10,208 research outputs found
On Properties of Update Sequences Based on Causal Rejection
We consider an approach to update nonmonotonic knowledge bases represented as
extended logic programs under answer set semantics. New information is
incorporated into the current knowledge base subject to a causal rejection
principle enforcing that, in case of conflicts, more recent rules are preferred
and older rules are overridden. Such a rejection principle is also exploited in
other approaches to update logic programs, e.g., in dynamic logic programming
by Alferes et al. We give a thorough analysis of properties of our approach, to
get a better understanding of the causal rejection principle. We review
postulates for update and revision operators from the area of theory change and
nonmonotonic reasoning, and some new properties are considered as well. We then
consider refinements of our semantics which incorporate a notion of minimality
of change. As well, we investigate the relationship to other approaches,
showing that our approach is semantically equivalent to inheritance programs by
Buccafurri et al. and that it coincides with certain classes of dynamic logic
programs, for which we provide characterizations in terms of graph conditions.
Therefore, most of our results about properties of causal rejection principle
apply to these approaches as well. Finally, we deal with computational
complexity of our approach, and outline how the update semantics and its
refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and
Practice of Logic Programming
On arithmetic and asymptotic properties of up-down numbers
Let , where , and let
denote the number of permutations of whose
up-down signature , for .
We prove that the set of all up-down numbers can be expressed by
a single universal polynomial , whose coefficients are products of
numbers from the Taylor series of the hyperbolic tangent function. We prove
that is a modified exponential, and deduce some remarkable congruence
properties for the set of all numbers , for fixed . We prove a
concise upper-bound for , which describes the asymptotic behaviour
of the up-down function in the limit .Comment: Recommended for publication in Discrete Mathematics subject to
revision
Exact dynamics of the critical Kauffman model with connectivity one
The critical Kauffman model with connectivity one is the simplest class of
critical Boolean networks. Nevertheless, it exhibits intricate behavior at the
boundary of order and chaos. We introduce a formalism for expressing the
dynamics of multiple loops as a product of the dynamics of individual loops.
Using it, we prove that the number of attractors scales as , where is
the number of nodes in loops - as fast as possible, and much faster than
previously believed
Properties of the recursive divisor function and the number of ordered factorizations
We recently introduced the recursive divisor function , a
recursive analogue of the usual divisor function. Here we calculate its
Dirichlet series, which is . We show that
is related to the ordinary divisor function by , where * denotes the Dirichlet convolution.
Using this, we derive several identities relating and some standard
arithmetic functions. We also clarify the relation between and the
much-studied number of ordered factorizations , namely,
Applying weighted network measures to microarray distance matrices
In recent work we presented a new approach to the analysis of weighted
networks, by providing a straightforward generalization of any network measure
defined on unweighted networks. This approach is based on the translation of a
weighted network into an ensemble of edges, and is particularly suited to the
analysis of fully connected weighted networks. Here we apply our method to
several such networks including distance matrices, and show that the clustering
coefficient, constructed by using the ensemble approach, provides meaningful
insights into the systems studied. In the particular case of two data sets from
microarray experiments the clustering coefficient identifies a number of
biologically significant genes, outperforming existing identification
approaches.Comment: Accepted for publication in J. Phys.
Transition from a Tomonaga-Luttinger liquid to a Fermi liquid in potassium intercalated bundles of single wall carbon nanotubes
We report on the first direct observation of a transition from a
Tomonaga-Luttinger liquid to a Fermi liquid behavior in potassium intercalated
mats of single wall carbon nanotubes (SWCNT). Using high resolution
photoemission spectroscopy an analysis of the spectral shape near the Fermi
level reveals a Tomonaga-Luttinger liquid power law scaling in the density of
states for the pristine sample and for low dopant concentration. As soon as the
doping is high enough to fill bands of the semiconducting tubes a distinct
transition to a bundle of only metallic SWCNT with a scaling behavior of a
normal Fermi liquid occurs. This can be explained by a strong screening of the
Coulomb interaction between charge carriers and/or an increased hopping matrix
element between the tubes.Comment: 5 pages, 4 figure
An ensemble approach to the analysis of weighted networks
We present a new approach to the calculation of measures in weighted
networks, based on the translation of a weighted network into an ensemble of
edges. This leads to a straightforward generalization of any measure defined on
unweighted networks, such as the average degree of the nearest neighbours, the
clustering coefficient, the `betweenness', the distance between two nodes and
the diameter of a network. All these measures are well established for
unweighted networks but have hitherto proven difficult to define for weighted
networks. Further to introducing this approach we demonstrate its advantages by
applying the clustering coefficient constructed in this way to two real-world
weighted networks.Comment: 4 pages 3 figure
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