Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity. This area of study has a long tradition in stochastic programming. However, the literature is lacking consistency analysis for problems in which the decision variables are taken from an infinite dimensional space, which arise in optimal control, scientific machine learning, and statistical estimation. By exploiting the typical problem structures found in these applications that give rise to hidden norm compactness properties for solution sets, we prove consistency results for nonconvex risk-averse stochastic optimization problems formulated in infinite dimensional space. The proof is based on several crucial results from the theory of variational convergence. The theoretical results are demonstrated for several important problem classes arising in the literature.Comment: 24 page

Comparison of satellite limb-sounding humidity climatologies of the uppermost tropical troposphere

International audienceHumidity climatologies of the tropical uppermost troposphere from satellite limb emission measurements have been compared. Four instruments are considered; UARS-MLS, Odin-SMR, and Aura-MLS operating in the microwave region, and MIPAS in the infrared region. A reference for the comparison is obtained by MOZAIC in-situ measurements. The upper tropospheric humidity products were compared on basis of their empirical probability density functions and seasonally averaged horizontal fields at two altitude layers, 12 and 15 km. The probability density functions of the microwave datasets were found to be in very good agreement with each other, and were also consistent with MOZAIC. The average seasonal humidities differ with less than 10%RHi between the instruments, indicating that stated measurement accuracies of 20?30% are conservative estimates. The systematic uncertainty in Odin-SMR data due to cloud correction was also independently estimated to be 10%RHi. MIPAS humidity profiles were found to suffer from cloud contamination, with only 30% of the measurements reaching into the upper troposphere, but under clear-sky conditions there is a good agreement between MIPAS, Odin-SMR and Aura-MLS. Odin-SMR and the two MLS datasets can be treated as independent, being based on different underlying spectroscopy and technology. The good agreement between the microwave limb-sounders, and MOZAIC, is therefore an important step towards understanding the upper tropospheric humidity. The found accuracy of 10%RHi is approaching the level required to validate climate modelling of the upper troposphere humidity. The comparison of microwave and infrared also stresses that microwave limb-sounding is necessary for a complete view of the upper troposphere

The cross-frequency mediation mechanism of intracortical information transactions

In a seminal paper by von Stein and Sarnthein (2000), it was hypothesized that "bottom-up" information processing of "content" elicits local, high frequency (beta-gamma) oscillations, whereas "top-down" processing is "contextual", characterized by large scale integration spanning distant cortical regions, and implemented by slower frequency (theta-alpha) oscillations. This corresponds to a mechanism of cortical information transactions, where synchronization of beta-gamma oscillations between distant cortical regions is mediated by widespread theta-alpha oscillations. It is the aim of this paper to express this hypothesis quantitatively, in terms of a model that will allow testing this type of information transaction mechanism. The basic methodology used here corresponds to statistical mediation analysis, originally developed by (Baron and Kenny 1986). We generalize the classical mediator model to the case of multivariate complex-valued data, consisting of the discrete Fourier transform coefficients of signals of electric neuronal activity, at different frequencies, and at different cortical locations. The "mediation effect" is quantified here in a novel way, as the product of "dual frequency RV-coupling coefficients", that were introduced in (Pascual-Marqui et al 2016, http://arxiv.org/abs/1603.05343). Relevant statistical procedures are presented for testing the cross-frequency mediation mechanism in general, and in particular for testing the von Stein & Sarnthein hypothesis.Comment: https://doi.org/10.1101/119362 licensed as CC-BY-NC-ND 4.0 International license: http://creativecommons.org/licenses/by-nc-nd/4.0

Differentially expressed microRNAs in maternal plasma for the noninvasive prenatal diagnosis of Down syndrome (trisomy 21).

OBJECTIVES: Most developmental processes are under the control of small regulatory RNAs called microRNAs (miRNAs). We hypothesize that different fetal developmental processes might be reflected by extracellular miRNAs in maternal plasma and may be utilized as biomarkers for the noninvasive prenatal diagnosis of chromosomal aneuploidies. In this proof-of-concept study, we report on the identification of extracellular miRNAs in maternal plasma of Down syndrome (DS) pregnancies. METHODS: Using high-throughput quantitative PCR (HT-qPCR), 1043 miRNAs were investigated in maternal plasma via comparison of seven DS pregnancies with age and fetal sex matched controls. RESULTS: Six hundred and ninety-five miRNAs were identified. Thirty-six significantly differentially expressed mature miRNAs were identified as potential biomarkers. Hierarchical cluster analysis of these miRNAs resulted in the clear discrimination of DS from euploid pregnancies. Gene targets of the differentially expressed miRNAs were enriched in signaling pathways such as mucin type-O-glycans, ECM-receptor interactions, TGF-beta, and endocytosis, which have been previously associated with DS. CONCLUSIONS: miRNAs are promising and stable biomarkers for a broad range of diseases and may allow a reliable, cost-efficient diagnostic tool for the noninvasive prenatal diagnosis of DS

Histomorphometric Assessment of Cancellous and Cortical Bone Material Distribution in the Proximal Humerus of Normal and Osteoporotic Individuals Significantly Reduced Bone Stock in the Metaphyseal and Subcapital Regions of Osteoporotic Individuals

