A neural network model composed of two-state and three-state neurons

A neural network model composed of two-state (1 and -1) and three-state (1, 0 and -1) neurons is proposed. The two-state neurons are connected with the three-state ones only and vice versa. We derive dynamic equations for the model under the assumption of non-symmetrical dilution of connections. A zero-noise phase diagram is obtained and a region in which two fixed point solutions can coexist is found. Basins of attraction for the solutions are also investigated. Received 26 October 1998 and Received in final form 12 February 1999     

The kinetic Potts chain and related potts models with competing interactions

We consider a general kinetic model for a chain of three-state Potts spins. From the time-evolution operator we infer points in two-dimensional Potts systems where certain spin correlations have one-dimensional character and the model is exactly solvable. This occurs in square lattice models with different kinds of competing interactions.     

The infrared and microwave spectra of ozone for the (0, 0, 0), (1, 0, 0), and (0, 0, 1) states

New measurements of the ozone spectrum in the microwave and 10-μm infrared regions have been made. These new lines have been fit to a three-state Hamiltonian model which includes Coriolis interactions beteen (0, 0, 1) and (1, 0, 0). The model requires additional Coriolis parameters, as well as an appreciation for the parameters which are indeterminate. Transition dipole moments have been derived from the intensities of selected infrared lines.     

The Phase Transition in the Three-State Potts Model: An Analytical Analysis

Weinvestigate thephase transition of the three-state Potts model in an analytical approachthe generalized cumtilant expansion with the effective mean field Itypothesis. We find a first order phase transition in the three-dimensional three-state Pot ts model with ferromagnetic nearest neighbor (nn) coupling. For the model with antiferromagnetic next-to-nearest neighbor (nnn) coupling, pe find a first order transition when tlle relative strength of the nnncoupling γ is fixed to -0.2. The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.     

A simple branching model that reproduces language family and language population distributions

Human history leaves fingerprints in human languages. Little is known about language evolution and its study is of great importance. Here we construct a simple stochastic model and compare its results to statistical data of real languages. The model is based on the recent finding that language changes occur independently of the population size. We find agreement with the data additionally assuming that languages may be distinguished by having at least one among a finite, small number of different features. This finite set is also used in order to define the distance between two languages, similarly to linguistics tradition since Swadesh.     

T>0 thermal properties of the generalized three-state potts model

A generalized three-state Potts model is proposed, the decimation renormalization-group method (DRG) is applied to the hamiltonian version of this three-state generalized Potts model, and T>0 thermal properties have been calculated. We find a nontrivial unstable fixed line in the finite temperature case, when T approaches zero it agrees with the result by using the T = 0 block renormalization-group method (BRG). The possibility of extending both the reliability of range of the DRG method is also mentioned.     

Scaling properties of target excitation cross sections in collisions between atoms and multiply charged ions

The scaling properties of one-electron target excitation cross sections in collisions between atoms and multiply charged ions are investigated. For the example of bare-ion (Z)-hydrogen collisions with various charge numbers Z it is shown that, in many-state calculations for Z ≥ 2 and energies E/Z ≈ 15–100 keV/amu, calculated 2p excitation cross sections lie approximately on a universal curve. This curve deviates from the one which has been derived earlier by Janev and Presnyakov for all Z on the basis of a simplified three-state model, and in fact results from a consistent three-state treatment show no scaling. The scaling properties of the excitation cross sections are easily understood in a purely classical model of distant collisions.     

Diffusion and trapping of muonium on silica surfaces

The spin relaxation rate λ_Mu of muonium atoms on fine silica powder surfaces was measured as a function of temperature and of the surface concentration of hydroxyl groups. Results indicate two-dimensional diffusion, trapping and detrapping of the muonium atoms on the silica surface. At low temperatures λ_Mu decreases dramatically as the concentration of surface hydroxyls is reduced. A three-state model is used to extract the muonium adsorption energy and other physical parameters.     

Escape for System with Non-Fluctuating Potential Barrier Only Driven by Three-State Noise

We study the escape for the mean first passage time （MFPT） over a potential barrier for a system with non- fluctuating potential barrier and only driven by a three-state noise. It is shown that in some circumstances, the three-state noise can induce the resonant activation for the MFPT over the potential barrier; but in other circumstances, it can not. There are three resonant activations for the MFPT over the potential barrier, which are respectively as the functions of the transition rates of the three-state noise.     

The four-state solution of the Yang-Baxter equation

A new four-state solution of the Yang-Baxter equation is constructed with the help of the lowest-dimensional cyclic L-operator related to a three-state R-matrix. Some special choice of the parameters on which this solution depends leads to an exactly solvable spin model on a chain with Hermitian Hamiltonian.     

Melting and wetting transitions in the three-state chiral clock model

The melting transition of the two-dimensional, three-state, asymmetric or chiral clock model is examined. Evidence from scaling arguments and analysis of perturbation series is presented, indicating that the chiral symmetry-breaking operator is relevant at the symmetric (or pure Potts) critical point with a crossover exponent of ø ≈ 0.2. The remainder of the commensurate-disordered phase boundary therefore appears to be in a new universality class, distinct from the pure three-state Potts transition. An interfacial wetting transition that plays an important role in the crossover between the two types of critical behavior is discussed. The location and exponents of this wetting transition are obtained both in a low-temperature limit using generating function techniques and in a systematic low-temperature expansion of the transfer matrix.     

