On the complete integrability of the discrete Nahm equations

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed

Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops

This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample

Validation of the Scale for the Assessment of Illness Behavior (SAIB) in a community sample of elderly people.

The aim of this study was to evaluate the construct validity of the SAIB in a community sample of elderly people. The SAIB was administered to a large community sample representative of the German population aged 60-85 years (n=1593). The original model was assessed and then refined through confirmatory and exploratory factor analyses. Criterion validity was evaluated by comparing SAIB scores with external criteria in 3 categories: subjective health, chronic illness and health care utilization. The originally suggested five factor structure of the SAIB yielded a comparative fit index (CFI) of 0.70 and the weighted root mean square residual (WRMR) was 3.68. A shortened questionnaire with 13 items and four factors resulted in better model fit (CFI 0.97 and WRMR 1.3). Correlations between subjective health and the new scales ranged from 0.06 to 0.33. Effect sizes (Cohens d) of mean differences in factor scores between those with and without healthcare system contact varied by healthcare type, ranging from 0.05 to 0.94; effect sizes were largest in relation to contact with psychotherapy and alternative medicine practitioners. We propose a shortened version of the SAIB with a different scale structure, which resulted in better model fit with our data. Neither the original nor revised SAIB appeared to discriminate well in terms of health care use, suggesting that the illness behavior as currently conceptualized may not fully explain the increased use of healthcare in the elderly

Collective excitations and instability of an optical lattice due to unbalanced pumping

We solve self-consistently the coupled equations of motion for trapped particles and the field of a one-dimensional optical lattice. Optomechanical coupling creates long-range interaction between the particles, whose nature depends crucially on the relative power of the pump beams. For asymmetric pumping, traveling density wave-like collective oscillations arise in the lattice, even in the overdamped limit. Increasing the lattice size or pump asymmetry these waves can destabilize the lattice.Comment: 5 pages, minor changes (SI units, new references

Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.Comment: 5 pages, 3 figures. Minor correction