Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks.

Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in recent years to layer-coupled multiplex networks. The layers of these networks can reflect different relationships and interactions between entities or changing interactions over time. We use the supra-adjacency matrix as network representation, which has already been used to generalize eigenvector centrality to temporal and multiplex networks. With a suitable choice of edge weights, the definition of single-layer matrix function-based centrality measures in terms of walks on networks carries over naturally to the multilayer case. In contrast to other walk-based centralities, matrix function-based centralities are parameterized measures, which have been shown to interpolate between (local) degree and (global) eigenvector centrality in the single-layer case. As the explicit evaluation of the involved matrix function expressions becomes infeasible for medium to large-scale networks, we present highly efficient approximation techniques from numerical linear algebra, which rely on Krylov subspace methods, Gauss quadrature, and stochastic trace estimation. We present extensive numerical studies on synthetic and real-world multiplex transportation, communication, and collaboration networks. The comparison with established multilayer centrality measures shows that our framework produces meaningful rankings of nodes, layers, and node-layer pairs. Furthermore, our experiments corroborate the linear computational complexity of the employed numerical methods in terms of the network size that is theoretically indicated under the assumption of sparsity in the supra-adjacency matrix. This excellent scalability allows the efficient treatment of large-scale networks with the number of node-layer pairs of order 10^{7} or higher.

Long-Term Results of the Modular Physiological Wrist Prosthesis (MPW®) in Patients with Inflammatory Diseases.

The wrist is among the predilection sites of over 90% of cases of rheumatoid arthritis (RA). In advanced cases, total wrist arthroplasty (TWA) is an alternative to arthrodesis. The aim of this study is to present the long-term results of the modular physiological wrist prosthesis (MPW®) and to match them in context with the results of a standard population survey. In a retrospective study with follow-up, patients with an MPW® endoprosthesis were evaluated concerning the clinical and radiological outcome, complications were reviewed (incidence and type), and conversion to wrist fusion was assessed. Patient function measurements included the Mayo wrist score, the patient-specific wrist test, and therefore the DASH score (arm, shoulder, and hand). Thirty-four MPW® wrist prostheses were implanted in 32 patients, including thirty primary implantations and four changes of the type of the endoprosthesis. Sixteen patients (18 prostheses) underwent clinical and radiological follow-up. The average follow-up time was 8.5 years (1 to 16). Poor results of the MPW prosthesis are caused by the issues of balancing with luxation and increased PE wear. Salvage procedures included revision of the TWA or fusion. In successful cases, the flexion and extension movement averaged 40 degrees. The grip force was around 2.5 kg. The common DASH score was 79 points, with limited and problematic joints of the upper extremity. The MPW wrist prosthesis offered good pain relief and functional movement in over 80% of cases. The issues of dislocation and increased PE wear prevent better long-term results, as do the joints affected. A follow-up study with fittings under a contemporary anti-rheumatic therapy with biologicals suggests increasing score results. Type of study/level of evidence: Case series, IV.

Tomographic X-ray scattering based on invariant reconstruction: analysis of the 3D nanostructure of bovine bone.

Small-angle X-ray scattering (SAXS) is an effective characterization technique for multi-phase nanocomposites. The structural complexity and heterogeneity of biological materials require the development of new techniques for the 3D characterization of their hierarchical structures. Emerging SAXS tomographic methods allow reconstruction of the 3D scattering pattern in each voxel but are costly in terms of synchrotron measurement time and computer time. To address this problem, an approach has been developed based on the reconstruction of SAXS invariants to allow for fast 3D characterization of nanostructured inhomogeneous materials. SAXS invariants are scalars replacing the 3D scattering patterns in each voxel, thus simplifying the 6D reconstruction problem to several 3D ones. Standard procedures for tomographic reconstruction can be directly adapted for this problem. The procedure is demonstrated by determining the distribution of the nanometric bone mineral particle thickness (T parameter) throughout a macroscopic 3D volume of bovine cortical bone. The T parameter maps display spatial patterns of particle thickness in fibrolamellar bone units. Spatial correlation between the mineral nano-structure and microscopic features reveals that the mineral particles are particularly thin in the vicinity of vascular channels.

