53 research outputs found
Generalized Buneman pruning for inferring the most parsimonious multi-state phylogeny
Accurate reconstruction of phylogenies remains a key challenge in
evolutionary biology. Most biologically plausible formulations of the problem
are formally NP-hard, with no known efficient solution. The standard in
practice are fast heuristic methods that are empirically known to work very
well in general, but can yield results arbitrarily far from optimal. Practical
exact methods, which yield exponential worst-case running times but generally
much better times in practice, provide an important alternative. We report
progress in this direction by introducing a provably optimal method for the
weighted multi-state maximum parsimony phylogeny problem. The method is based
on generalizing the notion of the Buneman graph, a construction key to
efficient exact methods for binary sequences, so as to apply to sequences with
arbitrary finite numbers of states with arbitrary state transition weights. We
implement an integer linear programming (ILP) method for the multi-state
problem using this generalized Buneman graph and demonstrate that the resulting
method is able to solve data sets that are intractable by prior exact methods
in run times comparable with popular heuristics. Our work provides the first
method for provably optimal maximum parsimony phylogeny inference that is
practical for multi-state data sets of more than a few characters.Comment: 15 page
Introduction of Empirical Topology in Construction of Relationship Networks of Informative Objects
Understanding the structure of relationships between objects in a given
database is one of the most important problems in the field of data mining. The
structure can be defined for a set of single objects (clustering) or a set of
groups of objects (network mapping). We propose a method for discovering
relationships between individuals (single or groups) that is based on what we
call the empirical topology, a system-theoretic measure of functional
proximity. To illustrate the suitability and efficiency of the method, we apply
it to an astronomical data base
Ownership and control in a competitive industry
We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control
The Random Quadratic Assignment Problem
Optimal assignment of classes to classrooms \cite{dickey}, design of DNA
microarrays \cite{carvalho}, cross species gene analysis \cite{kolar}, creation
of hospital layouts cite{elshafei}, and assignment of components to locations
on circuit boards \cite{steinberg} are a few of the many problems which have
been formulated as a quadratic assignment problem (QAP). Originally formulated
in 1957, the QAP is one of the most difficult of all combinatorial optimization
problems. Here, we use statistical mechanical methods to study the asymptotic
behavior of problems in which the entries of at least one of the two matrices
that specify the problem are chosen from a random distribution .
Surprisingly, this case has not been studied before using statistical methods
despite the fact that the QAP was first proposed over 50 years ago
\cite{Koopmans}. We find simple forms for and , the
costs of the minimal and maximum solutions respectively. Notable features of
our results are the symmetry of the results for and
and the dependence on only through its mean and standard deviation,
independent of the details of . After the asymptotic cost is determined for
a given QAP problem, one can straightforwardly calculate the asymptotic cost of
a QAP problem specified with a different random distribution
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