Biomagnetism and Ferritin Final Report

Methods for determining iron content in frog embryos and ferritin in rat intestine section

Popularity-Driven Networking

We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional to the degrees of the two nodes. Interestingly, this network exhibits two abrupt transitions, both occurring at finite times. The first is a percolation transition in which a giant component, containing a finite fraction of all nodes, is born. The second is a condensation transition in which the entire system condenses into a single, fully connected, component. We derive the size distribution of connected components as well as the degree distribution, which is purely exponential throughout the evolution. Furthermore, we present a criterion for the emergence of sudden condensation for general homogeneous connection rates.Comment: 5 pages, 2 figure

Superconformal Algebras and Mock Theta Functions

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of N=4 superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kahler manifolds in higher dimensions. In particular we determine the elliptic genera in the case of complex 4 dimensions of the Hilbert scheme of points on K3 surfaces K^{[2]} and complex tori A^{[[3]]}.Comment: 28 page

Revenue divergence and competitive balance in a divisional sports league

The North American model of resource allocation in professional sports leagues is adapted for English (association) football. The theoretical relationship between revenue and competitive balance is shown to be robust with respect to changes in teams’ objectives and labour market conditions. Empirical revenue functions are reported for 1926-1999. These indicate a shift in the composition of demand favouring big-city teams and an increase in the sensitivity of revenue to performance. An analysis of match results in the FA Cup competition suggests an increase in competitive imbalance between teams at different levels of the league’s divisional hierarchy, as the theory suggests

Silica stable isotopes and silicification in a carnivorous sponge Asbestopluma sp.

The stable isotope composition of benthic sponge spicule silica is a potential source of palaeoceanographic information about past deep seawater chemistry. The silicon isotope composition of spicules has been shown to relate to the silicic acid concentration of ambient water, although existing calibrations do exhibit a degree of scatter in the relationship. Less is known about how the oxygen isotope composition of sponge spicule silica relates to environmental conditions during growth. Here, we investigate the vital effects on silica, silicon and oxygen isotope composition in a carnivorous sponge, Asbestopluma sp., from the Southern Ocean. We find significant variations in silicon and oxygen isotopic composition within the specimen that are related to unusual spicule silicification. The largest variation in both isotope systems was associated with the differential distribution of an unconventional, hypersilicified spicule type (desma) along the sponge body. The absence an internal canal in the desmas suggests an unconventional silicification pattern leading to an unusually heavy isotope signature. Additional internal variability derives from a systematic offset between the peripheral skeleton of the body having systematically a higher isotopic composition than the internal skeleton. A simplified silicon isotope fractionation model, in which desmas were excluded, suggests that the lack of a system for seawater pumping in carnivorous sponges favours a low replenishment of dissolved silicon within the internal tissues, causing kinetic fractionation during silicification that impacts the isotope signature of the internal skeleton. Analysis of multiple spicules should be carried out to "average out" any artefacts in order to produce more robust downcore measurements

Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This consequently provides the solution for the exponential $e^{\lambda(q(a^\dag)a+v(a^\dag))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics "Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005), Myczkowce, Poland. 13 pages, 31 reference

Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms

A Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms has recently been proposed. Using a numerical procedure developed by McCoy et al., we find significant evidence that this solution can yield the complete set of eigenvalues for generic values of the bulk and boundary parameters satisfying one linear relation. Moreover, our results suggest that this solution is practical for investigating the ground state of this model in the thermodynamic limit.Comment: 15 pages, LaTeX; amssymb, amsmath, no figures, 5 tables; v2 contains an additional footnote and a "Note Added"; v3 contains an Addendu

Approximate substitutions and the normal ordering problem

In this paper, we show that the infinite generalised Stirling matrices associated with boson strings with one annihilation operator are projective limits of approximate substitutions, the latter being characterised by a finite set of algebraic equations

Effects of diet and exercise on weight-related outcomes for breast cancer survivors and their adult daughters: an analysis of the DAMES trial

Purpose Few trials have aimed to promote diet and exercise behaviors in both cancer survivors and their family members and examine their associations with weight-related outcomes. We conducted a secondary analysis to examine associations between change in diet and exercise behaviors and weight-related outcomes for overweight breast cancer survivors and their overweight adult daughters in the Daughters And MothErS Against Breast Cancer (DAMES) randomized trial. Methods The DAMES trial assessed the impact of two iteratively tailored, mailed print diet and exercise interventions against standard brochures over a 12-month period. This analysis examined change in diet and exercise behaviors and weight-related variables from baseline to post-intervention for the 50 breast cancer survivors and their adult daughters randomized to the intervention arms. To reduce the potential for type II error in this pilot, p values <0.10 were considered statistically significant. Results For mothers, change in diet quality was uniquely related to change in BMI (β = −0.12, p = 0.082), weight (β = −0.12, p = 0.060), and waist circumference (β = −0.38, p = 0.001), whereas change in caloric intake was related to waist circumference (β = 0.21, p = 0.002). For daughters, change in caloric intake was related to change in waist circumference (β = 0.12, p = 0.055). However, change in diet quality was not associated with weight-related outcomes in daughters. Additionally, change in exercise was not associated with weight-related outcomes in mothers or daughters. Conclusions Findings support mail-based and other tailored interventions for weight loss in this population, with an emphasis on diet quality for breast cancer survivors and caloric intake for their adult daughters

Entropy calculation for a toy black hole

In this note we carry out the counting of states for a black hole in loop quantum gravity, however assuming an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a nice and simplifying `laboratory' for questions about the full theory.Comment: 18 pages, 4 figures. v2: Corrected mistake in bibliography, added appendix with further result