Functionalisation of Non-Activated Positions in Steroids

The work described in this thesis attempted to introduce functionality into non-activated positions in readily available steroids. Section 3. 1 describes the ceric ammonium nitrate (CAN) oxidation of 25-hydroxy-5alpha-lanost-8-en-3beta-yl acetate. Oxidation mainly occurs at the allylic positions and this was confirmed by the CAN oxidation of 5alpha-lanost-8-en-3beta-yl acetate. An interesting nitrogenous compound was produced in which the starting material incorporated the solvent acetonitrile. CAN oxidation of 24(R,S)-hydroxy-5alpha-cholestan-3beta-yl acetate gave only dehydration products. Section 3.4 describes the functionalisation of the C-30 methyl group in 7alpha-hydroxy-5alpha-lanostan-3beta-yl acetate using various reagents. Long range functionalisation, using radical relay chlorinations developed by Breslow, was attempted on the bile acid derivative, 3-pyridylmethyl 3alpha-acetoxy-5beta-cholan-24-oate. Chlorination mainly occurred at the C-14 tertiary position. CrO3 oxidations of 5alpha-androstan-3beta-yl acetate and 5alpha-cholestan-3beta-yl acetate were performed in order to compare the selectivity of the oxidations. 5alpha-Cholestan-3beta-yl acetate produced degraded steroids whereas 5alpha-androstan-3beta-yl acetate gave the reported Delta14-16-ketone as the major product

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

A new microvertebrate fauna from the Middle Hettangian (early Jurassic) of Fontenoille (Province of Luxembourg, south Belgium)

A Lower Jurassic horizon from Fontenoille yielding fossil fish remains can be dated to the Middle Hettangian Liasicus zone on the basis of the early belemnite Schwegleria and the ammonite Alsatites Iciqueus francus. Hybodontiform sharks are represented by Hybodus reticularis, Lissodus sp„ Polxacrodus sp, and Neoselachians by Synechodus paludinensis nov. sp. and Synechodus streitzi, nov. sp. Earlier reports of a scyliorhinid are not confirmed; teeth of similar morphology to scyliorhinids seem to be juvenile variants of 5. paludinensis. Chimaeriform remains include Squaloraja sp., the earliest occurrence of the genus. The Actinopterygian fauna is introduced, comprising a palaeonisciform cf. Ptxcholepis, a possible late perleidiform cf. Platysiagum, the dapediid semionotiforms Dapedium and cf. Tetragonolepis, the pycnodontiform Eomesodon, halecomorphs cf. Furidae or Ophiopsidae, pholidophoriforms and/or Leptolepididae, and actinistians. Lepidosaur remains are also present

Assessing Alternatives for Directional Detection of a WIMP Halo

The future of direct terrestrial WIMP detection lies on two fronts: new, much larger low background detectors sensitive to energy deposition, and detectors with directional sensitivity. The former can large range of WIMP parameter space using well tested technology while the latter may be necessary if one is to disentangle particle physics parameters from astrophysical halo parameters. Because directional detectors will be quite difficult to construct it is worthwhile exploring in advance generally which experimental features will yield the greatest benefits at the lowest costs. We examine the sensitivity of directional detectors with varying angular tracking resolution with and without the ability to distinguish forward versus backward recoils, and compare these to the sensitivity of a detector where the track is projected onto a two-dimensional plane. The latter detector regardless of where it is placed on the Earth, can be oriented to produce a significantly better discrimination signal than a 3D detector without this capability, and with sensitivity within a factor of 2 of a full 3D tracking detector. Required event rates to distinguish signals from backgrounds for a simple isothermal halo range from the low teens in the best case to many thousands in the worst.Comment: 4 pages, including 2 figues and 2 tables, submitted to PR

Bad semidefinite programs: they all look the same

Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\em badly behaved} if the value of $\sup { | A x <= b }$ is finite but the dual program has no solution with the same value for {\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidefinite systems in the literature; we characterize such systems by certain {\em excluded matrices}, which are easy to spot in all published examples. We show how to transform semidefinite systems into a canonical form, which allows us to easily verify whether they are badly behaved. We prove several other structural results about badly behaved semidefinite systems; for example, we show that they are in $NP \cap co-NP$ in the real number model of computing. As a byproduct, we prove that all linear maps that act on symmetric matrices can be brought into a canonical form; this canonical form allows us to easily check whether the image of the semidefinite cone under the given linear map is closed.Comment: For some reason, the intended changes between versions 4 and 5 did not take effect, so versions 4 and 5 are the same. So version 6 is the final version. The only difference between version 4 and version 6 is that 2 typos were fixed: in the last displayed formula on page 6, "7" was replaced by "1"; and in the 4th displayed formula on page 12 "A_1 - A_2 - A_3" was replaced by "A_3 - A_2 - A_1

