A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

Empirical mode decomposition: a novel technique for the study of tremor time series

Tremor is a clinical feature characterized by oscillations of a part of the body. The detection and study of tremor is an important step in investigations seeking to explain underlying control strategies of the central nervous system under natural (or physiological) and pathological conditions. It is well established that tremorous activity is composed of deterministic and stochastic components. For this reason, the use of digital signal processing techniques (DSP) which take into account the nonlinearity and nonstationarity of such signals may bring new information into the signal analysis which is often obscured by traditional linear techniques (e.g. Fourier analysis). In this context, this paper introduces the application of the empirical mode decomposition (EMD) and Hilbert spectrum (HS), which are relatively new DSP techniques for the analysis of nonlinear and nonstationary time-series, for the study of tremor. Our results, obtained from the analysis of experimental signals collected from 31 patients with different neurological conditions, showed that the EMD could automatically decompose acquired signals into basic components, called intrinsic mode functions (IMFs), representing tremorous and voluntary activity. The identification of a physical meaning for IMFs in the context of tremor analysis suggests an alternative and new way of detecting tremorous activity. These results may be relevant for those applications requiring automatic detection of tremor. Furthermore, the energy of IMFs was visualized as a function of time and frequency by means of the HS. This analysis showed that the variation of energy of tremorous and voluntary activity could be distinguished and characterized on the HS. Such results may be relevant for those applications aiming to identify neurological disorders. In general, both the HS and EMD demonstrated to be very useful to perform objective analysis of any kind of tremor and can therefore be potentially used to perform functional assessment.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

A new RBF neural network with boundary value constraints

We present a novel topology of the radial basis function (RBF) neural network, referred to as the boundary value constraints (BVC)-RBF, which is able to automatically satisfy a set of BVC. Unlike most existing neural networks whereby the model is identified via learning from observational data only, the proposed BVC-RBF offers a generic framework by taking into account both the deterministic prior knowledge and the stochastic data in an intelligent manner. Like a conventional RBF, the proposed BVC-RBF has a linear-in-the-parameter structure, such that it is advantageous that many of the existing algorithms for linear-in-the-parameters models are directly applicable. The BVC satisfaction properties of the proposed BVC-RBF are discussed. Finally, numerical examples based on the combined D-optimality-based orthogonal least squares algorithm are utilized to illustrate the performance of the proposed BVC-RBF for completeness.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.

Space partitioning for scalable K-means

K-Means is a popular clustering algorithm which adopts an iterative refinement procedure to determine data partitions and to compute their associated centres of mass, called centroids. The straightforward implementation of the algorithm is often referred to as `brute force' since it computes a proximity measure from each data point to each centroid at every iteration of the K-Means process. Efficient implementations of the K-Means algorithm have been predominantly based on multi-dimensional binary search trees (KD-Trees). A combination of an efficient data structure and geometrical constraints allow to reduce the number of distance computations required at each iteration. In this work we present a general space partitioning approach for improving the efficiency and the scalability of the K-Means algorithm. We propose to adopt approximate hierarchical clustering methods to generate binary space partitioning trees in contrast to KD-Trees. In the experimental analysis, we have tested the performance of the proposed Binary Space Partitioning K-Means (BSP-KM) when a divisive clustering algorithm is used. We have carried out extensive experimental tests to compare the proposed approach to the one based on KD-Trees (KD-KM) in a wide range of the parameters space. BSP-KM is more scalable than KDKM, while keeping the deterministic nature of the `brute force' algorithm. In particular, the proposed space partitioning approach has shown to overcome the well-known limitation of KD-Trees in high-dimensional spaces and can also be adopted to improve the efficiency of other algorithms in which KD-Trees have been used.

Modelling the propagation of terahertz radiation through a tissue simulating phantom

