On the Equivalence of Quadratic APN Functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.Comment: 13 p

Non-positivity of Groenewold operators

A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Liouville densities, leading to what may be termed term Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Liouville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.Comment: 9 pages, 1 figures, submitted to Europhysics Letter

Presence and television.

Film and a number of emerging entertainment technologies offer media consumers an illusion of nonmediation known as presence. To investigate the possibility that television can evoke presence, 65 undergraduate students were shown brief examples of rapid point-of-view movement from commercially available videotapes on a television with either a small screen (12 inches [30.5 cm], measured diagonally) or a large screen (46 inches [116.8 cm]). Participants\u27 responses were measured via a questionnaire and a computer-based recording of arousal (electrodermal activity). Viewers of both televisions reported an enjoyable sense of physical movement, excitement, involvement, and a sense of participation. Furthermore, as predicted, participants who watched the large screen television thought the movement in the scenes was faster, experienced a greater sense of physical movement, enjoyed the movement to a greater extent, found the viewing experience more exciting, and were more physiologically aroused. Practical and theoretical implications are discussed

Tina Fuchs Interview 2016

A 2016 interview with Tina Fuchs, the Dean of Students at Western Oregon University. In her interview, she discusses her career and the changes in student diversity and sustainability that she has witnessed over her 27 years at as an administrator at Western Oregon University

Free Dirac evolution as a quantum random walk

Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be approximated arbitrarily closely by a quantum random walk, where the roles of coin and walker systems are naturally attributed to the spin and position degrees of freedom of the particle. Initially entangled and spatially localized spin-position states evolve with asymptotic two-horned distributions of the position probability, familiar from earlier studies of quantum walks. For the Dirac particle, the two horns travel apart at close to the speed of light.Comment: 16 pages, 1 figure. Latex2e fil

The effects of a single whole-body cryotherapy exposure on physiological, performance and perceptual responses of professional academy soccer players following repeated sprint exercise

In professional youth soccer players, the physiological, performance and perceptual effects of a single whole body cryotherapy (WBC) session performed shortly after repeated sprint exercise were investigated. In a randomized, counter-balanced and crossover design, 14 habituated English Premier League academy soccer players performed 15 x 30 m sprints (each followed by a 10 m forced deceleration) on two occasions. Within 20 min of exercise cessation, players entered a WBC chamber (Cryo: 30 s at -60°C, 120 s at -135°C) or remained seated (Con) indoors in temperate conditions (~25°C). Blood and saliva samples, peak power output (countermovement jump) and perceptual indices of recovery and soreness were assessed pre-exercise and immediately, 2 h and 24 h post exercise. When compared to Con, a greater testosterone response was observed at 2 h (+32.5 ± 32.3 pg·ml-1, +21%) and 24 h (+50.4 ± 48.9 pg·ml-1, +28%) post-exercise (both P=0.002) in Cryo (trial x treatment interaction: P=0.001). No between trial differences were observed for other salivary (cortisol and testosterone/cortisol ratio), blood (lactate and Creatine Kinase), performance (peak power output) or perceptual (recovery or soreness) markers (all trial x treatment interactions: P>0.05); all of which were influenced by exercise (time effects: all P<0.05). A single session of WBC performed within 20 min of repeated sprint exercise elevated testosterone concentrations for 24 h but did not affect any other performance, physiological or perceptual measurements taken. While unclear, WBC may be efficacious for professional soccer players during congested fixture periods

On boson algebras as Hopf algebras

Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of generalized Heisenberg algebras including those algebras including those underlying physical models such as that of Calogero-Sutherland, is isomorphic with one of the types of boson algebra proposed, and can be formulated as a Hopf algebra.Comment: LaTex, 18 page

Some Results on the Known Classes of Quadratic APN Functions

In this paper, we determine the Walsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by Gölo\u glu is affine equivalent to Gold functions

ISiS: The Indiana Silicon Sphere

This research was sponsored by the National Science Foundation Grant NSF PHY-931478