Repetition rate multiplication by phase-only filtering with multi-cavity optical structures

We propose several all-pass spectrally-periodic optical structures composed of simple optical cavities for the implementation of repetition rate multipliers of periodic pulse train with uniform output train envelope by phase-only filtering, and analyze them in terms of robustness and accuracy.

Genetic algorithms for discovery of matrix multiplication methods

We present a parallel genetic algorithm for nding matrix multiplication algo-rithms. For 3 x 3 matrices our genetic algorithm successfully discovered algo-rithms requiring 23 multiplications, which are equivalent to the currently best known human-developed algorithms. We also studied the cases with less mul-tiplications and evaluated the suitability of the methods discovered. Although our evolutionary method did not reach the theoretical lower bound it led to an approximate solution for 22 multiplications.

All-pass optical structures for repetition rate multiplication

We propose and analyze several simple all-pass spectrally-periodic optical structures, in terms of accuracy and robustness, for the implementation of repetition rate multipliers of periodic pulse train with uniform output train envelope, finding optimum solutions for multiplication factors of 3, 4, 6, and 12.

On Quasi-Normality of Two-Sided Multiplication

2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.

Le rôle de l'histoire des mathématiques dans la compréhension de l'algorithme usuel de la multiplication au 3e cycle du primaire

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Rôle de la protéine virale Vpu dans le cycle de multiplication du virus de l'immunodéficience humaine de type 1 (VIH-1)

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Le rôle de l'histoire des mathématiques dans la compréhension de l'algorithme usuel de la multiplication au 3e cycle du primaire

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Rôle de la protéine virale Vpu dans le cycle de multiplication du virus de l'immunodéficience humaine de type 1 (VIH-1)

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Enabling efficient publicly verifiable outsourcing computation for matrix multiplication

Outsourcing heavy computational tasks to remote cloud server, which accordingly significantly reduce the computational burden at the end hosts, represents an effective and practical approach towards extensive and scalable mobile applications and has drawn increasing attention in recent years. However, due to the limited processing power of the end hosts yet the keen privacy concerns on the outsourced data, it is vital to ensure both the efficiency and security of the outsourcing computation in the cloud computing. In this paper, we address the issue by developing a publicly verifiable outsourcing computation proposal. In particular, considering a large amount of applications of matrix multiplication in large datasets and image processing, we propose a publicly verifiable outsourcing computation scheme for matrix multiplication in the amortized model. Security analysis demonstrates that the proposed scheme is provable secure by blinding input and output in a simple way. By comparing the developed scheme with existing proposals, we show that our proposal is more efficient in terms of functionality, as well as the computation, communication and storage overhead.

In vitro seed germination and multiplication of Calophyllum brasiliense.

Calophyllum brasiliense é uma espécie arbórea com sistema de propagação natural limitada. A germinação in vitro pode ser uma alternativa para obtenção de plântulas de qualidade. Sementes foram mantidas em água antes da desinfestação e comparadas com sementes controle (não imersas), sem diferença entre os tratamentos. HgCl2 usado durante a desinfestação reduziu a contaminação das culturas. A contaminação fúngica foi reduzida com fungicida adicionado ao meio (23 para 6,4%), mas a porcentagem de bactérias foi aumentada (24 para 36%). Em outro experimento, as sementes foram imersas em plant preservative mixture (PPM?) antes da desinfestação. Combinando a imersão por 48 h e 2 mL L-1 no meio de cultura, a contaminação foi de 6%. A imersão das sementes em GA3 antes da desinfestação reduziu a formação de raízes conforme a concentração foi aumentada. A germinação e o IVG foram reduzidos, respectivamente, de 72% e 0,129 (24 h) para 60% e 0,092 (48 h), de acordo com o tempo de exposição a GA3. Após 90 dias em meio de multiplicação contendo benzilaminopurina, o número médio de brotações por segmento nodal foi 3,4. A germinação in vitro de C. brasiliense é viável em meio WPM sem sacarose, com até 93,3% de sobrevivência.

Twisted Edwards curves revisited

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use . It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to . This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

Jacobi quartic curves revisited

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

Faster group operations on elliptic curves

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 12M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA). Keywords: Efficient elliptic curve arithmetic,unified addition, side channel attack.