Total internal reflection fluorescence cross-correlation spectroscopy: theory and application for studying boundary slip phenomenon

I present a new experimental method called Total Internal Reflection Fluorescence Cross-Correlation Spectroscopy (TIR-FCCS). It is a method that can probe hydrodynamic flows near solid surfaces, on length scales of tens of nanometres. Fluorescent tracers flowing with the liquid are excited by evanescent light, produced by epi-illumination through the periphery of a high NA oil-immersion objective. Due to the fast decay of the evanescent wave, fluorescence only occurs for tracers in the ~100 nm proximity of the surface, thus resulting in very high normal resolution. The time-resolved fluorescence intensity signals from two laterally shifted (in flow direction) observation volumes, created by two confocal pinholes are independently measured and recorded. The cross-correlation of these signals provides important information for the tracers’ motion and thus their flow velocity. Due to the high sensitivity of the method, fluorescent species with different size, down to single dye molecules can be used as tracers. The aim of my work was to build an experimental setup for TIR-FCCS and use it to experimentally measure the shear rate and slip length of water flowing on hydrophilic and hydrophobic surfaces. However, in order to extract these parameters from the measured correlation curves a quantitative data analysis is needed. This is not straightforward task due to the complexity of the problem, which makes the derivation of analytical expressions for the correlation functions needed to fit the experimental data, impossible. Therefore in order to process and interpret the experimental results I also describe a new numerical method of data analysis of the acquired auto- and cross-correlation curves – Brownian Dynamics techniques are used to produce simulated auto- and cross-correlation functions and to fit the corresponding experimental data. I show how to combine detailed and fairly realistic theoretical modelling of the phenomena with accurate measurements of the correlation functions, in order to establish a fully quantitative method to retrieve the flow properties from the experiments. An importance-sampling Monte Carlo procedure is employed in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for both modern desktop PC machines and massively parallel computers. The latter allows making the data analysis within short computing times. I applied this method to study flow of aqueous electrolyte solution near smooth hydrophilic and hydrophobic surfaces. Generally on hydrophilic surface slip is not expected, while on hydrophobic surface some slippage may exists. Our results show that on both hydrophilic and moderately hydrophobic (contact angle ~85°) surfaces the slip length is ~10-15nm or lower, and within the limitations of the experiments and the model, indistinguishable from zero.

Developments for transactinide chemistry experiments behind the gas-filled separator TASCA

Topic of this thesis is the development of experiments behind the gas-filled separator TASCA(TransActinide Separator and Chemistry Apparatus) to study the chemical properties of the transactinide elements.rnIn the first part of the thesis, the electrodepositions of short-lived isotopes of ruthenium and osmium on gold electrodes were studied as model experiments for hassium. From literature it is known that the deposition potential of single atoms differs significantly from the potential predicted by the Nernst equation. This shift of the potential depends on the adsorption enthalpy of therndeposited element on the electrode material. If the adsorption on the electrode-material is favoured over the adsorption on a surface made of the same element as the deposited atom, the electrode potential is shifted to higher potentials. This phenomenon is called underpotential deposition.rnPossibilities to automatize an electro chemistry experiment behind the gas-filled separator were explored for later studies with transactinide elements.rnThe second part of this thesis is about the in-situ synthesis of transition-metal-carbonyl complexes with nuclear reaction products. Fission products of uranium-235 and californium-249 were produced at the TRIGA Mainz reactor and thermalized in a carbon-monoxide containing atmosphere. The formed volatile metal-carbonyl complexes could be transported in a gas-stream.rnFurthermore, short-lived isotopes of tungsten, rhenium, osmium, and iridium were synthesised at the linear accelerator UNILAC at GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt. The recoiling fusion products were separated from the primary beam and the transfer products in the gas-filled separator TASCA. The fusion products were stopped in the focal plane of TASCA in a recoil transfer chamber. This chamber contained a carbon-monoxide – helium gas mixture. The formed metal-carbonyl complexes could be transported in a gas stream to various experimental setups. All synthesised carbonyl complexes were identified by nuclear decay spectroscopy. Some complexes were studied with isothermal chromatography or thermochromatography methods. The chromatograms were compared with Monte Carlo Simulations to determine the adsorption enthalpyrnon silicon dioxide and on gold. These simulations based on existing codes, that were modified for the different geometries of the chromatography channels. All observed adsorption enthalpies (on silcon oxide as well as on gold) are typical for physisorption. Additionally, the thermalstability of some of the carbonyl complexes was studied. This showed that at temperatures above 200 °C therncomplexes start to decompose.rnIt was demonstrated that carbonyl-complex chemistry is a suitable method to study rutherfordium, dubnium, seaborgium, bohrium, hassium, and meitnerium. Until now, only very simple, thermally stable compounds have been synthesized in the gas-phase chemistry of the transactindes. With the synthesis of transactinide-carbonyl complexes a new compound class would be discovered. Transactinide chemistry would reach the border between inorganic and metallorganic chemistry.rnFurthermore, the in-situ synthesised carbonyl complexes would allow nuclear spectroscopy studies under low background conditions making use of chemically prepared samples.

