550 research outputs found
On Symbolic Ultrametrics, Cotree Representations, and Cograph Edge Decompositions and Partitions
Symbolic ultrametrics define edge-colored complete graphs K_n and yield a
simple tree representation of K_n. We discuss, under which conditions this idea
can be generalized to find a symbolic ultrametric that, in addition,
distinguishes between edges and non-edges of arbitrary graphs G=(V,E) and thus,
yielding a simple tree representation of G. We prove that such a symbolic
ultrametric can only be defined for G if and only if G is a so-called cograph.
A cograph is uniquely determined by a so-called cotree. As not all graphs are
cographs, we ask, furthermore, what is the minimum number of cotrees needed to
represent the topology of G. The latter problem is equivalent to find an
optimal cograph edge k-decomposition {E_1,...,E_k} of E so that each subgraph
(V,E_i) of G is a cograph. An upper bound for the integer k is derived and it
is shown that determining whether a graph has a cograph 2-decomposition, resp.,
2-partition is NP-complete
Partial Homology Relations - Satisfiability in terms of Di-Cographs
Directed cographs (di-cographs) play a crucial role in the reconstruction of
evolutionary histories of genes based on homology relations which are binary
relations between genes. A variety of methods based on pairwise sequence
comparisons can be used to infer such homology relations (e.g.\ orthology,
paralogy, xenology). They are \emph{satisfiable} if the relations can be
explained by an event-labeled gene tree, i.e., they can simultaneously co-exist
in an evolutionary history of the underlying genes. Every gene tree is
equivalently interpreted as a so-called cotree that entirely encodes the
structure of a di-cograph. Thus, satisfiable homology relations must
necessarily form a di-cograph. The inferred homology relations might not cover
each pair of genes and thus, provide only partial knowledge on the full set of
homology relations. Moreover, for particular pairs of genes, it might be known
with a high degree of certainty that they are not orthologs (resp.\ paralogs,
xenologs) which yields forbidden pairs of genes. Motivated by this observation,
we characterize (partial) satisfiable homology relations with or without
forbidden gene pairs, provide a quadratic-time algorithm for their recognition
and for the computation of a cotree that explains the given relations
First case of trans apical implantation of an aortic valve in a patient with dextrocardia
We describe the clinical presentation and implantation procedure of the first transcatheter aortic valve implantation described in a patient with dextrocardia
Quadrilateral-octagon coordinates for almost normal surfaces
Normal and almost normal surfaces are essential tools for algorithmic
3-manifold topology, but to use them requires exponentially slow enumeration
algorithms in a high-dimensional vector space. The quadrilateral coordinates of
Tollefson alleviate this problem considerably for normal surfaces, by reducing
the dimension of this vector space from 7n to 3n (where n is the complexity of
the underlying triangulation). Here we develop an analogous theory for
octagonal almost normal surfaces, using quadrilateral and octagon coordinates
to reduce this dimension from 10n to 6n. As an application, we show that
quadrilateral-octagon coordinates can be used exclusively in the streamlined
3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing
experimental running times by factors of thousands. We also introduce joint
coordinates, a system with only 3n dimensions for octagonal almost normal
surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using
cohomology, plus other minor changes; v3: Minor housekeepin
Three-way symbolic tree-maps and ultrametrics
Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis and have been used in areas such as psychology and phylogenetics, where three-way data tables can arise. Special examples of such dissimilarities are three-way tree-metrics and ultrametrics, which arise from leaf-labelled trees with edges labelled by positive real numbers. Here we consider three-way maps which arise from leaf-labelled trees where instead the interior vertices are labelled by an arbitrary set of values. For unrooted trees, we call such maps three-way symbolic tree-maps; for rooted trees, we call them three-way symbolic ultrametrics since they can be considered as a generalization of the (two-way) symbolic ultrametrics of Bocker and Dress. We show that, as with two- and three-way tree-metrics and ultrametrics, three-way symbolic tree-maps and ultrametrics can be characterized via certain k-point conditions. In the unrooted case, our characterization is mathematically equivalent to one presented by Gurvich for a certain class of edge-labelled hypergraphs. We also show that it can be decided whether or not an arbitrary three-way symbolic map is a tree-map or a symbolic ultrametric using a triplet-based approach that relies on the so-called BUILD algorithm for deciding when a set of 3-leaved trees or triplets can be displayed by a single tree. We envisage that our results will be useful in developing new approaches and algorithms for understanding 3-way data, especially within the area of phylogenetics
Health Literacy and Medication Practices in Senior Housing Residents
Objective: To conduct a descriptive analysis of health literacy, knowledge of prescribed medications, and methods of administering medications in a cohort of senior housing residents.https://scholarworks.uvm.edu/comphp_gallery/1027/thumbnail.jp
Beyond representing orthology relations by trees
Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple relations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view they are also attractive from a theoretical perspective in that e.\,g.\,a characterization is known for when such a relation is representable by a certain type of phylogenetic tree. For an orthology relation inferred from real biological data it is however generally too much to hope for that it satisfies that characterization. Rather than trying to correct the data in some way or another which has its own drawbacks, as an alternative, we propose to represent an orthology relation in terms of a structure more general than a phylogenetic tree called a phylogenetic network. To compute such a network in the form of a level-1 representation for , we formalize an orthology relation in terms of the novel concept of a symbolic 3- dissimilarity which is motivated by the biological concept of a ``cluster of orthologous groups'', or COG for short. For such maps which assign symbols rather that real values to elements, we introduce the novel {\sc Network-Popping} algorithm which has several attractive properties. In addition, we characterize an orthology relation on some set that has a level-1 representation in terms of eight natural properties for as well as in terms of level-1 representations of orthology relations on certain subsets of
Complementarity, quantum erasure and delayed choice with modified Mach-Zehnder interferometers
Often cited dictums in Quantum Mechanics include "observation disturbance
causes loss of interference" and "ignorance is interference". In this paper we
propose and describe a series of experiments with modified Mach-Zehnder
interferometers showing that one has to be careful when applying such dictums.
We are able to show that without interacting in any way with the light quantum
(or quanta) expected to behave "wave-like", interference fringes can be lost by
simply gaining (or having the potential to gain) the which-path knowledge.
Erasing this information may revive the interference fringes. Delayed choice
can be added, arriving to an experiment in line with Wheeler's original
proposal. We also show that ignorance is not always synonym with having the
interference fringes. The often-invoked "collapse of the wavefunction" is found
to be a non-necessary ingredient to describe our experiments.Comment: 8 pages, 3 figures; to appear in EPJ
A Delayed Choice Quantum Eraser
This paper reports a "delayed choice quantum eraser" experiment proposed by
Scully and Dr\"{u}hl in 1982. The experimental results demonstrated the
possibility of simultaneously observing both particle-like and wave-like
behavior of a quantum via quantum entanglement. The which-path or both-path
information of a quantum can be erased or marked by its entangled twin even
after the registration of the quantum.Comment: twocolumn, 4pages, submitted to PR
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