A generalized Winternitz Theorem

We prove that, for every simple polygon P having k ≥ 1 reflex vertices, there exists a point q ε P such that every half-polygon that contains q contains nearly 1/2(k + 1) times the area of P. We also give a family of examples showing that this result is the best possible

On the power of the semi-separated pair decomposition

A Semi-Separated Pair Decomposition (SSPD), with parameter s > 1, of a set is a set {(A i ,B i )} of pairs of subsets of S such that for each i, there are balls and containing A i and B i respectively such that min ( radius ) , radius ), and for any two points p, q S there is a unique index i such that p A i and q B i or vice-versa. In this paper, we use the SSPD to obtain the following results: First, we consider the construction of geometric t-spanners in the context of imprecise points and we prove that any set of n imprecise points, modeled as pairwise disjoint balls, admits a t-spanner with edges which can be computed in time. If all balls have the same radius, the number of edges reduces to . Secondly, for a set of n points in the plane, we design a query data structure for half-plane closest-pair queries that can be built in time using space and answers a query in time, for any ε> 0. By reducing the preprocessing time to and using space, the query can be answered in time. Moreover, we improve the preprocessing time of an existing axis-parallel rectangle closest-pair query data structure from quadratic to near-linear. Finally, we revisit some previously studied problems, namely spanners for complete k-partite graphs and l

Computing the greedy spanner in near-quadratic time

It is well-known that the greedy algorithm produces high quality spanners and therefore is used in several applications. However, for points in d-dimensional Euclidean space, the greedy algorithm has cubic running time. In this paper we present an algorithm that computes the greedy spanner (spanner computed by the greedy algorithm) for a set of n points from a metric space with bounded doubling dimension in time using space. Since the lower bound for computing such spanners is Ω(n 2), the time complexity of our algorithm is optimal to within a logarithmic factor

Identification of Widespread Ultra-Edited Human RNAs

Adenosine-to-inosine modification of RNA molecules (A-to-I RNA editing) is an important mechanism that increases transciptome diversity. It occurs when a genomically encoded adenosine (A) is converted to an inosine (I) by ADAR proteins. Sequencing reactions read inosine as guanosine (G); therefore, current methods to detect A-to-I editing sites align RNA sequences to their corresponding DNA regions and identify A-to-G mismatches. However, such methods perform poorly on RNAs that underwent extensive editing (“ultra”-editing), as the large number of mismatches obscures the genomic origin of these RNAs. Therefore, only a few anecdotal ultra-edited RNAs have been discovered so far. Here we introduce and apply a novel computational method to identify ultra-edited RNAs. We detected 760 ESTs containing 15,646 editing sites (more than 20 sites per EST, on average), of which 13,668 are novel. Ultra-edited RNAs exhibit the known sequence motif of ADARs and tend to localize in sense strand Alu elements. Compared to sites of mild editing, ultra-editing occurs primarily in Alu-rich regions, where potential base pairing with neighboring, inverted Alus creates particularly long double-stranded RNA structures. Ultra-editing sites are underrepresented in old Alu subfamilies, tend to be non-conserved, and avoid exons, suggesting that ultra-editing is usually deleterious. A possible biological function of ultra-editing could be mediated by non-canonical splicing and cleavage of the RNA near the editing sites

Anagram-free chromatic number is not pathwidth-bounded

The anagram-free chromatic number is a new graph parameter introduced independently by Kamčev, Łuczak, and Sudakov [1] and Wilson and Wood [5]. In this note, we show that there are planar graphs of pathwidth 3 with arbitrarily large anagram-free chromatic number. More specifically, we describe 2n-vertex planar graphs of pathwidth 3 with anagram-free chromatic number Ω(log n). We also describe kn vertex graphs with pathwidth 2 k- 1 having anagram-free chromatic number in Ω(klog n)

Overexpression of SERCA1a in the \u3cem\u3emdx\u3c/em\u3e Diaphragm Reduces Susceptibility to Contraction-Induced Damage

Although the precise pathophysiological mechanism of muscle damage in dystrophin-deficient muscle remains disputed, calcium appears to be a critical mediator of the dystrophic process. Duchenne muscular dystrophy patients and mouse models of dystrophin deficiency exhibit extensive abnormalities of calcium homeostasis, which we hypothesized would be mitigated by increased expression of the sarcoplasmic reticulum calcium pump. Neonatal adeno-associated virus gene transfer of sarcoplasmic reticulum ATPase 1a to the mdx diaphragm decreased centrally located nuclei and resulted in reduced susceptibility to eccentric contraction-induced damage at 6 months of age. As the diaphragm is the mouse muscle most representative of human disease, these results provide impetus for further investigation of therapeutic strategies aimed at enhanced cytosolic calcium removal

Bounding the locality of distributed routing algorithms

We examine bounds on the locality of routing. A local routing algorithm makes a sequence of distributed forwarding decisions, each of which is made using only local information. Specifically, in addition to knowing the node for which a message is destined, an intermediate node might also know (1) its local neighbourhood (the subgraph corresponding to all network nodes within k hops of itself, for some fixed k), (2) the node from which the message originated, and (3) the incoming port (which of its neighbours last forwarded the message). Our objective is to determine, as k varies, which of these parameters are necessary and/or sufficient to permit local routing on a network modelled by a connected undirected graph. In particular, we establish tight bounds on k for the feasibility of deterministic k-local routing for various combinations of these parameters, as well as corresponding bounds on dilation (the worst-case ratio of actual route length to shortest path length)

On bounded degree plane strong geometric spanners

Given a set P of n points in the plane, we show how to compute in O(nlogn) time a spanning subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong plane t-spanner of P with t=(1+√2) 2 * δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, the maximum degree bound can be reduced slightly to 6 while remaining a strong plane constant spanner at the cost of an increase in the spanning ratio and no longer being a subgraph of the Delaunay triangulation

The Most Likely Object to be Seen Through a Window

We study data structures to answer window queries using stochastic input sequences. The first problem is the most likely maximal point in a query window: Let α1,αc be constants, with 0 < α1 < α2 < < αc < 1. Let P = P1 P2 Pc be a set of n points in d, for some fixed d. For i = 1, 2,c, each point in Pi is associated with a probability αi of existence. A point p = (x1,xd) in P is on the maximal layer of P if there is no other point q = (x1′,x d′) in P such that x1′ x 1,x2′ x 2, and xd′ x d. Consider a random subset of P obtained by including, for i = 1, 2,c, each point of Pi independently with probability αi. For a query interval [i,j], with i ≤ j, we report the point in Pi,j = (pi,pj) that has the highest probability to be on the maximal layer of Pi,j in O(1) time using O(nlog n) space. We solve a special problem as follows. A sequence P of n points in d is given (d ≥ 2), where each point P has a probability (0, 1] of existence associated with it. Given a query interval [i,j] and an integer t with i