An Algorithm to Simplify Tensor Expressions

The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations and the renaming of dummy indices. The tensor indices are split into classes and a natural place for them is defined. The canonical form is the closest configuration to the natural configuration. In the second part, the Groebner basis method is used to simplify tensor expressions which obey the linear identities that come from cyclic symmetries (or more general tensor identities, including non-linear identities). The algorithm is suitable for implementation in general purpose computer algebra systems. Some timings of an experimental implementation over the Riemann package are shown.Comment: 15 pages, Latex2e, submitted to Computer Physics Communications: Thematic Issue on "Computer Algebra in Physics Research

Encouraging versatile thinking in algebra using the computer

In this article we formulate and analyse some of the obstacles to understanding the notion of a variable, and the use and meaning of algebraic notation, and report empirical evidence to support the hypothesis that an approach using the computer will be more successful in overcoming these obstacles. The computer approach is formulated within a wider framework ofversatile thinking in which global, holistic processing complements local, sequential processing. This is done through a combination of programming in BASIC, physical activities which simulate computer storage and manipulation of variables, and specific software which evaluates expressions in standard mathematical notation. The software is designed to enable the user to explore examples and non-examples of a concept, in this case equivalent and non-equivalent expressions. We call such a piece of software ageneric organizer because if offers examples and non-examples which may be seen not just in specific terms, but as typical, or generic, examples of the algebraic processes, assisting the pupil in the difficult task of abstracting the more general concept which they represent. Empirical evidence from several related studies shows that such an approach significantly improves the understanding of higher order concepts in algebra, and that any initial loss in manipulative facility through lack of practice is more than made up at a later stage

Long-Term Potentiation: One Kind or Many?

Do neurobiologists aim to discover natural kinds? I address this question in this chapter via a critical analysis of classification practices operative across the 43-year history of research on long-term potentiation (LTP). I argue that this 43-year history supports the idea that the structure of scientific practice surrounding LTP research has remained an obstacle to the discovery of natural kinds

Short-term efficacy of physical interventions in osteoarthritic knee pain. A systematic review and meta-analysis of randomised placebo-controlled trials.

BACKGROUND: Treatment efficacy of physical agents in osteoarthritis of the knee (OAK) pain has been largely unknown, and this systematic review was aimed at assessing their short-term efficacies for pain relief. METHODS: Systematic review with meta-analysis of efficacy within 1-4 weeks and at follow up at 1-12 weeks after the end of treatment. RESULTS: 36 randomised placebo-controlled trials (RCTs) were identified with 2434 patients where 1391 patients received active treatment. 33 trials satisfied three or more out of five methodological criteria (Jadad scale). The patient sample had a mean age of 65.1 years and mean baseline pain of 62.9 mm on a 100 mm visual analogue scale (VAS). Within 4 weeks of the commencement of treatment manual acupuncture, static magnets and ultrasound therapies did not offer statistically significant short-term pain relief over placebo. Pulsed electromagnetic fields offered a small reduction in pain of 6.9 mm [95% CI: 2.2 to 11.6] (n = 487). Transcutaneous electrical nerve stimulation (TENS, including interferential currents), electro-acupuncture (EA) and low level laser therapy (LLLT) offered clinically relevant pain relieving effects of 18.8 mm [95% CI: 9.6 to 28.1] (n = 414), 21.9 mm [95% CI: 17.3 to 26.5] (n = 73) and 17.7 mm [95% CI: 8.1 to 27.3] (n = 343) on VAS respectively versus placebo control. In a subgroup analysis of trials with assumed optimal doses, short-term efficacy increased to 22.2 mm [95% CI: 18.1 to 26.3] for TENS, and 24.2 mm [95% CI: 17.3 to 31.3] for LLLT on VAS. Follow-up data up to 12 weeks were sparse, but positive effects seemed to persist for at least 4 weeks after the course of LLLT, EA and TENS treatment was stopped. CONCLUSION: TENS, EA and LLLT administered with optimal doses in an intensive 2-4 week treatment regimen, seem to offer clinically relevant short-term pain relief for OAK

