Youichi Kobuchi

Fault tolerant cellular spaces

This paper treats the problem of designing a fault tolerant cellular space which simulates an arbitrary given cellular space in real time. A cellular space is called fault tolerant if it behaves normally even when its component cells misoperate. First such notions as simulation, misoperation, and K-separated misoperation are defined. Then a new multidimensional coding of configurations is introduced and explained using as typical example the two-dimensional space. The first main result is Theorem 1, which states that the introduced coding method is useful for correcting errors occurring at most once in every K=5x5 rectangle. The general theory is given in Section 6, where the second main result is given in the form of Theorem 8. It gives a necessary and sufficient condition for testing whether or not a given coding is adequate for error correction.

Some regular state sets in the system of one-dimensional iterative automata ☆

Abstract For the system of one-dimensional iterative automata, each set of all passive, Garden-of-Eden, and branching point state configurations is defined and shown to constitute a regular set. This regularity is proved to hold for the fixed, cyclic, open and reflexive boundary conditions. For proving theorems, a new device called N -automaton is introduced. Relationship with the gsm mapping is also discussed.

A Model for Rouleaux Pattern Formation of Red Blood Cells

Human red blood cells (RBCs) in a solution form rouleaux patterns under various conditions. The degree of rouleaux formation depends on, for example, the concentration and molecular weight of added large molecules. We present a two-dimensional discrete cellular space model in which an RBC is represented by a rectangle and differential adhesion is assumed among the longer (a-site), the shorter (b-site) sides of the rectangle and the solvent. The total sum of the adhesion energy is assumed to guide the step-by-step change of the model cell configuration and also define absolutely stable patterns. We compare the set of absolutely stable patterns and cell aggregate patterns for both actual and computer-simulated cases to obtain the basic validity of our framework. Then we proceed to assess the effects of added high polymers to the adhesion parameters. We first note that under suitable conditions, decrease in a-site-solvent affinity is necessary to have complex patterns rather than increase of a-a affinity. The hypothesis that addition of high polymers reduce the a-site-solvent affinity is concomitant with a newly proposed osmotic stress theory. The parameter fitting results for the experimental phase change curves can also be interpreted as supporting more the new theory than existing traditional explanations.

A spatial pattern formation model for Dictyostelium discoideum

In Dictyostelium discoideum , it is said that cells first differentiate into prestalk and prespore cells irrespective of their positions and then they sort out to form typical spatial patterns. We have investigated these pattern formation processes for the slug and for aggregates of dissociated slug cells through computer simulations in a two-dimensional discrete framework. Of the three possible factors of cell sorting mechanisms—i.e., randomness in cell movement, differential chemotaxis, and differential cell adhesion—we have shown that neither of the last two factors can be discarded, and that the differential cell adhesion should be working in such a way that prestalk and prespore cells intermingle with each other.

Repeatable words for substitution

A word w is said to be repeatable with respect to a substitution if it is a descendant of w itself. The repeatable language of a substitution system (a substitution with an axiom word) is defined as the set of the repeatable words which are the descendants of the axiom. In this paper, we give the characterizations of the repeatable words and the repeatable languages: The set of repeatable words for a rational (respectively context-free) substitution is a rational (respectively context-free) set. The repeatable language for a rational substitution system is a context-free language and a context-free language is the repeatable language for a finite substitution system.

Recurrent words for substitution

A wordw is called recurrent with respect to a substitution if any descendant of it can regeneratew itself by iterations of the substitution. The set of recurrent words with respect to a regular (resp. context free) substitution is a regular (resp. context free) language. The set of recurrent words which are the descendants of a single fixed word with respect to a context free substitution is context free.

Stability in OL systems

Some properties of recurrent strings with respect to an OL scheme and an OL system are discussed. A recurrent string is factorized into some elementary recurrent strings. The two decision problems are shown to be decidable: One is whether or not a given string is recurrent with respect to an OL scheme. The other is whether or not a given OL language contains some recurrent strings.

Decision problems of locally catenative property for DIL systems

Locally catenative properties of DIL systems are investigated. In particular, three types of decision problems for local catenativeness are set up and all of them are definitely answered. The first type of question is as follows: Given a DIL system G and integers i1 , i2 ,…, ik and p, is it decidable whether G is 〈i1 , i2 ,…, ik〉 locally catenative with cut p or not ? The other types of questions are obtained from the above-mentioned question by removing the condition of giving p (and ii , i2 ,…, ik) at the outset and by asking if there is an appropriate p (and i1 , i2 , …, ik). We show that the first question is decidable for D〈1, 1〉L systems, while the others are not even for D〈1, 0〉L systems.

On DIL schemes simulated by D0L schemes

Abstract We have investigated the simulation problem of DIL schemes to evaluate the strength of their cellular interactions. We give necessary and sufficient conditions under which some D0L scheme is isomorphic to a given D L scheme and to a subscheme of a given D L scheme, respectively. In this connection we mention one of the differences between DIL schemes with one-sided and both-sided dependencies. We also give a sufficient condition for some D0L subscheme to be isomorphic to a given DIL scheme. Further, we touch upon the case where some D0L system is isomorphic to a given DIL system.

On standard locally cantenative L schemes

Abstract A standard locally catenative L scheme extracts the essential feature of the locally catenative property. We investigate conditions under which a standard locally catenative L scheme has multiple locally catenative L systems.