Multilevel Double Loop Monte Carlo and Stochastic Collocation Methods with Importance Sampling for Bayesian Optimal Experimental Design

An optimal experimental set-up maximizes the value of data for statistical inferences and predictions. The efficiency of strategies for finding optimal experimental set-ups is particularly important for experiments that are time-consuming or expensive to perform. For instance, in the situation when the experiments are modeled by Partial Differential Equations (PDEs), multilevel methods have been proven to dramatically reduce the computational complexity of their single-level counterparts when estimating expected values. For a setting where PDEs can model experiments, we propose two multilevel methods for estimating a popular design criterion known as the expected information gain in simulation-based Bayesian optimal experimental design. The expected information gain criterion is of a nested expectation form, and only a handful of multilevel methods have been proposed for problems of such form. We propose a Multilevel Double Loop Monte Carlo (MLDLMC), which is a multilevel strategy with Double Loop Monte Carlo (DLMC), and a Multilevel Double Loop Stochastic Collocation (MLDLSC), which performs a high-dimensional integration by deterministic quadrature on sparse grids. For both methods, the Laplace approximation is used for importance sampling that significantly reduces the computational work of estimating inner expectations. The optimal values of the method parameters are determined by minimizing the average computational work, subject to satisfying the desired error tolerance. The computational efficiencies of the methods are demonstrated by estimating the expected information gain for Bayesian inference of the fiber orientation in composite laminate materials from an electrical impedance tomography experiment. MLDLSC performs better than MLDLMC when the regularity of the quantity of interest, with respect to the additive noise and the unknown parameters, can be exploited

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.Comment: 42 pages, 35 figure

Вплив нормального тиску на напружений стан гуми ступінчастого каната на робочому органі підйомної машини

Досліджено напружений стан гуми ступінчастого гумотросового каната у разі його застосування на підйомній машині з бобінним робочим органом та зі шківом тертя. Показано, що максимальні напруження в гумі залежать від конструкції каната та тиску, що виникає поміж шарами. Форма поперечного перерізу троса також впливає на напружений стан гуми.Исследовано напряженное состояние резины ступенчатого резинотросового каната в случае его применения на подъемной машине с бобинным рабочим органом и со шкивом трения. Показано, что максимальные напряжения в резине зависят от конструкции каната и давления, возникающего между слоями. Форма поперечного сечения троса также влияет на напряженное состояние резины.The stress-strain state of stepped rubber-rope cable in bobbin of winding and in pulley friction, are investigated. Shown that the maximum stress in the rubber depends on the design of the rope and the pressure appeared between the layers. Cable cross-sectional shape also affects to the stressstrain state of rubber

Prevalence of impaired glucose tolerance and other types of dysglycaemia among young twins and singletons in Guinea-Bissau

BACKGROUND: Twins may be at increased risk of dysglycaemic disorders due to adverse fetal conditions. Data from Africa regarding this association is limited. We studied impaired glucose tolerance (IGT) and other types of dysglycemia among twins and singletons in Guinea-Bissau. METHODS: The study was conducted from February 2011 until March 2012 at the Bandim Health Project, a health and demographic surveillance system site in the capital Bissau. Twins (n = 209) and singletons (n = 182) were recruited from a previously established cohort. Oral glucose tolerance tests (OGTT) were performed, along with anthropometrics and collection of clinical and dietary data. RESULTS: Median age was 16.6 and 14.2 years between twins and singletons, respectively (P = 0.08). Mean birth weight was 2410 vs. 3090 g, respectively (P < 0.001). Twins had higher median fasting- and two hour capillary plasma glucose, 5.4(3.2–8.2) vs. 5.0(3.2–11.5) mmol/L (P < 0.001) and 6.8(3.4–11.3) vs. 6.2(3.2–12.1) mmol/L (P < 0.001), respectively, compared to singletons. The prevalence of IGT was 2.5 % (5/209) vs. 3.5 % (6/182) (RR = 0.73, 95 % CI: 0.20–2.64). 12 % (25/209) of twins had impaired fasting glucose (IFG), compared to 3.5 % (6/182) of singletons (3.63, 1.53–8.62). Dysglycemia (IGT and/or IFG or overt diabetes) was found in 17 % (35/209) vs. 9 % (16/182) (1.90, 1.08–3.37), respectively. CONCLUSIONS: Twins had higher glucose levels in both the fasting and postprandial state. This may indicate a detrimental effect of the twin fetal environment on glucose metabolism later in life, a result contrary to Scandinavian register studies. The IGT burden was low in this young age group and the risk was similar in twins and singletons. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12902-016-0126-6) contains supplementary material, which is available to authorized users

From representing views to representativeness of views: illustrating a new (Q2S) approach in the context of health care priority setting in nine European countries

