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Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. The current literature on these classes of methods almost exclusively considers the case where also the smooth term is convex. Here we present a globalized proximal Newton-type method which allows the smooth term to be nonconvex. The method is shown to have nice global and local convergence properties, and some numerical results indicate that this method is very promising also from a practical point of view.
Abstract
To compare intravenous contrast material (CM) injection protocols for dual-energy CT pulmonary angiography (CTPA) in patients with suspected acute pulmonary embolism with regard to image quality and pulmonary perfused blood volume (PBV) values. A total of 198 studies performed with four CM injection protocols varying in CM volume and iodine delivery rates (IDR) were retrospectively included: (A) 60 ml at 5 ml/s (IDR = 1.75gI/s), (B) 50 ml at 5 ml/s (IDR = 1.75gI/s), (C) 50 ml at 4 ml/s (IDR = 1.40gI/s), (D) 40 ml at 3 ml/s (IDR = 1.05gI/s). Image quality and PBV values at different resolution settings were compared. Pulmonary arterial tract attenuation was highest for protocol A (397 ± 110 HU; p vs. B = 0.13; vs. C = 0.02; vs. D < 0.001). CTPA image quality of protocol A was rated superior compared to protocols B and D by reader 1 (p = 0.01; < 0.001), and superior to protocols B, C and D by reader 2 (p < 0.001; 0.02; < 0.001). Otherwise, there were no significant differences in CTPA quality ratings. Subjective iodine map ratings did not vary significantly between protocols A, B, and C. Both readers rated protocol D inferior to all other protocols (p < 0.05). PBV values did not vary significantly between protocols A and B at resolution settings of 1, 4 and 10 (p = 0.10; 0.10; 0.09), while otherwise PBV values displayed a decreasing trend from protocol A to D (p < 0.05). Higher CM volume and IDR are associated with superior CTPA and iodine map quality and higher absolute PBV values.
Purpose
Radiotherapy (RT) was identified as a risk factor for long-term cardiac effects in breast cancer patients treated until the 1990s. However, modern techniques reduce radiation exposure of the heart, but some exposure remains unavoidable. In a retrospective cohort study, we investigated cardiac mortality and morbidity of breast cancer survivors treated with recent RT in Germany.
Methods
A total of 11,982 breast cancer patients treated between 1998 and 2008 were included. A mortality follow-up was conducted until 06/2018. In order to assess cardiac morbidity occurring after breast cancer treatment, a questionnaire was sent out in 2014 and 2019. The effect of breast cancer laterality on cardiac mortality and morbidity was investigated as a proxy for radiation exposure. We used Cox Proportional Hazards regression analysis, taking potential confounders into account.
Results
After a median follow-up time of 11.1 years, there was no significant association of tumor laterality with cardiac mortality in irradiated patients (hazard ratio (HR) for left-sided versus right-sided tumor 1.09; 95% confidence interval (CI) 0.85–1.41). Furthermore, tumor laterality was not identified as a significant risk factor for cardiac morbidity (HR = 1.05; 95%CI 0.88–1.25).
Conclusions
Even though RT for left-sided breast cancer on average incurs higher radiation dose to the heart than RT for right-sided tumors, we found no evidence that laterality is a strong risk factor for cardiac disease after contemporary RT. However, larger sample sizes, longer follow-up, detailed information on individual risk factors and heart dose are needed to assess clinically manifest late effects of current cancer therapy.
Across Europe, calcareous grasslands become increasingly fragmented and their quality deteriorates through abandonment and land use intensification, both affecting biodiversity. Here, we investigated local and landscape effects on diversity patterns of several taxonomic groups in a landscape of highly fragmented calcareous grassland remnants. We surveyed 31 grassland fragments near Göttingen, Germany, in spring and summer 2017 for vascular plants, butterflies and birds, with sampling effort adapted to fragment area. Through regression modelling, we tested relationships between species richness and fragment size (from 314 to 51,395 m\(^2\)), successional stage, habitat connectivity and the per cent cover of arable land in the landscape at several radii. We detected 283 plant species, 53 butterfly species and 70 bird species. Of these, 59 plant species, 19 butterfly species and 9 bird species were grassland specialists. Larger fragments supported twice the species richness of plants than small ones, and hosted more species of butterflies, but not of birds. Larger grassland fragments contained more grassland specialist plants, but not butterfly or bird specialists. Increasing amounts of arable land in the landscape from 20 to 90% was related to the loss of a third of species of plants, and less so, of butterflies, but not of birds. Per cent cover of arable land negatively correlated to richness of grassland specialist plants and butterflies, but positively to grassland specialist birds. We found no effect by successional stages and habitat connectivity. Our multi-taxa approach highlights the need for conservation management at the local scale, complemented by measures at the landscape scale.
