Random Triangle Theory with Geometry and Applications

What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much more. One of the best distributions of random triangles takes all six vertex coordinates as independent standard Gaussians. Six can be reduced to four by translation of the center to $(0,0)$ or reformulation as a 2x2 matrix problem. In this note, we develop shape theory in its historical context for a wide audience. We hope to encourage other to look again (and differently) at triangles. We provide a new constructive proof, using the geometry of parallelians, of a central result of shape theory: Triangle shapes naturally fall on a hemisphere. We give several proofs of the key random result: that triangles are uniformly distributed when the normal distribution is transferred to the hemisphere. A new proof connects to the distribution of random condition numbers. Generalizing to higher dimensions, we obtain the "square root ellipticity statistic" of random matrix theory. Another proof connects the Hopf map to the SVD of 2 by 2 matrices. A new theorem describes three similar triangles hidden in the hemisphere. Many triangle properties are reformulated as matrix theorems, providing insight to both. This paper argues for a shift of viewpoint to the modern approaches of random matrix theory. As one example, we propose that the smallest singular value is an effective test for uniformity. New software is developed and applications are proposed

Inspection based evaluations

Usability inspection methods (UIMs) remain an important discount method for usability evaluation. They can be applied to any designed artefact during development: a paper prototype, a storyboard, a working prototype (e.g., in Macromedia Flash™ or in Microsoft PowerPoint™), tested production software, or an installed public release. They are analytical evaluation methods, which involve no typical end users, unlike empirical methods such as user testing. UIMs only require availability of a designed artefact and trained analysts. Thus, evaluation is possible with low resources (hence discount methods). Although risks arise from low resources, well-informed practices disproportionately improve analyst performance, improving cost-benefit ratios. This chapter introduces UIMs, covering six and one further method, and provides approaches to assessing existing, emerging and future UIMs and their effective uses

Falsification testing for usability inspection method assessment

We need more reliable usability inspection methods (UIMs), but assessment of UIMs has been unreliable [5]. We can only reliably improve UIMs if we have more reliable assessment. When assessing UIMs, we need to code analysts’ predictions as true or false positives or negatives, or as genuinely missed problems. Defenders of UIMs often claim that false positives cannot be accurately coded, i.e., that a prediction is true but has never shown up through user testing or other validation approaches. We show this and similar claims to be mistaken by briefly reviewing methods for reliable coding of each of five types of prediction outcome. We focus on falsification testing, which allows confident coding of false positives

Work and Poverty During Economic Restructuring:

Summaries Colombia escaped the worst of the debt crisis and has voluntarily adopted the kind of economic restructuring advocated by the World Bank and the IMF. Its experience represents a partial test of the effects of neo?liberal economic policy on the urban poor. Employment trends in Bogotá suggest that many of the fears about economic restructuring are unjustified. Despite liberalisation and a doubling in the numbers seeking work, unemployment rates have fallen. Jobs have been created, although principally in the informal sector. Feminisation has been operating very strongly in Bogotá and the sexual division of labour has begun to change. Since 1970 poverty in Bogotá has become both less common and less serious. If households are less poor, however, it is principally because more adults are working. Real personal incomes during the 1990s declined. If less people are hungry, every adult is also a great deal busier

Creative Worthwhile Interaction Design

Over the last two decades, creative, agile, lean and strategic design approaches have become increasingly prevalent in the development of interactive technologies, but tensions exist with longer established approaches such as human factors engineering and user-centered design. These tensions can be harnessed productively by first giving equal status in principle to creative, business and agile engineering practices, and then supporting this with flexible critical approaches and resources that can balance and integrate a range of multidisciplinary design practices

The 1985/1986 Amendments to the Comprehensive Environmental Response, Compensation, and Liability Act: A Background Paper

20 pages. Contains 2 attachments

The Heterogeneity, Distribution, and Environmental Associations of Borrelia burgdorferi Sensu Lato, the Agent of Lyme Borreliosis, in Scotland