Osteoporosis is a systemic disorder predominantly affecting postmenopausal women but also men at an advanced age. Both genders may suffer from low-energy fractures of, for example, the proximal humerus when reduction of the bone stock or/and quality has occurred. The aim of the current study was to compare the amount of bone in typical fracture zones of the proximal humerus in osteoporotic and non-osteoporotic individuals. The amount of bone in the proximal humerus was determined histomorphometrically in frontal plane sections. The donor bones were allocated to normal and osteoporotic groups using the T-score from distal radius DXA measurements of the same extremities. The T-score evaluation was done according to WHO criteria. Regional thickness of the subchondral plate and the metaphyseal cortical bone were measured using interactive image analysis. At all measured locations the amount of cancellous bone was significantly lower in individuals from the osteoporotic group compared to the non-osteoporotic one. The osteoporotic group showed more significant differences between regions of the same bone than the non-osteoporotic group. In both groups the subchondral cancellous bone and the subchondral plate were least affected by bone loss. In contrast, the medial metaphyseal region in the osteoporotic group exhibited higher bone loss in comparison to the lateral side. This observation may explain prevailing fracture patterns, which frequently involve compression fractures and certainly has an influence on the stability of implants placed in this medial region. It should be considered when planning the anchoring of osteosynthesis materials in osteoporotic patients with fractures of the proximal humerus

The dual frequency RV-coupling coefficient: a novel measure for quantifying cross-frequency information transactions in the brain

Identifying dynamic transactions between brain regions has become increasingly important. Measurements within and across brain structures, demonstrating the occurrence of bursts of beta/gamma oscillations only during one specific phase of each theta/alpha cycle, have motivated the need to advance beyond linear and stationary time series models. Here we offer a novel measure, namely, the "dual frequency RV-coupling coefficient", for assessing different types of frequency-frequency interactions that subserve information flow in the brain. This is a measure of coherence between two complex-valued vectors, consisting of the set of Fourier coefficients for two different frequency bands, within or across two brain regions. RV-coupling is expressed in terms of instantaneous and lagged components. Furthermore, by using normalized Fourier coefficients (unit modulus), phase-type couplings can also be measured. The dual frequency RV-coupling coefficient is based on previous work: the second order bispectrum, i.e. the dual-frequency coherence (Thomson 1982; Haykin & Thomson 1998); the RV-coefficient (Escoufier 1973); Gorrostieta et al (2012); and Pascual-Marqui et al (2011). This paper presents the new measure, and outlines relevant statistical tests. The novel aspects of the "dual frequency RV-coupling coefficient" are: (1) it can be applied to two multivariate time series; (2) the method is not limited to single discrete frequencies, and in addition, the frequency bands are treated by means of appropriate multivariate statistical methodology; (3) the method makes use of a novel generalization of the RV-coefficient for complex-valued multivariate data; (4) real and imaginary covariance contributions to the RV-coherence are obtained, allowing the definition of a "lagged-coupling" measure that is minimally affected by the low spatial resolution of estimated cortical electric neuronal activity.Comment: technical report, pre-print, 2016-03-1

Topology and zero energy edge states in carbon nanotubes with superconducting pairing

We investigate the spectrum of finite-length carbon nanotubes in the presence of onsite and nearest-neighbor superconducting pairing terms. A one-dimensional ladder-type lattice model is developed to explore the low-energy spectrum and the nature of the electronic states. We find that zero energy edge states can emerge in zigzag class carbon nanotubes as a combined effect of curvature-induced Dirac point shift and strong superconducting coupling between nearest-neighbor sites. The chiral symmetry of the system is exploited to define a winding number topological invariant. The associated topological phase diagram shows regions with nontrivial winding number in the plane of chemical potential and superconducting nearest-neighbor pair potential (relative to the onsite pair potential). A one-dimensional continuum model reveals the topological origin of the zero energy edge states: a bulk-edge correspondence is proven, which shows that the condition for nontrivial winding number and that for the emergence of edge states are identical. For armchair class nanotubes, the presence of edge states in the superconducting gap depends on the nanotube's boundary shape. For the minimal boundary condition, the emergence of the subgap states can also be deduced from the winding number

Intercomparison of ILAS-II version 1.4 and version 2 target parameters with MIPAS-Envisat measurements

This paper assesses the mean differences between the two ILAS-II data versions (1.4 and 2) by comparing them with MIPAS measurements made between May and October 2003. For comparison with ILAS-II results, MIPAS data processed at the Institut für Meteorologie und Klimaforschung, Karlsruhe, Germany (IMK) in cooperation with the Instituto de Astrofísica de Andalucía (IAA) in Granada, Spain, were used. The coincidence criteria of ±300 km in space and ±12 h in time for H<sub>2</sub>O, N<sub>2</sub>O, and CH<sub>4</sub> and the coincidence criteria of ±300 km in space and ±6 h in time for ClONO<sub>2</sub>, O<sub>3</sub>, and HNO<sub>3</sub> were used. The ILAS-II data were separated into sunrise (= Northern Hemisphere) and sunset (= Southern Hemisphere). For the sunrise data, a clear improvement from version 1.4 to version 2 was observed for H<sub>2</sub>O, CH<sub>4</sub>, ClONO<sub>2</sub>, and O<sub>3</sub>. In particular, the ILAS-II version 1.4 mixing ratios of H<sub>2</sub>O and CH<sub>4</sub> were unrealistically small, and those of ClONO<sub>2</sub> above altitudes of 30 km unrealistically large. For N<sub>2</sub>O and HNO<sub>3</sub>, there were no large differences between the two versions. Contrary to the Northern Hemisphere, where some exceptional profiles deviated significantly from known climatology, no such outlying profiles were found in the Southern Hemisphere for both versions. Generally, the ILAS-II version 2 data were in better agreement with the MIPAS data than the version 1.4, and are recommended for quantitative analysis in the stratosphere. For H<sub>2</sub>O data in the Southern Hemisphere, further data quality evaluation is necessary