333,333 research outputs found
A new characteristic property of rich words
Originally introduced and studied by the third and fourth authors together
with J. Justin and S. Widmer in arXiv:0801.1656, rich words constitute a new
class of finite and infinite words characterized by containing the maximal
number of distinct palindromes. Several characterizations of rich words have
already been established. A particularly nice characteristic property is that
all 'complete returns' to palindromes are palindromes. In this note, we prove
that rich words are also characterized by the property that each factor is
uniquely determined by its longest palindromic prefix and its longest
palindromic suffix.Comment: 6 page
A new characteristic property of rich words
Originally introduced and studied by the third and fourth authors together with J. Justin and S. Widmer (2008), rich words constitute a new class of finite and infinite words characterized by containing the maximal number of distinct palindromes. Several characterizations of rich words have already been established. A particularly nice characteristic property is that all 'complete returns' to palindromes are palindromes. In this note, we prove that rich words are also characterized by the property that each factor is uniquely determined by its longest palindromic prefix and its longest palindromic suffix
Closed, Palindromic, Rich, Privileged, Trapezoidal, and Balanced Words in Automatic Sequences
We prove that the property of being closed (resp., palindromic, rich,
privileged trapezoidal, balanced) is expressible in first-order logic for
automatic (and some related) sequences. It therefore follows that the
characteristic function of those n for which an automatic sequence x has a
closed (resp., palindromic, privileged, rich, trape- zoidal, balanced) factor
of length n is automatic. For privileged words this requires a new
characterization of the privileged property. We compute the corresponding
characteristic functions for various famous sequences, such as the Thue-Morse
sequence, the Rudin-Shapiro sequence, the ordinary paperfolding sequence, the
period-doubling sequence, and the Fibonacci sequence. Finally, we also show
that the function counting the total number of palindromic factors in a prefix
of length n of a k-automatic sequence is not k-synchronized
Generalized Signal Richness Preservation Problem and Vandermonde-Form Preserving Matrices
In this paper, a theoretical problem arising in digital communications, namely the generalized signal richness preservation problem, is addressed and studied. In order to solve the problem, a special class of square matrices, namely the "Vandermonde-form preserving" (VFP) matrices, is introduced and found to be highly relevant to the problem. Several properties of VFP matrices are studied in detail. The necessary and sufficient conditions of the problem have been found, and a systematic proof is also presented
Repetitions in infinite palindrome-rich words
Rich words are characterized by containing the maximum possible number of
distinct palindromes. Several characteristic properties of rich words have been
studied; yet the analysis of repetitions in rich words still involves some
interesting open problems. We address lower bounds on the repetition threshold
of infinite rich words over 2 and 3-letter alphabets, and construct a candidate
infinite rich word over the alphabet with a small critical
exponent of . This represents the first progress on an open
problem of Vesti from 2017.Comment: 12 page
Fingerprint for Network Topologies
A network's topology information can be given as an adjacency matrix. The
bitmap of sorted adjacency matrix(BOSAM) is a network visualisation tool which
can emphasise different network structures by just looking at reordered
adjacent matrixes. A BOSAM picture resembles the shape of a flower and is
characterised by a series of 'leaves'. Here we show and mathematically prove
that for most networks, there is a self-similar relation between the envelope
of the BOSAM leaves. This self-similar property allows us to use a single
envelope to predict all other envelopes and therefore reconstruct the outline
of a network's BOSAM picture. We analogise the BOSAM envelope to human's
fingerprint as they share a number of common features, e.g. both are simple,
easy to obtain, and strongly characteristic encoding essential information for
identification.Comment: 12papes, 3 figures, in pres
The Commons Concept and Intellectual Property Rights Regime: Whither Plant Genetic Resources and Traditional Knowledge?
[Excerpt] The classification of plant genetic resources (PGRs) as the common heritage of humankind continues to generate controversies. The debate is between developing countries that are the primary sources of these resources and industrialized, biotechnologically advanced countries that appropriate and utilize PGRs as raw materials for various commercial products, such as medicine, seed variety, or pesticides. Scholars of diverse backgrounds express various opinions on whether PGRs obtained from plants found within a territory of a sovereign state should properly be designated âcommon heritage of humankindâ or regarded as part of the âcommons,â and therefore freely accessible. The debate also extends to and challenges the status of traditional knowledge on the uses of PGRs. The dominant but not necessarily the correct view is that such knowledge is information in the public domain, incapable of private ownership or control
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