Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Reducing CT radiation dose with iterative reconstruction algorithms: the influence of scan and reconstruction parameters on image quality and CTDIvol

OBJECTIVES In this phantom CT study, we investigated whether images reconstructed using filtered back projection (FBP) and iterative reconstruction (IR) with reduced tube voltage and current have equivalent quality. We evaluated the effects of different acquisition and reconstruction parameter settings on image quality and radiation doses. Additionally, patient CT studies were evaluated to confirm our phantom results. METHODS Helical and axial 256 multi-slice computed tomography scans of the phantom (Catphan(®)) were performed with varying tube voltages (80-140kV) and currents (30-200mAs). 198 phantom data sets were reconstructed applying FBP and IR with increasing iterations, and soft and sharp kernels. Further, 25 chest and abdomen CT scans, performed with high and low exposure per patient, were reconstructed with IR and FBP. Two independent observers evaluated image quality and radiation doses of both phantom and patient scans. RESULTS In phantom scans, noise reduction was significantly improved using IR with increasing iterations, independent from tissue, scan-mode, tube-voltage, current, and kernel. IR did not affect high-contrast resolution. Low-contrast resolution was also not negatively affected, but improved in scans with doses <5mGy, although object detectability generally decreased with the lowering of exposure. At comparable image quality levels, CTDIvol was reduced by 26-50% using IR. In patients, applying IR vs. FBP resulted in good to excellent image quality, while tube voltage and current settings could be significantly decreased. CONCLUSIONS Our phantom experiments demonstrate that image quality levels of FBP reconstructions can also be achieved at lower tube voltages and tube currents when applying IR. Our findings could be confirmed in patients revealing the potential of IR to significantly reduce CT radiation doses.

Feasible Dose Reduction in Routine Chest Computed Tomography Maintaining Constant Image Quality Using the Last Three Scanner Generations: From Filtered Back Projection to Sinogram-affirmed Iterative Reconstruction and Impact of the Novel Fully Integrated Detector Design Minimizing Electronic Noise

OBJECTIVE The aim of the present study was to evaluate a dose reduction in contrast-enhanced chest computed tomography (CT) by comparing the three latest generations of Siemens CT scanners used in clinical practice. We analyzed the amount of radiation used with filtered back projection (FBP) and an iterative reconstruction (IR) algorithm to yield the same image quality. Furthermore, the influence on the radiation dose of the most recent integrated circuit detector (ICD; Stellar detector, Siemens Healthcare, Erlangen, Germany) was investigated. MATERIALS AND METHODS 136 Patients were included. Scan parameters were set to a thorax routine: SOMATOM Sensation 64 (FBP), SOMATOM Definition Flash (IR), and SOMATOM Definition Edge (ICD and IR). Tube current was set constantly to the reference level of 100 mA automated tube current modulation using reference milliamperes. Care kV was used on the Flash and Edge scanner, while tube potential was individually selected between 100 and 140 kVp by the medical technologists at the SOMATOM Sensation. Quality assessment was performed on soft-tissue kernel reconstruction. Dose was represented by the dose length product. RESULTS Dose-length product (DLP) with FBP for the average chest CT was 308 mGy*cm ± 99.6. In contrast, the DLP for the chest CT with IR algorithm was 196.8 mGy*cm ± 68.8 (P = 0.0001). Further decline in dose can be noted with IR and the ICD: DLP: 166.4 mGy*cm ± 54.5 (P = 0.033). The dose reduction compared to FBP was 36.1% with IR and 45.6% with IR/ICD. Signal-to-noise ratio (SNR) was favorable in the aorta, bone, and soft tissue for IR/ICD in combination compared to FBP (the P values ranged from 0.003 to 0.048). Overall contrast-to-noise ratio (CNR) improved with declining DLP. CONCLUSION The most recent technical developments, namely IR in combination with integrated circuit detectors, can significantly lower radiation dose in chest CT examinations.

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensionality, we keep numerical complexity at bay by restricting the space of solutions and by exploiting an efficient Primal-Dual formulation. Comparisons with state of the art techniques, on both synthetic and real data, show promising performances.

Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated 3D lumbar intervertebral disc (IVD) segmentation strategy from MRI data. Starting from two user supplied landmarks, the geometrical parameters of all lumbar vertebral bodies and intervertebral discs are automatically extracted from a mid-sagittal slice using a graphical model based approach. After that, a three-dimensional (3D) variable-radius soft tube model of the lumbar spine column is built to guide the 3D disc segmentation. The disc segmentation is achieved as a multi-kernel diffeomorphic registration between a 3D template of the disc and the observed MRI data. Experiments on 15 patient data sets showed the robustness and the accuracy of the proposed algorithm.

A steerable UV laser system for the calibration of liquid argon time projection chambers

A number of liquid argon time projection chambers (LAr TPCs) are being built or are proposed for neutrino experiments on long- and short baseline beams. For these detectors, a distortion in the drift field due to geometrical or physics reasons can affect the reconstruction of the events. Depending on the TPC geometry and electric drift field intensity, this distortion could be of the same magnitude as the drift field itself. Recently, we presented a method to calibrate the drift field and correct for these possible distortions. While straight cosmic ray muon tracks could be used for calibration, multiple coulomb scattering and momentum uncertainties allow only a limited resolution. A UV laser instead can create straight ionization tracks in liquid argon, and allows one to map the drift field along different paths in the TPC inner volume. Here we present a UV laser feed-through design with a steerable UV mirror immersed in liquid argon that can point the laser beam at many locations through the TPC. The straight ionization paths are sensitive to drift field distortions, a fit of these distortion to the linear optical path allows to extract the drift field, by using these laser tracks along the whole TPC volume one can obtain a 3D drift field map. The UV laser feed-through assembly is a prototype of the system that will be used for the MicroBooNE experiment at the Fermi National Accelerator Laboratory (FNAL).

