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Fast Polynomial Multiplication over F260

David Harvey, Joris van der Hoeven, Grégoire Lecerf
2016 Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16  
In this paper, we show how central ideas of our recent asymptotically fast algorithms turn out to be of practical interest for multiplication of polynomials over nite fields of characteristic two.  ...  It outperforms existing implementations in large degree, especially for polynomial matrix multiplication over nite elds.  ...  OTHER GROUND FIELDS Usually, fast polynomial multiplication over F 2 is used as the basic building block for other fast polynomial arithmetic over nite elds in characteristic two.  ... 
doi:10.1145/2930889.2930920 dblp:conf/issac/HarveyHL16 fatcat:3uwa3q4i3rgljmwplbfl43plji

The Emirates Exploration Imager (EXI) Instrument on the Emirates Mars Mission (EMM) Hope Mission

A. R. Jones, M. Wolff, M. Alshamsi, M. Osterloo, P. Bay, N. Brennan, K. Bryant, Z. Castleman, A. Curtin, E. DeVito, V. A. Drake, D. Ebuen (+27 others)
2021 Space Science Reviews  
By combining multiple observations within an orbit with planetary rotation, EXI is able to provide diurnal sampling over most of the planet on the scale of 10 days.  ...  Similarly, during the Martian capture orbit, EXI will make measurements of the Martian disk near perigee, when the disk will over-fill the detectors, and the S/C is moving fast.  ...  Both stars were observed with all 6 filters in multiple locations on the detector on multiple dates for a total of 134 and 53 images of αLyr and ηUMa (respectively).  ... 
doi:10.1007/s11214-021-00852-5 fatcat:cpyn2bbvarbj5en3ttlc4w34eu

On Exact Polya and Putinar's Representations [article]

Victor Magron, Mohab Safey El Din
2018 arXiv   pre-print
Next, we apply this algorithm to compute exact Polya and Putinar's representations respectively for positive definite forms and positive polynomials over basic compact semi-algebraic sets.  ...  We prove that bit complexity estimates on output size and runtime are both polynomial in the degree of the input polynomial and simply exponential in the number of variables.  ...  A positive definite form f ∈ R[X] is a homogeneous polynomial which is positive over Sn−1 .  ... 
arXiv:1802.10339v1 fatcat:vjokpnlsujhpjnp3dxkuxidqva

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

Y. Salathé, M. Mondal, M. Oppliger, J. Heinsoo, P. Kurpiers, A. Potočnik, A. Mezzacapo, U. Las Heras, L. Lamata, E. Solano, S. Filipp, A. Wallraff
2015 Physical Review X  
This approach is universal and efficient, employing only resources which are polynomial in the number of spins and indicates a path towards the controlled simulation of general spin dynamics in superconducting  ...  First steps in these directions have been taken by realizing and working with devices combining multiple qubits with multiple resonators [52] [53] [54] [55] .  ...  This design flexibility, in combination with fast gate operations [39] , fast initialization [40, 41] , and high-fidelity readout based on quantum-limited amplifiers [42, 43] , sets the circuit QED  ... 
doi:10.1103/physrevx.5.021027 fatcat:rbym4ps3djf7njvmvaygksn5em

Image feature subsets for predicting the quality of consumer camera images and identifying quality dimensions

Mikko Nuutinen, Toni Virtanen, Pirkko Oittinen
2014 Journal of Electronic Imaging (JEI)  
The computed values are fitted to a third-degree polynomial. Feature F7 is the second parameter of that polynomial, feature F8 is the third, and feature F9 is the fourth.  ...  However, NR measures tend to perform poorly in the case of images with multiple distortion sources.  ... 
doi:10.1117/1.jei.23.6.061111 fatcat:4wovprnv7ze6hj6nrc5k5dqube

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

Yves Salathé, Mintu Mondal, Markus Oppliger, Johannes Heinsoo, Philipp Kurpiers, Anton Potočnik, Antonio Mezzacapo, Urtzi Las Heras, Lucas Lamata, Enrique Solano, S. Filipp, Andreas Wallraff
2015
First steps in these directions have been taken by realizing and working with devices combining multiple qubits with multiple resonators [52] [53] [54] [55] .  ...  This design flexibility, in combination with fast gate operations [39] , fast initialization [40, 41] , and high-fidelity readout based on quantum-limited amplifiers [42, 43] , sets the circuit QED  ... 
doi:10.3929/ethz-b-000102098 fatcat:mnmqmmy7wvg3tibxohenowqnhu