Perspex machine X: software development

The Perspex Machine arose from the unification of computation with geometry. We now report significant redevelopment of both a partial C compiler that generates perspex programs and of a Graphical User Interface (GUI). The compiler is constructed with standard compiler-generator tools and produces both an explicit parse tree for C and an Abstract Syntax Tree (AST) that is better suited to code generation. The GUI uses a hash table and a simpler software architecture to achieve an order of magnitude speed up in processing and, consequently, an order of magnitude increase in the number of perspexes that can be manipulated in real time (now 6,000). Two perspex-machine simulators are provided, one using trans-floating-point arithmetic and the other using transrational arithmetic. All of the software described here is available on the world wide web. The compiler generates code in the neural model of the perspex. At each branch point it uses a jumper to return control to the main fibre. This has the effect of pruning out an exponentially increasing number of branching fibres, thereby greatly increasing the efficiency of perspex programs as measured by the number of neurons required to implement an algorithm. The jumpers are placed at unit distance from the main fibre and form a geometrical structure analogous to a myelin sheath in a biological neuron. Both the perspex jumper-sheath and the biological myelin-sheath share the computational function of preventing cross-over of signals to neurons that lie close to an axon. This is an example of convergence driven by similar geometrical and computational constraints in perspex and biological neurons.

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

On combination of SMOTE and particle swarm optimization based radial basis function classifier for imbalanced problems

The combination of the synthetic minority oversampling technique (SMOTE) and the radial basis function (RBF) classifier is proposed to deal with classification for imbalanced two-class data. In order to enhance the significance of the small and specific region belonging to the positive class in the decision region, the SMOTE is applied to generate synthetic instances for the positive class to balance the training data set. Based on the over-sampled training data, the RBF classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier structure and the parameters of RBF kernels are determined using a particle swarm optimization algorithm based on the criterion of minimizing the leave-one-out misclassification rate. The experimental results on both simulated and real imbalanced data sets are presented to demonstrate the effectiveness of our proposed algorithm.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Synthesis and X-ray crystal structure of the copper(I) dicarboxylic acid complex [Cu(η1-bdoaH)(PPh3)3] (bdoaH2 = benzene-1,2- dioxyacetic acid)

The copper(II) complex [Cu(bdoa)(H2O)2] (bdoaH2 = benzene-1,2-dioxyacetic acid) reacts with triphenylphosphine (1:4 mol ratio) to give the colourless copper(I) complex [Cu(η1-bdoaH)(PPh3)3] (1) in good yield. The X-ray crystal structure of the complex shows the copper atom at the centre of a distorted tetrahedron, and is ligated by the phosphorus atoms of the three triphenylphosphines and one carboxylate oxygen atom of the bdoaH− ligand. Significant intermolecular hydrogen-bonding exists between the pendant carboxylate OH function of one molecule and the uncoordinated “ketonic” oxygen of a neighbouring molecule. Complex 1 is non-conducting in chloroform but ionizes readily in acetonitrile. The cyclic voltammogram of an acetonitrile solution of 1 shows a single irreversible anodic peak for the oxidation of the PPh3 ligands and the copper(I) centre, and a single irreversible cathodic peak for the reduction of the bdoaH− ion. IR and mass spectral data for 1 are given.

The effect of exogenous gonadotropins on ovarian function in goats actively immunized against inhibin

The aim of this investigation was to compare the ovarian response to superovulatory treatments in does before and after inhibin immunization, with a view to optimizing the superovulatory potential of the caprine ovary. To avoid interference by the ovarian cycle, the experiment was conducted out-of-season. At the onset of the experiment 48 does were subjected to treatment with an sc implant of the progestogen norgestomet, combined with a gonadotropin; eight does each received a single injection of 1200 IU eCG, 400 IU eCG or 2 mL physiological saline (control) or six injections (at 12 h intervals) constituting 16 or 5.4 AU pFSH. The does were mated and subjected to embryo collection 6 to 7 d later. Throughout the experiment ovarian function (by ultrasonography) and plasma levels of inhibin antibodies and progesterone were monitored. Of 40 does treated during the first part of the experiment, 48% showed estrus. The ovarian response in does treated with a high or low dose of eCG or a low dose of pFSH was barely in excess of the ovarian response in the saline-treated controls, whereas a superovulatory dose of pFSH (16 AU) gave a satisfactory response of, on average, 14.5 ovulations (yielding 8.8 flushed ova and embryos). Immediately after the does had been subjected to embryo collection they were actively immunized against inhibin by administering two injections of a recombinant α-subunit of ovine inhibin at four week intervals. All immunized does produced antibodies with the maximal titer reached two weeks after the second injection. Groups of immunized does were subjected to the same gonadotropin treatments as before (avoiding allocation of individuals to the same treatments). This time all does showed estrous symptoms. The ovulatory response to the various treatments, including the saline controls, was virtually identical, the overall average being 21.8 follicles and 9.1 ovulations. The average embryo yield per doe was 5.7. The results imply that inhibin acted as the key factor in determining the ovulatory response since no impact of any of the supplementary gonadotropins was noted in inhibin-immunized does. This finding gives rise to the notion that inhibin antibodies may act primarily by an intraovarian paracrine action rather than by reducing the suppressive action of inhibin on pituitary FSH release. Further, these findings confirm earlier reports that eCG is less suitable than FSH for inducing superovulation in goats, and indicate that active immunization against inhibin may be considered a viable alternative to using exogenous gonadotropin for inducing superovulation in goats.

