We prove, that every connected graph with s vertices of degree 3 and t vertices of degree at least 4 has a spanning tree with at least 2 5 t + 1 5 s + α leaves, where α ≥ 8 5 . Moreover, α ≥ 2 for all graphs besides three exclusions. All exclusion are regular graphs of degree 4, they are explicitly described in the paper. We present infinite series of graphs, containing only vertices of degrees...

Local search for combinatorial optimization problems is becoming a dominant algorithmic paradigm, with several papers using it to resolve long-standing open problems. In this paper, we prove the following ‘4-local’ version of Hall’s theorem for planar graphs: given a bipartite planar graph G = (B,R,E) such that |N(B′)| ≥ |B′| for all |B′| ≤ 4, there exists a matching of size at least |B| 4 in G...

(with 1 , q , ̀ ) . An infinite family of simply connected examples for this diagram with q 5 2 is obtained by truncating Coxeter complexes of type D n . Two dif ferent finite families with three members and q 5 4 arise from the Steiner systems for the Mathieu groups M 2 2 , M 2 3 and M 2 4 . The geometries of these two families are simply connected . Three more simply connected examples of rank...

Animal experiments confirmed the neuropeptide nature of delta-sleep-inducing-peptide (DSIP) and a species-specific sleep promotion. Five different human studies were carried out with single and repeated intravenous injections of DSIP under double-blind conditions, and with assessing treatment effects by psychophysiological tests and polygraphic recordings. Compatibility of DSIP was good. Slow i...

Mechanical ventilation has been the mainstay of treatment for respiratory failure. Modern-day mechanical ventilation has evolved from the days of the polio epidemic (1). As intensivists we have appreciated its benefits and risks through many years of experience and research. In striving to “do no harm,” we have adopted methods to ventilate patients that subject them to less lung injury as we tr...

PEA attenuates chemotherapy-induced neuropathies by attenuating endoneueral edema in myelinated nerve fibers [2]. Similarly, PEA improves distal motor latency in individuals with carpal tunnel syndrome [3]. Similar benefits have been noticed in pudendal neuralgias [4]. PEA also exerts beneficial effects in patients with multiple sclerosis by ameliorating neuropathic pain [5]. PEA also increases...

OBJECTIVE To demonstrate, quantify, and mechanistically dissect antiatherosclerotic effects of fenofibrate besides lowering plasma cholesterol per se. METHODS AND RESULTS ApoE*3Leiden transgenic mice received either a high-cholesterol diet (HC) or HC containing fenofibrate (HC+FF) resulting in 52% plasma cholesterol-lowering. In a separate low-cholesterol diet (LC) control group, plasma chole...

Osterix (Osx or Sp7) is a zinc-finger-family transcriptional factor essential for osteoblast differentiation in mammals. The Osx-Cre mouse line (also known as Osx1-GFP::Cre) expresses GFP::Cre fusion protein from a BAC transgene containing the Osx regulatory sequence. The mouse strain was initially characterized during embryogenesis, and found to target mainly osteoblast-lineage cells. Because ...