A generalisation of the Delogne-Kasa method for fitting hyperspheres

In this paper, we examine the problem of fitting a hypersphere to a set of noisy measurements of points on its surface. Our work generalises an estimator of Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972,117-123) which he proposed for circles and which has been shown by Kasa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. We also generalise Chan's 'circular functional relationship' to describe the distribution of points. We derive the Cramer-Rao lower bound (CRLB) under this model and we derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We perform a statistical analysis of the estimate of the hypersphere's centre. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than M + 1, where M is the dimension of the hypersphere. The variance exists when the number of sample points is greater than M + 2. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the CRLB. We provide simulation results to support our findings.

Language disorders in dementia of the Alzheimer type

The language profile of a group of 18 Alzheimer patients is documented and their performance on a standard aphasia test battery compared to a group of institutionalized, nonneurologically impaired control subjects matched for age, sex, and educational level. The Alzheimer patients scored significantly lower than the controls in the areas of verbal expression, auditory comprehension, repetition, reading, and writing. Articulation abilities were the same in each group. A language deficit was evident in all Alzheimer patients. The language disorder exhibited resembled a transcortical sensory aphasia. Syntax and phonology remained relatively intact but semantic abilities were impaired. The results support the inclusion of a language deficit as a diagnostic criterion of Alzheimer's disease.

La Pointe Saint Mathieu, Brittany, France

The "Pointe Saint Mathieu" is one of the most westerly continental landmarks of France. The promontory is located at the entrance of the "Goulet de la Rade de Brest", that is the entrance channel of the harbour of Brest in Brittany (France). It marks also the Southern end of the "Chenal du Four" that is the main navigation channel between the islands of Ouessant, Molène and Béniquet, and Brittany. The "Chenal du Four" is reputed for its dangers. The tidal range is greater than 7 m in spring tides, and the mid-tide current may exceed 5 knots. The Saint Mathieu promontory is equipped with a lighthouse and a semaphore. The former is located in the ruins of an old monastery, founded during the 6th century AD by Saint Tanguy. The present ruins are the remnants of buildings from the 11th to 15th centuries. The first lighthouse was installed in 1689, although the monks of the monastery used to maintain a signal light since the 1250s. Completed in 1835, the present "Phare de la Pointe Saint-Mathieu" is 37 m high and it reaches 58.8 m above sea level During World War 2, the Pointe Saint Mathieu was defended by a series of concrete fortifications built by the Germans. Some were based upon some earlier French bunker systems, like the coastal battery at the Rospects which included 4 main gun bunkers (4*150 mm, or 2*150 mm & 2*105 mm), an observation bunker on the Western side close to sea, and several smaller structures. There was also the large Kéringar Blockhaus system, near Lochrist, located about 1 km inland and designed for 4 guns of 280 mm. Its command bunker remains a landmark along the main road. All this area was very-heavily bombed between 1943 and 1944, and particularly during the battle of Brest in August-September 1944 ("L'Enfer de Brest").

Improved constraints on possible variation of physical constants from HI 21-cm and molecular QSO absorption lines

Quasar (QSO) absorption spectra provide an extremely useful probe of possible cosmological variation in various physical constants. Comparison of H i 21-cm absorption with corresponding molecular (rotational) absorption spectra allows us to constrain variation in , where α is the fine-structure constant and gp is the proton g-factor. We analyse spectra of two QSOs, PKS 1413+135 and TXS 0218+357, and derive values of at absorption redshifts of and 0.6847 by simultaneous fitting of the H i 21-cm and molecular lines. We find and respectively, indicating an insignificantly smaller y in the past. We compare our results with other constraints from the same two QSOs given recently by Drinkwater et al. and Carilli et al., and with our recent optical constraints, which indicated a smaller α at higher redshifts.

Random numbers from astronomical imaging

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Transient response of diffusion cell containing a porous solid

Transient response of an adsorbing or non-adsorbing tracer injected as step or square pulse input in a diffusion cell with two flowing streams across the pellet is theoretically investigated in this paper. Exact solutions and the asymptotic solutions in the time domain and in three different limits are obtained by using an integral transform technique and a singular perturbation technique, respectively. Parametric dependence of the concentrations in the top and bottom chambers can be revealed by investigating the asymptotic solutions, which are far simpler than their exact counterpart. In the time domain investigation, it is found that the bottom-chamber concentration is very sensitive to the value of the macropore effective diffusivity. Therefore this concentration could be used to extract diffusivity by fitting in the time domain. The bottom-chamber concentration is also sensitive to flow rate, pellet length chamber volume and the type of input (step and square input).