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Although taxonomy is often used informally to evaluate the results of phylogenetic inference and the root of phylogenetic trees, algorithmic methods to do so are lacking.
In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a "subcoloring" problem to express the difference between a taxonomy and a phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy.
The algorithms in this paper, and the associated freely-available software, will help biologists better use and understand taxonomically labeled phylogenetic trees.
Since the beginnings of phylogenetics, researchers have used a combination of phylogenetic inference and taxonomic knowledge to understand evolutionary relationships. Taxonomic classifications are often used to diagnose problems with phylogenetic inferences, and conversely, phylogeny is used to bring taxonomies up to date with recent inferences and to find misclassified sequences. Similarly, biologists often evaluate a putative "root" of a phylogenetic tree by looking at the taxonomic classifications of the subtrees branching off that node.
Despite the long history of interaction between phylogeny and taxonomy, automated tools for the automated curation of taxonomies have only recently been developed. In 2007, Dalevi et. al. [1] released the GRUNT tool to refine existing taxonomic classifications and propose novel ones. This was followed just recently by McDonald et. al. [2], who developed the tax2tree tool to update taxonomies based on a measure of precision and recall for classifications. These tools aim to update taxonomies to be closer to phylogenetic inferences.
In this paper we approach the commonly encountered simpler problem of a researcher inferring a phylogenetic tree and wishing to understand the level of agreement of that tree with a taxonomy at various ranks and wishing to root the tree taxonomically. We state the agreement problem between a taxonomy and a phylogeny in terms of an "subcoloring" problem previously described in the computer science literature [3,4]. As described below, we make algorithmic improvements over previous work in the relevant parameter regime and present the first computer implementation to solve the subcoloring problem. Our choice of algorithms is guided by the parameter regime of relevance for modern molecular phylogenetics on marker genes: that of large bifurcating trees and a limited amount of discord with a taxonomy. For rooting, we show that the "obvious" definition has major defects when there is discordance between a phylogeny and a taxonomy at the highest multiply-occupied taxonomic rank. We then present a more robust alternative definition and algorithms that can quickly find a taxonomically-defined root.
We emphasize that our work is in describing discordance between a taxonomy and a phylogeny and performing taxonomic rooting rather than updating taxonomies, in contrast to the work described above. However, our approach to expressing discord between a taxonomy and a phylogeny can be used to suggest that certain sequences are misclassified; we will explore this direction in future work.
In this paper we will consider agreement with a taxonomy one taxonomic rank at a time, in order to separate out the different factors that can lead to discord between taxonomy and phylogeny. These factors include phylogenetic methodology problems, out of date taxonomic hierarchies, and mislabeling. Various such factors lead to discordance at distinct ranks. For example, we have observed rampant mislabeling at the species level in public databases, whereas higher-level assignments are typically more accurate. Phylogenetic signal saturation or model mis-specification problems can lead to an incorrect branching pattern near the root of the tree at the higher taxonomic levels, although the genus-level reconstructions can be correct.
An alternative to considering agreement one rank at a time would be to look for the largest set of taxa for which the induced taxonomy and phylogenetic tree agree on all levels. Agreement between taxonomy and phylogeny at all taxonomic ranks simultaneously is equivalent to requiring complete agreement of a phylogeny and a taxonomic tree. Finding a subset of leaves on which two trees agree is known as the Maximum Compatible Subtree (MCST) problem, known to be polynomial for trees of bounded degree and NP-hard otherwise [5]. Although such a solution is useful information, we have pursued a rank-by-rank approach here for the reasons described above.
We formalize the agreement of a taxonomy with a phylogeny on a rank-by-rank basis in terms of convex colorings [3,4]. Informally, a convex coloring is an assignment of the leaves of a tree to elements of a set called "colors" such that the induced subtrees for each color are disjoint. In this paper we will say that a phylogeny agrees with taxonomic classifications at taxonomic rank r if the taxonomic classifications at rank r induce a convex coloring of the tree. For example, in Figure Figure11 the tree is not convex at the species rank due to nonconvexity between species s1 and s2, although it is convex at the genus rank, as the g1 and g2 genera fall into distinct clades. In terms of the convex coloring definition, there is nontrivial overlap between the induced trees on s1 and s2.
We will express the level of agreement between a taxonomy and a phylogeny at a rank r in terms of the size of a maximal convex subcoloring. Given an arbitrary leaf coloring, a subcoloring is a coloring of some subset of the leaves S of the tree that agrees with the original coloring on the set S. The maximal convex subcoloring is the convex subcoloring of maximal cardinality. For a tree that is taxonomically labeled at the tips, the discord at rank r is defined to be the size of the maximal convex subcoloring when the leaves are colored according to the taxonomic classifications at rank r.
Our algorithmic contributions result in efficient algorithms for the convex subcoloring problem in the parameter regime of interest: a limited amount of discord for large trees. First, by developing an algorithm that only investigates removing colors when such a removal could make a difference, we show that the maximal convex subcoloring problem can be solved in a number of steps that scales in terms of a local measure of nonconvexity rather than the total number of nonconvex colors. Second, we implement a branch and bound algorithm that terminates exploration early; this algorithm makes orders of magnitude improvement in run times for difficult problems.
Before proceeding on to outline how the algorithm works, note that the original definition of convexity is not the only way to formalize the agreement with a taxonomy at a given rank: a stronger way of defining convexity is possible (Figure (Figure2).2). In this "strong" version, colors must sit in disjoint rooted subtrees rather than just in disjoint induced subtrees. The algorithmic solution for this stronger version will be a special case of the previous one as described below. It may be of more limited use for two reasons. First, it depends on the position of the root: a tree that is strongly convex with one rooting may not be so in another. Also, it is not uncommon for phylogenetic algorithms to return a tree like in Figure 2(ii) although Figure 2(i) may actually be the correct tree; thus an algorithm that threw out all leaves except those that are convex in the strong sense might be overly strict.
The tree in Figure Figure33 serves to explain why the problem is combinatorially complex and motivates a recursive solution. The idea of this solution is to recursively descend through subtrees, starting at the root. Say this recursion has descended to an internal node x, and there are nodes of the color c somewhere above x. If the set of leaf colors in the subtree T1 is {b, c} and if the set of leaf colors in the subtree T2 is {a, b, d}, then some removal of colors is needed due to nonconvexity between the b and c colors. Assuming the leaf colors above x are fixed, the choices are to uncolor the c nodes in T1 or the b nodes in either T1 or T2.
One can think of "allocating" the cut colors to the subtrees: the possible choices are to allocate c to T1 but choose one of T1 or T2 to have b, or to disallow c in T1 and allow b in both T1 and T2. Here and in general, the crux of devising an efficient recursion is to efficiently decide which colors get allocated to which subtrees. Convexity can be insured by explicitly choosing a color for each internal node, and making sure that the color allocations respect those internal node choices in terms of convexity.
In fact, selecting these color allocations is the only problem, as a complete set of color allocations is trivially equivalent to a choice of coloring. Indeed, given an optimal color allocation for each internal node, one can simply look at the allocations for the internal nodes just above the leaves to decide whether those leaves get uncolored or not. Conversely, given a leaf coloring, one can simply look at the color set of the descendants of that internal node to get the set of colors allocated to the subtrees.
In deciding the color allocations, we can restrict our serious attention to colors that are present on either side of an edge, such as b and c on either side of the edge directly above the root of T1 in Figure Figure3.3. We will say that these colors are cut by the edge. Colors that are not cut by an edge should not require any decision making when the recursive algorithm is visiting the node just above that edge. However, doing the accounting is not completely straightforward: of the cut colors, one might only allocate b to T2, but a and d can be used as well. Thus, allocations including some colors not cut by the current edge must be considered, motivating the definition of the colors in play (Definition 10). The colors in play for an internal node are those colors cut by edges directly below that node that are available for allocation to the trees below that internal node.
Note that the ingredients of the decision being made in Figure Figure33 are the color specified by the coloring just above x (in this case fixed to be c), and the colors available in the subtrees below x. Given a set of colors to allocate to the leaves below x, the algorithm needs to decide how to allocate the possible colors to T1 and T2. One way of doing that is to test every possible allocation using the results of the recursion for below subtrees and score them in terms of the size of the corresponding subcoloring. Doing this with an awareness of the cut colors leads to an algorithm expressed in terms of the maximum number of colors cut by a given edge.
However, building such a comprehensive optimality map is not necessary. By simply counting the number of leaves of each color below x, one can get upper bounds on the sizes of the corresponding subcolorings and only evaluate those that have the potential to be worth exploring. This observation is the basis of the branch and bound algorithm (Algorithm 1).
A rooted subtree is a subtree that can be obtained from a rooted tree T by removing an edge of T and taking the component that does not contain the original root of T. The proximal direction in a rooted tree is towards the root, while the distal direction is away from the root. Given a tree T , let N(T), E(T), and L(T) denote the nodes, edges, and leaves of T. Given a set U, let 2U denote the set of subsets of U. If the input tree to the algorithm is not rooted, root it arbitrarily. Following the terminology of [3,4], a color set will be an arbitrary finite set, always denoted in this paper by the letter C.
Definition 1. Let T be a rooted tree, and let F L (T). A leaf coloring is a map χ: F → C.
A color c is cut by an edge e if there is at least one leaf of color c on either side of e. A multicoloring is defined to be a map from the edges of the tree to subsets of the colors.
Definition 2. Given a coloring χ on a rooted tree T, the induced multicoloring for χ is the map such that is the (possibly empty) set of colors cut by that edge.
Definition 3. Define the badness β of a coloring χ to be . We say that a coloring is convex if it has badness equal to zero or one.
Definition 4. The total number of bad colors of a coloring χ is where is the set of edges where .
Definition 5. A subcoloring of a leaf coloring χ: F → C is a coloring χ': G → C with G F such that χ' agrees with χ on the domain of χ'.
Subcolorings are partially ordered by inclusion of domains; the size of a subcoloring is defined to be the size of its domain.
Problem 1 (Moran and Snir [3,4]). Given a leaf coloring χ on a tree T, find a largest convex subcoloring.
The foundational work in this area was done by Moran and Snir [3,4]. Their work is phrased in terms of "convex recoloring," i.e. finding the minimal number of changes in a coloring in order to obtain one that is convex.
It suffices to consider subcolorings for the case of leaf colorings. Indeed, any recoloring can be turned into a subcoloring by removing the color of all of the leaves that get recolored. Conversely, any convex subcoloring can be turned into a convex recoloring in linear time [6]. For internal nodes, the color to be used for a given internal node is given by the definition of convex coloring. For leaf nodes, simply take the color of the closest colored node. In this equivalence, the number of leaves whose color is removed is equal to the number of leaves who get recolored; thus a minimal recoloring is equivalent to a maximal subcoloring. Because of this equivalence, we only consider subcolorings in this paper.
In [4], Moran and Snir investigate both the general case of leaf colorings as well as the case of colorings including internal nodes. They also consider non-uniform recoloring cost functions, where a "cost" is associated with recoloring individual nodes and the goal is to find a convex recoloring minimizing total cost. In all settings, they demonstrate that the relevant recoloring problem is NP-hard. They also demonstrate fixed parameter tractablity (FPT) of the problems as described in the next paragraph. In [3] they present, among other results, a 3-approximation for tree recoloring.
The FPT bound for leaf coloring an n taxon tree from [4], O(n4 τ Bell(τ)), comes from an elegant argument using the Hungarian algorithm for maximum weight perfect matching on a bipartite graph. In fact, an inspection of their proof reveals that their algorithm is O(n d3 τ Bell(τ)), where d is the maximum degree of the tree. Bell(k) denotes the kth Bell number, which is the number of unordered partitions of k items; these numbers are known to satisfy the bounds [7]. Their recursion at a given internal node iterates over every unordered partition of the nonconvex colors, constructing a bipartite graph with edge weightings determined by the sizes of subcolorings of subtrees using those color sets for the set of excluded colors. Applying the Hungarian algorithm to each such graph results in optimal solutions for every possible set of colors to exclude from the subtree at that internal node. Because every unordered partition of the non-convex colors is considered, the algorithm is exponential in τ. For the case of general (i.e. not just leaf) colorings, Moran and Snir show that a dynamic program gives an O (n τ dτ+2) algorithm. This of course also gives the same bound for leaf colorings.
The work of Moran and Snir was followed up by many authors. For leaf-colored trees, Bachoore and Bodlaender [8] propose a collection of reductions to simplify the problem under investigation. These reductions encode some of the logic of the algorithm presented here, such as that trees that have disjoint color sets can be solved independently. They also use the fact that nonconvexity can be expressed in terms of the crossings of paths connecting leaves of the same color to show that the recoloring problem can be solved in O(n4OPT) time, where OPT is the optimal number of uncolored leaves. Note that this sort of bound is different than those described above, as OPT can get large even when the total number of bad colors is small. The work for the general case culminated in the work of Ponta, Hüffner, and Niedermeier [9], who use the childwise iterative approach to dynamic programing to construct an algorithm of complexity O(n τ 3τ).
For trees built from real data, taxonomic identifiers are not randomly spread across the tree in a uniform fashion. For example, species-level mislabeling will lead to trees that are mostly convex with a couple of outliers, while a horizontal gene transfer will effectively "transplant" one clade into another. In both of these situations there is a non-uniform distribution of taxonomic identifiers across the tree, and nonconvexity in these cases may be local. Indeed, in Figure Figure44 we show the relationship between the badness β and the total number of bad colors τ for our example trees, showing that the badness β is significantly smaller than the total badness on a collection of phylogenetic trees for non-marker genes. This motivates the search for a fixed parameter tractable algorithm that is exponential in β rather than τ.
Furthermore, phylogenetics is typically concerned with a setting of trees with small degree. For example, many commonly used phylogenetic inference packages such as RAxML [10] and FastTree [11] only return bifurcating trees; these sorts of programs are the intended source of trees for our algorithm. Even when multifurcations are allowed, the setting of interest is that of degree much smaller than β or τ, which has ramifications for algorithm choice as described below.
In this section we present our algorithm, which makes two improvements over previous work for the parameter regime of interest. First, it restricts attention to cut colors, resulting in an algorithm that is exponential in β rather than τ. Still, such a complete recursion evaluates many sub-solutions that do not end up being used. Because the problem is NP-hard, we cannot avoid some such evaluation, but we might hope to do better than evaluating everything.
This motivates the second aspect, a branch and bound strategy that can make orders of magnitude improvements in the run time of the algorithm. In order to make the branch and bound algorithm possible, the algorithm enumerates all legal color allocations first, and ranks them according to the upper bound function. By bounding the size of a solution for a given color allocation, we can avoid fully evaluating the sub-solution for that color allocation. A simple way of bounding the size of a solution for a color allocation is the maximal size of the solution when convexity is ignored.
Given a rooted subtree T' of T, the root edge of T' in T is the edge connecting the root of T' to the rest of T .
Definition 6. Given a rooted subtree T' of T, define κ(T') to be the colors of χ cut by the root edge T' as it sits inside T.
Assume that T has been embedded in the plane, and that every internal node has been uniquely labeled. For every such label i let t(i) be the ordered tuple of labels of the nodes directly descendant from i in the tree, let T(i) be the subtree below i, and use κ(i) as shorthand for κ(T(i)). Vector subscript notation will be used to index both t(i) and the color set κ-tuples defined next; i.e. t(i)j is the jth entry of t(i).
Definition 7. A color set k-tuple is an ordered k-tuple of subsets of C. They will be denoted with π.
