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Труды XI научной конференции по радиофизике, ННГУ, 2007

АНГЛИЙСКИЙ ЯЗЫК В РАДИОФИЗИКЕ

VARIETY OF SYNCHRONOUS REGIMES IN NEURON-LIKE OSCILLATORSA.K. Kryukov, G.V. Osipov, A.V. Polovinkin

Nizhny Novgorod State University

In this work, the feature under consideration is synchronization in ensembles of lo-cally coupled non-identical Bonhoeffer–Van der Pol oscillators.

In our study, we use the Bonhoeffer–Van der Pol model as neuron-like oscillators:

.Here, N is the number of elements in the chain, d is the coupling parameter, and ε is a small parameter. Each element has its own value of the parameter a.

Two coupled elements can be described by the 4th-order system.Typical time series of synchronous regimes in the system of 2 coupled elements

are shown in Fig.1.

Fig. 1

There is an in-phase regime in the left-hand part of the figure, and an anti-phase regime in the right-hand part. If coupling is very weak, there is no synchronization in this system. If coupling is not too weak and not too strong, then both of these regimes can be realized.

At strong coupling, the anti-phase regime becomes unstable and only the in-phase regime is realized. For a stronger coupling, the in-phase regime sets faster.

We have found 4 synchronous regimes in the system of 3 coupled elements: in-phase regime and three mixed regimes in which 2 of 3 oscillators are in-phase synchro -

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nized and the third one oscillates in anti-phase to others. So 2 N-1, or 4 different regimes of global synchronization are possible for the same values of parameters.

In a chain of 20 elements, we have found several synchronous regimes in the nu -merical simulation. It allows us to suppose that in the chain of N elements, 2N-1 different regimes of global synchronization are possible.

If coupling is not enough for global synchronization, then we can see groups of el -ements which oscillate at the same frequencies (Fig. 2).

Fig. 2

In the absence of coupling, each element has its own frequency. As the coupling increases, we can see cluster synchronization. With the further increase in the coupling, the quantity of clusters decreases. Once the coupling value has become greater than some boundary value, we can see global synchronization.

Thus, in the system of N locally coupled Bonhoeffer – Van der Pol oscillators for fixed values of parameters, 2N-1 different regimes of global synchronization are possi-

ble, which was numerically confirmed for the system of 3 coupled elements. Transi-tion to global synchronization is accompanied by the formation of synchronization clus-ters.

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VENTRICAL FIBRILLATION AND OVERDRIVE PACING FOR ITS SUPPRESSION

L.S. Averyanova1), G.V. Osipov1), C.K. Chan2)

1)Nizhny Novgorod State University 2)Institute of Physics, Taiwan

Our objective was to investigate wave interactions in excitable and oscillatory me-dia and to explore the feasibility of using overdrive pacing to suppress fibrillation in cardiac tissue. It is known that ventricular fibrillation can arise from spiral wave chaos. Our objective in this computational study was to investigate wave interactions in ex -citable media and to explore the feasibility of using overdrive pacing to suppress spiral wave chaos.

Under sinus rhythm, waves of electrical activity propagate throughout the heart, eliciting a simultaneous contraction of the ventricles. It is known that a spiral wave arises from one of arrhythmias in cardiac muscle, known as tachycardia. Its rotation frequency is higher than a frequency of normal sequence of dirge pulse. These spiral waves break up into spiral wave chaos [1]. Then ventricular fibrillation might arise. To-day there exists only one clinical method for treating a heart in ventricular fibrillation, namely, applying a large voltage shock to the heart.

One of the alternative methods for annihilating spiral wave chaos is based on the property that the wave with the highest frequency suppresses all other waves.

These findings suggest that low-amplitude, high-frequency overdrive pacing, in combination with a low-amplitude positive direct current can be useful for eliminating fibrillation.

The model is presented in [2]. The first equation of the model describes the evolu-tion of the membrane potential:

.

When the value of Iext in an isolated cell exceeds a bifurcation value approximately equal to 2.21 at the chosen values of parame-ters, a limit cycle appears in the phase space of the model, so that the cell becomes oscil-latory (Fig. 1). Thus, there can be different regimes for other kinds of cells: (i) synchro-nization for oscillatory cells or (ii) stimu-lated oscillations for excitable cells.

