On Unbounded Composition Operators in L2L^2-Spaces

Fundamental properties of unbounded composition operators in $L^2$-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert's characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied

Diffusion tensor image segmentation of the cerebrum provides a single measure of cerebral small vessel disease severity related to cognitive change.

Cerebral small vessel disease (SVD) is the primary cause of vascular cognitive impairment and is associated with decline in executive function (EF) and information processing speed (IPS). Imaging biomarkers are needed that can monitor and identify individuals at risk of severe cognitive decline. Recently there has been interest in combining several magnetic resonance imaging (MRI) markers of SVD into a unitary score to describe disease severity. Here we apply a diffusion tensor image (DTI) segmentation technique (DSEG) to describe SVD related changes in a single unitary score across the whole cerebrum, to investigate its relationship with cognitive change over a three-year period. 98 patients (aged 43-89) with SVD underwent annual MRI scanning and cognitive testing for up to three years. DSEG provides a vector of 16 discrete segments describing brain microstructure of healthy and/or damaged tissue. By calculating the scalar product of each DSEG vector in reference to that of a healthy ageing control we generate an angular measure (DSEG θ) describing the patients' brain tissue microstructural similarity to a disease free model of a healthy ageing brain. Conventional MRI markers of SVD brain change were also assessed including white matter hyperintensities, cerebral atrophy, incident lacunes, cerebral-microbleeds, and white matter microstructural damage measured by DTI histogram parameters. The impact of brain change on cognition was explored using linear mixed-effects models. Post-hoc sample size analysis was used to assess the viability of DSEG θ as a tool for clinical trials. Changes in brain structure described by DSEG θ were related to change in EF and IPS (p < 0.001) and remained significant in multivariate models including other MRI markers of SVD as well as age, gender and premorbid IQ. Of the conventional markers, presence of new lacunes was the only marker to remain a significant predictor of change in EF and IPS in the multivariate models (p = 0.002). Change in DSEG θ was also related to change in all other MRI markers (p < 0.017), suggesting it may be used as a surrogate marker of SVD damage across the cerebrum. Sample size estimates indicated that fewer patients would be required to detect treatment effects using DSEG θ compared to conventional MRI and DTI markers of SVD severity. DSEG θ is a powerful tool for characterising subtle brain change in SVD that has a negative impact on cognition and remains a significant predictor of cognitive change when other MRI markers of brain change are accounted for. DSEG provides an automatic segmentation of the whole cerebrum that is sensitive to a range of SVD related structural changes and successfully predicts cognitive change. Power analysis shows DSEG θ has potential as a monitoring tool in clinical trials. As such it may provide a marker of SVD severity from a single imaging modality (i.e. DTIs)

The functional and clinical outcomes of exercise training following a very low energy diet for severely obese women: Study protocol for a randomised controlled trial

BACKGROUND: Clinical practice guidelines globally recommend lifestyle modification including diet and exercise training as first-line treatment for obesity. The clinical benefits of exercise training in adults with obesity is well-documented; however, there is no strong evidence for the effectiveness of exercise training for weight loss in class II and class III obesity. The purpose of the randomised controlled trial described in this protocol article is to examine the effect of exercise training, in addition to a very low energy diet (VLED), in clinically severe obese women for changes in body composition, physical function, quality of life, and markers of cardiometabolic risk. METHODS/DESIGN: Sixty women, aged 18-50 years with a body mass index (BMI) greater than 34.9 kg.m(2) and at least one obesity-related co-morbidity, will be recruited for this 12-month study. Participants will be randomised to either exercise plus energy restriction (n = 30), or energy restriction alone (n = 30). All participants will follow an energy-restricted individualised diet incorporating a VLED component. The exercise intervention group will also receive exercise by supervised aerobic and resistance training and a home-based exercise programme totalling 300 minutes per week. Primary outcome measures include body composition and aerobic fitness. Secondary outcome measures include: physical function, cardiometabolic risk factors, quality of life, physical activity, and mental health. All outcome measures will be conducted at baseline, 3, 6 and 12 months. DISCUSSION: Previous research demonstrates various health benefits of including exercise training as part of a healthy lifestyle at all BMI ranges. Although clinical practice guidelines recommend exercise training as part of first-line treatment for overweight and obesity, there are few studies that demonstrate the effectiveness of exercise in class II and class III obesity. The study aims to determine whether the addition of exercise training to a VLED provides more favourable improvements in body composition, physical function, quality of life, and markers of cardiometabolic risk for women with clinically severe obesity, compared to VLED alone.<br /

Towards automated characterisation of fatigue damage in composites using thermoelastic stress analysis