These color set k-tuples will represent the allocation of colors to subtrees. We will ensure convexity of these color allocations using the following two definitions.
Definition 8. Given a color set k-tuple π,
Definition 9. An almost partition of Y C is an ordered 2-tuple (b, π) where b C and π is a color set k-tuple such that A(π) = Y and B(π) {b}.
These will be the color allocations at a given internal node x with color b; this definition guarantees convexity locally, such that the b color is a legal color for the internal node. As described in the Introduction, we would like to primarily restrict our attention to cut colors, but this requires some attention because not all of the colors that need to be allocated at a given internal node are necessarily cut by the edge above that node. This motivates the following definition, which describes how all of the colors that are cut on the edges around a given internal node i are available for allocation at i except for those colors that are in κ(i) but not in X.
Definition 10. Given i an internal node index and X κ(i) define
G(i, X) will be called the colors in play for (i, X).
Definition 11. Assume we are given an internal node i, X κ(i), and c C. A legal color allocation for (i, c, X) is an almost partition (b, π) of G(i, X) such that
1. πj κ(t(i)j)
2. if c X then b = c.
Denote the set of such legal color allocations with Δ(i, c, X), and let Δ(i) = c, X Δ(i, c, X).
These color allocations are exactly the set of choices that are allowed when developing a subsolution for a cut set X such that the color c is just above X. The first condition ensures that the color allocation for each subtree sits inside the correct set of cut colors. The second condition says that an internal node must take on any color found above and below it.
Definition 12. An implicit subcoloring for T' is a choice of (b(i), π(i)) Δ(i) for every i N(T') satisfying the following compatibility property for every k t(i):
That is, the color allocation for every node descending from i is a legal color allocation given the choices of b(i) and π(i) made at i.
As described in the Introduction, an implicit subcoloring defines an actual subcoloring via the implicit subcoloring just proximal to leaf nodes. Indeed, say t(i)j is a leaf, and that (b(i), π(i)) is the color allocation for internal node i. Then π(i)j is empty or a single element by definition, and the color for leaf t(i)j is used in the subcoloring if π(i)j ≠ . Every convex subcoloring can be written in this form.
Proposition 1. Implicit subcolorings define convex colorings.
Proof. Assume an implicit subcoloring {(b(j), π(j))}iN(T). Let χ be the coloring defined by an implicit subcoloring. If χ is not convex, then there is an edge e such that . Say . Without loss of generality, the colors will be positioned as in one of the two cases depicted in Figure Figure55 (note that the subtrees marked a, b can contain other colors in addition to these). In case (i), |B(π(i))| ≥ 2, contradicting the definition of an almost partition. In case (ii), b(i1) is a by the definition of almost partition because a B(π(i1)). Then b(i) = a for every i between i1 and i2, inclusive, by part 2 of Definition 11 and Definition 12. However, b B(π(i2)), contradicting the definition of almost partition. □
With this in mind, we can now speak of the size of an implicit subcoloring as the size of its associated convex subcoloring. The goal, then, is to find the largest implicit subcoloring.
Theorem 1. There is an O(n d β2 2d+β (d-1)dβ/2) complexity algorithm to solve the subcoloring problem for leaf labeled trees.
Proof. For every internal node i, define the question domain Q(i) to be C × 2κ(i). An answer map at internal node i (resp. answer size map) is a map Y → Δ(i) (resp. Y → ) for some Y Q(i).
We will fill out an answer map i and an answer size map ωi as needed at every internal node i recursively as follows. For a given i, say we are given a question (c, X) Q(i). If i is a leaf, then i(c, X) = X and ωi(c, X) = |X|. Otherwise, say there are descendants of i. For each (b, π) Δ(i, c, X), find the answers (b, πj), and their associated by recursion. Let
Let ωi(c, X) be the maximum value of , and let i(c, X) be the (b, π) obtaining this maximum, concluding the recursive step. The result of this recursion after starting at the root with every color for c will be a collection of answer maps for every i.
These maps define an implicit subcoloring. This can be seen by descending through the tree recursively, using the i to get almost partitions from questions and passing the resulting questions onto subtrees. Specifically, for question (c, X) at internal node i, let (b(i), π(i)): = i(c, X) then recur by passing question (b(i)j, π(i)j) to for every descendant j. Start at the root (call its index ρ), pick the color cρ maximizing ωρ (cρ, ), and begin the recursion with (cρ, ).
This subcoloring is maximal by construction. The assertion is clear for 1-leaf trees. Now say that the algorithm finds optimal solutions for all allocations of colors to trees of less than n leaves. Then, given a tree on n leaves and an allocation of colors to the root, the algorithm tries every legal allocation of those colors to each of the subtrees and taxes the maximum thereof. Because every legal color allocation is tried, and the algorithm finds maximal subcolorings for each of the subtrees, the subcoloring for the entire tree must be maximal.
The computation required for a single internal node is as follows. The number of colors in play is bounded above by dβ /2, as each color in play must be cut in at least two edges. Thus, for a given question (c, X) and color b for the internal node, choosing the allocation can take (d - 1)dβ/2 steps for the colors other than b, while deciding where b is present can take 2d trials. There are at most β2β choices of question and dβ/2 choices of internal node color for a given internal node.
There are O(n) internal nodes, giving the bound. □
An upper bound for can be used to construct a branch and bound recursion as follows.
Algorithm 1 (Branch and bound recursion to find optimal implicit subcoloring). Assume a function for all (b, π) Δ(i). Proceed as in the proof of Theorem 1, with the following modification. For a given internal node i with c C and X κ(i), find i(c, X) as follows:
1. sort the elements (b, π) of Δ(i, c, X) in decreasing size with respect to vi.
2. proceed down this ordered list as follows, starting with q = 0:
(a) compute
(b) call the next item in the ordered list (b', π'). If q ≥ vi (b', π') then stop, otherwise recur to (a)
3. let i(c, X) be the (b, π) corresponding to q.
The correctness of this algorithm follows directly from Theorem 1, as the only solutions that are thrown away are strictly sub-optimal.
A simple upper bound is the number of leaves that could be used given the restrictions in π but ignoring convexity. That is, let be the number of leaves of T(i) with colors in X. Then define . This upper bound gives significant improvement in time used over the algorithm in Theorem 1 (Figure (Figure66).
The original algorithm described in Theorem 1 and the branch and bound algorithm in Algorithm 1 have been implemented in the rppr binary of the pplacer suite of programs (http://matsen.fhcrc.org/pplacer). The code is in written in OCaml [12], an appropriate choice as it has O(log n) immutable set operations in the standard library. The input can either be a "reference package" containing both taxonomic and phylogenetic information, or simply a phylogenetic tree along with a comma separated value file specifying the color assignments. Our implementation has been validated using an independent "brute-force" implementation in Python; the two codes return identical results on a testing corpus consisting of all colorings on all trees of three to eight leaves with up to six colors. These trees and results can be downloaded at http://matsen.fhcrc.org/pplacer/data/convexify-validation.tar.gz. The algorithm is invoked via a single command line call, which outputs a list of uncolored taxa for every nonconvex taxonomic rank as well as displaying them on a taxonomically labeled tree by highlighting them in red.
One time saving difference between our implementation and the algorithm described in the previous section is that the computer implementation has a notion of "no color." This is motivated by the fact that in the case that c X and B(π) is empty for an internal node i, there are a number of colorings of i that will provide a convex subtree. By collapsing all of the possible colors into a single "no color" in this case, we gain some savings in time and memory.
The "no color" version of the algorithm can also be used to solve the case of strong convexity described in the Introduction. Specifically, restricting every internal node to have no color except for the internal nodes of subtrees that consist of entirely one color leads to an algorithm for strong convexity. This strong convexity version is available via a command line flag.
The data set used as a test set was a collection of 100 trees built from automatically recruiting sequences via a BLAST search via HMMs built from COG [13] alignments. Taxonomic identifiers for the various ranks were found using the taxtastic software, available at http://github.com/fhcrc/taxtastic. Each trial was run three times and the results averaged; if any of the runs did not finish in 8 hours, exceeded 16 G RAM usage, or encountered a stack overflow, the trial was marked as "DNF." Every trial that completed according to these criteria using the full recursion also completed using the branch-and-bound. Colored trees with badness strictly greater than 14 were excluded from Figure Figure6,6, as were trials that did not complete using either algorithm. The full recursion and the branch and bound implementations only differ by a switch that controls if the algorithm terminates early. Trials run on Intel Xeon (X5650) cluster nodes with 48 G of RAM. This test data set is available upon request.
Researchers generally like to root phylogenetic trees in a way that the progression along edges from the root to the leaves is one of evolutionary descent. There are a number of ways of achieving this, from using outgroups to using non-reversible models of mutation [14]. However, there has been surprisingly little work on one of the most commonly used informal means of rerooting, which is by using taxonomic classifications. By that we mean looking for a rooting such that the leaf sets of the descendant subtrees each have a single taxonomic classification at the highest taxonomic rank that contains multiple taxonomic identifiers. Here we formalize this process and describe algorithms for finding the taxonomic root or roots.
The work in this section will be based on the following formalization of ranks in taxonomies.
Definition 13. A rank function for a set U is a map rk: 2U→ such that
for all A and B in 2U
It follows immediately that rk(A) ≤ rk(B) when A B 2U. By an abuse of notation, we also let rk(T) signify rk(L(T)) for a (sub)tree T with leaf set in the domain of the rank function. From a taxonomic perspective, rk(U) will represent the rank of the most specific taxonomic classification containing all of the taxonomic labels in U. For this section, a taxonomically labeled phylogenetic tree is one for which we have a rank function on the leaves.
Given x a node of T, let Ψ(x; T) represent the set of trees obtained by rooting T at x and deleting x and its incident edges from T .
Definition 14. Define the subrank subrk(x; T) to be maxSΨ(x;T) rk(S), the maximum rank of the subtrees of T when rooted at x. We will say x is a delicate taxonomic root of T if
This definition formalizes an intuitive definition of taxonomic root. For example, imagine that we have a tree with the three domains of cellular life in three distinct subtrees: Bacteria, Archaea, and Eukaryota; call the internal node that sits between these subtrees x. The subrank of x is domain. Any other internal node will contain some of each of the domains, and thus will have rank strictly higher than domain. In this case, x is the unique taxonomic root.
However, if the tree is not convex at the subrank of the delicate taxonomic root then every internal node will be a delicate taxonomic root; thus the "delicate" terminology. Indeed, assume an internal node y and A, B Ψ(y; T) such that a1, a2 L(A), b1, b2 L(B), and subrk(a1, a2) = subrk(b1, b2) = subrk(T). Then for any rooting, there must exist a subtree containing either {a1, a2} or {b1, b2}, and the subrank must be equal to that of T.
We now develop a more robust definition of taxonomic root, which will require several definitions. The edges of the tree will be thought of as unordered pairs {x, y} of nodes.
Definition 15. An arrow on an edge {x, y} is an ordered pair of nodes (x, y). The first node of the pair is called the origin of the arrow, and the second is called the direction.
Definition 16. An arrow tree is an ordered pair consisting of a tree T and a set of arrows on the edges of T. A complete arrow tree is an arrow tree such that for every node x of the tree there is some arrow in with origin x.
Note that (x, y) and (y, x) may both be part of an arrow set for a tree with an edge {x, y}. We will use "pointing towards" and "pointing away" in their usual senses as they relate to arrows in the real world.
Definition 17. The induced arrow tree for a tree T and a rank function rk is a complete arrow tree defined as follows. For a given internal node x N(T), say {S1, · · ·, Sn} = Ψ(x; T) and let ri = rk(Si) for 1 ≤ i ≤ n. Assume without loss of generality that r1 ≤ r2 ≤ · · · ≤ rn. There is some minimal 1 ≤ j ≤ n such that rj = · · · = rn. Let Ax be
Then is the union of the for all nodes x along with the set of (x, y) where x is a leaf and y is adjacent to x.
Intuitively, induced arrows point towards potential taxonomic roots.
Lemma 1. Say is an induced arrow tree for a rank function rk, and that {x, y} and {y, z} are adjacent edges of T. If then .
Proof. When x is a leaf, is automatic, thus assume it is not. Using terminology from Figure Figure7,7, because ,
This implies that
and thus that . □
Induction on the edges of a path shows the following:
Corollary 1. Say is an induced arrow tree, and that {u, v} and {x, y} are edges of T such that the path from u to y contains both v and x. If then . □
Informally, this corollary says that any time there is an arrow on edge e2 pointing away from edge e1, that there must be an arrow on e1 pointing towards e2.
Definition 18. A multi arrow node (MAN) for a taxonomically labeled tree is a node x such that there are two or more arrows in the induced arrow tree with x as an origin.
Proposition 2. Say is an induced arrow tree. If node x is a MAN then for any node y there must be an arrow in with origin y pointing towards x.
Proof. Since x is a MAN, there must be at least one arrow in with origin x pointing away from y. This implies the proposition by Corollary 1. □
Now imagine that x and z are two MANs, and y is on the path between x and z. By the above proposition, there must be arrows with origin y pointing towards both x and z, showing that y will be a MAN. Thus:
Proposition 3. MANs form a convex set in the tree. □
Definition 19. An edge {x, y} is a bi-arrow edge of an arrow set A if (x, y) and (y, x) are in A.
Proposition 4. If the set of MANs is empty, then there is exactly one bi-arrow edge.
Proof. First note that there cannot be two or more bi-arrow edges when the set of MANs is empty; in that case by Corollary 1 there would have to be a MAN between them. Now assume there are no bi-arrow edges. Since the set of MANs is empty, then for every leaf of the tree the sequence of nodes determined by following arrows is well defined. Note that the arrow on every leaf is pointing into the interior of the tree, and thus the sequence of nodes starting from an arbitrary leaf cannot hit another leaf. Therefore the sequence of nodes must backtrack somewhere, contradicting that there are no bi-arrow edges. □
Definition 20. Assume a taxonomically labeled tree T. If there is at least one MAN then define the set of taxonomic roots to be the set of MANs. Otherwise define it to be the set of nodes of the bi-arrow edge.
Let diam(T) be the node-diameter of T, i.e. the number of steps from edge to edge required to traverse the tree. Because every arrow with a non-root origin points in the direction of the taxonomic roots:
Proposition 5. A taxonomic root for a tree T with n leaves can be found in at most diam(T) steps. □
Taxonomic rerooting has been implemented in the rppr binary of the pplacer suite of programs (http://matsen.fhcrc.org/pplacer). However, rather than finding all possible taxonomic roots as described above, the program reports one of the roots after applying the maximal subcoloring algorithm as described in the previous section to the highest multiply occupied taxonomic rank. Such a root is the closest approximation to the one "best" taxonomic root in the presence of nonconvexity.
We have formalized the question of describing the discordance of a phylogenetic tree with its taxonomic classifications in terms of a convex subcoloring problem previously described in the literature. This coloring problem has some elegant solutions for the general case, but the parameter regime of interest here consists of trees of small degree and local nonconvexity. These considerations motivate a solution that solves a given recursion for as few "questions" as possible. The first component of this is to restrict attention to cut colors, resulting in a smaller base for the exponential complexity (Figure (Figure4).4). The second is a branch and bound algorithm that gives a significant improvement in runtime compared to the algorithm in Theorem 1 (Figure (Figure6).6). To enable this the i are only built up "upon demand," that is, when a given question is asked. The implementation described here is the first of which we are aware, and certainly the first that conveniently integrates with taxonomic annotation.
We also develop the first formalism for taxonomic rooting of phylogenetic trees, show that the obvious definition is useless in the presence of nonconvexity, and develop a more robust definition. This version can be found in time linear in the diameter in the tree.
We are currently developing a computational pipeline to find misclassified sequences in public databases using these algorithms. We are also using these algorithms together to develop a collection of automatically curated "reference packages" that bring together taxonomic and phylogenetic for the purposes of environmental short read classification, visualization, and comparison.
The authors declare that they have no competing interests.
FAM conceived of the project, designed the algorithms, and wrote the paper. AG designed the algorithms and implemented the algorithms and validations. Both authors read and approved the final manuscript.
This work was motivated by joint work with David Fredricks, Noah Hoffman, Martin Morgan, and Sujatha Srinivasan at the Fred Hutchinson Cancer Research Center. We are especially grateful to Noah Hoffman for providing feedback on early results of the algorithm, to Shlomo Moran and Sagi Snir for help understanding their algorithm, and to Robin Kodner for allowing the COG trees to be used as test data for our algorithm. Both authors were supported in part by NIH grant HG005966-01.
PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers.


