A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems

The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

Modelling ocular monochromatic aberrations using schematic eyes with homogeneous optical media

Previous research has indicated that schematic eyes incorporating aspheric surfaces but lacking gradient index are unable to model ocular spherical aberration and peripheral astigmatism simultaneously. This limits their use as wide-angle schematic eyes. This thesis challenges this assumption by investigating the flexibility of schematic eyes comprising aspheric optical surfaces and homogeneous optical media. The full variation of ocular component dimensions found in human eyes was established from the literature. Schematic eye parameter variants were limited to these dimensions. The levels of spherical aberration and peripheral astigmatism modelled by these schematic eyes were compared to the range of measured levels. These were also established from the literature. To simplify comparison of modelled and measured data, single value parameters were introduced; the spherical aberration function (SAF), and peripheral astigmatism function (PAF). Some ocular components variations produced a wide range of aberrations without exceeding the limits of human ocular components. The effect of ocular component variations on coma was also investigated, but no comparison could be made as no empirical data exists. It was demonstrated that by combined manipulation of a number of parameters in the schematic eyes it was possible to model all levels of ocular spherical aberration and peripheral astigmatism. However, the unique parameters of a human eye could not be obtained in this way, as a number of models could be used to produce the same spherical aberration and peripheral astigmatism, while giving very different coma levels. It was concluded that these schematic eyes are flexible enough to model the monochromatic aberrations tested, the absence of gradient index being compensated for by altering the asphericity of one or more surfaces.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Precipitation of magnesium ammonium phosphate from homogeneous solution

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Fundamental Pd0/PdII redox steps in cross-coupling reactions:homogeneous, hybrid homogeneous-heterogeneous to heterogeneous mechanistic pathways for C-C couplings

C–C bond-forming, cross-coupling reactions of organohalides with nucleophilic compounds, catalysed by palladium, are amongst the most important chemical reactions available to the synthetic chemist. The intimate mechanisms of these reactions, involving Pd0/PdII redox steps, have been of great historical interest and continue to be so. The myriad of possible mechanisms is reviewed in this chapter. The interplay of mononuclear Pd species with higher order Pd species, e.g. nanoclusters/nanoparticles are considered as being equally important in cross-coupling reaction mechanisms. A focus is placed on trichotomic behaviour of cross-coupling catalytic manifolds, from homogeneous to hybrid homogeneous–heterogeneous to truly heterogeneous behaviour. For the latter, surface chemistry and metal atom leaching (and various experimental techniques) are broadly discussed. It is now clear that mechanism for general cross‐coupling reactions, that is as presented to undergraduate students studying Chemistry degrees across the world, is undoubtedly more complex than first thought. New opportunities for catalyst design have therefore emerged in the area of Pd nanoparticles and nanocatalysis, with some wonderful applications especially in chemical biology, providing a snapshot of what the future might hold.

Evolution, recurrency and kernels in learning to model inflation

This paper provides the most fully comprehensive evidence to date on whether or not monetary aggregates are valuable for forecasting US inflation in the early to mid 2000s. We explore a wide range of different definitions of money, including different methods of aggregation and different collections of included monetary assets. We use non-linear, artificial intelligence techniques, namely, recurrent neural networks, evolution strategies and kernel methods in our forecasting experiment. In the experiment, these three methodologies compete to find the best fitting US inflation forecasting models and are then compared to forecasts from a naive random walk model. The best models were non-linear autoregressive models based on kernel methods. Our findings do not provide much support for the usefulness of monetary aggregates in forecasting inflation. There is evidence in the literature that evolutionary methods can be used to evolve kernels hence our future work should combine the evolutionary and kernel methods to get the benefits of both.

Selective in vitro glycosylation of recombinant proteins:semi-synthesis of novel homogeneous glycoforms of human erythropoietin

