Deterministic one-dimensional cellular automata

A formal treatment of some of the properties of deterministic, rule 150, elementary one-dimensional cellular automata (CA) with null boundary conditions is presented. The general form of the characteristic polynomial of the CA global rule transition matrix is obtained. Mathematical relationships between the CA register lengths and the order of the corresponding group or semigroup structures are derived.     

On the decidability of the word problem for amalgamated free products of inverse semigroups

We study inverse semigroup amalgams [S ₁,S ₂;U], where S ₁ and S ₂ are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S ₁ and S ₂. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the ℛ-classes of S ₁* _U S ₂ to state sufficient conditions for the amalgamated free products S ₁* _U S ₂ having decidable word problem.     

Computer simulation of a cellular automata model for the immune response in a retrovirus system

Immune response in a retrovirus system is modeled by a network of three binary cell elements to take into account some of the main functional features of T4 cells, T8 cells, and viruses. Two different intercell interactions are introduced, one of which leads to three fixed points while the other yields bistable fixed points oscillating between a healthy state and a sick state in a mean field treatment. Evolution of these cells is studied for quenched and annealed random interactions on a simple cubic lattice with a nearest neighbor interaction using inhomogenous cellular automata. Populations of T4 cells and viral cells oscillate together with damping (with constant amplitude) for annealed (quenched) interaction on increasing the value of mixing probabilityB from zero to a characteristic valueB _ca (B _cq). For higherB, the average number of T4 cells increases while that of the viral infected cells decreases monotonically on increasingB, suggesting a phase transition atB _ca (B _cq).     

Porous product with reduced apparent density keeps good mechanical properties. Extruded composites of poly(vinyl chloride) blown under microwave irradiation

New foaming method, enhanced by microwave irradiation, was elaborated and applied to obtain porous poly(vinyl chloride) and its composites with fine cell structure. The so called “thermal runaway” effect was observed during the heating of poly(vinyl chloride) under microwave irradiation. The temperature of this effect decreases as a result of additives incorporation into polymer matrix. Microwave irradiation allowed effective heating of extruded poly(vinyl chloride) and its composites with carbon black (CB) filler, behind the extruder head and decomposing azodicarbonamide (ADC) to obtain porous products. The use of CB additive to poly(vinyl chloride) significantly increased its ability to be heated under microwave irradiation as well as improved the cell structure and decreased the apparent density of final products.Among additionally used fillers (1 wt%) the montmorillonite caused the apparent density decrease of foamed materials ca. 10%, however beneficially influenced on the quality of cells structure, giving the products with isotropic cells and the highest cell density as well as keeping the tensile strength on similar level as in the case of the materials with CB and ADC only.     

Simulation numérique des détonations à double structure cellulaireNumerical simulation of detonations with double cellular structure

We present the results of numerical two-dimensional simulations of detonation cellular structures under non-monotonous heat release provided by a chemical reaction comprising two successive exothermic steps. The influence of the rate of the second step of chemical reaction on the detonation cellular structure has been investigated. Our simulations are the first that reproduce a cellular structure composed of two clearly distinct sets of cells with different characteristic sizes where fine cells completely fill up larger ones, as has been observed experimentally. To cite this article: V. Guilly et al., C. R. Mecanique 334 (2006).     

Novel prenylated and geranylated aromatic compounds isolated from Polysphondylium cellular slime molds

We have studied the diversity of secondary metabolites of cellular slime molds to utilize them as new biological resources for natural product chemistry. From the methanol extract of fruiting bodies of Polysphondylium tenuissimum, we obtained five prenylated and geranylated aromatic compounds, Pt-1-5 (1-5). An additional aromatic compound, Ppc-1 (6), was isolated from Polysphondylium pseudo-candidum. The structures of these compounds were determined by spectral analysis, and synthetic routes to 4, 5, and 6 were developed. Compound 5 showed the glucose consumption-promotive activity on 3T3-L1 cells.     

Analysis of E. coli soluble proteins by non‐denaturing micro 2‐DE/3‐DE and MALDI‐MS‐PMF

Escherichia coli (strain K‐12)‐soluble proteins were analyzed by nondenaturing micro 2‐DE and MALDI‐MS‐PMF. The reported conditions of nondenaturing IEF in agarose column gels [Jin, Y., Manabe, T., Electrophoresis 2009, 30, 939–948] were modified to optimize the resolution of cellular soluble proteins. About 300 CBB‐stained spots, the apparent molecular masses of which ranged from ca. 6000 to 10 kDa, were detected. All the spots on two reference 2‐DE gels (one for wide mass range and one for low‐molecular‐mass range) were numbered and subjected to MALDI‐MS‐PMF for the assignment of constituting polypeptides. Most of the spots (310 spots out of 329) provided significant match (p<0.05) with polypeptides in Swiss‐Prot database and totally 228 polypeptide species were assigned. Activity staining of enzymes such as alkaline phosphatase and catalases was performed on the 2‐DE gels and the locations of the activity spots matched well with those of the MS‐assigned polypeptides of the enzymes. Most of the polypeptides with subunit information in Swiss‐Prot (119 polypeptides as homo‐multimers and 25 as hetero‐multimers out of the 228), such as pyruvate dehydrogenase complex which is composed of three enzymatic components, were detected at the apparent mass positions of their polymers, suggesting that the proteins were separated retaining their subunit structures. When a nondenaturing 2‐DE gel was vertically cut into 2 mm strips and one of the strips was subjected to a third‐dimension micro SDS‐PAGE (micro 3‐DE), about 190 CBB‐stained spots were detected. The assignment of the polypeptides separated on the 3‐DE gel would further provide information on protein/polypeptide interactions.     

On the Tutte–Krushkal–Renardy polynomial for cell complexes

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte–Krushkal–Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte–Krushkal–Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte–Krushkal–Renardy polynomial.     

Emergence of density dynamics by surface interpolation in elementary cellular automata

A classic problem in elementary cellular automata (ECAs) is the specification of numerical tools to represent and study their dynamical behaviour. Mean field theory and basins of attraction have been commonly used; however, although the first case gives the long term estimation of density, frequently it does not show an adequate approximation for the step-by-step temporal behaviour; mainly for non-trivial behaviour. In the second case, basins of attraction display a complete representation of the evolution of an ECA, but they are limited up to configurations of 32 cells; and for the same ECA, one can obtain tens of basins to analyse. This paper is devoted to represent the dynamics of density in ECAs for hundreds of cells using only two surfaces calculated by the nearest-neighbour interpolation. A diversity of surfaces emerges in this analysis. Consequently, we propose a surface and histogram based classification for periodic, chaotic and complex ECA.