Ultra-efficient MCMC for Bayesian longitudinal functional data analysis

Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only provide either scalable computing or accurate approximations to the posterior distribution, but not both. We introduce a new MCMC sampling strategy for highly efficient and fully Bayesian regression with longitudinal functional data. Using a novel blocking structure paired with an orthogonalized basis reparametrization, our algorithm jointly samples the fixed effects regression functions together with all subject- and replicate-specific random effects functions. Crucially, the joint sampler optimizes sampling efficiency for these key parameters while preserving computational scalability. Perhaps surprisingly, our new MCMC sampling algorithm even surpasses state-of-the-art algorithms for frequentist estimation and variational Bayes approximations for functional mixed models -- while also providing accurate posterior uncertainty quantification -- and is orders of magnitude faster than existing Gibbs samplers. Simulation studies show improved point estimation and interval coverage in nearly all simulation settings over competing approaches. We apply our method to a large physical activity dataset to study how various demographic and health factors associate with intraday activity

Decentralized event-triggered control of large-scale systems with saturated actuators

We consider a large-scale LTI system with multiple local communication networks connecting sensors, controllers, and actuators. The local networks operate asynchronously and independently of one another. The main novelty is that the decentralized controllers are subject to saturation. Our objective is to achieve a regional exponential stability providing a decentralized bound on the domain of attraction for each plant. We introduce a sampled-data event-Triggering mechanism from sensors to controllers to reduce the amount of transmitted signals. Using the time-delay approach to networked control systems and appropriate Lyapunov-Krasovskii functionals, we derive linear matrix inequalities that allow to find the decentralized bounds on the domains of attraction for each plant. Numerical example of coupled cart-pendulums illustrates the efficiency of the method

Decoherence in Disordered Conductors at Low Temperatures, the effect of Soft Local Excitations

The conduction electrons' dephasing rate, $\tau_{\phi}^{-1}$, is expected to vanish with the temperature. A very intriguing apparent saturation of this dephasing rate in several systems was recently reported at very low temperatures. The suggestion that this represents dephasing by zero-point fluctuations has generated both theoretical and experimental controversies. We start by proving that the dephasing rate must vanish at the $T\to 0$ limit, unless a large ground state degeneracy exists. This thermodynamic proof includes most systems of relevance and it is valid for any determination of $\tau_{\phi}$ from {\em linear} transport measurements. In fact, our experiments demonstrate unequivocally that indeed when strictly linear transport is used, the apparent low-temperature saturation of $\tau_{\phi}$ is eliminated. However, the conditions to be in the linear transport regime are more strict than hitherto expected. Another novel result of the experiments is that introducing heavy nonmagnetic impurities (gold) in our samples produces, even in linear transport, a shoulder in the dephasing rate at very low temperatures. We then show theoretically that low-lying local defects may produce a relatively large dephasing rate at low temperatures. However, as expected, this rate in fact vanishes when $T \to 0$, in agreement with our experimental observations.Comment: To appear in the proceedings of the Euresco Conference on Fundamental Problems of Mesoscopic Physics, Granada, September 2003, Kluwe

Quantifying the Gurken morphogen gradient in Drosophila oogenesis

Quantitative information about the distribution of morphogens is crucial for understanding their effects on cell-fate determination, yet it is difficult to obtain through direct measurements. We have developed a parameter estimation approach for quantifying the spatial distribution of Gurken, a TGFα-like EGFR ligand that acts as a morphogen in Drosophila oogenesis. Modeling of Gurken/EGFR system shows that the shape of the Gurken gradient is controlled by a single dimensionless parameter, the Thiele modulus, which reflects the relative importance of ligand diffusion and degradation. By combining the model with genetic alterations of EGFR levels, we have estimated the value of the Thiele modulus in the wild-type egg chamber. This provides a direct characterization of the shape of the Gurken gradient and demonstrates how parameter estimation techniques can be used to quantify morphogen gradients in development

Which phase is measured in the mesoscopic Aharonov-Bohm interferometer?