Composite materials demonstrate complicated fatigue behaviour due to their microstructure and the varied types of defects that can occur during loading. This necessitates experimentation to determine their performance under loading. In this study an algorithm is introduced for identifying and categorising different defects forming during fatigue tests. Thermoelastic stress analysis was used to obtain high spatial and temporal resolution stress information from the surface of notched composite specimens. Specimens with three different geometries were loaded in tension–tension fatigue to failure. An algorithm was used to identify when and where matrix cracking and delaminations formed within the specimens as well as quantify how this changed over time. By improving how damage events are identified and characterised, the algorithm reduces the amount of time needed to process experimental fatigue data and helps to provide greater understanding of fatigue processes in new materials from early small-scale cracking all the way to final failure

(1,0) superconformal models in six dimensions

We construct six-dimensional (1,0) superconformal models with non-abelian gauge couplings for multiple tensor multiplets. A crucial ingredient in the construction is the introduction of three-form gauge potentials which communicate degrees of freedom between the tensor multiplets and the Yang-Mills multiplet, but do not introduce additional degrees of freedom. Generically these models provide only equations of motions. For a subclass also a Lagrangian formulation exists, however it appears to exhibit indefinite metrics in the kinetic sector. We discuss several examples and analyze the excitation spectra in their supersymmetric vacua. In general, the models are perturbatively defined only in the spontaneously broken phase with the vev of the tensor multiplet scalars serving as the inverse coupling constants of the Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which complete the field content to that of superconformal (2,0) theories.Comment: 30 pages, v2: Note, some comments and references adde

Solutions from boundary condition changing operators in open string field theory

We construct analytic solutions of open string field theory using boundary condition changing (bcc) operators. We focus on bcc operators with vanishing conformal weight such as those for regular marginal deformations of the background. For any Fock space state phi, the component string field of the solution Psi exhibits a remarkable factorization property: it is given by the matter three-point function of phi with a pair of bcc operators, multiplied by a universal function that only depends on the conformal weight of phi. This universal function is given by a simple integral expression that can be computed once and for all. The three-point functions with bcc operators are thus the only needed physical input of the particular open string background described by the solution. We illustrate our solution with the example of the rolling tachyon profile, for which we prove convergence analytically. The form of our solution, which involves bcc operators instead of explicit insertions of the marginal operator, can be a natural starting point for the construction of analytic solutions for arbitrary backgrounds.Comment: 21 pages, 1 figure, LaTeX2e; v2: minor changes, version published in JHE

Higgsing M2 to D2 with gravity: N=6 chiral supergravity from topologically gauged ABJM theory

We present the higgsing of three-dimensional N=6 superconformal ABJM type theories coupled to conformal supergravity, so called topologically gauged ABJM theory, thus providing a gravitational extension of previous work on the relation between N M2 and N D2-branes. The resulting N=6 supergravity theory appears at a chiral point similar to that of three-dimensional chiral gravity introduced recently by Li, Song and Strominger, but with the opposite sign for the Ricci scalar term in the lagrangian. We identify the supersymmetry in the broken phase as a particular linear combination of the supersymmetry and special conformal supersymmetry in the original topologically gauged ABJM theory. We also discuss the higgsing procedure in detail paying special attention to the role played by the U(1) factors in the original ABJM model and the U(1) introduced in the topological gauging.Comment: 53 pages, Late

Monopoles, three-algebras and ABJM theories with N=5,6,8\N=5,6,8 supersymmetry

We extend the hermitian three-algebra formulation of ABJM theory to include $U(1)$ factors. With attention payed to extra $U(1)$ factors, we refine the classification of $\N=6$ ABJM theories. We argue that essentially the only allowed gauge groups are $SU(N)\times SU(N)$, $U(N)\times U(M)$ and $Sp(N)\times U(1)$ and that we have only one independent Chern-Simons level in all these cases. Our argument is based on integrality of the $U(1)$ Chern-Simons levels and supersymmetry. A relation between monopole operators and Wilson lines in Chern-Simons theory suggests certain gauge representations of the monopole operators. From this we classify cases where we can not expect enhanced $\N=8$ supersymmetry. We also show that there are two equivalent formulations of $\N=5$ ABJM theories, based on hermitian three-algebra and quaternionic three-algebra respectively. We suggest properties of monopoles in $\N=5$ theories and show how these monopoles may enhance supersymmetry from $\N=5$ to $\N=6$.Comment: 52 page

Slx8 removes Pli1-dependent protein-SUMO conjugates including SUMOylated Topoisomerase I to promote genome stability

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