Palindromes

We define a new relation on words by a finite series of insertions and/or deletions of palindromic subwords. In particular we concentrate on insertion or deletion of Watson–Crick palindromes. We show that the new relation ∼θ is, in fact, an equivalence relation where θ is any arbitrary antimorphic involution that is not the identity on the letters of the alphabet. We also show that the set of all θ-palindromic free words defined in (Daley et al. in preparation) is ∼θ-independent. Using the relation we define a new subclass of primitive words which we call as ∼θ-primitive words and show that the class of all ∼θ-primitive words is closed under circular permutations. We also define ∼θ-conjugates and ∼θ-commutativity and study the properties of such words and show that they are similar to that of conjugate words and words that commute.

Set against the back drop of the Belgian Congo made famous by Heart of Darkness by Joseph Conrad, Barbara Kingsolver‟s The Poisonwood Bible depicts the trial and tribulation of a missionary's family and the inner lives of its five women protagonists who travel to Belgian Congo in the wake of the family patriarch, Mr. Price. By presenting the story through the narrative voices of Orleanna Price, the wife of the missionary and her four daughters, Kingsolver explores issues of "double colonisation" of women through colonial and post-colonial times. Western women traveling to Africa during colonization find themselves in a problematic position insofar as they consider themselves superior to the natives or colonized and yet are disempowered within Western patriarchy. In order to cope with the contradictory position in which they find themselves they employ different strategies for survival. The intersection of colonial and feminist discourses in the novel creates ambivalenc...

In this paper we consider several types of equations on words, motivated by the attempt of characterizing the class of polyominoes that tile the plane by translation in two distinct ways. Words coding the boundary of these polyominoes satisfy an equation whose solutions are in bijection with a subset of the solutions of equations of the form ABA˜B˜≡XYX˜Y˜. It turns

A transcription of Machaut's Rondeau 14, "Ma fin est ma commencement" ("my end is my beginning"). The score is rendered to be read both forwards and backwards as necessitated by the music. For an animated video of the score with a performance visit https://www.youtube.com/watch?v=dcfPr4IN2MM

Archeoastronomia: un'interpretazione astronomica del quadrato magico del Sator proposta alla luce dello splendido e recentissimo rinvenimento di Aosta. Nella chiesa dedicata a Sant'Orso, ad Aosta, è infatti venuto alla luce un grande mosaico, risalente al XII secolo, carico di significati simbolici e religiosi. La peculiarità della scritta, disposta in forma circolare, suggerisce una nuova e più convincente interpretazione del Sator.

В статье рассматривается ряд формальных литературных приемов, основанных на математических закономерностях. Эти приемы предложили и (или) практиковали участники французской группы "УЛИПО", основанной Раймоном Кено и Франсуа Ле Лионне. В статье обсуждается необходимость формальных ограничений для литературного творчества. - Опубликовано в журнале "Новое литературное обозрение", 57 (2002), cc.246-270.

The discovery of the pilot wave that creates a simple algorithm that allows access to the Quantum Gravitational Memories. In the Memories are found nearly infinite amounts of data and information presented by the waves in the form of animated high definition hologram videos. This information gives clear and concise explanations of how palindromes combine with gravity to create the cosmological constant, strong and weak force. Introducing entirely new concepts and strong evidence that gravity is the reaction to coiled light wave expansion and these coils when passing through a magnetic field create Alternating Current = to the Cosmological constant of 1 x10^120 .

El presente estudio consiste en un análisis en torno a los palíndromos utilizados por el compositor Anton Webern, localizados específicamente en su Sinfonía Opus 21 (Segundo movimiento). Este trabajo recorre y reúne algunos análisis existentes sobre esta particularidad.

