62,467 research outputs found
Embedding a -invariant code into a complete one
Let A be a finite or countable alphabet and let be a literal
(anti-)automorphism onto A * (by definition, such a correspondence is
determinated by a permutation of the alphabet). This paper deals with sets
which are invariant under (-invariant for short) that is,
languages L such that (L) is a subset of L.We establish an extension
of the famous defect theorem. With regards to the so-called notion of
completeness, we provide a series of examples of finite complete
-invariant codes. Moreover, we establish a formula which allows to
embed any non-complete -invariant code into a complete one. As a
consequence, in the family of the so-called thin --invariant codes,
maximality and completeness are two equivalent notions.Comment: arXiv admin note: text overlap with arXiv:1705.0556
Origin of symbol-using systems: speech, but not sign, without the semantic urge
Natural language—spoken and signed—is a multichannel phenomenon, involving facial and body expression, and voice and visual intonation that is often used in the service of a social urge to communicate meaning. Given that iconicity seems easier and less abstract than making arbitrary connections between sound and meaning, iconicity and gesture have often been invoked in the origin of language alongside the urge to convey meaning. To get a fresh perspective, we critically distinguish the origin of a system capable of evolution from the subsequent evolution that system becomes capable of. Human language arose on a substrate of a system already capable of Darwinian evolution; the genetically supported uniquely human ability to learn a language reflects a key contact point between Darwinian evolution and language. Though implemented in brains generated by DNA symbols coding for protein meaning, the second higher-level symbol-using system of language now operates in a world mostly decoupled from Darwinian evolutionary constraints. Examination of Darwinian evolution of vocal learning in other animals suggests that the initial fixation of a key prerequisite to language into the human genome may actually have required initially side-stepping not only iconicity, but the urge to mean itself. If sign languages came later, they would not have faced this constraint
Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors
DNA as a data storage medium has several advantages, including far greater
data density compared to electronic media. We propose that schemes for data
storage in the DNA of living organisms may benefit from studying the
reconstruction problem, which is applicable whenever multiple reads of noisy
data are available. This strategy is uniquely suited to the medium, which
inherently replicates stored data in multiple distinct ways, caused by
mutations. We consider noise introduced solely by uniform tandem-duplication,
and utilize the relation to constant-weight integer codes in the Manhattan
metric. By bounding the intersection of the cross-polytope with hyperplanes, we
prove the existence of reconstruction codes with greater capacity than known
error-correcting codes, which we can determine analytically for any set of
parameters.Comment: 11 pages, 2 figures, Latex; version accepted for publicatio
Review on DNA Cryptography
Cryptography is the science that secures data and communication over the
network by applying mathematics and logic to design strong encryption methods.
In the modern era of e-business and e-commerce the protection of
confidentiality, integrity and availability (CIA triad) of stored information
as well as of transmitted data is very crucial. DNA molecules, having the
capacity to store, process and transmit information, inspires the idea of DNA
cryptography. This combination of the chemical characteristics of biological
DNA sequences and classical cryptography ensures the non-vulnerable
transmission of data. In this paper we have reviewed the present state of art
of DNA cryptography.Comment: 31 pages, 12 figures, 6 table
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