13 research outputs found

    On Generating Binary Words Palindromically

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    We regard a finite word u=u1u2⋯unu=u_1u_2\cdots u_n up to word isomorphism as an equivalence relation on {1,2,
,n}\{1,2,\ldots, n\} where ii is equivalent to jj if and only if xi=xj.x_i=x_j. Some finite words (in particular all binary words) are generated by "{\it palindromic}" relations of the form k∌j+i−kk\sim j+i-k for some choice of 1≀i≀j≀n1\leq i\leq j\leq n and k∈{i,i+1,
,j}.k\in \{i,i+1,\ldots,j\}. That is to say, some finite words uu are uniquely determined up to word isomorphism by the position and length of some of its palindromic factors. In this paper we study the function ÎŒ(u)\mu(u) defined as the least number of palindromic relations required to generate u.u. We show that every aperiodic infinite word must contain a factor uu with ÎŒ(u)≄3,\mu(u)\geq 3, and that some infinite words xx have the property that ÎŒ(u)≀3\mu(u)\leq 3 for each factor uu of x.x. We obtain a complete classification of such words on a binary alphabet (which includes the well known class of Sturmian words). In contrast for the Thue-Morse word, we show that the function ÎŒ\mu is unbounded

    Combinatorics on Words. New Aspects on Avoidability, Defect Effect, Equations and Palindromes

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    In this thesis we examine four well-known and traditional concepts of combinatorics on words. However the contexts in which these topics are treated are not the traditional ones. More precisely, the question of avoidability is asked, for example, in terms of k-abelian squares. Two words are said to be k-abelian equivalent if they have the same number of occurrences of each factor up to length k. Consequently, k-abelian equivalence can be seen as a sharpening of abelian equivalence. This fairly new concept is discussed broader than the other topics of this thesis. The second main subject concerns the defect property. The defect theorem is a well-known result for words. We will analyze the property, for example, among the sets of 2-dimensional words, i.e., polyominoes composed of labelled unit squares. From the defect effect we move to equations. We will use a special way to define a product operation for words and then solve a few basic equations over constructed partial semigroup. We will also consider the satisfiability question and the compactness property with respect to this kind of equations. The final topic of the thesis deals with palindromes. Some finite words, including all binary words, are uniquely determined up to word isomorphism by the position and length of some of its palindromic factors. The famous Thue-Morse word has the property that for each positive integer n, there exists a factor which cannot be generated by fewer than n palindromes. We prove that in general, every non ultimately periodic word contains a factor which cannot be generated by fewer than 3 palindromes, and we obtain a classification of those binary words each of whose factors are generated by at most 3 palindromes. Surprisingly these words are related to another much studied set of words, Sturmian words.Siirretty Doriast

    On prefixal factorizations of words

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    We consider the class P1{\cal P}_1 of all infinite words x∈Aωx\in A^\omega over a finite alphabet AA admitting a prefixal factorization, i.e., a factorization x=U0U1U2⋯x= U_0 U_1U_2 \cdots where each UiU_i is a non-empty prefix of x.x. With each x∈P1x\in {\cal P}_1 one naturally associates a "derived" infinite word ÎŽ(x)\delta(x) which may or may not admit a prefixal factorization. We are interested in the class P∞{\cal P}_{\infty} of all words xx of P1{\cal P}_1 such that ÎŽn(x)∈P1\delta^n(x) \in {\cal P}_1 for all n≄1n\geq 1. Our primary motivation for studying the class P∞{\cal P}_{\infty} stems from its connection to a coloring problem on infinite words independently posed by T. Brown in \cite{BTC} and by the second author in \cite{LQZ}. More precisely, let P{\bf P} be the class of all words x∈Aωx\in A^\omega such that for every finite coloring φ:A+→C\varphi : A^+ \rightarrow C there exist c∈Cc\in C and a factorization x=V0V1V2⋯x= V_0V_1V_2\cdots with φ(Vi)=c\varphi(V_i)=c for each i≄0.i\geq 0. In \cite{DPZ} we conjectured that a word x∈Px\in {\bf P} if and only if xx is purely periodic. In this paper we show that P⊆P∞,{\bf P}\subseteq {\cal P}_{\infty}, so in other words, potential candidates to a counter-example to our conjecture are amongst the non-periodic elements of P∞.{\cal P}_{\infty}. We establish several results on the class P∞{\cal P}_{\infty}. In particular, we show that a Sturmian word xx belongs to P∞{\cal P}_{\infty} if and only if xx is nonsingular, i.e., no proper suffix of xx is a standard Sturmian word