Feasibility studies of the pp pi 0 e + e - electromagnetic channel at PANDA

Among all possible realizations of quark and antiquark assembly, the nucleon (the proton and the neutron) is the most stable of all hadrons and consequently has been the subject of intensive studies. Mass, shape, radius and more complex representations of its internal structure are measured since several decades using different probes. The proton (spin 1/2) is described by the electric GE and magnetic GM form factors which characterise its internal structure. The simplest way to measure the proton form factors consists in measuring the angular distribution of the electron-proton elastic scattering accessing the so-called Space-Like region where q2 < 0. Using the crossed channel antiproton proton <--> e+e-, one accesses another kinematical region, the so-called Time-Like region where q2 > 0. However, due to the antiproton proton <--> e+e- threshold q2th, only the kinematical domain q2 > q2th > 0 is available. To access the unphysical region, one may use the antiproton proton --> pi0 e+ e- reaction where the pi0 takes away a part of the system energy allowing q2 to be varied between q2th and almost 0. This thesis aims to show the feasibility of such measurements with the PANDA detector which will be installed on the new high intensity antiproton ring at the FAIR facility at Darmstadt. To describe the antiproton proton --> pi0 e+ e- reaction, a Lagrangian based approach is developed. The 5-fold differential cross section is determined and related to linear combinations of hadronic tensors. Under the assumption of one nucleon exchange, the hadronic tensors are expressed in terms of the 2 complex proton electromagnetic form factors. An extraction method which provides an access to the proton electromagnetic form factor ratio R = |GE|/|GM| and for the first time in an unpolarized experiment to the cosine of the phase difference is developed. Such measurements have never been performed in the unphysical region up to now. Extended simulations were performed to show how the ratio R and the cosine can be extracted from the positron angular distribution. Furthermore, a model is developed for the antiproton proton --> pi0 pi+ pi- background reaction considered as the most dangerous one. The background to signal cross section ratio was estimated under different cut combinations of the particle identification information from the different detectors and of the kinematic fits. The background contribution can be reduced to the percent level or even less. The corresponding signal efficiency ranges from a few % to 30%. The precision on the determination of the ratio R and of the cosine is determined using the expected counting rates via Monte Carlo method. A part of this thesis is also dedicated to more technical work with the study of the prototype of the electromagnetic calorimeter and the determination of its resolution.

A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Feasibility studies for accessing nucleon structure observables with the PANDA experiment at the future FAIR facility

The availability of a high-intensity antiproton beam with momentum up to 15,GeV/c at the future FAIR will open a unique opportunity to investigate wide areas of nuclear physics with the $overline{P}$ANDA (anti{$overline{P}$}roton ANnihilations at DArmstadt) detector. Part of these investigations concern the Electromagnetic Form Factors of the proton in the time-like region and the study of the Transition Distribution Amplitudes, for which feasibility studies have been performed in this Thesis. rnMoreover, simulations to study the efficiency and the energy resolution of the backward endcap of the electromagnetic calorimeter of $overline{P}$ANDA are presented. This detector is crucial especially for the reconstruction of processes like $bar pprightarrow e^+ e^- pi^0$, investigated in this work. Different arrangements of dead material were studied. The results show that both, the efficiency and the energy resolution of the backward endcap of the electromagnetic calorimeter fullfill the requirements for the detection of backward particles, and that this detector is necessary for the reconstruction of the channels of interest. rnrnThe study of the annihilation channel $bar pprightarrow e^+ e^-$ will improve the knowledge of the Electromagnetic Form Factors in the time-like region, and will help to understand their connection with the Electromagnetic Form Factors in the space-like region. In this Thesis the feasibility of a measurement of the $bar pprightarrow e^+ e^-$ cross section with $overline{P}$ANDA is studied using Monte-Carlo simulations. The major background channel $bar pprightarrow pi^+ pi^-$ is taken into account. The results show a $10^9$ background suppression factor, which assure a sufficiently clean signal with less than 0.1% background contamination. The signal can be measured with an efficiency greater than 30% up to $s=14$,(GeV/c)$^2$. The Electromagnetic Form Factors are extracted from the reconstructed signal and corrected angular distribution. Above this $s$ limit, the low cross section will not allow the direct extraction of the Electromagnetic Form Factors. However, the total cross section can still be measured and an extraction of the Electromagnetic Form Factors is possible considering certain assumptions on the ratio between the electric and magnetic contributions.rnrnThe Transition Distribution Amplitudes are new non-perturbative objects describing the transition between a baryon and a meson. They are accessible in hard exclusive processes like $bar pprightarrow e^+ e^- pi^0$. The study of this process with $overline{P}$ANDA will test the Transition Distribution Amplitudes approach. This work includes a feasibility study for measuring this channel with $overline{P}$ANDA. The main background reaction is here $bar pprightarrow pi^+ pi^- pi^0$. A background suppression factor of $10^8$ has been achieved while keeping a signal efficiency above 20%.rnrnrnPart of this work has been published in the European Physics Journal A 44, 373-384 (2010).rn

