Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

Characterization of granite matrix porosity and pore-space geometry by in situ and laboratory methods

Most available studies of interconnected matrix porosity of crystalline rocks are based on laboratory investigations; that is, work on samples that have undergone stress relaxation and were affected by drilling and sample preparation. The extrapolation of the results to in situ conditions is therefore associated with considerable uncertainty, and this was the motivation to conduct the ‘in situ Connected Porosity’ experiment at the Grimsel Test Site (Central Swiss Alps). An acrylic resin doped with fluorescent agents was used to impregnate the microporous granitic matrix in situ around an injection borehole, and samples were obtained by overcoring. The 3-D structure of the porespace, represented by microcracks, was studied by U-stage fluorescence microscopy. Petrophysical methods, including the determination of porosity, permeability and P -wave velocity, were also applied. Investigations were conducted both on samples that were impregnated in situ and on non-impregnated samples, so that natural features could be distinguished from artefacts. The investigated deformed granites display complex microcrack populations representing a polyphase deformation at varying conditions. The crack population is dominated by open cleavage cracks in mica and grain boundary cracks. The porosity of non-impregnated samples lies slightly above 1 per cent, which is 2–2.5 times higher than the in situ porosity obtained for impregnated samples. Measurements of seismic velocities (Vp ) on spherical rock samples as a function of confining pressure, spatial direction and water saturation for both non-impregnated and impregnated samples provide further constraints on the distinction between natural and induced crack types. The main conclusions are that (1) an interconnected network of microcracks exists in the whole granitic matrix, irrespective of the distance to ductile and brittle shear zones, and (2) conventional laboratory methods overestimate the matrix porosity. Calculations of contaminant transport through fractured media often rely on matrix diffusion as a retardation mechanism.

Discrete Improvement in Racial Disparity in Survival among Patients with Stage IV Colorectal Cancer: a 21-Year Population-Based Analysis

Purpose Recently, multiple clinical trials have demonstrated improved outcomes in patients with metastatic colorectal cancer. This study investigated if the improved survival is race dependent. Patients and Methods Overall and cancer-specific survival of 77,490 White and Black patients with metastatic colorectal cancer from the 1988–2008 Surveillance Epidemiology and End Results registry were compared using unadjusted and multivariable adjusted Cox proportional hazard regression as well as competing risk analyses. Results Median age was 69 years, 47.4 % were female and 86.0 % White. Median survival was 11 months overall, with an overall increase from 8 to 14 months between 1988 and 2008. Overall survival increased from 8 to 14 months for White, and from 6 to 13 months for Black patients. After multivariable adjustment, the following parameters were associated with better survival: White, female, younger, better educated and married patients, patients with higher income and living in urban areas, patients with rectosigmoid junction and rectal cancer, undergoing cancer-directed surgery, having well/moderately differentiated, and N0 tumors (p<0.05 for all covariates). Discrepancies in overall survival based on race did not change significantly over time; however, there was a significant decrease of cancer-specific survival discrepancies over time between White and Black patients with a hazard ratio of 0.995 (95 % confidence interval 0.991–1.000) per year (p=0.03). Conclusion A clinically relevant overall survival increase was found from 1988 to 2008 in this population-based analysis for both White and Black patients with metastatic colorectal cancer. Although both White and Black patients benefitted from this improvement, a slight discrepancy between the two groups remained.

Mechanical constraints imposed by 3D cellular geometry and arrangement modulate growth patterns in the Arabidopsis embryo

Morphogenesis occurs in 3D space over time and is guided by coordinated gene expression programs. Here we use postembryonic development in Arabidopsis plants to investigate the genetic control of growth. We demonstrate that gene expression driving the production of the growth-stimulating hormone gibberellic acid and downstream growth factors is first induced within the radicle tip of the embryo. The center of cell expansion is, however, spatially displaced from the center of gene expression. Because the rapidly growing cells have very different geometry from that of those at the tip, we hypothesized that mechanical factors may contribute to this growth displacement. To this end we developed 3D finite-element method models of growing custom-designed digital embryos at cellular resolution. We used this framework to conceptualize how cell size, shape, and topology influence tissue growth and to explore the interplay of geometrical and genetic inputs into growth distribution. Our simulations showed that mechanical constraints are sufficient to explain the disconnect between the experimentally observed spatiotemporal patterns of gene expression and early postembryonic growth. The center of cell expansion is the position where genetic and mechanical facilitators of growth converge. We have thus uncovered a mechanism whereby 3D cellular geometry helps direct where genetically specified growth takes place.

