7,658 research outputs found
Unification in the Description Logic EL
The Description Logic EL has recently drawn considerable attention since, on
the one hand, important inference problems such as the subsumption problem are
polynomial. On the other hand, EL is used to define large biomedical
ontologies. Unification in Description Logics has been proposed as a novel
inference service that can, for example, be used to detect redundancies in
ontologies. The main result of this paper is that unification in EL is
decidable. More precisely, EL-unification is NP-complete, and thus has the same
complexity as EL-matching. We also show that, w.r.t. the unification type, EL
is less well-behaved: it is of type zero, which in particular implies that
there are unification problems that have no finite complete set of unifiers.Comment: 31page
A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching
It is well-known that optimizing network topology by switching on and off
transmission lines improves the efficiency of power delivery in electrical
networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that
the U.S. should "encourage, as appropriate, the deployment of advanced
transmission technologies" including "optimized transmission line
configurations". As such, many authors have studied the problem of determining
an optimal set of transmission lines to switch off to minimize the cost of
meeting a given power demand under the direct current (DC) model of power flow.
This problem is known in the literature as the Direct-Current Optimal
Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on
heuristic algorithms for generating quality solutions or on the application of
DC-OTS to crucial operational and strategic problems such as contingency
correction, real-time dispatch, and transmission expansion. The mathematical
theory of the DC-OTS problem is less well-developed. In this work, we formally
establish that DC-OTS is NP-Hard, even if the power network is a
series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's
Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new
formulation to build a cycle-induced relaxation. We characterize the convex
hull of the cycle-induced relaxation, and the characterization provides strong
valid inequalities that can be used in a cutting-plane approach to solve the
DC-OTS. We give details of a practical implementation, and we show promising
computational results on standard benchmark instances
Post-Newtonian Initial Data with Waves: Progress in Evolution
In Kelly et al. [Phys. Rev. D, 76:024008, 2007], we presented new binary
black-hole initial data adapted to puncture evolutions in numerical relativity.
This data satisfies the constraint equations to 2.5 post-Newtonian order, and
contains a transverse-traceless "wavy" metric contribution, violating the
standard assumption of conformal flatness. We report on progress in evolving
this data with a modern moving-puncture implementation of the BSSN equations in
several numerical codes. We discuss the effect of the new metric terms on junk
radiation and continuity of physical radiation extracted.Comment: 13 pages, 9 figures. Invited paper from Numerical Relativity and Data
Analysis (NRDA) 2009, Albert Einstein Institute, Potsdam. Corrected to match
published version
On consecutive pattern-avoiding permutations of length 4, 5 and beyond
We review and extend what is known about the generating functions for
consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their
asymptotic behaviour. There are respectively, seven length-4 and twenty-five
length-5 consecutive-Wilf classes. D-finite differential equations are known
for the reciprocal of the exponential generating functions for four of the
length-4 and eight of the length-5 classes. We give the solutions of some of
these ODEs. An unsolved functional equation is known for one more class of
length-4, length-5 and beyond. We give the solution of this functional
equation, and use it to show that the solution is not D-finite. For three
further length-5 c-Wilf classes we give recurrences for two and a
differential-functional equation for a third. For a fourth class we find a new
algebraic solution. We give a polynomial-time algorithm to generate the
coefficients of the generating functions which is faster than existing
algorithms, and use this to (a) calculate the asymptotics for all classes of
length 4 and length 5 to significantly greater precision than previously, and
(b) use these extended series to search, unsuccessfully, for D-finite solutions
for the unsolved classes, leading us to conjecture that the solutions are not
D-finite. We have also searched, unsuccessfully, for differentially algebraic
solutions.Comment: 23 pages, 2 figures (update of references, plus web link to
enumeration data). Minor update. Typos corrected. One additional referenc
Separability and distillability in composite quantum systems -a primer-
Quantum mechanics is already 100 years old, but remains alive and full of
challenging open problems. On one hand, the problems encountered at the
frontiers of modern theoretical physics like Quantum Gravity, String Theories,
etc. concern Quantum Theory, and are at the same time related to open problems
of modern mathematics. But even within non-relativistic quantum mechanics
itself there are fundamental unresolved problems that can be formulated in
elementary terms. These problems are also related to challenging open questions
of modern mathematics; linear algebra and functional analysis in particular.
Two of these problems will be discussed in this article: a) the separability
problem, i.e. the question when the state of a composite quantum system does
not contain any quantum correlations or entanglement and b) the distillability
problem, i.e. the question when the state of a composite quantum system can be
transformed to an entangled pure state using local operations (local refers
here to component subsystems of a given system).
Although many results concerning the above mentioned problems have been
obtained (in particular in the last few years in the framework of Quantum
Information Theory), both problems remain until now essentially open. We will
present a primer on the current state of knowledge concerning these problems,
and discuss the relation of these problems to one of the most challenging
questions of linear algebra: the classification and characterization of
positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod.
Optics, minor typos corrected, references adde
- …