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The first issue of LeftLiberty turned into a bit of an olio of material that has appeared here and there before, together with notes on the Proudhon text. Longtime readers of my blogs will find a lot that is familiar, but in the new context of a more systematic exploration of mutualism. My hope is that each issue will clarify a bit more what was at stake, historically, in the movement, and what it has to offer contemporary anarchists. There has been no way to avoid including some potentially obscure and difficult texts, and some material which draws on traditions that are almost entirely forgotten now. I hope readers will approach those texts with a healthy curiosity, and withhold judgment for a little while, as the contexts become gradually clearer. Anyway, here they are:
- LeftLiberty 1, "The Unfinished Business of Liberty" (pamphlet)
- New Proudhon Library 20.1, "The Philosophy of Progress" (pamphlet)
UPDATE: Several readers asked for non-pamphlet versions of these releases. Now, as I told Neverfox, I'm fairly certain that these are the kinds of things that require a little tree-killing, and probably a coffee- or whiskey-stain or three, before you're likely to really take them in, but for those who want or need to skip those more satisfying steps, here are some conventionally formatted pdfs:


text:
The Perfect 3 Winning Recipes
In search of the perfect recipe? Look no further. We've got the winning recipes from The Perfect 3 recipe contest for burgers, brownies, tacos, cakes and more.
Monkey Tail Banana Cake
Rich banana cake is studded with chocolate chips, layered with chocolate-hazelnut spread and topped with fluffy whipped-cream frosting in Sara Hodgson's winning cake recipe.
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Jalapenos add heat to Lauren Beth Walker's winning corn cake recipe. Serve in pancake form for breakfast, or cook the batter in a skillet for a dinnertime side.
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Follow Nate Bedford's lead and serve homemade BBQ sauce with your burgers. It's just one of many flavorful elements in his winning burger recipe.
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"I Want to Marry You" Cookies
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Beef Brisket Bonanza Sandwich
The secret to Candy Gold's sandwich is the addition of gingersnaps while cooking the brisket. The cookies help thicken the sauce and add a touch of sweetness to the final dish.
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Coconut lovers will go crazy for Lorie Roach's winning pie recipe: It features coconut flavor four ways.
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Stuffed Grape Leaves
Christa Haggai's recipe for stuffed grape leaves is perfect for a small-plates party.
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Pork Tenderloin Salad With Strawberries and Goat Cheese
Laura Lufkin's vinaigrette recipe does double duty in her winning salad: It marinates the pork and serves as the salad dressing.
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Grilled Steak Tacos With Chipotle Cream and Chimichurri
Pair a cold margarita with Dawn Richards' winning recipe for grilled steak tacos.
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Panhandle Chili
The secret ingredient in Vanessa Chavez's recipe for Panhandle Chili is beer.
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Craving More?
Browse through our entire collection of recipes from the show The Perfect 3. From Kelsey's roast chicken to Roger's lamb burger, we've got your new favorite.


