The magnetic reversal in dot arrays recognized by the self-organized adaptive neural network

The remagnetization dynamics of monolayer dot array superlattice XY 2-D spin model with dipole-dipole interactions is simulated. Within the proposed model of array, the square dots are described by the spatially modulated exchange-couplings. The dipole-dipole interactions are approximated by the hierarchical sums and spin dynamics is considered in regime of the Landau-Lifshitz equation. The simulation of reversal for $40 000$ spins exhibits formation of nonuniform intra-dot configurations with nonlinear wave/anti-wave pairs developed at intra-dot and inter-dot scales. Several geometric and parametric dependences are calculated and compared with oversimplified four-spin model of reversal. The role of initial conditions and the occurrence of coherent rotation mode is also investigated. The emphasis is on the classification of intra-dot or inter-dot (interfacial) magnetic configurations done by adaptive neural network with varying number of neurons.Comment: 16 figure

Properties of iterative Monte Carlo single histogram reweighting

We present iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The 2d Ising model of ferromagnet is studied numerically as an illustration. In that case, the iterations uncovered stationary regime with invariant probability distribution function of temperature which is peaked nearly the pseudocritical temperature of specific heat. The sequence of generated temperatures is analyzed in terms of stochastic autoregressive model. The error of histogram reweighting can be better understood within the suggested model. The presented model yields a simple relation, connecting variance of pseudocritical temperature and parameter of linear filtering.Comment: 3 figure

Structurally dynamic spin market networks

The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent "brain" is modeled by a recursive neural network with local and global inputs and feedback connections. For specific parametric combination the complex network displays small-world phenomenon combined with scale-free behavior. The identification of a local leader (network hub, agent whose strategies are frequently adapted by its neighbors) is carried out by repeated random walk process through network. The simulations show empirically relevant dynamics of price returns and volatility clustering. The additional emerging aspects of stylized market statistics are Zipfian distributions of fitness.Comment: 13 pages, 5 figures, accepted in IJMPC, references added, minor changes in model, new results and modified figure

A self-adjusted Monte Carlo simulation as model of financial markets with central regulation

Properties of the self-adjusted Monte Carlo algorithm applied to 2d Ising ferromagnet are studied numerically. The endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random walk of the temperature that converges to criticality without an external tuning. The robustness of a stationary regime with respect to partial accessibility of the information is demonstrated. Several statistical and scaling aspects have been identified which allow to establish an alternative spin lattice model of the financial market. It turns out that our model alike model suggested by S. Bornholdt, Int. J. Mod. Phys. C {\bf 12} (2001) 667, may be described by L\'evy-type stationary distribution of feedback variations with unique exponent $\alpha_1 \sim 3.3$. However, the differences reflected by Hurst exponents suggest that resemblances between the studied models seem to be nontrivial.Comment: 19 pages, 9 figures, 30 reference

Analysis of the Lead-Lag Relationship on South Africa capital market

Despite the efficient market hypothesis (EHM), lead-lag relationships can be observed mainly between financial derivatives and underlying asset prices, prices of large and small companies, etc. In our paper, we examined the lead- lag relationship between prices of open ended funds and an all-share index as a representative of the capital market. Along with more traditional methods of using cross correlations, partial correlation and Toda-Yamamoto causality tests, we also analysed the speed of adjustment of assets to their intrinsic values and identified the most prevalent lag using rolling time windows. The analysis was performed using data from the South Africa capital market

Analysis of the Lead-Lag Relationship on South Africa capital market

Despite the efficient market hypothesis (EHM), lead-lag relationships can be observed mainly between financial derivatives and underlying asset prices, prices of large and small companies, etc. In our paper, we examined the lead- lag relationship between prices of open ended funds and an all-share index as a representative of the capital market. Along with more traditional methods of using cross correlations, partial correlation and Toda-Yamamoto causality tests, we also analysed the speed of adjustment of assets to their intrinsic values and identified the most prevalent lag using rolling time windows. The analysis was performed using data from the South Africa capital market

The co-evolutionary dynamics of directed network of spin market agents

The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings between the nodes of dynamic directed stochastic network. The co-evolutionary principles are applied in the frame of Bak - Sneppen self-organized dynamics [P. Bak, K. Sneppen, Phys. Rev. Letter 71 (1993) 4083] that includes the processes of selection and extinction actuated by the local (node) fitness. The local fitness is related to orientation of spin agent with respect to instant magnetization. The stationary regime characterized by a fat tailed distribution of the log-price returns with index $\alpha\simeq 3.6$ (out of the Levy range) is identified numerically. The non-trivial consequence of the extremal dynamics is the partially power-law decay (an effective exponent varies between -0.3 and -0.6) of the autocorrelation function of volatility. Broad-scale network topology with node degree distribution characterized by the exponent $\gamma=1.8$ from the range of social networks is obtained.Comment: 10 pages, 4 figures. accepted for publication in Physica

Magnetic dot arrays modeling via the system of the radial basis function networks

Two dimensional square lattice general model of the magnetic dot array is introduced. In this model the intradot self-energy is predicted via the neural network and interdot magnetostatic coupling is approximated by the collection of several dipolar terms. The model has been applied to disk-shaped cluster involving 193 ultrathin dots and 772 interaction centers. In this case among the intradot magnetic structures retrieved by neural networks the important role play single-vortex magnetization modes. Several aspects of the model have been understood numerically by means of the simulated annealing method.Comment: 16 pages, 8 figure