibre of importance for design prominence.

Converse consumption : the converse blank canvas project

Research background For almost 80 years the Chuck Taylor (or Chuck T's) All Star basketball shoe has been an iconic item of fashion apparel. The Chuck T's were first designed in 1921 by Converse, an American shoe company and over the decades they became a popular item not purely for sports and athletic purposes but rather evolved into the shoe of choice for many subcultural groups as a fashion item. In some circles the Chuck Taylor is still seen as the "coolest" sneaker of all time - one which will never go out of fashion regardless of changing trends. With over 600 millions pairs sold all over the world since its release, the Converse shoe is representative of not only a fashion culture - but also of a consumption culture - that evolved as the driving force behind the massive growth of the Western economic system during the 20th Century. Artisan Gallery (Brisbane), in conjunction with the exhibition Reboot: Function, Fashion and the Sneaker, a history of the sneaker, selected 20 designers to customise and re-design the classic Converse Chuck Taylor All Stars shoe and in doing so highlighted the diversity of forms possible for creative outcomes. As Artisan Gallery Curator Kirsten Fitzpatrick states “We were expecting people to draw and paint on them. Instead, we had shoes... mounted as trophies.." referring to the presentation of "Converse Consumption". The exhibition ran from 21 June – 16 August 2012: Research question The Chuck T’s is one of many overwhelmingly commercially successful designs of the last century. Nowadays we are faced with the significant problems of overconsumption and the stress this causes on the natural ecosystem; and on people as a result. As an active member of the industrial design fraternity – a discipline that sits at the core of this problem - how can I use this opportunity to comment on the significant issue of consumption? An effective way to do this was to associate consumption of goods with consumption of sugar. There are significant similarities between our ceaseless desires to consume products and our fervent need to consume indulgent sweet foods. Artisan Statement Delicious, scrumptious, delectable... your pupils dilate, your blood pressure spikes, your liver goes into overdrive. Immediately, your brain cuts off the adenosine receptors, preventing drowsiness. Your body increases dopamine production, in-turn stimulating the pleasure receptors in your brain. Your body absorbs all the sweetness and turns it into fat – while all the nutrients that you actually require are starting to be destroyed, about to be expelled. And this is only after one bite! After some time though, your body comes crashing back to earth. You become irritable and begin to feel sluggish. Your eyelids seem heavy while your breathing pattern changes. Your body has consumed all the energy and destroyed all available nutrients. You literally begin to shut down. These are the physiological effects of sugar consumption. A perfect analogy for our modern day consumer driven world. Enjoy your dessert! Research contribution “Converse Consumption” contributes to the conversation regarding over-consumption by compelling people to reflect on their consumption behaviour through the reconceptualising of the deconstructed Chuck T’s in an attractive edible form. By doing so the viewer has to deal with the desire to consume the indulgent looking dessert with the contradictory fact that it is comprised of a pair of shoes. The fact that the shoes are Chuck T’s make the effect even more powerful due to their iconic status. These clashing motivations are what make “Converse Consumption” a bizarre yet memorable experience. Significance The exhibition was viewed by an excess of 1000 people and generated exceptional media coverage and public exposure/impact. As Artisan Gallery Curator Kirsten Fitzpatrick states “20 of Brisbane's best designers were given the opportunity to customise their own Converse Sneakers, with The Converse Blank Canvas Project.” And to be selected in this category demonstrates the calibre of importance for design prominence.

Stabilization of parametric roll resonance with active u-tanks via Lyapunov control design

Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via simulation on a high-fidelity model of a vessel under parametric roll resonance.

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.

Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound dconverse result for a natural class of extensions of the Wiener attack, which are guaranteed to succeed even when δ > 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

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 validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.