On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Mathematical images in advertising: constructing difference and shaping identity, in global consumer culture

Mathematics educators have long emphasised the importance of attitudes and feelings towards mathematics, as crucial in motivating (or not) its learning and use, and as influenced in turn by its social images. This paper is about images of mathematics. Our search for advertisements containing such images of in UK daily newspapers, during 2006-2008, found that 4.7% of editions included a ‘mathematical’ advert, compared with 1.7% in pilot work for 1994-2003. The incidence varied across type of newspaper, being correlated with class and gender profiles of the readership. Three-quarters of advertisements were classified as containing only very simple mathematics. ‘Semiotic-discursive’ analysis of selected advertisements suggests that they draw on mathematics not to inform, but to connote qualities like precision, certainty and authority. We discuss the discourse on mathematics in advertising as ‘quasi-pedagogic’ discourse, and argue that its oversimplified forms, being empty of mathematical content, become powerful means for regulating and ‘pedagogising’ today’s global consumers

A case of learning mathematics the hard way as a teaching assistant

This paper develops early data from a qualitative longitudinal study of the first cohort of five students making the transition from teaching assistant in secondary school to specialist teacher of secondary mathematics. Data from a second cohort of four women and one man starting in 2003 is less complete, but used as appropriate. Bernstein's work on subject classification frames an argument that this student group navigates simultaneously two mathematics discourses: hard university mathematics, and everyday mathematics as experienced by the lower ability school pupils that the students support. This raises questions about the purpose and scope of the students work in school with respect to their mathematics learning, and vice versa. The study of conventional mathematics undergraduates for the ESRC (Macrae, Brown, and Rodd, 2003) provides a foil against which to compare approaches to learning mathematics, raising the possibility of a rethink of pre-requisite pre-qualification, and potential relations between university mathematics and work-place learning in secondary schools

Endophenotypes in a Dynamically Connected Brain

We examined the longitudinal genetic architecture of three parameters of functional brain connectivity. One parameter described overall connectivity (synchronization likelihood, SL). The two others were derived from graph theory and described local (clustering coefficient, CC) and global (average path length, L) aspects of connectivity. We measured resting state EEG in 1,438 subjects from four age groups of about 16, 18, 25 and 50 years. Developmental curves for SL and L indicate that connectivity is more random at adolescence and old age, and more structured in middle-aged adulthood. Individual variation in SL and L were moderately to highly heritable at each age (SL: 40–82%; L: 29–63%). Genetic factors underlying these phenotypes overlapped. CC was also heritable (25–49%) but showed no systematic overlap with SL and L. SL, CC, and L in the alpha band showed high phenotypic and genetic stability from 16 to 25 years. Heritability for parameters in the beta band was lower, and less stable across ages, but genetic stability was high. We conclude that the connectivity parameters SL, CC, and L in the alpha band show the hallmarks of a good endophenotype for behavior and developmental disorders

Development of a nurse home visitation intervention for intimate partner violence

<p>Abstract</p> <p>Background</p> <p>Despite an increase in knowledge about the epidemiology of intimate partner violence (IPV), much less is known about interventions to reduce IPV and its associated impairment. One program that holds promise in preventing IPV and improving outcomes for women exposed to violence is the Nurse-Family Partnership (NFP), an evidence-based nurse home visitation program for socially disadvantaged first-time mothers. The present study developed an intervention model and modification process to address IPV within the context of the NFP. This included determining the extent to which the NFP curriculum addressed the needs of women at risk for IPV or its recurrence, along with client, nurse and broader stakeholder perspectives on how best to help NFP clients cope with abusive relationships.</p> <p>Methods</p> <p>Following a preliminary needs assessment, an exploratory multiple case study was conducted to identify the core components of the proposed IPV intervention. This included qualitative interviews with purposeful samples of NFP clients and community stakeholders, and focus groups with nurse home visitors recruited from four NFP sites. Conventional content analysis and constant comparison guided data coding and synthesis. A process for developing complex interventions was then implemented.</p> <p>Results</p> <p>Based on data from 69 respondents, an IPV intervention was developed that focused on identifying and responding to IPV; assessing a client's level of safety risk associated with IPV; understanding the process of leaving and resolving an abusive relationship and system navigation. A need was identified for the intervention to include both universal elements of healthy relationships and those tailored to a woman's specific level of readiness to promote change within her life. A clinical pathway guides nurses through the intervention, with a set of facilitators and corresponding instructions for each component.</p> <p>Conclusions</p> <p>NFP clients, nurses and stakeholders identified the need for modifications to the existing NFP program; this led to the development of an intervention that includes universal and targeted components to assist NFP nurses in addressing IPV with their clients. Plans for feasibility testing and evaluation of the effectiveness of the IPV intervention embedded within the NFP, and compared to NFP-only, are discussed.</p

