Algebraic properties of generalized Rijndael-like ciphers

We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field \GF (p^k) ($p\geq 2$ a prime number) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen the AES (Rijndael block cipher with specific block sizes) in case AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (2^k) is equal to the alternating group on the state space. In this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (p^k) ($p\geq 2$) is equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0

Elliptic Reciprocity

The paper introduces the notions of an elliptic pair, an elliptic cycle and an elliptic list over a square free positive integer d. These concepts are related to the notions of amicable pairs of primes and aliquot cycles that were introduced by Silverman and Stange. Settling a matter left open by Silverman and Stange it is shown that for d=3 there are elliptic cycles of length 6. For d not equal to 3 the question of the existence of proper elliptic lists of length n over d is reduced to the the theory of prime producing quadratic polynomials. For d=163 a proper elliptic list of length 40 is exhibited. It is shown that for each d there is an upper bound on the length of a proper elliptic list over d. The final section of the paper contains heuristic arguments supporting conjectured asymptotics for the number of elliptic pairs below integer X. Finally, for d congruent to 3 modulo 8 the existence of infinitely many anomalous prime numbers is derived from Bunyakowski's Conjecture for quadratic polynomials.Comment: 17 pages, including one figure and two table

Vibration Modelling and Control Experiments for a Thin-Walled Cylindrical Rotor with Piezo Patch Actuation and Sensing

This paper describes a dynamic model formulation and control experiments concerning the vibration behaviour of a thin-walled cylindrical rotor with internal piezoelectric patch transducers. Model development, validation and controller design procedures were undertaken for an experimental rotordynamic system comprising a tubular steel rotor (length 0.8 m, diameter 0.166 m and wall-thickness 3.06 mm) supported by two radial active magnetic bearings. Analytical solutions for mode shapes and natural frequencies for free vibration were first derived using a shell theory model, and these used to construct a speed-dependent parametric model for the rotor structure, including piezo patch actuators and sensors. The results confirm that the developed shell theory model can accurately capture the rotating frame dynamics and accounts correctly for frequency splitting from Coriolis effects. The model is also shown to be suitable for active controller design and optimization. Model-based H2 feedback control using the rotor-mounted actuators and sensors is shown to achieve vibration suppression of targeted flexural modes, both with and without rotation

Retrieving sea ice drag coefficients and turning angles from in situ and satellite observations using an inverse modeling framework

Author Posting. © American Geophysical Union, 2019. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Oceans 124(8), (2019): 6388-6413, doi: 10.1029/2018JC014881.For ice concentrations less than 85%, internal ice stresses in the sea ice pack are small and sea ice is said to be in free drift. The sea ice drift is then the result of a balance between Coriolis acceleration and stresses from the ocean and atmosphere. We investigate sea ice drift using data from individual drifting buoys as well as Arctic‐wide gridded fields of wind, sea ice, and ocean velocity. We perform probabilistic inverse modeling of the momentum balance of free‐drifting sea ice, implemented to retrieve the Nansen number, scaled Rossby number, and stress turning angles. Since this problem involves a nonlinear, underconstrained system, we used a Monte Carlo guided search scheme—the Neighborhood Algorithm—to seek optimal parameter values for multiple observation points. We retrieve optimal drag coefficients of CA=1.2×10−3 and CO=2.4×10−3 from 10‐day averaged Arctic‐wide data from July 2014 that agree with the AIDJEX standard, with clear temporal and spatial variations. Inverting daily averaged buoy data give parameters that, while more accurately resolved, suggest that the forward model oversimplifies the physical system at these spatial and temporal scales. Our results show the importance of the correct representation of geostrophic currents. Both atmospheric and oceanic drag coefficients are found to decrease with shorter temporal averaging period, informing the selection of drag coefficient for short timescale climate models.The scripts developed for this publication are available at the GitHub (https://github.com/hheorton/Freedrift_inverse_submit). The Neighborhood Algorithm was developed and kindly supplied by M. Sambridge (http://www.iearth.org.au/codes/NA/). Ice‐Tethered Profiler data are available via the Ice‐Tethered Profiler program website (http://whoi.edu/itp). Buoy data were collected as part of the Marginal Ice Zone program (www.apl.washington.edu/miz) funded by the U.S. Office of Naval Research. The ice drift data were kindly supplied by N. Kimura. H. H. was funded by the Natural Environment Research Council (Grants NE/I029439/1 and NE/R000263/1). M. T. was partially funded by the SKIM Mission Science Study (SKIM‐SciSoc) Project ESA RFP 3‐15456/18/NL/CT/gp. T. A. was supported at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. M. T. and H. H. thank Dr. Nicolas Brantut for early discussions on the implementation of inverse modeling techniques.2020-02-1

A Highly Overmoded Structure for Hundred-Kilowatt-Class <italic>Ka</italic>-Band Extended Interaction Klystron

Here, we report on the development of highly overmoded structure for a millimeter-wave (MMW) extended interaction klystron (EIK). To enhance electron beam loading, a new method for designing an oversized beam tunnel in a large cavity by concentrating the axial field is demonstrated. The transmission and oscillation characteristics of the interaction circuit operating in the quasi-TM04 mode are tested by the developed mode conversion circuit. Results suggest that a five-cavity EIK based on this highly overmoded structure can achieve an output power of 289 kW at 32.92 GHz with a saturated gain of 51.6 dB by injecting a 3.3-mm-diameter electron beam with a current of 18 A. The output power exceeds 100 kW at a bandwidth of 100 MHz.</p

Senior Recital: Thomas Kieffer, alto saxophone and Tyler Elvidge, trumpet

This recital is presented in partial fulfillment of requirements for the degrees Bachelor of Music in Music Education. Mr. Kieffer studies saxophone with Sam Skelton. Mr. Elvidge studies trumpet with Douglas Lindsey.https://digitalcommons.kennesaw.edu/musicprograms/1179/thumbnail.jp

Labelling imaging datasets on the basis of neuroradiology reports: a validation study

Natural language processing (NLP) shows promise as a means to automate the labelling of hospital-scale neuroradiology magnetic resonance imaging (MRI) datasets for computer vision applications. To date, however, there has been no thorough investigation into the validity of this approach, including determining the accuracy of report labels compared to image labels as well as examining the performance of non-specialist labellers. In this work, we draw on the experience of a team of neuroradiologists who labelled over 5000 MRI neuroradiology reports as part of a project to build a dedicated deep learning-based neuroradiology report classifier. We show that, in our experience, assigning binary labels (i.e. normal vs abnormal) to images from reports alone is highly accurate. In contrast to the binary labels, however, the accuracy of more granular labelling is dependent on the category, and we highlight reasons for this discrepancy. We also show that downstream model performance is reduced when labelling of training reports is performed by a non-specialist. To allow other researchers to accelerate their research, we make our refined abnormality definitions and labelling rules available, as well as our easy-to-use radiology report labelling app which helps streamline this process