Three Dimensional Chern-Simons Theory as a Theory of Knots and Links

Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants within this field theoretic framework. The monodromy properties of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field theory on a two-dimensional sphere prove to be useful tools. The method is simple enough to yield a whole variety of new knot invariants of which the Jones polynomials are the simplest example.Comment: 45 pages (without figures

A successful clinical pilot registry of four radiation oncology practices in Africa and Ontario

A journal article on radiation oncology practices in Africa and Ontario, Canada.Cancer is a major disease category in higher-income countries (HIC), In HIC, health resources are substantial, with budgets for health care exceeding 10% of Gross Domestic Product of large economies. This resourcing is many times higher than that in low- and-middle-income countries (LMIC) where there are fewer infrastructures and less political and sociocultural support. However, cancer is an increasing concern in LMIC's due to improving longevity and the changing prevalences of etiological agents and broader determinants of disease. Indeed, global mortality from cancer exceeds that from tuberculosis, malaria and HIV-AIDS combined2, and there are many more cancer cases in LMIC than in HIC

An analogue of the BGG resolution for locally analytic principal series

Let G be a connected reductive quasisplit algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal series representations for G(L). This leads to an exact sequence involving spaces of overconvergent p-adic automorphic forms for certain groups compact modulo centre at infinity.Comment: 36 pages; corrected proof of Theorem 26; extended results to locally analytic principal series for G(L); cut unnecessary expository materia

Knot invariants from rational conformal field theories

A framework for studying knot and link invariants from any rational conformal field theory is developed. In particular, minimal models, superconformal models and $W_N$ models are studied. The invariants are related to the invariants obtained from the Wess-Zumino models associated with the coset representations of these models. Possible Chern-Simons representation of these models is also indicated. This generalises the earlier work on knot and link invariants from Chern-Simons theories.Comment: 18pages+6 figures (available on request through email

Using a cognitive architecture to examine what develops

Different theories of development propose alternative mechanisms by which development occurs. Cognitive architectures can be used to examine the influence of each proposed mechanism of development while keeping all other mechanisms constant. An ACT-R computational model that matched adult behavior in solving a 21-block pyramid puzzle was created. The model was modified in three ways that corresponded to mechanisms of development proposed by developmental theories. The results showed that all the modifications (two of capacity and one of strategy choice) could approximate the behavior of 7-year-old children on the task. The strategy-choice modification provided the closest match on the two central measures of task behavior (time taken per layer, r = .99, and construction attempts per layer, r = .73). Modifying cognitive architectures is a fruitful way to compare and test potential developmental mechanisms, and can therefore help in specifying “what develops.

Effective theory of the Delta(1232) in Compton scattering off the nucleon

We formulate a new power-counting scheme for a chiral effective field theory of nucleons, pions, and Deltas. This extends chiral perturbation theory into the Delta-resonance region. We calculate nucleon Compton scattering up to next-to-leading order in this theory. The resultant description of existing $\gamma$p cross section data is very good for photon energies up to about 300 MeV. We also find reasonable numbers for the spin-independent polarizabilities $\alpha_p$ and $\beta_p$.Comment: 29 pp, 9 figs. Minor revisions. To be published in PR

The Off-diagonal Goldberger-Treiman Relation and Its Discrepancy

We study the off-diagonal Goldberger-Treiman relation (ODGTR) and its discrepancy (ODGTD) in the N, Delta, pi sector through O(p^2) using heavy baryon chiral perturbation theory. To this order, the ODGTD and axial vector N to Delta transition radius are determined solely by low energy constants. Loop corrections appear at O(p^4). For low-energy constants of natural size, the ODGTD would represent a ~ 2% correction to the ODGTR. We discuss the implications of the ODGTR and ODGTD for lattice and quark model calculations of the transition form factors and for parity-violating electroexcitation of the Delta.Comment: 11 pages, 1 eps figur