Formal deformations, contractions and moduli spaces of Lie algebras

Jump deformations and contractions of Lie algebras are inverse concepts, but the approaches to their computations are quite different. In this paper, we contrast the two approaches, showing how to compute jump deformations from the miniversal deformation of a Lie algebra, and thus arrive at the contractions. We also compute contractions directly. We use the moduli spaces of real 3-dimensional and complex 3 and 4-dimensional Lie algebras as models for explaining a deformation theory approach to computation of contractions.Comment: 27 page

The virtual haptic back: A simulation for training in palpatory diagnosis

<p>Abstract</p> <p>Background</p> <p>Models and simulations are finding increased roles in medical education. The Virtual Haptic Back (VHB) is a virtual reality simulation of the mechanical properties of the human back designed as an aid to teaching clinical palpatory diagnosis.</p> <p>Methods</p> <p>Eighty-nine first year medical students of the Ohio University College of Osteopathic Medicine carried out six, 15-minute practice sessions with the VHB, plus tests before and after the sessions in order to monitor progress in identifying regions of simulated abnormal tissue compliance. Students palpated with two digits, fingers or thumbs, by placing them in gimbaled thimbles at the ends of PHANToM 3.0^®haptic interface arms. The interface simulated the contours and compliance of the back surface by the action of electric motors. The motors limited the compression of the virtual tissues induced by the palpating fingers, by generating counterforces. Users could see the position of their fingers with respect to the back on a video monitor just behind the plane of the haptic back. The abnormal region varied randomly among 12 locations between trials. During the practice sessions student users received immediate feedback following each trial, indicating either a correct choice or the actual location of the abnormality if an incorrect choice had been made. This allowed the user to feel the actual abnormality before going on to the next trial. Changes in accuracy, speed and Weber fraction across practice sessions were analyzed using a repeated measures analysis of variance.</p> <p>Results</p> <p>Students improved in accuracy and speed of diagnosis with practice. The smallest difference in simulated tissue compliance users were able to detect improved from 28% (SD = 9.5%) to 14% (SD = 4.4%) during the practice sessions while average detection time decreased from 39 (SD = 19.8) to 17 (SD = 11.7) seconds. When asked in anonymous evaluation questionnaires if they judged the VHB practice to be helpful to them in the clinical palpation and manual medicine laboratory, 41% said yes, 51% said maybe, and 8% said no.</p> <p>Conclusion</p> <p>The VHB has potential value as a teaching aid for students in the initial phases of learning palpatory diagnosis.</p

An analysis of first-time enquirers to the CancerBACUP information service: variations with cancer site, demographic status and geographical location

A retrospective comparison of cancer incidence data and, where relevant, population data with 16 955first-time users (patients, relatives and friends) of a national cancer information service (CancerBACUP) during the period April1995 to March 1996 is presented. The number of events observed was compared with the number of events expected, were the nationalrates of cancer incidence and population demographics apply. Standardized incidence ratios (SIRs) (observed – expectedratios) were used to indicate any differences. Statistically significant differences (P< 0.001) in the observed andexpected sex, age and primary site distribution of patients enquired about were found. Statistically significant differences(P< 0.001) were also identified for the age, employment status, socioeconomic class and geographical location offirst-time enquirers (patients, relatives and friends). Enquiries about brain, testis and breast cancers and non-Hodgkin'slymphoma (NHL) were substantially higher than expected; enquiries about bladder, lung, stomach and colorectal cancers were muchlower than expected. As the service is provided via a freephone number, it is available to all, and users might be expected to berandomly distributed across the variables listed. The underlying reasons for the differences identified need to be investigated,and the role of information in the care of cancer patients should be formally evaluated. © 1999 Cancer Research Campaig

Biorthogonal Systems in <i>l^p</i>-Spaces

Our aim in this paper is to generalize certain ideas and results of Bary (1) on biorthogonal systems in separable Hilbert spaces to their counterparts in separable lp-spaces, 1 &lt; p.The main result of Bary is to characterize a natural generalization of the concept of orthonormal basis for a Hilbert space. That of this paper is to characterize the concept of a Bary basis which is a generalization of the idea of standard basis of an lp-space. The result is interesting for lp-spaces because of the paucity of standard bases in these spaces.Before summarizing our results, we shall introduce some notation and recall a few pertinent definitions and facts. The symbols and denote mutually conjugate lp-spaces, where is the space lt and the space lswith 1 &lt; r &lt;2 and 2 &lt; s = r/(r – 1).</jats:p