389 research outputs found
A Backtracking-Based Algorithm for Computing Hypertree-Decompositions
Hypertree decompositions of hypergraphs are a generalization of tree
decompositions of graphs. The corresponding hypertree-width is a measure for
the cyclicity and therefore tractability of the encoded computation problem.
Many NP-hard decision and computation problems are known to be tractable on
instances whose structure corresponds to hypergraphs of bounded
hypertree-width. Intuitively, the smaller the hypertree-width, the faster the
computation problem can be solved. In this paper, we present the new
backtracking-based algorithm det-k-decomp for computing hypertree
decompositions of small width. Our benchmark evaluations have shown that
det-k-decomp significantly outperforms opt-k-decomp, the only exact hypertree
decomposition algorithm so far. Even compared to the best heuristic algorithm,
we obtained competitive results as long as the hypergraphs are not too large.Comment: 19 pages, 6 figures, 3 table
High precision Monte Carlo study of the 3D XY-universality class
We present a Monte Carlo study of the two-component model on the
simple cubic lattice in three dimensions. By suitable tuning of the coupling
constant we eliminate leading order corrections to scaling. High
statistics simulations using finite size scaling techniques yield
and , where the statistical and
systematical errors are given in the first and second bracket, respectively.
These results are more precise than any previous theoretical estimate of the
critical exponents for the 3D XY universality class.Comment: 13 page
Perfect Scalars on the Lattice
We perform renormalization group transformations to construct optimally local
perfect lattice actions for free scalar fields of any mass. Their couplings
decay exponentially. The spectrum is identical to the continuum spectrum, while
thermodynamic quantities have tiny lattice artifacts. To make such actions
applicable in simulations, we truncate the couplings to a unit hypercube and
observe that spectrum and thermodynamics are still drastically improved
compared to the standard lattice action. We show how preconditioning techniques
can be applied successfully to this type of action. We also consider a number
of variants of the perfect lattice action, such as the use of an anisotropic or
triangular lattice, and modifications of the renormalization group
transformations motivated by wavelets. Along the way we illuminate the
consistent treatment of gauge fields, and we find a new fermionic fixed point
action with attractive properties.Comment: 26 pages, 11 figure
The XY Model and the Three-state Antiferromagnetic Potts model in Three Dimensions: Critical Properties from Fluctuating Boundary Conditions
We present the results of a Monte Carlo study of the three-dimensional XY
model and the three-dimensional antiferromagnetic three-state Potts model. In
both cases we compute the difference in the free energies of a system with
periodic and a system with antiperiodic boundary conditions in the
neighbourhood of the critical coupling. From the finite-size scaling behaviour
of this quantity we extract values for the critical temperature and the
critical exponent nu that are compatible with recent high statistics Monte
Carlo studies of the models. The results for the free energy difference at the
critical temperature and for the exponent nu confirm that both models belong to
the same universality class.Comment: 13 pages, latex-file+2 ps-files KL-TH-94/8 and CERN-TH.7290/9
ON THE LOW-TEMPERATURE ORDERING OF THE 3D ATIFERROMAGNETIC THREE-STATE POTTS MODEL
The antiferromagnetic three-state Potts model on the simple-cubic lattice is
studied using Monte Carlo simulations. The ordering in a medium temperature
range below the critical point is investigated in detail. Two different regimes
have been observed: The so-called broken sublattice-symmetry phase dominates at
sufficiently low temperatures, while the phase just below the critical point is
characterized by an effectively continuous order parameter and by a fully
restored rotational symmetry. However, the later phase is not the
permutationally sublattice symmetric phase recently predicted by the cluster
variation method.Comment: 20 pages with 9 figures in a single postscript file (compressed and
uuencoded by uufiles -gz -9) plus two big figures in postscript file
Observable Signature of the Berezinskii-Kosterlitz-Thouless Transition in a Planar Lattice of Bose-Einstein Condensates
We investigate the possibility that Bose-Einstein condensates (BECs), loaded
on a 2D optical lattice, undergo - at finite temperature - a
Berezinskii-Kosterlitz-Thouless (BKT) transition. We show that - in an
experimentally attainable range of parameters - a planar lattice of BECs is
described by the XY model at finite temperature. We demonstrate that the
interference pattern of the expanding condensates provides the experimental
signature of the BKT transition by showing that, near the critical temperature,
the k=0 component of the momentum distribution and the central peak of the
atomic density profile sharply decrease. The finite-temperature transition for
a 3D optical lattice is also discussed, and the analogies with superconducting
Josephson junction networks are stressed through the text
Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model
on the three-dimensional simple cubic lattice with nearest neighbour
interactions. For this purpose, we use Monte Carlo simulations in connection
with a finite size scaling method. We find that there exists a finite value of
the coupling lambda^*, for both values of N, where leading corrections to
scaling vanish. As a first application, we compute the critical exponents
nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for
N=4.Comment: 21 pages, 2 figure
Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules
Association rules are among the most widely employed data analysis methods in
the field of Data Mining. An association rule is a form of partial implication
between two sets of binary variables. In the most common approach, association
rules are parameterized by a lower bound on their confidence, which is the
empirical conditional probability of their consequent given the antecedent,
and/or by some other parameter bounds such as "support" or deviation from
independence. We study here notions of redundancy among association rules from
a fundamental perspective. We see each transaction in a dataset as an
interpretation (or model) in the propositional logic sense, and consider
existing notions of redundancy, that is, of logical entailment, among
association rules, of the form "any dataset in which this first rule holds must
obey also that second rule, therefore the second is redundant". We discuss
several existing alternative definitions of redundancy between association
rules and provide new characterizations and relationships among them. We show
that the main alternatives we discuss correspond actually to just two variants,
which differ in the treatment of full-confidence implications. For each of
these two notions of redundancy, we provide a sound and complete deduction
calculus, and we show how to construct complete bases (that is,
axiomatizations) of absolutely minimum size in terms of the number of rules. We
explore finally an approach to redundancy with respect to several association
rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape
On the tree-transformation power of XSLT
XSLT is a standard rule-based programming language for expressing
transformations of XML data. The language is currently in transition from
version 1.0 to 2.0. In order to understand the computational consequences of
this transition, we restrict XSLT to its pure tree-transformation capabilities.
Under this focus, we observe that XSLT~1.0 was not yet a computationally
complete tree-transformation language: every 1.0 program can be implemented in
exponential time. A crucial new feature of version~2.0, however, which allows
nodesets over temporary trees, yields completeness. We provide a formal
operational semantics for XSLT programs, and establish confluence for this
semantics
Quantum phase transitions in the J-J' Heisenberg and XY spin-1/2 antiferromagnets on square lattice: Finite-size scaling analysis
We investigate the critical parameters of an order-disorder quantum phase
transitions in the spin-1/2 Heisenberg and XY antiferromagnets on square
lattice. Basing on the excitation gaps calculated by exact diagonalization
technique for systems up to 32 spins and finite-size scaling analysis we
estimate the critical couplings and exponents of the correlation length for
both models. Our analysis confirms the universal critical behavior of these
quantum phase transitions: They belong to 3D O(3) and 3D O(2) universality
classes, respectively.Comment: 7 pages, 3 figure
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