Denis Horvath

Mean-field solution of the mixed spin-1 and spin-32 Ising system with different single-ion anisotropies

The mixed spin-1 and spin-32 Ising ferrimagnetic system with different anisotropies is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. Global phase diagrams are obtained in the temperature-anisotropy plane. In particular we find first-order transition lines separating different low-temperature ordered phases (characterized by different values of the sublattice magnetizations) each one terminating at an isolated critical point. The existence and dependence of a compensation temperature on single-ion anisotropies is also investigated.

Magnetic properties of a mixed ferro–ferrimagnetic ternary alloy

We have studied the magnetic properties of a mixed ferro–ferrimagnet composed of three different metal ions with spins 12,1, and 32 which includes both ferromagnetic and antiferromagnetic interactions. The system is considered in the frame of an Ising model in the effective-field theory with correlations. The general expressions for calculating the sublattice magnetizations, internal energy, specific heat, and susceptibility are given. In particular, these thermodynamical quantities for the system on the honeycomb lattice are numerically examined. The investigation of phase diagrams and thermal variation of total magnetization indicates the possible existence of one or even two compensation points. Some unexpected features are observed in the temperature dependencies of the total initial magnetic susceptibility χ, such as non-divergence of the χ in a vicinity of the critical and compensation temperatures, and the existence of sharp (or broad) maxima in the low-temperature region.

A Compensation Temperature Induced by Transverse Fields in a Mixed Spin-1 and Spin-3/2 Ising Ferrimagnetic System

A mean-field theory is developed for a mixed Ising ferrimagnetic system consisting of spin 1 and spin 3/2 with different transverse fields. The phase diagram and the thermal behaviour of magnetizations are studied. We find that a compensation point induced by different transverse fields can be observed, although the system never exhibits any compensation point for either zero or uniform transverse fields. The anomalous behaviour of the initial longitudinal magnetic susceptibility in the vicinity of the compensation and critical temperatures is also obtained.

A self-adjusted Monte Carlo simulation as a model for 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 Bornholdt [Int. J. Mod. Phys. C 12 (2001) 667], may be described by Levy-type stationary distribution of feedback variations with unique exponent α1∼3.3. However, the differences reflected by Hurst exponents suggest that resemblances between the studied models seem to be non-trivial.

Inverse geometric approach for the simulation of close-to-circular growth. The case of multicellular tumor spheroids

We demonstrate the power of genetic algorithms to construct a cellular automata model simulating the growth of 2D close-to-circular clusters, revealing the desired properties, such as the growth rate and, at the same time, the fractal behavior of their contours. The possible application of the approach in the field of tumor modeling is outlined.

Agent-based modeling of the cooperative spectrum management with insurance in cognitive radio networks

We propose and numerically analyze an agent-based simulation model of the spectrum frequency trading mechanism, where the heterogeneous agents take on the role of primary users. The interactions with the demand of the secondary users are considered. The model is constructed on the basis of Bak-Sneppen model of coevolution where the extremal dynamics is used to activate the low profitable users. Here, the strategies of the primary users are coevolving. They are characterized by the spectrum prices and cooperation intensity levels. The primary users interact indirectly by means of the demand stimulation of the secondary users and an insurance pool, which is provided by the spectrum exchange management system. The existence of the insurance pool is motivated by the needs of avoidance of the financial losses. The simulation results indicate the reliability of the insurance mechanism. In addition, several notable phenomena have emerged from the interactions of agents. The price increase resulting from the spontaneously formed oligopolistic practices of agents is considered as the most emergent feature of the model.

THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

The Ferrimagnetic Mixed Spin-1/2 and Spin-1 Ising System on Layered Honeycomb Lattice

A mixed spin-1/2 and spin-1 Ising ferrimagnet with a layered honeycomb structure is studied within the framework of an effective-field theory with correlations. The effect of interlayer interactions and a single-ion anisotropy on the existence of the compensation temperature and tricritical point is investigated. In particular, it is pointed out that the tricritical point may be only possible if interlayer interactions are nonzero.

Self-organised manifold learning and heuristic charting via adaptive metrics

ABSTRACT Classical metric and non-metric multidimensional scaling (MDS) variants represent the well-known manifold learning (ML) methods which enable construction of low-dimensional representation (projections) of high-dimensional data inputs. However, their use is limited to the cases when data are inherently reducible to low dimensionality. In general, drawbacks and limitations of these, as well as pure, MDS variants become more apparent when the exploration (learning) is exposed to the structured data of high intrinsic dimension. As we demonstrate on artificial as well as real-world datasets, the over-determination problem can be solved by means of the hybrid and multi-component discrete-continuous multi-modal optimisation heuristics. A remarkable feature of the approach is that projections onto 2D are constructed simultaneously with the data categorisation compensating in part for the loss of original input information. We observed that the optimisation module integrated with ML modelling, metric learning and categorisation leads to a nontrivial mechanism resulting in heuristic charting of data.

Towards inverse modeling of intratumor heterogeneity

Abstract Development of resistance limits efficiency of present anticancer therapies and preventing it remains a big challenge in cancer research. It is accepted, at the intuitive level, that resistance emerges as a consequence of the heterogeneity of cancer cells at the molecular, genetic and cellular levels. Produced by many sources, tumor heterogeneity is extremely complex time dependent statistical characteristics which may be quantified by measures defined in many different ways, most of them coming from statistical mechanics. In this paper, we apply the Markovian framework to relate population heterogeneity to the statistics of the environment. As, from an evolutionary viewpoint, therapy corresponds to a purposeful modi- fication of the cells’ fitness landscape, we assume that understanding general relationship between the spatiotemporal statistics of a tumor microenvironment and intratumor heterogeneity will allow to conceive the therapy as an inverse problem and to solve it by optimization techniques. To account for the inherent stochasticity of biological processes at cellular scale, the generalized distancebased concept was applied to express distances between probabilistically described cell states and environmental conditions, respectively.