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Zerfallspionenspektroskopie leichter Hyperkerne in der Elektroproduktion

Am Mainzer Mikrotron können Lambda-Hyperkerne in (e,e'K^+)-Reaktionen erzeugt werden. Durch den Nachweis des erzeugten Kaons im KAOS-Spektrometer lassen sich Reaktionen markieren, bei denen ein Hyperon erzeugt wurde. Die Spektroskopie geladener Pionen, die aus schwachen Zweikörperzerfällen leichter Hyperkerne stammen, erlaubt es die Bindungsenergie des Hyperons im Kern mit hoher Präzision zu bestimmen. Neben der direkten Produktion von Hyperkernen ist auch die Erzeugung durch die Fragmentierung eines hoch angeregten Kontinuumszustands möglich. Dadurch können unterschiedliche Hyperkerne in einem Experiment untersucht werden. Für die Spektroskopie der Zerfallspionen stehen hochauflösende Magnetspektrometer zur Verfügung. Um die Grundzustandsmasse der Hyperkerne aus dem Pionimpuls zu berechnen, ist es erforderlich, dass das Hyperfragment vor dem Zerfall im Target abgebremst wird. Basierend auf dem bekannten Wirkungsquerschnitt der elementaren Kaon-Photoproduktion wurde eine Berechnung der zu erwartenden Ereignisrate vorgenommen. Es wurde eine Monte-Carlo-Simulation entwickelt, die den Fragmentierungsprozess und das Abbremsen der Hyperfragmente im Target beinhaltet. Diese nutzt ein statistisches Aufbruchsmodell zur Beschreibung der Fragmentierung. Dieser Ansatz ermöglicht für Wasserstoff-4-Lambda-Hyperkerne eine Vorhersage der zu erwartenden Zählrate an Zerfallspionen. In einem Pilotexperiment im Jahr 2011 wurde erstmalig an MAMI der Nachweis von Hadronen mit dem KAOS-Spektrometer unter einem Streuwinkel von 0° demonstriert, und koinzident dazu Pionen nachgewiesen. Es zeigte sich, dass bedingt durch die hohen Untergrundraten von Positronen in KAOS eine eindeutige Identifizierung von Hyperkernen in dieser Konfiguration nicht möglich war. Basierend auf diesen Erkenntnissen wurde das KAOS-Spektrometer so modifiziert, dass es als dedizierter Kaonenmarkierer fungierte. Zu diesem Zweck wurde ein Absorber aus Blei im Spektrometer montiert, in dem Positronen durch Schauerbildung abgestoppt werden. Die Auswirkung eines solchen Absorbers wurde in einem Strahltest untersucht. Eine Simulation basierend auf Geant4 wurde entwickelt mittels derer der Aufbau von Absorber und Detektoren optimiert wurde, und die Vorhersagen über die Auswirkung auf die Datenqualität ermöglichte. Zusätzlich wurden mit der Simulation individuelle Rückrechnungsmatrizen für Kaonen, Pionen und Protonen erzeugt, die die Wechselwirkung der Teilchen mit der Bleiwand beinhalteten, und somit eine Korrektur der Auswirkungen ermöglichen. Mit dem verbesserten Aufbau wurde 2012 eine Produktionsstrahlzeit durchgeführt, wobei erfolgreich Kaonen unter 0° Streuwinkel koninzident mit Pionen aus schwachen Zerfällen detektiert werden konnten. Dabei konnte im Impulsspektrum der Zerfallspionen eine Überhöhung mit einer Signifikanz, die einem p-Wert von 2,5 x 10^-4 entspricht, festgestellt werden. Diese Ereignisse können aufgrund ihres Impulses, den Zerfällen von Wasserstoff-4-Lambda-Hyperkernen zugeordnet werden, wobei die Anzahl detektierter Pionen konsistent mit der berechneten Ausbeute ist.

