An Ostrowski type inequality in two dimensions using the three point rule

An Ostrowski Type inequality in two dimensions for double integrals on a rectangle is developed. The resulting integral inequalities are valid for the class of functions with bounded first derivatives. They are employed to approximate the double integral by up to 6 one dimensional integrals and nine functions evaluations. Examples using the resulting cubature formulae are presented

On weighted three point quadrature rules

Weighted three point quadrature rules are obtained in the current work giving explicit a priori bounds on the error. The results are valid for general weight functions. The robustness of the bounds are explored for specific weight functions and for a variety of integrands. A comparison of the current development is made with traditional quadrature rules and it is demonstrated that the current development has some advantages. In particular, this method allows the nodes and weights of an n point rule to be easily obtained, which may be preferential if the region of integration varies. Other explicit error bounds may be obtained in advance, thus making it possible to determine the partition required to achieve a certain error tolerance

HSP90-CDC37-PP5 forms a structural platform for kinase dephosphorylation.

Activation of client protein kinases by the HSP90 molecular chaperone system is affected by phosphorylation at multiple sites on HSP90, the kinase-specific co-chaperone CDC37, and the kinase client itself. Removal of regulatory phosphorylation from client kinases and their release from the HSP90-CDC37 system depends on the Ser/Thr phosphatase PP5, which associates with HSP90 via its N-terminal TPR domain. Here, we present the cryoEM structure of the oncogenic protein kinase client BRAFV600E bound to HSP90-CDC37, showing how the V600E mutation favours BRAF association with HSP90-CDC37. Structures of HSP90-CDC37-BRAFV600E complexes with PP5 in autoinhibited and activated conformations, together with proteomic analysis of its phosphatase activity on BRAFV600E and CRAF, reveal how PP5 is activated by recruitment to HSP90 complexes. PP5 comprehensively dephosphorylates client proteins, removing interaction sites for regulatory partners such as 14-3-3 proteins and thus performing a 'factory reset' of the kinase prior to release

Nonlinear force-free reconstruction of the global solar magnetic field: methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday's equation, give rise to a respective normal field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modelled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition - the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic

The Impact of Implementing Hypofractionation Prescription Regimens and Modernizing Delivery Technique on Treatment Resources in Breast Radiotherapy

Purpose/Objective(s): To determine the change in treatment resources due to the implementation of hypofractionated prescription regimen. Materials/Methods: All patients between January 1, 2012 and December 31, 2021 receiving curative intent breast radiotherapy at a tertiary cancer center were included. Plan and patient data were extracted from the patient database with the treatment planning system and direct database query. Treatment plan categorization was completed using data elements to include only curative intent. Treatment plans for seroma boost or supraclavicular irradiation were excluded to ensure this analysis did not double-count regional nodal irradiation contribution or confound boost with hypofractionation. Treatment delivery time is recorded in the database for each patient treatment delivered. Average patient treatment time per year was estimated by multiplying the average fractions each year by average time in the same year. The standard fractionation regimens (95% of patients) are 42.56 Gy in 16, 40 Gy in 16, 27 Gy in 5 (accelerated partial breast irradiation), and 26 Gy in 5 (FAST-Forward). In the analysis, implementation milestones are indicated for new prescription regimens and delivery technique changes including deep inspiration breath hold (DIBH) for left-sided patient treatments and daily verification imaging. Results: A total of 6505 patients were included. Table 1 details the total number of patients per year, the average number of fractions treated per patient, and the average treatment time of each patient plan. The average total fractions per treatment decreased from 17.5 in 2012 to 10.9 in 2021. The average treatment delivery time increased from 12.9 minutes to 21.4 minutes. Conclusion: In considering total treatment resources, the interplay between hypofractionation and modernization delivery techniques is complex. The impact of hypofractionation reduced the average number of fractions but total treatment resources are offset with the implementation of modern treatment delivery techniques. Hypofractionated prescription regimens reduce the time and travel commitment required of patients on an individual basis, contributing to person-centered care

Magnetic Connectivity between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation

