Magnification factors for the GTM algorithm

The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.

Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

Mixture density network training by computation in parameter space

Training Mixture Density Network (MDN) configurations within the NETLAB framework takes time due to the nature of the computation of the error function and the gradient of the error function. By optimising the computation of these functions, so that gradient information is computed in parameter space, training time is decreased by at least a factor of sixty for the example given. Decreased training time increases the spectrum of problems to which MDNs can be practically applied making the MDN framework an attractive method to the applied problem solver.

Structure and regulation of type 2 transglutaminase in relation to its physiological functions and pathological roles

This chapter contains sections titled: Introduction Structure and Regulation Physiologic Functions of TG2 Disruption of TG2 Functions in Pathologic Conditions Perspectives for Pharmacologic Interventions Concluding Comments Acknowledgements References

Neurophysiology of CSWS-associated cognitive dysfunction

The phenomenon of continuous spikes and waves during slow-wave sleep (CSWS) is associated with a number of epileptic syndromes, which share a behavioral phenotype characterized by deterioration of cognitive, behavioral, or sensorimotor functions. Available evidence seems to suggest that spike-wave activity is a result of a complex interaction between cortical and subcortical inhibitory networks and can "per se" produce a transient loss of underlying cortical functions. Syndromes like Landau-Kleffner syndrome, CSWS, and phenomena such as negative myoclonus could share in common--at least at the neurophysiological level--some similarities. Differences in behavioral phenotypes could be explained in term of maturational and genetic differences, as well as by the functional specificity of the involved areas.

Transition from time-continuous systems to discrete mappings

Detailed transport studies in plasmas require the solution of the time evolution of many different initial positions of test particles in the phase space of the systems to be investigated. To reduce this amount of numerical work, one would like to replace the integration of the time-continues system with a mapping.

Batch and continuous fermentation methods for the production of dextransucrase

The available literature concerning dextransucrase and dextran production and purification has been reviewed along with the reaction mechanisms of the enzyme. A discussion of basic fermentation theory is included, together with a brief description of bioreactor hydrodynamics and general biotechnology. The various fermenters used in this research work are described in detail, along with the various experimental techniques employed. The micro-organism Leuconostoc mesenteroides NRRL B512 (F) secretes dextransucrase in the presence of an inducer, sucrose, this being the only known inducer of the enzyme. Dextransucrase is a growth related product and a series of fed-batch fermentations have been carried out to extend the exponential growth phase of the organism. These experiments were carried out in a number of different sized vessels, ranging in size from 2.5 to 1,000 litres. Using a 16 litre vessel, dextransucrase activities in excess of 450 DSU/cm3 (21.67 U/cm3) have been obtained under non-aerated conditions. It has also been possible to achieve 442 DSU/cm3 (21.28 U/cm3) using the 1,000 litre vessel, although this has not been done consistently. A 1 litre and a 2.5 litre vessel were used for the continuous fermentations of dextransucrase. The 2.5 litre vessel was a very sophisticated MBR MiniBioreactor and was used for the majority of continuous fermentations carried out. An enzyme activity of approximately 108 DSU/cm3 (5.20 U/cm3) was achieved at a dilution rate of 0.50 h-1, which corresponds to the maximum growth rate of the cells under the process conditions. A number of continuous fermentations were operated for prolonged periods of time, with experimental run-times of up to 389 h being recorded without any incidence of contamination. The phenomenon of enzyme enhancement on hold-up of up to 100% was also noted during these fermentations, with dextransucrase of activity 89.7 DSU/cm3 (4.32 U/cm3) being boosted to 155.7 DSU/cm3 (7.50 U/cm3) following 24 hours of hold-up. These findings support the recommendation of a second reactor being placed in series with the existing vessel.

Simultaneous biochemical reaction and separation in a continuous rotating annular chromatograph

