Towards a statement of the S-adic conjecture through examples

The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be "a good Condition $C$".Comment: 2

On the subword complexity of Thue–Morse polynomial extractions

AbstractLet the (subword) complexity of a sequence u=(un)n=0∞ over a finite set Σ be the function m↦Pu(m), where Pu(m) is the number of distinct blocks of length m in u. Let t=(tn)n=0∞ denote the Thue–Morse sequence. In this paper we study the complexity of the sequences tH=(tH(n))n=0∞, when H(n)∈Q[n] is a polynomial with H(N)⊆N. In particular, we solve an open problem of Allouche and Shallit regarding (tn2)n=0∞. We also study the vector space over Z/2Z, spanned by the sequences tH

Asymptotic Abelian Complexities of Certain Morphic Binary Words

We study asymptotic Abelian complexities of morphic binary words. We completethe classification of upper Abelian complexities of pure morphic binary words initiatedrecently by F. Blanchet-Sadri, N. Rampersad, and N. Fox. We also study a class ofmorphic binary words having different asymptotic factor complexities despite havingthe same asymptotic Abelian complexity.</p

Script Effects as the Hidden Drive of the Mind, Cognition, and Culture

This open access volume reveals the hidden power of the script we read in and how it shapes and drives our minds, ways of thinking, and cultures. Expanding on the Linguistic Relativity Hypothesis (i.e., the idea that language affects the way we think), this volume proposes the “Script Relativity Hypothesis” (i.e., the idea that the script in which we read affects the way we think) by offering a unique perspective on the effect of script (alphabets, morphosyllabaries, or multi-scripts) on our attention, perception, and problem-solving. Once we become literate, fundamental changes occur in our brain circuitry to accommodate the new demand for resources. The powerful effects of literacy have been demonstrated by research on literate versus illiterate individuals, as well as cross-scriptal transfer, indicating that literate brain networks function differently, depending on the script being read. This book identifies the locus of differences between the Chinese, Japanese, and Koreans, and between the East and the West, as the neural underpinnings of literacy. To support the “Script Relativity Hypothesis”, it reviews a vast corpus of empirical studies, including anthropological accounts of human civilization, social psychology, cognitive psychology, neuropsychology, applied linguistics, second language studies, and cross-cultural communication. It also discusses the impact of reading from screens in the digital age, as well as the impact of bi-script or multi-script use, which is a growing trend around the globe. As a result, our minds, ways of thinking, and cultures are now growing closer together, not farther apart. ; Examines the origin, emergence, and co-evolution of written language, the human mind, and culture within the purview of script effects Investigates how the scripts we read over time shape our cognition, mind, and thought patterns Provides a new outlook on the four representative writing systems of the world Discusses the consequences of literacy for the functioning of the min