33,577 research outputs found
Locations of multicritical points for spin glasses on regular lattices
We present an analysis leading to precise locations of the multicritical
points for spin glasses on regular lattices. The conventional technique for
determination of the location of the multicritical point was previously derived
using a hypothesis emerging from duality and the replica method. In the present
study, we propose a systematic technique, by an improved technique, giving more
precise locations of the multicritical points on the square, triangular, and
hexagonal lattices by carefully examining relationship between two partition
functions related with each other by the duality. We can find that the
multicritical points of the Ising model are located at
on the square lattice, where means the probability of ,
at on the triangular lattice, and at on the
hexagonal lattice. These results are in excellent agreement with recent
numerical estimations.Comment: 17pages, this is the published version with some minnor corrections.
Previous title was "Precise locations of multicritical points for spin
glasses on regular lattices
Pressure inequalities for nuclear and neutron matter
We prove several inequalities using lowest-order effective field theory for
nucleons which give an upper bound on the pressure of asymmetric nuclear matter
and neutron matter. We prove two types of inequalities, one based on convexity
and another derived from shifting an auxiliary field.Comment: 16 pages, published journal version - includes inequalities for spin
polarized system
Analytical learning and term-rewriting systems
Analytical learning is a set of machine learning techniques for revising the representation of a theory based on a small set of examples of that theory. When the representation of the theory is correct and complete but perhaps inefficient, an important objective of such analysis is to improve the computational efficiency of the representation. Several algorithms with this purpose have been suggested, most of which are closely tied to a first order logical language and are variants of goal regression, such as the familiar explanation based generalization (EBG) procedure. But because predicate calculus is a poor representation for some domains, these learning algorithms are extended to apply to other computational models. It is shown that the goal regression technique applies to a large family of programming languages, all based on a kind of term rewriting system. Included in this family are three language families of importance to artificial intelligence: logic programming, such as Prolog; lambda calculus, such as LISP; and combinatorial based languages, such as FP. A new analytical learning algorithm, AL-2, is exhibited that learns from success but is otherwise quite different from EBG. These results suggest that term rewriting systems are a good framework for analytical learning research in general, and that further research should be directed toward developing new techniques
Inductive types in the Calculus of Algebraic Constructions
In a previous work, we proved that an important part of the Calculus of
Inductive Constructions (CIC), the basis of the Coq proof assistant, can be
seen as a Calculus of Algebraic Constructions (CAC), an extension of the
Calculus of Constructions with functions and predicates defined by higher-order
rewrite rules. In this paper, we prove that almost all CIC can be seen as a
CAC, and that it can be further extended with non-strictly positive types and
inductive-recursive types together with non-free constructors and
pattern-matching on defined symbols.Comment: Journal version of TLCA'0
Bootstrapping Lexical Choice via Multiple-Sequence Alignment
An important component of any generation system is the mapping dictionary, a
lexicon of elementary semantic expressions and corresponding natural language
realizations. Typically, labor-intensive knowledge-based methods are used to
construct the dictionary. We instead propose to acquire it automatically via a
novel multiple-pass algorithm employing multiple-sequence alignment, a
technique commonly used in bioinformatics. Crucially, our method leverages
latent information contained in multi-parallel corpora -- datasets that supply
several verbalizations of the corresponding semantics rather than just one.
We used our techniques to generate natural language versions of
computer-generated mathematical proofs, with good results on both a
per-component and overall-output basis. For example, in evaluations involving a
dozen human judges, our system produced output whose readability and
faithfulness to the semantic input rivaled that of a traditional generation
system.Comment: 8 pages; to appear in the proceedings of EMNLP-200
Generalization of the Fortuin-Kasteleyn transformation and its application to quantum spin simulations,
We generalize the Fortuin-Kasteleyn (FK) cluster representation of the
partition function of the Ising model to represent the partition function of
quantum spin models with an arbitrary spin magnitude in arbitrary dimensions.
This generalized representation enables us to develop a new cluster algorithm
for the simulation of quantum spin systems by the worldline Monte Carlo method.
Because the Swendsen-Wang algorithm is based on the FK representation, the new
cluster algorithm naturally includes it as a special case. As well as the
general description of the new representation, we present an illustration of
our new algorithm for some special interesting cases: the Ising model, the
antiferromagnetic Heisenberg model with , and a general Heisenberg model.
The new algorithm is applicable to models with any range of the exchange
interaction, any lattice geometry, and any dimensions.Comment: 46 pages, 10 figures, to appear in J.Stat.Phy
Tree Regular Model Checking for Lattice-Based Automata
Tree Regular Model Checking (TRMC) is the name of a family of techniques for
analyzing infinite-state systems in which states are represented by terms, and
sets of states by Tree Automata (TA). The central problem in TRMC is to decide
whether a set of bad states is reachable. The problem of computing a TA
representing (an over- approximation of) the set of reachable states is
undecidable, but efficient solutions based on completion or iteration of tree
transducers exist. Unfortunately, the TRMC framework is unable to efficiently
capture both the complex structure of a system and of some of its features. As
an example, for JAVA programs, the structure of a term is mainly exploited to
capture the structure of a state of the system. On the counter part, integers
of the java programs have to be encoded with Peano numbers, which means that
any algebraic operation is potentially represented by thousands of applications
of rewriting rules. In this paper, we propose Lattice Tree Automata (LTAs), an
extended version of tree automata whose leaves are equipped with lattices. LTAs
allow us to represent possibly infinite sets of interpreted terms. Such terms
are capable to represent complex domains and related operations in an efficient
manner. We also extend classical Boolean operations to LTAs. Finally, as a
major contribution, we introduce a new completion-based algorithm for computing
the possibly infinite set of reachable interpreted terms in a finite amount of
time.Comment: Technical repor
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