Search results for " Matrix"
showing 10 items of 2053 documents
Non-linear Invertible Representation for Joint Statistical and Perceptual Feature Decorrelation
2000
The aim of many image mappings is representing the signal in a basis of decorrelated features. Two fundamental aspects must be taken into account in the basis selection problem: data distribution and the qualitative meaning of the underlying space. The classical PCA techniques reduce the statistical correlation using the data distribution. However, in applications where human vision has to be taken into account, there are perceptual factors that make the feature space uneven, and additional interaction among the dimensions may arise. In this work a common framework is presented to analyse the perceptual and statistical interactions among the coefficients of any representation. Using a recen…
Image Recognition through Incremental Discriminative Common Vectors
2010
An incremental approach to the discriminative common vector (DCV) method for image recognition is presented. Two different but equivalent ways of computing both common vectors and corresponding subspace projections have been considered in the particular context in which new training data becomes available and learned subspaces may need continuous updating. The two algorithms are based on either scatter matrix eigendecomposition or difference subspace orthonormalization as with the original DCV method. The proposed incremental methods keep the same good properties than the original one but with a dramatic decrease in computational burden when used in this kind of dynamic scenario. Extensive …
Reconfigurable photonic routers based on multimode interference couplers
2015
We present a design approach for compact reconfigurable light routers with N access waveguides (WGs) based on multimode interference (MMI) couplers. The proposed devices comprise two MMI couplers, which are employed as power splitters and combiners, respectively, linked by an array of N single-mode WGs. When the effective refractive index of the WGs is modulated with the proper relative optical phase difference, the light can switch paths between the preset output channel and the remaining output WGs. Taking advantage of the transfer phases between the access ports of the MMI couplers, we derive very simple phase relations between the modulated WGs that enable the reconfiguration of the out…
Listwise Recommendation Approach with Non-negative Matrix Factorization
2018
Matrix factorization (MF) is one of the most effective categories of recommendation algorithms, which makes predictions based on the user-item rating matrix. Nowadays many studies reveal that the ultimate goal of recommendations is to predict correct rankings of these unrated items. However, most of the pioneering efforts on ranking-oriented MF predict users’ item ranking based on the original rating matrix, which fails to explicitly present users’ preference ranking on items and thus might result in some accuracy loss. In this paper, we formulate a novel listwise user-ranking probability prediction problem for recommendations, that aims to utilize a user-ranking probability matrix to predi…
Numerical experiments with a parallel fast direct elliptic solver on Cray T3E
1997
A parallel fast direct O(N log N) solver is shortly described for linear systems with separable block tridiagonal matrices. A good parallel scalability of the proposed method is demonstrated on a Cray T3E parallel computer using MPI in communication. Also, the sequential performance is compared with the well-known BLKTRI-implementation of the generalized. cyclic reduction method using a single processor of Cray T3E.
Parallelization strategies for density matrix renormalization group algorithms on shared-memory systems
2003
Shared-memory parallelization (SMP) strategies for density matrix renormalization group (DMRG) algorithms enable the treatment of complex systems in solid state physics. We present two different approaches by which parallelization of the standard DMRG algorithm can be accomplished in an efficient way. The methods are illustrated with DMRG calculations of the two-dimensional Hubbard model and the one-dimensional Holstein-Hubbard model on contemporary SMP architectures. The parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential DMRG calculations.
Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices
2008
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static …
Supersolid-superfluid phase separation in the extended Bose-Hubbard model
2021
Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitatio…
Uniform analytic description of dephasing effects in two-state transitions
2007
We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, …
Exact Numerical Treatment of Finite Quantum Systems Using Leading-Edge Supercomputers
2005
Using exact diagonalization and density matrix renormalization group techniques a finite-size scaling study in the context of the Peierls-insulator Mott-insulator transition is presented. Program implementation on modern supercomputers and performance aspects are discussed.