Governments across Europe are required to make decisions about how best to allocate scarce health care resources. There are legitimate arguments for eliciting societal vales in relation to health care resource allocation given the roles of the general public as payers and potential patients. However, relatively little is known about the views of the general public on general principles which could guide these decisions. In this paper we present five societal viewpoints on principles for health care resources allocation and develop a new approach, Q2S, designed to investigate the extent to which these views are held across a range of European countries. An online survey was developed, based on a previously completed study Q methodology, and delivered between November 2009 and February 2010 across nine countries to 33,515 respondents. The largest proportion of our respondents (44%), were found to most associate themselves with an egalitarian perspective. Differences in views were more strongly associated with countries than with socio-demographic characteristics. These results provide information which could be useful for decision makers in understanding the pluralistic context in which they are making health care resource allocation decisions and how different groups in society may respond to such decisions

Conditional generation of sub-Poissonian light from two-mode squeezed vacuum via balanced homodyne detection on idler mode

A simple scheme for conditional generation of nonclassical light with sub-Poissonian photon-number statistics is proposed. The method utilizes entanglement of signal and idler modes in two-mode squeezed vacuum state generated in optical parametric amplifier. A quadrature component of the idler mode is measured in balanced homodyne detector and only those experimental runs where the absolute value of the measured quadrature is higher than certain threshold are accepted. If the threshold is large enough then the conditional output state of signal mode exhibits reduction of photon-number fluctuations below the coherent-state level.Comment: 7 pages, 6 figures, REVTe

New features of quantum discord uncovered by q-entropies

The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88, 017901 (2001)] (see also Henderson and Vedral [J. Phys. A 34, 6899 (2001)]) has attracted increasing attention, in recent years, as an entropic quantifier of non-classical features pertaining to the correlations exhibited by bipartite quantum systems. Here we generalize the notion so as to encompass power-law q-entropies (that reduce to the standard Shannon entropy in the limit $q \to 1$) and study the concomitant consequences. The ensuing, new discord-like measures we advance describe aspects of non-classicality that are different from those associated with the standard quantum discord. A particular manifestation of this difference concerns a feature related to order. Let $D_1$ stand for the standard, Shannon-based discord measure and $D_q$ for the $q \ne 1$ one. If two quantum states $A$, $B$ are such that $D_1(A) > D_1(B)$, this order-relation does not remain invariant under a change from $D_1$ to $D_q$.Comment: 11 pages, 8 figure

A prospective study of twinning and perinatal mortality in urban Guinea-Bissau

BACKGROUND: Despite twinning being common in Africa, few prospective twin studies have been conducted. We studied twinning rate, perinatal mortality and the clinical characteristics of newborn twins in urban Guinea-Bissau. METHODS: The study was conducted at the Bandim Health Project (BHP), a health and demographic surveillance site in Bissau, the capital of Guinea-Bissau. The cohort included all newborn twins delivered at the National Hospital Simão Mendes and in the BHP study area during the period September 2009 to August 2011 as well as singleton controls from the BHP study area. Data regarding obstetric history and pregnancy were collected at the hospital. Live children were examined clinically. For a subset of twin pairs zygosity was established by using genetic markers. RESULTS: Out of the 5262 births from mothers included in the BHP study area, 94 were twin births, i.e. a community twinning rate of 18/1000. The monozygotic rate was 3.4/1000. Perinatal mortality among twins vs. singletons was 218/1000 vs. 80/1000 (RR = 2.71, 95% CI: 1.93-3.80). Among the 13783 hospital births 388 were twin births (28/1000). The hospital perinatal twin mortality was 237/1000. Birth weight < 2000g (RR = 4.24, CI: 2.39-7.51) and caesarean section (RR = 1.78, CI: 1.06-2.99) were significant risk factors for perinatal twin mortality. Male sex (RR = 1.38, CI: 0.97-1.96), unawareness of twin pregnancy (RR = 1.64, CI: 0.97-2.78) and high blood pressure during pregnancy (RR = 1.77, CI: 0.88-3.57) were borderline non-significant. Sixty-five percent (245/375) of the mothers who delivered at the hospital were unaware of their twin pregnancy. CONCLUSIONS: Twins had a very high perinatal mortality, three-fold higher than singletons. A birth weight < 2000g was the strongest risk factor for perinatal death, and unrecognized twin pregnancy was common. Urgent interventions are needed to lower perinatal twin mortality in Guinea-Bissau

Spectroscopic indications of tunnel barrier charging as the switching mechanism in memristive devices

Resistive random access memory is a promising, energy-efficient, low-power “storage class memory” technology that has the potential to replace both flash storage and on-chip dynamic memory. While the most widely employed systems exhibit filamentary resistive switching, interface-type switching systems based on a tunable tunnel barrier are of increasing interest. They suffer less from the variability induced by the stochastic filament formation process and the choice of the tunnel barrier thickness offers the possibility to adapt the memory device current to the given circuit requirements. Heterostructures consisting of a yttria-stabilized zirconia (YSZ) tunnel barrier and a praseodymium calcium manganite (PCMO) layer are employed. Instead of spatially localized filaments, the resistive switching process occurs underneath the whole electrode. By employing a combination of electrical measurements, in operando hard X-ray photoelectron spectroscopy and electron energy loss spectroscopy, it is revealed that an exchange of oxygen ions between PCMO and YSZ causes an electrostatic modulation of the effective height of the YSZ tunnel barrier and is thereby the underlying mechanism for resistive switching in these devices