How does the ascending aorta geometry change when it dissects?

OBJECTIVES The purpose of this study is to delineate changes in aortic geometry and diameter due to dissection. BACKGROUND Aortic diameter is the major criterion for elective ascending aortic replacement for dilated ascending aortas to prevent aortic dissection. However, recommendations are made on the basis of clinical experience and observation of diameters of previously dissected aortas. METHODS Six tertiary centers on 2 continents reviewed their acute aortic dissection type A databases, which contained 1,821 patients. Included were all non-Marfan patients with nonbicuspid aortic valves who had undergone computed tomography angiography <2 years before and within 12 h after aortic dissection onset. Aortic geometry before and after dissection onset were compared. RESULTS Altogether, 63 patients were included (27 spontaneous and 36 retrograde dissections, median age 68 [57; 77] years; 54% were men). In all but 1 patient, maximum ascending aortic diameter was <55 mm before aortic dissection onset. The largest increase in diameter and volume induced by the dissection were observed in the ascending aorta (40.1 [36.6; 45.3] mm vs. 52.9 [46.1; 58.6] mm, +12.8 mm; p < 0.001; 124.0 [90.8; 162.5] cm(3) vs. 171.0 [147.0; 197.0] cm(3), +47 cm(3); p < 0.001). Mean aortic arch diameter increased from 39.8 (30.5; 42.6) mm to 46.4 (42.0; 51.6) mm (+6.6 mm; p < 0.001) and descending thoracic aorta diameter from 31.2 (27.0; 33.3) mm to 34.9 (30.9; 39.5) mm (+3.7 mm; p < 0.001). Changes in thoracic aorta geometry were similar for spontaneous and retrograde etiology. CONCLUSIONS Geometry of the thoracic aorta is affected by aortic dissection, leading to an increase in diameter that is most pronounced in the ascending aorta. Both spontaneous and retrograde dissection result in similar aortic geometry changes.

Microbe sampling by mucosal dendritic cells is a discrete, MyD88-independent step in DeltainvG S. Typhimurium colitis.

Intestinal dendritic cells (DCs) are believed to sample and present commensal bacteria to the gut-associated immune system to maintain immune homeostasis. How antigen sampling pathways handle intestinal pathogens remains elusive. We present a murine colitogenic Salmonella infection model that is highly dependent on DCs. Conditional DC depletion experiments revealed that intestinal virulence of S. Typhimurium SL1344 DeltainvG mutant lacking a functional type 3 secretion system-1 (DeltainvG)critically required DCs for invasion across the epithelium. The DC-dependency was limited to the early phase of infection when bacteria colocalized with CD11c(+)CX3CR1(+) mucosal DCs. At later stages, the bacteria became associated with other (CD11c(-)CX3CR1(-)) lamina propria cells, DC depletion no longer attenuated the pathology, and a MyD88-dependent mucosal inflammation was initiated. Using bone marrow chimeric mice, we showed that the MyD88 signaling within hematopoietic cells, which are distinct from DCs, was required and sufficient for induction of the colitis. Moreover, MyD88-deficient DCs supported transepithelial uptake of the bacteria and the induction of MyD88-dependent colitis. These results establish that pathogen sampling by DCs is a discrete, and MyD88-independent, step during the initiation of a mucosal innate immune response to bacterial infection in vivo.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Geometry and kinematics of the Roisan-Cignana Shear Zone, and the orogenic evolution of the Dent Blanche Tectonic System (Western Alps)