A stable pattern of EEG spectral coherence distinguishes children with autism from neuro-typical controls - a large case control study

<p>Abstract</p> <p>Background</p> <p>The autism rate has recently increased to 1 in 100 children. Genetic studies demonstrate poorly understood complexity. Environmental factors apparently also play a role. Magnetic resonance imaging (MRI) studies demonstrate increased brain sizes and altered connectivity. Electroencephalogram (EEG) coherence studies confirm connectivity changes. However, genetic-, MRI- and/or EEG-based diagnostic tests are not yet available. The varied study results likely reflect methodological and population differences, small samples and, for EEG, lack of attention to group-specific artifact.</p> <p>Methods</p> <p>Of the 1,304 subjects who participated in this study, with ages ranging from 1 to 18 years old and assessed with comparable EEG studies, 463 children were diagnosed with autism spectrum disorder (ASD); 571 children were neuro-typical controls (C). After artifact management, principal components analysis (PCA) identified EEG spectral coherence factors with corresponding loading patterns. The 2- to 12-year-old subsample consisted of 430 ASD- and 554 C-group subjects (n = 984). Discriminant function analysis (DFA) determined the spectral coherence factors' discrimination success for the two groups. Loading patterns on the DFA-selected coherence factors described ASD-specific coherence differences when compared to controls.</p> <p>Results</p> <p>Total sample PCA of coherence data identified 40 factors which explained 50.8% of the total population variance. For the 2- to 12-year-olds, the 40 factors showed highly significant group differences (<it>P </it>< 0.0001). Ten randomly generated split half replications demonstrated high-average classification success (C, 88.5%; ASD, 86.0%). Still higher success was obtained in the more restricted age sub-samples using the jackknifing technique: 2- to 4-year-olds (C, 90.6%; ASD, 98.1%); 4- to 6-year-olds (C, 90.9%; ASD 99.1%); and 6- to 12-year-olds (C, 98.7%; ASD, 93.9%). Coherence loadings demonstrated reduced short-distance and reduced, as well as increased, long-distance coherences for the ASD-groups, when compared to the controls. Average spectral loading per factor was wide (10.1 Hz).</p> <p>Conclusions</p> <p>Classification success suggests a stable coherence loading pattern that differentiates ASD- from C-group subjects. This might constitute an EEG coherence-based phenotype of childhood autism. The predominantly reduced short-distance coherences may indicate poor local network function. The increased long-distance coherences may represent compensatory processes or reduced neural pruning. The wide average spectral range of factor loadings may suggest over-damped neural networks.</p

Quality of life and home enteral tube feeding: a French prospective study in patients with head and neck or oesophageal cancer

A prospective study was conducted to evaluate the impact of home enteral tube feeding on quality of life in 39 consecutive patients treated for head and neck or oesophageal cancer at the Centre François Baclesse in Caen, France. Patients were taken as their own controls. Quality of life was evaluated using the EORTC QLQ-C30 core questionnaire, and the EORTC H&N35 and OES24 specific questionnaires. The feeding technique tolerance was evaluated using a questionnaire specifically developed for this study. Two evaluations were made, the first a week after hospital discharge (n = 39) and the second 3 weeks later (n = 30). Overall, the global health status/quality of life scale score slightly improved; among symptoms, scale scores that significantly improved (P< 0.05) concerned constipation, coughing, social functioning and body image/sexuality. The physical feeding technique tolerance was acceptable while the technique was psychologically less tolerated with two-thirds of the patients longing to have the tube removed. Onethird of the patients was also uncomfortable about their body image. Home enteral tube feeding was responsible for not visiting family or close relations in 15% of patients, and not going out in public in 23%. We conclude that home enteral tube feeding is a physically well accepted technique although a substantial proportion of patients may experience psychosocial distress. © 2000 Cancer Research Campaig