4,278 research outputs found
Reconstructing fully-resolved trees from triplet cover distances
It is a classical result that any finite tree with positively weighted edges, and without vertices of degree 2, is uniquely determined by the weighted path distance between each pair of leaves. Moreover, it is possible for a (small) strict subset L of leaf pairs to suffice for reconstructing the tree and its edge weights, given just the distances between the leaf pairs in L. It is known that any set L with this property for a tree in which all interior vertices have degree 3 must form a cover for T {that is, for each interior vertex v of T, L must contain a pair of leaves from each pair of the three components of T ̶ v. Here we provide a partial converse of this result by showing that if a set L of leaf pairs forms a cover of a certain type for such a tree T then T and its edge weights can be uniquely determined from the distances between the pairs of leaves in L. Moreover, there is a polynomial-time algorithm for achieving this reconstruction. The result establishes a special case of a recent question concerning `triplet covers', and is relevant to a problem arising in evolutionary genomics
Linear Global Translation Estimation with Feature Tracks
This paper derives a novel linear position constraint for cameras seeing a
common scene point, which leads to a direct linear method for global camera
translation estimation. Unlike previous solutions, this method deals with
collinear camera motion and weak image association at the same time. The final
linear formulation does not involve the coordinates of scene points, which
makes it efficient even for large scale data. We solve the linear equation
based on norm, which makes our system more robust to outliers in
essential matrices and feature correspondences. We experiment this method on
both sequentially captured images and unordered Internet images. The
experiments demonstrate its strength in robustness, accuracy, and efficiency.Comment: Changes: 1. Adopt BMVC2015 style; 2. Combine sections 3 and 5; 3.
Move "Evaluation on synthetic data" out to supplementary file; 4. Divide
subsection "Evaluation on general data" to subsections "Experiment on
sequential data" and "Experiment on unordered Internet data"; 5. Change Fig.
1 and Fig.8; 6. Move Fig. 6 and Fig. 7 to supplementary file; 7 Change some
symbols; 8. Correct some typo
Electroweak Multiplet Dark Matter at Future Lepton Colliders
An electroweak multiplet stable due to a new global symmetry is a simple and
well-motivated candidate for thermal dark matter. We study how direct searches
at a future linear collider, such as the proposed CLIC, can constrain scalar
and fermion triplets, quintets and septets, as well as a fermion doublet. The
phenomenology is highly sensitive to charged state lifetimes and thus the mass
splitting between the members of the multiplet. We include both radiative
corrections and the effect of non-renormalisable operators on this splitting.
In order to explore the full range of charged state lifetimes, we consider
signals including long-lived charged particles, disappearing tracks, and
monophotons. By combining the different searches we find discovery and
exclusion contours in the mass-lifetime plane. In particular, when the mass
splitting is generated purely through radiative corrections, we can exclude the
pure-Higgsino doublet below 310 GeV, the pure-wino triplet below 775 GeV, and
the minimal dark matter fermion quintet below 1025 GeV. The scenario where the
thermal relic abundance of a Higgsino accounts for the whole dark matter of the
Universe can be excluded if the mass splitting between the charged and neutral
states is less than 230 MeV. Finally, we discuss possible improvements to these
limits by using associated hard leptons to idenify the soft visible decay
products of the charged members of the dark matter multiplet.Comment: 24 pages, 14 figures; version 2, additional reference
Tile2Vec: Unsupervised representation learning for spatially distributed data
Geospatial analysis lacks methods like the word vector representations and
pre-trained networks that significantly boost performance across a wide range
of natural language and computer vision tasks. To fill this gap, we introduce
Tile2Vec, an unsupervised representation learning algorithm that extends the
distributional hypothesis from natural language -- words appearing in similar
contexts tend to have similar meanings -- to spatially distributed data. We
demonstrate empirically that Tile2Vec learns semantically meaningful
representations on three datasets. Our learned representations significantly
improve performance in downstream classification tasks and, similar to word
vectors, visual analogies can be obtained via simple arithmetic in the latent
space.Comment: 8 pages, 4 figures in main text; 9 pages, 11 figures in appendi
Cophenetic metrics for phylogenetic trees, after Sokal and Rohlf
Phylogenetic tree comparison metrics are an important tool in the study of
evolution, and hence the definition of such metrics is an interesting problem
in phylogenetics. In a paper in Taxon fifty years ago, Sokal and Rohlf proposed
to measure quantitatively the difference between a pair of phylogenetic trees
by first encoding them by means of their half-matrices of cophenetic values,
and then comparing these matrices. This idea has been used several times since
then to define dissimilarity measures between phylogenetic trees but, to our
knowledge, no proper metric on weighted phylogenetic trees with nested taxa
based on this idea has been formally defined and studied yet. Actually, the
cophenetic values of pairs of different taxa alone are not enough to single out
phylogenetic trees with weighted arcs or nested taxa. In this paper we define a
family of cophenetic metrics that compare phylogenetic trees on a same set of
taxa by encoding them by means of their vectors of cophenetic values of pairs
of taxa and depths of single taxa, and then computing the norm of the
difference of the corresponding vectors. Then, we study, either analytically or
numerically, some of their basic properties: neighbors, diameter, distribution,
and their rank correlation with each other and with other metrics.Comment: The "authors' cut" of a paper published in BMC Bioinformatics 14:3
(2013). 46 page
On the universal structure of human lexical semantics
How universal is human conceptual structure? The way concepts are organized
in the human brain may reflect distinct features of cultural, historical, and
environmental background in addition to properties universal to human
cognition. Semantics, or meaning expressed through language, provides direct
access to the underlying conceptual structure, but meaning is notoriously
difficult to measure, let alone parameterize. Here we provide an empirical
measure of semantic proximity between concepts using cross-linguistic
dictionaries. Across languages carefully selected from a phylogenetically and
geographically stratified sample of genera, translations of words reveal cases
where a particular language uses a single polysemous word to express concepts
represented by distinct words in another. We use the frequency of polysemies
linking two concepts as a measure of their semantic proximity, and represent
the pattern of such linkages by a weighted network. This network is highly
uneven and fragmented: certain concepts are far more prone to polysemy than
others, and there emerge naturally interpretable clusters loosely connected to
each other. Statistical analysis shows such structural properties are
consistent across different language groups, largely independent of geography,
environment, and literacy. It is therefore possible to conclude the conceptual
structure connecting basic vocabulary studied is primarily due to universal
features of human cognition and language use.Comment: Press embargo in place until publicatio
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