The Dent Blanche Tectonic System (DBTS) is a composite thrust sheet derived from the previously thinned passive Adriatic continental margin. A kilometric high-strain zone, the Roisan-Cignana Shear Zone (RCSZ) defines the major tectonic boundary within the DBTS and separates it into two subunits, the Dent Blanche s.s. nappe to the northwest and the Mont Mary nappe to the southeast. Within this shear zone, tectonic slices of Mesozoic and pre-Alpine meta-sediments became amalgamated with continental basement rocks of the Adriatic margin. The occurrence of high pressure assemblages along the contact between these tectonic slices indicates that the amalgamation occurred prior to or during the subduction process, at an early stage of the Alpine orogenic cycle. Detailed mapping, petrographic and structural analysis show that the Roisan-Cignana Shear Zone results from several superimposed Alpine structural and metamorphic stages. Subduction of the continental fragments is recorded by blueschist-facies deformation, whereas the Alpine collision is reflected by a greenschist facies overprint associated with the development of large-scale open folds. The postnappe evolution comprises the development of low-angle brittle faults, followed by large-scale folding (Vanzone phase) and finally brittle extensional faults. The RCSZ shows that fragments of continental crust had been torn off the passive continental margin prior to continental collision, thus recording the entire history of the orogenic cycle. The role of preceding Permo-Triassic lithospheric thinning, Jurassic rifting, and ablative subduction processes in controlling the removal of crustal fragments from the reactivated passive continental margin is discussed. Results of this study constrain the temporal sequence of the tectono-metamorphic processes involved in the assembly of the DBTS, but they also show limits on the interpretation. In particular it remains difficult to judge to what extent precollisional rifting at the Adriatic continental margin preconditioned the efficiency of convergent processes, i.e. accretion, subduction, and orogenic exhumation.

Functional and discrete digital sustainability within the sustainable development goals

The Sustainable Development Goals (SDGs) present the new global agenda by the United Nations for the next 15 years from 2016 to 2030. In this research paper we examine how digital resources may contribute to the achievement of the SDGs. Based on a broad literature review we argue functional digital sustainability supports the SDGs while discrete digital sustainability is required to create and progress knowledge necessary to advance the SDGs. First we explain the perspectives of functional and discrete sustainability; secondly we map the two perspectives onto the 17 SDGs with examples incorporating both perspectives of digital sustainability. We conclude that digital sustainability should encompass both perspectives in order to exploit the full potential of information systems in regard to sustainability transformations.

Human skin is protected by four functionally and phenotypically discrete populations of resident and recirculating memory T cells

The skin of an adult human contains about 20 billion memory T cells. Epithelial barrier tissues are infiltrated by a combination of resident and recirculating T cells in mice, but the relative proportions and functional activities of resident versus recirculating T cells have not been evaluated in human skin. We discriminated resident from recirculating T cells in human-engrafted mice and lymphoma patients using alemtuzumab, a medication that depletes recirculating T cells from skin, and then analyzed these T cell populations in healthy human skin. All nonrecirculating resident memory T cells (TRM) expressed CD69, but most were CD4(+), CD103(-), and located in the dermis, in contrast to studies in mice. Both CD4(+) and CD8(+) CD103(+) TRM were enriched in the epidermis, had potent effector functions, and had a limited proliferative capacity compared to CD103(-) TRM. TRM of both types had more potent effector functions than recirculating T cells. We observed two distinct populations of recirculating T cells, CCR7(+)/L-selectin(+) central memory T cells (TCM) and CCR7(+)/L-selectin(-) T cells, which we term migratory memory T cells (TMM). Circulating skin-tropic TMM were intermediate in cytokine production between TCM and effector memory T cells. In patients with cutaneous T cell lymphoma, malignant TCM and TMM induced distinct inflammatory skin lesions, and TMM were depleted more slowly from skin after alemtuzumab, suggesting that TMM may recirculate more slowly. In summary, human skin is protected by four functionally distinct populations of T cells, two resident and two recirculating, with differing territories of migration and distinct functional activities.