We periodically paced one isolated cell with a square-wave stimulus (amplitude A = 2, 5, 10). So, the most promising amplitudes of the input high-frequency current are as follows: (i) for amplitude A = 5, there is the area which corresponds to oscillatory cell; (ii) for A = 5, 10, there may be positive values of the input high-frequency current.

Fig. 1

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For a chain of 10 Luo–Rudy cells, the most promissing amplitudes of the input high-frequency

current are as follows: (i) for minimal amplitude of the input high-frequency current A=-10, the low direct current ranges from 0.5 to 1.5; (ii) for A =-30 the direct current is higher than 2; (iii) for A=-50, the direct current is higher than 4.

We periodically paced a two-dimensional grid of 300x300 cells with a square-wave stimulus (with amplitude A=-30). It was shown that the application of a positive current leads to a decrease in the action potential duration (APD) (Fig.2).

The spiral wave chaos is suppressed successfully for the low amplitude direct cur-rent, and the frequency of the high-frequency current was found to be (a) 0.15 and (b) 0.16. The spiral wave chaos was eliminated after 4.00-s pacing in a grid of 300x300 cells (Fig.3).

It was shown that the overdrive pacing method makes it possible to annihilate spi -

ral wave chaos. The most promising region of values of the direct low- amplitude cur-rent lies over 0. We explain that using the positive direct current results in step-down APD of cells. As a result, spiral wave chaos becomes more regular, which allows one to suppress the chaos more efficiently. These findings meen that low-amplitude, high-fre-quency overdrive pacing along with a low-amplitude positive direct current can be use-ful for eliminating fibrillation.

This work was supported by the RFBR-NSC (project No.05-02-90567), the RFBR-MF (project No.05-02-19815), and the RFBR (project No.06-02-16596).

[1] Stamp A.T., Osipov G.V., Collins J.J. // Chaos. 2002. V.12, No3. P.931.

Fig. 2

Fig. 3

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[2] Luo C.H., Rudy Y. // Circ. Res. 1991. V.68. P.1501.

LOW-COST ADAPTIVE WI-FI ANTENNA FOR LONG-DISTANCE COMMUNICATIONS

M.A. Sokolov, M.O. Shuralev, A.L. UmnovNizhny Novgorod State University

There is a tremendous need for affordable, robust wireless networking in rural ar -eas of the developing world. Existing infrastructure that is useful in high-density areas, where costs can be spread over many users, is not appropriate for sparsely populated ru-ral regions. The use of parabolic antennas with high gains can meet some difficulties. The antennas need to be precisely aligned with one another. The changing conditions could greatly make the link quality worse, but the mechanical tuning of such antennas results in additional expenses and system complexity.

Our approach is to use an electrically steerable antenna with low-cost. The antenna consists of an adaptive parabolic reflector constructed of an array of passive scattering elements with tunable reactive loads, an optimizer running on a computer system that changes the phases and amplitudes of the reflected electromagnetic waves, based on the received signal strength, and a small hardware controller that manages the varactor bias voltage logic.

Each scatterer is a symmetric dipole with a trans-mission line transformer that is loaded with a tunable varactor diode (Fig.1). So the antenna consists of multi-ple rows of scatterers with parabolic profile shown in Fig.2. The scatters are excited by a dipole antenna at the parabolic focus. The pattern is changed by variation in the re-emitted scatterer field created by an antenna ex-citer. The beam pattern is controlled by variation in the phase, which is perfomed by the hardware controller.

Finding the right beam pattern direction means the voltage distribution optimiza-tion based on the received signal strength indicator (RSSI). The RSSI is obtained from

the conventional hardware such as a Wi-Fi card. Optimization can be divided into two stages: initial finding of a signal source and further link maintenance. The first step is limited in time and should therefore be done as fast as possible, while the link mainte-nance can be performed at any other time. The optimization task represents a challenge in view of the number of parameters (bias voltages in our case) and the RSSI noise.

