Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristic even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytucal expressions for the velocity correlation functions. Knowledge of the results presented here are expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.Comment: 15 pages, 15 figures; References adde

Modelling Costs of Interventional Pulmonary Embolism Treatment: Implications of US Trends for a European Healthcare System

BACKGROUND Catheter-directed treatment (CDT) of acute pulmonary embolism (PE) is entering a growth phase in Europe following a steady increase in the United States (US) in the past decade, but the potential economic impact on European healthcare systems remains unknown. METHODS AND RESULTS We built two statistical models for the monthly trend of proportion of CDT among patients with severe (intermediate- or high-risk) PE in the US. The conservative model was based on admission data from the National Inpatient Sample (NIS) 2016-2020, and the model reflecting increasing access to advanced treatment from the PERTTM national quality assurance database registry 2018-2021. By applying these models to the forecast of annual PE-related hospitalizations in Germany, we calculated the annual number of severe PE cases and the expected increase in CDT use for the period 2025-2030. The NIS-based model yielded a slow increase, reaching 3.1% (95% CI 3.0-3.2%) among all hospitalizations with PE in 2030; in the PERT-based model, increase would be steeper, reaching 8.7% (8.3-9.2%). Based on current reimbursement rates, we estimated an increase of annual costs for PE-related hospitalizations in Germany ranging from 15.3 to 49.8 million euros by 2030. This calculation does not account for potential cost savings, including those from reduced length of hospital stay. CONCLUSION Our approach and results, which may be adapted to other European healthcare systems, provide a benchmark for healthcare costs expected to result from CDT. Data from ongoing trials on clinical benefits and cost savings are needed to determine cost-effectiveness and inform reimbursement decisions

Cottontail species identification: zooarchaeological use of mandibular measurements

Volume: 5Start Page: 51End Page: 5

Interpolated cut cell method for simulating behavior of granular materials

We develop methods for well-approximating boundaries of complicated domains in numerical partial differential schemes. The main interest is methods to solve non-Newtonian Navier-Stokes based systems of equations representing the behavior of granular materials. We present the developed interpolated cut-cell method (ICCM), which includes different interpolation schemes

3D image based structural analysis of leather for macroscopic structure - property simulation

The intrinsic structure significantly influences the mechanical properties of leather. In consequence, knowledge of leather’s hierarchical structure is essential in order to find the most suited leather for specific application. Leather structure based parameters are of major importance for both manufacturing and leather processing industries. In this respect, intensive structure investigations have been subjected in continuous research work. Quantitative image analysis combined with stochastic micro-structure modelling and numerical simulation of macroscopic properties is a promising approach to gain a deeper understanding of complex relations between material’s micro-structure geometry and macroscopic properties. Key ingredient is a reliable geometric description provided by the quantitative analysis of 3D images of the material micro-structures. For leather, both imaging and image analysis are particularly challenging, due to the multi-scale nature of the leather’s micro-structure. Scales in leather are not well separated. Previously, high resolution computed tomography allowed 3D imaging of purely vegetable tanned leather samples at micro- and submicro- scale. Segmentation of leather structure as well as of typical structural elements in resulting image data is however hampered by a strong heterogeneity caused by lower scale structural information. The first method for automatic segmentation of typical structural elements at varying scales combined morphological smoothing with defining and iteratively coarsening regions using the waterfall algorithm on local orientations. It yields a hierarchical segmentation of the leather into coarse and fine structural elements that can be used to analyze and compare the structure of leather samples. Size and shape of the structural elements as well as their sub-structure yield information, e. g. on undulation, branching, thickness, cross-sectional shape, and preferred directions. In order to compare the micro-structure of leather samples from various body parts or even species, the segmentation has to be applicable without extensive pre-processing and parameter tuning. Robustness can be gained by applying smoothing methods that are adapted to the goal of defining image regions by similar local orientation. The challenge is that the space of fiber orientations in 3D is not equipped with an order. Motivated by a recent approach for nevertheless defining erosion and dilation on the sphere, we suggest new definitions for these morphological base transformations on the space of directions in 3D. We present segmentation results for 3D images of leather samples derived by these new morphological smoothing methods. Take-Away: The intrinsic structure significantly influences the mechanical properties of leather. Leather’s hierarchical structure can be analyzed by quantitative 3D image analysis combined with stochastic micro-structure modelling. Segmentation results for 3D images of leather samples derived by new morphological smoothing methods