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.

Fatal contact shot to the chest caused by the gas jet from a muzzle-loading pistol discharging only black powder and no bullet: case study and experimental simulation of the wounding effect.

In modern medico-legal literature, only a small number of publications deal with fatal injuries from black powder guns. Most of them focus on the morphological features such as intense soot soiling, blast tattooing and burn effects in close-range shots or describe the wound ballistics of spherical lead bullets. Another kind of "unusual" and potentially lethal weapons are handguns destined for firing only blank cartridges such as starter and alarm pistols. The dangerousness of these guns is restricted to very close and contact range shots and results from the gas jet produced by the deflagration of the propellant. The present paper reports on a suicide committed with a muzzle-loading percussion pistol cal. 45. An unusually large stellate entrance wound was located in the precordial region, accompanied by an imprint mark from the ramrod and a faint greenish discoloration (apparently due to the formation of sulfhemoglobin). Autopsy revealed an oversized powder cavity, multiple fractures of the anterior thoracic wall as well as ruptures of the heart, the aorta, the left hepatic lobe and the diaphragm. In total, the zone of mechanical destruction had a diameter of approx. 15 cm. As there was no exit wound and no bullet lodged in the body, the injury was caused exclusively by the inrushing combustion gases of the propellant (black powder) comparable with the gas jet of a blank cartridge gun. In contact shots to ballistic gelatine using the suicide's pistol loaded with black powder but no projectile, the formation of a nearly spherical cavity could be demonstrated by means of a high-speed camera. The extent of the temporary cavity after firing with 5 g of black powder roughly corresponded to the zone of destruction found in the suicide's body.

Extended duration of torsional loading reduced the survival of the NP cells of the intervertebral disc

Introduction Previous studies on the influence of torsion and combined torsion-compression loading revealed a positive effect on the cell viability when a repetitive short-term torsion was applied at a physiological magnitude to intervertebral disc organ culture.1 However, after an extended period (8 hours) of combined torsion-compression loading, substantial cell death was detected in the nucleus pulposus (NP).2 In this follow-up study, we aimed to investigate the relationship, if any, between the duration of torsion applied to the intervertebral disc (IVD) and the level of NP cell viability. Materials and Methods Bovine caudal discs were harvested and cultured in a custom-built multiaxis dynamic loading bioreactor.2 Torsion (± 2 degrees) was applied to the samples at a frequency of 0.2 Hz. Torsion was applied for durations of 0, 1, 4, and 8 h/d, repeated over 7 days. After the last day of loading, disc tissue was dissected for analysis of cell viability and gene expression. Results Disc NP cell viability remained above 85% after torsional loading for 0, 1, or 4 h/d. Viability was statistical significantly reduced to below 70% when torsion was applied for 8 h/d (p = 0.03) (Table 1). The daily duration of torsional loading did not affect the AF cell viability (> 80% for all loading durations). The trend of collagen 2 gene upregulation and matrix metalloproteases 13 downregulation with an increasing duration of torsion was observed in both NP and AF (Fig. 1).Conclusion We have demonstrated that an extended duration of torsion could inhibit the survival of NP cells within the IVD in organ culture. Acknowledgments Funds from the Orthopedic Department of the Insel University Hospital of Bern and a private donation from Prof. Dr. Paul Heini, Spine Surgeon, Sonnenhof Clinic Bern were received to support this work. Disclosure of Interest None declared References References 1 Chan SC, Ferguson SJ, Wuertz K, Gantenbein-Ritter B. Biological response of the intervertebral disc to repetitive short-term cyclic torsion. Spine 2011;36(24):2021–2030 2 Chan SC, Walser J, Käppeli P, Shamsollahi MJ, Ferguson SJ, Gantenbein-Ritter B. Region specific response of intervertebral disc cells to complex dynamic loading: an organ culture study using a dynamic torsion-compression bioreactor. PLoS ONE 2013;8(8):e72489

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Biomechanical loading modulates proinflammatory and bone resorptive mediators in bacterial-stimulated PDL cells.

