Min-Max Theorems for Packing and Covering Odd (u,v)(u,v)-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd $(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that intersects every odd $(u,v)$-trail. We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$. Our proof also yields a polynomial-time algorithm for finding a cover and a collection of trails satisfying the above bounds. Our proof is simple and has two main ingredients. We show that (loosely speaking) the problem can be reduced to the problem of packing and covering odd $(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or the size of the cover). Complementing this, we show that the odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting a powerful min-max result of [Chudnovsky et al 2006] for packing vertex-disjoint nonzero $A$-paths in group-labeled graphs

Officials can nudge public behavior by showing that they are responding to people's demands

A key aim of public policymaking is to change public behavior in one way or another. In new research which focuses on voting patterns in Colorado, Andrew Menger and Robert M. Stein tested a number of ways of encouraging people to return their mail-in ballots early. They find that only message which increased early voting was one which explained that ..

Macrophages promote network formation and maturation of transplanted adipose tissue-derived microvascular fragments

Adipose tissue-derived microvascular fragments rapidly reassemble into microvascular networks within implanted scaffolds. Herein, we analyzed the contribution of macrophages to this process. C57BL/6 mice received clodronate (clo)-containing liposomes for macrophage depletion, whereas animals treated with phosphate-buffered-saline-containing liposomes served as controls. Microvascular fragments were isolated from clo- and phosphate-buffered-saline-treated donor mice and seeded onto collagen-glycosaminoglycan matrices, which were implanted into dorsal skinfold chambers of clo- and phosphate-buffered-saline-treated recipient mice. The implants' vascularization and incorporation were analyzed by stereomicroscopy, intravital fluorescence microscopy, histology, and immunohistochemistry. Compared to controls, matrices within clo-treated animals exhibited a significantly reduced functional microvessel density. Moreover, they contained a lower fraction of microvessels with an α-smooth muscle actin (SMA)+ cell layer, indicating impaired vessel maturation. This was associated with a deteriorated implant incorporation. These findings demonstrate that macrophages not only promote the reassembly of microvascular fragments into microvascular networks, but also improve their maturation during this process

Erythropoietin exposure of isolated pancreatic islets accelerates their revascularization after transplantation

Aims The exposure of isolated pancreatic islets to pro-angiogenic factors prior to their transplantation represents a promising strategy to accelerate the revascularization of the grafts. It has been shown that erythropoietin (EPO), a glycoprotein regulating erythropoiesis, also induces angiogenesis. Therefore, we hypothesized that EPO exposure of isolated islets improves their posttransplant revascularization. Methods Flow cytometric, immunohistochemical and quantitative real-time (qRT)-PCR analyses were performed to study the effect of EPO on the viability, cellular composition and gene expression of isolated islets. Moreover, islets expressing a mitochondrial or cytosolic H2O2 sensor were used to determine reactive oxygen species (ROS) levels. The dorsal skinfold chamber model in combination with intravital fluorescence microscopy was used to analyze the revascularization of transplanted islets. Results We found that the exposure of isolated islets to EPO (3 units/mL) for 24 h does not affect the viability and the production of ROS when compared to vehicle-treated and freshly isolated islets. However, the exposure of islets to EPO increased the number of CD31-positive cells and enhanced the gene expression of insulin and vascular endothelial growth factor (VEGF)-A. The revascularization of the EPO-cultivated islets was accelerated within the initial phase after transplantation when compared to both controls. Conclusion These findings indicate that the exposure of isolated islets to EPO may be a promising approach to improve clinical islet transplantation

Darbepoetin-α increases the blood volume flow in transplanted pancreatic islets in mice

Aims The minimal-invasive transplantation of pancreatic islets is a promising approach to treat diabetes mellitus type 1. However, islet transplantation is still hampered by the insufficient process of graft revascularization, leading to a poor clinical outcome. Accordingly, the identification of novel compounds, which accelerate and improve the revascularization of transplanted islets, is of great clinical interest. Previous studies have shown that darbepoetin (DPO)-α, a long lasting analogue of erythropoietin, is capable of promoting angiogenesis. Hence, we investigated in this study whether DPO improves the revascularization of transplanted islets. Methods Islets were isolated from green fluorescent protein-positive FVB/N donor mice and transplanted into dorsal skinfold chambers of FVB/N wild-type animals, which were treated with DPO low dose (2.5 µg/kg), DPO high dose (10 µg/kg) or vehicle (control). The revascularization was assessed by repetitive intravital fluorescence microscopy over an observation period of 14 days. Subsequently, the cellular composition of the grafts was analyzed by immunohistochemistry. Results The present study shows that neither low- nor high-dose DPO treatment accelerates the revascularization of free pancreatic islet grafts. However, high-dose DPO treatment increased the blood volume flow of the transplanted islet. Conclusions These findings demonstrated that DPO treatment does not affect the revascularization of transplanted islets. However, the glycoprotein increases the blood volume flow of the grafts, which results in an improved microvascular function and may facilitate successful transplantation

Parathyroid hormone stimulates bone regeneration in an atrophic non-union model in aged mice

Background Non-union formation still represents a major burden in trauma and orthopedic surgery. Moreover, aged patients are at an increased risk for bone healing failure. Parathyroid hormone (PTH) has been shown to accelerate fracture healing in young adult animals. However, there is no information whether PTH also stimulates bone regeneration in atrophic non-unions in the aged. Therefore, the aim of the present study was to analyze the efect of PTH on bone regeneration in an atrophic non-union model in aged CD-1 mice. Methods After creation of a 1.8 mm segmental defect, mice femora were stabilized by pin-clip fxation. The animals were treated daily with either 200 mg/kg body weight PTH 1–34 (n=17) or saline (control; n=17) subcutaneously. Bone regeneration was analyzed by means of X-ray, biomechanics, micro-computed tomography (µCT) imaging as well as histological, immunohistochemical and Western blot analyses. Results In PTH-treated animals bone formation was markedly improved when compared to controls. This was associated with an increased bending stifness as well as a higher number of tartrate-resistant acid phosphatase (TRAP)- positive osteoclasts and CD31-positive microvessels within the callus tissue. Furthermore, PTH-treated aged animals showed a decreased infammatory response, characterized by a lower number of MPO-positive granulocytes and CD68-positive macrophages within the bone defects when compared to controls. Additional Western blot analyses demonstrated a signifcantly higher expression of cyclooxygenase (COX)-2 and phosphoinositide 3-kinase (PI3K) in PTH-treated mice. Conclusion Taken together, these fndings indicate that PTH is an efective pharmacological compound for the treatment of non-union formation in aged animals

Strong Field Control of the Interatomic Coulombic Decay Process in Quantum Dots

In recent years the laser induced interatomic Coulombic decay ICD process in paired quantum dots has been predicted [J. Chem. Phys. 138 2013 214104]. In this work we target the enhancement of ICD by scanning over a range of strong field laser intensities. The GaAs quantum dots are modeled by a one dimensional double well potential in which simulations are done with the space resolved multi configuration time dependent Hartree method including antisymmetrization to account for the fermions. As a novelty a complementary state resolved ansatz is developed to consolidate the interpretation of transient state populations, widths obtained for the ICD and the competing direct ionization channel, and Fano peak profiles in the photoelectron spectra. The major results are that multi photon processes are unimportant even for the strongest fields. Further, below pi to pi pulses display the highest ICD efficiency while the direct ionization becomes less dominan

(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor changes added relating to previous wor