A Study of Particle Motion in the Presence of Clusters

The motivation for this study came from the task of analysing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given measurements of both the motion of clusters and molecules, the main task consists in detecting if a molecule belongs to a cluster. While the exact size of the clusters is usually unknown, upper bounds are available. In this study, we simulate the cluster movement by a Brownian motion and those of the particles by a Gaussian mixture model with two modes depending on the position of the particle within or outside a cluster. We propose various variational models to detect if a particle lies within a cluster based on the Wasserstein and maximum mean discrepancy distances between measures. We compare the performance of the proposed models for simulated data

Glassy correlations and microstructures in randomly crosslinked homopolymer blends

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerges upon sufficient crosslinking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of crosslinking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellae or random structures with a unique wavelength, can be energetically favorable.Comment: 19 pages, 10 figures. Submitted to the Journal of Chemical Physics (http://jcp.aip.org

Generative Sliced MMD Flows with Riesz Kernels

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^r$, $r \in (0,2)$ have exceptional properties which allow for their efficient computation. First, the MMD of Riesz kernels coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for $r=1$, a simple sorting algorithm can be applied to reduce the complexity from $O(MN+N^2)$ to $O((M+N)\log(M+N))$ for two empirical measures with $M$ and $N$ support points. For the implementations we approximate the gradient of the sliced MMD by using only a finite number $P$ of slices. We show that the resulting error has complexity $O(\sqrt{d/P})$, where $d$ is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for large scale applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10

Extra force in f(R)f(R) modified theories of gravity

The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.Comment: Revtex4 file, 5 pages. Version to appear in Physical Review

Die Europäische Agrarpolitik im Spannungsfeld von Osterweiterung und WTO-Verhandlungen

Der Artikel umfasst eine quantitative polit-ökonomische Analyse aktueller und zukünftiger Reformen der Gemeinsamen Europäischen Agrarpolitik unter unterschiedlichen Szenarios einer zukünftigen EU-Osterweiterung und zukünftigen WTO-Verhandlungen. Theoretische Grundlage der Analysen ist ein politisches Tauschmodells von HENNING (2000). Zentrale Ergebnisse der quantitativen Analysen sind: (i) Es lässt sich ein signifikanter Einfluss der Agrarlobby auf die aktuelle und zukünftige Neuformulierung der Agrarpolitik in der EU-15 bzw. erweiterten EU-25 feststellen. (ii) Eine Osterweiterung hätte im Ve rgleich zu verschärften WTO-Restriktionen einen erheblich stärkeren Einfluss auf zukünftige Agrarreformen. Inhaltlich induziert eine Osterweiterung ein deutlich niedrigeres Agrarprotektionsniveau sowie eine geringere Förderung der Multifunktionalität der Landwirtschaft. (iii) Während innerhalb der EU-15 eine qualifizierte Mehrheit für eine entsprechende Agrarreform wäre, würde diese in einer erweiterten EU-25 am ?Veto? der osteuropäischen Mitglieder scheitern. Insofern ist das timing der Reform wichtig. (iv) Die Mehrheit der politischen Akteure in der EU-15 bewertet die außenpolitisch induzierten Reformen negativ, während diese aus gesamtgesellschaftlicher Perspektive der EU-15 positiv zu bewerten sind. -- The paper presents a quantitative politico-economic analysis of the present and future CAP-reform induced under different policy scenarios regarding a potential EU-enlargement and future WTO-agreements. Theoretically, the analysis is based on a political exchange model suggested by Henning (2000). Main results are: (i) Both present and future CAP-reforms are significantly biased by the political influence of farmer?s lobby. (ii) In quantitative terms an EU-enlargement would induce a much stronger shift in the future CAP when compared to increased WTO-restrictions. Generally, induced CAP-reforms imply a significant lower level of protection and a lower support of multifunctional services of the agricultural sector. (iii) The timing of the reform is important, given the fact that induced CAP-reforms would be supported by a qualified majority within the EU-15, but within the EU-25 these reforms would be defeated by coalition of the new Eastern European member states using their common veto-power. (iv) The majority of political actors within the EU-15 including both politicians and interest groups evaluate induced CAP-reforms negatively in comparison to the status quo, while from society?s perspective these imply a positive shift of total economic welfare within EU-15.

