The identification of cellular automata

Although cellular automata have been widely studied as a class of the spatio temporal systems, very few investigators have studied how to identify the CA rules given observations of the patterns. A solution using a polynomial realization to describe the CA rule is reviewed in the present study based on the application of an orthogonal least squares algorithm. Three new neighbourhood detection methods are then reviewed as important preliminary analysis procedures to reduce the complexity of the estimation. The identification of excitable media is discussed using simulation examples and real data sets and a new method for the identification of hybrid CA is introduced

The mass estimate in narrow-line Seyfert 1 galaxies

It is possible that narrow-line Seyfert 1 galaxies (NLS1s) are in the early stage of active galactic nuclei (AGNs) evolution. It is important to estimate the mass of supermassive black hole (SBH) in NLS1s. Here we considered the different kinds of methods to estimate the SBH masses in NLS1s. The virial mass from the H$\beta$ linewidth assuming random orbits of broad line regions (BLRs) is consistent with that from the statured soft X-ray luminosity, which showed that most of NLS1s are in the super-Eddington accretion state. The mass from the [O III] linewidth is systematically larger than that from above two methods. It is necessary to measure he bulge stellar dispersion and/or bulge luminosity in NLS1s.Comment: 2 Pages, 1 figure, in Prof. IAU Symposium No. 222, "The interplay among Black Holes, Stars and ISM in Galactic Nuclei ", eds. T. Storchi-Bergmann, Luis Ho and H. R. Schmit

Towards understanding the probability of 0+0^+ ground states in even-even many-body systems

For single-$j$ shells with $j={7/2}, {9/2}$ and 11/2, we relate the large probability of $I^+$ ground states to the largest (smallest) coefficients $\alpha^J_{I(v \beta)} = <nv \beta I |$ $A^{J \dagger} \cdot A^J | n v\beta I>$, where $n$ is the particle number, $v$ is the seniority, $\beta$ is an additional quantum number, and $I$ is the angular momentum of the state. Interesting regularities of the probabilities of $I^+$ ground states are noticed and discussed for 4-particle systems. Several counter examples of the $0^+$ ground state (0GS) predominance are noticed for the first time.Comment: 5 pages, 1 figure. Phys. Rev. C64, in pres

PTPT Symmetric Real Dirac Fermions and Semimetals

Recently Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the $PT$ symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, $2$D sub topological insulators and Fermi arcs, are studied in the $PT$ symmetric Dirac semimetals, and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about $PT$ symmetric Dirac nodal line semimetals.Comment: 7.5 pages, 5 figures. Accepted by Phys. Rev. Let

Generalised additive multiscale wavelet models constructed using particle swarm optimisation and mutual information for spatio-temporal evolutionary system representation

A new class of generalised additive multiscale wavelet models (GAMWMs) is introduced for high dimensional spatio-temporal evolutionary (STE) system identification. A novel two-stage hybrid learning scheme is developed for constructing such an additive wavelet model. In the first stage, a new orthogonal projection pursuit (OPP) method, implemented using a particle swarm optimisation(PSO) algorithm, is proposed for successively augmenting an initial coarse wavelet model, where relevant parameters of the associated wavelets are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be a redundant model. In the second stage, a forward orthogonal regression (FOR) algorithm, implemented using a mutual information method, is then applied to refine and improve the initially constructed wavelet model. The proposed two-stage hybrid method can generally produce a parsimonious wavelet model, where a ranked list of wavelet functions, according to the capability of each wavelet to represent the total variance in the desired system output signal is produced. The proposed new modelling framework is applied to real observed images, relative to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, and the associated identification results show that the new modelling framework is applicable and effective for handling high dimensional identification problems of spatio-temporal evolution sytems

General response theory of topologically stable Fermi points and its implications for disordered cases

We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective non-linear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge `2' are respectively illustrated for the classes A and AIII. We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the non-linear sigma models, based on the one-to-one classification correspondence.Comment: 8 pages and 2 figures, revised version with appendi