The present study aimed to evaluate in vitro whether biomechanical loading modulates proinflammatory and bone remodeling mediators production by periodontal ligament (PDL) cells in the presence of bacterial challenge. Cells were seeded on BioFlex culture plates and exposed to Fusobacterium nucleatum ATCC 25586 and/or cyclic tensile strain (CTS) of low (CTSL) and high (CTSH) magnitudes for 1 and 3 days. Synthesis of cyclooxygenase-2 (COX2) and prostaglandin E2 (PGE2) was evaluated by ELISA. Gene expression and protein secretion of osteoprotegerin (OPG) and receptor activator of nuclear factor kappa-B ligand (RANKL) were evaluated by quantitative RT-PCR and ELISA, respectively. F. nucleatum increased the production of COX2 and PGE2, which was further increased by CTS. F. nucleatum-induced increase of PGE2 synthesis was significantly (P < 0.05) increased when CTSH was applied at 1 and 3 days. In addition, CTSH inhibited the F. nucleatum-induced upregulation of OPG at 1 and 3 days, thereby increasing the RANKL/OPG ratio. OPG and RANKL mRNA results correlated with the protein results. In summary, our findings provide original evidence that CTS can enhance bacterial-induced syntheses of molecules associated with inflammation and bone resorption by PDL cells. Therefore, biomechanical, such as orthodontic or occlusal, loading may enhance the bacterial-induced inflammation and destruction in periodontitis.

Classification of interstitial lung disease patterns using local DCT features and random forest.

Over the last decade, a plethora of computer-aided diagnosis (CAD) systems have been proposed aiming to improve the accuracy of the physicians in the diagnosis of interstitial lung diseases (ILD). In this study, we propose a scheme for the classification of HRCT image patches with ILD abnormalities as a basic component towards the quantification of the various ILD patterns in the lung. The feature extraction method relies on local spectral analysis using a DCT-based filter bank. After convolving the image with the filter bank, q-quantiles are computed for describing the distribution of local frequencies that characterize image texture. Then, the gray-level histogram values of the original image are added forming the final feature vector. The classification of the already described patches is done by a random forest (RF) classifier. The experimental results prove the superior performance and efficiency of the proposed approach compared against the state-of-the-art.

Mechanical Loading Promoted Discogenic Differentiation of Human Mesenchymal Stem Cells Incorporated in 3D-PEG Scaffolds with RhGDF5 and RGD

Hydrogels have been described as ideal scaffolds for cells of 3D tissue constructs and hold strong promises with respect to in vitro 3D-cell-culture, where cells are isolated from native extracellular matrix (ECM). Synthesized polyethyleneglycol (PEG) hydrogels are appealing with regard to potential for cell therapy or as vehicles for drug delivery or even to regenerate tissue with similar hydrogel-like properties such as the nucleus pulposus of the intervertebral disc (IVD). Here, we tested whether incorporation of RGD motive would hinder discogenic differentiation of primary bone marrow-derived human mesenchymal stem cells (hMSCs) but favor proliferation of undifferentiated hMSCs. HMSCs were embedded in +RGD containing or without RGD PEG hydrogel and pre-conditioned with or without growth and differentiation factor-5 (rhGDF-5) for 13 days. Afterwards, all hMSCs-PEG gels were subsequently cyclically loaded (15% strain, 1Hz) for 5 consecutive days in a bioreactor to generate an IVD-like phenotype. Higher metabolic activity (resazurin assay) was found in groups with rhGDF5 in both gel types with and without RGD. Cell viability and morphology measured by confocal laser microscopy and DNA content showed decreased values (~60%) after 18 days of culture. Real-time RT-PCR of an array of 15 key genes suspected to be distinctive for IVD cells revealed moderate response to rhGDF5 and mechanical loading as also shown by histology staining. Preconditioning and mechanical loading showed relatively moderate responses revealed from both RT-PCR and histology although hMSCs were demonstrated to be potent to differentiate into chondrocyte-progenitor cells in micro- mass and 3D alginate bead culture.