IV Computational Mechanics 9 A Causal States . . . . . . . . . . . . . . 9 Causal States of a Process Defined . . . 9 1 Morphs . . . . . . . . . . . . . . . . 10 Independence of Past and Future Conditional on a Causal State . . . 10 2 Homogeneity . . . . . . . . . . . . . 11 Strict Homogeneity . . . . . . . . . 11 Weak Homogeneity . . . . . . . . . 11 Strict Homogeneity of Causal States 11 B Ca...

L systems were originally introduced by A. Lindenmayer to model the development of simple filamentous organisms [6, 7]. The challenging and fruitful study of these systems in the 70s and 80s created many new results and notions [9]. In this paper we consider the important problem of recognizing ultimately periodic D0L sequences. Let A be a finite alphabet and denote the empty word by ε . A D0L ...

We consider a recently defined notion of k-abelian equivalence of words by concentrating on avoidability problems. The equivalence class of a word depends on the number of occurrences of different factors of length k for a fixed natural number k and the prefix of the word. We show that over a ternary alphabet, k-abelian squares cannot be avoided in pure morphic words for any natural number k. N...

If the fth dimension is one-dimensional connected manifold, up to diieo-morphic, the only possible space-time will be M =Z 2. And there exist two possibilities on cosmology constant: the cosmology constant is constant along the fth dimension, and the cosmology constant is sectional constant along the fth dimension. We construct the general models with parallel 3-branes on those kinds of the spa...

We compute certain one-loop corrections to F 4 couplings of the het-erotic string compactified on T 2 , and show that they can be characterized by holomorphic prepotentials G. We then discuss how some of these couplings can be obtained in F-theory, or more precisely from 7–brane geometry in type IIB language. We in particular study theories with E 8 × E 8 and SO(8) 4 gauge symmetry, on certain ...

The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the “Segre map”) of infinite loop spaces. Moreover, the associated Chern character map on rational homotopy groups is shown to be a ring isomorphism. A technique is introduced which establishe...

Recently, Mandal and Gong [23] refined and analyzed the recursive method by Lempel and Mykkeltveit et al. for generating de Bruijn sequences, where the recursive feedback function is the sum of a feedback function with k-th order composition and a sum of (k + 1) product-of-sum terms. In this paper we first determine the linear complexity of a composited de Bruijn sequence. We then conduct a pro...

The nematode Caenorhabditis elegans is widely used to study aging, development, behavior and other basic metazoan processes [1-3]. The only mutants directly identified on the basis of their extended longevity in any metazoan have been isolated in C. elegans [4,5]. All life-extension mutants (Age mutants) previously identified in C. elegans result from hypo-morphic or nullo-morphic mutations. We...