Se conoce a Juan Filloy como el escritor de tres siglos y el autor de miles de palíndromos que, según él, le confieren el récord mundial (Ambort 59). Escribió aproximadamente cincuenta novelas, la mitad de las cuales permanece inédita todavía; la primera, Periplo, se publicó en 1930 y la última, Decio 8A, en 1997. Hubo un lapso de silencio entre la publicación de Finesse (1939) y la reedición en 1967 de Op Oloop (1934) después de lo cual volvió a publicar con más frecuencia. Filloy explica que su silencio se debió a su carrera como juez en Río Cuarto, Argentina, donde vivió por casi toda su vida. En el presente ensayo, me interesa analizar el gesto político y estético de "Yo y los intrusos", un cuento que apareció en Yo, yo y yo. (Monodiálogos paranoicos) en 1971, en diálogo con sus ensayos sobre el arte de escribir palíndromos que se publicaron en Karcino. Tratado de palindromía (1988). En primer lugar, interpreto el cuento como la ficcionalización de los palíndromos en la estructura de la torre-cueva desde el "desierto" argentino donde el protagonista del cuento se refugia. En segundo lugar, esta torre-cueva se presta para una lectura alegórica que se asemeja a la de la caverna de Platón; por otro lado, el cuento de Filloy requiere una lectura al revés como si fuera un palíndromo, pero un palíndromo errante e irónico. Así, el texto de Filloy abre un nuevo itinerario que atraviesa los discursos políticos y estéticos de los años sesenta y setenta desde la ficción.

Some music, more than others, prompts heightened awareness of the passage of time—certainly some passages from Beethoven’s late sonatas and quartets, or, in Feldman’s Rothko Chapel, the chord conspicuously sustained by the chorus whose time is marked by the toll of chimes. Ben Boretz’s string quartet Qixingshan (2011) is in this category, but with a difference: its self-conscious temporality is much more infused with teleology or directedness. It puts its ears ever to the future—in this case perhaps a future of geological change, change which is usually slow, but which in some geological formations can also be violently quick.  The article presents an analysis of the Boretz's quartet Qixingshan. Connections to Stravinsky, Gershwin, 12-tone theory, canon, and palindrome are discussed.

The paper analyzes the phenomenon of wolf in apocryphal prayers, whether those be the prayers referring to the direct action taken against the rabid wolf, or the ones in which wolf appears only as a segment, but which are aimed at the healing of “nežit” as a major disease or the main cause of all diseases. The appearance of palin-drome apocryphal saToR aREpo formula is particularly significant. Though apoc-ryphal in nature, it is recorded in religious service books and religious literature. in apocryphal prayers wolf occurs either as a demonic animal, with the fore-sign “ex -traneous”, hence the need for the protection from it, as well as for the healing from its bite and transmitted rabies disease, or a wolf becomes the means by which the disease is transmitted from man to the other side, transcending the world of the domestic, sacred and pure. Key  words:  wolf,  apocryphal  prayer,  rabies,  palindrome,  formula,  magic, healing, Stuplje, Studenica
*
У  раду  се  анализира  појава  вука  у  апокрифним  молитвама, било  да  се  ради  о  молитвама  које  су  усмерене  на  директно  дело-вање против бесног вука, било да се ради о молитвама у којима се само као сегмент појављује вук, а које су усмерене на исцељење од нежита као главне болести или главног узрока свим болестима. Као посебно битна узима се појава палиндромске апокрифне формуле saToR aREpo, која, иако апокрифна по природи, постоји у запи-сима на богослужбеним књигама и верској литератури. Дефинише се двострука појавност: вука као демонског бића од којег се човек штити, и као средства, преносника болести од човека до места ње-ног ишчезнућа. кључне  речи:  вук,  апокрифна  молитва,  беснило,  палиндром, формула, магија, исцељење, Ступље, Студеница

In 1979 and 1980, Word Ways: The Journal of Recreational Linguistics printed a series of articles on the early history, religious symbolism, and cultural significance of the rotas square, an ancient Latin-language palindromic word square.  The articles were attributed to Dmitri A. Borgmann, the noted American writer on wordplay and former editor of Word Ways.  While they attracted little attention at the time, some 35 years after their publication (and 29 years after Borgmann's death), questions began to be raised about their authorship.  There is much internal and external evidence that, taken together, compellingly supports the notion that Borgmann did not write the articles himself.  This paper surveys this evidence and solicits help in identifying the articles' original source.

