Sava Milošević

Detrended fluctuation analysis of time series of a firing fusimotor neuron

We study the interspike intervals (ISI) time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk model analysis. Thus, we have found evidence for the white noise characteristics of the ISI time series, which means that the fusimotor activity does not possess temporal correlations. We conclude that such an activity represents the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles.

Wavelet analysis of discharge dynamics of fusimotor neurons

We study the interspike intervals (ISI) time series of the spontaneous fusimotor neuron activity by applying the wavelet transform analysis and confirm the existence of the white noise characteristics of the ISI time series. This means that the neuron activity may serve as the requisite noisy component for occurrence of the stochastic resonance mechanism in the neural coordination of muscle spindles. Besides, we apply the multifractal formalism adapted for the wavelet transform time series analysis. Thus, we have established the multifractality of the ISI data and achieved an additional insight into fusimotor discharge dynamics.

Towards finding exact residual entropies of the Ising antiferromagnets

We investigate various methods to evaluate exact residual entropies of the Ising antiferromagnets in the maximum critical field on infinite lattices, starting from results established for growing finite-size lattices. For the square Ising antiferromagnet we obtain residual entropy with 14 correct digits, σ = 0.40749510126068.

Exact and Monte Carlo study of adsorption of a self-interacting polymer chain for a family of three-dimensional fractals

We study the problem of adsorption of self-interacting linear polymers situated in fractal containers that belong to the three-dimensional (3D) Sierpinski gasket (SG) family of fractals. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface (which is, in fact, 2D SG fractal) and can be labelled by an integer b (2 ≤ b ≤ ∞). By applying the exact and Monte Carlo renormalization group (MCRG) method, we calculate the critical exponents ν (associated with the mean-squared end-to-end distance of polymers) and (associated with the number of adsorbed monomers), for a sequence of fractals with 2 ≤ b ≤ 4 (exactly) and 2 ≤ b ≤ 40 (Monte Carlo). We find that both ν and monotonically decrease with increasing b (that is, with increase of the container fractal dimension df), and the interesting fact that both functions, ν(b) and (b), cross the estimated Euclidean values. Besides, we establish the phase diagrams, for fractals with b = 3 and b = 4, which reveal the existence of six different phases that merge together at a multi-critical point, whose nature depends on the value of the monomer energy in the layer adjacent to the adsorbing surface.

Geometric criteria for phase transitions: The Ising model with nearest and next-nearest neighbor interactions

We describe a geometric approach for studying phase transitions, based upon the analysis of the “density of states” (DOS) functions (exact partition functions) for finite Ising systems. This approach presents a complementary method to the standard Monte Carlo method, since with a single calculation of the density of states (which is independent of parameters and depends only on the topology of the system), the entire range of parameter values can be studied with minimal additional effort. We calculate the DOS functions for the nearest-neighbor (nn) Ising model in nonzero field for square lattices up to 12 × 12 spins, and for triangular lattices up to 12 spins in the base; this work significantly extends previous exact calculations of the partition function in nonzero field (8 × 8 spins for the square lattice). To recognize features of the DOS functions that correspond to phase transitions, we compare them with the DOS functions for the Ising chain and for the Ising model defined on a Sierpinski gasket. The DOS functions define a surface with respect to the dimensionless independent energy and magnetization variables; this surface is convex with respect to magnetization in the low-energy region for systems displaying a second-order phase transition. On the other hand, for systems for which there is no phase transition, the DOS surfaces are concave. We show that thos geometrical property of the DOS functions is generally related to the existence of phase transitions, thereby providing a graphic tool for exploring various features of phase transitions. For each given temperature and field, we also define a “free energy surface”, from which we obtain the most probable energy and magnetization. We test this method of free energy surfaces on Ising systems with both nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions for various values of the ratio R ≡ J1/J2. For one particular choice, R = −0.1, we show how the “free energy surface” may be utilize to discern a first-order phase transition. We also carry out Monte Carlo simulations and compare these quantitatively with our results for the phase diagram.

Detecting long-range correlations in time series of dorsal horn neuron discharges.

Abstract: We have studied the discharge dynamics of dorsal horn neurons by applying the detrended fluctuation analysis and the wavelet transform technique. We have adopted that the neuronal discharge dynamics is manifested by the random time series of interspike intervals. In all cases studied, we found two different power‐law type behaviors across interspike intervals enumeration scale, that are separated by crossover regions (which implies existence of two different types of neuronal noise). Our results reveal that complex neuronal dynamics may change in the presence of external stimulation, manifested by changing of the noise characteristics that appear before crossover.

Monte Carlo renormalization group study of crosslinked polymer chains on fractals

We study the problem of two crosslinked polymer chains in a good solvent, modelled by two mutually crossing self-avoiding walks situated on fractals that belong to the Sierpinski gasket (SG) family (whose members are labelled by an integer b, ). By applying the Monte Carlo renormalization group (MCRG) method, we calculate the critical exponent y associated with the number of crossings of the two self-avoiding-walk paths, for a sequence of SG fractals with . For the problem under study, we find that our MCRG approach provides results that are virtually rigorous, that is, results with exceptionally small deviations (at most 0.07%) from the available exact renormalization group results. We discuss our set of MCRG data for y as a function of the fractal parameter b, and compare its behaviour with the finite-size scaling predictions.

Pattern recognition in damaged neural networks

We have studied the effect of various kinds of damaging that may occur in a neural network whose synaptic bonds have been trained (before damaging) so as to preserve a definite number of patterns. We have used the Hopfield model of the neural network, and applied the Hebbian rule of training (learning). We have studied networks with 600 elements (neurons) and investigated several types of damaging, by performing very extensive numerical investigation. Thus, we have demonstrated that there is no difference between symmetric and asymmetric damaging of bonds. Besides, it turns out that the worst damaging of synaptic bonds is the one that starts with ruining the strongest bonds, whereas in the opposite case, that is, in the case of damaging that starts with ruining the weakest bonds, the learnt patterns remain preserved even for a large percentage of extinguished bonds.

Equivalence of two parallel approaches to the cluster variation method: the multisite correlation functions method and the cluster effective fields method

We have analyzed relationship between two parallel approaches to the cluster variation method (CVM) as a theoretical tool for studying statistical properties of binary systems. The first approach to the method uses the multisite correlation functions as variational variables, while the other approach is the one that uses the cluster effective fields as variational variables. Using the Ising model description of physical systems studied, we have shown that the two approaches should produce identical final results, although they deal with quite different systems of nonlinear equations (which, in particular cases under study, must be solved numerically for a given temperature and chemical potential). To achieve identical final results, we show that it is necessary to introduce cluster fields for those clusters which appear to be subclusters of at least two different members of the Kikuchi cluster family. In addition, we demonstrate that variational variables of the two approaches generate two sets of cluster probabilities, whose intersection contains solution of the CVM approximation which corresponds to the thermodynamic equilibrium state. We also analyze the existence of the so-called consistency relations in both approaches to the CVM method, and, finally, we discuss the problem of convergency of numerical procedures that are used to analyze the low-temperature states of the model systems under study.

Ising model on the Sierpiński gasket: thermodynamic limit versus infinitesimal field

Owing to extremely slow decay of correlations, the limit H → 0 presents a poor approximation for the Ising model on the Sierpinski gasket. We present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model, where both finite size and finite field induce an apparent phase transition. These observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions.