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.

Comparison between Radiographic (2-dimensional and 3-dimensional) and Histologic Findings of Periapical Lesions Treated with Apical Surgery.

INTRODUCTION The aim of this study was to evaluate the concordance of 2- and 3-dimensional radiography and histopathology in the diagnosis of periapical lesions. METHODS Patients were consecutively enrolled in this study provided that preoperative periapical radiography (PR) and cone-beam computed tomographic imaging of the tooth to be treated with apical surgery were performed. The periapical lesional tissue was histologically analyzed by 2 blinded examiners. The final histologic diagnosis was compared with the radiographic assessments of 4 blinded observers. The initial study material included 62 teeth in the same number of patients. RESULTS Four lesions had to be excluded during processing, resulting in a final number of 58 evaluated cases (31 women and 27 men, mean age = 55 years). The final histologic diagnosis of the periapical lesions included 55 granulomas (94.8%) and 3 cysts (5.2%). Histologic analysis of the tissue samples from the apical lesions exhibited an almost perfect agreement between the 2 experienced investigators with an overall agreement of 94.83% (kappa = 0.8011). Radiographic assessment overestimated cysts by 28.4% (cone-beam computed tomographic imaging) and 20.7% (periapical radiography), respectively. Comparing the correlation of the radiographic diagnosis of 4 observers with the final histologic diagnosis, 2-dimensional (kappa = 0.104) and 3-dimensional imaging (kappa = 0.111) provided only minimum agreement. CONCLUSIONS To establish a final diagnosis of an apical radiolucency, the tissue specimen should be evaluated histologically and specified as a granuloma (with/without epithelium) or a cyst. Analysis of 2-dimensional and 3-dimensional radiographic images alike results only in a tentative diagnosis that should be confirmed with biopsy.

Composition Space Analysis in the Development of Copper Molybdate Hybrids Decorated by a Bifunctional Pyrazolyl/1,2,4-Triazole Ligand

A bitopic ligand, 4-(3,5-dimethylpyrazol-4-yl)-1,2,4-triazole (Hpz-tr) (1), containing two different heterocyclic moieties was employed for the design of copper(II)–molybdate solids under hydrothermal conditions. In the multicomponent CuII/Hpz-tr/MoVI system, a diverse set of coordination hybrids, [Cu(Hpz-tr)2SO4]·3H2O (2), [Cu(Hpz-tr)Mo3O10] (3), [Cu4(OH)4(Hpz-tr)4Mo8O26]·6H2O (4), [Cu(Hpz-tr)2Mo4O13] (5), and [Mo2O6(Hpz-tr)]·H2O (6), was prepared and characterized. A systematic investigation of these systems in the form of a ternary crystallization diagram approach was utilized to show the influence of the molar ratios of starting reagents, the metal (CuII and MoVI) sources, the temperature, etc., on the reaction products outcome. Complexes 2–4 dominate throughout a wide crystallization range of the composition triangle, while the other two compounds 5 and 6 crystallize as minor phases in a narrow concentration range. In the crystal structures of 2–6, the organic ligand behaves as a short [N–N]-triazole linker between metal centers Cu···Cu in 2–4, Cu···Mo in 5, and Mo···Mo in 6, while the pyrazolyl function remains uncoordinated. This is the reason for the exceptional formation of low-dimensional coordination motifs: 1D for 2, 4, and 6 and 2D for 3 and 5. In all cases, the pyrazolyl group is involved in H bonding (H-donor/H-acceptor) and is responsible for π–π stacking, thus connecting the chain and layer structures in more complicated H-bonding architectures. These compounds possess moderate thermal stability up to 250–300 °C. The magnetic measurements were performed for 2–4, revealing in all three cases antiferromagnetic exchange interactions between neighboring CuII centers and long-range order with a net moment below Tc of 13 K for compound 4.

Investigation of hemodynamics in an in vitro system simulating left ventricular support through the right subclavian artery using 4-dimensional flow magnetic resonance imaging.

OBJECTIVES Left ventricular assist devices are an important treatment option for patients with heart failure alter the hemodynamics in the heart and great vessels. Because in vivo magnetic resonance studies of patients with ventricular assist devices are not possible, in vitro models represent an important tool to investigate flow alterations caused by these systems. By using an in vitro magnetic resonance-compatible model that mimics physiologic conditions as close as possible, this work investigated the flow characteristics using 4-dimensional flow-sensitive magnetic resonance imaging of a left ventricular assist device with outflow via the right subclavian artery as commonly used in cardiothoracic surgery in the recent past. METHODS An in vitro model was developed consisting of an aorta with its supra-aortic branches connected to a left ventricular assist device simulating the pulsatile flow of the native failing heart. A second left ventricular assist device supplied the aorta with continuous flow via the right subclavian artery. Four-dimensional flow-sensitive magnetic resonance imaging was performed for different flow rates of the left ventricular assist device simulating the native heart and the left ventricular assist device providing the continuous flow. Flow characteristics were qualitatively and quantitatively evaluated in the entire vessel system. RESULTS Flow characteristics inside the aorta and its upper branching vessels revealed that the right subclavian artery and the right carotid artery were solely supported by the continuous-flow left ventricular assist device for all flow rates. The flow rates in the brain-supplying arteries are only marginally affected by different operating conditions. The qualitative analysis revealed only minor effects on the flow characteristics, such as weakly pronounced vortex flow caused by the retrograde flow via the brachiocephalic artery. CONCLUSIONS The results indicate that, despite the massive alterations in natural hemodynamics due to the retrograde flow via the right subclavian and brachiocephalic arteries, there are no drastic consequences on the flow in the brain-feeding arteries and the flow characteristics in the ascending and descending aortas. It may be beneficial to adjust the operating condition of the left ventricular assist device to the residual function of the failing heart.