Background: A natural glycoprotein usually exists as a spectrum of glycosylated forms, where each protein molecule may be associated with an array of oligosaccharide structures. The overall range of glycoforms can have a variety of different biophysical and biochemical properties, although details of structure–function relationships are poorly understood, because of the microheterogeneity of biological samples. Hence, there is clearly a need for synthetic methods that give access to natural and unnatural homogeneously glycosylated proteins. The synthesis of novel glycoproteins through the selective reaction of glycosyl iodoacetamides with the thiol groups of cysteine residues, placed by site-directed mutagenesis at desired glycosylation sites has been developed. This provides a general method for the synthesis of homogeneously glycosylated proteins that carry saccharide side chains at natural or unnatural glycosylation sites. Here, we have shown that the approach can be applied to the glycoprotein hormone erythropoietin, an important therapeutic glycoprotein with three sites of N-glycosylation that are essential for in vivo biological activity. Results: Wild-type recombinant erythropoietin and three mutants in which glycosylation site asparagine residues had been changed to cysteines (His10-WThEPO, His10-Asn24Cys, His10-Asn38Cys, His10-Asn83CyshEPO) were overexpressed and purified in yields of 13 mg l−1 from Escherichia coli. Chemical glycosylation with glycosyl-β-N-iodoacetamides could be monitored by electrospray MS. Both in the wild-type and in the mutant proteins, the potential side reaction of the other four cysteine residues (all involved in disulfide bonds) were not observed. Yield of glycosylation was generally about 50% and purification of glycosylated protein from non-glycosylated protein was readily carried out using lectin affinity chromatography. Dynamic light scattering analysis of the purified glycoproteins suggested that the glycoforms produced were monomeric and folded identically to the wild-type protein. Conclusions: Erythropoietin expressed in E. coli bearing specific Asn→Cys mutations at natural glycosylation sites can be glycosylated using β-N-glycosyl iodoacetamides even in the presence of two disulfide bonds. The findings provide the basis for further elaboration of the glycan structures and development of this general methodology for the synthesis of semi-synthetic glycoproteins. Results: Wild-type recombinant erythropoietin and three mutants in which glycosylation site asparagine residues had been changed to cysteines (His10-WThEPO, His10-Asn24Cys, His10-Asn38Cys, His10-Asn83CyshEPO) were overexpressed and purified in yields of 13 mg l−1 from Escherichia coli. Chemical glycosylation with glycosyl-β-N-iodoacetamides could be monitored by electrospray MS. Both in the wild-type and in the mutant proteins, the potential side reaction of the other four cysteine residues (all involved in disulfide bonds) were not observed. Yield of glycosylation was generally about 50% and purification of glycosylated protein from non-glycosylated protein was readily carried out using lectin affinity chromatography. Dynamic light scattering analysis of the purified glycoproteins suggested that the glycoforms produced were monomeric and folded identically to the wild-type protein. Conclusions: Erythropoietin expressed in E. coli bearing specific Asn→Cys mutations at natural glycosylation sites can be glycosylated using β-N-glycosyl iodoacetamides even in the presence of two disulfide bonds. The findings provide the basis for further elaboration of the glycan structures and development of this general methodology for the synthesis of semi-synthetic glycoproteins

MRI pressure and stress measurement in novel homogeneous soft solids

This paper presents MRI measurements of a novel semi solid MR contrast agent to pressure. The agent is comprised of potassium chloride cross linked carageenan gum at a concentration of 2% w/v, with micron size lipid coated bubbles of air at a concentration of 3% v/v. The choice for an optimum suspending medium, the methods of production and the preliminary MRI results are presented herein. The carageenan gum is shown to be ideally elastic for compressions relating to volume changes less than 15%, in contrast to the inelastic gellan gum also tested. Although slightly lower than that of gellan gum, carageenan has a water diffusion coefficient of 1.72×10-9 m2.s-1 indicating its suitability to this purpose. RARE imaging is performed whilst simultaneously compressing test and control samples and a maximum sensitivity of 1.6% MR signal change per % volume change is found which is shown to be independent of proton density variations due to the presence of microbubbles and compression. This contrast agent could prove useful for numerous applications, and particularly in chemical engineering. More generally the method allows the user to non-invasively image with MRI any process that causes, within the solid, local changes either in bubble size or bubble shape. © 2008 American Institute of Physics.

About Homogeneous Spaces and Conditions of Completeness of Spaces

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Въведени са понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако lo-хомогенно пространство X има отворено подпространство, което е q-пълно, то и самото X е q-пълно. Показано е, че ако lo-хомогенно пространство X съдържа навсякъде гъсто екстремално несвързано подпространство, тогава X е екстремално несвързано.

About Homogeneous Spaces and the Baire Property in Remainders

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - В съобщението е продължено изследването на понятията o-хомогенно пространство, lo-хомогенно пространство, do-хомогенно пространство и co-хомогенно пространство. Показано е, че ако co-хомогенното пространство X съдържа Gδ -гъсто Московско подпространство, тогава X е Московско пространство.

Viability Kernels of Higher Order

AMS subject classification: Primary 34A60, Secondary 49K24.