Moving Walkways, Escalators, and Elevators

We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of points is defined as a time distance, in such a way that a customer uses the transportation facility only if it is helpful. We give algorithms for finding the optimal location of such a transportation facility, where optimality is defined with respect to the maximum travel time between two points in a given set.Comment: 16 pages. Presented at XII Encuentros de Geometria Computacional, Valladolid, Spai

Large Coercivity in Nanostructured Rare-earth-free MnxGa Films

The magnetic hysteresis of MnxGa films exhibit remarkably large coercive fields as high as 2.5 T when fabricated with nanoscale particles of a suitable size and orientation. This coercivity is an order of magnitude larger than in well-ordered epitaxial film counterparts and bulk materials. The enhanced coercivity is attributed to the combination of large magnetocrystalline anisotropy and ~ 50 nm size nanoparticles. The large coercivity is also replicated in the electrical properties through the anomalous Hall effect. The magnitude of the coercivity approaches that found in rare-earth magnets, making them attractive for rare-earth-free magnet applications

Unsplittable coverings in the plane

A system of sets forms an {\em $m$-fold covering} of a set $X$ if every point of $X$ belongs to at least $m$ of its members. A $1$-fold covering is called a {\em covering}. The problem of splitting multiple coverings into several coverings was motivated by classical density estimates for {\em sphere packings} as well as by the {\em planar sensor cover problem}. It has been the prevailing conjecture for 35 years (settled in many special cases) that for every plane convex body $C$, there exists a constant $m=m(C)$ such that every $m$-fold covering of the plane with translates of $C$ splits into $2$ coverings. In the present paper, it is proved that this conjecture is false for the unit disk. The proof can be generalized to construct, for every $m$, an unsplittable $m$-fold covering of the plane with translates of any open convex body $C$ which has a smooth boundary with everywhere {\em positive curvature}. Somewhat surprisingly, {\em unbounded} open convex sets $C$ do not misbehave, they satisfy the conjecture: every $3$-fold covering of any region of the plane by translates of such a set $C$ splits into two coverings. To establish this result, we prove a general coloring theorem for hypergraphs of a special type: {\em shift-chains}. We also show that there is a constant $c>0$ such that, for any positive integer $m$, every $m$-fold covering of a region with unit disks splits into two coverings, provided that every point is covered by {\em at most} $c2^{m/2}$ sets

Chronic hindlimb ischemia impairs functional vasodilation and vascular reactivity in mouse feed arteries

Vasodilation of lower leg arterioles is impaired in animal models of chronic peripheral ischemia. In addition to arterioles, feed arteries are a critical component of the vascular resistance network, accounting for as much as 50% of the pressure drop across the arterial circulation. Despite the critical importance of feed arteries in blood flow control, the impact of ischemia on feed artery vascular reactivity is unknown. At 14 days following unilateral resection of the femoral–saphenous artery–vein pair, functional vasodilation of the profunda femoris artery was severely impaired, 11 ± 9 versus 152 ± 22%. Although endothelial and smooth muscle-dependent vasodilation were both impaired in ischemic arteries compared to control arteries (Ach: 40 ± 14 versus 81 ± 11%, SNP: 43 ± 12 versus and 85 ± 11%), the responses to acetylcholine and sodium nitroprusside were similar, implicating impaired smooth muscle-dependent vasodilation. Conversely, vasoconstriction responses to norepinephrine were not different between ischemic and control arteries, −68 ± 3 versus −66 ± 3%, indicating that smooth muscle cells were functional following the ischemic insult. Finally, maximal dilation responses to acetylcholine, ex vivo, were significantly impaired in the ischemic artery compared to control, 71 ± 9 versus 97 ± 2%, despite a similar generation of myogenic tone to the same intravascular pressure (80 mmHg). These data indicate that ischemia impairs feed artery vasodilation by impairing the responsiveness of the vascular wall to vasodilating stimuli. Future studies to examine the mechanistic basis for the impact of ischemia on vascular reactivity or treatment strategies to improve vascular reactivity following ischemia could provide the foundation for an alternative therapeutic paradigm for peripheral arterial occlusive disease

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Identification of MEN1 gene mutations in families with MEN 1 and related disorders

Following identification of the MEN1 gene, we analysed patients from 12 MEN 1 families, 8 sporadic cases of MEN 1, and 13 patients with MEN 1-like symptoms (e.g. cases of familial isolated hyperparathyroidism (FIHPT), familial acromegaly, or atypical MEN 1 cases) for the presence of germline MEN1 mutations. The entire coding region of the MEN1 gene was sequenced, and mutations were detected in 11 MEN 1 families; one sporadic MEN 1 patient, one case of FIHPT and one MEN 1-like case. Constitutional DNA samples from individuals without MEN1 mutations were digested with several restriction enzymes, Southern blotted and probed with MEN1 cDNA to analyse for the presence of larger deletions of the MEN1 gene unable to be detected by PCR. One MEN 1 patient was found to carry such a deletion. This patient was heterozygous for the D418D polymorphism, however sequence analysis of RT-PCR products showed that only the variant allele was transcribed, thus confirming the result obtained by Southern analysis, which indicated loss of a region containing the initiation codon of one allele. © 2000 Cancer Research Campaig

An abstract approach to polychromatic coloring

The goal of this paper is to give a new, abstract approach to cover-decomposition and polychromatic colorings using hypergraphs on ordered vertex sets. We introduce an abstract version of a framework by Smorodinsky and Yuditsky, used for polychromatic coloring halfplanes, and apply it to so-called ABA-free hypergraphs, which are a generalization of interval graphs. Using our methods, we prove that (2k−1)-uniform ABA-free hypergraphs have a polychromatic k-coloring, a problem posed by the second author. We also prove the same for hypergraphs defined on a point set by pseudohalfplanes. These results are best possible. We also introduce several new notions that seem to be important for investigating polychromatic colorings and ϵ -nets, such as shallow hitting sets. We pose several open problems related to them. For example, is it true that given a finite point set S on a sphere and a set of halfspheres F, such that {S ∩ F | F ∈ F} is a Sperner family, we can select an R ⊂ S such that 1 ≤ |F ∩ R| ≤ 2 holds for every F ∈ F?. © Springer International Publishing Switzerland 2016

Kitaev's quantum double model from a local quantum physics point of view

A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of view of local quantum physics. In particular, we will review how in the abelian case, one can do a Doplicher-Haag-Roberts analysis to study the different superselection sectors of the model. In this way one finds that the charges are in one-to-one correspondence with the representations of $\mathcal{D}(G)$, and that they are in fact anyons. Interchanging two of such anyons gives a non-trivial phase, not just a possible sign change. The case of non-abelian groups $G$ is more complicated. We outline how one could use amplimorphisms, that is, morphisms $A \to M_n(A)$ to study the superselection structure in that case. Finally, we give a brief overview of applications of topologically ordered systems to the field of quantum computation.Comment: Chapter contributed to R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds), Advances in Algebraic Quantum Field Theory (Springer 2015). Mainly revie