Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

Branes and fluxes in special holonomy manifolds and cascading field theories

We conduct a study of holographic RG flows whose UV is a theory in 2+1 dimensions decoupled from gravity, and the IR is the N=6,8 superconformal fixed point of ABJM. The solutions we consider are constructed by warping the M-theory background whose eight spatial dimensions are manifolds of special holonomies sp(1) times sp(1) and spin(7). Our main example for the spin(7) holonomy manifold is the A8 geometry originally constructed by Cvetic, Gibbons, Lu, and Pope. On the gravity side, our constructions generalize the earlier construction of RG flow where the UV was N=3 Yang-Mills-Chern-Simons matter system and are simpler in a number of ways. Through careful consideration of Page, Maxwell, and brane charges, we identify the discrete and continuous parameters characterizing each system. We then determine the range of the discrete data, corresponding to the flux/rank for which the supersymmetry is unbroken, and estimate the dynamical supersymmetry breaking scale as a function of these data. We then point out the similarity between the physics of supersymmetry breaking between our system and the system considered by Maldacena and Nastase. We also describe the condition for unbroken supersymmetry on class of construction based on a different class of spin(7) manifolds known as B8 spaces whose IR is different from that of ABJM and exhibit some interesting features.Comment: 51 pages, 12 figures. Update in quantization of G4 on B8 in equations (5.12) and (5.13

Microscopic Realization of the Kerr/CFT Correspondence

Supersymmetric M/string compactifications to five dimensions contain BPS black string solutions with magnetic graviphoton charge P and near-horizon geometries which are quotients of AdS_3 x S^2. The holographic duals are typically known 2D CFTs with central charges c_L=c_R=6P^3 for large P. These same 5D compactifications also contain non-BPS but extreme Kerr-Newman black hole solutions with SU(2)_L spin J_L and electric graviphoton charge Q obeying Q^3 \leq J_L^2. It is shown that in the maximally charged limit Q^3 -> J_L^2, the near-horizon geometry coincides precisely with the right-moving temperature T_R=0 limit of the black string with magnetic charge P=J_L^{1/3}. The known dual of the latter is identified as the c_L=c_R=6J_L CFT predicted by the Kerr/CFT correspondence. Moreover, at linear order away from maximality, one finds a T_R \neq 0 quotient of the AdS_3 factor of the black string solution and the associated thermal CFT entropy reproduces the linearly sub-maximal Kerr-Newman entropy. Beyond linear order, for general Q^3<J_L^2, one has a finite-temperature quotient of a warped deformation of the magnetic string geometry. The corresponding dual deformation of the magnetic string CFT potentially supplies, for the general case, the c_L=c_R=6J_L CFT predicted by Kerr/CFT.Comment: 18 pages, no figure

MUTYH-Associated Polyposis: The Irish Experience>.

MUTYH is involved in DNA damage repair. Bi-allelic MUTYH mutations predispose to polyposis and gastrointestinal malignancies, distinct genetically from autosomal dominant familial adenomatous polyposis coli. Two common European MUTYH mutations account for 90% of MUTYH-associated polyposis (MAP). We aimed to examine the incidence of MAP in Ireland. A retrospective cohort study was undertaken. Patients undergoing MUTYH testing from 2003-2016 were identified by searching electronic databases using terms "MUTYH" and "MYH". Phenotypic and genotypic details were obtained by chart review. Bi-allelic mutations were confirmed in 26 individuals (17 families), of whom 16 (62%) developed colorectal malignancies, and 22(85%) polyposis. Eleven families had bi-allelic status for one/both common European mutations. Regional variation was noted, with over-representation of bi-allelic mutation carriers in the South-west of Ireland. MAP is under-diagnosed in Ireland. Increased awareness is required to facilitate appropriate identification and surveillance of bi-allelic mutation carriers for colorectal pathology

'Just’ punishment? Offenders’ views on the meaning and severity of punishment

In England and Wales, ‘punishment’ is a central element of criminal justice. What punishment entails exactly, however, and how it relates to the other aims of sentencing (crime reduction, rehabilitation, public protection and reparation), remains contested. This article outlines different conceptualizations of punishment and explores to what extent offenders subscribe to these perspectives. The analysis is supported by findings from two empirical studies on the subjective experiences of imprisonment and probation, respectively. Semi-structured interviews were conducted with 15 male and 15 female prisoners and seven male and two female probationers. Two primary conceptualizations of punishment were identified: ‘punishment as deprivation of liberty’ and ‘punishment as hard treatment’. The comparative subjective severity of different sentences and the collateral (unintended) consequences of punishment are also discussed. It is shown that there are large individual differences in the interpretation and subjective experience of punishment, which has implications for the concept of retributive proportionality, as well as the function of punishment more generally

