Faster polynomial multiplication over finite fields

Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the iterated logarithm. This is the first known F\"urer-type complexity bound for F_p[X], and improves on the previously best known bound M_p(n) = O(n log n log log n log p)

Ultimate Compression After Impact Load Prediction in Graphite/Epoxy Coupons Using Neural Network and Multivariate Statistical Analyses

The goal of this research was to accurately predict the ultimate compressive load of impact damaged graphite/epoxy coupons using a Kohonen self-organizing map (SOM) neural network and multivariate statistical regression analysis (MSRA). An optimized use of these data treatment tools allowed the generation of a simple, physically understandable equation that predicts the ultimate failure load of an impacted damaged coupon based uniquely on the acoustic emissions it emits at low proof loads. Acoustic emission (AE) data were collected using two 150 kHz resonant transducers which detected and recorded the AE activity given off during compression to failure of thirty-four impacted 24-ply bidirectional woven cloth laminate graphite/epoxy coupons. The AE quantification parameters duration, energy and amplitude for each AE hit were input to the Kohonen self-organizing map (SOM) neural network to accurately classify the material failure mechanisms present in the low proof load data. The number of failure mechanisms from the first 30% of the loading for twenty-four coupons were used to generate a linear prediction equation which yielded a worst case ultimate load prediction error of 16.17%, just outside of the ±15% B-basis allowables, which was the goal for this research. Particular emphasis was placed upon the noise removal process which was largely responsible for the accuracy of the results

Fast Polynomial Multiplication over F_(2^60)

Can post-Schönhage–Strassen multiplication algorithms be competitive in practice for large input sizes? So far, the GMP library still outperforms all implementations of the recent, asymptotically more efficient algorithms for integer multiplication by Fürer, De–Kurur–Saha–Saptharishi, and ourselves. 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 finite fields of characteristic two. Our Mathemagix implementation is based on the automatic generation of assembly codelets. It outperforms existing implementations in large degree, especially for polynomial matrix multiplication over finite fields

Even faster integer multiplication

We give a new proof of F\"urer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike F\"urer, our method does not require constructing special coefficient rings with "fast" roots of unity. Moreover, we prove the more explicit bound O(n log n K^(log^* n))$ with K = 8. We show that an optimised variant of F\"urer's algorithm achieves only K = 16, suggesting that the new algorithm is faster than F\"urer's by a factor of 2^(log^* n). Assuming standard conjectures about the distribution of Mersenne primes, we give yet another algorithm that achieves K = 4

Physiological requirements in triathlon

This article aims to present the current knowledge on physiological requirements in Olympic distance and Ironman triathlon. Showing the data available from a “traditional point of view” (aerobic power, anaerobic threshold, heart rate, running economy) and from a “contemporary” point of view (V̇ O2 kinetics), it emphasises where we are currently and the areas that remain unknown

Experimental and modeling investigations of adsorption-induced swelling and damage in microporous materials

International audienceThe purpose of this work is to achieve a better understanding of the coupling between adsorption and swelling in microporous materials. This is typically of utmost importance in the enhancement of non-conventional reservoirs or in the valorization of CO 2 geological storage. We consider here the case of fully saturated porous solids with pores down to the nanometer size (≤ 2nm). Hardened cement paste, tight rocks, activated carbon or coal are among those materials. Experimentally, different authors tried to combine gas adsorption results and volumetric swelling data, especially for bituminous coal. However, most results in the literature are not complete in a sense that the adsorption experiments and the swelling experiments were not performed on the exact same coal sample. Other authors present simultaneous in-situ adsorption and swelling results but the volumetric strain is extrapolated from a local measurement on the surface sample or by monitoring the two-dimensional silhouette expansion. Only elastic and reversible swellings are reported in the literature. Theoretically, most continuum approaches to swelling upon adsorption of gas rely on a coupling between the adsorption isotherms and the mechanical deformation. A new poromechanical framework has been recently proposed to express the swelling increment as a function of the increment of bulk pressure with constant porosity. However, this framework has to be extended to take into account the porosity evolution upon swelling. This paper aims at presenting a new experimental setup where both adsorption and strain are measured in-situ and simultaneously and where the full-field swelling is monitored by digital image correlation. Permanent strain and damage are observed. On the other hand, we present an extended poromechanical framework where the porosity is variable upon swelling. A new incremental nonlinear scheme is proposed where the poromechanical properties are updated at each incremental pressure step, depending on the porosity changes. Interactions between swelling and the adsorption isotherms are examined and a correction to the classical Gibbs formalism is proposed. Predicted swellings are compared with results from the literature