The Y-chromosome is a powerful tool for population geneticists to study human evolutionary history. Haploid and largely non-recombining, it should contain a simple record of past mutational events. However, this apparent simplicity is compromised by Y-linked duplicons, which make up ∼ 35% of this chromosome; 25% of these duplicons are large inverted repeats (palindromes). For microsatellites lying in these palindromes, two loci cannot be easily distinguished due to PCR co-amplification, and this order misspecification of alleles generates an additional variance component. Due to this ambiguity, population geneticists have traditionally used an arbitrary method to assign the alleles (shorter allele to locus 1, larger allele to locus 2). Here, we simulate these posterior estimate distributions under three different novel allele assignment priors and compare this with the original method. We use a sample of 33 human populations, typed for duplicated microsatellites lying within palindrome P8, to illustrate our approach. We show that both intra-and inter-population statistics can be dramatically affected by order misspecification. Surprisingly, matrices of pairwise F-statistics or distance estimates appear far less sensitive to order misspecification and remain relatively unchanged under the priors considered, suggesting that these microsatellites can be considered as useful markers for population genetic studies using an appropriate data treatment. Duplicated microsatellites represent an attractive source of information to investigate the extensive structural polymorphism observed among human Y chromosomes, as well as processes of intra-chromosomal gene conversion acting between duplicons.

A lossless compression algorithm, for genetic sequences, based on searching individual exact Repeats, Reverse, Complement & Palindrome is reported. The compression results obtained in the algorithm show that the exact R2CP are one of the main hidden regularities in DNA sequences. The proposed DNA sequence compression algorithm is based on R2CP substring and creates online Library file. The substrings are replaced by corresponding ASCII characters starting from 33(!). The substring length depends on the user. The online library file acts as a signature. Our main objective was to reduce the compression ratio, called 1st pass compression, again compress it using any compression algorithm for better compression ratio is called 2nd pass compression and send it over the mail such that the receiver gets the DNA sequences in more compressed format. We compressed it using Huffman algorithm in 2nd pass compression. The reverse process has been applied to get the original DNA sequence. Information security is the most challenging question for protecting data from unauthorized user, this proposed method may protect the data from hackers. When a user searches for any sequence for an organism, an encrypted compressed sequence file can be sent from the data source to the user. The encrypted compressed file then can be decompressed at the client end resulting in reduced transmission time over the Internet. A encrypted compression algorithm that provides a moderately high compression ratio with encryption minimal decompression time. Compressing the genome sequences will help to increase the efficiency of their uses. This algorithm is tested on benchmark DNA sequences and also tested on Reverse, Complement & Reverse Complement of the hole DNA sequences and artificial DNA sequences also their other orientation. The algorithm can approach a compression ratio in repeat techniques on normal sequence of 3.5940 bit/base ,better than other three orientation and at the REVHUFF algorithm can approach a compression ratio of 2.143942 bit/base

During Jacques Derrida’s earlier phases, his stylistique acts-out (in the sense of "performs") the same project evident in his semantic. Derridean stylistic practice and thematics both undertake the project of deconstructing entitative thinking. Anglophonic philosophers often ignore (or cannot even detect) his stylistic games, which are often Talmudic in provenance or unique to French. Derrida did not have an express Buddhist agenda, but two of my well-received past books do show that Derridean deconstruction intersects with Mādhyamikan deconstruction of the self-identical. (Intersection does not imply "common ground": lines have no width so there is no "common ground" when they intersect). This article demonstrates Derridean/Buddhist intersections via (1) themes (cryptically) undoing themselves, (2) image motifs undoing themselves, (3) ambiguous referents dissolving Proper Names, (4) the "Uncanny" deconstructing logic, (5) enumeration undoing ontology, and (6) homophones and homographs unsettling  correspondence-theory. The article closes with an exhibition of how Derrida's "free-floating syllables," "floating graphic traits," "palindromes," and "scrambled words" function to dissolve entitative constructs.
Keywords:    Jacques Derrida  Buddhism  deconstruction  stylistique  Mādhyamaka  Śūnyatā

