Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

The effect of different baryons impurities

We demonstrate the different effect of different baryons impurities on the static properties of nuclei within the framework of the relativistic mean-field model. Systematic calculations show that $\Lambda_c^+$ and $\Lambda_b$ has the same attracting role as $\Lambda$ hyperon does in lighter hypernuclei. $\Xi^-$ and $\Xi_c^0$ hyperon has the attracting role only for the protons distribution, and has a repulsive role for the neutrons distribution. On the contrary, $\Xi^0$ and $\Xi^+_c$ hyperon attracts surrounding neutrons and reveals a repulsive force to the protons. We find that the different effect of different baryons impurities on the nuclear core is due to the different third component of their isospin.Comment: 9 page

Uncomputably noisy ergodic limits

V'yugin has shown that there are a computable shift-invariant measure on Cantor space and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages A_n f. Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given epsilon

CHARACTERISTICS OF THE DEGREE OF GRADE IN GRADE-ADDED ROUGH SET FOR LAND COVER CLASSIFICATION

This paper aims to clarify the meaning of the membership which is produced as by-products of land cover classification by Grade-added rough set (GRS). A new land cover classification method by using GRS was developed. The classification scheme of GRS which calculates membership (degree of grade) for each class is similar to those of MLC and SVM. But there are two things that are not clear. One is a meaning of the membership of GRS and the other is a reason why the larger membership in GRS employed works well. In this study, aerial images were used to visualize the relation of membership between GRS and existing classifiers, MLC and SVM. Furthermore, a model experiment in two-dimensional feature space was conducted. From these experiments, it was found that the meaning of degree of grade is a distance from a nearest training data of other class. That is, the meaning of membership of GRS is similar to that of SVM, because SVM also calculates a distance from boundary line which is determined by support vectors, while the meaning of membership of MLC is a distance from a centroid of own class. Also it was found that what the distance from the closest other class is given as the degree of grade implies that the higher the grade, the higher the certainty. In this research we could clarify some of the features of land cover classification using GRS

Isotopic dependence of the giant monopole resonance in the even-A ^{112-124}Sn isotopes and the asymmetry term in nuclear incompressibility

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A=112--124) with inelastic scattering of 400-MeV $\alpha$ particles in the angular range $0^\circ$--$8.5^\circ$. We find that the experimentally-observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in $^{208}$Pb and $^{90}$Zr very well. From the GMR data, a value of $K_{\tau} = -550 \pm 100$ MeV is obtained for the asymmetry-term in the nuclear incompressibility.Comment: Submitted to Physical Review Letters. 10 pages; 4 figure

Perturbative QCD Forbidden Charmonium Decays and Gluonia

We address the problem of observed charmonium decays which should be forbidden in perturbative QCD. We examine the model in which these decays proceed through a gluonic component of the $J/\Psi$ and the $\eta_c$, arising from a mixing of $(c\bar c)$ and glueball states. We give some bounds on the values of the mixing angles and propose the study of the $p \bar{p} \to \phi \phi$ reaction, at $\sqrt{s} \simeq 3$ GeV, as an independent test of the model.Comment: 8pages, lateX, DFTT 64-9

Transcriptional impairment of β-catenin/E-cadherin complex is not associated with β-catenin mutations in colorectal carcinomas

We report the absence of β-catenin mutations in 63 sporadic colorectal carcinomas (SCRCs) with demonstrated decreased β-catenin and E-cadherin mRNA expression and E-cadherin protein expression in a subset of carcinomas examined, suggesting that β-catenin mutations are an extremely rare phenomenon in SCRCs and are not responsible for the transcriptional impairment of the β-catenin/E-cadherin adhesion complex observed in these tumours

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page