1,001 research outputs found
Reconstructing pedigrees: some identifiability questions for a recombination-mutation model
Pedigrees are directed acyclic graphs that represent ancestral relationships
between individuals in a population. Based on a schematic recombination
process, we describe two simple Markov models for sequences evolving on
pedigrees - Model R (recombinations without mutations) and Model RM
(recombinations with mutations). For these models, we ask an identifiability
question: is it possible to construct a pedigree from the joint probability
distribution of extant sequences? We present partial identifiability results
for general pedigrees: we show that when the crossover probabilities are
sufficiently small, certain spanning subgraph sequences can be counted from the
joint distribution of extant sequences. We demonstrate how pedigrees that
earlier seemed difficult to distinguish are distinguished by counting their
spanning subgraph sequences.Comment: 40 pages, 9 figure
On projections of knots, links and spatial graphs
制度:新 ; 報告番号:甲3007号 ; 学位の種類:博士(理学) ; 授与年月日:2010/3/15 ; 早大学位記番号:新525
Bimodules and branes in deformation quantization
We prove a version of Kontsevich's formality theorem for two subspaces
(branes) of a vector space . The result implies in particular that the
Kontsevich deformation quantizations of and
associated with a quadratic Poisson structure are Koszul dual. This answers an
open question in Shoikhet's recent paper on Koszul duality in deformation
quantization.Comment: 40 pages, 15 figures; a small change of notations in the definition
of the 4-colored propagators; an Addendum about the appearance of loops in
the -quasi-isomorphism and a corresponding change in the proof of
Theorem 7.2; several changes regarding completions, when dealing with general
-structure
Tree-edges deletion problems with bounded diameter obstruction sets
AbstractWe study the following problem: given a tree G and a finite set of trees H, find a subset O of the edges of G such that G-O does not contain a subtree isomorphic to a tree from H, and O has minimum cardinality. We give sharp boundaries on the tractability of this problem: the problem is polynomial when all the trees in H have diameter at most 5, while it is NP-hard when all the trees in H have diameter at most 6. We also show that the problem is polynomial when every tree in H has at most one vertex with degree more than 2, while it is NP-hard when the trees in H can have two such vertices.The polynomial-time algorithms use a variation of a known technique for solving graph problems. While the standard technique is based on defining an equivalence relation on graphs, we define a quasiorder. This new variation might be useful for giving more efficient algorithm for other graph problems
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