Vladimir Miljković

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.

Dynamics of beryllium-7 specific activity in relation to meteorological variables, tropopause height, teleconnection indices and sunspot number

The dynamics of the beryllium-7 specific activity in surface air over 1987–2011 is analyzed using wavelet transform (WT) analysis and time-dependent detrended moving average (tdDMA) method. WT analysis gives four periodicities in the beryllium-7 specific activity: one month, three months, one year, and three years. These intervals are further used in tdDMA to calculate local autocorrelation exponents for precipitation, tropopause height and teleconnection indices. Our results show that these parameters share common periods with the beryllium-7 surface concentration. tdDMA method indicates that on the characteristic intervals of one year and shorter, the beryllium-7 specific activity is strongly autocorrelated. On the three-year interval, the beryllium-7 specific activity shows periods of anticorrelation, implying slow changes in its dynamics that become evident only over a prolonged period of time. A comparison of the Hurst exponents of all the variables on the one- and three-year intervals suggest some similarities in their dynamics. Overall, a good agreement in the behavior of the teleconnection indices and specific activity of beryllium-7 in surface air is noted.

Scaling analysis of time series of daily prices from stock markets of transitional economies in the Western Balkans

In this paper we have analyzed scaling properties of time series of stock market indices (SMIs) of developing economies of Western Balkans, and have compared the results we have obtained with the results from more developed economies. We have used three different techniques of data analysis to obtain and verify our findings: detrended fluctuation analysis (DFA) method, detrended moving average (DMA) method, and wavelet transformation (WT) analysis. We have found scaling behavior in all SMI data sets that we have analyzed. The scaling of our SMI series changes from long-range correlated to slightly anti-correlated behavior with the change in growth or maturity of the economy the stock market is embedded in. We also report the presence of effects of potential periodic-like influences on the SMI data that we have analyzed. One such influence is visible in all our SMI series, and appears at a period Tp ≈ 90 days. We propose that the existence of various periodic-like influences on SMI data may partially explain the observed difference in types of correlated behavior of corresponding scaling functions.

Analysis of cyclical behavior in time series of stock market returns

In this paper we have analyzed scaling properties and cyclical behavior of the three types of stock market indexes (SMI) time series: data belonging to stock markets of developed economies, emerging economies, and of the underdeveloped or transitional economies. We have used two techniques of data analysis to obtain and verify our findings: the wavelet spectral analysis to study SMI returns data, and the Hurst exponent formalism to study local behavior around market cycles and trends. We have found cyclical behavior in all SMI data sets that we have analyzed. Moreover, the positions and the boundaries of cyclical intervals that we have found seam to be common for all markets in our dataset. We list and illustrate the presence of nine such periods in our SMI data. We also report on the possibilities to differentiate between the level of growth of the analyzed markets by way of statistical analysis of the properties of wavelet spectra that characterize particular peak behaviors. Our results show that measures like the relative WT energy content and the relative WT amplitude for the peaks in the small scales region could be used for partial differentiation between market economies. Finally, we propose a way to quantify the level of development of a stock market based on the Hurst scaling exponent approach. From the local scaling exponents calculated for our nine peak regions we have defined what we named the Development Index, which proved, at least in the case of our dataset, to be suitable to rank the SMI series that we have analyzed in three distinct groups.

Exact and Monte Carlo study of the two self‐avoiding random walks on the three‐dimensional Sierpinski lattices

We consider the phenomena of entanglement of the two interacting self‐avoiding walks (SAW) situated in a member of the three‐dimensional Sierpinski Gasket (SG) fractal family. We focus our attention to determine number of point contacts between the two SAW paths M, which turns out to be a set of power laws whose characteristics depend predominantly on the interactions between SAW steps. The phase diagrams have been establised and corresponding values of the contact critical exponents φ, associated with the two‐path mutual contacts, have been found.

Percolation approach to formation of synfire chains in two dimensional neural networks

We consider the propagation of spike packets in two dimensional networks consisting of locally coupled neural pools. The dynamic attractors of this model, synfire chains, appear for some values of network parameters. The synfire chain formation exhibits behavior, which may be discribed with the percolation phase transition. Using finite-size scaling method, we obtained the critical probabilities and the critical parameter ratio beta/v for different sets of refractoriness and synaptic weights, connecting neighbouring neural pools