Multidimensional cellular automata and generalization of Fekete's lemma

Fekete's lemma is a well known combinatorial result on number sequences: we extend it to functions defined on $d$-tuples of integers. As an application of the new variant, we show that nonsurjective $d$-dimensional cellular automata are characterized by loss of arbitrarily much information on finite supports, at a growth rate greater than that of the support's boundary determined by the automaton's neighbourhood index.Comment: 6 pages, no figures, LaTeX. Improved some explanations; revised structure; added examples; renamed "hypercubes" into "right polytopes"; added references to Arratia's paper on EJC, Calude's book, Cook's proof of Rule 110 universality, and arXiv paper 0709.117

I visualised how algorithms ‘see’ urban environments and build detailed profiles of citizens

Final Published versio

Fekete's lemma for componentwise subadditive functions of two or more real variables

We prove an analogue of Fekete's subadditivity lemma for functions of several real variables which are subadditive in each variable taken singularly. This extends both the classical case for subadditive functions of one real variable, and a result in a previous paper by the author. While doing so, we prove that the functions with the property mentioned above are bounded in every closed and bounded subset of their domain. The arguments follows those of Chapter 6 in E. Hille's 1948 textbook.Comment: 22 pages. Revised and expanded. Longer introduction, more detailed background, statement of main theorem extende

Classification of the types of modern criminals and the scientific methods used in the detection of crime

Thesis (M.A.)--Boston Universit