We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coecient rings with fast roots of unity. Moreover, we prove the more explicit bound O(n logn K log n) with K = 8. We show that an optimised variant of Fürer's algorithm achieves only K = 16, suggesting that the new algorithm ...

In this paper, we propose a watermarking technique based on Haar Discrete Wavelet Transform-Discrete Cosine Transform (HDWT-DCT) by using matrixbased Two-dimensional Linear Discriminant Analysis (2DLDA) for color images. By embedding the reference watermark and using matrix-based 2DLDA scheme, we do not need all the embedded information of watermark and apply only part of matrix-based samples f...

The form factor of the unitary group U(N) endowed with the Haar measure characterizes the correlations within the spectrum of a typical unitary matrix. It can be decomposed into a sum over pairs of ‘periodic orbits’, where by periodic orbit we understand any sequence of matrix indices. From here the diagonal approximation can be defined in the usual fashion as a sum only over pairs of identical...

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators wh...

Abstract. We study random vectors of the form (Tr(AV ), . . . ,Tr(AV )), where V is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the A are deterministic parameter matrices. We show that for increasing matrix sizes these random vectors converge to a joint Gaussian limit, and compute its covariances. This generalizes previous work of Diaconis et ...

Haar transform is known to have the smallest computational requirement and has been used mainly for pattern recognition and image processing. Although the properties of Haar spectra of Boolean functions have considerable interest and attraction, the majority of publications to date have employed the Walsh rather than Haar transform in their considerations. It is mainly due to the fact that up t...

Methods based on hypothesis tests (HTs) in the Haar domain are widely used to denoise Poisson count data. Facing large datasets or real-time applications, Haar-based denoisers have to use the decimated transform to meet limited-memory or computation-time constraints. Unfortunately, for regular underlying intensities, decimation yields discontinuous estimates and strong "staircase" artifacts. In...

the euclidean group (rn,+) where (n?n, plays a key role in harmonic analysis. if we consider the lebesgue measure ()nd?xr as the haar measure of this group then 12(2)()nd?x=d?rr. in this article we look for lca groups k, whose haar measures have a similar property. in fact we will show that for some lca groups k with the haar measure k?, there exists a constant such that 0kc>()(2)kkk?a=c?a for ...

We investigate the statistical properties of $C=uvu^{-1}v^{-1}$, when $u$ and $v$ are independent random matrices, uniformly distributed with respect to Haar measure groups $U(N)$ $O(N)$. An exact formula is derived for average value power sum symmetric functions $C$, also products matrix elements similar Weingarten functions. The density eigenvalues $C$ shown become constant in large-$N$ limit...

Methods based on hypothesis tests (HTs) in the Haar domain are widely used to denoise Poisson count data. However, facing large datasets or real-time applications, Haar-based denoisers have to use the decimated transform to meet limited-memory or computation-time constraints. Unfortunately, for regular underlying intensities, decimation yields discontinuous estimates and strong “staircase” arti...