332,987 research outputs found
On the complexity of computing the capacity of codes that avoid forbidden difference patterns
We consider questions related to the computation of the capacity of codes
that avoid forbidden difference patterns. The maximal number of -bit
sequences whose pairwise differences do not contain some given forbidden
difference patterns increases exponentially with . The exponent is the
capacity of the forbidden patterns, which is given by the logarithm of the
joint spectral radius of a set of matrices constructed from the forbidden
difference patterns. We provide a new family of bounds that allows for the
approximation, in exponential time, of the capacity with arbitrary high degree
of accuracy. We also provide a polynomial time algorithm for the problem of
determining if the capacity of a set is positive, but we prove that the same
problem becomes NP-hard when the sets of forbidden patterns are defined over an
extended set of symbols. Finally, we prove the existence of extremal norms for
the sets of matrices arising in the capacity computation. This result makes it
possible to apply a specific (even though non polynomial) approximation
algorithm. We illustrate this fact by computing exactly the capacity of codes
that were only known approximately.Comment: 7 pages. Submitted to IEEE Trans. on Information Theor
Termination of Rewriting with and Automated Synthesis of Forbidden Patterns
We introduce a modified version of the well-known dependency pair framework
that is suitable for the termination analysis of rewriting under forbidden
pattern restrictions. By attaching contexts to dependency pairs that represent
the calling contexts of the corresponding recursive function calls, it is
possible to incorporate the forbidden pattern restrictions in the (adapted)
notion of dependency pair chains, thus yielding a sound and complete approach
to termination analysis. Building upon this contextual dependency pair
framework we introduce a dependency pair processor that simplifies problems by
analyzing the contextual information of the dependency pairs. Moreover, we show
how this processor can be used to synthesize forbidden patterns suitable for a
given term rewriting system on-the-fly during the termination analysis.Comment: In Proceedings IWS 2010, arXiv:1012.533
Forbidden patterns and shift systems
The scope of this paper is two-fold. First, to present to the researchers in
combinatorics an interesting implementation of permutations avoiding
generalized patterns in the framework of discrete-time dynamical systems.
Indeed, the orbits generated by piecewise monotone maps on one-dimensional
intervals have forbidden order patterns, i.e., order patterns that do not occur
in any orbit. The allowed patterns are then those patterns avoiding the
so-called forbidden root patterns and their shifted patterns. The second scope
is to study forbidden patterns in shift systems, which are universal models in
information theory, dynamical systems and stochastic processes. Due to its
simple structure, shift systems are accessible to a more detailed analysis and,
at the same time, exhibit all important properties of low-dimensional chaotic
dynamical systems (e.g., sensitivity to initial conditions, strong mixing and a
dense set of periodic points), allowing to export the results to other
dynamical systems via order-isomorphisms.Comment: 21 pages, expanded Section 5 and corrected Propositions 3 and
Universal diagrams for te waves guided by thin films bounded by saturable nonlinear media
It is shown that universal V-b diagrams provide a powerful tool when analyzing the stationary waveguiding properties of the TE waves guided by a thin film bounded by a saturable nonlinear substrate or cladding. For a wide class of nonlinearities, the allowed and forbidden regions of these diagrams, for a stationary guided propagation to occur, display a universal pattern, the marginal loci separating different allowed regions from the forbidden ones being simple functions of only the asymmetry measure of the waveguide and the saturation value of the nonlinear permittivity. Relevant information for device design purposes is summarized on a few diagrams, so general waveguiding properties can be immediately read-off from them, and threshold power-independent values of the normalized thickness of the waveguide for a particular kind of guided wave to be allowed are obtained. Qualitative information concerning both the guided power and the stability of guided waves is also included in the diagrams.Peer ReviewedPostprint (published version
Sequential weak measurement
The notion of weak measurement provides a formalism for extracting
information from a quantum system in the limit of vanishing disturbance to its
state. Here we extend this formalism to the measurement of sequences of
observables. When these observables do not commute, we may obtain information
about joint properties of a quantum system that would be forbidden in the usual
strong measurement scenario. As an application, we provide a physically
compelling characterisation of the notion of counterfactual quantum
computation
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