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Fig. 1

Fig. 2


Several prototype antennas have been constructed. By now the following results have been achieved: 18 dBi gain across operational 50 degrees of azimuth with a beam width of 10 degrees. Higher gains can be achieved with a reduced range of steerability. Future works will focuse on reducing the cost by choosing appropriate materials and the antenna structure, improving the optimization algorithms, and achieving higher gains.

[1] Cheng J., Hashiguchi M., Ligusa K. and Ohira T. // IEE Proceedings – Microwaves, Antennas and Propagation, 2003. V.150, No.4. P.203.

[2] Lamensdorf D. Capacitively Tuned Dipole // Electronic Letters, 1973. V.9, № 19. P.445.

[3] Ohira T. and Gyoda K. // 2000 IEEE International Conference on Phased Array Systems and Technology, Dana Point, CA. 2002. P.101-104.

TRANSIENT EFFECTS IN PHASE-MATCHED EXCITATION OF TERAHERTZ SURFACE WAVE BY A FEMTOSECOND LASER PULSE

M.I. Bakunov1) and M.V. Tsarev 2)

1) Nizhny Novgorod State University 2)Institute of Applied Physics, Russian Academy of Sciences

Terahertz surface plasmon-polari-tons (SPPs) propagating on semiconduc-tor surfaces are a promising tool for per-forming terahertz spectroscopy of sur-faces and surface deposits, especially biomolecules [1]. Recently, we have proposed two techniques that can poten-tially allow the generation of surface plasmon-polaritons using femtosecond laser pulses [2,3]. The idea behind these proposals is to make optical-to-terahertz conversion directly on the semiconduc-tor surfaces: The surface waves are gen-erated by the moving spot of nonlinear polarization created by the laser pulse via optical rectification. Two excitation schemes – with superluminal [2] and subluminal [3] spots – were considered. In the more efficient subluminal scheme, the surface of a semiconductor is illuminated with a weakly focused

Fig. 1. Subluminal excitation scheme for SPPs: a normally incident laser pulse with tilted inten-sity front produces a strip-like optical spot which moves with velocity V and scans the dis-tance L on the surface

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Fig. 2


femtosecond laser pulse with tilted intensity front. Such pulses are already used for the generation of bulk THz radiation in nonlinear crystals [4]. If the tilt angle exceeds 45 , the strip-like optical spot, which is created on the surface by the pulse, moves with sub-luminal velocity and the phase-matched excitation of a surface wave can be realized.

The theories developed in [2, 3] treat the ideal case of a uniform motion of the op-tical spot over the infinite distance on the surface. Meanwhile, in experiments the pump laser beam always has a finite aperture. This restricts the distance scanned by the opti -cal spot on the surface to a finite value and, therefore, imparts a nonstationary character to the excitation process.

In this paper, we extend the theory of SPP generation using the subluminal scheme to the case when the strip-like optical spot scans a finite distance on a semiconductor surface. According to the subluminal excitation scheme [3], we assume that the surface is illuminated by a weakly focused femtosecond laser pulse with tilted intensity front. The phase fronts of the pulse are parallel to the semiconductor surface y = 0 (normal incidence) and the intensity front of the pulse is tilted at an angle with respect to the surface (see figure). The illuminated area on the semiconductor surface is a strip ori -ented along the x axis and moving in the +z direction with velocity V = ccot. Due to weak focusing of the incident pulse, we approximate it by a two-dimensional pulse with fields independent of x. Unlike Ref. [3], we assume that the optical strip travels a finite distance L (-L/2 < z < L/2) along the surface. We consider the case of above-bandgap excitation when the penetration depth of the laser beam in the semiconductor is small compared to the extent of the SPP evanescent tail in the semiconductor. This assump -tion is adequate to the typical experimental situation of the excitation of GaAs surface with Ti:sapphire laser pulses (~800 nm wavelength). The nonlinear polarization can be written as

P NL = p (y) f(t-z/V) (z),

where (y) is a delta function. The function (z) = 1 inside the interval -L/2 < z < L/2 and (z) = 0 elsewhere. The function f(t-z/V) is the time-dependent envelope of the in-tensity of the optical pulse (e.g., Gaussian envelope). The orientation of the amplitude vector p is determined by the polarization of the optical beam and the orientation of the crystallographic axes of the sample.

