Finding the point on Bezier Curves with the normal vector passing an external point

Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.

Asynchronous distributed parallelization of mobile network optimization algorithms

It has been years since the introduction of the Dynamic Network Optimization (DNO) concept, yet the DNO development is still at its infant stage, largely due to a lack of breakthrough in minimizing the lengthy optimization runtime. Our previous work, a distributed parallel solution, has achieved a significant speed gain. To cater for the increased optimization complexity pressed by the uptake of smartphones and tablets, however, this paper examines the potential areas for further improvement and presents a novel asynchronous distributed parallel design that minimizes the inter-process communications. The new approach is implemented and applied to real-life projects whose results demonstrate an augmented acceleration of 7.5 times on a 16-core distributed system compared to 6.1 of our previous solution. Moreover, there is no degradation in the optimization outcome. This is a solid sprint towards the realization of DNO.

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.

Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.

Fusion of motion segmentation algorithms

Many algorithms have been developed to achieve motion segmentation for video surveillance. The algorithms produce varying performances under the infinite amount of changing conditions. It has been recognised that individually these algorithms have useful properties. Fusing the statistical result of these algorithms is investigated, with robust motion segmentation in mind.

A customizable multi-agent system for distributed data mining

We present a general Multi-Agent System framework for distributed data mining based on a Peer-to-Peer model. Agent protocols are implemented through message-based asynchronous communication. The framework adopts a dynamic load balancing policy that is particularly suitable for irregular search algorithms. A modular design allows a separation of the general-purpose system protocols and software components from the specific data mining algorithm. The experimental evaluation has been carried out on a parallel frequent subgraph mining algorithm, which has shown good scalability performances.

Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Generic systolic array for genetic algorithms

The authors present a systolic design for a simple GA mechanism which provides high throughput and unidirectional pipelining by exploiting the inherent parallelism in the genetic operators. The design computes in O(N+G) time steps using O(N2) cells where N is the population size and G is the chromosome length. The area of the device is independent of the chromosome length and so can be easily scaled by replicating the arrays or by employing fine-grain migration. The array is generic in the sense that it does not rely on the fitness function and can be used as an accelerator for any GA application using uniform crossover between pairs of chromosomes. The design can also be used in hybrid systems as an add-on to complement existing designs and methods for fitness function acceleration and island-style population management