Based on the ray transformation matrix formalism, we propose a simple method for generation of paraxial beams performing anisotropic rotation in the phase space during their propagation through isotropic optical systems. The widely discussed spiral beams are the particular case of these beams. The propagation of these beams through the symmetric fractional Fourier transformer is demonstrated by...

An algorithm for making consistent 2-D to 3-D geometric inference in polyhedral world using one perspective line drawing is described. Hypotheses are made on the internal angles of visible faces. The normals to the face planes are then determined. Valid normals lead to the reconstruction of the 3-D polyhedral world up to a scale factor. The performance of the algorithm is verified by using cova...

Traditional temporal relations propagating is based on Allen’ s Interval Algebra. This paper proposes an alternative method to propagate temporal relations among intervals, in which 5£ 5 matrices are used to represent temporal relations of intervals. Hence, the propagation of temporal relations is transformed into a numerical computation. For ef® ciency, we use the special values of the thirtee...

In a recent letter [Hegewisch and Tomsovic, Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as...

Considerable disparity exists between the current state of the art for categorical spatial data error modeling and the current state of the practice for reporting categorical data quality. On one hand, the general Monte Carlo simulation-based error propagation framework is a fixture in spatial data error handling; researchers have identified potentially powerful approaches to characterizing cat...

Update propagation is a technique for the weakly consistent replication of a database. Operations are performed at the local copy of the database, then are asynchronously propagated to the replicas. In large scale applications where the weak consistency can be tolerated (e.g., network routing tables, bulletin boards etc.), update propagation can give much better performance than conventional da...

6 The convolution layer 13 6.1 What is a convolution? . . . . . . . . . . . . . . . . . . . . . . . . 13 6.2 Why to convolve? . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6.3 Convolution as matrix product . . . . . . . . . . . . . . . . . . . 18 6.4 The Kronecker product . . . . . . . . . . . . . . . . . . . . . . . 20 6.5 Backward propagation: update the parameters . . . . . . . . ...

INTRODUCTION The diffusion tensor is a 3x3 positive definite matrix and, therefore, possesses several distinct matrix decompositions, e.g. the Cholesky, and the Eigenvalue decompositions. To date, the Eigenvalue decomposition has been used only in computing tensor-derived quantities [1-4] but not as a parametrization (or equivalently, a representation) in DTI error propagation [5]. Treating a m...

In machine learning problems, labeled data are often in short supply. One of the feasible solution for this problem is transfer learning. It can make use of the labeled data from other domain to discriminate those unlabeled data in the target domain. In this paper, we propose a transfer learning framework based on similarity matrix approximation to tackle such problems. Two practical algorithms...