Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is non-intrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier-Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods

A representer theorem for deep kernel learning

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. As a direct consequence in the finite-sample case, the corresponding infinite-dimensional minimization problems can be recast into (nonlinear) finite-dimensional minimization problems, which can be tackled with nonlinear optimization algorithms. Moreover, we show how concatenated machine learning problems can be reformulated as neural networks and how our representer theorem applies to a broad class of state-of-the-art deep learning methods

Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms

Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal rates for the whole RKHS are often known. Schaback added the doubling trick, which shows that functions having double the smoothness required by the RKHS (along with complicated, but well understood boundary behavior) can be approximated with higher convergence rates than the optimal rates for the whole space. Other advances allowed interpolation of target functions which are less smooth, and different norms which measure interpolation error. The current state of the art of error analysis for RBF interpolation treats target functions having smoothness up to twice that of the native space, but error measured in norms which are weaker than that required for membership in the RKHS. Motivated by the fact that the kernels and the approximants they generate are smoother than required by the native space, this article extends the doubling trick to error which measures higher smoothness. This extension holds for a family of kernels satisfying easily checked hypotheses which we describe in this article, and includes many prominent RBFs. In the course of the proof, new convergence rates are obtained for the abstract operator considered by Devore and Ron, and new Bernstein estimates are obtained relating high order smoothness norms to the native space norm

Paraneoplastic cerebellar degeneration associated with lymphoepithelial carcinoma of the tonsil

Background: Paraneoplastic cerebellar degeneration (PCD) is a classical tumor-associated, immune-mediated disease typically associated with gynecological malignancies, small-cell lung-cancer or lymphoma. Case presentation: Here we present the case of a 38-year old male with an over 12 months rapidly progressive cerebellar syndrome. Extensive diagnostic workup revealed selective hypermetabolism of the right tonsil in whole-body PET. Histological examination after tonsillectomy demonstrated a lymphoepithelial carcinoma of the tonsil and the tongue base strongly suggesting a paraneoplastic cause of the cerebellar syndrome. To the best of our knowledge this is the first case of an association of a lymphoepithelial carcinoma, a rare pharyngeal tumor, with PCD. Conclusions: In cases of classical paraneoplastic syndromes an extensive search for neoplasms should be performed including whole-body PET to detect tumors early in the course of the disease

A prognosis oriented microscopic stock market model

We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the supply and demand fixing after each round (time step) the new price of the stock according to which the limited buy and sell orders are then executed and new forecasts are made. We show via numerical simulation of this model that the distribution of price differences obeys an exponentially truncated Levy-distribution with a self similarity exponent mu~5.Comment: 14 pages RevTeX, 5 eps-figures include

Weight Loss and Decrease of Body Mass Index during Allogeneic Stem Cell Transplantation Are Common Events with Limited Clinical Impact

Purpose Weight loss in cancer patients has been attributed with significant morbidity and mortality. During allogeneic stem cell transplantation (SCT),oral nutrition is often hampered and hence total parenteral nutrition (TPN) is necessary. We therefore investigated the course of weight during stem cell transplantation and the clinical consequences of weight change. Methods 180 consecutive patients who received allogeneic SCT between January 2010 and December 2011 at our center were analyzed for weight loss, laboratory and clinical parameters. Results During SCT, a median decrease of 6.6% of body mass index (BMI) was observed for the whole population (from 25.3 at admission to 23.6 at discharge),and a 1.6fold increase of malnutrition despite use of TPN (28.3% to 45.0%). 55.6% of patients experienced a significant weight loss of >= 5% with a median decrease of 9.2% in BMI. Serum levels of albumin, total protein and cholesterol rapidly decreased during conditioning therapy. After a median of 2.4 years, the median BMI was still only 23.4 (not different from discharge). However, we did not observe a meaningful difference in side effects and survival between patients that did or did not lose weight. Conclusion Weight loss is commonly observed during allogeneic SCT despite TPN, but the clinical consequences thereof seem limited: we observed no significant impact on patients with a decrease >= 5% in BMI on transplant outcome, side effects or survival

Inexpensive, Portable, Smartphone-Based 12-Lead Electrocardiogram

The electronics industry is constantly focusing on creating cheaper, more portable electronics that integrate with smartphone technology and the increasing demand for affordable and effective medical instrumentation. This Major Qualifying Project aims to complete preliminary development of an inexpensive, accurate, portable, Bluetooth 12-lead electrocardiogram (ECG) that interfaces with any Android smartphone. The current market lacks in mobile ECGs for portable devices to use clinically and other portable ECGs are extremely expensive. This project aims to use a compact analog front-end board, an embedded processor with Bluetooth adapter, and generic Android smartphone to revolutionize the way the healthcare industry envisions portable 12-lead ECGs

Ecological analysis of molluscs in the Bavarian Forest National Park

As part of the BIOKLIM Project, data was obtained for various groups of animals and plants, as well as for environmental factors. The following analysis concerns only the molluscs (Gastropoda, Bivalvia). Altitude, stand age, magnesium and pH values of soil were identified as main influencing variables for abundance of individuals, using quasi-Poisson models. The parameter “number of plant species” (VegRich) and management type also affect the species number. Individual species are influenced by very different factors, resulting partly from their highly specialized habitat requirements, so that their abundance can not always be described directly in terms of the measured and collated influencing variables. The mollusc-assemblages are determined most of all by altitude above sea level, temperature and light conditions (openness of canopy), as demonstrated using several different methods of statistical analysis.Im Rahmen des BIOKLIM-Projekts wurden im Nationalpark Bayerischer Wald Daten zu verschiedenen Tier- und Pflanzenarten sowie Umweltfaktoren erhoben. Die folgende Auswertung beschränkt sich auf die Weichtiere (Gastropoda, Bivalvia). Ziel war es, herauszufinden, welche Umweltfaktoren die Arten- und Individuenanzahlen beeinflussen, was die Lebensgemeinschaften steuert und welche Parameter sich auf ausgewählte Einzelarten auswirken. In Quasi-Poisson-Modellen haben sich als Einflussgrößen für die Individuenanzahl Höhe, Alter, Magnesium und pH-Wert feststellen lassen. Auf die Artenanzahl wirkte sich der Vegetationsreichtum, die Höhe und der Managementtyp aus. Die Einzelarten werden von sehr unterschiedlichen Faktoren beeinflusst. Die Lebensgemeinschaften werden vor allem von der Höhe über dem Meeresspiegel, der Temperatur und dem Auflichtungsgrad bestimmt, was sich in verschiedenen Ordinationsverfahren gezeigt hat