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MedWatch: The FDA Safety Information and Adverse Event Reporting Program
Your FDA gateway for clinically important safety information and reporting serious problems with human medical products.
What's New
HeartMate II LVAS Pocket System Controller by Abbott-Thoratec: Class I Recall - Due to Risk of Patient Injury and/or Death during Backup Controller Exchange A slow or improper driveline changeover places certain patients at risk of serious injury or death. Posted 05/23/2017 Tri-Ton by Dynamic Technical Formulations, LLC: Recall - Contains Andarine and Ostarine Drug Ingredients Use or consumption of products containing SARMs and anabolic steroid-like substances may cause acute liver injury, which is known to be a possible harmful effect of using steroid containing products. Posted 05/22/2017 V60 Non-invasive Ventilator by Respironics: Class I Recall - Unexpected Device Shut Down Unexpected stop in ventilation therapy may cause serious adverse health consequences, including death. Posted 05/22/2017 Gadolinium-based Contrast Agents for Magnetic Resonance Imaging (MRI): Drug Safety Communication - No Harmful Effects Identified With Brain Retention Health care professionals should continue to limit GBCA use to circumstances in which additional information provided by the contrast agent is necessary, and assess the necessity of repetitive MRIs with GBCAs. Posted 05/22/2017 LeadCare Testing Systems (with Blood Obtained from a Vein) by Magellan Diagnostics: FDA Safety Communication - Risk of Inaccurate Results Falsely lower test results may lead to improper patient management and treatment for lead exposure or poisoning. Posted 05/17/2017 Wingman35 Crossing Catheters by ReFlow Medical: Recall - Tip Splitting or Separation UPDATED 05/17/2017 Recall classified as class I. Tip splitting has the potential to lead to loss of device function. Tip separation may require medical intervention to retrieve a separated segment or may occlude blood flow to end organs. Posted 05/03/2017
FDA Approved Safety Information
DailyMed (National Library of Medicine)
Current Drug Prescribing Information. (NOTE: Drugs marked "unapproved" on this site have not been reviewed by FDA for safety and efficacy, and their labeling has not been approved.)
Medication Guides
Paper handouts that come with many prescription medicines. Medication Guides address issues specific to particular drugs and drug classes. They contain FDA-approved information that can help patients avoid serious adverse events.
Potential Signals of Serious Risks/New Safety Information Identified from the FDA Adverse Event Reporting System (FAERS) Postmarket Drug and Biologic Safety Evaluations
Evaluations performed 18 months after drug approval, or after its use by 10,000 individuals.