Trapezoidal words are words having at most n+1 distinct factors of length n for every n ≥ 0. They therefore encompass finite Sturmian words. We give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration. We then separate trapezoidal words into two disjoint classes: open and closed. A trapezoidal word is closed if it has a factor that occurs only as a prefix and as a suffix; otherwise it is open. We investigate open and closed trapezoidal words, in relation with their special factors. We prove that Sturmian palindromes are closed trapezoidal words and that a closed trapezoidal word is a Sturmian palindrome if and only if its longest repeated prefix is a palindrome. We also define a new class of words, semicentral words, and show that they are characterized by the property that they can be written as uxyu, for a central word u and two different letters x, y. Finally, we investigate the prefixes of the Fibonacci word with respect to the property of being open or closed trapezoidal words, and show that the sequence of open and closed prefixes of the Fibonacci word follows the Fibonacci sequence.

Single-and multi-base (loop) mismatches can arise in DNA by replication errors, during recombination, and by chemical modification of DNA. Single-base and loop mismatches of several nucleotides are efficiently repaired in mammalian cells by a nick-directed, MSH2-dependent mechanism. Larger loop mismatches (≥12 bases) are repaired by an MSH2-independent mechanism. Prior studies have shown that 12-and 14-base palindromic loops are repaired with bias toward loop retention, and that repair bias is eliminated when five single-base mismatches flank the loop mismatch. Here we show that one single-base mismatch near a 12-base palindromic loop is sufficient to eliminate loop repair bias in wild-type, but not MSH2-defective mammalian cells. We also show that palindromic loop and single-base mismatches separated by 12 bases are repaired independently at least 10% of the time in wild-type cells, and at least 30% of the time in MSH2-defective cells. Palindromic loop and single-base mismatches separated by two bases were never repaired independently. These and other data indicate that loop repair tracts are variable in length. All tracts extend at least 2 bases, some extend <12 bases, and others >12 bases, on one side of the loop. These properties distinguish palindromic loop mismatch repair from the three known excision repair pathways: base excision repair which has one to six base tracts, nucleotide excision repair which has ∼30 base tracts, and MSH2-dependent mismatch repair, which has tracts that extend for several hundred bases.

A four-page article about palindromic poetry that traces a feminine genealogy, considering Su Hui's multi-directional, fourth-century, Star Gauge; Sinologist and Oulipo member Michèle Métail's study, Wild Geese Returning: Chinese Reversible Forms; Erika Greber's "Chronotope of Revolution"; and Jen Bervin's contemporary poetry and embroidery project, Silk Poems; closing with an original palindromic poem by me.

Visual Poetry: Tacit Ore strives to make bijoux (a reversible necklace) of seven letters, palindromically arrayed on the collarbones. Each dangling line is also a palindrome that in one way or another describes the glyph from which it dangles: Some reference the glyph’s visual appearance, others its phonetic qualities.

In this paper we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if ϑ is an involutory antimorphism of A * , then both ϑ-palindromic closures of any factor of a ϑ-standard word are also factors of some ϑ-standard word. We also introduce the class of pseudostandard words with "seed", obtained by iterated pseudopalindrome closure starting from a nonempty word. We prove that pseudostandard words with seed are morphic images of standard episturmian words. Moreover, for any given pseudostandard word s with seed, there exists an integer N such that for any n ≥ N , s has at most one right (resp. left) special factor of length n. * The work for this paper has been supported by the Italian Ministry of Education under Project COFIN 2005 -Automi e Linguaggi Formali: aspetti matematici e applicativi.

