3,737 research outputs found
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 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
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