Comparing Local Fitting to Other Automatic Smoothers

In a public service enterprise by Breiman and Peters (1991) various automatic smoothers, such as the supersmoother (SSMU), cross-validated smoothing splines (BART), delete-knot regression splines (DKS) and the cross-validated kernel smooth (KERNEL) were compared by simulation on a variety of sample sizes, noise levels and functions. The intention was to give practitioners guidelines when to use which type of smoother. The given work completes those simulations by including the increasingly popular local fitting approach, that was introduced to the statistical literature by Cleveland (1979). Fedorov et al. (1993) have modified the technique in order to take account possible misspecification bias, termed 'optimized moving local regression', and here we use an automated version (by crossvalidation) of it as given in Fedorov et al. (1994). (author's abstract)Series: Forschungsberichte / Institut für Statisti

Characterizing Rhodopsin-Arrestin Interactions with the Fragment Molecular Orbital (FMO) Method

Arrestin binding to G protein-coupled receptors (GPCRs) plays a vital role in receptor signaling. Recently, the crystal structure of rhodopsin bound to activated visual arrestin was resolved using XFEL (X-ray free electron laser). However, even with the crystal structure in hand, our ability to understand GPCR-arrestin binding is limited by the availability of accurate tools to explore receptor-arrestin interactions. We applied fragment molecular orbital (FMO) method to explore the interactions formed between the residues of rhodopsin and arrestin. FMO enables ab initio approaches to be applied to systems that conventional quantum mechanical (QM) methods would be too compute-expensive. The FMO calculations detected 35 significant interactions involved in rhodopsin-arrestin binding formed by 25 residues of rhodopsin and 28 residues of arrestin. Two major regions of interaction were identified: at the C-terminal tail of rhodopsin (D330-S343) and where the "finger loop" (G69-T79) of arrestin directly inserts into rhodopsin active core. Out of these 35 interactions, 23 were mainly electrostatic and 12 hydrophobic in nature

Optimal experimental design for predator–prey functional response experiments

Functional response models are important in understanding predator–prey interactions. The development of functional response methodology has progressed from mechanistic models to more statistically motivated models that can account for variance and the over-dispersion commonly seen in the datasets collected from functional response experiments. However, little information seems to be available for those wishing to prepare optimal parameter estimation designs for functional response experiments. It is worth noting that optimally designed experiments may require smaller sample sizes to achieve the same statistical outcomes as non-optimally designed experiments. In this paper, we develop a model-based approach to optimal experimental design for functional response experiments in the presence of parameter uncertainty (also known as a robust optimal design approach). Further, we develop and compare new utility functions which better focus on the statistical efficiency of the designs; these utilities are generally applicable for robust optimal design in other applications (not just in functional response). The methods are illustrated using a beta-binomial functional response model for two published datasets: an experiment involving the freshwater predator Notonecta glauca (an aquatic insect) preying on Asellus aquaticus (a small crustacean), and another experiment involving a ladybird beetle (Propylea quatuordecimpunctata L.) preying on the black bean aphid (Aphis fabae Scopoli). As a by-product, we also derive necessary quantities to perform optimal design for beta-binomial regression models, which may be useful in other applications

Reconstructing complex states of a 20-qubit quantum simulator

A prerequisite to the successful development of quantum computers and simulators is precise understanding of the physical processes occurring therein, which can be achieved by measuring the quantum states that they produce. However, the resources required for traditional quantum state estimation scale exponentially with the system size, highlighting the need for alternative approaches. Here, we demonstrate an efficient method for reconstruction of significantly entangled multiqubit quantum states. Using a variational version of the matrix-product-state ansatz, we perform the tomography (in the pure-state approximation) of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases, with 1000 measurements in each basis. We observe superior state-reconstruction quality and faster convergence compared to the methods based on neural-network quantum state representations: restricted Boltzmann machines and feed-forward neural networks with autoregressive architecture. Our results pave the way toward efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems

Extremal measures maximizing functionals based on simplicial volumes

We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension k ≤ d formed by k + 1 independent copies and raised to some power δ. We study properties of extremal measures that maximize these functionals. In particular, for positive δ we characterize their support and for negative δ we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented

High resolution 3-Dimensional imaging of the human cardiac conduction system from microanatomy to mathematical modeling

Cardiac arrhythmias and conduction disturbances are accompanied by structural remodelling of the specialised cardiomyocytes known collectively as the cardiac conduction system. Here, using contrast enhanced micro-computed tomography, we present, in attitudinally appropriate fashion, the first 3-dimensional representations of the cardiac conduction system within the intact human heart. We show that cardiomyocyte orientation can be extracted from these datasets at spatial resolutions approaching the single cell. These data show that commonly accepted anatomical representations are oversimplified. We have incorporated the high-resolution anatomical data into mathematical simulations of cardiac electrical depolarisation. The data presented should have multidisciplinary impact. Since the rate of depolarisation is dictated by cardiac microstructure, and the precise orientation of the cardiomyocytes, our data should improve the fidelity of mathematical models. By showing the precise 3-dimensional relationships between the cardiac conduction system and surrounding structures, we provide new insights relevant to valvar replacement surgery and ablation therapies. We also offer a practical method for investigation of remodelling in disease, and thus, virtual pathology and archiving. Such data presented as 3D images or 3D printed models, will inform discussions between medical teams and their patients, and aid the education of medical and surgical trainees