On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem.

A Radial Basis Function Approach to Financial Time Series Analysis

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Characteristics of elution profile in radial chromatography under linear conditions

Based on the mass balance equations of solute transfer in the radial chromatographic column, the theoretical expression to describe the column efficiency and shape of elution profile is obtained under linear isotherm case. Moreover, the tendency for the variation of column efficiency and symmetry of peak profile is systematically discussed. The results showed that in radial chromatography the relationship between the column efficiency and volumetric flow rate is similar with that relationship in axial chromatography; relatively high column efficiency still can be obtained under high flow rate in radial chromatography. Accompanying the increase of retention factor of solutes and injection time, the column efficiency decreases monotonously. The effect of column diameter and column length on the column efficiency interfere with each other. It is more advantageous to increase the column efficiency by applying columns with larger column diameter and shorter column length. According to the discussion of the effect of diffusion on the column efficiency, radial chromatography is proved to be suitable for the separation of samples with relatively high diffusion coefficient, which predicts its obvious advantage in the preparative separation of samples such as proteins and DNA.

Undrained behaviour of two silica sands and practical implications for modelling SSI in liquefiable soils.

The aim of the present study is twofold. Firstly, the paper investigates the undrained cyclic and post-cyclic behaviour of two silica sands by means of multi-stage cyclic triaxial tests. Secondly, based on the post-cyclic response observed in the element test, the authors formulate a simplified stress–strain relationship that can be conveniently used for the construction of p–y curves for liquefiable soils. The multi-stage loading condition consists of an initial cyclic loading applied to cause liquefaction, followed by undrained monotonic loading that aimed to investigate the post-cyclic response of the liquefied sample. It was found that due to the tendency of the liquefied soil to dilate upon undrained shearing, the post-liquefaction strain–stress response was characterised by a distinct strain–hardening behaviour. The latter is idealized by means of a bi-linear stress–strain model, which can be conveniently formulated in terms of three parameters, i.e.: (i) take-off shear strain, γto, i.e. shear strain required to mobilize 1 kPa of shear strength; (b) initial secant shear modulus, G1, defined as 1/γto; (c) post-liquefied shear modulus at large strain, G2 (γ⪢γto). Based on the experimental results, it is concluded that these parameters are strongly influenced by the initial relative density of the sample, whereby γto decreases with increasing relative density. Differently both shear moduli (G1 and G2) increases with increasing relative density. Lastly, the construction of new p–y curves for liquefiable soils based on the idealized bi-linear model is described.

Influence of fat percentage, front thigh skinfold and girth on the maximum radial displacement of the dominant rectus femoris

4.171 JCR (2013) Q1, 6/81 Sport sciences

Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks

Q. Meng and M. H Lee, Automated cross-modal mapping in robotic eye/hand systems using plastic radial basis function networks, Connection Science, 19(1), pp 25-52, 2007.

Error-driven active learning in growing radial basis function networks for early robot learning

Q. Meng and M.H. Lee, 'Error-driven active learning in growing radial basis function networks for early robot learning', 2006 IEEE International Conference on Robotics and Automation (IEEE ICRA 2006), 2984-90, Orlando, Florida, USA.

A Direct Algorithm for the Type Interference in the Rank 2 Fragment of the Second--Order λ-Calculus

We study the problem of type inference for a family of polymorphic type disciplines containing the power of Core-ML. This family comprises all levels of the stratification of the second-order lambda-calculus by "rank" of types. We show that typability is an undecidable problem at every rank k ≥ 3 of this stratification. While it was already known that typability is decidable at rank ≤ 2, no direct and easy-to-implement algorithm was available. To design such an algorithm, we develop a new notion of reduction and show how to use it to reduce the problem of typability at rank 2 to the problem of acyclic semi-unification. A by-product of our analysis is the publication of a simple solution procedure for acyclic semi-unification.