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I Want A Reputation.
I'm in the process of creating something...brilliant.
I'm creating my background.
My story, my ambitions, whatever they may be.
I'm creating my future and my past,
It'll be...interesting....you'll see.
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Building it upwards... from the ground.
So that I'll be having a fine time, on cloud nine,
And I don't ever plan on coming down.
I'm creating myself.
And acquiring skills...whatever they may be,
Leadership, discipline, heart, and ambition,
Everything...I'm creating me.
I'm creating my reputation.
Building my experience, for when duty calls,
Something for me to reflect on...and be proud of!
And when i enter a conversing room, silence falls.
Of course, it's built over time,
Time...the older me, will allow.
But at the moment I'm young, and impatient.
I want a reputation, and i want it now!
Ryan Smith – 16/06/11


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3908 Clarnin Street, Kalamazoo MI, 49004
Sold Price:
3 beds , 2 Full baths
1,428 sqft
Status: Closed
Last Updated: 5/22/2017 4:27 PM
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Welcome to 3908 Clarnin, a 3 bedroom brick Cape Cod home nestled on an immaculate property near the Parchment area. Terraced yard with flower gardens, fenced back, and a huge backyard deck. The 2-car garage includes another access door leading into the yard, perfect for storing tools and toys alike. Inside you'll find the spacious living room with its brick hearth fireplace, formal dining room, and a spacious kitchen with beautifully crafted cabinetry and lots of work space. There are two bedrooms and one bath on the main floor. The second bath and third bedroom are upstairs along with a great loft space. Central air conditioning, new water heater, new garage door, and lots of extras you need to see for yourself - schedule a tour today!
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Sold Date:06/19/2015
Kalamazoo City
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1,428 (approx)
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Kevin O'Leary will not take the stage at Tuesday night's Conservative leadership debate, choosing instead to host his own event. If this all sounds familiar, it might be because Donald Trump did pretty much the same thing one year ago.
The businessman and aspiring politician — known best for his reality TV career — said on Monday he would not face off against his Tory leadership opponents in Edmonton because he doesn't like the format of the debate. O'Leary is hosting a "fireside chat" in Edmonton instead. It takes place at the Westin Edmonton in the Turner Valley Room starting at 6:00.
READ MORE: Kevin O'Leary: The millionaire reality show host who wants to be Canada's prime minister
In January 2016 Trump skipped a Republican debate and held an event the same night dubbed 'Special Event to Benefit Veterans Organizations.'
Trump said he wanted to take part in the GOP debate, but that he had to stick to his guns since he was boycotting the debate's host, Fox News, due to poor treatment.
"I didn't want to be here, I have to be honest. I wanted to be about five minutes away," Trump said the night of the debate.
"You know what, I don't know, is it for me a good thing, a bad thing, will I get more votes, less votes? Nobody knows, who the hell knows."
Perhaps not surprisingly, the Trump-less GOP debate pulled in poor ratings — and we all know how things turned out for Trump.
O'Leary, who has been accused of trying to be Canada's version of Trump, has said he recognizes where the comparisons come from.
"I've heard that analogy many times," O'Leary told Global News in December 2016.
"We enjoy the benefits of celebrity and to a certain extent that seems to matter in politics these days."
READ MORE: 'Canada's Donald Trump': Kellie Leitch blasts 'elites' and 'insiders' during Fox interview
But leadership isn't about celebrity, O'Leary said — and policy sets him far apart from Trump.
"I'm half-Lebanese, half-Irish, if there was a wall in Canada I wouldn't even be here. So I don't believe in many of the metrics he's put in place in defining his leadership."
Though it seems he'd rather be compared to Trump than to Prime Minister Justin Trudeau.
"Trump vs. Trudeau is Bambi vs. Godzilla," said O'Leary.
This isn't the first time O'Leary has been accused of skipping a debate.
O'Leary, who could face a $10,000 dollar fine for pulling out of Tuesday's bilingual debate, was previously accused of waiting until after a French-language debate before officially announcing his leadership bid.
During his first debate on Feb 4, O'Leary was the clear target of his opponents. Kellie Leitch — who has been accused of working Trump-style politics into her own campaign — even referred to him as a "con-conservative."
Global News reached out to O'Leary for comment regarding his fireside chat, but did not hear back by time of publication.
The next leader of the federal Conservatives party will be chosen on May 27.
© 2017 Global News, a division of Corus Entertainment Inc.


text:
Distances given are in a straight line from the centre of Ossett but travel routes may be longer.
Batley Hall Nursing & Residential Home
3.8 Miles
Old Hall Road, Batley WF17 0AX
Batley Hall Nursing & Residential Home is located in Batley and has easy access to the M62 (junction 27). Local shops, hairdressers, library, surgery, pharmacy and public house are all within walking distance of the home. The property was originally… more
Group / Provider:
Maria Mallaband Care Group Ltd
Care provided for Muscular Dystrophy
1.7 Miles
Rectory Park, Church Lane, Thornhill, Dewsbury WF12 0JZ
Field Court is situated in Dewsbury, where an experienced team of carers offer an ideal environment for residential short or long stay, respite care and specialising in palliative care. The home sits in mature grounds with impressive, scenic surroundings… more
Group / Provider:
Roche Healthcare Ltd
Care provided for Muscular Dystrophy
Cluntergate, Horbury, Wakefield WF4 5DB
1.9 Miles


text:
Recent Appearances
Book Retailers Panel Discussion
Mr. Kirshbaum moderated a panel discussion on the role of retailers in the world of books and publishing. Ms. Blake, Mr.…
Book Sales 2000
Mr. Mutter discussed book industry trends and how book sales were in the 2000 holiday season. Ms. Meade and Mr. Ollila…


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Re: Drinking, Driving, & Conniving
After some scotch, I'm going to take my red rover to the swingers convention.
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Jewish antiquities : or, a course of lectures on the three first books of Godwin's Moses and Aaron, to which is annexed a Dissertation on the Hebrew language / by David Jennings. London [u.a.] : Baynes, 1825
- Endpaper
- Title page
- Stamp
- The Preface by the Editor.
- Contents.
- Jewish Antiquities. Book I. Concerning Persons.
- Jewish Antiquities. Book II. Concerning Places.
- Jewish Antiquities. Book III. Concerning Times.
- Appendix, Concerning the Language of the Jews.
- Index of Texts Illustrated or Explained.
- Index of Hebrew Words and Phrases Explained.
- Index of Greek Words.
- Index.


