Cycles comme produit de deux permutations de classes donnees

AbstractSoit dans le groupe symétrique de degré n, deux classes de conjugasion H et K de partitions respectives (m1,…,mh) et (n1,…,nk), soit δ le plus grand commun diviseur des entiers m1,…,mh, n1,…,nk, et soit λ = h + k + ε avec ε = -1 ou 1 suivant que (h+k − 1) δ $̌r.ou n < (h+k−)δ. Le résultat principal de cet article est le suivant: pour qu'il existe α ϵ H et β ϵ K teis que αβsoit un ι-cycle et tels que le groupe〈α, β〉 scit transitif, il faut et il suffit que ι = λ (mod 2) et λ⩽ι⩽n. On en déduit une caractérisation de l'ensemble des entiers ι pour lesquels un ι-cycle peut être décomposé e; un produit de deux permutations appatenant respectivement aux classes H et K. Dans le cas oú cet ensemble n'est pas vide, c'est l'ensemble des termes d'une progression arithmétique decision 2

Conservation Laws in Cellular Automata

If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F if G is constant under the action of F. We characterize such `conservation laws' in several ways, deriving both theoretical consequences and practical tests, and provide a method for constructing all one-dimensional CA exhibiting a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To appear in Nonlinearity. (v2) minor changes/corrections; new references added to bibliograph

Probabilistic cellular automata with conserved quantities

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation conditions for deterministic cellular automata. Conservation condition for PCA can also be written in the form of a current conservation law. For deterministic nearest-neighbour CA the current can be computed exactly. Local structure approximation can partially predict the equilibrium current for non-deterministic cases. For linear segments of the fundamental diagram it actually produces exact results.Comment: 17 pages, 2 figure

Defocus test and defocus correction in full-field optical coherence tomography

We report experimental evidence and correction of defocus in full-field OCT of biological samples due to mismatch of the refractive index of biological tissues and water. Via a metric based on the image quality, we demonstrate that we are able to compensate this index-induced defocus and to recover a sharp image in depth.Comment: 7 pages, 3 figures, minor changes, 1 figure adde

Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.

The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod. Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly method. Reliable estimate was found for the $\beta$ critical exponent, based on moderate sized ($n \le 7$) clusters.Comment: 6 pages, RevTeX file, figure available from [email protected]

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

Universal behavior at discontinuous quantum phase transitions

Discontinuous quantum phase transitions besides their general interest are clearly relevant to the study of heavy fermions and magnetic transition metal compounds. Recent results show that in many systems belonging to these classes of materials, the magnetic transition changes from second order to first order as they approach the quantum critical point (QCP). We investigate here some mechanisms that may be responsible for this change. Specifically the coupling of the order parameter to soft modes and the competition between different types of order near the QCP. For weak first order quantum phase transitions general results are obtained. In particular we describe the thermodynamic behavior at this transition when it is approached from finite temperatures. This is the discontinuous equivalent of the non-Fermi liquid trajectory close to a conventional QCP in a heavy fermion material.Comment: 7 pages, 3 figure

Monte Carlo simulation of the transmission of measles: Beyond the mass action principle

We present a Monte Carlo simulation of the transmission of measles within a population sample during its growing and equilibrium states by introducing two different vaccination schedules of one and two doses. We study the effects of the contact rate per unit time $\xi$ as well as the initial conditions on the persistence of the disease. We found a weak effect of the initial conditions while the disease persists when $\xi$ lies in the range 1/L-10/L ($L$ being the latent period). Further comparison with existing data, prediction of future epidemics and other estimations of the vaccination efficiency are provided. Finally, we compare our approach to the models using the mass action principle in the first and another epidemic region and found the incidence independent of the number of susceptibles after the epidemic peak while it strongly fluctuates in its growing region. This method can be easily applied to other human, animals and vegetable diseases and includes more complicated parameters.Comment: 15 pages, 4 figures, 1 table, Submitted to Phys.Rev.

Cellular automaton rules conserving the number of active sites

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure

Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a new chain criterion, which distinguishes massive (rotationally inequivalent) irrep basis functions and allows for multiple branching paths, and are verified by inspection. These results are relevant to the determination of the symmetry of a material from its linear and nonlinear optical properties and to the choices of order parameters for symmetry breaking in liquid crystals.Comment: 28 pages and 3 figure