The aim of this work has been to investigate the behaviour of a continuous rotating annular chromatograph (CRAC) under a combined biochemical reaction and separation duty. Two biochemical reactions have been employed, namely the inversion of sucrose to glucose and fructose in the presence of the enzyme invertase and the saccharification of liquefied starch to maltose and dextrin using the enzyme maltogenase. Simultaneous biochemical reaction and separation has been successfully carried out for the first time in a CRAC by inverting sucrose to fructose and glucose using the enzyme invertase and collecting continuously pure fractions of glucose and fructose from the base of the column. The CRAC was made of two concentric cylinders which form an annulus 140 cm long by 1.2 cm wide, giving an annular space of 14.5 dm3. The ion exchange resin used was an industrial grade calcium form Dowex 50W-X4 with a mean diameter of 150 microns. The mobile phase used was deionised and dearated water and contained the appropriate enzyme. The annular column was slowly rotated at speeds of up to 240°h-1 while the sucrose substrate was fed continuously through a stationary feed pipe to the top of the resin bed. A systematic investigation of the factors affecting the performance of the CRAC under simultaneous biochemical reaction and separation conditions was carried out by employing a factorial experimental procedure. The main factors affecting the performance of the system were found to be the feed rate, feed concentrations and eluent rate. Results from the experiments indicated that complete conversion could be achieved for feed concentrations of up to 50% w/v sucrose and at feed throughputs of up to 17.2 kg sucrose per m3 resin/h. The second enzymic reaction, namely the saccharification of liquefied starch to maltose employing the enzyme maltogenase has also been successfully carried out on a CRAC. Results from the experiments using soluble potato starch showed that conversions of up to 79% were obtained for a feed concentration of 15.5% w/v at a feed flowrate of 400 cm3/h. The product maltose obtained was over 95% pure. Mathematical modelling and computer simulation of the sucrose inversion system has been carried out. A finite difference method was used to solve the partial differential equations and the simulation results showed good agreement with the experimental results obtained.

The effects of the environment on the stability and expression of genetically engineered plasmids

The lac promoter is widely used in plasmid expression systems, even though it is prone to catabolite repression. As a consequence glycerol is often used as an alternative carbon source. Three plasmids containing various sizes of the staphylococcal protein A (SPA) gene, which are under the control of the lac promoter were investigated in continuous culture, to evaluate the effects of nutrient limitations on their stability and expression. The fears of catabolite repression were dispelled as a low expression plasmid (pPA16) produced a greater amount of truncated SPA under glucose limiting conditions (11 ug mg-1 cell protein) when compared to that using glycerol (8 ug mg-1 cell protein). Segregational instability was also observed under glycerol limiting conditions at all the dilution rates investigated. Whereas pPA16 was relatively stable under glucose limiting conditions, with SPA production being continuous. Experiments using excess glycerol with limited ammonium increased the stability of pPA16, (when compared to limited glycerol) with expression of SPA being continuous but reduced (6 ug mg-1 cell protein). With excess glucose and limited ammonium the copy numbers remained high but expression of SPA paralled that produced under glucose limiting conditions. This might indicate that the higher levels of glucose are reducing expression (catabolite repression) or that the low level of ammonium is affecting protein production. A high expression plasmid (pPA31) produced nearly 100 ug full length SPA mg-1 cell protein, while another high expression plasmid (pPA34) producing truncated SPA proved to be very unstable. An ELISA was developed to detect the SPA produced by these experiments, which could be adapted for western blotting or immunogold probing using electron microscopy. SPA was localised in electron lucent areas present in the periplasmic space of the E. coli host harbouring pPA16. While in the same host containing pPA31, SPA was localised not only in electron lucent areas but also around the whole of the outer-membrane.

A survey of urban open space using colour infra-red aerial photographs

There has been a dramatic change in the U.K. government policy regarding the establishment of new towns. The emphasis is now on the redevelopment of existing cities rather than on building new ones. This has created an urgent need to carry out detailed surveys and inventories of many aspects of urban land use in metropolitan areas: this study concentrates on just one aspect - urban open space. In the first stage a comparison was made between 1:10,000 scale black and white and 1:10,000 scale colour infra-red aerial photographs, to compare the type and amount of open space information which could be obtained from these two sources. The advantages of using colour infra-red photography were clearly demonstrated in this comparison. The second stage was the use of colour infra-red photography as the sole source of data to survey and map the urban open space of a sample area in Merseyside Metropolitan County. This sample area comprised eleven 1/4km2 squares, on each of which a 20m x 20m grid cell was placed to record, directly from the photography, 625 sets of data. Each set of data recorded the type and amount of open space, its surface cover, maintenance status and management. The data recorded were fed into a computer and a suite of programs was developed to provide output in both computer map and statistical form, for each of the eleven -1/4km2 -sample areas. The third stage involved a comparison of open space data with socio-economic status. Merseyside County Planning Authority had previously conducted a socio-economic survey of the county, and this information was used to identify ' the socio-economic status of the population in the eleven ilkm2 areas of this project. This comparison revealed many interesting and useful relationships between the provision of urban open space and socio-economic status.