Computer simulation of rod-coil block copolymers and tetrapod,polymer mixtures

In this thesis I present a new coarse-grained model suitable to investigate the phase behavior of rod-coil block copolymers on mesoscopic length scales. In this model the rods are represented by hard spherocylinders, whereas the coil block consists of interconnected beads. The interactions between the constituents are based on local densities. This facilitates an efficient Monte-Carlo sampling of the phase space. I verify the applicability of the model and the simulation approach by means of several examples. I treat pure rod systems and mixtures of rod and coil polymers. Then I append coils to the rods and investigate the role of the different model parameters. Furthermore, I compare different implementations of the model. I prove the capability of the rod-coil block copolymers in our model to exhibit typical micro-phase separated configurations as well as extraordinary phases, such as the wavy lamellar state, percolating structuresrnand clusters. Additionally, I demonstrate the metastability of the observed zigzag phase in our model. A central point of this thesis is the examination of the phase behavior of the rod-coil block copolymers in dependence of different chain lengths and interaction strengths between rods and coil. The observations of these studies are summarized in a phase diagram for rod-coil block copolymers. Furthermore, I validate a stabilization of the smectic phase with increasing coil fraction.rnIn the second part of this work I present a side project in which I derive a model permitting the simulation of tetrapods with and without grafted semiconducting block copolymers. The effect of these polymers is added in an implicit manner by effective interactions between the tetrapods. While the depletion interaction is described in an approximate manner within the Asakura-Oosawa model, the free energy penalty for the brush compression is calculated within the Alexander-de Gennes model. Recent experiments with CdSe tetrapods show that grafted tetrapods are clearly much better dispersed in the polymer matrix than bare tetrapods. My simulations confirm that bare tetrapods tend to aggregate in the matrix of excess polymers, while clustering is significantly reduced after grafting polymer chains to the tetrapods. Finally, I propose a possible extension enabling the simulation of a system with fluctuating volume and demonstrate its basic functionality. This study is originated in a cooperation with an experimental group with the goal to analyze the morphology of these systems in order to find the ideal morphology for hybrid solar cells.

A probabilistic approach to classify the levee reliability

This work aims to evaluate the reliability of these levee systems, calculating the probability of “failure” of determined levee stretches under different loads, using probabilistic methods that take into account the fragility curves obtained through the Monte Carlo Method. For this study overtopping and piping are considered as failure mechanisms (since these are the most frequent) and the major levee system of the Po River with a primary focus on the section between Piacenza and Cremona, in the lower-middle area of the Padana Plain, is analysed. The novelty of this approach is to check the reliability of individual embankment stretches, not just a single section, while taking into account the variability of the levee system geometry from one stretch to another. This work takes also into consideration, for each levee stretch analysed, a probability distribution of the load variables involved in the definition of the fragility curves, where it is influenced by the differences in the topography and morphology of the riverbed along the sectional depth analysed as it pertains to the levee system in its entirety. A type of classification is proposed, for both failure mechanisms, to give an indication of the reliability of the levee system based of the information obtained by the fragility curve analysis. To accomplish this work, an hydraulic model has been developed where a 500-year flood is modelled to determinate the residual hazard value of failure for each stretch of levee near the corresponding water depth, then comparing the results with the obtained classifications. This work has the additional the aim of acting as an interface between the world of Applied Geology and Environmental Hydraulic Engineering where a strong collaboration is needed between the two professions to resolve and improve the estimation of hydraulic risk.

Different Learning Curves for Axillary Brachial Plexus Block: Ultrasound Guidance versus Nerve Stimulation

Little is known about the learning of the skills needed to perform ultrasound- or nerve stimulator-guided peripheral nerve blocks. The aim of this study was to compare the learning curves of residents trained in ultrasound guidance versus residents trained in nerve stimulation for axillary brachial plexus block. Ten residents with no previous experience with using ultrasound received ultrasound training and another ten residents with no previous experience with using nerve stimulation received nerve stimulation training. The novices' learning curves were generated by retrospective data analysis out of our electronic anaesthesia database. Individual success rates were pooled, and the institutional learning curve was calculated using a bootstrapping technique in combination with a Monte Carlo simulation procedure. The skills required to perform successful ultrasound-guided axillary brachial plexus block can be learnt faster and lead to a higher final success rate compared to nerve stimulator-guided axillary brachial plexus block.