Extrapolation codes for modelling the magnetic field in the corona in cartesian geometry do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, \textit{e.g.}, a single active region. We apply a method for nonlinear force-free coronal magnetic field modelling of photospheric vector magnetograms in spherical geometry which allows us to study the connectivity between multi-active regions. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic field, where we study three neighbouring magnetically connected active regions (ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between the active regions(ARs). We have studied the time evolution of magnetic field over the period of three days and found no major changes in topologies as there was no major eruption event. From this study we have concluded that active regions are much more connected magnetically than the electric current.Comment: Solar Physic

Triggering an eruptive flare by emerging flux in a solar active-region complex

A flare and fast coronal mass ejection originated between solar active regions NOAA 11514 and 11515 on July 1, 2012 in response to flux emergence in front of the leading sunspot of the trailing region 11515. Analyzing the evolution of the photospheric magnetic flux and the coronal structure, we find that the flux emergence triggered the eruption by interaction with overlying flux in a non-standard way. The new flux neither had the opposite orientation nor a location near the polarity inversion line, which are favorable for strong reconnection with the arcade flux under which it emerged. Moreover, its flux content remained significantly smaller than that of the arcade (approximately 40 %). However, a loop system rooted in the trailing active region ran in part under the arcade between the active regions, passing over the site of flux emergence. The reconnection with the emerging flux, leading to a series of jet emissions into the loop system, caused a strong but confined rise of the loop system. This lifted the arcade between the two active regions, weakening its downward tension force and thus destabilizing the considerably sheared flux under the arcade. The complex event was also associated with supporting precursor activity in an enhanced network near the active regions, acting on the large-scale overlying flux, and with two simultaneous confined flares within the active regions.Comment: Accepted for publication in Topical Issue of Solar Physics: Solar and Stellar Flares. 25 pages, 12 figure

Physics of Solar Prominences: II - Magnetic Structure and Dynamics

Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them.Comment: 75 pages, 31 pictures, review pape

Status and perspectives of hospital mortality in a public urban Hellenic hospital, based on a five-year review

<p>Abstract</p> <p>Background</p> <p>Analysis of hospital mortality helps to assess the standards of health-care delivery.</p> <p>Methods</p> <p>This is a retrospective cohort study evaluating the causes of deaths which occurred during the years 1995–1999 in a single hospital. The causes of death were classified according to the International Statistical Classification of Diseases (ICD-10).</p> <p>Results</p> <p>Of the 149,896 patients who were discharged the 5836 (3.4%) died. Males constituted 55% and females 45%. The median age was 75.1 years (1 day – 100 years).</p> <p>The seven most common ICD-10 chapters IX, II, IV, XI, XX, X, XIV included 92% of the total 5836 deaths.</p> <p>The most common contributors of non-neoplasmatic causes of death were cerebrovascular diseases (I60–I69) at 15.8%, ischemic heart disease (I20–I25) at 10.3%, cardiac failure (I50.0–I50.9) at 7.9%, diseases of the digestive system (K00–K93) at 6.7%, diabetes mellitus (E10–E14) at 6.6%, external causes of morbidity and mortality (V01–Y98) at 6.2%, renal failure (N17–N19) at 4.5%, influenza and pneumonia (J10–J18) at 4.1% and certain infectious and parasitic diseases (A00–B99) at 3.2%, accounting for 65.3% of the total 5836 deaths.</p> <p>Neoplasms (C00–D48) caused 17.7% (n = 1027) of the total 5836 deaths, with leading forms being the malignant neoplasms of bronchus and lung (C34) at 3.5% and the malignant neoplasms of large intestine (C18–21.2) at 1.5%. The highest death rates occurred in the intensive care unit (23.3%), general medicine (10.7%), cardiology (6.5%) and nephrology (5.5%).</p> <p>Key problems related to certification of death were identified. Nearly half of the deaths (49.3%: n = 2879) occurred by the completion of the third day, which indicates the time limits for investigation and treatment. On the other hand, 6% (n = 356) died between the 29^thand 262^nddays after admission.</p> <p>Inadequacies of the emergency care service, infection control, medical oncology, rehabilitation, chronic and terminal care facilities, as well as lack of regional targets for reducing mortality related to diabetes, recruitment of organ donors, provision for the aging population and lack of prevention programs were substantiated.</p> <p>Conclusion</p> <p>Several important issues were raised. Disease specific characteristics, as well as functional and infrastructural inadequacies were identified and provided evidence for defining priorities and strategies for improving the standards of care. Effective transformation can promise better prospects.</p