Fault-tolerant additive weighted geometric spanners

Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance d_w(p, q) between two points p,q belonging to S is defined as w(p) + d(p, q) + w(q) if p \ne q and it is zero if p = q. Here, d(p, q) denotes the (geodesic) Euclidean distance between p and q. A graph G(S, E) is called a t-spanner for the additive weighted set S of points if for any two points p and q in S the distance between p and q in graph G is at most t.d_w(p, q) for a real number t > 1. Here, d_w(p,q) is the additive weighted distance between p and q. For some integer k \geq 1, a t-spanner G for the set S is a (k, t)-vertex fault-tolerant additive weighted spanner, denoted with (k, t)-VFTAWS, if for any set S' \subset S with cardinality at most k, the graph G \ S' is a t-spanner for the points in S \ S'. For any given real number \epsilon > 0, we obtain the following results: - When the points in S belong to Euclidean space R^d, an algorithm to compute a (k,(2 + \epsilon))-VFTAWS with O(kn) edges for the metric space (S, d_w). Here, for any two points p, q \in S, d(p, q) is the Euclidean distance between p and q in R^d. - When the points in S belong to a simple polygon P, for the metric space (S, d_w), one algorithm to compute a geodesic (k, (2 + \epsilon))-VFTAWS with O(\frac{k n}{\epsilon^{2}}\lg{n}) edges and another algorithm to compute a geodesic (k, (\sqrt{10} + \epsilon))-VFTAWS with O(kn(\lg{n})^2) edges. Here, for any two points p, q \in S, d(p, q) is the geodesic Euclidean distance along the shortest path between p and q in P. - When the points in $S$ lie on a terrain T, an algorithm to compute a geodesic (k, (2 + \epsilon))-VFTAWS with O(\frac{k n}{\epsilon^{2}}\lg{n}) edges.Comment: a few update

Non-Monochromatic and Conflict-Free Coloring on Tree Spaces and Planar Network Spaces

It is well known that any set of n intervals in $\mathbb{R}^1$ admits a non-monochromatic coloring with two colors and a conflict-free coloring with three colors. We investigate generalizations of this result to colorings of objects in more complex 1-dimensional spaces, namely so-called tree spaces and planar network spaces

Hes1 Is Expressed in the Second Heart Field and Is Required for Outflow Tract Development

Background: Rapid growth of the embryonic heart occurs by addition of progenitor cells of the second heart field to the poles of the elongating heart tube. Failure or perturbation of this process leads to congenital heart defects. In order to provide further insight into second heart field development we characterized the insertion site of a transgene expressed in the second heart field and outflow tract as the result of an integration site position effect. Results: Here we show that the integration site of the A17-Myf5-nlacZ-T55 transgene lies upstream of Hes1, encoding a basic helix-loop-helix containing transcriptional repressor required for the maintenance of diverse progenitor cell populations during embryonic development. Transgene expression in a subset of Hes1 expression sites, including the CNS, pharyngeal epithelia, pericardium, limb bud and lung endoderm suggests that Hes1 is the endogenous target of regulatory elements trapped by the transgene. Hes1 is expressed in pharyngeal endoderm and mesoderm including the second heart field. Analysis of Hes1 mutant hearts at embryonic day 15.5 reveals outflow tract alignment defects including ventricular septal defects and overriding aorta. At earlier developmental stages, Hes1 mutant embryos display defects in second heart field proliferation, a reduction in cardiac neural crest cells and failure to completely extend the outflow tract. Conclusions: Hes1 is expressed in cardiac progenitor cells in the early embryo and is required for development of the arteria

A well-separated pairs decomposition algorithm for k-d trees implemented on multi-core architectures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Variations of k-d trees represent a fundamental data structure used in Computational Geometry with numerous applications in science. For example particle track tting in the software of the LHC experiments, and in simulations of N-body systems in the study of dynamics of interacting galaxies, particle beam physics, and molecular dynamics in biochemistry. The many-body tree methods devised by Barnes and Hutt in the 1980s and the Fast Multipole Method introduced in 1987 by Greengard and Rokhlin use variants of k-d trees to reduce the computation time upper bounds to O(n log n) and even O(n) from O(n2). We present an algorithm that uses the principle of well-separated pairs decomposition to always produce compressed trees in O(n log n) work. We present and evaluate parallel implementations for the algorithm that can take advantage of multi-core architectures.The Science and Technology Facilities Council, UK

Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.Comment: 12 pages, 1 figur

Cinnamon: A Natural Feed Additive for Poultry Health and Production—A Review

The increased bacterial resistance to synthetic antibiotics and consumer awareness about the health and food safety concerns have triggered the ban on the use of antibiotic growth promotors (AGPs) in the poultry industry. This situation encouraged the poultry sector and industry to explore safe alternatives to AGPs and focus on developing more sustainable feed management strategies to improve the intestinal health and growth performance of poultry. Consequently, phytogenic feed additives (PFAs) have emerged as natural alternatives to AGPs and have great potential in the poultry industry. In recent years, cinnamon (one of the most widely used spices) has attracted attention from researchers as a natural product with numerous health benefits for poultry. The essential oils in cinnamon, in particular, are of interest because of their antioxidant, anti-microbial, anti-inflammatory, antifungal, and hypocholesterolaemic effects, in addition to their ability to stimulate digestive enzymes in the gut. This review mainly emphasizes the potential impact of cinnamon as a natural feed additive on overall gut health, nutrient digestibility, blood biochemical profile, gene expression, gut microbiota and immune response