A guide to the construction of the DGSM Nottingham Melton Lithoframe 250K model

This report describes the rationale behind the construction of the Nottingham Melton Lithoframe 250K GOCAD model. This work was carried out between April 2001-March 2005, as part of the Nottingham Melton DGSM-UK project (E1362S96 Task 06). This model comprises the area of the combined Nottingham and Melton 50K geological map sheets

Vinculin binding angle in podosomes revealed by high resolution microscopy

Podosomes are highly dynamic actin-rich adhesive structures formed predominantly by cells of the monocytic lineage, which degrade the extracellular matrix. They consist of a core of F-actin and actin-regulating proteins, surrounded by a ring of adhesion-associated proteins such as vinculin. We have characterised the structure of podosomes in macrophages, particularly the structure of the ring, using three super-resolution fluorescence microscopy techniques: stimulated emission depletion microscopy, structured illumination microscopy and localisation microscopy. Rather than being round, as previously assumed, we found the vinculin ring to be created from relatively straight strands of vinculin, resulting in a distinctly polygonal shape. The strands bind preferentially at angles between 116° and 135°. Furthermore, adjacent vinculin strands are observed nucleating at the corners of the podosomes, suggesting a mechanism for podosome growth

Drivers of the Distribution of Fisher Effort at Lake Alaotra, Madagascar

Understanding how fishers make decisions is important for improving management of fisheries. There is debate about the extent to which small-scale fishers follow an ideal free distribution (IFD) – distributing their fishing effort efficiently according to resource availability, rather than being influenced by social factors or personal preference. Using detailed data from 1,800 fisher catches and from semi-structured interviews with over 700 fishers at Lake Alaotra, the largest inland fishery in Madagascar, we showed that fishers generally conformed to the IFD. However, there were differences in catch:effort relationships between fishers using different gear types as well as other revealing deviations from the predictions of IFD. Fishers report routine as the primary determinant of their choice of fishing location, explaining why they do not quickly respond to changes in catch at a site. Understanding the influences on fishers’ spatial behaviour will allow better estimates of costs of fishing policies on resource users, and help predict their likely responses. This information can inform management strategies to minimise the negative impacts of interventions, increasing local support and compliance with rules

On the idempotents of Hecke algebras

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu--Markov trace of the idempotents.Comment: 11 page

On the Representation Theory of an Algebra of Braids and Ties

We consider the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for ${\cal E}_n(u)$ and show that this is faithful. We use it to give a basis for ${\cal E}_n(u)$ and to classify its irreducible representations.Comment: 24 pages. Final version. To appear in Journal of Algebraic Combinatorics

Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if $K_{n=1}^{\infty}a_{n}/b_{n}$ is the even part); (ii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.Comment: 16 page

Excitation of High-Spin States by Inelastic Proton Scattering

This work was supported by National Science Foundation Grant PHY 76-84033 and Indiana Universit

Excitation of High-Spin States by Inelastic Proton Scattering

This work was supported by National Science Foundation Grant PHY 75-00289 and Indiana Universit