Nuclear magnetic resonance and small-angle X-ray scattering studies of mixed sodium dodecyl sulfate and N,N-dimethyldodecylamine N-oxide aqueous systems performed at low temperatures

Surfactant crystallisation is important in many applications in the food, consumer product and medical sectors. However, these processes are not well understood. In particular, surfactant crystallisation can be detrimental to the stability of detergent formulations, such as dish liquid products, resulting in a turbid solution that fails appearance criteria. With the rising global demand for detergent products, understanding the factors that influence formulation stability is of increasing importance. To enable industry to build more robust formulations, it is important to understand the underlying chemistry of the crystallisation process. Here, a model system containing anionic (sodium dodecyl sulfate, SDS) and amphoteric (N,N-dimethyldodecylamine N-oxide, DDAO) surfactants, at concentrations typical of dish liquid products, is studied. Variable temperature 1H nuclear magnetic resonance (NMR) spectroscopy and small-angle X-ray scattering (SAXS) is used to probe the compositional and structural properties of this system, as a function of pH. On cooling, at pH 9, a mixture of hydrated crystals, predominately composed of SDS, and micelles containing both surfactants, have been observed prior to complete freezing. At pH 2, both surfactants appear to undergo a simultaneous phase transition, resulting in the removal of micelles and the formation of hydrated crystals of mixed composition

Online versus paper-based screening for depression and anxiety in adults with cystic fibrosis in Ireland: a cross-sectional exploratory study

Objective: To compare online and paper-based screening for depression and anxiety in adults with cystic fibrosis (CF). Design and setting: Cross-sectional study in CF clinics in Ireland and through the Cystic Fibrosis Ireland online community. Participants: 160 adult patients aged 18 or above were recruited. Of these, 147 were included in the analysis; 83 online and 64 paper-based. The remaining 13 were excluded because of incomplete data. Measures: Depression and anxiety were measured using the Hospital Anxiety and Depression Scale (HADS). Data on pulmonary function (forced expiratory volume in 1 s %) and body mass index were self-reported based on clinical assessments. Sociodemographic data were collected. Results: Compared with the paper-based participants, the online participants were more likely to be female (61.7% vs 48.4%), older (mean 32.2 vs 28.2 years) and were more likely to be married (32.5% vs 15.6%), living with their spouse or partner (42.5% vs 22.6%) and working either full time (33.7% vs 15.9%) or part time (30.1%vs 17.5%). The prevalence rates of elevated anxiety and depression were not significantly different (P=0.71 and P=0.56). HADS anxiety and depression scores were not statistically different between online (P=0.83) and paper-based (P=0.92) participants based on Mann-Whitney U test. A significant negative correlation was found between depression and pulmonary function (r=−0.39, P=0.01) and anxiety and pulmonary function (r=−0.36, P=0.02). Based on Cronbach’s alpha, there were no statistically significant differences between the online and paper-based participants on the internal consistency of the HADS anxiety (P=0.073) and depression (P=0.378) scales. Conclusions: Our findings suggest that online and paper-based screening for depression and anxiety in adult patients with CF yield comparable findings on prevalence rates and scores, associations with health and internal consistency of subscales. This study highlights that online screening offers an alternative method to paper-based screening. Further research with a larger sample and assessment of measurement equivalence between online and paper based screening is needed to confirm our results

Holographic Vitrification

We establish the existence of stable and metastable stationary black hole bound states at finite temperature and chemical potentials in global and planar four-dimensional asymptotically anti-de Sitter space. We determine a number of features of their holographic duals and argue they represent structural glasses. We map out their thermodynamic landscape in the probe approximation, and show their relaxation dynamics exhibits logarithmic aging, with aging rates determined by the distribution of barriers.Comment: 100 pages, 25 figure

Mind the gap: sentencing, rehabilitation and civic purgatory

This article discusses the relationships and tensions between the sentencing, statutory supervision and legal rehabilitation of lawbreakers under UK legislation. It does so with reference to both the Rehabilitation of Offenders Act 1974, which allows some criminal records to become ‘spent’ after a set period of time, and the Offender Rehabilitation Act 2014, which was designed to significantly expand statutory supervision arrangements. The article also demonstrates how, post-supervision, many former lawbreakers are cast into a state of ‘civic purgatory’, before suggesting that a more fully integrated approach to rehabilitation is required