Rademacher and Gaussian complexities: Risk bounds and structural results

We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.

Vector quantization based Gaussian modeling for speaker verification

Gaussian mixture models (GMMs) have become an established means of modeling feature distributions in speaker recognition systems. It is useful for experimentation and practical implementation purposes to develop and test these models in an efficient manner particularly when computational resources are limited. A method of combining vector quantization (VQ) with single multi-dimensional Gaussians is proposed to rapidly generate a robust model approximation to the Gaussian mixture model. A fast method of testing these systems is also proposed and implemented. Results on the NIST 1996 Speaker Recognition Database suggest comparable and in some cases an improved verification performance to the traditional GMM based analysis scheme. In addition, previous research for the task of speaker identification indicated a similar system perfomance between the VQ Gaussian based technique and GMMs

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Gaussian process models for sensor-centric robot localisation

This paper presents an approach to building an observation likelihood function from a set of sparse, noisy training observations taken from known locations by a sensor with no obvious geometric model. The basic approach is to fit an interpolant to the training data, representing the expected observation, and to assume additive sensor noise. This paper takes a Bayesian view of the problem, maintaining a posterior over interpolants rather than simply the maximum-likelihood interpolant, giving a measure of uncertainty in the map at any point. This is done using a Gaussian process framework. To validate the approach experimentally, a model of an environment is built using observations from an omni-directional camera. After a model has been built from the training data, a particle filter is used to localise while traversing this environment

PySSM : a Python module for Bayesian inference of linear Gaussian state space models

PySSM is a Python package that has been developed for the analysis of time series using linear Gaussian state space models (SSM). PySSM is easy to use; models can be set up quickly and efficiently and a variety of different settings are available to the user. It also takes advantage of scientific libraries Numpy and Scipy and other high level features of the Python language. PySSM is also used as a platform for interfacing between optimised and parallelised Fortran routines. These Fortran routines heavily utilise Basic Linear Algebra (BLAS) and Linear Algebra Package (LAPACK) functions for maximum performance. PySSM contains classes for filtering, classical smoothing as well as simulation smoothing.

Probability analysis of machine angle stability with non-gaussian wind power input

The security of power transfer across a given transmission link is typically a steady state assessment. This paper develops tools to assess machine angle stability as affected by a combination of faults and uncertainty of wind power using probability analysis. The paper elaborates on the development of the theoretical assessment tool and demonstrates its efficacy using single machine infinite bus system.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

Pharmacokinetic studies of a Chinese triple herbal drug formula

Yin Chen Hao Tang preparation (YCHTP) is a classic traditional Chinese medicine formula, which is commonly used for clinical treatment of hepatological diseases. In this study, a rapid and validated high-performance liquid chromatography (HPLC) method was developed to simultaneously identify 6,7-dimethylesculetin and geniposide in rat plasma. This assay was performed on a Dikma Diamonsil RP(18) column (200 mmx4.6 mm, 5 mum) with acetonitrile-methanol-water (0.1% formic acid) as the mobile phase, showing acceptable linearity, intra- and inter-day precision and accuracy (R.S.D.=5%), and absolute recovery for two analytes (74%); the limits of quantitation were 0.4 and 1.12 mug/ml, and the limits of detection were 0.06 and 0.09 mug/ml for two analytes. The developed method was successfully applied to study the effect of formula compatibility on the pharmacokinetics of 6,7-dimethylesculetin and geniposide in YCHTP when orally administrating an effective human daily dose of YCHTP to rats. We surmise that formula compatibility can significantly influence the pharmacokinetics of YCHTP, and we have elucidated and validated the compatible administration of YCHTP.

Pharmacokinetics-based elucidation on disparity in clinical effectiveness between varieties of Zhi Zhu Wan, a traditional Chinese medical formula

