Numerical discretization of rotated diffusion operators in ocean models

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on the so-called z-coordinate system is presented. The authors then focus exclusively on the dynamically passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather complex, while simpler, linear schemes are shown to produce unphysical undershooting and overshooting. It is suggested that the choice of an appropriate discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically active or not

A Simple Empirical Calibration of Energy Dispersive X-Ray Analysis (EDXA) on the Cornea

Monitoring of the corneal electrolyte content is important for the study of chemical eye burns. This paper describes quantitative measurements on gelatin standards, corneas and a cornea homogenate with an energy dispersive X-ray analyzer (EDX) in the scanning electron microscope (SEM). Ten micrometers thick cryosections were freeze-dried and mounted on solid carbon supports. The applied quantification procedure was a local peak background analysis with a specifically designed computer program. Similar chemical and physical properties of gelatin, cornea homogenate, and cornea were proven by EDX-analysis and wet chemical analysis. Gelatin standards with known concentrations of different added salts showed linear correlations with a correlation coefficient higher than 0.95 for all considered elements. The local background generation on carbon supports was the same for gelatin standards and corneal tissue. The results demonstrate that quantitative EDX analysis of semi-thin samples, mounted on neutral carbon supports, can be reliably used for the assessment of the corneal mineral composition

Numerical issues of the Total Exchange Flow (TEF) analysis framework for quantifying estuarine circulation

For more than a century, estuarine exchange flow has been quantified by means of the Knudsen relations which connect bulk quantities such as inflow and outflow volume fluxes and salinities. These relations are closely linked to estuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which uses salinity coordinates to calculate these bulk quantities, allows an exact formulation of the Knudsen relations in realistic cases. There are however numerical issues, since the original method does not converge to the TEF bulk values for an increasing number of salinity classes. In the present study, this problem is investigated and the method of dividing salinities, described by MacCready et al. (2018), is mathematically introduced. A challenging yet compact analytical scenario for a well-mixed estuarine exchange flow is investigated for both methods, showing the proper convergence of the dividing salinity method. Furthermore, the dividing salinity method is applied to model results of the Baltic Sea to demonstrate the analysis of realistic exchange flows and exchange flows with more than two layers.</p

Segmentation of Retinal Low-Cost Optical Coherence Tomography Images using Deep Learning

The treatment of age-related macular degeneration (AMD) requires continuous eye exams using optical coherence tomography (OCT). The need for treatment is determined by the presence or change of disease-specific OCT-based biomarkers. Therefore, the monitoring frequency has a significant influence on the success of AMD therapy. However, the monitoring frequency of current treatment schemes is not individually adapted to the patient and therefore often insufficient. While a higher monitoring frequency would have a positive effect on the success of treatment, in practice it can only be achieved with a home monitoring solution. One of the key requirements of a home monitoring OCT system is a computer-aided diagnosis to automatically detect and quantify pathological changes using specific OCT-based biomarkers. In this paper, for the first time, retinal scans of a novel self-examination low-cost full-field OCT (SELF-OCT) are segmented using a deep learning-based approach. A convolutional neural network (CNN) is utilized to segment the total retina as well as pigment epithelial detachments (PED). It is shown that the CNN-based approach can segment the retina with high accuracy, whereas the segmentation of the PED proves to be challenging. In addition, a convolutional denoising autoencoder (CDAE) refines the CNN prediction, which has previously learned retinal shape information. It is shown that the CDAE refinement can correct segmentation errors caused by artifacts in the OCT image.Comment: Accepted for SPIE Medical Imaging 2020: Computer-Aided Diagnosi

Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

A detailed view of filaments and sheets in the warm-hot intergalactic medium. I. Pancake formation

Numerical simulations predict a considerable fraction of the missing baryons at redshift z ~ 0 resting in the so called warm-hot intergalactic medium (WHIM). The filaments and sheets of the WHIM have high temperatures 10^5 - 10^7 K) and a high degree of ionization while having only low to intermediate densities. The particular physical conditions of the WHIM structures, e.g. density and temperature profiles, velocity fields, are expected to leave their special imprint on spectroscopic observations. In order to get further insight into these conditions, we perform hydrodynamical simulations of the WHIM. Instead of analyzing large simulations of cosmological structure formation, we simulate particular well-defined structures and study the impact of different physical processes as well as of the scale dependencies. We start with the comprehensive study of the one-dimensional collapse (pancake) and examine the influence of radiative cooling, heating due to an UV background, and thermal conduction. We investigate the effect of small scale perturbations given according to the initial cosmological power spectrum. If the initial perturbation length scale L exceeds ~ 2 Mpc the collapse leads to shock confined structures. As a result of radiative cooling and of heating due to an UV background a relatively cold and dense core forms in the one-dimensional case. The properties of the core (extension, density, and temperature) are correlated with L. For larger L the core sizes are more concentrated. Thermal conduction enhances this trend and may even result in an evaporation of the core. Our estimates predict that a core may start to evaporate for perturbation lengths larger than L ~ 30 Mpc. The obtained detailed profiles for density and temperature for prototype WHIM structures allow for the determination of possible spectral signatures by the WHIM.Comment: 14 pages, 9 figures, accepted for publication in A&

Topological effects in ring polymers: A computer simulation study

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction \Phi=0.5 and show that rings in the melt are more compact than gaussian chains. A careful finite size analysis of the average ring size R \propto N^{\nu} yields an exponent \nu \approx 0.39 \pm 0.03 in agreement with a Flory-like argument for the topologica interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale \tau_{ee} \propto N^{2.0(2); this is shown by the collapse of several mean-square displacements and correlation functions onto corresponding master curves. Because of the shrunken state of the chain, this scaling is not compatible with simple Rouse motion. It applies for all sizes of ring studied and no sign of a crossover to any entangled regime is found.Comment: 20 Pages,11 eps figures, Late