Mesoscopic solid state Aharonov-Bohm interferometers have been used to measure the "intrinsic" phase, $\alpha_{QD}$, of the resonant quantum transmission amplitude through a quantum dot (QD). For a two-terminal "closed" interferometer, which conserves the electron current, Onsager's relations require that the measured phase shift $\beta$ only "jumps" between 0 and $\pi$. Additional terminals open the interferometer but then $\beta$ depends on the details of the opening. Using a theoretical model, we present quantitative criteria (which can be tested experimentally) for $\beta$ to be equal to the desired $\alpha_{QD}$: the "lossy" channels near the QD should have both a small transmission and a small reflection

An inhomogeneous Josephson phase in thin-film and High-Tc superconductors

In many cases inhomogeneities are known to exist near the metal (or superconductor)-insulator transition, as follows from well-known domain-wall arguments. If the conducting regions are large enough (i.e. when the T=0 superconducting gap is much larger than the single-electron level spacing), and if they have superconducting correlations, it becomes energetically favorable for the system to go into a Josephson-coupled zero-resistance state before (i.e. at higher resistance than) becoming a "real" metal. We show that this is plausible by a simple comparison of the relevant coupling constants. For small grains in the above sense, the electronic grain structure is washed out by delocalization and thus becomes irrelevant. When the proposed "Josephson state" is quenched by a magnetic field, an insulating, rather then a metallic, state should appear. This has been shown to be consistent with the existing data on oxide materials as well as ultra-thin films. We discuss the Uemura correlations versus the Homes law, and derive the former for the large-grain Josephson array (inhomogenous superconductor) model. The small-grain case behaves like a dirty homogenous metal. It should obey the Homes law provided that the system is in the dirty supeconductivity limit. A speculation why that is typically the case for d-wave superconductors is presented.Comment: Conference proceeding for "Fluctuations in Superconductors" held in Nazareth, Israel in June, 2007; 6 pages with 1 figure, to appear in Physica

Evidence of Vortices on the Insulating Side of the Superconductor-Insulator Transition

The magnetoresistance of ultrathin insulating films of Bi has been studied with magnetic fields applied parallel and perpendicular to the plane of the sample. Deep in the strongly localized regime, the magnetoresistance is negative and independent of field orientation. As film thicknesses increase, the magnetoresistance becomes positive, and a difference between values measured in perpendicular and parallel fields appears, which is a linear function of the magnetic field and is positive. This is not consistent with the quantum interference picture. We suggest that it is due to vortices present on the insulating side of the superconductor-insulator transition.Comment: 4 pages, 3 figure

Prediction of improvement in skin fibrosis in diffuse cutaneous systemic sclerosis: a EUSTAR analysis

OBJECTIVES Improvement of skin fibrosis is part of the natural course of diffuse cutaneous systemic sclerosis (dcSSc). Recognising those patients most likely to improve could help tailoring clinical management and cohort enrichment for clinical trials. In this study, we aimed to identify predictors for improvement of skin fibrosis in patients with dcSSc. METHODS We performed a longitudinal analysis of the European Scleroderma Trials And Research (EUSTAR) registry including patients with dcSSc, fulfilling American College of Rheumatology criteria, baseline modified Rodnan skin score (mRSS) ≥7 and follow-up mRSS at 12±2 months. The primary outcome was skin improvement (decrease in mRSS of >5 points and ≥25%) at 1 year follow-up. A respective increase in mRSS was considered progression. Candidate predictors for skin improvement were selected by expert opinion and logistic regression with bootstrap validation was applied. RESULTS From the 919 patients included, 218 (24%) improved and 95 (10%) progressed. Eleven candidate predictors for skin improvement were analysed. The final model identified high baseline mRSS and absence of tendon friction rubs as independent predictors of skin improvement. The baseline mRSS was the strongest predictor of skin improvement, independent of disease duration. An upper threshold between 18 and 25 performed best in enriching for progressors over regressors. CONCLUSIONS Patients with advanced skin fibrosis at baseline and absence of tendon friction rubs are more likely to regress in the next year than patients with milder skin fibrosis. These evidence-based data can be implemented in clinical trial design to minimise the inclusion of patients who would regress under standard of care

Quantum Graphs: A simple model for Chaotic Scattering

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay time and conductance distributions, Ericson fluctuations, and when considered statistically, the ensemble of scattering matrices reproduce quite well the predictions of appropriately defined Random Matrix ensembles. The underlying classical dynamics can be defined, and it provides important parameters which are needed for the quantum theory. In particular, we derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. We use this in order to investigate the origin of the connection between Random Matrix Theory and the underlying classical chaotic dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the fore-front of the research in chaotic scattering and related fields.Comment: 28 pages, 13 figures, submitted to J. Phys. A Special Issue -- Random Matrix Theor