We give an O(n log n)-time, O(n)-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string S[1..n], in O(n log n) time our algorithm returns the minimum number of palindromes S 1 ,. .. , S ℓ such that S = S 1 • • • S ℓ. We also show that the time complexity is O(n) on average and Ω(n log n) in the worst case. The last result is based on a characterization of the palindromic structure of Zimin words.

In this paper we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if ϑ is an involutory antimorphism of A * , then both ϑ-palindromic closures of any factor of a ϑ-standard word are also factors of some ϑ-standard word. We also introduce the class of pseudostandard words with "seed", obtained by iterated pseudopalindrome closure starting from a nonempty word. We prove that pseudostandard words with seed are morphic images of standard episturmian words. Moreover, for any given pseudostandard word s with seed, there exists an integer N such that for any n ≥ N , s has at most one right (resp. left) special factor of length n. * The work for this paper has been supported by the Italian Ministry of Education under Project COFIN 2005 -Automi e Linguaggi Formali: aspetti matematici e applicativi.

We investigate the least number of palindromic factors in an infinite word. We first consider general alphabets, and give answers to this problem for periodic and non-periodic words, closed or not under reversal of factors. We then investigate the same problem when the alphabet has size two.

The artistic and literary practices in Internet have achieved, in addition to consolidating a fragmented aesthetic,
the ambitious avant-garde project of dematerialization of the work of art. New electronic creations
reflect a different logic from the textual reality of the book-object: the logic of access or distribution practiced
by many of the artists on social networks. In this paper I will focus on two of the most interesting creations
in the Mexican “Twitterature” because of the success and ingenious of its professional and amateur practitioners:
the #Amalgamas and palindromes.

This paper discusses four newly discovered technopaegnia in Musaeus’s Hero and
Leander. The author argues that they are interconnected and constitute a complex
literary game that spreads almost over the whole poem. The characteristic elements
of the technopaegnia discussed in the article are the apostrophes, their palindromic
character, and the numbers 9 and 10. Based on the latter feature, the author tries to
show that lines 1-10 hide references to the Pythagoreans’ teachings about the first ten
numbers.

The Y-chromosome is a powerful tool for population geneticists to study human evolutionary history. Haploid and largely non-recombining, it should contain a simple record of past mutational events. However, this apparent simplicity is compromised by Y-linked duplicons, which make up ∼ 35% of this chromosome; 25% of these duplicons are large inverted repeats (palindromes). For microsatellites lying in these palindromes, two loci cannot be easily distinguished due to PCR co-amplification, and this order misspecification of alleles generates an additional variance component. Due to this ambiguity, population geneticists have traditionally used an arbitrary method to assign the alleles (shorter allele to locus 1, larger allele to locus 2). Here, we simulate these posterior estimate distributions under three different novel allele assignment priors and compare this with the original method. We use a sample of 33 human populations, typed for duplicated microsatellites lying within palindrome P8, to illustrate our approach. We show that both intra-and inter-population statistics can be dramatically affected by order misspecification. Surprisingly, matrices of pairwise F-statistics or distance estimates appear far less sensitive to order misspecification and remain relatively unchanged under the priors considered, suggesting that these microsatellites can be considered as useful markers for population genetic studies using an appropriate data treatment. Duplicated microsatellites represent an attractive source of information to investigate the extensive structural polymorphism observed among human Y chromosomes, as well as processes of intra-chromosomal gene conversion acting between duplicons.

In this paper we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if ϑ is an involutory antimorphism of A * , then both ϑ-palindromic closures of any factor of a ϑ-standard word are also factors of some ϑ-standard word. We also introduce the class of pseudostandard words with "seed", obtained by iterated pseudopalindrome closure starting from a nonempty word. We prove that pseudostandard words with seed are morphic images of standard episturmian words. Moreover, for any given pseudostandard word s with seed, there exists an integer N such that for any n ≥ N , s has at most one right (resp. left) special factor of length n. * The work for this paper has been supported by the Italian Ministry of Education under Project COFIN 2005 -Automi e Linguaggi Formali: aspetti matematici e applicativi.