Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation

The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter $\epsilon$. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter $\epsilon$ is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.Comment: 17pages, 15 figure

Boundary Conditions in Stepwise Sine-Gordon Equation and Multi-Soliton Solutions

We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities before and after collisions. We investigate the possibility of formation of heavy soliton pairs from light ones and vise versa. The concept of soliton gun is introduced for the first time; a light pair is produced moving with high velocity, after the annihilation of a bound, heavy pair. We also apply boundary conditions to static, periodic and quasi-periodic solutions.Comment: 14 pages, 8 figure

Quantification and expert evaluation of evidence for chemopredictive biomarkers to personalize cancer treatment.

Predictive biomarkers have the potential to facilitate cancer precision medicine by guiding the optimal choice of therapies for patients. However, clinicians are faced with an enormous volume of often-contradictory evidence regarding the therapeutic context of chemopredictive biomarkers.We extensively surveyed public literature to systematically review the predictive effect of 7 biomarkers claimed to predict response to various chemotherapy drugs: ERCC1-platinums, RRM1-gemcitabine, TYMS-5-fluorouracil/Capecitabine, TUBB3-taxanes, MGMT-temozolomide, TOP1-irinotecan/topotecan, and TOP2A-anthracyclines. We focused on studies that investigated changes in gene or protein expression as predictors of drug sensitivity or resistance. We considered an evidence framework that ranked studies from high level I evidence for randomized controlled trials to low level IV evidence for pre-clinical studies and patient case studies.We found that further in-depth analysis will be required to explore methodological issues, inconsistencies between studies, and tumor specific effects present even within high evidence level studies. Some of these nuances will lend themselves to automation, others will require manual curation. However, the comprehensive cataloging and analysis of dispersed public data utilizing an evidence framework provides a high level perspective on clinical actionability of these protein biomarkers. This framework and perspective will ultimately facilitate clinical trial design as well as therapeutic decision-making for individual patients

RAFT-based polystyrene and polyacrylate melts under thermal and mechanical stress

Although controlled/living radical polymerization processes have significantly facilitated the synthesis of well-defined low polydispersity polymers with specific functionalities, a detailed and systematic knowledge of the thermal stability of the products-highly important for most industrial processes-is not available. Linear polystyrene (PS) carrying a trithiocarbonate mid-chain functionality (thus emulating the structure of the Z-group approach via reversible addition-fragmentation chain transfer (RAFT) based macromolecular architectures) with various chain lengths (20 kDa ≤ Mn,SEC ≤ 150 kDa, 1.27 ≤ Crossed D sign = Mw/Mn ≤ 1.72) and chain-end functionality were synthesized via RAFT polymerization. The thermal stability behavior of the polymers was studied at temperatures ranging from 100 to 200 C for up to 504 h (3 weeks). The thermally treated polymers were analyzed via size exclusion chromatography (SEC) to obtain the dependence of the polymer molecular weight distribution on time at a specific temperature under air or inert atmospheres. Cleavage rate coefficients of the mid-chain functional polymers in inert atmosphere were deduced as a function of temperature, resulting in activation parameters for two disparate Mn starting materials (Ea = 115 ± 4 kJ·mol-1, A = 0.85 × 109 ± 1 × 109 s-1, M n,SEC = 21 kDa and Ea = 116 ± 4 kJ·mol -1, A = 6.24 × 109 ± 1 × 109 s-1, Mn,SEC = 102 kDa). Interestingly, the degradation proceeds significantly faster with increasing chain length, an observation possibly associated with entropic effects. The degradation mechanism was explored in detail via SEC-ESI-MS for acrylate based polymers and theoretical calculations suggesting a Chugaev-type cleavage process. Processing of the RAFT polymers via small scale extrusion as well as a rheological assessment at variable temperatures allowed a correlation of the processing conditions with the thermal degradation properties of the polystyrenes and polyacrylates in the melt. © 2013 American Chemical Society.C.B.-K and M.W. gratefully acknowledge financial support from the German Research Council (DFG). M.L.C gratefully acknowledges generous allocations of supercomputing time from the Australian National Computing Facility, financial support from the Australian Research Council (ARC) Centre of Excellence for Free-radical Chemistry and Biotechnology and an ARC Future Fellowship. C.B.-K. acknowledges additional funding from the Karlsruhe Institute of Technology (KIT) in the context of the Helmholtz programs

Rotating Solution of Einstein-Maxwell Dilaton Gravity with Unusual Asymptotics

We study electrically charged, dilaton black holes, which possess infinitesimal angular momentum in the presence of one or two Liouville type potentials. These solutions are neither asymptotically flat nor (anti)-de Sitter. Some properties of the solutions are discussed.Comment: 11 pages, Accepted (Int. J. Theor. Phys.

Foveal avascular zone segmentation in optical coherence tomography angiography images using a deep learning approach

The purpose of this study was to introduce a new deep learning (DL) model for segmentation of the fovea avascular zone (FAZ) in en face optical coherence tomography angiography (OCTA) and compare the results with those of the device�s built-in software and manual measurements in healthy subjects and diabetic patients. In this retrospective study, FAZ borders were delineated in the inner retinal slab of 3 � 3 enface OCTA images of 131 eyes of 88 diabetic patients and 32 eyes of 18 healthy subjects. To train a deep convolutional neural network (CNN) model, 126 enface OCTA images (104 eyes with diabetic retinopathy and 22 normal eyes) were used as training/validation dataset. Then, the accuracy of the model was evaluated using a dataset consisting of OCTA images of 10 normal eyes and 27 eyes with diabetic retinopathy. The CNN model was based on Detectron2, an open-source modular object detection library. In addition, automated FAZ measurements were conducted using the device�s built-in commercial software, and manual FAZ delineation was performed using ImageJ software. Bland�Altman analysis was used to show 95 limit of agreement (95 LoA) between different methods. The mean dice similarity coefficient of the DL model was 0.94 ± 0.04 in the testing dataset. There was excellent agreement between automated, DL model and manual measurements of FAZ in healthy subjects (95 LoA of � 0.005 to 0.026 mm2 between automated and manual measurement and 0.000 to 0.009 mm2 between DL and manual FAZ area). In diabetic eyes, the agreement between DL and manual measurements was excellent (95 LoA of � 0.063 to 0.095), however, there was a poor agreement between the automated and manual method (95 LoA of � 0.186 to 0.331). The presence of diabetic macular edema and intraretinal cysts at the fovea were associated with erroneous FAZ measurements by the device�s built-in software. In conclusion, the DL model showed an excellent accuracy in detection of FAZ border in enfaces OCTA images of both diabetic patients and healthy subjects. The DL and manual measurements outperformed the automated measurements of the built-in software. © 2021, The Author(s)

Flat galaxies with dark matter halos - existence and stability

We consider a model for a flat, disk-like galaxy surrounded by a halo of dark matter, namely a Vlasov-Poisson type system with two particle species, the stars which are restricted to the galactic plane and the dark matter particles. These constituents interact only through the gravitational potential which stars and dark matter create collectively. Using a variational approach we prove the existence of steady state solutions and their nonlinear stability under suitably restricted perturbations.Comment: 39 page