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May act as a protease inhibitor to modulate the host immune response against tumor cells.. Additionally we are shipping Squamous Cell Carcinoma Antigen 1 Kits (3) and Squamous Cell Carcinoma Antigen 1 Proteins (2) and many more products for this protein.
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Data indicate that serum tumor markers showed significant shorter 3-year progression-free survival (PFS) in higher levels compared to lower levels for S-CYFRA 21-1 (cytokeratin 19 (show KRT19 Antibodies) fragment), S-SCCA and S-CEA (show CEACAM5 Antibodies).
SerpinB3 (show SERPINB3 Antibodies) indirectly increased the transcription of Myc (show MYC Antibodies) through the induction of Yap (show YAP1 Antibodies) pathway.
Data show that oropharyngeal squamous cell carcinomas (OPSCCs) express granzyme inhibitors SERPINB1 (show SERPINB1 Antibodies), SERPINB4 (show SERPINB4 Antibodies) and SERPINB9 (show SERPINB9 Antibodies) for cytotoxicity and the expression was not different between human papillomavirus (HPV)-positive and HPV-negative tumors.
Data show that serum neuron-specific enolase (show ENO2 Antibodies), cytokeratin 19 (show KRT19 Antibodies) fragment 21-1, pro-gastrin-releasing peptide (show GRP Antibodies), squamous cell carcinoma antigen, tissue inhibitor of metalloproteinase-1, and human epididymis protein 4 are not associated with brain metastases.
Pediatric CNS-PNETs evade immune recognition by downregulating cell surface MHC (show HLAE Antibodies)-I and CD1d (show CD1D Antibodies) expression. Intriguingly, expression of SERPINB9 (show SERPINB9 Antibodies), SERPINB1 (show SERPINB1 Antibodies), and SERPINB4 (show SERPINB4 Antibodies) is acquired during tumorigenesis in 29%, 29%, and 57% of the tumors
The diagnostic performance of SCCA-IgM immune complexes for hepatocellular carcinoma was found to be frequently superior to that of alpha-fetoprotein (show AFP Antibodies). (Review)
High SCC (show CYP11A1 Antibodies) serum levels are associated with Head and Neck Cancer.
Data indicate that hypoxia-induced cysteine-proteases inhibitor SERPINB3 (show SERPINB3 Antibodies) up-regulation is dependent on hypoxia-inducible factor-2alpha (HIF-2alpha (show EPAS1 Antibodies)).
High levels of neuron-specific enolase (NSE (show ENO2 Antibodies)), carbohydrate antigen 125 (CA125 (show MUC16 Antibodies)) and squamous cell carcinoma antigen (SCC (show CYP11A1 Antibodies)) were detected in 306 (63.6%), 89 (18.5%) and 125 (26.0%) non-small cell lung cancer patients, respectively.
High serpinB3 (show SERPINB3 Antibodies) protein content was found to be a biomarker of successful healing in diabetic patients.
May act as a protease inhibitor to modulate the host immune response against tumor cells.
protein T4-A
, serine (or cysteine) proteinase inhibitor, clade B (ovalbumin), member 3
, serpin B3
, squamous cell carcinoma antigen 1
, SCCA2/SCCA1 fusion protein
, peptidase inhibitor 11
, protease inhibitor (leucine-serpin)
, serine (or cysteine) proteinase inhibitor, clade B (ovalbumin), member 4
, serpin B4
, squamous cell carcinoma antigen 2


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|Message view
|« Date » · « Thread »
|« Date » · « Thread »
|Martin Sebor <se...@roguewave.com>
|Re: error on tuple copy ctor
|Wed, 02 Jul 2008 21:54:37 GMT
Eric Lemings wrote: > > >> -----Original Message----- >> From: Martin Sebor [mailto:email@example.com] On Behalf Of Martin Sebor >> Sent: Wednesday, July 02, 2008 3:18 PM >> To: email@example.com >> Subject: Re: error on tuple copy ctor >> > ... >>> Should we add the ctor even if the standard does not >> (currently) specify it? >> >> I don't think it's needed or desirable. In the test case I >> posted, we want to call the const T& overload. > > That's the only workaround I can think of. You have another one in > mind? A workaround for what? This is a valid definition of a CopyConstructible and MoveConstructible class (like tuple): struct S { S (const S&); S (S&&); }; I don't see why S would need another copy ctor with the signature of S(S&). I realize tuple is quite a bit more complicated than S, too complicated for me to understand why the ctor might be necessary if, if fact, it really is. Could you show in a small isolated example the problem that this ctor works around? Martin
|View raw message


text:
Embossed Card & Gift Tag
- 3-5 Hours
- Intermediate
Additional Information
- Walnut Hollow® Creative Metal: Beginner Kit
Metal Squares: red, green
Design Border A
Metal tape
- Cream cardstock: 5 1/2"x8 1/2" card, 4 3/4"x2 1/2" tag, 1 3/4" square
- 4"x5" red cardstock:
- Black acrylic paint
- Ribbon
- Brush
- Decorative scissors
- Fine sandpaper
- Hole punch
- Paper glue
- Paper towels
1. Attach nylon detailer point and medium roller onto handle from the Beginner Kit. Lay stocking pattern on top of green metal square, trace around stocking with Detailer. Cut with Metal scissors. Lay stocking pattern on red metal square and trace toe, heel & cuff patterns with detailer. Cut with scissors.
2. To emboss metal, use detailer to "doodle" on back of stocking. Press lightly with the detailer to write HAPPY HOLIDAYS on cuff. Flip cuff over and go over the letters, pressing a little harder so they are embossed on the front of the cuff. On the back of the cuff, also add short squiggle lines on sides.
3. To antique the metal, thin black acrylic paint with water; use brush to apply paint to all metal surfaces. Use paper towel to blot excess paint off metal. Let dry.
4. Use fine sandpaper to highlight embossing on metal pieces.
5. Fold cream cardstock in half. Use paper glue to adhere ribbon on red cardstock, and adhere red cardstock on top of cream card. Tie small bow and adhere where ribbon crosses.
6. Use Metal Tape to attach toe, heel, and cuff to stocking. Attach stocking to card.
1. Cut green metal 2 1/4"x4". Cut red metal strip 1"x 2 1/4 " & square 1 3/8".
2. Emboss back of green metal, using ruler with medium roller, leaving a small space between embossing. Use Nylon Detailer to make a wavy line by Roller embossing.
3. Emboss small red metal square, placing front of metal on top of Design Border. Use Texture tool to emboss design.
4. Emboss red metal strip the same way the green piece was embossed. Cut on edge with decorative scissors.
5. Antique metal same as above for card. Assemble pieces & glue in place.
6. Punch hole in top of tag. Tie with ribbon.


text:
Awards won in 2006 by Guardian News & Media:
Plain English Awards, December 2006
The Guardian has won the award for the best national newspaper for the second year running.
Record of the Day Awards, November 2006
The Guardian was named the newspaper with the best music coverage.
Alex Petridis won record review writer of the year and music features writer of the year.
ABI Financial Media Awards, November 2006
Guardain Money was named the the best personal finance section in any national newspaper.
Bradford and Bingley Personal Finance Media Awards, November 2006
Guardian Money was named the personal finance newspaper of the year.
European Federation of Black Women In Business, October 2006
Hannah Pool received the media award.
IFRA Award, October 2006
Best Cross-Media Award for the Guardian and Guardian Unlimited's World Cup coverage. Judge Mario Garcia said: "This was a textbook case of how to live in a multiplatform world."
AOP Awards, October 2006
Best Online Advertising Sales Team
Best Editorial Team, Comment is Free
Mental Health Media Awards, October 2006.
Guardian Film won the Best Television and Radio News category
European School of Oncology, July 2006
Sarah Boseley has been named best cancer reporter by the European School of Oncology.
Cartoon Arts Trust Awards, December 2005
Steve Bell was named Political Cartoonist of the Year.
Race in the Media Awards, June 2006
Leo Benedictus and Michael Robinson were rewarded with the national award for their G2 special which mapped immigrant populations across the UK.
OSM won the sport award for an article on Spanish football
D&AD Awards, May 2006
The Berliner Guardian won two prizes at the D&AD awards, known as the Yellow Pencils.The Guardian picked up a Yellow Pencil in the Best Designed Newspaper and a Black Pencil for Best Overall Design. Judges commented "In the new design of the Berliner Guardian, the readers met their match."
London Press Club Awards, May 2006
The Guardian won Daily Paper of the Year. The judges said the Guardian had relaunched in its new Berliner format with enormous panache, producing a sharp, readable, quirky and literate paper.
European Newspaper Awards, May 2006
The Guardian was named best-designed national title for its Berliner launch.
Webby Awards, May 2006
Guardian Unlimited has won the best newspaper category for the second year in a row, at the 10th annual Webby Awards - the most prestigious international awards for the internet.
Newspaper Awards, May 2006
The Guardian Print Centre was named Newspaper of the Year. The Guardian and Observer were also commended in a futher six categories
HeadlineMoney/Halifax Awards, May 2006
Guardian Money was voted best national newspaper consumer finance section.
Orwell Prize, April 2006
Timothy Garton Ash won this year's award.
Martha Gellhorn Prize, April 2006
Ghaith Abdul Ahad won the Prize for Jounalism.
For the first time since the inception of the Prize, the judges decided to make a Special Martha Gellhorn Award to Jonathan Steele.
Malofiej Awards, April 2006
The Guardian won two silver awards for graphic design.
James Carmeron Memorial Awards, April 2006
Dan Chung was awarded a special prize in recognition of his press photography.
British Press Awards, March 2006
The Guardian was named Newspaper of the Year.
Tom Jenkins won Sports Photographer of the Year.
Observer Food Monthly won Supplement of the Year.
Rachel Cooke was named Interviewer of the Year.
Jay Rayner was named Critic of the Year.
ACE Circulation Awards, March 2006
The GNL circulation team won the Gold Award for Circulation Excellence and Endeavour by a National Newspaper, the highest acolade at the ACE circulation awards.
Society for News Design, February 2006
The Guardian was judged 'The World's Best Designed Newspaper.'
What the Papers Say Awards, December 2005
Alan Rusbridger became the first recipient of the Judges Award in the 48 year history of the programme.
Dan Chung won Photographer of the Year.
Peter Preston was awarded a Lifetime Achievement Award.


