Computing the antiperiod(s) of a string

A string S[1, n] is a power (or repetition or tandem repeat) of order k and period n/k, if it can be decomposed into k consecutive identical blocks of length n/k. Powers and periods are fundamental structures in the study of strings and algorithms to compute them efficiently have been widely studied. Recently, Fici et al. (Proc. ICALP 2016) introduced an antipower of order k to be a string composed of k distinct blocks of the same length, n/k, called the antiperiod. An arbitrary string will have antiperiod t if it is prefix of an antipower with antiperiod t. In this paper, we describe efficient algorithm for computing the smallest antiperiod of a string S of length n in O(n) time. We also describe an algorithm to compute all the antiperiods of S that runs in O(n log n) time. © Hayam Alamro, Golnaz Badkobeh, Djamal Belazzougui, Costas S. Iliopoulos, and Simon J. Puglisi.Peer reviewe

Circular pattern matching with k mismatches

The k-mismatch problem consists in computing the Hamming distance between a pattern P of length m and every length-m substring of a text T of length n, if this distance is no more than k. In many real-world applications, any cyclic shift of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P. This is the circular pattern m

Internal Quasiperiod Queries

Internal pattern matching requires one to answer queries about factors of a given string. Many results are known on answering internal period queries, asking for the periods of a given factor. In this paper we investigate (for the first time) internal queries asking for covers (also known as quasiperiods) of a given factor. We propose a data structure that answers such queries in $O(\log n \log \log n)$ time for the shortest cover and in $O(\log n (\log \log n)^2)$ time for a representation of all the covers, after $O(n \log n)$ time and space preprocessing.Comment: To appear in the SPIRE 2020 proceeding

Circular pattern matching with k mismatches

We consider the circular pattern matching with k mismatches (k-CPM) problem in which one is to compute the minimal Hamming distance of every length-m substring of T and any cyclic rotation of P, if this distance is no more than k. It is a variation of the well-studied k-mismatch problem. A multitude of papers has been devoted

Powers and Anti-Powers in Binary Words

Fici et al. recently introduced the notion of anti-powers in the context of combinatorics on words. A power (also called tandem repeat) is a sequence of consecutive identical blocks. An anti-power is a sequence of consecutive distinct blocks of the same length. Fici et al. showed that the existence of powers or anti-powers is an unavoidable regularity for sufficiently long words. In this thesis we explore this notion further in the context of binary words and obtain new results

On the Concept of Power

This dissertation provides a definition of “power”, and examines the implication of said definition for the study of politics. The exam of extant debates, from Dahl to Lukes and Morriss, shows that a proper definition of power is still to be had; those so far proposed are either circular and/or so detached from the concept’s meaning in ordinary language that they cease to be about power. Re-connecting power to its meaning in natural languages is the necessary premise to any study of politics, be it empirical, theoretical, or normative: without the concept of power, we could not conceive of politics as a specific domain, either to be scientifically inquired or acted into. To formulate a viable definition, we have to recognize that “power” is not a “thing” or phenomenon, but rather refers to a state, or a modality, within which persons may be situated. Power is a modal concept, and the relevant modality, or category, is that of possibility. More specifically, “power” denotes the status, or condition, of having possibilities available and representing them as such. If and only if both conditions are present, then power can meaningfully be attributed. The implications of this definition are far reaching, as they show how, by adopting perspectives that variously eschew the category of possibility, significant portions of political science and political philosophy are, by their own design, incapable of properly conceptualizing power, and therefore politics. The main problem with political science is the attempt to methodologically reduce politics to causal and probabilistic regularities, which entails the disappearance of possibility in favor of necessity. Political philosophy, on the other hand, tends to prioritize various forms of a teleologically oriented normativity, which results in discarding possibility in favor of necessity, again losing sight of politics

Forming responsible citizens in the euro-mediterranean region empowering youth as agents for sustainable human development

Accessing and obtaining a value-based quality education is the foundation for youth to become agents for sustainable development. Building on Amartya Sen’s capabilities approach as a basis for human-centred education policies, the MA thesis endeavours in an investigation on the role of citizenship education with respect to sustainable human development. The analysis and assessment of ideaborn’s “Forming Responsible Citizens” (FRC) experience in Tunisia highlight that citizenship education can be valuable as an instrument in itself as well as a methodology and behaviour applied to education in general, provided that it is anchored in a democratic educational ecosystem that is conducive of sustainable human development