Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure

Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients

In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a vertex. The motivation of our study comes from the theory of non-ideal gases and, more specifically, from the virial equation of state. It is a known result of Statistical Mechanics that the coefficients in the virial equation of state are sums over labelled 2-connected graphs. These graphs correspond to clusters of particles. Thus, theoretically, the virial coefficients of any order can be calculated by means of 2-connected graphs used in the virial coefficient of the previous order. Our main result gives a method for constructing inductively all simple 2-connected graphs, by induction on the number of vertices. Moreover, the two operations we are using maintain the correspondence between graphs and clusters of particles.Comment: 23 pages, 5 figures, 3 table

Library Design in Combinatorial Chemistry by Monte Carlo Methods

Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.Comment: 5 pages, 3 figure

Vascularization of Microvascular Fragment Isolates from Visceral and Subcutaneous Adipose Tissue of Mice

Background: Adipose tissue-derived microvascular fragments (MVF) represent effective vascularization units for tissue engineering. Most experimental studies in rodents exclusively use epididymal adipose tissue as a visceral fat source for MVF isolation. However, in future clinical practice, MVF may be rather isolated from liposuctioned subcutaneous fat tissue of patients. Therefore, we herein compared the vascularization characteristics of MVF isolates from visceral and subcutaneous fat tissue of murine origin. Methods: MVF isolates were generated from visceral and subcutaneous fat tissue of donor mice using two different enzymatic procedures. For in vivo analyses, the MVF isolates were seeded onto collagen-glycosaminoglycan scaffolds and implanted into full-thickness skin defects within dorsal skinfold chambers of recipient mice. Results: By means of the two isolation procedures, we isolated a higher number of MVF from visceral fat tissue when compared to subcutaneous fat tissue, while their length distribution, viability and cellular composition were comparable in both groups. Intravital fluorescence microscopy as well as histological and immunohistochemical analyses revealed a significantly reduced vascularization of implanted scaffolds seeded with subcutaneous MVF isolates when compared to implants seeded with visceral MVF isolates. Light and scanning electron microscopy showed that this was due to high amounts of undigested connective tissue within the subcutaneous MVF isolates, which clogged the scaffold pores and prevented the interconnection of individual MVF into new microvascular networks. Conclusion: These findings indicate the need for improved protocols to generate connective tissue-free MVF isolates from subcutaneous fat tissue for future translational studies

Improvement of islet transplantation by the fusion of islet cells with functional blood vessels

Pancreatic islet transplantation still represents a promising therapeutic strategy for curative treatment of type 1 diabetes mellitus. However, a limited number of organ donors and insufficient vascularization with islet engraftment failure restrict the successful transfer of this approach into clinical practice. To overcome these problems, we herein introduce a novel strategy for the generation of prevascularized islet organoids by the fusion of pancreatic islet cells with functional native microvessels. These insulin-secreting organoids exhibit a significantly higher angiogenic activity compared to freshly isolated islets, cultured islets, and non-prevascularized islet organoids. This is caused by paracrine signaling between the β-cells and the microvessels, mediated by insulin binding to its corresponding receptor on endothelial cells. In vivo, the prevascularized islet organoids are rapidly blood-perfused after transplantation by the interconnection of their autochthonous microvasculature with surrounding blood vessels. As a consequence, a lower number of islet grafts are required to restore normoglycemia in diabetic mice. Thus, prevascularized islet organoids may be used to improve the success rates of clinical islet transplantation

Myocardial effective transverse relaxation time T(2)* correlates with left ventricular wall thickness: a 7.0 T MRI study

PURPOSE: Myocardial effective relaxation time T2* is commonly regarded as a surrogate for myocardial tissue oxygenation. However, it is legitimate to assume that there are multiple factors that influence T2*. To this end, this study investigates the relationship between T2* and cardiac macromorphology given by left ventricular (LV) wall thickness and left ventricular radius, and provides interpretation of the results in the physiological context. METHODS: High spatio-temporally resolved myocardial CINE T2* mapping was performed in 10 healthy volunteers using a 7.0 Tesla (T) full-body MRI system. Ventricular septal wall thickness, left ventricular inner radius, and T2* were analyzed. Macroscopic magnetic field changes were elucidated using cardiac phase-resolved magnetic field maps. RESULTS: Ventricular septal T2* changes periodically over the cardiac cycle, increasing in systole and decreasing in diastole. Ventricular septal wall thickness and T2* showed a significant positive correlation, whereas the inner LV radius and T2* were negatively correlated. The effect of macroscopic magnetic field gradients on T2* can be considered minor in the ventricular septum. CONCLUSION: Our findings suggest that myocardial T2* is related to tissue blood volume fraction. Temporally resolved T2* mapping could be beneficial for myocardial tissue characterization and for understanding cardiac (patho)physiology in vivo

The combinatorics of the Baer-Specker group

Denote the integers by Z and the positive integers by N. The groups Z^k (k a natural number) are discrete, and the classification up to isomorphism of their (topological) subgroups is trivial. But already for the countably infinite power Z^N of Z, the situation is different. Here the product topology is nontrivial, and the subgroups of Z^N make a rich source of examples of non-isomorphic topological groups. Z^N is the Baer-Specker group. We study subgroups of the Baer-Specker group which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Ko\v{c}inac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and Scheepers.Comment: To appear in IJ

Towards a Tetravalent Chemistry of Colloids

We propose coating spherical particles or droplets with anisotropic nano-sized objects to allow micron-scale colloids to link or functionalize with a four-fold valence, similar to the sp3 hybridized chemical bonds associated with, e.g., carbon, silicon and germanium. Candidates for such coatings include triblock copolymers, gemini lipids, metallic or semiconducting nanorods and conventional liquid crystal compounds. We estimate the size of the relevant nematic Frank constants, discuss how to obtain other valences and analyze the thermal distortions of ground state configurations of defects on the sphere.Comment: Replaced to improve figures. 4 figures Nano Letter

CK2 Activity Mediates the Aggressive Molecular Signature of Glioblastoma Multiforme by Inducing Nerve/Glial Antigen (NG)2 Expression

Nerve/glial antigen (NG)2 expression crucially determines the aggressiveness of glioblastoma multiforme (GBM). Recent evidence suggests that protein kinase CK2 regulates NG2 expression. Therefore, we investigated in the present study whether CK2 inhibition suppresses proliferation and migration of NG2-positive GBM cells. For this purpose, CK2 activity was suppressed in the NG2-positive cell lines A1207 and U87 by the pharmacological inhibitor CX-4945 and CRISPR/Cas9- mediated knockout of CK2α. As shown by quantitative real-time PCR, luciferase-reporter assays, flow cytometry and western blot, this significantly reduced NG2 gene and protein expression when compared to vehicle-treated and wild type controls. In addition, CK2 inhibition markedly reduced NG2-dependent A1207 and U87 cell proliferation and migration. The Cancer Genome Atlas (TCGA)- based data further revealed not only a high expression of both NG2 and CK2 in GBM but also a positive correlation between the mRNA expression of the two proteins. Finally, we verified a decreased NG2 expression after CX-4945 treatment in patient-derived GBM cells. These findings indicate that the inhibition of CK2 represents a promising approach to suppress the aggressive molecular signature of NG2-positive GBM cells. Therefore, CX-4945 may be a suitable drug for the future treatment of NG2-positive GBM