A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets

In 1954 Marstrand proved that if K is a subset of R^2 with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we give a combinatorial proof of this theorem when K is the product of regular Cantor sets of class C^{1+a}, a>0, for which the sum of their Hausdorff dimension is greater than 1.Comment: 9 pages, 1 figure, referee suggestions incorporated, to appear in Expositiones Mathematica

Explorations between ethnomathematics and anthropology in relation to mathematics education

Conferência realizada em Monterrey, México de 6 -13 de julho de 2008.Mathematical activity has flourished all over the world. Such activity is organized either in formal systems of knowledge, or embedded in daily life, emerging in work, educational, leisure practices, professions, norms and artifacts. Several fields of study have contributed to uncovering the human diversity of mathematical ideas and practices, including the history of mathematics, psychology, theology, anthropology and ethnomathematics. Addressing the question, “What is ethnomathematics (how is it related to mathematics, anthropology and the politics of mathematics education?)” posed by Discussion Group18 - the role of ethnomathematics in mathematics education, this paper focuses on the relationship between anthropology and ethnomathematics, explored from the view point of their connection to the field of mathematics education.info:eu-repo/semantics/publishedVersio

Influence of nonuniform critical current density profile on magnetic field behavior of AC susceptibility in 2D Josephson Junction Arrays

Employing mutual-inductance measurements we study the magnetic field dependence of complex AC susceptibility of artificially prepared highly ordered (periodic) two-dimensional Josephson junction arrays of unshunted Nb-AlO_x-Nb junctions. The observed behavior can be explained assuming single-plaquette approximation of the overdamped model with an inhomogeneous critical current distribution within a single junction.Comment: 4 pages (REVTEX), 6 figure

Universality and Decidability of Number-Conserving Cellular Automata

Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in \Zset, and show that they can be always extended to ``usual'' NCCA with contiguous states. We show a way to simulate any one dimensional CA through a one dimensional NCCA, proving the existence of intrinsically universal NCCA. Finally, we give an algorithm to decide, given a CA, if its states can be labeled with integers to produce a NCCA, and to find this relabeling if the answer is positive.Comment: 13 page

Genetic Algorithms for the Imitation of Genomic Styles in Protein Backtranslation

Several technological applications require the translation of a protein into a nucleic acid that codes for it (``backtranslation''). The degeneracy of the genetic code makes this translation ambiguous; moreover, not every translation is equally viable. The common answer to this problem is the imitation of the codon usage of the target species. Here we discuss several other features of coding sequences (``coding statistics'') that are relevant for the ``genomic style'' of different species. A genetic algorithm is then used to obtain backtranslations that mimic these styles, by minimizing the difference in the coding statistics. Possible improvements and applications are discussed.Comment: 17 pages, 13 figures. Submitted to Theor. Comp. Scienc