General Position Subsets and Independent Hyperplanes in d-Space

Erd\H{o}s asked what is the maximum number $\alpha(n)$ such that every set of $n$ points in the plane with no four on a line contains $\alpha(n)$ points in general position. We consider variants of this question for $d$-dimensional point sets and generalize previously known bounds. In particular, we prove the following two results for fixed $d$: - Every set $H$ of $n$ hyperplanes in $\mathbb{R}^d$ contains a subset $S\subseteq H$ of size at least $c \left(n \log n\right)^{1/d}$, for some constant $c=c(d)>0$, such that no cell of the arrangement of $H$ is bounded by hyperplanes of $S$ only. - Every set of $cq^d\log q$ points in $\mathbb{R}^d$, for some constant $c=c(d)>0$, contains a subset of $q$ cohyperplanar points or $q$ points in general position. Two-dimensional versions of the above results were respectively proved by Ackerman et al. [Electronic J. Combinatorics, 2014] and by Payne and Wood [SIAM J. Discrete Math., 2013].Comment: 8 page

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

Finding Multiple New Optimal Locations in a Road Network

We study the problem of optimal location querying for location based services in road networks, which aims to find locations for new servers or facilities. The existing optimal solutions on this problem consider only the cases with one new server. When two or more new servers are to be set up, the problem with minmax cost criteria, MinMax, becomes NP-hard. In this work we identify some useful properties about the potential locations for the new servers, from which we derive a novel algorithm for MinMax, and show that it is efficient when the number of new servers is small. When the number of new servers is large, we propose an efficient 3-approximate algorithm. We verify with experiments on real road networks that our solutions are effective and attains significantly better result quality compared to the existing greedy algorithms

Decoherence suppression via environment preparation

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For models in which a two-state system interacts with a dynamical environment, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.Comment: 4 pages, 2 figure

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

An experimental study of how variation in deer density affects vegetation and songbird assemblages of recently harvested boreal forests

Intense browsing by abundant large herbivores can threaten the ecological integrity of ecosystems by inducing modifications in the structure and composition of vegetation that trigger trophic cascades affecting plant and animal communities. We investigated the relationships between density of white-tailed deer (Odocoileus virginianus (Zimmermann, 1780)), forest succession after clear-cut, and songbird communities on Anticosti Island, Quebec, Canada. We hypothesized that lower deer densities would alter the trajectory of forest succession after clear-cutting and lead to a rapid recovery of habitat attributes favorable to songbirds associated with a dense complex shrub layer. Six years after establishing a controlled browsing experiment (0, 7.5, 15, and >27 deer·km–2) in recent clearcuts, reducing deer densities ≤7.5 deer·km–2 initiated the restoration of balsam fir (Abies balsamea (L.) Mill.) forests and increased the regeneration of paper birch (Betula papyrifera Marshall). Increasing birch ground cover from 10% to 20% increased songbird total abundance, species richness, and diversity by 17%, 39%, and 31%, respectively. Alder Flycatcher (Empidonax alnorum Brewster, 1895) was only present at ≤7.5 deer·km–2 and strongly associated with birch regeneration. The regeneration of browse-resistant plants such as white spruce (Picea glauca (Moench) Voss) in some areas at high deer density favored the maintenance of many shrub-dependent songbirds but also species usually associated with forest canopy. Active management of deer populations in Canadian harvested boreal forests will mitigate losses in vegetation and songbirds caused by over-browsing.Le broutement intensif par de nombreux grands herbivores peut menacer l’intégrité écologique d’écosystèmes en induisant des modifications de la structure et de la composition de la végétation qui déclenchent des cascades trophiques ayant des incidences sur les communautés végétales et animales. Nous nous sommes penchés sur les liens entre la densité du cerf de Virginie (Odocoileus virginianus (Zimmermann, 1780)), la succession forestière après la coupe à blanc et les communautés d’oiseaux chanteurs sur l’île d’Anticosti (Québec, Canada). Nous avons émis l’hypothèse que de plus faibles densités de cerfs modifieraient la trajectoire de succession forestière après une coupe à blanc et mèneraient au rétablissement rapide des attributs d’habitat favorables aux oiseaux chanteurs associés à une strate arbustive complexe et dense. Six ans après l’établissement d’une expérience de broutement contrôlé (0, 7,5, 15 et >27 cerfs·km–2) dans des coupes récentes, la réduction des densités de cerfs à ≤7,5 cerfs·km–2 s’est traduite par le début du rétablissement des forêts de sapin baumier (Abies balsamea (L.) Mill.) et une régénération accrue du bouleau à papier (Betula papyrifera Marshall). Un passage de la couverture de bouleau de 10 % à 20 % s’est traduit par des augmentations de l’abondance totale d’oiseaux chanteurs, de la richesse spécifique et de la diversité de 17 %, 39 % et 31 %, respectivement. Le moucherolle des aulnes (Empidonax alnorum Brewster, 1895) n’était présent qu’à des densités ≤7,5 cerfs·km–2 et était fortement associé à la régénération du bouleau. La régénération de plantes résistantes au broutement, telles que l’épinette blanche (Picea glauca (Moench) Voss) dans certaines zones à forte densité de cerfs a favorisé le maintien de nombreux oiseaux chanteurs dépendants des arbustes, mais également d’espèces généralement associées à la canopée. La gestion active des populations de cerfs dans les forêts boréales canadiennes exploitées atténuera les pertes de végétation et d’oiseaux chanteurs causées par le surbroutemen

Phylogeny of the Subfamilies of Ichneumonidae (Hymenoptera)

A combined morphological and molecular phylogenetic analysis was performed to evaluate the subfamily relationships of the parasitoid wasp family Ichneumonidae (Hymenoptera). Data were obtained by coding 135 morphological and 6 biological characters for 131 exemplar species of ichneumonids and 3 species of Braconidae (the latter as outgroups). The species of ichneumonids represent all of the 42 currently recognized subfamilies. In addition, molecular sequence data (cytochrome oxidase I “DNA barcoding” region, the D2 region of 28S rDNA and part of the F2 copy of elongation factor 1-alpha) were obtained from specimens of the same species that were coded for morphology (1309 base pairs total). The data were analyzed using parsimony and Bayesian analyses. The parsimony analysis using all data recovered previ-ously recognized informal subfamily groupings (Pimpliformes, Ophioniformes, Ichneumoniformes), al-though the relationships of these three groups to each other differed from previous studies and some of the subfamily relationships within these groupings had not previously been suggested. Specifically, Ophioni-formes was the sister group to (Ichneumoniformes + Pimplformes), and Labeninae was placed near Ich-neumoniformes, not as sister group to all Ichneumonidae except Xoridinae. The parsimony analysis using only morphological characters was poorly resolved and did not recover any of the three informal subfamily groupings and very few of the relationships were similar to the total-evidence parsimony analysis. The mo-lecular-only parsimony analysis and both Bayesian analyses (total-evidence and molecular-only) recovered Pimpliformes, a restricted Ichneumoniformes grouping and many of the subfamily groupings recovered in the total-evidence parsimony analysis. A comparison and discussion of the results obtained by each phylo-genetic method and different data sets is provided. It is concluded that the molecular characters produced results that were relatively consistent with traditional, non-phylogenetic concepts of relationships between the ichneumonid subfamilies, whereas the morphological characters did not (at least not by themselves). The inclusion of both molecular and morphological characters using parsimony produced a topology that was the closest to the traditional subfamily relationships. The method of analysis did not greatly affect the overall topology for the molecular-only analyses, but there were differences between Bayesian and parsi-mony results for the total-evidence analyses (especially near the root of the tree). The Bayesian results did not seem to be altered very much by the inclusion of morphological characters, unlike in the parsimony analysis. In summary, the following groups were supported in multiple analyses regardless of the characters used or method of tree-building: Pimpliformes, higher Ophioniformes, higher Pimpliformes, (Claseinae + Pedunculinae), (Banchinae + Stilbopinae), Campopleginae, Cremastinae, Diplazontinae, Ichneumoninae (including Alomya), Labeninae, Ophioninae, Poemeniinae, Rhyssinae, and Tersilochinae sensu stricto. Conversely, Ctenopelmatinae and Tryphoninae were never recovered without inclusion of other taxa. Based on the hypothesis of relationships obtained by the total-evidence parsimony analysis, the following formal taxonomic changes are proposed: Alomyinae Förster (= Alomya Panzer and Megalomya Uchida) is once again synonymized with Ichneumoninae and is now considered a tribe (Alomyini rev. stat.); and Notostilbops Townes is transferred from Stilbopinae to Banchinae, tribe Atrophini

The Complexity of Drawing Graphs on Few Lines and Few Planes

It is well known that any graph admits a crossing-free straight-line drawing in $\mathbb{R}^3$ and that any planar graph admits the same even in $\mathbb{R}^2$. For a graph $G$ and $d \in \{2,3\}$, let $\rho^1_d(G)$ denote the minimum number of lines in $\mathbb{R}^d$ that together can cover all edges of a drawing of $G$. For $d=2$, $G$ must be planar. We investigate the complexity of computing these parameters and obtain the following hardness and algorithmic results. - For $d\in\{2,3\}$, we prove that deciding whether $\rho^1_d(G)\le k$ for a given graph $G$ and integer $k$ is ${\exists\mathbb{R}}$-complete. - Since $\mathrm{NP}\subseteq{\exists\mathbb{R}}$, deciding $\rho^1_d(G)\le k$ is NP-hard for $d\in\{2,3\}$. On the positive side, we show that the problem is fixed-parameter tractable with respect to $k$. - Since ${\exists\mathbb{R}}\subseteq\mathrm{PSPACE}$, both $\rho^1_2(G)$ and $\rho^1_3(G)$ are computable in polynomial space. On the negative side, we show that drawings that are optimal with respect to $\rho^1_2$ or $\rho^1_3$ sometimes require irrational coordinates. - Let $\rho^2_3(G)$ be the minimum number of planes in $\mathbb{R}^3$ needed to cover a straight-line drawing of a graph $G$. We prove that deciding whether $\rho^2_3(G)\le k$ is NP-hard for any fixed $k \ge 2$. Hence, the problem is not fixed-parameter tractable with respect to $k$ unless $\mathrm{P}=\mathrm{NP}$