Compositional semantics of dataflow networks with query-driven communication of exact values

We develop and study the concept of dataflow process networks as used for exampleby Kahn to suit exact computation over data types related to real numbers, such as continuous functions and geometrical solids. Furthermore, we consider communicating these exact objectsamong processes using protocols of a query-answer nature as introduced in our earlier work. This enables processes to provide valid approximations with certain accuracy and focusing on certainlocality as demanded by the receiving processes through queries. We define domain-theoretical denotational semantics of our networks in two ways: (1) directly, i. e. by viewing the whole network as a composite process and applying the process semantics introduced in our earlier work; and (2) compositionally, i. e. by a fixed-point construction similarto that used by Kahn from the denotational semantics of individual processes in the network. The direct semantics closely corresponds to the operational semantics of the network (i. e. it iscorrect) but very difficult to study for concrete networks. The compositional semantics enablescompositional analysis of concrete networks, assuming it is correct. We prove that the compositional semantics is a safe approximation of the direct semantics. Wealso provide a method that can be used in many cases to establish that the two semantics fully coincide, i. e. safety is not achieved through inactivity or meaningless answers. The results are extended to cover recursively-defined infinite networks as well as nested finitenetworks. A robust prototype implementation of our model is available.

Consumer trial, continuous use, and economic benefits of a retail service innovation:the case of the personal shopping assistant

Service innovations in retailing have the potential to benefit consumers as well as retailers. This research models key factors associated with the trial and continuous use of a specific self-service technology (SST), the personal shopping assistant (PSA), and estimates retailer benefits from implementing that innovation. Based on theoretical insights from prior SST studies, diffusion of innovation literature, and the technology acceptance model (TAM), this study develops specific hypotheses and tests them on a sample of 104 actual users of the PSA and 345 nonusers who shopped at the retail store offering the PSA device. Results indicate that factors affecting initial trial are different from those affecting continuous use. More specifically, consumers' trust toward the retailer, novelty seeking, and market mavenism are positively related to trial, while technology anxiety hinders the likelihood of trying the PSA. Perceived ease of use of the device positively impacts continuous use while consumers' need for interaction in shopping environments reduces the likelihood of continuous use. Importantly, there is evidence on retailer benefits from introducing the innovation since consumers using the PSA tend to spend more during each shopping trip. However, given the high costs of technology, the payback period for recovery of investments in innovation depends largely upon continued use of the innovation by consumers. Important implications are provided for retailers considering investments in new in-store service innovations. Incorporation of technology within physical stores affords opportunities for the retailer to reduce costs, while enhancing service provided to consumers. Therefore, service innovations in retailing have the potential to benefit consumers as well as retailers. This research models key factors associated with the trial and continuous use of a specific SST in the retail context, the PSA, and estimates retailer benefits from implementing that innovation. In so doing, the study contributes to the nascent area of research on SSTs in the retail sector. Based on theoretical insights from prior SST studies, diffusion of innovation literature, and the TAM, this study develops specific hypotheses regarding the (1) antecedent effects of technological anxiety, novelty seeking, market mavenism, and trust in the retailer on trial of the service innovation; (2) the effects of ease of use, perceived waiting time, and need for interaction on continuous use of the innovation; and (3) the effect of use of innovation on consumer spending at the store. The hypotheses were tested on a sample of 104 actual users of the PSA and 345 nonusers who shopped at the retail store offering the PSA device, one of the early adopters of PSA in Germany. Data were analyzed using logistic regression (antecedents of trial), multiple regression (antecedents of continuous use), and propensity score matching (assessing retailer benefits). Results indicate that factors affecting initial trial are different from those affecting continuous use. More specifically, consumers' trust toward the retailer, novelty seeking, and market mavenism are positively related to trial, while technology anxiety hinders the likelihood of trying the PSA. Perceived ease of use of the device positively impacts continuous use, while consumers' need for interaction in shopping environments reduces the likelihood of continuous use. Importantly, there is evidence on retailer benefits from introducing the innovation since consumers using the PSA tend to spend more during each shopping trip. However, given the high costs of technology, the payback period for recovery of investments in innovation depends largely upon continued use of the innovation by consumers. Important implications are provided for retailers considering investments in new in-store service innovations. The study contributes to the literature through its (1) simultaneous examination of antecedents of trial and continuous usage of a specific SST, (2) the demonstration of economic benefits of SST introduction for the retailer, and (3) contribution to the stream of research on service innovation, as against product innovation.

Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

An Example Concerning Valdivia Compact Spaces

∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998

The Point of Continuity Property: Descriptive Complexity and Ordinal Index

∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142