To find the terahertz fields produced by the moving nonlinear polarization, we apply the Fourier transform with respect to t and z to Maxwell's equations and the equa-tion for electron motion. Then we match the solutions of the resultant equations by the boundary conditions at the surface y = 0 and extract the fields of the generated surface wave from the total terahertz field using contour integration technique in the complex wavenumber plane. The conversion efficiency into the terahertz surface wave is ana -lyzed as a function of the optical spot velocity V and the distance L.

To summarize, we developed a theory of the optical excitation of terahertz surface waves on semiconductor surfaces that accounts for the finite distance scanned by the optical spot on the surface. The theory predicts that the results of [3] are adequate if only the scanned distance exceeds the characteristic value we called the SPP formation length. Additionally, we have shown that one can control the generated SPP spectrum

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by varying the scanned distance, for example, via changing the laser beam transverse size or slanting the laser beam with respect to the surface. Finally, we have found the optimal parameters maximizing the terahertz yield.

[1] Bakunov M.I., Maslov A.V., and Bodrov S.B. // Opt. Photon. News. 2005. V.12, No.16. P.29.

[2] Bakunov M.I., Maslov A.V., and Bodrov S.B. // Phys. Rev. B. 2005, No.72. P.195336.

[3] Bakunov M.I., Maslov A.V., and Bodrov S.B. // J. Appl. Phys. 2005, No.98. P.033101.

[4] Hebling J., Almasi G., Kozma I., and Kuhl J. // Opt. Express. 2002, No.10. P.1161.

THE MODEL OF THE DIGITAL RADIO RECEIVER WITH THE WIDE DYNAMIC RANGE

V.A. Kanakov, P.V. KuznetsovNizhny Novgorod State University

It is well known that the mobile communication is quickly becoming the primary mode of the communication for the most part of the world. With increasing density of the working radio systems, the requirement to the interference immunity rises. With de-creasing power, the dynamic range narrows. That is why greater values of the dynamic range are required to ensure the interference immunity. This work is concerned with a dynamic range increase in the digital-radio systems [1] for the interference immunity. It is one of the branches of electromagnetic compatibility of radioelectronic devices.

The aim of this work is development of a prototype of the digital radio receiver (DRR) with the wide dynamic range (DR). Unlike devices with the automatic gain con-trol or the logarithmic amplifiers, the model to be discussed is capable of decreasing faint signal blocking by strong noise.

A signal after an analog-to-digital conversion is processed in a digital area. Digital processing gives some advantages such as a receiver adaptability and flexibility. But it is necessary to amplify the analog signal before the analog-to-digital conversion. That is why some rigid parameters for analog part of the receiver are required. One of them is a linearity of the amplifiers. Thus it is necessary to increase the receiver dynamic range.

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Fig.1. The model of the digital receiver with the wide dynamic range

Fig.1 shows the model of DRR with the wide DR. From our point of view, one of the ways to increase the dynamic range is combining some analog receiver and analog-to-digital converter (ADC) functions. The input signal after the amplification by a pri -mary amplifier and demodulation enters the main amplifier and, at this stage, the signal can exceed the dynamic range of the main amplifier. But if some voltage is subtracted from the signal, the signal is amplified without clipping.

Let us examine some necessary conditions for the operation of this model. They are the bandwidth of an analog part, the ADC frequency, a duration strobe, and an algo-rithm for bias forming.

The first condition is the bandwidth of an analog part. The signal is represented as the sum of the two signals: useful signal and noise. A demodulated signal is represented as a harmonic signal and a fixed bias. For rejecting the interference in the digital area, it is necessary that the bandwidth of an analog part is greater than the difference be -tween the carrier and noise frequencies.

The second condition is an algorithm for bias forming. This algorithm is continu-ous variable-slope delta-modulation. This method will track the signal and forming bias.

The third and fourth conditions are the ADC frequency and the duration strobe. If it is necessary to track signal variations correctly, we must have as many digital sam-ples as required to reach the pick of the demodulated signal. It will be the number of subtracting voltages which suit the demodulated signal amplitude. The analog-to-digital converter frequency will show the ratio of this number to the duration strobe.