    Sensitivity of the Burrows-Wheeler Transform to small modifications, and other problems on string compressors in Bioinformatics

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    Extensive amount of data is produced in textual form nowadays, especially in bioinformatics. Several algorithms exist to store and process this data efficiently in compressed space. In this thesis, we focus on both combinatorial and practical aspects of two of the most widely used algorithms for compressing text in bioinformatics: the Burrows-Wheeler Transform (BWT) and Lempel-Ziv compression (LZ77). In the first part, we focus on combinatorial aspects of the BWT. Given a word v, r = r(v) denotes the number of maximal equal-letter runs in BWT(v). First, we investigate the relationship between r of a word and r of its reverse. We prove that there exist words for which these two values differ by a logarithmic factor in the length of the word. In other words, although the repetitiveness in the two words is preserved, the number of runs can change by a non-constant factor. This suggests that the number of runs may not be an ideal repetitiveness measure. The second combinatorial aspect we are interested in is how small alterations in a word may affect its BWT in a relevant way. We prove that the number of runs of the BWT of a word can change (increase or decrease) by up to a logarithmic factor in the length of the word by just adding, removing, or substituting a single character. We then consider the special character usedinreal−lifeapplicationstomarktheendofaword.WeinvestigatetheimpactofthischaracteronwordswithrespecttotheBWT.Wecharacterizepositionsinawordwhere used in real-life applications to mark the end of a word. We investigate the impact of this character on words with respect to the BWT. We characterize positions in a word where can be inserted in order to turn it into the BWT of a −terminatedwordoverthesamealphabet.Weshowthat,whetherandwhere-terminated word over the same alphabet. We show that, whether and where is allowed, depends entirely on the structure of a specific permutation of the indices of the word, which is called the standard permutation of the word. The final part of this thesis treats more applied aspects of text compressors. In bioinformatics, BWT-based compressed data structures are widely used for pattern matching. We give an algorithm based on the BWT to find Maximal Unique Matches (MUMs) of a pattern with respect to a reference text in compressed space, extending an existing tool called PHONI [Boucher et. al, DCC 2021]. Finally, we study some aspects of the Lempel-Ziv 77 (LZ77) factorization of a word. Modeling DNA short reads, we provide a bound on the compression size of the concatenation of regular samples of a word

    Batch and incremental learning of decision trees

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    Strategic Transgressions and Agency in Postcolonial Indian Literature in English: Rohinton Mistry, Arundhati Roy, and Salman Rushdie