text: VACATION Images Featuring Ed Helms, Christina Applegate, Chris Hemsworth, and More August 6, 2015 The next generation of Griswolds is at it again—and on the road for another ill-fated adventure. Following in his father's footsteps and hoping for some much-needed family bonding, a grown-up Rusty Griswold (Ed Helms) surprises his wife, Debbie (Christina Applegate), and their two sons with a cross-country trip back to America's "favourite family fun park," Walley World. VACATION hits Irish cinemas August 21, 2015.


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The Russian connection: See all our coverage | Read about our investigation
Julia WhittyJul. 26, 2007 7:23 PM
New research shows that air pollution plays a role in atherosclerosis or hardening of the arteries. This in turn contributes to heart attacks and/or strokes, according to a study published in the open access journal Genome Biology. The fats that clog arteries apparently work in conjunction with air pollution particles to trigger the genes behind inflammation, which leads to increased lesions in the clogged arteries, and the potential for thrombi, and resultant heart attacks or strokes. . . Listen up Dick Cheney, master of the clot. Clean air is good for you. JULIA WHITTY
Julia WhittyJul. 25, 2007 5:27 PM
Two government entities are investigating the Bush administration over the Endangered Species Act (ESA). The Christian Science Monitor reports the US Interior Department is reviewing the scientific integrity of decisions made by a political appointee, Julie MacDonald, who recently resigned under fire. Fish and Wildlife Service employees complained that MacDonald bullied, insulted, and harassed the professional staff to alter their biological reporting. The inspector noted that although she has no formal educational background in biology, she nevertheless labored long and hard editing, commenting on, and reshaping the endangered species program's scientific reports from the field. Last week Fish and Wildlife announced that eight decisions MacDonald made under the ESA would be examined for scientific and legal discrepancies.
Meanwhile Congress is investigating evidence that Vice President Dick Cheney interfered with decisions involving water in California and Oregon resulting in a mass kill of Klamath River salmon, including threatened species. As the CSM reports, both episodes illustrate the Bush administration's resistance to the law. Earlier, the Washington Post ran the story of Cheney's personal interference in the water decision that killed the salmon in 2002:
In Oregon, a battleground state that the Bush-Cheney ticket had lost by less than half of 1 percent, drought-stricken farmers and ranchers were about to be cut off from the irrigation water that kept their cropland and pastures green. Federal biologists said the Endangered Species Act left the government no choice: The survival of two imperiled species of fish was at stake. Law and science seemed to be on the side of the fish. Then the vice president stepped in. First Cheney looked for a way around the law, aides said. Next he set in motion a process to challenge the science protecting the fish, according to a former Oregon congressman who lobbied for the farmers. Because of Cheney's intervention, the government reversed itself and let the water flow in time to save the 2002 growing season, declaring that there was no threat to the fish. What followed was the largest fish kill the West had ever seen, with tens of thousands of salmon rotting on the banks of the Klamath River.
Or, in the words of Bruce Barcott in MoJo's piece, What's A River For?:
On the morning of September 19, 2002, the Yurok fishermen who set their gill nets near the mouth of the Klamath River arrived to find the largest salmon run in years fully under way. The fish had returned from the ocean to the Klamath, on the Northern California coast, to begin their long trip upstream to spawn; there were thousands of them, as far as the eye could see. And they were dying. Full-grown 30-pounders lay beached on shore-line rocks. Smaller fish floated in midriver eddies. Day after day they kept washing up; by the third day, biologists were estimating that 33,000 fish had been killed [since revised upward to 70,000] in one of the largest salmon die-offs in U.S. history. The Yurok knew immediately what had happened. For months they, along with state experts and commercial fishermen, had been pleading with the federal government to stop diverting most of the river's water into the potato and alfalfa fields of Oregon's upper Klamath Basin. But the Bureau of Reclamation, the agency in charge of federal irrigation projects, refused to intervene.
The CSM reports the House Natural Resources Committee has scheduled a hearing next week to investigate political influence on agency science and decisionmaking. As reported in the Blue Marble scientists are aware of the persistent unsciencing of their work. Thirty-eight prominent wildlife biologists and environmental ethics specialists recently signed a letter protesting a new Bush administration interpretation of the Endangered Species Act. They're concerned for the future of animals such as wolves and grizzly bears. If Interior Department Solicitor David Bernhardt has his way, the U.S. Fish and Wildlife Service will have to protect animals and plants only where they're actually battling for survival, not where they're in good shape. That means, for instance, that Bald Eagles would never have been protected decades ago since they were doing fine in Alaska, although practically extinct in the lower 48.
During Bush/Cheney, the listing of endangered and threatened species has slowed to a fraction the number the Bush senior made in only four years (58 new listings compared with 231), and most of those were court-ordered, according to the CSM. New funding has been cut as well, and only 278 candidate species are waiting to join the list of 1,352. Mother Jones' recent piece, Gone, detailed why the presence of many kinds of life on earth is important to the survival of life itself. Seven of 10 biologists believe the sixth great extinction currently underway is a greater threat to life on earth than even global climate change.
It's ephemerally comforting to think George W. Bush might go down in history as the worst of all U.S. presidents. More realistically, Dick Cheney will get the honor. . . Assuming there's a history to come. JULIA WHITTY
Cameron ScottJul. 25, 2007 11:54 AM
Remember the '80s hit by Midnight Oil, "Beds Are Burning"? The Aussie song posits with some disbelief that the "western desert lives and breathes in 45 degrees." (That's Celsius, y'all.) Singer-turned-politician Peter Garrett would be even more stunned to learn that southern Europe lived, breathed, and tried to sleep in 45 degrees this week. That's 113 Fahrenheit, in a region where air conditioners are less common even than Oreos. Greece, Bosnia, and Macedonia suffered most. In Hungary, the mercury hit 107 degrees, causing at least 500 heat-related deaths. Sound like fun? Try adding in several deadly fires and another record-breaking heat wave last month. So next time you hear "next year will be the hottest on record," don't plan on summering it away in Greece.
Julia WhittyJul. 24, 2007 7:23 PM
The Tibetan plateau is heating up by 0.3°C each decade. At more than twice the worldwide average, according to a new study from the Tibet Meteorological Bureau, as reported by New Scientist. The research reinforces a growing realization that high altitudes in tropical regions are experiencing dramatic temperature increases similar to those at the poles. Over the last 50 years, temperatures in the Arctic and Antarctica have risen by 0.2°C and approximately 0.5°C per decade, respectively, according to data from the Intergovernmental Panel on Climate Change. The reason surface temperatures at the poles are warming so quickly is because the seawater temperature around them has risen faster there than anywhere else on Earth. Warming waters also play a role in the tropics. When the already warm tropical waters heat up further, due to global warming, they evaporate even more moisture, which rises straight to the upper atmosphere.
In 2000, researchers published a study looking at temperature changes on the Tibetan plateau since the 1950s, which found that temperature was not only increasing with time, but also with elevation across the plateau. They concluded the plateau is one of the most sensitive areas in the world in its response to global climate change. A study published in 2006 in Science found similar increases in air temperature at high-elevation weather stations in the Andes.
The Tibetan Plateau is also one of John Schellnhuber's tipping points, reported on in Mother Jones "The Thirteenth Tipping Point." Check out what happens when it tips. JULIA WHITTY
Julia WhittyJul. 24, 2007 5:56 PM
Greenhouse-gas emissions have made the Northern Hemisphere wetter &mdash and climate models appear to have underestimated the changes. Research from the Canadian Centre for Climate Modelling and Analysis, published in Nature, finds that human activity has made the weather wetter in a large slice of the Northern Hemisphere, while making the regions just south of the Equator wetter, and those just north of it drier. Agriculture and human health have already been affected. The proof that human activity has altered rainfall patterns was found in comparisons of observed changes with climate models. Specifically with observed rainfall during the twentieth century compared to rainfall predicted by 14 climate models. In the zone between 40 and 70 °N, which includes much of North America and most of Europe, rainfall increased by 62 millimeters per century between 1925 and 1999. The researchers estimate that between 50 and 85% of this increase can be attributed to human activity.
So how many British naysayers have been converted in these past wet weeks? JULIA WHITTY
Julia WhittyJul. 24, 2007 5:22 PM
Greenpeace short on Japanese whaling, changing attitudes, need to change. JULIA WHITTY
Julia WhittyJul. 24, 2007 4:40 PM
A quarter of adult New Yorkers have elevated blood mercury levels. According to survey results released today by the New York City Health Department (read the full stats here), the elevations are closely tied to fish consumption. Asian and higher-income New Yorkers eat more fish, and have higher average mercury levels, than others both locally and nationally. The Health Department says these levels may increase the risk of cognitive delays for children whose mothers had high mercury levels during pregnancy. The Department also claims these elevated levels pose little if any health risk for most adults. . . Hmm. Right. So how come Canada's "safe" mercury level is half that of the U.S., while Britain's and China's are one-third? JULIA WHITTY
Julia WhittyJul. 24, 2007 2:32 AM
More than half the whales killed by Japanese whalers in the Antarctic last summer were pregnant females. The Mercury, in Hobart, Tasmania, reports on the claims of the Humane Society International that of the 505 Antarctic minke whales killed, 262 were pregnant females, while one of the three giant fin whales killed was also pregnant. The findings came from a review of Japanese reports from their most recent 2006-07 whale hunt in Antarctic waters and were released ahead of the resumption of an Australian Federal Court case the HSI is taking against Japanese whaling company Kyodo Senpaku Kaisha Ltd. "These are gruesome statistics that the Japanese government dresses up as science," HSI spokeswoman Nicola Beynon said in a statement. "The full hearing will be to determine whether Japanese whalers are in breach of Australian law when they hunt whales in the Australian Whale Sanctuary in Antarctica and whether the court will issue an injunction for the hunt to be stopped," Ms Beynon said. . . Fingers crossed. JULIA WHITTY
Julia WhittyJul. 20, 2007 7:37 PM
Researchers have developed an inexpensive solar cell that can be painted or printed on flexible plastic sheets. Someday homeowners will be able to print sheets of these solar cells with inexpensive home-based inkjet printers, say the inventors from the New Jersey Institute of Technology (NJIT). Consumers can then slap the finished product on a wall, roof or billboard to create their own power stations. "Imagine some day driving in your hybrid car with a solar panel painted on the roof, which is producing electricity to drive the engine," says author Somenath Mitra of NJIT. . . Bring it on. There are millions of us waiting. JULIA WHITTY
Julia WhittyJul. 20, 2007 6:47 PM
Still paying for his evilheart in so many ways. JULIA WHITTY
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Knowing what to do in an emergency could be the difference between life and death for you and
your family. The safety briefing and the safety information card provided near your seat give vital
information on the location of exits and emergency equipment. As this can vary from one aircraft
type to another, it is important to pay attention to the safety briefing and read the safety card
each time you fly. You should check the location of your nearest emergency exit which may be behind
you. Safety equipment will typically include life jackets, oxygen masks, seat belts/harnesses and
floor lighting.
The safety briefing will typically include information on the use of portable electronic
devices, storage of hand baggage and the need for your seat to be in the upright position with the
tray table stowed during take-off and landing.
You are recommended to keep your belt fastened throughout the flight, and must do so whenever
the "seat belt" sign is on (during taxi, take-off, landing and during turbulence). You should
adjust your belt so that it is tight but comfortable with the buckle the right way round so that it
can be released easily. If you have a blanket over your lap and are likely to fall asleep, it is
recommended that you fasten the seat belt over the blanket so cabin crew can see you have the belt
fastened. After landing, you must wait until the "seat belt" sign goes off before undoing your belt
at the end of the flight.
Some UK airlines now allow passengers to use electronic devices such as smartphones, tablets and
e-readers, during the entire duration of a flight. These airlines have conducted safety tests to
ensure electronic gadgets do not adversely affect their aircraft. Currently, all electronic devices
must remain in Flight Mode when switched on unless passengers are advised otherwise by cabin
A number of international airlines have equipped some of their aircraft to also allow mobile
phone voice calls and texts in-flight. Other aircraft also have WiFi installed, allowing passengers
to browse the web. However, the situation will vary from one airline to another. Passengers will
always be instructed by cabin crew as to exactly what electronic devices can be used, and in what
mode, at the beginning of a flight. If in any doubt, always check with a member of cabin crew,
before using a device.
Most airlines also publish details about travelling with portable electronic devices on their
websites, as well as in their in-flight magazines.
UK airlines do not permit smoking on board therefore the 'no smoking' signs will remain on
throughout the flight.
Passengers are not permitted to smoke in toilets and these are fitted with smoke detectors.
Tampering with an aircraft smoke detector is a serious offence and may lead to prosecution.
RT @ATOLprotected: Whether it's on paper or online, always keep your #ATOL certificate handy when holidaying abroad. #Travel https://t.co/V…
3 days ago
Want to complain about a flight? Find out how alternative dispute resolution services can help you > https://t.co/JkMBfy5ck3 #airpassengers
12 days ago
Experienced a flight delay? Information about your rights during disruption is available at> https://t.co/A9vK7HGKkp #airpassengers
19 days ago
Read all @UK_CAA
CAA statement on the disruption affecting British Airways flights
28 May, 2017
UK families need a holiday 'buffer budget' of £536.80 to cover unexpected costs
12 April, 2017
Travel company failures provides timely reminder to check for protection
17 March, 2017
Read all News
Passengers with hidden disabilities
8 December, 2016
Holiday travel tips
7 December, 2016
'Saturday Night' at 30,000ft
24 August, 2016
Read All Blogs


