On the Number of Nodal Domains of Toral Eigenfunctions

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov–Sodin’s results for random fields and Bourgain’s de-randomisation procedure we establish a precise asymptotic result for “generic” eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions.     

Degradation of the BAF Complex Factor BRD9 by Heterobifunctional Ligands

The bromodomain-containing protein BRD9, a subunit of the human BAF (SWI/SNF) nucleosome remodeling complex, has emerged as an attractive therapeutic target in cancer. Despite the development of chemical probes targeting the BRD9 bromodomain, there is a limited understanding of BRD9 function beyond acetyl-lysine recognition. We have therefore created the first BRD9-directed chemical degraders, through iterative design and testing of heterobifunctional ligands that bridge the BRD9 bromodomain and the cereblon E3 ubiquitin ligase complex. Degraders of BRD9 exhibit markedly enhanced potency compared to parental ligands (10- to 100-fold). Parallel study of degraders with divergent BRD9-binding chemotypes in models of acute myeloid leukemia resolves bromodomain polypharmacology in this emerging drug class. Together, these findings reveal the tractability of non-BET bromodomain containing proteins to chemical degradation, and highlight lead compound dBRD9 as a tool for the study of BRD9.     

Prediction of stress in a linear viscoelastic solid strained while cooling

A simplethermoelastic method is proposed, and justified, for predicting stresses arising during cooling of a linearviscoelastic solid. It is equivalent to representing the material by an array of spring-switch thermoelastic elements. The final stress resulting from an increment of strain is calculated using isochronal modulus data applying to the temperature at which the strain was applied, modified to accommodate temperature dependence of the limiting moduli. The method is exact for a material whose relaxation times and limiting moduli scale uniformly with change in temperature, with time-temperature shift factora _T obeying the Arrhenius equation, cooled such that reciprocal absolute temperature is linear in time. For other cooling sequences it is useful as an approximation. In particular, it assists the computational prediction of stresses arising during cooling in polymer processes.     

Towards the in vivo prediction of fragility fractures with Raman spectroscopy

Fragility fractures, those fractures which result from low level trauma, have a large and growing socio‐economic cost in countries with aging populations. Bone‐density‐based assessment techniques are vital for identifying populations that are at higher risk of fracture, but do not have high sensitivity when it comes to identifying individuals who will go on to have their first fragility fracture. We are developing Spatially Offset Raman Spectroscopy (SORS) as a tool for retrieving chemical information from bone non‐invasively in vivo. Unlike X‐ray‐based techniques SORS can retrieve chemical information from both the mineral and protein phases of the bone. This may enable better discrimination between those who will or will not go on to have a fragility fracture because both phases contribute to bone's mechanical properties. In this study we analyse excised bone with Raman spectroscopy and multivariate analysis, and then attempt to look for similar Raman signals in vivo using SORS. We show in the excised work that on average, bone fragments from the necks of fractured femora are more mineralised (by 5–10%) than (cadaveric) non‐fractured controls, but the mineralisation distributions of the two cohorts are largely overlapped. In our in vivo measurements, we observe similar, but as yet statistically underpowered, differences. After the SORS data (the first SORS measurements reported of healthy and diseased human cohorts), we identify methodological developments which will be used to improve the statistical significance of future experiments and may eventually lead to more sensitive prediction of fragility fractures. © 2015 The Authors. Journal of Raman Spectroscopy Published by John Wiley & Sons, Ltd.     

Catalyst and substituent effects on the rhodium(II)-catalysed intramolecular Buchner reaction

Intramolecular rhodium(II)-catalysed aromatic addition (Buchner) reactions of a range of α- and β-substituted α-diazoketones are reported. Both steric and electronic effects are evident for the aromatic additions investigated. In general, highly efficient aromatic addition is achieved through use of rhodium carboxylates bearing electronegative ligands, such as rhodium trifluoroacetate, while aromatic addition employing rhodium catalysts with more electron-donating ligands, such as rhodium caprolactam, is less efficient. Excellent levels of diastereoselectivity are possible for this process in the presence of rhodium acetate and rhodium caprolactam, however, a reduction in diastereocontrol is generally associated with use of the more reactive, electronegative catalysts. Interestingly, these catalyst effects can be overcome through the steric effects of the substituents on the α-diazoketone substrates, with the presence of sterically bulky substituents at the 2- or 3-position rendering the aromatic addition essentially catalyst independent in terms of efficiency and diastereocontrol.     

Solid targets for 99mTc production on medical cyclotrons

Recent disruptions in the molybdenum-technetium generator supply chain prompted a review of non-reactor based production methods for both ⁹⁹Mo and ^99mTc. Small medical cyclotrons (E _p ~ 16–24 MeV) are capable of producing Curie quantities of ^99mTc from isotopically enriched ¹⁰⁰Mo using the ¹⁰⁰Mo(p,2n)^99mTc reaction. Unlike most other metallic target materials for routine production of medical radioisotopes, molybdenum cannot be deposited by reductive electroplating from aqueous salt solutions. To overcome this issue, we developed a new process for solid molybdenum targets based on the electrophoretic deposition of fine ¹⁰⁰Mo powder onto a tantalum plate, followed by high temperature sintering. The targets obtained were mechanically robust and thermally stable when irradiated with protons at high power density.     

Multiple goal non-cooperative conflicts under uncertainty: A fuzzy set approach

This paper investigates strategy selection for a participant in a two-party non-cooperative conflict which involves both uncertainty and multiple goals. Uncertainty arises from the players not knowing the utility functions. Multiple objectives appear as the result of the payoff being a vector of prizes and the players attempt to attain various goals for each prize separately. The main objective is to present a fuzzy set/fuzzy programming solution concept to the conflict situation. In doing so, we compare a Bayesian player to one that employs fuzzy set techniques. We point out some of the advantages of the fuzzy set method. The necessary computations in the fuzzy set method are explained in detail through an example.     

Warped Products and Conformal Boundaries of CAT(0)-Spaces

We discuss the conformal boundary of a warped product of two length spaces and provide a method to calculate this in terms of the individual conformal boundaries. This technique is then applied to produce CAT(0)-spaces with complicated conformal boundaries. Finally, we prove that the conformal boundary of an Hadamard n-manifold is always simply connected for n≥3, thus providing a bound for the level of complication of the boundary of such a manifold.