65,282 research outputs found
Axioms for graph clustering quality functions
We investigate properties that intuitively ought to be satisfied by graph
clustering quality functions, that is, functions that assign a score to a
clustering of a graph. Graph clustering, also known as network community
detection, is often performed by optimizing such a function. Two axioms
tailored for graph clustering quality functions are introduced, and the four
axioms introduced in previous work on distance based clustering are
reformulated and generalized for the graph setting. We show that modularity, a
standard quality function for graph clustering, does not satisfy all of these
six properties. This motivates the derivation of a new family of quality
functions, adaptive scale modularity, which does satisfy the proposed axioms.
Adaptive scale modularity has two parameters, which give greater flexibility in
the kinds of clusterings that can be found. Standard graph clustering quality
functions, such as normalized cut and unnormalized cut, are obtained as special
cases of adaptive scale modularity.
In general, the results of our investigation indicate that the considered
axiomatic framework covers existing `good' quality functions for graph
clustering, and can be used to derive an interesting new family of quality
functions.Comment: 23 pages. Full text and sources available on:
http://www.cs.ru.nl/~T.vanLaarhoven/graph-clustering-axioms-2014
Non-perturbative \lambda\Phi^4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
During the '70, several relativistic quantum field theory models in
and also in have been constructed in a non-perturbative way. That was
done in the so-called {\it constructive quantum field theory} approach, whose
main results have been obtained by a clever use of Euclidean functional
methods. Although in the construction of a single model there are several
technical steps, some of them involving long proofs, the constructive quantum
field theory approach contains conceptual insights about relativistic quantum
field theory that deserved to be known and which are accessible without
entering in technical details. The purpose of this note is to illustrate such
insights by providing an oversimplified schematic exposition of the simple case
of (with ) in . Because of the absence of
ultraviolet divergences in its perturbative version, this simple example
-although does not capture all the difficulties in the constructive quantum
field theory approach- allows to stress those difficulties inherent to the
non-perturbative definition. We have made an effort in order to avoid several
of the long technical intermediate steps without missing the main ideas and
making contact with the usual language of the perturbative approach.Comment: 63 pages. Typos correcte
Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
We study the form factors of local operators of integrable QFT's between
states with finite energy density. These states arise, for example, at finite
temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form
factor axioms, formulating them for a set of particle/hole excitations on top
of the thermodynamic background, instead of the vacuum. We show that exact form
factors can be found as minimal solutions of these new axioms. The
thermodynamic form factors can be used to construct correlation functions on
thermodynamic states. The expression found for the two-point function is
similar to the conjectured LeClair-Mussardo formula, but using the new form
factors dressed by the thermodynamic background, and with all singularities
properly regularized. We study the different infrared asymptotics of the
thermal two-point function, and show there generally exist two different
regimes, manifesting massive exponential decay, or effectively gapless behavior
at long distances, respectively. As an example, we compute the few-excitations
form factors of vertex operators for the sinh-Gordon model.Comment: 41 pages, 10 figure
Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative
We answer Klop and de Vrijer's question whether adding surjective-pairing
axioms to the extensional lambda calculus yields a conservative extension. The
answer is positive. As a byproduct we obtain a "syntactic" proof that the
extensional lambda calculus with surjective pairing is consistent.Comment: To appear in Logical Methods in Computer Scienc
String field theory vertex from integrability
We propose a framework for computing the (light cone) string field theory
vertex in the case when the string worldsheet QFT is a generic integrable
theory. The prime example and ultimate goal would be the
superstring theory cubic string vertex and the chief application will be to use
this framework as a formulation for SYM theory OPE coefficients
valid at any coupling up to wrapping corrections. In this paper we propose
integrability axioms for the vertex, illustrate them on the example of the
pp-wave string field theory and also uncover similar structures in weak
coupling computations of OPE coefficients.Comment: pdflatex, 52 pages, 20 figures,v2: references added, typos correcte
Tableaux Modulo Theories Using Superdeduction
We propose a method that allows us to develop tableaux modulo theories using
the principles of superdeduction, among which the theory is used to enrich the
deduction system with new deduction rules. This method is presented in the
framework of the Zenon automated theorem prover, and is applied to the set
theory of the B method. This allows us to provide another prover to Atelier B,
which can be used to verify B proof rules in particular. We also propose some
benchmarks, in which this prover is able to automatically verify a part of the
rules coming from the database maintained by Siemens IC-MOL. Finally, we
describe another extension of Zenon with superdeduction, which is able to deal
with any first order theory, and provide a benchmark coming from the TPTP
library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117
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