Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions

Microscopic models of classical degrees of freedom coupled to non-interacting fermions occur in many different contexts. Prominent examples from solid state physics are descriptions of colossal magnetoresistance manganites and diluted magnetic semiconductors, or auxiliary field methods for correlated electron systems. Monte Carlo simulations are vital for an understanding of such systems, but notorious for requiring the solution of the fermion problem with each change in the classical field configuration. We present an efficient, truncation-free O(N) method on the basis of Chebyshev expanded local Green functions, which allows us to simulate systems of unprecedented size N.Comment: 4 pages, 3 figure

Approximation of the scattering amplitude

The simultaneous solution of Ax=b and ATy=g is required in a number of situations. Darmofal and Lu have proposed a method based on the Quasi-Minimal residual algorithm (QMR). We will introduce a technique for the same purpose based on the LSQR method and show how its performance can be improved when using the Generalized LSQR method. We further show how preconditioners can be introduced to enhance the speed of convergence and discuss different preconditioners that can be used. The scattering amplitude gTx, a widely used quantity in signal processing for example, has a close connection to the above problem since x represents the solution of the forward problem and g is the right hand side of the adjoint system. We show how this quantity can be efficiently approximated using Gauss quadrature and introduce a Block-Lanczos process that approximates the scattering amplitude and which can also be used with preconditioners

Quaternion Singular Value Decomposition based on Bidiagonalization to a Real Matrix using Quaternion Householder Transformations

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from the product of the Householder transformations and the real singular vectors of B. We show in the paper that left and right quaternionic Householder transformations are different because of the noncommutative multiplication of quaternions and we present formulae for computing the Householder vector and matrix in each case

Parallel density matrix propagation in spin dynamics simulations

Several methods for density matrix propagation in distributed computing environments, such as clusters and graphics processing units, are proposed and evaluated. It is demonstrated that the large communication overhead associated with each propagation step (two-sided multiplication of the density matrix by an exponential propagator and its conjugate) may be avoided and the simulation recast in a form that requires virtually no inter-thread communication. Good scaling is demonstrated on a 128-core (16 nodes, 8 cores each) cluster.Comment: Submitted for publicatio

Fluctuation-induced interactions between dielectrics in general geometries

We study thermal Casimir and quantum non-retarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant which we discretize and evaluate with the help of Cholesky factorization. The quantum partition function is treated by path integral quantization of a set of interacting dipoles and reduces to a product of determinants. We compare the approximations of pairwise additivity and proximity force with our numerical methods. We propose a ``factorization approximation'' which gives rather good numerical results in the geometries that we study

An Efficient Approximate kNN Graph Method for Diffusion on Image Retrieval

The application of the diffusion in many computer vision and artificial intelligence projects has been shown to give excellent improvements in performance. One of the main bottlenecks of this technique is the quadratic growth of the kNN graph size due to the high-quantity of new connections between nodes in the graph, resulting in long computation times. Several strategies have been proposed to address this, but none are effective and efficient. Our novel technique, based on LSH projections, obtains the same performance as the exact kNN graph after diffusion, but in less time (approximately 18 times faster on a dataset of a hundred thousand images). The proposed method was validated and compared with other state-of-the-art on several public image datasets, including Oxford5k, Paris6k, and Oxford105k

Developments in new aircraft tire tread materials

Comparative laboratory and field tests were conducted on experimental and state-of-the-art aircraft tire tread materials in a program aimed at seeking new elastomeric materials which would provide improved aircraft tire tread wear, traction, and blowout resistance in the interests of operational safety and economy. The experimental stock was formulated of natural rubber and amorphous vinyl polybutadiene to provide high thermal-oxidative resistance, a characteristic pursued on the premise that thermal oxidation is involved both in the normal abrasion or wear of tire treads and probably in the chain of events leading to blowout failures. Results from the tests demonstrate that the experimental stock provided better heat buildup (hysteresis) and fatigue properties, at least equal wet and dry traction, and greater wear resistance than the state-of-the-art stock

Separable states can be used to distribute entanglement

We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.Comment: 4 pages, 2 figures. Slight modification

Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets