1,455 research outputs found
Graphical Markov models: overview
We describe how graphical Markov models started to emerge in the last 40
years, based on three essential concepts that had been developed independently
more than a century ago. Sequences of joint or single regressions and their
regression graphs are singled out as being best suited for analyzing
longitudinal data and for tracing developmental pathways. Interpretations are
illustrated using two sets of data and some of the more recent, important
results for sequences of regressions are summarized.Comment: 22 pages, 9 figure
Characterizations and algorithms for generalized Cops and Robbers games
We propose a definition of generalized Cops and Robbers games where there are
two players, the Pursuer and the Evader, who each move via prescribed rules. If
the Pursuer can ensure that the game enters into a fixed set of final
positions, then the Pursuer wins; otherwise, the Evader wins. A relational
characterization of the games where the Pursuer wins is provided. A precise
formula is given for the length of the game, along with an algorithm for
computing if the Pursuer has a winning strategy whose complexity is a function
of the parameters of the game. For games where the position of one player does
not affect the available moves of he other, a vertex elimination ordering
characterization, analogous to a cop-win ordering, is given for when the
Pursuer has a winning strategy
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efficient
implementation of a large range of basic operations on simplicial complexes. In
this paper, we show how to optimally compress the Simplex Tree while retaining
its functionalities. In addition, we propose two new data structures called the
Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the
compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List
under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
Treewidth of display graphs: bounds, brambles and applications
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a function of many common dissimilarity measures between phylogenetic trees and this has been leveraged in fixed parameter tractability results. Here we further elucidate the properties of display graphs and their interaction with treewidth. We show that it is NP-hard to recognize display graphs, but that display graphs of bounded treewidth can be recognized in linear time. Next we show that if a phylogenetic network displays (i.e. topologically embeds) a phylogenetic tree, the treewidth of their display graph is bounded by a function of the treewidth of the original network (and also by various other parameters). In fact, using a bramble argument we show that this treewidth bound is sharp up to an additive term of 1. We leverage this bound to give an FPT algorithm, parameterized by treewidth, for determining whether a network displays a tree, which is an intensively-studied problem in the field. We conclude with a discussion on the future use of display graphs and treewidth in phylogenetics
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