Genospecies controls were obtained from the laboratory of Dr. Muriel Cornet at the Institut Pasteur, Paris. We thank Bob Furness for collecting ticks from passerine birds, Steph Vollmer for processing the samples from one site, E. Packer, A. Wiebe, J. Low, E. Stephen, and J. Arthur for help collecting ticks, Kenny Raey for laboratory assistance, and Jackie Potts for statistical advice. Marianne C. James was funded by a Biotechnology and Biological Sciences Research Council (BBSRC) Doctoral Training Grant with CASE support from the Macaulay Development Trust awarded to Alan S. Bowman and Lucy Gilbert. Lucy Gilbert was supported by the Scottish Government’s Rural and Environment Science and Analytical Services Division (RESAS).Peer reviewedPublisher PD

Medical aspects of partial gastrectomy: a review of seventy-five cases

Seventy -five cases of partial gastrectomy for peptic ulceration have been reviewed. The site of the lesion was in twenty -seven instances gastric, forty duodenal, and eight stomal, and the sex relation sixty -four males to eleven females. The investigations have been essentially those of interest to the physician, but the results are of mutual interest to surgeon and physician alike.The object of this review was twofold. Firstly in order that we might investigate the cause of the lack of success which not infrequently follows this procedure. Secondly, in light of the recent adoption of vagal section in the therapy of peptic ulcer, it is necessary that we be au fait with the results of partial gastrectomy, the gauge by which the results of vagal section will be judged.The method of selecting patients for investigation has been explained. As Hollander and Mage (1943) have pointed out the results of a series of patients admitted for follow up investigations can be applied to the patients not investigated but subjected to similar therapy for a similar complaint.CLASSIFICATION OF RESULTS - A rigid classification of results was laid down. The three criteria of classification being the relief of ulcer symptoms, the post- operative working capacity and the presence or absence of new symptoms directly / attributable 197. attributable to the operation. Results were grouped into four categories - cured, improved, in statu quo, and failures. The cured and improved patients were labelled satisfactory and the in statu quo and failures unsatisfactory.RESULTS IN GENERAL - Cured 38.66 per cent; improved 26.66 per cent i.e. 65.32 per cent satisfactory. In statu quo 10.66 per cent and failures 24 per cent, i.e. unsatisfactory 34.66 per cent. The percentage of satisfactory results is below the published figures of most authorities.Following simple medical therapy such as the correction of anaemia, and dietetic therapy for post -prandial distension, there was an increase in the percentage of satisfactory results to 72 per cent. This illustrates the importance of an adequate follow up chiefly by a physician.Throughout the whole series the results of partial gastrectomy were much less satisfactory in females than males. On admission the sex difference in satisfactory results was males 71.87 per cent, females 27.27 per cent. The poor results in women were greatly improved following simple medical therapy increasing the percentage of satisfactory results to 54.54 per cent.RESULTS IN RELATION TO SITE OF LESION - On admission patients operated on for duodenal ulcer gave the highest percentage of satisfactory results 70 per cent. gastric ulcer 66.66 per cent, stomal ulcer 37.5 per cent. Most authorities / state 198. state results to be superior following resection for gastric ulcer. The poorer results in our series were we believe due to the large percentage of females in the gastric ulcer group - eight out of twenty- seven. The poorer results in females would therefore explain the less satisfactory results for that group.Following simple medical therapy, however, the results were superior in the gastric ulcer group - 77.04 per cent satisfactory.In general the results of partial gastrectomy tended to deteriorate with time.INDICATIONS FOR PARTIAL GASTRECTOMY - Intra.ctable pain was the commonest indication in this series. The results were best when the operation was performed for recurrent bleeding, 83.33 per cent satisfactory. Stornai ulcer gave the poorest results.POST OPERATIVE :PERIOD PRIOR TO RETURN TO WORK AND WORKING CAPACITY - Of the patients returning to work 75 per cent did so in the first six post operative months. In general early return to work and good results were parallel.Fifty -four patients had a post operative working capacity of between 75 and 100 per cent, forty of whom were 100 per cent. Males recovered