Triangle finding (deciding if a graph contains a triangle or not) is a central problem in quantum query complexity. The quantum communication complexity of this problem, where the edges of the graph are distributed among the players, was considered recently by Ivanyos et al. in the twoparty setting. In this paper we consider its k-party quantum communication complexity with k ≥ 3. Our main resu...

Heilbronn’s triangle problem asks for the least ∆ such that n points lying in the unit disc necessarily contain a triangle of area at most ∆. Heilbronn initially conjectured ∆ = O(1/n). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c logn/n ≤ ∆ ≤ C/n for every constant ǫ > 0. We resolve Heilbronn’s problem in the expected ...

Human renal cell carcinoma (RCC) tissue and a cell line derived therefrom. SMKT-R3, showed markedly increased glycolipid sulfotransferase [cerebroside Sulfotransferase iCS'l'i: EC 2.8.2.11] activity and ac cumulated Sulfoglycolipids. Recently, we cloned a human CST cDNA from a SMKT-R3 cDNA library (K. Honke et al., J. Biol. Chem., 272: 48644868, 1997). In this study, we investigated the express...

Previous studies have shown that sprouting of corticospinal tract (CST) fibers after spinal cord injury (SCI) contributes to recovery of motor functions. However, the neuroanatomical mechanism underlying the functional recovery through sprouting CST fibers remains unclear. Here we investigated the pattern of reorganization of CST fibers below the lesion site after SCI in adult macaques. Unilate...

Catestatin (Cst) is a 21-amino acid peptide deriving from Chromogranin A. Cst exerts an overall protective effect against an excessive sympathetic stimulation of cardiovascular system, being able to antagonize catecholamine secretion and to reduce their positive inotropic effect, by stimulating the release of nitric oxide (NO) from endothelial cells. Moreover, Cst reduces ischemia/reperfusion (...

Let X be a geodesic metric space. Gromov proved that there exists ε0 > 0 such that if every sufficiently large triangle ∆ satisfies the Rips condition with constant ε0 · pr(∆), where pr(∆) is the perimeter ∆, then X is hyperbolic. We give an elementary proof of this fact, also giving an estimate for ε0. We also show that if all the triangles ∆ ⊆ X satisfy the Rips condition with constant ε0 · p...

Evidence suggests that motor experience plays a role in shaping development of the corticospinal system and voluntary motor control, which is a key motor function of the system. Here we used a mouse model with conditional forebrain deletion of the gene for EphA4 (Emx1-Cre:EphA4tm2Kldr), which regulates development of the laterality of corticospinal tract (CST). We combined study of Emx1-Cre:Eph...

Studies that have assessed regeneration of corticospinal tract (CST) axons in mice after genetic modifications or other treatments have tacitly assumed that there is little if any regeneration of CST axons in normal mice in the absence of some intervention. Here, we document a previously unrecognized capability for regenerative growth of CST axons in normal mice that involves growth past the le...

INTRODUCTION In the continental US, four terrestrial mammalian species are reservoirs for seven antigenic rabies virus variants. Cross species transmission (CST) occurs when a rabies virus variant causes disease in non-reservoir species. METHODS This study analyzed national surveillance data for rabies in terrestrial mammals. The CST rate was defined as: number of rabid non-reservoir animals/...