Interfacial tension of the three-state Potts model on a square lattice at a negative fields

We calculate the interfacial tension of the three-state Potts model on a square lattice at a negative field by extending the method of Selke and Pesch, which is used in the model at zero field. The transition temperature and therefore the phase diagram of the model are determined by the vanishing of the interfacial tension.     

Fast convergence in language games induced by majority rule

We propose a simple model to investigate the evolutionary dynamics of a naming game on well-mixed populations. We assume that each individual has an inherent propensity to maintain his own word about an object whereas other individuals would affect his decision when they communicate. On the one hand, individuals learn the word of another one with a probability pertaining to their propensities. On the other hand, the focal individual would adopt the word held by the majority in a randomly selected group. We have numerically explored how dynamical behavior evolves as a result of combination of these two competing update patterns. A parameter governs the time scale ratio at which the two update patterns separately progress. We find that an increasing tendency to adopt the word held by the majority results in a rapid extinction of most words, thus more easily induces the system to a global consensus. Large initial probabilities denoting propensity are found to be unfavorable for the achievement of the consensus. Interestingly, simulation results indicate that the convergence time is negligibly affected by the number of initial distinct words when this number exceeds a certain value. Results from our model may offer an insight into better understanding the intricate dynamics of naming games.     

Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories

The operator content of unitary conformally invariant theories with c<1 is further analysed by deriving the spectrum of the transfer matrix for finite width strips and a variety of boundary conditions: antiperiodic, cyclic, twisted, free, fixed and a mixture of the last two. Complete results are obtained for the Ising model and for the three-state Potts model, as illustrations of the method. They demonstrate how the internal symmetries of these theories are tied in with their conformal properties.     

Interface properties of the three-state potts model in two dimensions

Interface properties, in particular the interface free energy and the interface profile of the three-state Potts model in two dimensions are studied using Monte Carlo techniques and a generalized version of the method of Müller-Hartmann and Zittartz. The role of the third state in characterizing the interface between the two other states is elucidated.     

Theoretical Analysis of Kinesin KIF1A Transport Along Microtubule

Recently, a three-state model is presented to describe the intracellular traffic of unconventional (single-headed) kinesin KIF1A (Phys. Rev. Lett. 95:118101, 2005), in which each motor can bind strongly or weakly to its microtubule track, and each binding site of the track might be empty or occupied by one motor. As the usual two-state model, i.e. the totally asymmetric simple exclusion process (TASEP) with motor detachment and attachment, in steady state of the system, this three-state model also exhibits shock (or domain wall separating the high-density and low density phases) and boundary layers. In this study, using mean-field analysis, the conditions of existence of shock and boundary layers are obtained theoretically. Combined with numerical calculations, the properties of shock are also studied. This study will be helpful to understand the biophysical properties of the collective transport of kinesin KIF1A.     

Behavioral and computational aspects of language and its acquisition

One of the greatest challenges facing the cognitive sciences is to explain what it means to know a language, and how the knowledge of language is acquired. The dominant approach to this challenge within linguistics has been to seek an efficient characterization of the wealth of documented structural properties of language in terms of a compact generative grammar—ideally, the minimal necessary set of innate, universal, exception-less, highly abstract rules that jointly generate all and only the observed phenomena and are common to all human languages. We review developmental, behavioral, and computational evidence that seems to favor an alternative view of language, according to which linguistic structures are generated by a large, open set of constructions of varying degrees of abstraction and complexity, which embody both form and meaning and are acquired through socially situated experience in a given language community, by probabilistic learning algorithms that resemble those at work in other cognitive modalities.     

Ground State of an Antiferromagnetic Three-State Potts Model on a Triangular Lattice with Competing Interactions

The ground state of the spin structures described by an antiferromagnetic three-state Potts model on a triangular lattice is studied with allowance for the next-nearest neighbors. The numerical data obtained by the Monte Carlo method are used to reveal the ranges of ordered and disordered phases in these structures.     

Potts Model on Maple Leaf Lattice with Pure Three-Site Interaction

We use Monte Carlo method to study three-state Potts model on maple leaf lattice with pure three-site interaction. The critical behavior of both ferromagnetic and antiferromagnetic cases is studied. Our results confirm that the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. For the antiferromagnetic case the transition is of the first order. We have calculated the energy jump and critical temperature in this area. We find there is a tricritical point separating the first order and second order phases for this system.     

Theoretical simulation of the photoassociation process for NaCs

We investigate the two-step association process of NaCs using the time-dependent wave packet method.Ground state atoms can be photoassociated to the low vibrational levels of the ground state for an NaCs molecule by the two-step association.The time-dependent Schro¨dinger equation of the association process is solved within a three-state model and the wave packet is propagated with the "split operator-Fourier transform" scheme and the rotating-wave approximation(RWA).The vibrational population distribution of the ground state can be obtained by projecting the wave packet to every vibrational level of the ground state.The results not only show that for NaCs achievement of photoassociation production is accompanied by the photodissociation of the higher vibrational molecules,but also show that the vibrational distribution in lower vibrational levels of the ground state changes with the laser parameters.