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

Dose-dependent new bone formation by extracorporeal shock wave application on the intact femur of rabbits

Background: Whereas various molecular working mechanisms of shock waves have been demonstrated, no study has assessed in detail the influence of varying energy flux densities (EFD) on new bone formation in vivo. Methods: Thirty Chinchilla bastard rabbits were randomly assigned to 5 groups (EFD 0.0, 0.35, 0.5, 0.9 and 1.2 mJ/mm(2)) and treated with extracorporeal shock waves at the distal femoral region (1,500 pulses; 1 Hz frequency). To investigate new bone formation, animals were injected with oxytetracycline at days 5-9 after shock wave application and sacrificed on day 10. Histological sections of all animals were examined using broad-band epifluorescent illumination, contact microradiography and Giemsa-Eosin staining. Results: Application of shock waves induced new bone formation beginning with 0.5 mJ/mm(2) EFD and increasing with 0.9 mJ/mm(2) and 1.2 mJ/mm(2). The latter EFD resulted in new bone formation also on the dorsal cortical bone; cortical fractures and periosteal detachment also occurred. Conclusion: Here, for the first time, a threshold level is presented for new bone formation after applying shock waves to intact bone in vivo. The findings of this study are of considerable significance for preventing unwanted side effects in new approaches in the clinical application of shock waves. Copyright (c) 2008 S. Karger AG, Basel

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

The innervation of the enthesis organ of the rat achilles tendon

PURPOSE: The enthesis (bony insertion of a tendon or ligament) is a common site of overuse injuries in sport. Because enthesopathies can be painful, it is often assumed that the enthesis is highly innervated-but with little evidence to support the assumption. The Achilles tendon has one of the most complex of attachment sites, for together with adjacent tissues, the enthesis itself forms part of an 'enthesis organ' which reduces stress concentration at the bony interface. These adjacent structures include a 'sesamoid fibrocartilage' in the tendon, a 'periosteal fibrocartilage' on the superior tuberosity of the calcaneus, and a fat pad which extends into the retrocalcaneal bursa during plantarflexion. The purpose of the present study is to investigate the innervation of the whole enthesis organ complex. METHODS: The tendon attachment site was removed from one leg of 3 male Wistar rats at each of the following ages-neonates, 4 weeks, 12 weeks, and 24 months. The tissue was fixed in 4% paraformaldehyde, prepared for routine indirect immunohistochemistry and cryosectioned in the sagittal plane. Serial sections were immunolabelled with polyclonal antibodies to protein gene product 9.5, substance P, calcitonin gene related peptide and neurofilament 200. Histology reference sections were stained with toluidine blue. RESULTS: No nerve fibers were detected at the enthesis itself or in the sesamoid and periosteal fib ro cartilages in rats of any age. However, the fat pad was richly supplied by nerve fibers which immunolabelled with all of the antibodies used. It also contained abundant mast cells. The innervation of the fat pad was confirmed in 10 human Achilles tendons obtained from the Department of Forensic Medicine at the Ludwig-Maximilians-Universität, in accordance with the ethical regulations of Munich University. The nerve fibers again immunolabelled with all antibodies and formed an intricate network in which the fibers lay between individual fat cells. CONCLUSION: We suggest that healthy entheses are not innervated because of the high levels of mechanical loading experienced at insertion sites. However, the striking innervation of the adjacent fat pad suggests that it may have an unheralded proprioceptive role monitoring changes in insertional angle between tendon and bone that occur as a result of foot movements

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

A novel implantation technique for engineered osteo-chondral grafts

We present a novel method to support precise insertion of engineered osteochondral grafts by pulling from the bone layer, thereby minimizing iatrogenic damage associated with direct manipulation of the cartilage layer. Grafts were generated by culturing human expanded chondrocytes on Hyaff®-11 meshes, sutured to Tutobone® spongiosa cylinders. Through the bone layer, shaped to imitate the surface-contours of the talar dome, two sutures were applied: the first for anterograde implantation, to pull the graft into the defect, and the second for retrograde correction, in case of a too deep insertion. All grafts could be correctly positioned into osteochondral lesions created in cadaveric ankle joints with good fit to the surrounding cartilage. Implants withstood short-term dynamic stability tests applied to the ankle joint, without delamination or macroscopic damage. The developed technique, by allowing precise and stable positioning of osteochondral grafts without iatrogenic cartilage damage, is essential for the implantation of engineered tissues, where the cartilage layer is not fully mechanically developed, and could be considered also for conventional autologous osteochondral transplantatio