Physical regimes characterized by low Mach numbers and steep stratifications pose severe challenges to standard finite volume methods. We present three new methods specifically designed to navigate these challenges by being both low Mach compliant and well-balanced. These properties are crucial for numerical methods to efficiently and accurately compute solutions in the regimes considered.
First, we concentrate on the construction of an approximate Riemann solver within Godunov-type finite volume methods. A new relaxation system gives rise to a two-speed relaxation solver for the Euler equations with gravity. Derived from fundamental mathematical principles, this solver reduces the artificial dissipation in the subsonic regime and preserves hydrostatic equilibria. The solver is particularly stable as it satisfies a discrete entropy inequality, preserves positivity of density and internal energy, and suppresses checkerboard modes.
The second scheme is designed to solve the equations of ideal MHD and combines different approaches. In order to deal with low Mach numbers, it makes use of a low-dissipation version of the HLLD solver and a partially implicit time discretization to relax the CFL time step constraint. A Deviation Well-Balancing method is employed to preserve a priori known magnetohydrostatic equilibria and thereby reduces the magnitude of spatial discretization errors in strongly stratified setups.
The third scheme relies on an IMEX approach based on a splitting of the MHD equations. The slow scale part of the system is discretized by a time-explicit Godunov-type method, whereas the fast scale part is discretized implicitly by central finite differences. Numerical dissipation terms and CFL time step restriction of the method depend solely on the slow waves of the explicit part, making the method particularly suited for subsonic regimes. Deviation Well-Balancing ensures the preservation of a priori known magnetohydrostatic equilibria.
The three schemes are applied to various numerical experiments for the compressible Euler and ideal MHD equations, demonstrating their ability to accurately simulate flows in regimes with low Mach numbers and strong stratification even on coarse grids.
Based on an embodied account of language comprehension, this study investigated the dynamic characteristics of children and adults’ perceptual simulations during sentence comprehension, using a novel paradigm to assess the perceptual simulation of objects moving up and down a vertical axis. The participants comprised adults (N = 40) and 6-, 8-, and 10-year-old children (N = 116). After listening in experimental trials to sentences implying that objects moved upward or downward, the participants were shown pictures and had to decide as quickly as possible whether the objects depicted had been mentioned in the sentences. The target pictures moved either up or down and then stopped in the middle of the screen. All age groups’ reaction times were found to be shorter when the objects moved in the directions that the sentences implied. Age exerted no developmental effect on reaction times. The findings suggest that dynamic perceptual simulations are fundamental to language comprehension in text recipients aged 6 and older.
Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper, we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.
Quantitative information is omnipresent in the world and a wide range of species has been shown to use quantities to optimize their decisions. While most studies have focused on vertebrates, a growing body of research demonstrates that also insects such as honeybees possess basic quantitative abilities that might aid them in finding profitable flower patches. However, it remains unclear if for insects, quantity is a salient feature relative to other stimulus dimensions, or if it is only used as a “last resort” strategy in case other stimulus dimensions are inconclusive. Here, we tested the stingless bee Trigona fuscipennis, a species representative of a vastly understudied group of tropical pollinators, in a quantity discrimination task. In four experiments, we trained wild, free-flying bees on stimuli that depicted either one or four elements. Subsequently, bees were confronted with a choice between stimuli that matched the training stimulus either in terms of quantity or another stimulus dimension. We found that bees were able to discriminate between the two quantities, but performance differed depending on which quantity was rewarded. Furthermore, quantity was more salient than was shape. However, quantity did not measurably influence the bees' decisions when contrasted with color or surface area. Our results demonstrate that just as honeybees, small-brained stingless bees also possess basic quantitative abilities. Moreover, invertebrate pollinators seem to utilize quantity not only as "last resort" but as a salient stimulus dimension. Our study contributes to the growing body of knowledge on quantitative cognition in invertebrate species and adds to our understanding of the evolution of numerical cognition.