Mapping tibiofemoral gonarthrosis: an MRI analysis of non-traumatic knee cartilage defects

OBJECTIVE Arthroscopy is "the gold standard" for the diagnosis of knee cartilage lesions. However, it is invasive and expensive, and displays all the potential complications of an open surgical procedure. Ultra-high-field MRI now offers good opportunities for the indirect assessment of the integrity and structural changes of joint cartilage of the knee. The goal of the present study is to determine the site of early cartilaginous lesions in adults with non-traumatic knee pain. METHODS 3-T MRI examinations of 200 asymptomatic knees with standard and three-dimensional double-echo steady-state (3D-DESS) cartilage-specific sequences were prospectively studied for early degenerative lesions of the tibiofemoral joint. Lesions were classified and mapped using the modified Outerbridge and modified International Cartilage Repair Society classifications. RESULTS A total of 1437 lesions were detected: 56.1% grade I, 33.5% grade II, 7.2% grade III and 3.3% grade IV. Cartographically, grade I lesions were most common in the anteromedial tibial areas; grade II lesions in the anteromedial L5 femoral areas; and grade III in the centromedial M2 femoral areas. CONCLUSION 3-T MRI with standard and 3D-DESS cartilage-specific sequences demonstrated that areas predisposed to early osteoarthritis are the central, lateral and ventromedial tibial plateau, as well as the central and medial femoral condyle. ADVANCES IN KNOWLEDGE In contrast with previous studies reporting early cartilaginous lesions in the medial tibial compartment and/or in the medial femoral condyle, this study demonstrates that, regardless of grade, lesions preferentially occur at the L5 and M4 tibial and L5 and L2 femoral areas of the knee joint.

Two-Dimensional Crystallisation of Membrane Proteins and Structural Assessment

Two-dimensional (2D) crystallisation of Membrane proteins reconstitutes them into their native environment, the lipid bilayer. Electron crystallography allows the structural analysis of these regular protein–lipid arrays up to atomic resolution. The crystal quality depends on the protein purity, ist stability and on the crystallisation conditions. The basics of 2D crystallisation and different recent advances are reviewed and electron crystallography approaches summarised. Progress in 2D crystallisation, sample preparation, image detectors and automation of the data acquisition and processing pipeline makes 2D electron crystallography particularly attractive for the structural analysis of membrane proteins that are too small for single-particle analyses and too unstable to form three-dimensional (3D) crystals.

Three-dimensional culture and characterization of mononuclear cells from human bone marrow

BACKGROUND AIMS The diverse phenotypic changes and clinical and economic disadvantages associated with the monolayer expansion of bone marrow-derived mesenchymal stromal cells (MSCs) have focused attention on the development of one-step intraoperative cells therapies and homing strategies. The mononuclear cell fraction of bone marrow, inclusive of discrete stem cell populations, is not well characterized, and we currently lack suitable cell culture systems in which to culture and investigate the behavior of these cells. METHODS Human bone marrow-derived mononuclear cells were cultured within fibrin for 2 weeks with or without fibroblast growth factor-2 supplementation. DNA content and cell viability of enzymatically retrieved cells were determined at days 7 and 14. Cell surface marker profiling and cell cycle analysis were performed by means of multi-color flow cytometry and a 5-ethynyl-2'-deoxyuridine incorporation assay, respectively. RESULTS Total mononuclear cell fractions, isolated from whole human bone marrow, was successfully cultured in fibrin gels for up to 14 days under static conditions. Discrete niche cell populations including MSCs, pericytes and hematopoietic stem cells were maintained in relative quiescence for 7 days in proportions similar to that in freshly isolated cells. Colony-forming unit efficiency of enzymatically retrieved MSCs was significantly higher at day 14 compared to day 0; and in accordance with previously published works, it was fibroblast growth factor-2-dependant. CONCLUSIONS Fibrin gels provide a simple, novel system in which to culture and study the complete fraction of bone marrow-derived mononuclear cells and may support the development of improved bone marrow cell-based therapies.

Mapping Emotion Terms into Affective Space: Further Evidence for a Four-Dimensional Structure

Recent empirical work on the semantics of emotion terms across many different cultures and languages, using a theoretical componential approach, suggested that four dimensions are needed to parsimoniously describe the semantic space of the emotion domain as reflected in emotion terms (Fontaine, Scherer, Roesch, & Ellsworth, 2007; Fontaine, Scherer, & Soriano, 2013). In addition to valence, power, and arousal, a novelty dimension was discovered that mostly differentiated surprise from other emotions. Here, we further explore the existence and nature of the fourth dimension in semantic emotion space using a much larger and much more representative set of emotion terms. A group of 156 participants each rated 10 out of a set of 80 French emotion terms with respect to semantic meaning. The meaning of an emotion term was evaluated with respect to 68 emotion features representing the appraisal, action tendency, bodily reaction, expression, and feeling components of the emotion process. A principal component analysis confirmed the four-dimensional valence, power, arousal, and novelty structure. Moreover, this larger and much more representative set of emotion terms revealed that the novelty dimension not only differentiates surprise terms from other emotion terms, but also identifies substantial variation within the fear and joy emotion families.