The platelet-surface thiol isomerase enzyme ERp57 modulates platelet function

Background: Thiol isomerases are a family of endoplasmic reticulum enzymes which orchestrate redox-based modifications of protein disulphide bonds. Previous studies have identified important roles for the thiol isomerases PDI and ERp5 in the regulation of normal platelet function. Objectives: Recently, we demonstrated the presence of a further five thiol isomerases at the platelet surface. In this report we aim to report the role of one of these enzymes - ERp57 in the regulation of platelet function. Methods/Results: Using enzyme activity function blocking antibodies, we demonstrate a role for ERp57 in platelet aggregation, dense granule secretion, fibrinogen binding, calcium mobilisation and thrombus formation under arterial conditions. In addition to the effects of ERp57 on isolated platelets, we observe the presence of ERp57 in the developing thrombus in vivo. Furthermore the inhibition of ERp57 function was found to reduce laser-injury induced arterial thrombus formation in a murine model of thrombosis. Conclusions: These data suggest that ERp57 is important for normal platelet function and opens up the possibility that the regulation of platelet function by a range of cell surface thiol isomerases may represent a broad paradigm for the regulation of haemostasis and thrombosis.

A wide-angle X-ray study of the development of molecular orientation in crosslinked natural rubber

Molecular orientation parameters have been measured for the non-crystalline component of crosslinked natural rubber samples deformed in uniaxial tension as a function of the extension ratio and of temperature. The orientation parapeters 〈P2(cosα)〉 and 〈P4(cosα)〉 were obtained by an analysis of the anisotropy of the wide-angle X-ray scattering functions. For the measurements made at high temperatures the level of crystallinity detected was negligible and the orientation-strain behaviour could be compared directly with the predictions of molecular models of rubber elasticity. The molecular orientation behaviour with strain was found to be at variance with the estimates of the affine model particularly at low and moderate strains. Extension of the crosslinked rubber at room temperature led to strain-crystallization and measurements of both the molecular orientation of the non-crystalline chains and the degree of crystallinity during extension and relaxation enabled the role of the crystallites in the deformation process to be considered in detail. The intrinsic birefringence of the non-crystalline component was estimated, through the use of the 〈P2(cosα)〉 values obtained from X-ray scattering measurements, to be 0.20±0.02.

Experimental separation of the coherent component of X-ray scattering prior to RDF analysis of non-crystalline polymers

An experimental method is described which enables the inelastically scattered X-ray component to be removed from diffractometer data prior to radial density function analysis. At each scattering angle an energy spectrum is generated from a Si(Li) detector combined with a multi-channel analyser from which the coherently scattered component is separated. The data obtained from organic polymers has an improved signal/noise ratio at high values of scattering angle, and a commensurate enhancement of resolution of the RDF at low r is demonstrated for the case of PMMA (ICI `Perspex'). The method obviates the need for the complicated correction for multiple scattering.

Conformational analysis of oriented non-crystalline polymers using wide angle X-ray scattering

A procedure is presented for obtaining conformational parameters from oriented but non-crystalline polymers. This is achieved by comparison of the experimental wide angle X-ray scattering with that calculated from models but in such a way that foreknowledge of the orientation distribution function is not required. X-ray scattering intensity values for glassy isotactic poly(methylmethacrylate) are analysed by these techniques. The method could be usefully applied to other oriented molecular systems such as liquid crystalline materials.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.