their working capacity more completely and more readily than did females.POST OPERATIVE TEST MEALS - The special technique used has been described. Using the non histamine / test 199. test meal, aehlorhydria was present in 92.5 per cent of patients with resection for gastric ulcer 55 per cent for duodenal ulcer and 75 per cent for stomal ulcer. Using the histamine test the incidence of aehlorhydria was 85.55 per cent in the gastric ulcer group and 40 per cent in the duodenal ulcer group, the stomal group remaining unchanged at 75 per cent.The most significant single finding in the test meals was free acid in the fasting juice. Such a finding was invariably accompanied by a high free acid in the test meal.There was no significant difference in the results of the achlorhydric patients and those showing free acid. The presence rather than the absence of pepsin in the post -operative test meal was associated with favourable results. POST -OPERATIVE GASTRIC EMPTYING TIME AND POST PRANDIAL DISTENSION - Almost invariably the period of gastric evacuation is markedly diminished by the operation of partial gastrectomy. Basing the results on the period of gastric evacuation we failed to note any correlation between a prolonged evacuation period and satisfactory results.Thirty -eight patients suffered from post prandial distension in the first few post -operative months, and twenty mild symptoms after six months. The cause of the symptoms, we believe, is the small gastric remnant which had not yet distended sufficiently to cope with a full meal. .We found / no 200. no support for the suggestion that post- operative hypoproteinaemia causing stomal obstruction was the basis of post prandial distension.HYPOGLYCAEMIA AND THE DUMPING SYNDROME - Post prandial hypoglycaemia occurred in seventeen out of forty -five consecutive patients on whom a partial gastrectomy had been performed for peptic ulcer, and constituted the commonest complication of the operation in this series.The symptoms produced were severe enough in five patients to preclude them from earning a livelihood.It is suggested that rapid gastric evacuation is the basis of this hypoglycaemia, and that the "dumping" syndrome has identical clinical manifestations and an identical aetiology, so that the two conditions need not be distinguished.The most effective method of treatment has proved to be a high-fat diet, six small meals a day instead of three large ones, and 1/2 gr. (32 mg.) of ephedrine before the three main meals.Carbohydrate, fat, protein and vitamine absorption was normal. There were no cases of chronic post -gastrectomy diarrhoea.POST OPERATIVE WEIGHT -.Pre -operatively all patients were below their correct weight varying from -2 to -58 lbs. Following resection forty - five gained weight, the average being 11.6 lbs. while thirty lost weight, the average being 10.6 lbs. Failure to gain weight was more marked in females..There is a very close correlation between post -operative gain in weight and satisfactory results.The details of three patients, fully investigated in relation to post -operative weight were given. We concluded that failure to gain weight in spite of an adequate calorific intake was due not to malabsorption but failure to utilise protein which was rapidly excreted in the urine. Testosterone had some effect in improving the nitrogen balance in one such case. The cause of this failure to utilise protein is problematical.SERUM CALCIUM - Was normal in all but three patients, two males and one female. All had had previous perforations before the partial gastrectomy was performed - the woman three times and one man three times. The rarity of perforations in women has been remarked upon. There was no relationship between achlorhydria and the serum calcium. Is a low serum calcium a factor in causing a duodenal ulcer to perforate?POST -OPERATIVE HAEMOPOIESIS - There was no evidence of macrocytic anaemia. Twenty patients suffered from microcytic hypochromic and normochronic anaemia, of whom six had a haemoglobin of less than 80 per cent. The incidence of anaemia was greater in females than in males, and in the gastric ulcer group than in the duodenal group. The high proportion of females in the gastric ulcer group would therefore account for the higher incidence of anaemia. Based on the histamine test we found no correlation between achlorhydria and anaemia. Using the non -histamine test, however, there was a greater incidence of achlorhydria in the anaemic group.A marked parallel existed between poor results and severe anaemia, and between the incidence of anaemia and the length of the post -operative period. All cases of anaemia responded to ferrous sulphate