AIM: Zhi Zhu Wan (ZZW) is a classical Chinese medical formulation used for the treatment of functional dyspepsia that attributed to Spleen-deficiency Syndrome. ZZW contains Atractylodes Rhizome and Fructus Citrus Immaturus, the later originates from both Citrus aurantium L. (BZZW) and Citrus sinensis Osbeck (RZZW). The present study is designed to elucidate disparities in the clinical efficacy of two ZZW varieties based on the pharmacokinetics of naringenin and hesperetin. MEHTOD: After oral administration of ZZWs, blood sample was collected from healthy volunteers at designed time points. Naringenin and hesperetin were detected in plasma by RP-HPLC, pharmacokinetic parameters were processed using mode-independent methods with WINNONLIN. RESULTS: After oral administration of BZZW, both naringenin and hesperetin were detected in plasma, and demonstrated similar pharmacokinetic parameters. Ka was 0.384+/-0.165 and 0.401+/-0.159, T(1/2(ke))(h) was 5.491+/-3.926 and 5.824+/-3.067, the AUC (mg/Lh) was 34.886+/-22.199 and 39.407+/-19.535 for naringenin and hesperetin, respectively. However, in the case of RZZW, only hesperetin was found in plasma, but the pharmacokinetic properties for hesperetin in RZZW was different from that in BZZW. T(max) for hesperetin in RZZW is about 8.515h, and its C(max) is much larger than that of BZZW. Moreover, it was eliminated slowly as it possessed a much larger AUC value. CONCLUSION: The distinct therapeutic orientations of the Chinese medical formula ZZWs with different Fructus Citrus Immaturus could be elucidated based on the pharmacokinetic parameters of constituents after oral administration.

Improved ultra-performance liquid chromatography with electrospray ionization quadrupole-time-of-flight high-definition mass spectrometry method for the rapid analysis of the chemical constituents of a typical medical formula: Liuwei Dihuang Wan

Liuwei Dihuang Wan (LWD), a classic Chinese medicinal formulae, has been used to improve or restore declined functions related to aging and geriatric diseases, such as impaired mobility, vision, hearing, cognition and memory. It has attracted increasingly much attention as one of the most popular and valuable herbal medicines. However, the systematic analysis of the chemical constituents of LDW is difficult and thus has not been well established. In this paper, a rapid, sensitive and reliable ultra-performance liquid chromatography with electrospray ionization quadrupole time-of-flight high-definition mass spectrometry (UPLC-ESI-Q-TOF-MS) method with automated MetaboLynx analysis in positive and negative ion mode was established to characterize the chemical constituents of LDW. The analysis was performed on a Waters UPLCTM HSS T3 using a gradient elution system. MS/MS fragmentation behavior was proposed for aiding the structural identification of the components. Under the optimized conditions, a total of 50 peaks were tentatively characterized by comparing the retention time and MS data. It is concluded that a rapid and robust platform based on UPLC-ESI-Q-TOF-MS has been successfully developed for globally identifying multiple-constituents of traditional Chinese medicine prescriptions. This is the first report on systematic analysis of the chemical constituents of LDW. This article is protected by copyright. All rights reserved.

Laser-radar data fusion with Gaussian Process Implicit Surfaces

This work considers the problem of building high-fidelity 3D representations of the environment from sensor data acquired by mobile robots. Multi-sensor data fusion allows for more complete and accurate representations, and for more reliable perception, especially when different sensing modalities are used. In this paper, we propose a thorough experimental analysis of the performance of 3D surface reconstruction from laser and mm-wave radar data using Gaussian Process Implicit Surfaces (GPIS), in a realistic field robotics scenario. We first analyse the performance of GPIS using raw laser data alone and raw radar data alone, respectively, with different choices of covariance matrices and different resolutions of the input data. We then evaluate and compare the performance of two different GPIS fusion approaches. The first, state-of-the-art approach directly fuses raw data from laser and radar. The alternative approach proposed in this paper first computes an initial estimate of the surface from each single source of data, and then fuses these two estimates. We show that this method outperforms the state of the art, especially in situations where the sensors react differently to the targets they perceive.

Traversability estimation for a planetary rover via experimental kernel learning in a Gaussian process framework

A critical requirement for safe autonomous navigation of a planetary rover is the ability to accurately estimate the traversability of the terrain. This work considers the problem of predicting the attitude and configuration angles of the platform from terrain representations that are often incomplete due to occlusions and sensor limitations. Using Gaussian Processes (GP) and exteroceptive data as training input, we can provide a continuous and complete representation of terrain traversability, with uncertainty in the output estimates. In this paper, we propose a novel method that focuses on exploiting the explicit correlation in vehicle attitude and configuration during operation by learning a kernel function from vehicle experience to perform GP regression. We provide an extensive experimental validation of the proposed method on a planetary rover. We show significant improvement in the accuracy of our estimation compared with results obtained using standard kernels (Squared Exponential and Neural Network), and compared to traversability estimation made over terrain models built using state-of-the-art GP techniques.