The computer experiment has shown the possibility for increasing the dynamic range of the digital radio receivers described above. The computer simulation was per -formed with the MatLab software. There is a possibility to implement the DRR in a field programmable gate array (FPGA). The FPGA gives comprehensive facilities for digital signal processing (DSP) including adaptive digital filtering.

[1] Побережский Е.С. Цифровые радиоприемные устройства. М.: Радио и связь, 1987. 184 c.

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A FAILURE OF EXISTING PACKET SCHEDULERS TO SERVE VOICE TRAFFIC ADEQUATELY

A.V. Malygin, L.U. RotkovNizhny Novgorod State University

Nowadays, Internet telephony tends to become a reliable alternative to a conven-tional one. Unfortunately, there are still some problems in this field (see [1]). A large group of engineering tasks is concerned with Quality of Service (QoS) that must be pro-vided as strictly as possible. Disregarding it causes a decrease in voice quality. It is necessary that the QoS support be integrated at any point of the path between interlocu -tors [2]. The packet scheduler that operates at the output link of the router seems to be one of them. This paper aims to show unacceptability of existing schedulers to serve voice traffic. The work does not propose any solution. We only try to reveal a problem as it is.

In this paper, we consider voice traffic features that must be taken into account by any operation over it. We also formulate the requirements of the effective scheduler and examine wether schedulers proposed are able to meet them all at once.

In contrast to ordinary data traffic, voice flows need to be treated in a favor. The network must guarantee a worst-case performance to them as follows:1) voice packet delay needs to remain within a budget (according to ITU-T G.114, the

acceptable delay in local connections is upper bounded by 150 ms);2) the network must provide voice packet delay to avoid varying as strictly as possible;3) the probability of the voice packet loss must be limited by 0,01.

Taking into account these requirements the effective scheduler must also provide fair link allocation among flows and an isolation of the flows from each other. Given the ac-ceptable QoS it must also utilize link band-width as fully as possible at any time.

The first scheduling discipline given for consideration is Weighted Fair Queueing (WFQ) [3]. It is the earliest known packet approximation of the Generalized Processor Sharing (GPS) fluid model. To achieve GPS fairness, the WFQ uses the notion of vir -tual time. Upon arrival at a WFQ scheduler, any packet is assigned a tag that represents the virtual time of finishing service under GPS. After that the packets are picked up for transmission in an increasing order of their tags. Such a discipline is only aimed at a fair link allocation among competing flows according to their reserved rates. But packet delay variation is not tightly bounded. In order to reveal such a drawback, we consider an example of packet arrivals illustrated in Fig.1 [4]. The horizontal axis shows the

Fig. 1

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time line and the vertical axis shows the sample path of each session. Let the first ses-sion link share be 0,5 and share of any other session be 0,05.

Fig. 2 presents a packets service order under WFQ [4]. There is a huge gap be -tween serving times of packets 10 and 11 from the first session. In order to decrease a voice packet service delay, we would have to increase its session link share but, as the example shows, it would cause a wider-range packet delay variance.

Such a drawback was overcome by Worst-case Fair Weighted Fair Queueing (WF2Q) discipline [4]. The problem was solved by introducing the notion of packet eli -gibility. Only packets already picked up for transmission under GPS become candidates for receiving service under WF2Q. The corresponding service order is presented in Fig.3 [4]. But avoiding extreme packet delay variation under WF2Q requires excess link bandwidth reservation because of referring to WFQ. Such a scheduler could not be called an effective one.

Priority-based WFQ (PWFQ) has introduced the notion of sliding window [5]. As-signing voice packets the highest priority and determining the optimal sliding window size help to save link bandwidth at the cost of voice packet delay bound depending on the maximum packet transmission time. Hence, sliding window does not work under a low-speed link.

Thus, voice traffic needs a new scheduler to be designed. Its heart might be as fol -lows. In order to improve link utilization, it is possible to increase inter-word and inter-phrase pauses without perceptible decrease in voice quality. Phrases may be entirely de-layed up to several hundred milliseconds. Design and analysis of such a scheduler is the work to be done in future.

[1] Goode B. // Proc. of the IEEE. 2002. V.90, No.9. P.1495.

