31,624 research outputs found
Aperiodic and correlated disorder in XY-chains: exact results
We study thermodynamic properties, specific heat and susceptibility, of XY
quantum chains with coupling constants following arbitrary substitution rules.
Generalizing an exact renormalization group transformation, originally
formulated for Ising quantum chains, we obtain exact relevance criteria of
Harris-Luck type for this class of models. For two-letter substitution rules, a
detailed classification is given of sequences leading to irrelevant, marginal
or relevant aperiodic modulations. We find that the relevance of the same
aperiodic sequence of couplings in general will be different for XY and Ising
quantum chains. By our method, continuously varying critical exponents may be
calculated exactly for arbitrary (two-letter) substitution rules with marginal
aperiodicity. A number of examples are given, including the period-doubling,
three-folding and precious mean chains. We also discuss extensions of the
renormalization approach to a special class of long-range correlated random
chains, generated by random substitutions.Comment: 19 page
Uniform Substitution for Differential Game Logic
This paper presents a uniform substitution calculus for differential game
logic (dGL). Church's uniform substitutions substitute a term or formula for a
function or predicate symbol everywhere. After generalizing them to
differential game logic and allowing for the substitution of hybrid games for
game symbols, uniform substitutions make it possible to only use axioms instead
of axiom schemata, thereby substantially simplifying implementations. Instead
of subtle schema variables and soundness-critical side conditions on the
occurrence patterns of logical variables to restrict infinitely many axiom
schema instances to sound ones, the resulting axiomatization adopts only a
finite number of ordinary dGL formulas as axioms, which uniform substitutions
instantiate soundly. This paper proves soundness and completeness of uniform
substitutions for the monotone modal logic dGL. The resulting axiomatization
admits a straightforward modular implementation of dGL in theorem provers
Generalized Heisenberg algebras and k-generalized Fibonacci numbers
It is shown how some of the recent results of de Souza et al. [1] can be
generalized to describe Hamiltonians whose eigenvalues are given as
k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases
considered by de Souza et al. corespond to k=2.Comment: 8 page
Pac-Learning Recursive Logic Programs: Efficient Algorithms
We present algorithms that learn certain classes of function-free recursive
logic programs in polynomial time from equivalence queries. In particular, we
show that a single k-ary recursive constant-depth determinate clause is
learnable. Two-clause programs consisting of one learnable recursive clause and
one constant-depth determinate non-recursive clause are also learnable, if an
additional ``basecase'' oracle is assumed. These results immediately imply the
pac-learnability of these classes. Although these classes of learnable
recursive programs are very constrained, it is shown in a companion paper that
they are maximally general, in that generalizing either class in any natural
way leads to a computationally difficult learning problem. Thus, taken together
with its companion paper, this paper establishes a boundary of efficient
learnability for recursive logic programs.Comment: See http://www.jair.org/ for any accompanying file
Some Novel Applications of Explanation-Based Learning to Parsing Lexicalized Tree-Adjoining Grammars
In this paper we present some novel applications of Explanation-Based
Learning (EBL) technique to parsing Lexicalized Tree-Adjoining grammars. The
novel aspects are (a) immediate generalization of parses in the training set,
(b) generalization over recursive structures and (c) representation of
generalized parses as Finite State Transducers. A highly impoverished parser
called a ``stapler'' has also been introduced. We present experimental results
using EBL for different corpora and architectures to show the effectiveness of
our approach.Comment: uuencoded postscript fil
Black holes and neutron stars in the generalized tensor-vector-scalar theory
Bekenstein's Tensor-Vector-Scalar (TeVeS) theory has had considerable success
as a relativistic theory of Modified Newtonian Dynamics (MoND). However, recent
work suggests that the dynamics of the theory are fundamentally flawed and
numerous authors have subsequently begun to consider a generalization of TeVeS
where the vector field is given by an Einstein-Aether action. Herein, I develop
strong-field solutions of the generalized TeVeS theory, in particular exploring
neutron stars as well as neutral and charged black holes. I find that the
solutions are identical to the neutron star and black hole solutions of the
original TeVeS theory, given a mapping between the parameters of the two
theories, and hence provide constraints on these values of the coupling
constants. I discuss the consequences of these results in detail including the
stability of such spacetimes as well as generalizations to more complicated
geometries.Comment: Accepted for publication in Physical Review
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