GTM: the generative topographic mapping

This thesis describes the Generative Topographic Mapping (GTM) --- a non-linear latent variable model, intended for modelling continuous, intrinsically low-dimensional probability distributions, embedded in high-dimensional spaces. It can be seen as a non-linear form of principal component analysis or factor analysis. It also provides a principled alternative to the self-organizing map --- a widely established neural network model for unsupervised learning --- resolving many of its associated theoretical problems. An important, potential application of the GTM is visualization of high-dimensional data. Since the GTM is non-linear, the relationship between data and its visual representation may be far from trivial, but a better understanding of this relationship can be gained by computing the so-called magnification factor. In essence, the magnification factor relates the distances between data points, as they appear when visualized, to the actual distances between those data points. There are two principal limitations of the basic GTM model. The computational effort required will grow exponentially with the intrinsic dimensionality of the density model. However, if the intended application is visualization, this will typically not be a problem. The other limitation is the inherent structure of the GTM, which makes it most suitable for modelling moderately curved probability distributions of approximately rectangular shape. When the target distribution is very different to that, theaim of maintaining an `interpretable' structure, suitable for visualizing data, may come in conflict with the aim of providing a good density model. The fact that the GTM is a probabilistic model means that results from probability theory and statistics can be used to address problems such as model complexity. Furthermore, this framework provides solid ground for extending the GTM to wider contexts than that of this thesis.

Triangulation mobility of auto-theft offenders

This research paper presents an examination of the journey to and from crime for autotheft offenders in the UK. For 852 offences, ‘wheel’ distances are calculated for triangles formed by offenders’ home location, theft location, and vehicle disposal location. The study demonstrates typical isosceles mobility triangles; distances travelled to and from home locations are roughly equal, whereas distances between theft and disposal points were shorter. Distances travelled by offenders under 17 years old and offences involving drug and drink were shown to be shorter than comparison groups. Prolifi c offenders tend to travel further, although there is signifi cant variation in this subgroup. Explanations and implications are discussed.

Accuracy and applications of group MEG studies using cortical source locations estimated from participants' scalp surfaces

We contend that powerful group studies can be conducted using magnetoencephalography (MEG), which can provide useful insights into the approximate distribution of the neural activity detected with MEG without requiring magnetic resonance imaging (MRI) for each participant. Instead, a participant's MRI is approximated with one chosen as a best match on the basis of the scalp surface from a database of available MRIs. Because large inter-individual variability in sulcal and gyral patterns is an inherent source of blurring in studies using grouped functional activity, the additional error introduced by this approximation procedure has little effect on the group results, and offers a sufficiently close approximation to that of the participants to yield a good indication of the true distribution of the grouped neural activity. T1-weighted MRIs of 28 adults were acquired in a variety of MR systems. An artificial functional image was prepared for each person in which eight 5 × 5 × 5 mm regions of brain activation were simulated. Spatial normalisation was applied to each image using transformations calculated using SPM99 with (1) the participant's actual MRI, and (2) the best matched MRI substituted from those of the other 27 participants. The distribution of distances between the locations of points using real and substituted MRIs had a modal value of 6 mm with 90% of cases falling below 12.5 mm. The effects of this -approach on real grouped SAM source imaging of MEG data in a verbal fluency task are also shown. The distribution of MEG activity in the estimated average response is very similar to that produced when using the real MRIs. © 2003 Wiley-Liss, Inc.

Practical network coding for two way relay channels in LTE networks

In this paper, the implementation aspects and constraints of the simplest network coding (NC) schemes for a two-way relay channel (TWRC) composed of a user equipment (mobile terminal), an LTE relay station (RS) and an LTE base station (eNB) are considered in order to assess the usefulness of the NC in more realistic scenarios. The information exchange rate gain (IERG), the energy reduction gain (ERG) and the resource utilization gain (RUG) of the NC schemes with and without subcarrier division duplexing (SDD) are obtained by computer simulations. The usefulness of the NC schemes are evaluated for varying traffic load levels, the geographical distances between the nodes, the RS transmit powers, and the maximum numbers of retransmissions. Simulation results show that the NC schemes with and without SDD, have the throughput gains 0.5% and 25%, the ERGs 7 - 12% and 16 - 25%, and the RUGs 0.5 - 3.2%, respectively. It is found that the NC can provide performance gains also for the users at the cell edge. Furthermore, the ERGs of the NC increase with the transmit power of the relay while the ERGs of the NC remain the same even when the maximum number of retransmissions is reduced.

Cross-category demand effects of price promotions

Do promotions in a certain category lead to higher revenues in other categories? If so, to what degree? The answers to these questions are highly relevant for retailers that supply products in different categories. Empirical findings in studies that consider a limited number of categories indicate small promotional cross-category effects. This study develops a framework to determine the impact of price promotions on category revenues that include interdependencies among a substantial number of categories at the category demand level. The own- and cross-category demand effects are moderated by variables such as promotion intensity, category characteristics (own-category effects), and spatial distances between shelf locations (cross-category effects). The empirical results based on daily store-level scanner data show that approximately half of all price promotions expand own-category revenues, especially for categories with deeper supported discounts. There is a high probability (61%) that a price promotion affects sales of at least one other category. The number of categories affected is not greater than two. Moderate evidence supports the existence of cross-promotional effects between categories more closely located in a store.