Terahertz (THz) frequency radiation, 0.1 THz to 20 THz, is being investigated for biomedical imaging applications following the introduction of pulsed THz sources that produce picosecond pulses and function at room temperature. Owing to the broadband nature of the radiation, spectral and temporal information is available from radiation that has interacted with a sample; this information is exploited in the development of biomedical imaging tools and sensors. In this work, models to aid interpretation of broadband THz spectra were developed and evaluated. THz radiation lies on the boundary between regions best considered using a deterministic electromagnetic approach and those better analysed using a stochastic approach incorporating quantum mechanical effects, so two computational models to simulate the propagation of THz radiation in an absorbing medium were compared. The first was a thin film analysis and the second a stochastic Monte Carlo model. The Cole–Cole model was used to predict the variation with frequency of the physical properties of the sample and scattering was neglected. The two models were compared with measurements from a highly absorbing water-based phantom. The Monte Carlo model gave a prediction closer to experiment over 0.1 to 3 THz. Knowledge of the frequency-dependent physical properties, including the scattering characteristics, of the absorbing media is necessary. The thin film model is computationally simple to implement but is restricted by the geometry of the sample it can describe. The Monte Carlo framework, despite being initially more complex, provides greater flexibility to investigate more complicated sample geometries.

Identification and minimization of IIR tap coefficients for the cancellation of complex multipath in terrestrial television

By using a deterministic approach, an exact form for the synchronous detected video signal under a ghosted condition is presented. Information regarding the phase quadrature-induced ghost component derived from the quadrature forming nature of the vestigial sideband (VSB) filter is obtained by crosscorrelating the detected video with the ghost cancel reference (GCR) signal. As a result, the minimum number of taps required to correctly remove all the ghost components is subsequently presented. The results are applied to both National Television System Committee (NTSC) and phase alternate line (PAL) television.

On-line handwritten segmentation in linear drawings

This paper addresses the problem of tracking line segments corresponding to on-line handwritten obtained through a digitizer tablet. The approach is based on Kalman filtering to model linear portions of on-line handwritten, particularly, handwritten numerals, and to detect abrupt changes in handwritten direction underlying a model change. This approach uses a Kalman filter framework constrained by a normalized line equation, where quadratic terms are linearized through a first-order Taylor expansion. The modeling is then carried out under the assumption that the state is deterministic and time-invariant, while the detection relies on double thresholding mechanism which tests for a violation of this assumption. The first threshold is based on an approach of layout kinetics. The second one takes into account the jump in angle between the past observed direction of layout and its current direction. The method proposed enables real-time processing. To illustrate the methodology proposed, some results obtained from handwritten numerals are presented.

A specific pole placement technique to minimise hardware requirements within a real time terrestrial and cable video echo canceller

The real time hardware architecture of a deterministic video echo canceller (deghoster) system is presented. The deghoster is capable of calculating all the multipath channel distortion characteristics from terrestrial and cable television in one single pass while performing real time video in-line ghost cancellation. The results from the actual system are also presented in this paper.

The findings from a single pass deghoster prototype for terrestrial transmitted video

A deterministic prototype video deghoster is presented which is capable of calculating all the multipath channel distortion characteristics in one single pass and subsequently removing the multipath distortions, commonly termed ghosts. Within the system, a channel identification algorithm finds in isolation all the ghost components while a dedicated DSP filter subsystem is capable of removing ghosts in real time. The results from the system are presented.

A new method for multipath channel characterisation for terrestrial transmitted video

Under the multipath conditions of terrestrial television transmission, ghost carriers cause additive information to be generated by the VSB filter within the television receiver. By analysis of this a priori effect of the VSB filter under a ghosted condition the inphase and phase quadrature detected video signals are defined. Derived from these results, a new algorithm based upon correlation techniques is presented which finds the characteristics of the amplitude and delay of individual ghosts. These characteristics are then passed to a deterministic deghoster to minimise ghost effects.

Robot free will

We introduce the perspex machine which unifies projective geometry and Turing computation and results in a supra-Turing machine. We show two ways in which the perspex machine unifies symbolic and non-symbolic AI. Firstly, we describe concrete geometrical models that map perspexes onto neural networks, some of which perform only symbolic operations. Secondly, we describe an abstract continuum of perspex logics that includes both symbolic logics and a new class of continuous logics. We argue that an axiom in symbolic logic can be the conclusion of a perspex theorem. That is, the atoms of symbolic logic can be the conclusions of sub-atomic theorems. We argue that perspex space can be mapped onto the spacetime of the universe we inhabit. This allows us to discuss how a robot might be conscious, feel, and have free will in a deterministic, or semi-deterministic, universe. We ground the reality of our universe in existence. On a theistic point, we argue that preordination and free will are compatible. On a theological point, we argue that it is not heretical for us to give robots free will. Finally, we give a pragmatic warning as to the double-edged risks of creating robots that do, or alternatively do not, have free will.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.