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.

Genetic diversity among horse populations with a special focus on the Franches-Montagnes breed

Genetic characterization helps to assure breed integrity and to assign individuals to defined populations. The objective of this study was to characterize genetic diversity in six horse breeds and to analyse the population structure of the Franches-Montagnes breed, especially with regard to the degree of introgression with Warmblood. A total of 402 alleles from 50 microsatellite loci were used. The average number of alleles per locus was significantly lower in Thoroughbreds and Arabians. Average heterozygosities between breeds ranged from 0.61 to 0.72. The overall average of the coefficient of gene differentiation because of breed differences was 0.100, with a range of 0.036-0.263. No significant correlation was found between this parameter and the number of alleles per locus. An increase in the number of homozygous loci with increasing inbreeding could not be shown for the Franches-Montagnes horses. The proportion of shared alleles, combined with the neighbour-joining method, defined clusters for Icelandic Horse, Comtois, Arabians and Franches-Montagnes. A more disparate clustering could be seen for European Warmbloods and Thoroughbreds, presumably from frequent grading-up of Warmbloods with Thoroughbreds. Grading-up effects were also observed when Bayesian and Monte Carlo resampling approaches were used for individual assignment to a given population. Individual breed assignments to defined reference populations will be very difficult when introgression has occurred. The Bayesian approach within the Franches-Montagnes breed differentiated individuals with varied proportions of Warmblood.

Financial analysis of various strategies for the control of Neospora caninum in dairy cattle in Switzerland

The present study was conducted to estimate the direct losses due to Neospora caninum in Swiss dairy cattle and to assess the costs and benefits of different potential control strategies. A Monte Carlo simulation spreadsheet module was developed to estimate the direct costs caused by N. caninum, with and without control strategies, and to estimate the costs of these control strategies in a financial analysis. The control strategies considered were "testing and culling of seropositive female cattle", "discontinued breeding with offspring from seropositive cows", "chemotherapeutical treatment of female offspring" and "vaccination of all female cattle". Each parameter in the module that was considered to be uncertain, was described using probability distributions. The simulations were run with 20,000 iterations over a time period of 25 years. The median annual losses due to N. caninum in the Swiss dairy cow population were estimated to be euro 9.7 million euros. All control strategies that required yearly serological testing of all cattle in the population produced high costs and thus were not financially profitable. Among the other control strategies, two showed benefit-cost ratios (BCR) >1 and positive net present values (NPV): "Discontinued breeding with offspring from seropositive cows" (BCR=1.29, NPV=25 million euros ) and "chemotherapeutical treatment of all female offspring" (BCR=2.95, NPV=59 million euros). In economic terms, the best control strategy currently available would therefore be "discontinued breeding with offspring from seropositive cows".

Choosing Smoothness Parameters for Smoothing Splines by Minimizing and Estimate of Risk

Smoothing splines are a popular approach for non-parametric regression problems. We use periodic smoothing splines to fit a periodic signal plus noise model to data for which we assume there are underlying circadian patterns. In the smoothing spline methodology, choosing an appropriate smoothness parameter is an important step in practice. In this paper, we draw a connection between smoothing splines and REACT estimators that provides motivation for the creation of criteria for choosing the smoothness parameter. The new criteria are compared to three existing methods, namely cross-validation, generalized cross-validation, and generalization of maximum likelihood criteria, by a Monte Carlo simulation and by an application to the study of circadian patterns. For most of the situations presented in the simulations, including the practical example, the new criteria out-perform the three existing criteria.

Power Calculations for Preclinical Studies Using a K-Sample Rank Test and the Lehmann Alternative Hypothesis

Power calculations in a small sample comparative study, with a continuous outcome measure, are typically undertaken using the asymptotic distribution of the test statistic. When the sample size is small, this asymptotic result can be a poor approximation. An alternative approach, using a rank based test statistic, is an exact power calculation. When the number of groups is greater than two, the number of calculations required to perform an exact power calculation is prohibitive. To reduce the computational burden, a Monte Carlo resampling procedure is used to approximate the exact power function of a k-sample rank test statistic under the family of Lehmann alternative hypotheses. The motivating example for this approach is the design of animal studies, where the number of animals per group is typically small.