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.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

3D documentation and visualization of external injury findings by integration of simple photography in CT/MRI data sets (IprojeCT).

This study evaluated the feasibility of documenting patterned injury using three dimensions and true colour photography without complex 3D surface documentation methods. This method is based on a generated 3D surface model using radiologic slice images (CT) while the colour information is derived from photographs taken with commercially available cameras. The external patterned injuries were documented in 16 cases using digital photography as well as highly precise photogrammetry-supported 3D structured light scanning. The internal findings of these deceased were recorded using CT and MRI. For registration of the internal with the external data, two different types of radiographic markers were used and compared. The 3D surface model generated from CT slice images was linked with the photographs, and thereby digital true-colour 3D models of the patterned injuries could be created (Image projection onto CT/IprojeCT). In addition, these external models were merged with the models of the somatic interior. We demonstrated that 3D documentation and visualization of external injury findings by integration of digital photography in CT/MRI data sets is suitable for the 3D documentation of individual patterned injuries to a body. Nevertheless, this documentation method is not a substitution for photogrammetry and surface scanning, especially when the entire bodily surface is to be recorded in three dimensions including all external findings, and when precise data is required for comparing highly detailed injury features with the injury-inflicting tool.

Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets

This paper proposed an automated three-dimensional (3D) lumbar intervertebral disc (IVD) segmentation strategy from Magnetic Resonance Imaging (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 template matching approach. Based on the estimated two-dimensional (2D) geometrical parameters, a 3D variable-radius soft tube model of the lumbar spine column is built by model fitting to the 3D data volume. Taking the geometrical information from the 3D lumbar spine column as constraints and segmentation initialization, the disc segmentation is achieved by 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.

Blocking the epithelial-to-mesenchymal transition pathway abrogates resistance to anti-folate chemotherapy in lung cancer.

Anticancer therapies currently used in the clinic often can neither eradicate the tumor nor prevent disease recurrence due to tumor resistance. In this study, we showed that chemoresistance to pemetrexed, a multi-target anti-folate (MTA) chemotherapeutic agent for non-small cell lung cancer (NSCLC), is associated with a stem cell-like phenotype characterized by an enriched stem cell gene signature, augmented aldehyde dehydrogenase activity and greater clonogenic potential. Mechanistically, chemoresistance to MTA requires activation of epithelial-to-mesenchymal transition (EMT) pathway in that an experimentally induced EMT per se promotes chemoresistance in NSCLC and inhibition of EMT signaling by kaempferol renders the otherwise chemoresistant cancer cells susceptible to MTA. Relevant to the clinical setting, human primary NSCLC cells with an elevated EMT signaling feature a significantly enhanced potential to resist MTA, whereas concomitant administration of kaempferol abrogates MTA chemoresistance, regardless of whether it is due to an intrinsic or induced activation of the EMT pathway. Collectively, our findings reveal that a bona fide activation of EMT pathway is required and sufficient for chemoresistance to MTA and that kaempferol potently regresses this chemotherapy refractory phenotype, highlighting the potential of EMT pathway inhibition to enhance chemotherapeutic response of lung cancer.

Blocking of LFA-1 enhances expansion of Th17 cells induced by human CD14(+) CD16(++) nonclassical monocytes.

Among human peripheral blood (PB) monocyte (Mo) subsets, the classical CD14(++) CD16(-) (cMo) and intermediate CD14(++) CD16(+) (iMo) Mos are known to activate pathogenic Th17 responses, whereas the impact of nonclassical CD14(+) CD16(++) Mo (nMo) on T-cell activation has been largely neglected. The aim of this study was to obtain new mechanistic insights on the capacity of Mo subsets from healthy donors (HDs) to activate IL-17(+) T-cell responses in vitro, and assess whether this function was maintained or lost in states of chronic inflammation. When cocultured with autologous CD4(+) T cells in the absence of TLR-2/NOD2 agonists, PB nMos from HDs were more efficient stimulators of IL-17-producing T cells, as compared to cMo. These results could not be explained by differences in Mo lifespan and cytokine profiles. Notably, however, the blocking of LFA-1/ICAM-1 interaction resulted in a significant increase in the percentage of IL-17(+) T cells expanded in nMo/T-cell cocultures. As compared to HD, PB Mo subsets of patients with rheumatoid arthritis were hampered in their T-cell stimulatory capacity. Our new insights highlight the role of Mo subsets in modulating inflammatory T-cell responses and suggest that nMo could become a critical therapeutic target against IL-17-mediated inflammatory diseases.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.