Die Europäische Agrarpolitik im Spannungsfeld von Osterweiterung und WTO-Verhandlungen

The paper presents a political economy analysis of the present and future CAP reform induced under different policy scenarios regarding future EU enlargement and future WTO agreements. Theoretically, the analysis is based on a political exchange model suggested by HENNING (2000). Main results are: (i) Both present and future CAP reforms are significantly biased by the political influence of farmers' lobby. (ii) In quantitative terms an EU enlargement would induce a much stronger shift in the future CAP when compared to increased WTO restrictions. (iii) The timing of the reform is important, given the fact that induced CAP reforms would be supported by a qualified majority within the EU-15, but within the EU-25 these reforms would be defeated by coalition of the new Eastern European member states using their common veto-power. (iv) The majority of political actors within the EU-15 including both politicians and interest groups evaluate induced CAP reforms negatively in comparison to the status quo, while from society’s perspective these imply a positive shift of total economic welfare within EU-15.political economy analysis, CAP, EU enlargement, WTO, Agricultural and Food Policy, International Relations/Trade, Political Economy,

Retinometer predicts visual outcome in Descemet membrane endothelial keratoplasty.

PURPOSE To analyze the preoperative predictive value of retinometer visual acuity (VA) in eyes following Descemet membrane endothelial keratoplasty (DMEK). METHODS Patients undergoing DMEK between August 2011 and July 2020 were included. Preoperative interference visual acuity was assessed using Heine Lambda 100 Retinometer. Depending on the presence or absence of concomitant ocular disease, the Retinometer was evaluated for its ability to preoperatively predict best-corrected visual acuity (BCVA) six months after surgery using correlation, simple and multiple linear regression, contingency analyses, and receiver operating characteristic (ROC) analysis. Preoperative corneal backscatter was correlated with Retinometer prediction accuracy. RESULTS A total of 198 eyes were included in the analysis. There was a significant correlation between Retinometer VA and postoperative BCVA (r = 0.647, P < 0.001). Regardless of the presence or absence of concomitant ocular disease and the surgery procedure (DMEK & triple DMEK), Retinometer VA was the most significant predictor of postoperative BCVA (P < 0.001). ROC analysis revealed reliable diagnostic performance of the Retinometer (AUC = 0.829, P < 0.001). A Retinometer VA ≥ 0.5 accurately predicted a postoperative BCVA ≥ 0.5 in 91% of cases. No association was found between corneal backscatter and prediction accuracy (P = 0.566). CONCLUSIONS Retinometer VA can be used for preoperative prediction of postoperative BCVA in DMEK and triple DMEK patients, independent of increased backscatter values and the presence or absence of concomitant ocular disease. By using this simple but effective tool, indication for DMEK can be facilitated and postoperative outcomes can be realistically predicted preoperatively

Piezoelectric titanium based microfluidic pump and valves for implantable medical applications

Medical devices often require precise movement of fluids. Automated implants with no need for manual handling improve patient care significantly. However, existing microfluidic devices do not fulfil the necessary specifications of size, safety, hermetic sealing, and artefact free medical imaging, as well as energy efficiency combined with adapted fluidic properties. In this work we designed, manufactured, and experimentally evaluated three piezoelectric microfluidic devices for implant automation: a diaphragm pump, a normally closed valve, and a normally open valve. All devices are made of titanium, minimizing the risk of artefacts in medical imaging. They have similar form factors and use the same actuation method. For the later, a specific mounting process of the piezo actuator enables outstanding fluidic performance during experimental evaluations. The titanium micropumps show a maximal flow of (14 ± 2.2) ml/min and pressure build-up of 75 kPa. The normally closed valve’s leakage rates are extremely low with less than 1 μL/min. Detailed investigations further include the actuator stroke, a lifetime study for normally open valves, and a numerical and experimental evaluation of the normally closed valve’s spring foil. The introduced titanium technology platform is ideally suited for system integration accounted for by the use of the same actuation principle and the similar form factor and a simple design. The development of small, smart, and energy efficient implants for improved treatment is possible based on the introduced platform