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Functional Maps Representation on Product Manifolds

We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace--Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.Comment: Accepted to Computer Graphics Foru

Long-term follow up to assess criteria for ovarian tissue cryopreservation for fertility preservation in young women and girls with cancer

Funding: K.D. is supported by a CRUK grant (C157/A25193). This work was undertaken in part in the MRC Centre for Reproductive Health, (supported by MRC grant MR/N022556/1). R.A.A. has received consulting fees from Ferring and Roche Diagnostics; payment from Merck and IBSA for educational events; and laboratory materials from Roche Diagnostics.STUDY QUESTION Do the Edinburgh Selection Criteria correctly identify female cancer patients under the age of 18 who are at risk of premature ovarian insufficiency (POI) as candidates for ovarian tissue cryopreservation (OTC)? SUMMARY ANSWER Patient assessment using these criteria accurately identifies those at risk of POI, who can be offered OTC and future transplantation as a means of fertility preservation. WHAT IS KNOWN ALREADY Treatment for childhood cancer can have adverse consequences on future fertility; at the time of diagnosis, fertility risk assessment should be undertaken in order to identify patients to whom fertility preservation should be offered. The Edinburgh selection criteria, based on planned cancer treatment and patient health status, are utilized to identify those at high risk and therefore eligible for OTC. However, this procedure is not without risk and there are few data on the efficacy of the procedure in prepubertal patients. As such, long-term follow-up of reproductive outcomes is necessary, to ensure that OTC is being offered appropriately. STUDY DESIGN, SIZE, DURATION Cohort study encompassing all females diagnosed with cancer under the age of 18 in South East Scotland, from 1 January 1996 to 30 April 2020. Patients were followed up for reproductive outcomes to assess for diagnosis of POI. PARTICIPANTS/MATERIALS, SETTING, METHODS A total of 638 eligible patients were identified; patients under the age of 12 or deceased before the age of 12 were excluded from the study, leaving a study population of 431 patients. Electronic records were reviewed for reproductive function, assessed by current menstruation, pregnancy (in the absence of POI diagnosis), reproductive hormone measurements, pubertal progression, or diagnosis of POI. Patients on hormonal contraception (other than for treatment of POI or panhypopituitarism with no history of gonadatoxic treatment) were excluded from analysis (n = 9). Analysis on remaining 422 patients was carried out using the Kaplan–Meier methods, with POI as the defined event, and Cox proportional hazards model. MAIN RESULTS AND THE ROLE OF CHANCE In the study population of 431 patients, median ages at diagnosis and analysis were 9.8 and 22.2 years, respectively. Reproductive outcomes were unavailable in 142 patients; the assumption was made that these patients did not have POI, but a subanalysis excluding these patients was also performed. Of the 422 patients aged >12 at analysis and not taking hormonal contraception, OTC was offered to 37 patients and successfully performed in 25 patients. Of the 37 patients offered OTC (one at time of relapse), nine (24.3%) developed POI. Of the 386 not offered OTC, 11 (2.9%) developed POI. The probability of developing POI was significantly higher in those offered OTC (hazard ratio [HR] 8.7 [95% CI 3.6–21]; P < 0.0001), even when those patients with unknown outcomes were excluded from the analysis (HR 8.1 [95% CI 3.4–20]; P < 0.001). All patients offered OTC who developed POI did so after treatment for primary disease; in those not offered OTC, five patients (45.5%) developed POI after treatment for disease relapse. LIMITATIONS, REASONS FOR CAUTION A significant number of patients had unknown reproductive outcomes; many of these patients were engaged in ongoing follow-up but did not have documented reproductive assessment. This may have introduced bias to the analysis and highlights the need for reproductive follow-up as part of routine cancer aftercare. In addition, the relatively young age of the patient population and short duration of follow-up in some cases demonstrates the need for ongoing follow-up of this cohort. WIDER IMPLICATIONS OF THE FINDINGS The prevalence of POI after childhood cancer is low, but the Edinburgh selection criteria remain a robust tool for selecting those at high risk at the time of diagnosis, to offer OTC appropriately. However, disease relapse necessitating more intensive treatments remains a challenge. This study additionally highlights the importance of routine assessment and documentation of reproductive status in haematology/oncology follow-up.Publisher PDFPeer reviewe