Results 1  10
of
134
SPECTRAL HASH: SHA3 CANDIDATE
"... Abstract. We describe a new family of hash functions using the discrete Fourier transform and a nonlinear transformation constructed via data dependent permutations. DFT is a wellknown cryptographic primitive perfect for generating diffusion and confusion. Due to the usage of the DFT with a nonline ..."
Abstract
 Add to MetaCart
Abstract. We describe a new family of hash functions using the discrete Fourier transform and a nonlinear transformation constructed via data dependent permutations. DFT is a wellknown cryptographic primitive perfect for generating diffusion and confusion. Due to the usage of the DFT with a
An Efficient Hardware Architecture for Spectral Hash Algorithm
"... The Spectral Hash algorithm is one of the Round 1 candidates for the SHA3 family, and is based on spectral arithmetic over a finite field, involving multidimensional discrete Fourier transformations over a finite field, data dependent permutations, Rubictype rotations, and affine and nonlinear fun ..."
Abstract
 Add to MetaCart
The Spectral Hash algorithm is one of the Round 1 candidates for the SHA3 family, and is based on spectral arithmetic over a finite field, involving multidimensional discrete Fourier transformations over a finite field, data dependent permutations, Rubictype rotations, and affine and nonlinear
Fredholm properties of nonlocal differential operators via spectral flow
, 2013
"... We establish Fredholm properties for a class of nonlocal differential operators. Using mild convergence and localization conditions on the nonlocal terms, we also show how to compute Fredholm indices via a generalized spectral flow, using crossing numbers of generalized spatial eigenvalues. We illus ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
We establish Fredholm properties for a class of nonlocal differential operators. Using mild convergence and localization conditions on the nonlocal terms, we also show how to compute Fredholm indices via a generalized spectral flow, using crossing numbers of generalized spatial eigenvalues. We
SPECTRAL CONSERVATION LAWS FOR PERIODIC NONLINEAR EQUATIONS OF THE MELNIKOV TYPE
, 2008
"... In the seminal paper [24] in 1974 S.P. Novikov, in particular, established that the spectral curve of the onedimensional periodic Schrödinger operator H = − d2 + u(x) dx2 is preserved when the realvalued potential u(x,t) evolves via the Korteweg– de Vries (KdV) equation and that for finitezone ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
of the stability zones, i.e., E0,...,E2N, supply the necessary family of first integrals. The article [24] was the starting point for the development of the finite gap integration theory in which the spectral curves play the main role. In this article we consider the deformation of the spectral curve via
/ ON THE ANALYTICITY OF THE SPECTRAL DENSITY FOR SEMICLASSICAL NLS
"... In [KMM], we analyzed the semiclassical behavior of solutions to the focusing, completely integrable nonlinear Schrödinger equation, under the assumption of real analytic initial data (among others). We provided global semiclassical asymptotics under the socalled ”finite gap ” assumption. In a subs ..."
Abstract
 Add to MetaCart
In [KMM], we analyzed the semiclassical behavior of solutions to the focusing, completely integrable nonlinear Schrödinger equation, under the assumption of real analytic initial data (among others). We provided global semiclassical asymptotics under the socalled ”finite gap ” assumption. In a
Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive Lanczos Bisection
, 2008
"... Nearest neighbor graphs are widely used in data mining and machine learning. The bruteforce method to compute the exact kNN graph takes Θ(dn 2) time for n data points in the d dimensional Euclidean space. We propose two divide and conquer methods for computing an approximate kNN graph in Θ(dn t) ti ..."
Abstract

Cited by 28 (4 self)
 Add to MetaCart
) time for high dimensional data (large d). The exponent t depends on an internal parameter and is larger than one. Experiments show that a high quality graph usually requires a small t which is close to one. A few of the practical details of the algorithms are as follows. First, the divide step uses
Algorithm Inventors/Developers:
"... Abstract. We describe a new family of hash functions using the discrete Fourier transform and a nonlinear transformation constructed via data dependent permutations. The discrete Fourier transform is a wellknown cryptographic primitive perfect for generating diffusion and confusion. Due to the usag ..."
Abstract
 Add to MetaCart
Abstract. We describe a new family of hash functions using the discrete Fourier transform and a nonlinear transformation constructed via data dependent permutations. The discrete Fourier transform is a wellknown cryptographic primitive perfect for generating diffusion and confusion. Due
Numerical verification of a gap condition for linearized NLS
, 2008
"... We make a detailed numerical study of the spectrum of two Schrödinger operators L ± arising in the linearization of the supercritical nonlinear Schrödinger equation (NLS) about the standing wave, in three dimensions. This study was motivated by a recent result of the second author on conditional asy ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
asymptotic stability of solitary waves in the case of a cubic nonlinearity. Underlying the validity of this result is a spectral condition on the operators L±, namely that they have no eigenvalues nor resonances in the gap (a region of the positive real axis between zero and the continuous spectrum,) which
Spectral methods for neural characterization using generalized quadratic models
 in Adv in Neural Info Proc Sys 26
, 2013
"... We describe a set of fast, tractable methods for characterizing neural responses to highdimensional sensory stimuli using a model we refer to as the generalized quadratic model (GQM). The GQM consists of a lowrank quadratic function followed by a point nonlinearity and exponentialfamily noise. T ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
] and the elliptical LinearNonlinearPoisson model [3]. Here we show that for “canonical form ” GQMs, spectral decomposition of the first two responseweighted moments yields approximate maximumlikelihood estimators via a quantity called the expected loglikelihood. The resulting theory generalizes moment
Results 1  10
of
134