95,990 research outputs found
Efficient Identification of Equivalences in Dynamic Graphs and Pedigree Structures
We propose a new framework for designing test and query functions for complex
structures that vary across a given parameter such as genetic marker position.
The operations we are interested in include equality testing, set operations,
isolating unique states, duplication counting, or finding equivalence classes
under identifiability constraints. A motivating application is locating
equivalence classes in identity-by-descent (IBD) graphs, graph structures in
pedigree analysis that change over genetic marker location. The nodes of these
graphs are unlabeled and identified only by their connecting edges, a
constraint easily handled by our approach. The general framework introduced is
powerful enough to build a range of testing functions for IBD graphs, dynamic
populations, and other structures using a minimal set of operations. The
theoretical and algorithmic properties of our approach are analyzed and proved.
Computational results on several simulations demonstrate the effectiveness of
our approach.Comment: Code for paper available at
http://www.stat.washington.edu/~hoytak/code/hashreduc
Nested Markov Properties for Acyclic Directed Mixed Graphs
Directed acyclic graph (DAG) models may be characterized in at least four
different ways: via a factorization, the d-separation criterion, the
moralization criterion, and the local Markov property. As pointed out by Robins
(1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of
DAG models also imply equality constraints that are not conditional
independences. The well-known `Verma constraint' is an example. Constraints of
this type were used for testing edges (Shpitser et al., 2009), and an efficient
marginalization scheme via variable elimination (Shpitser et al., 2011).
We show that equality constraints like the `Verma constraint' can be viewed
as conditional independences in kernel objects obtained from joint
distributions via a fixing operation that generalizes conditioning and
marginalization. We use these constraints to define, via Markov properties and
a factorization, a graphical model associated with acyclic directed mixed
graphs (ADMGs). We show that marginal distributions of DAG models lie in this
model, prove that a characterization of these constraints given in (Tian and
Pearl, 2002b) gives an alternative definition of the model, and finally show
that the fixing operation we used to define the model can be used to give a
particularly simple characterization of identifiable causal effects in hidden
variable graphical causal models.Comment: 67 pages (not including appendix and references), 8 figure
A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
The clustered planarity problem (c-planarity) asks whether a hierarchically
clustered graph admits a planar drawing such that the clusters can be nicely
represented by regions. We introduce the cd-tree data structure and give a new
characterization of c-planarity. It leads to efficient algorithms for
c-planarity testing in the following cases. (i) Every cluster and every
co-cluster (complement of a cluster) has at most two connected components. (ii)
Every cluster has at most five outgoing edges.
Moreover, the cd-tree reveals interesting connections between c-planarity and
planarity with constraints on the order of edges around vertices. On one hand,
this gives rise to a bunch of new open problems related to c-planarity, on the
other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure
Knowledge-based support in Non-Destructive Testing for health monitoring of aircraft structures
Maintenance manuals include general methods and procedures for industrial maintenance and they contain information about principles of maintenance methods. Particularly, Non-Destructive Testing (NDT) methods are important for the detection of aeronautical defects and they can be used for various kinds of material and in different environments. Conventional non-destructive evaluation inspections are done at periodic maintenance checks. Usually, the list of tools used in a maintenance program is simply located in the introduction of manuals, without any precision as regards to their characteristics, except for a short description of the manufacturer and tasks in which they are employed. Improving the identification concepts of the maintenance tools is needed to manage the set of equipments and establish a system of equivalence: it is necessary to have a consistent maintenance conceptualization, flexible enough to fit all current equipment, but also all those likely to be added/used in the future. Our contribution is related to the formal specification of the system of functional equivalences that can facilitate the maintenance activities with means to determine whether a tool can be substituted for another by observing their key parameters in the identified characteristics. Reasoning mechanisms of conceptual graphs constitute the baseline elements to measure the fit or unfit between an equipment model and a maintenance activity model. Graph operations are used for processing answers to a query and this graph-based approach to the search method is in-line with the logical view of information retrieval. The methodology described supports knowledge formalization and capitalization of experienced NDT practitioners. As a result, it enables the selection of a NDT technique and outlines its capabilities with acceptable alternatives
Testing List H-Homomorphisms
Let be an undirected graph. In the List -Homomorphism Problem, given
an undirected graph with a list constraint for each
variable , the objective is to find a list -homomorphism , that is, for every and whenever .
We consider the following problem: given a map as an oracle
access, the objective is to decide with high probability whether is a list
-homomorphism or \textit{far} from any list -homomorphisms. The
efficiency of an algorithm is measured by the number of accesses to .
In this paper, we classify graphs with respect to the query complexity
for testing list -homomorphisms and show the following trichotomy holds: (i)
List -homomorphisms are testable with a constant number of queries if and
only if is a reflexive complete graph or an irreflexive complete bipartite
graph. (ii) List -homomorphisms are testable with a sublinear number of
queries if and only if is a bi-arc graph. (iii) Testing list
-homomorphisms requires a linear number of queries if is not a bi-arc
graph
Quiet Planting in the Locked Constraint Satisfaction Problems
We study the planted ensemble of locked constraint satisfaction problems. We
describe the connection between the random and planted ensembles. The use of
the cavity method is combined with arguments from reconstruction on trees and
first and second moment considerations; in particular the connection with the
reconstruction on trees appears to be crucial. Our main result is the location
of the hard region in the planted ensemble. In a part of that hard region
instances have with high probability a single satisfying assignment.Comment: 21 pages, revised versio
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