Determining which factors influence the optimum multifocal contact lens correction for presbyopia

Presbyopia is a consequence of ageing and is therefore increasing inprevalence due to an increase in the ageing population. Of the many methods available to manage presbyopia, the use of contact lenses is indeed a tried and tested reversible option for those wishing to be spectacle free. Contact lens options to correct presbyopia include multifocal contact lenses and monovision.Several options have been available for many years with available guides to help choose multifocal contact lenses. However there is no comprehensive way to help the practitioner selecting the best option for an individual. An examination of the simplest way of predicting the most suitable multifocal lens for a patient will only enhance and add to the current evidence available. The purpose of the study was to determine the current use of presbyopic correction modalities in an optometric practice population in the UK and to evaluate and compare the optical performance of four silicone hydrogel soft multifocal contact lenses and to compare multifocal performance with contact lens monovision. The presbyopic practice cohort principal forms of refractive correction were distance spectacles (with near and intermediate vision providedby a variety of other forms of correction), varifocal spectacles and unaided distance with reading spectacles, with few patients wearing contact lenses as their primary correction modality. The results of the multifocal contact lens randomised controlled trial showed that there were only minor differences in corneal physiology between the lens options. Visual acuity differences were observed for distance targets, but only for low contrast letters and under mesopic lighting conditions. At closer distances between 20cm and 67cm, the defocus curves demonstrated that there were significant differences in acuity between lens designs (p < 0.001) and there was an interaction between the lens design and the level of defocus (p < 0.001). None of the lenses showed a clear near addition, perhaps due to their more aspheric rather than zoned design. As expected, stereoacuity was reduced with monovision compared with the multifocal contact lens designs, although there were some differences between the multifocal lens designs (p < 0.05). Reading speed did not differ between lens designs (F = 1.082, p = 0.368), whereas there was a significant difference in critical print size (F = 7.543, p < 0.001). Glare was quantified with a novel halometer and halo size was found to significantly differ between lenses(F = 4.101, p = 0.004). The rating of iPhone image clarity was significantly different between presbyopic corrections (p = 0.002) as was the Near Acuity Visual Questionnaire (NAVQ) rating of near performance (F = 3.730, p = 0.007).The pupil size did not alter with contact lens design (F = 1.614, p = 0.175), but was larger in the dominant eye (F = 5.489, p = 0.025). Pupil decentration relative to the optical axis did not alter with contact lens design (F = 0.777, p =0.542), but was also greater in the dominant eye (F = 9.917, p = 0.003). It was interesting to note that there was no difference in spherical aberrations induced between the contact lens designs (p > 0.05), with eye dominance (p > 0.05) oroptical component (ocular, corneal or internal: p > 0.05). In terms of subjective patient lens preference, 10 patients preferred monovision,12 Biofinity multifocal lens, 7 Purevision 2 for Presbyopia, 4 AirOptix multifocal and 2 Oasys multifocal contact lenses. However, there were no differences in demographic factors relating to lifestyle or personality, or physiological characteristics such as pupil size or ocular aberrations as measured at baseline,which would allow a practitioner to identify which lens modality the patient would prefer. In terms of the performance of patients with their preferred lens, it emerged that Biofinity multifocal lens preferring patients had a better high contrast acuity under photopic conditions, maintained their reading speed at smaller print sizes and subjectively rated iPhone clarity as better with this lens compared with the other lens designs trialled. Patients who preferred monovision had a lower acuity across a range of distances and a larger area of glare than those patients preferring other lens designs that was unexplained by the clinical metrics measured. However, it seemed that a complex interaction of aberrations may drive lens preference. New clinical tests or more diverse lens designs which may allow practitioners to prescribe patients the presbyopic contact lens option that will work best for them first time remains a hope for the future.

Transfer of patients from health care centres to special care services:analysis of travel distances in Nordic countries

Objectives: This paper highlights the importance of analysing patient transportation in Nordic circumpolar areas. The research questions we asked are as follows: How many Finnish patients have been transferred to special care intra-country and inter-country in 2009? Does it make any difference to health care policymakers if patients are transferred inter-country? Study design: We analysed the differences in distances from health care centres to special care services within Finland, Sweden and Norway and considered the health care policy implica tions. Methods: An analysis of the time required to drive between service providers using the "Google distance meter" (http://maps.google.com/); conducting interviews with key Finnish stakeholders; and undertaking a quantitative analyses of referral data from the Lapland Hospital District. Results: Finnish patients are generally not transferred for health care services across national borders even if the distances are shorter. Conclusion: Finnish patients have limited access to health care services in circumpolar are as across the Nordic countries for 2 reasons. First, health professionals in Norway and Sweden do not speak Finnish, which presents a language problem. Second, The Social Insurance Institution of Finland does not cover the expenditures of travel or the costs of medicine. In addition, it seems that in circumpolar areas the density of Finnish service providers is greater than Swedish ones, causing many Swedish citizens to transfer to Finnish health care providers every year. However, future research is needed to determine the precise reasons for this.

Direct observation of R...R distances in rare-earth (R) phosphate glasses by magnetic difference neutron diffraction

A magnetic difference neutron diffraction study of a rare-earth (Tb) phosphate glass has revealed exclusively the Tb...Tb distances. The difference between data taken with and without an applied magnetic field of 4 T shows Tb...Tb pairwise atomic correlations at 3.9 and 6.4 A, respectively, with relative coordination numbers of 1:14. The first distance arises when two Tb3+ ions share a common oxygen neighbor, and indicates a clustering of rare-earth ions. The second distance arises when two Tb3+ ions are coordinated to different oxygens in the same PO4 group, in a near-linear arrangement.