Correlation of mammographic density and serum calcium levels in patients with primary breast cancer.

Percentage mammographic breast density (PMD) is one of the most important risk factors for breast cancer (BC). Calcium, vitamin D, bisphosphonates, and denosumab have been considered and partly confirmed as factors potentially influencing the risk of BC. This retrospective observational study investigated the association between serum calcium level and PMD. A total of 982 BC patients identified in the research database at the University Breast Center for Franconia with unilateral BC, calcium and albumin values, and mammogram at the time of first diagnosis were included. PMD was assessed, using a semiautomated method by two readers. Linear regression analyses were conducted to investigate the impact on PMD of the parameters of serum calcium level adjusted for albumin level, and well-known clinical predictors such as age, body mass index (BMI), menopausal status and confounder for serum calcium like season in which the BC was diagnosed. Increased calcium levels were associated with reduced PMD (P = 0.024). Furthermore, PMD was inversely associated with BMI (P < 0.001) and age (P < 0.001). There was also an association between PMD and menopausal status (P < 0.001). The goodness-of-fit of the regression model was moderate. This is the first study assessing the association between serum calcium level and PMD. An inverse association with adjusted serum calcium levels was observed. These findings add to previously published data relating to vitamin D, bisphosphonates, denosumab, and the RANK/RANKL signaling pathway in breast cancer risk and prevention.

Treatment with anticoagulants in cerebral events (TRACE).

90 patients with acute stroke and a concomitant cardiac embolism source or a symptomatic high-grade stenosis of an extra-or intracranial vessel received in a mulitcenter, randomized, controlled study either Enoxaparin 1 mg/kg BW s.c. b.i.d. or i.v. heparin aPTT-adjusted daily for 8 +/- 2 days as secondary prophylaxis. There were no significant differences between the two groups regarding cerebral and systemic embolic events, bleeding complications, length of hospital stay, number of diagnostic and therapeutic measures and outcome after three months. This suggests that Enoxaparin, which is easier to administer and monitor, is a safe drug in patients with acute cerebral events.

Regio- and Stereoselective Synthesis of γ-Alkylidenebutenolides by Cyclization of Dilithiated 1,3-Dicarbonyl Compounds with N,N'-Dimethoxy-N,N'-dimethylethane- diamide.

The remarkably simple synthesis of γ-alkylidenebutenolides 3 is achieved by cyclization of the dilithiated 1,3-dicarbonyl compounds 1 with N,N'-dimethoxy-N,N'-dimethylethanediamide (2). This regio- and stereoselective cyclization provides a route to a wide range of butenolides, which are of pharmacological relevance and of importance for natural product synthesis.

Influence of long-term volume therapy with hydroxyethyl starch on leukocytes in patients with acute stroke.

A repeated administration of hydroxyethyl starch affects hemostasiological and rheological factors such as the concentration of factor VIII/von Willebrand factor, platelet volume and plasma viscosity. An earlier study showed that HES also lowers the concentration of fibronectin, a molecule important in the reticuloendothelial system (RES). RES has a "clearing function" and is a part of the non-immune-specific defense mechanisms of the body. It is involved in the elimination of HES from the blood. Since leukocytes are another important part of the unspecific defense system, the goal of the present study was to investigate whether HES affects leukocytes. After giving their informed consent, 20 patients with cerebral perfusion disorders were randomized and underwent a double-blind 10-day hypervolemic hemodilution with HES 200/0.5/13 or HES 70/0.5/4. The numbers of leukocytes, percentage of lymphocytes, percentage of neutrophilic granulocytes and hemoglobin concentration were measured. The absolute number of leukocytes did not change significantly, but the share of neutrophilic granulocytes increased. The increase in neutrophilic granulocytes reflects an increase in phagocytic activity. HEs 200/0.5/13, which has the larger in vivo molecular weight (MW = 95 kD), caused a larger increase in neutrophilic granulocytes than HES 70/0.5/4, which has an in vivo MW of 58 kD.