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    Transgression as a mode of resistance and transformation is significant yet largely untheorized in postcolonial literature. This dissertation is concerned with theoretical and textual practices by which transgression can be studied as a locus of agency and difference toward the possibility of fostering moments and spaces of transformation. To that end, it explores various enabling counter-hegemonic modes of strategy and tactic with a focus on the body in the texts of Rohinton Mistry, Arundhati Roy, and Salman Rushdie. Transgression does not simply give rise to the capacity of resistance to transform the dominant structure. Rather than dwelling on a mere sequence or repeat of events, this dissertation focuses on critical points of grounding for a new beginning as well as powerful metaphorical effects of practice, which defy essentialist discourses and raise possibilities of an alternative discursive space. Drawing upon a range of textual examples, the study critically examines not only the workings of prevailing norms but also the ways in which transgressive desire and practice enable marginalized characters to become ‘bodies that matter’ rather than being banished to the ‘abject zone.’ This dissertation reflects a complex intertwining of postcolonial, sexuality and gender, feminist, and cultural studies vis-à-vis transgression and agency. Therefore, the arguments made in this study represent an array of ideas drawn from various disciplines and discourses, especially from theorists such as Michel Foucault, Homi Bhabha, Judith Butler, Gayatri Spivak, Edward Said, Bill Ashcroft, Mikhail Bakhtin, and Jacques Lacan. This hybrid approach puts essentialist discourses—mediated by colonial history and postcolonial reality—under scrutiny to rethink the question of power and agency in exploring the possibility of subaltern others’ transformation into subjects of their own history and experience in specific contexts. By arguing the importance of the strategic use of essentialism based on everyday practice, I also emphasize the need to problematize the hegemonic concept of history so as to trace reterritorialization and repossession on the part of the silenced or invisible who live on borrowed time in minimal space. The highlight of this research is to explore how the established boundaries are expanded, redefined and redrawn in the circulatory, recursive structure of transgression and protest, opening the way for transforming oppression or abjection into agency. With this critical lens in mind, I heed the dynamics of similarity and difference in the narrative as a framework of postcolonial critique to provide a new reading of postcolonial texts

    Eco-Traffic: Globalization, Materiality, and Subalternity in Asia-Pacific Literature

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    This project implicates globalization – the spreading of capital, neoliberalism, and Western totalitarianism – as a primary contributor to the continuing subalternity of colonized cultures and environments in the Global South. Under the guise of shrinking the world or spreading freedom, globalization has resulted in profound material consequences to biomes attempting political decolonization. Where postcolonial theory demands that attention be paid to anthropological difference, be it social, political, economic, or gendered, some ecocritical scholars of the Anthropocene wish to decenter the human from an era in which they – as a species – have emerged as a hazardous geologic force. This project offers “traffic” as a literal and metaphorical framework for the meshing of human subalternity within the material biomes of the Asia-Pacific region, as captured in literature. Examining texts from India, Sri Lanka, Hong Kong, Taiwan, and the United States reveals multiple traffics within globalization that intertwine the subaltern subject within their environs: the mapping and zoning of cities, the congestion of foreign-made automobiles and persons within cities, and the historical and current trade of illegal narcotics and humans. The dissertation actively contributes to a developing subset of ecocriticism that recognizes the subaltern in the intra-action of environmental entities, showing that each animal, plant, object and person has its own vibrancy, its own directionality, which leads to congestion and accidents, but often to new pathways

    Artless Gardens: Time, space, and the ‘ritual of cultural identity’ in music by Veljo Tormis

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    Attracting such diverse labels as ‘a modern shaman’s call’ and ‘bland inventions,’ Veljo Tormis’s (b. 1930) music has drawn a cult following, in spite – or because of – its simplicity, which may be seen as unchallenging or monotonous. Is this minimalistic, non-linear, monumental, ‘ecological’ music solely based on features of ancient Estonian runic folk song, or does it bear fingerprints of trauma? Does it embody the alleged qualities of indigenous Estonian culture that the poet Jaan Kaplinski has promoted as crucial to an idealized ‘Finno-Ugric mode of seeing’? Or is it just another product of the homogenizing meat grinder of Socialist Realism – ‘glib, bland, and corny’? Is it a Soviet ‘nationalist’ prototype, shunted along the via negativa production line and filled with carbon copies of authentic Estonian content? Or is it an invaluable ‘ritual of cultural identity’? Beyond their superficial correlation with Soviet-approved nation-building projects, their popular accessibility, reliance on folk material, and an apparent general avoidance of the vilified ‘bourgeois formalism,’ Tormis’s ‘bland inventions’ betray a network of connections with the ‘postmodern,’ the post-traumatic, and the (notionally) ‘Finno-Ugric.’ The music itself might at first seem unremarkable, but its relationships with contextual issues are more nuanced and complicated. This thesis builds on extant scholarship, firstly, by taking a slightly different approach to analysis of this music. Focusing on how Tormis’s work might be perceived can allow for connections to be made with a wider variety of extra-musical ideas – perhaps to a greater extent than a more technical or ‘classificatory’ analysis (which also seems unsuitable given the simplicity of much of the music in question). This study also attempts to broaden the frames of reference of the (English language) conversation around this music. A more ‘critical’ approach to the study of Tormis’s work and its context here involves engagement with anthropology, philosophy, and literary theory and its borrowings from feminist theory and psychoanalysis. Analytical and ‘critical’ observations are distributed across four chapters dealing with essentially separable but interrelated themes: ‘Repetition and Ritual’; ‘Time and Telos’; ‘Balance and Biophilia’; and ‘Boundaries and Binaries’