Accounting Problems Under the Excess Profits Tax

DNA vaccines based on subunits from pathogens have several advantages over other vaccine strategies. DNA vaccines can easily be modified, they show good safety profiles, are stable and inexpensive to produce, and the immune response can be focused to the antigen of interest. However, the immunogenicity of DNA vaccines which is generally quite low needs to be improved. Electroporation and co-delivery of genetically encoded immune adjuvants are two strategies aiming at increasing the efficacy of DNA vaccines. Here, we have examined whether targeting to antigen-presenting cells (APC) could increase the immune response to surface envelope glycoprotein (Env) gp120 from Human Immunodeficiency Virus type 1 (HIV- 1). To target APC, we utilized a homodimeric vaccine format denoted vaccibody, which enables covalent fusion of gp120 to molecules that can target APC. Two molecules were tested for their efficiency as targeting units: the antibody-derived single chain Fragment variable (scFv) specific for the major histocompatilibility complex (MHC) class II I-E molecules, and the CC chemokine ligand 3 (CCL3). The vaccines were delivered as DNA into muscle of mice with or without electroporation. Targeting of gp120 to MHC class II molecules induced antibodies that neutralized HIV-1 and that persisted for more than a year after one single immunization with electroporation. Targeting by CCL3 significantly increased the number of HIV-1 gp120-reactive CD8(+) T cells compared to non-targeted vaccines and gp120 delivered alone in the absence of electroporation. The data suggest that chemokines are promising molecular adjuvants because small amounts can attract immune cells and promote immune responses without advanced equipment such as electroporation.Funding Agencies|Research Council of Norway; Odd Fellow</p

Industrial diversification: its relation to selected indices of urban development

Thesis (M.C.P.)--Massachusetts Institute of Technology, Dept. of City and Regional Planning, 1964.Includes bibliographical references (leaves 97-100).by Norma R. Bogen.M.C.P

The influence of individual cognitive style on performance in management education

This paper reports the outcomes of an empirical study undertaken to explore the possibility that cognitive style may be an important factor influencing performance on certain types of task in management education. Four hundred and twelve final-year undergraduate degree students studying management and business administration were tested using the Allinson-Hayes Cognitive Style Index. Their cognitive styles were then compared with assessment grades achieved for academic modules, the task categories of which were deemed to be consonant with either the wholist/intuitive or the analytic style of working. Overall ability defined by final degree grades was also tested against individuals’ cognitive styles. As expected, students whose dominant cognitive styles were analytic attained higher grades for long term solitary tasks involving careful planning and analysis of information. However, contrary to expectations, performance on tasks believed to be more suited to the wholist/intuitive style was also higher for analytic individuals, as was overall ability defined by final degree grades. The results were discussed in terms of the nature of the tasks and the need for methods of performance assessment that are independent of an orientation bias. Without this, it is argued, employment selection criteria may favour the wrong type of candidate in some circumstances

Classificatory Theory in Data-Intensive Science: The Case of Open Biomedical Ontologies

publication-status: Publishedtypes: ArticleThis is the author's version of a paper that was subsequently published in International Studies in the Philosophy of Science. Please cite the published version by following the DOI link.Knowledge-making practices in biology are being strongly affected by the availability of data on an unprecedented scale, the insistence on systemic approaches and growing reliance on bioinformatics and digital infrastructures. What role does theory play within data-intensive science, and what does that tell us about scientific theories in general? To answer these questions, I focus on Open Biomedical Ontologies, digital classification tools that have become crucial to sharing results across research contexts in the biological and biomedical sciences, and argue that they constitute an example of classificatory theory. This form of theorizing emerges from classification practices in conjunction with experimental know-how and expresses the knowledge underpinning the analysis and interpretation of data disseminated online.Economic and Social Research Council (ESRC)The British AcademyLeverhulme Trus