Fabrication, characterisation and electroanalysis at 1-dimensional nanostructures

Integrated nanowire electrodes that permit direct, sensitive and rapid electrochemical based detection of chemical and biological species are a powerful emerging class of sensor devices. As critical dimensions of the electrodes enter the nanoscale, radial analyte diffusion profiles to the electrode dominate with a corresponding enhancement in mass transport, steady-state sigmoidal voltammograms, low depletion of target molecules and faster analysis. To optimise these sensors it is necessary to fully understand the factors that influence performance limits including: electrode geometry, electrode dimensions, electrode separation distances (within nanowire arrays) and diffusional mass transport. Therefore, in this thesis, theoretical simulations of analyte diffusion occurring at a variety of electrode designs were undertaken using Comsol Multiphysics®. Sensor devices were fabricated and corresponding experiments were performed to challenge simulation results. Two approaches for the fabrication and integration of metal nanowire electrodes are presented: Template Electrodeposition and Electron-Beam Lithography. These approaches allow for the fabrication of nanowires which may be subsequently integrated at silicon chip substrates to form fully functional electrochemical devices. Simulated and experimental results were found to be in excellent agreement validating the simulation model. The electrochemical characteristics exhibited by nanowire electrodes fabricated by electronbeam lithography were directly compared against electrochemical performance of a commercial ultra-microdisc electrode. Steady-state cyclic voltammograms in ferrocenemonocarboxylic acid at single ultra-microdisc electrodes were observed at low to medium scan rates (≤ 500 mV.s-1). At nanowires, steady-state responses were observed at ultra-high scan rates (up to 50,000 mV.s-1), thus allowing for much faster analysis (20 ms). Approaches for elucidating faradaic signal without the requirement for background subtraction were also developed. Furthermore, diffusional process occurring at arrays with increasing inter-electrode distance and increasing number of nanowires were explored. Diffusion profiles existing at nanowire arrays were simulated with Comsol Multiphysics®. A range of scan rates were modelled, and experiments were undertaken at 5,000 mV.s-1 since this allows rapid data capture required for, e.g., biomedical, environmental and pharmaceutical diagnostic applications.

A binding site for the cyclic adenosine 3',5'-monophosphate-response element-binding protein as a regulatory element in the grp78 promoter.

The 78-kDa glucose-regulated protein (GRP78) is ubiquitously expressed in many cell types. Its promoter contains multiple protein-binding sites and functional elements. In this study we examined a high affinity protein-binding site spanning bp -198 to -180 of the rat grp78 promoter, using nuclear extracts from both B-lymphoid and HeLa cells. This region contains a sequence TGACGTGA which, with the exception of one base, is identical to the cAMP-response element (CRE). Site-directed mutagenesis reveals that this sequence functions as a major basal level regulatory element in hamster fibroblast cells and is also necessary to maintain high promoter activity under stress-induced conditions. By gel mobility shift analysis, we detect two specific protein complexes. The major specific complex I, while immunologically distinct from the 42-kDa CRE-binding protein (CREB), binds most strongly to the grp site, but also exhibits affinity for the CRE consensus sequence. As such, complex I may consist of other members of the CREB/activating transcription factor protein family. The minor specific complex II consists of CREB or a protein antigenically related to it. A nonspecific complex III consists of the Ku autoantigen, an abundant 70- to 80-kDa protein complex in HeLa nuclear extracts. By cotransfection experiments, we demonstrate that in F9 teratocarcinoma cells, the grp78 promoter can be transactivated by the phosphorylated CREB or when the CREB-transfected cells are treated with the calcium ionophore A23187. The differential regulation of the grp78 gene by cAMP in specific cell types and tissues is discussed.

Harmonic source wavefront aberration correction for ultrasound imaging.

A method is proposed which uses a lower-frequency transmit to create a known harmonic acoustical source in tissue suitable for wavefront correction without a priori assumptions of the target or requiring a transponder. The measurement and imaging steps of this method were implemented on the Duke phased array system with a two-dimensional (2-D) array. The method was tested with multiple electronic aberrators [0.39π to 1.16π radians root-mean-square (rms) at 4.17 MHz] and with a physical aberrator 0.17π radians rms at 4.17 MHz) in a variety of imaging situations. Corrections were quantified in terms of peak beam amplitude compared to the unaberrated case, with restoration between 0.6 and 36.6 dB of peak amplitude with a single correction. Standard phantom images before and after correction were obtained and showed both visible improvement and 14 dB contrast improvement after correction. This method, when combined with previous phase correction methods, may be an important step that leads to improved clinical images.