Fig. 2

Fig. 3

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[2] Chandra S. // Seminar Report done under Prof. Anirudha Sahoo, 2004. P.12. Avail -able at: http://www.it.iitb.ac.in/~sarat/seminar/seminar_QoS_VoIP.pdf

[3] Parekh A.K., and Gallager R.G. // IEEE/ACM Transactions on Networking. 1993. V.1, No.3. P.344.

[4] Bennet J.C.R., and Zhang H. // IEEE INFOCOM’96. 1996. P.120.[5] Wang, S., Wang Y.-C. and Lin K.-J. // Proc. of the Sixth International Conference

on Real-Time Computing Systems and Applications. 1999. P.312.

ATTENTION FOCUS FORMATION MODEL BASED ON THE ARCHITECTURE WITH A CENTRAL ELEMENT

A.Yu. SimonovNizhny Novdorod State University

Principles of investigation of information representation and processing in the brain still remains very urgent. Oscillatory neural networks provide appropriate facili -

ties for understanding mechanisms of some brain functions. This paper describes one of oscillatory neural network models. The network has a star-like architecture which was proposed in [1]. The studied attention focus formation phenomenon is based on fre -quency synchronization between one subgroup of peripheral oscillators and the central oscillator (Fig. 1). For simplicity, what kind of objects is in the focus of attention is as-sumed unimportant. FitzHugh–Nagumo [2] oscillators were chosen as units of the net -work.

FitzHugh–Nagumo model parameters are taken so that the cell is in the mode of periodic sequence of pulses generation. The cell natural frequencies ( fi) are set by the values of small parameters (εi) which are responsible for splitting motions into fast and slow parts. By means of the time replacement, the relation between fi and εi turns out to be of a square-law character (fi

2=cεi), where c is a factor of proportionality calculated

Fig. 1

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with the help of a numerical experiment (the natural frequency is determined as the number of oscillation periods divided by time).

Mathematical description of the model with N peripheral elements is as follows:

(1)

where the variable U qualitatively describes the membrane potential dynamics, V is a slow variable which corresponds to ion currents dynamics, f(Ui)=Ui(Ui–1)(ai–Ui), d is the coupling strength, the parameter γ gives the rate of adaptation of the central cell in-trinsic frequency to its current frequency, and ai and bi are the parameters of the FitzHugh–Nagumo model. The cell with index “0” is the central element.

Several computer experiments were made to illustrate that the model is workable. The description of the experiments is given below.

In the experiments under discussion, 75 peripheral cells are grouped into 3 sub-groups. The cell natural frequencies in each subgroup are uniformly distributed in an interval on the frequency axis. It is assumed that all the intervals have identical lengths and are spaced by empty intervals. The value of ε0 is changed by jumps in every 500-time units. That is why the attention focus is switched. Between the moments of switch-ing, ε0 satisfies the third equation of system (1). The results of the experiment are pre-sented in Fig.2.

The plots illustrate evolution of the current peripheral cell frequencies (thin lines) and the central cell natural frequency (thick line). Throughout the entire simulation pe-riod, subgroups of oscillators underwent synchronization with the central element in the following order: subgroup 1, subgroup 2, subgroup 1, and, finally, subgroup 3.

Fig.3 illustrates the instant values of all cell membrane potentials at the moment when the attention focus is formed on the 3rd subgroup. The values are coded by colors

Fig. 2

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of squares (black color corresponds to a minimal value and white color corresponds to a maximal value).

Other experiments gave similar results. It is noteworthy that the absence of back -ward connections between the central cell and peripheral cells causes worse attention focus formation. Adding weak local connections between peripheral oscillators does not break the effect, in contrast to adding strong local connections. In the last case, fre-quency synchronization between peripheral oscillators is possible without the influence by the central element.

Finally, a few remarks should be made about the attention focus formation. The presented model qualitatively explains the attention focus formation phenomenon. Neu-ral oscillators used as units of the network make the model closer to an actual system.

[1] Borisyuk G.N., Borisyuk R.M., Kazanovich Y.B., & Ivanitskii G.R. //Physics-Us-pekhi. 2002. V.45, №10. P.1073.

[2] Скотт Э. Волны в активных и нелинейных средах в приложении к электронике. М.: Советское радио, 1977. 368 с.