Von Fuzzy-Sets zu Computing-with-Words

Dieser Artikel bietet einen Überblick über die Entwicklung und Zusammenhänge der einzelnen Elemente der Fuzzy-Logik, wovon Fuzzy-Set-Theorie die Grundlage bildet. Die Grundproblematik besteht in der Handhabung von linguistischen Informationen, die häufig durch Ungenauigkeit gekennzeichnet sind. Die verschiedenen technischen Anwendungen von Fuzzy-Logik bieten eine Möglichkeit, intelligentere Computersysteme zu konstruieren, die mit unpräzisen Informationen umgehen können. Solche Systeme sind Indizien für die Entstehung einer neuen Ära des Cognitive-Computing, di in diesemArtikel ebenfalls zur Sprache kommt. Für das bessere Verständnis wird der Artikel mit einem Beispiel aus der Meteorologie (d. h. Schnee in Adelboden) begleitet.

Global carbon budget 2013

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and a methodology to quantify all major components of the global carbon budget, including their uncertainties, based on the combination of a range of data, algorithms, statistics and model estimates and their interpretation by a broad scientific community. We discuss changes compared to previous estimates, consistency within and among components, alongside methodology and data limitations. CO2 emissions from fossil-fuel combustion and cement production (EFF) are based on energy statistics, while emissions from land-use change (ELUC), mainly deforestation, are based on combined evidence from land-cover change data, fire activity associated with deforestation, and models. The global atmospheric CO2 concentration is measured directly and its rate of growth (GATM) is computed from the annual changes in concentration. The mean ocean CO2 sink (SOCEAN) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. The variability in SOCEAN is evaluated for the first time in this budget with data products based on surveys of ocean CO2 measurements. The global residual terrestrial CO2 sink (SLAND) is estimated by the difference of the other terms of the global carbon budget and compared to results of independent dynamic global vegetation models forced by observed climate, CO2 and land cover change (some including nitrogen–carbon interactions). All uncertainties are reported as ± 1 σ, reflecting the current capacity to characterise the annual estimates of each component of the global carbon budget. For the last decade available (2003–2012), EFF was 8.6 ± 0.4 GtC yr − 1, ELUC 0.9 ± 0.5 GtC yr − 1, GATM 4.3 ± 0.1 GtC yr − 1, S OCEAN 2.5 ± 0.5 GtC yr − 1, and S LAND 2.8 ± 0.8 GtC yr − 1. For year 2012 alone, EFF grew to 9.7 ± 0.5 GtC yr − 1, 2.2 % above 2011, reflecting a continued growing trend in these emissions, GATM was 5.1 ± 0.2 GtC yr − 1, SOCEANwas 2.9 ± 0.5 GtC yr −1, and assuming an ELU Cof 1.0 ± 0.5 GtC yr − 1 (based on the 2001–2010 average), SLAND was 2.7 ± 0.9 GtC yr − 1. GATM was high in 2012 compared to the 2003–2012 average, almost entirely reflecting the high EFF. The global atmospheric CO2 con- centration reached 392.52 ± 0.10 ppm averaged over 2012. We estimate that EFF will increase by 2.1 % (1.1–3.1 %) to 9.9 ± 0.5 GtC in 2013, 61 % above emissions in 1990, based on projections of world gross domestic product and recent changes in the carbon intensity of the economy. With this projection, cumulative emissions of CO2 will reach about 535 ± 55 GtC for 1870–2013, about 70 % from EFF (390 ± 20 GtC) and 30 % from ELUC (145 ± 50 GtC). This paper also documents any changes in the methods and data sets used in this new carbon budget from previous budgets (Le Quéré et al., 2013). All observations presented here can be downloaded from the Carbon Dioxide Information Analysis Center.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Dimethyloxalylglycine lyophilized onto bone substitutes increase vessel area in rat calvarial defects.

AIM Pharmacological inhibitors of prolyl hydroxylases, also termed hypoxia-mimetic agents (HMAs), when repeatedly injected can support angiogenesis and bone regeneration. However, the possible role of HMA loaded onto bone substitutes to support angiogenesis and bone regeneration under diabetic condition is unknown. The capacity of HMA loaded onto deproteinized bovine bone mineral (DBBM) to support angiogenesis and bone formation was examined in diabetic Wistar rats. METHODS Diabetes was induced by intraperitoneal injection of streptozotocin. The HMA dimethyloxalylglycine (DMOG) and desferrioxamine (DFO) were lyophilized onto DBBM. Calvarial defects were created with a trephine drill and filled with the respective bone substitutes. After 4 weeks of healing, the animals were subjected to histological and histomorphometric analysis. RESULTS In this report, we provide evidence that DMOG loaded onto DBBM can support angiogenesis in vivo. Specifically, we show that DMOG increased the vessel area in the defect site to 2.4% ± 1.3% compared with controls 1.1% ± 0.48% (P = 0.012). There was a trend toward an increased vessel number in the defect site with 38.6 ± 17.4 and 31.0 ± 10.3 in the DMOG and the control group (P = 0.231). The increase in angiogenesis, however, did not translate into enhanced bone formation in the defect area with 9.2% ± 7.1% and 8.4% ± 5.6% in DMOG and control group, respectively. No significant changes were caused by DFO. CONCLUSIONS The results suggest that DMOG loaded onto DBBM can support angiogenesis, but bone formation does not increase accordingly in a type 1 diabetic rat calvarial defect model at the indicated time point.