    Self-Determination, Sovereignty and History: Situating Zionism in the Settler-Colonial Archive

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    Pre-existing models of Zionism as a Central European organic nationalist movement have sought to locate its rise to historic prominence primarily in the context of British imperial instrumentality which Zionist national histories themselves that have sought to emphasize. This thesis finds this specific connection unsatisfying, and therefore takes a broader historic and thematic view. Using the settler colonial research paradigm as a starting point, and its inherently comparative, trans-national and trans-historical perspective, it will attempt to trace several genealogies. The first, of the post-Enlightenment construction of the reasoning subject and the theory of self-determination, would be constituted against, and in front of, or prior to, the extended world, and the Others of a similarly constructed “mankind” that were seen to inhabit it. Through the philosophies of these self-determining subjects in common, in relation to private property and to the state that would secure it for them, it will come to an as yet unresolved problem of the sovereign subject and the universalization of that subject’s freedom in the sovereignty of the modern democratic state, a problem that many European thinkers would seek the resolution of in the potentiality of the settler colonial frontier. A second genealogy will trace the self-determining subjects of post-Enlightenment philosophy as they made their transits on the stage of history in and between what James Belich termed the “Settler Empire.” This imperium, encompassing the Second British Empire and the United States of America, contained and produced imagined communities, myths of racialized identity, technologies of racial government and settlement and attitudes to history and the future of the planet, that prefigured Zionism and practices of the state of Israel, which have proven to be one of its lasting legacies. A final genealogy will trace the sacred and secular messianic of Protestantism in Britain and America, which I argue after Gabriel Piterberg and Amnon Raz-Krakotzkin shows that Zionism is largely a continuance of Christian historicism and restorationist traditions rather than of the Jewish tradition and that the history of Protestantism in the settler colonial world had profound import on this development historically. This argument is reinforced by a close reading of key Christian and Jewish Zionist texts, analysed from the perspective of comparative settler colonial studies. This reveals that key ideological tropes of Zionism were pre-figured in the Christian Zionist tradition, that Jewish Zionism re-articulated Christian restorationist traditions, and importantly, that the legacies of settler colonial histories played an important role in shaping the development of Zionist ideology and the work of some of its key thinkers. The genealogy ultimately concludes that British elites and Zionist lobbyists in 1917 in many ways shared the same teleology of history and notion of history itself and their adoption of the Balfour Declaration was in large part consequence of this. The thesis closes by returning to the question of the unresolved problem of the universalization of self-determination in the modern democratic state and the question of sovereign violence in said state. This was a problem that European thought arguably has never fully resolved, but has found a heuristic outlet for the playing out of these issues in the open frontier of the settler colonies. We will show h0w profoundly dangerous a heuristic scheme this is by closely examining the play of sovereignties on the settler colonial frontier in America, Australia and then in contemporary Palestine, to indicate that such heuristic outlets are not to be seen as “practices of freedom” but rather mechanisms of structural invasion, elimination, and necropolitical violence
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