Elliptic operators, connections and gauge transformations

A study is made of the action of various Banach Lie groups of principal bundle automorphims (gauge transformations) on corresponding spaces of connections on some principal bundle, using standard theorems of global analysis together with elliptic regularity theorems. A proof of elliptic regularity theorems in Sobolev and Holder norms for linear elliptic partial differential operators with smooth coefficients acting on sections of smooth vector bundles is presented. This proofassumes acquaintance with the theory of tempered distributions and their Fourier transforms and with the theory of compact and Fredholm operators, and also uses results from the papers of Calderon and Zygmund and from the early papers of Hormander on pseuoo-differential operators, but is otherwise intended to be self-contained. Elliptic regularity theorems arc proved for elliptic orcrators with non-smooth coefficients, using only the regularity theorems for elliptic operators with smooth coefficients, together with the Sobolev embedding theorems, the Rellich-Kondrakov theorem and the Sobolev multiplication theorems.For later convenience these elliptic regularity results are presented as a generalization of the analytical aspects of Hodge theory. Various theorems concerning the action of automorphisms on connections are proved, culminating in the slice theorems obtained in chapter VIII. Regularity theorems for Yang-Mills connections and for Yang-Mills Higgs systems arc obtained, In chapter IX analytical properties of the covariant derivative operators associated with a connection arc related to the holonomy group of the connection via a theorem which shows the existence of an upper bound on the length of loop required Lo generate the holonomy group of a connection with compact holonomygroup

Depressive rumination and experiential avoidance: A task based exploration

© 2014 John Wiley & Sons, Ltd. Depressive rumination has been conceptualized as being closely connected with experiential avoidance. Evidence supporting this hypothesis derives primarily from studies using self-report measures. The present study explores this idea using a task-based assessment of avoidance. College students (N=100) rated their emotional responses to 60 computer-presented images (positive, negative and neutral). Response times for the image-rating task were surreptitiously recorded, along with Ruminative Response Scale and Beck Depression Inventory II scores. Rumination was correlated with faster response times for negative, but not positive or neutral images. These findings are interpreted as lending support to the experiential avoidance conceptualization of rumination; however, consideration is also given to a potentially synergistic interpretation implicating heightened threat monitoring

Two-phase free boundary problems in convex domains

We study the regularity of minimizers of a two-phase free boundary problem. For a class of n-dimensional convex domains, we establish the Lipschitz continuity of the minimizer up to the fixed boundary under Neumann boundary conditions. Our proof uses an almost monotonicity formula for the Alt-Caffarelli-Friedman functional restricted to the convex domain. This requires a variant of the classical Friedland-Hayman inequality for geodesically convex subsets of the sphere with Neumann boundary conditions. To apply this inequality, in addition to convexity, we require a Dini condition governing the rate at which the fixed boundary converges to its limit cone at each boundary point.Comment: 34 page

Gender differences in health and medicine information seeking behaviour : a review

Consumers periodically seek information about their health and medicines to increase their knowledge and understanding, and to support self-management. Gender has an impact on people’s attitudes and behaviour; gaining a better understanding of how males and females differ in the way in which they find and use health and medicine information may help to enhance patient-health care provider communication and the information that they receive. Based on a review of the literature, women overall are more active information seekers than men. A number of differences do exist, notably in: sources of information consulted, information desired and degree of engagement in information seeking.peer-reviewe

Providing additional information about the benefits of statins in a leaflet for patients with coronary heart disease : a qualitative study of the impact on attitudes and beliefs

OBJECTIVE: To explore the impact of providing additional information about the potential benefits of simvastatin in a patient leaflet on attitudes and beliefs. DESIGN: Interview-based study using a generic qualitative approach and framework analysis. PARTICIPANTS: 21 participants receiving a prescription for simvastatin were recruited from a general practitioner practice (from a total of 120). 8 participants were women; the age range was 55-92. INTERVENTION: Participants were provided with leaflets showing one of 3 types of additional benefit information: (1) textual statement, (2) number needed to treat (NNT) or (3) natural frequency. Semistructured interviews explored patient's attitudes and beliefs. RESULTS: A descriptive narrative of preferences for format suggested patients prefer textual as opposed to numerical benefit information. Significant barriers to the acceptance of numerical benefit information included difficulty in understanding the numbers. Patients overestimated the benefits of statins and expressed surprise at the numerical information. CONCLUSIONS: Textual information was preferred but numerical information, in particular in the form of a natural frequency, may help patients make judgements about their medicines. NNTs were found to be very difficult to understand. This raises the prospect that some patients might reject medicines because of disappointment with the perceived low benefits of their medicines. The self-reported impact on behaviour appeared minimal with reports of intentions to 'do what the doctor tells me'. Further research is needed to explore the impact of such statements on people who are yet to be prescribed a statin

A Review of Different Behavior Modification Strategies Designed to Reduce Sedentary Screen Behaviors in Children

Previous research suggests that reducing sedentary screen behaviors may be a strategy for preventing and treating obesity in children. This systematic review describes strategies used in interventions designed to either solely target sedentary screen behaviors or multiple health behaviors, including sedentary screen behaviors. Eighteen studies were included in this paper; eight targeting sedentary screen behaviors only, and ten targeting multiple health behaviors. All studies used behavior modification strategies for reducing sedentary screen behaviors in children (aged 1–12 years). Nine studies only used behavior modification strategies, and nine studies supplemented behavior modification strategies with an electronic device to enhance sedentary screen behaviors reductions. Many interventions (50%) significantly reduced sedentary screen behaviors; however the magnitude of the significant reductions varied greatly (−0.44 to −3.1 h/day) and may have been influenced by the primary focus of the intervention, number of behavior modification strategies used, and other tools used to limit sedentary screen behaviors

Identification of circulating tumour cells in early stage breast cancer patients using multi marker immunobead RT-PCR

Introduction The ability to screen blood of early stage operable breast cancer patients for circulating tumour cells is of potential importance for identifying patients at risk of developing distant relapse. We present the results of a study of the efficacy of the immunobead RT-PCR method in identifying patients with circulating tumour cells. Results Immunomagnetic enrichment of circulating tumour cells followed by RT-PCR (immunobead RT-PCR) with a panel of five epithelial specific markers (ELF3, EPHB4, EGFR, MGB1 and TACSTD1) was used to screen for circulating tumour cells in the peripheral blood of 56 breast cancer patients. Twenty patients were positive for two or more RT-PCR markers, including seven patients who were node negative by conventional techniques. Significant increases in the frequency of marker positivity was seen in lymph node positive patients, in patients with high grade tumours and in patients with lymphovascular invasion. A strong trend towards improved disease free survival was seen for marker negative patients although it did not reach significance (p = 0.08). Conclusion Multi-marker immunobead RT-PCR analysis of peripheral blood is a robust assay that is capable of detecting circulating tumour cells in early stage breast cancer patients