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Mobile App
BCDC Bhopal
Bhabha College Of Dental Sciences
Madhya Pradesh
Ministry of Health and Family Welfare
Total Students
Fees Range
How to reach
Bhabha College Of Dental Sciences is situated at NH-12,Hoshangabad Road Jatkhedi Bhopal-462026 Madhya Pradesh in Bhopal.
Courses Offered
- 5 Years
- Bachelor of Dental Surgery-B.D.S.
- Medicine / Beauty / Health Care
Bhabha College Of Dental Sciences - BCDC Bhopal - BCDC
The college is recognised by Ministry of Health & Family Welfare,Government of India & the Dental Council of India.It is affiliated to Barkatullah University, Bhopal & Madhya Pradesh Medical Sciences University and has a ISO-9001 2008-Certification.The college is headed by Dr. Dilip Dhamankar MDS(Prosthodontics,Crown & Bridge & Oral Implantology) F.I.C.D.,U.S.A. with clear vision & mission to generate excellent professionals.It is an innovative & progress oriented Institute which aims to provide excellent dental education to the students,laying stress on basis as well as recent development so that the student can serve the society by his profession in a better way.Bhabha College Of Dental Sciences is 'to foster critical analysis by training students both in theory and practice so as to equip them with skills needed for facing global challenges with team work and human values. And to build quality network with the Industry, educationists and the society for exchanging knowledge'. The modern teaching methodology assists the students in getting an all around view of engineering, technology and the entrepreneur world. The diligent faculty team of the college possesses hands-on experience and up to date knowledge of their subject and area of expertise. The infrastructure and facilities of Bhabha College Of Dental Sciences consists of spread-out campus alongside various amenities in the form of library, computer center, classrooms with proper teaching and learning aids, medical facilities etc. The institute seeks to place each of its students in an organization/company of great repute.
Why join Bhabha Dental College Bhopal
Computers, Laboratory, Playground For Indoor & Outdoor Games, Phone, Library, Hostel.
1 Type Courses Available
- 1 UG Courses
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BERI was established in the year 2003.Bhabha institute is identified by leading MNCs for in campus Training and Industry institute.Bhabha is producing Engineering/ Management/Pharmacy professionals through several programs organised in association with the leading corporate.The Training and Placement Office has come in its inception since quite a long and is performing the following activities:-Arranging inplant training for students and Inviting various organizations for campus recruitment. For placement a large number of prospective employers are contacted during the year and the number of companies visiting regularly this Institute are increasing every year which has reached to around 20-30 by now.Some of the frontline companies have made Bhabha a nodal centre for their campus placement offering packages from 2.1 lacs p.a. to 4.2 lacs p.a.The recruiters are highly impressed by the faculty provided by the institute and the quality of the students.
Visiting Companies
Student Placement
The college has E-Library with computer and internet facilities for Students and staff and already holding exclusive books on every Homoeopathic subject rarely available in the market, our library is regularly updated. All important journals published at home are subscribed.The e-library is a place where students can use Internet Services, Printer Services, and CDs on various courses; and can prepare their Seminar presentations and other project related work.College's has canteen in the college campus and provides hygienic eatables at reasonable charges for students and patients.Institution has separate hostels for boys and girls in the college campus.
Try our extensive database of FAQs or submit your own question...
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