INVESTIGATING ASTROCYTE ACTIVITY DYNAMICSA.S. Pimashkin1), A.V. Semyanov2), A.A. Lebedinsky1)

1)Nizhny Novgorod State University 2)RIKEN Brain Science Institute

Several recent studies in neuroscience have significantly challenged our under-standing of astrocytic functions in the brain. For many years glial cells were considered to be supporting glue for the neuronal networks and their functions were limited by ex -isting theories to nutrition, protection and homeostasis maintenance of neighboring neuronal networks. Several years ago it was discovered that astrocytes have calcium ac-tivity, which can be evoked by synaptic activity of ambient neurons which leads to the release of gliotransmitters. Therefore, we propose a hypothesis of the mutual influence between neuronal networks and astrocytic syncytium in the brain. We suggest a feed-back scheme of neuron-glia interaction in which astrocytic activity evoked by signal

Fig. 3

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processing in the neighboring neurons forms specific time-spatial patterns of gliatrans -mitter release. This gliatransmitter release can in its turn act as a diffuse chemical sig -nal on extrasynaptic neuronal receptors and thereby modulate the propagation of a sig-nal through the neuronal network (i.e., information processing). To address the question of mutual interactions between glia and neurons in the brain, several studies have been done and more experiments are in progress. This work is a collaboration project of the Department of Neuronal Dynamics and Neurobiology of the University of Nizhny Novgorod under lead by Semyanov Research Unit in RIKEN Brain Science Institute in Japan.

To study astrocytic activity, we use hippocampal slices obtained from rat's and mice's brain. To visualize astrocytic calcium oscillations we load cells with cell-perme-able form of calcium indicator such as Oregon Green BAPTA-1 AM. This calcium sen-sitive dye allows us to observe all intracellular changes of calcium concentration as changes in fluorescence intensity, acquired by Nikon C-1 confocal system equipped with two visual lasers. To distinguish between cell types, actrocyte-specific fluorescent morphological tracer Sulforhodamine 101 is used.

At present, our studies are focused on searching for specific patterns of the astro-cytic calcium activity and astrocyte-to-astrocyte signal propagation properties. At first we had to analyze different pulse parameters such as amplitude, duration, rise time, fall time, latency between peaks, frequency, etc. This information allows us to classify dy-namic characteristics of pulse activity propagation for different types of organisms, whose brain is being investigated.

Fig. 1

Fig. 2

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To investigate interrelations between astrocytes we have used some signal analysis methods, i.e., correlation analysis of two cells activities:

where xi and yi are two astrocytic calcium activities and T is the activity observation time (about 30 min). As we assume that information patterns are represented by pulse propagation between cells, we have to apply time-shift correlation analysis to find out which cells are connected. If the value of maximum correlation is not defined by chaotic pulse distribution in time inside the network, then we can find the average time shift and the velocity and direction of a signal between two cells.

As we can observe approximately one layer of astrocytes, we can not take into ac -count the influence of deeper located cells. Therefore, there is probability of the mediocrely influence on the cells. But still we can see the patterns of highly correlated activities that form clusters of different-type-connected cells. As the distance and pas-sage time of series of pulses are given, we can calculate different parameters of chemi -cal signal processing which can make it possible to propose a theory for principles of a functioning astrocyte network. By using different methods of analyzing information systems, we have made tools for analyzing calcium activities of astrocytes and for modeling architecture similar to that existing in real slices of brain.

INVESTIGATION OF A POLYHARMONIC EXTRAPOLATION ALGORITHMV.V. Badanov, A.P. Evseev

Nizhny Novgorod State University

A solution of many actual engineering problems is concerned with usage of extrap -olation (forecasting) algorithms and devices which allow one to make estimations of the unknown and inaccessible future part of the time series, based on the known (in other words available for observation) past history of the time series which is pro-cessed.

In particular, it is possible to use extrapolation algorithms in a different inertial au-tomatic control systems (e.g., anticipatory aiming of the antiaircraft gun to the maneu-vering aircraft), telecommunication systems (e.g., load balancing), radar systems (adap-tive adjustment to the target), super-resolution problems (increasing the aperture of the antenna), and problems of econometrics and financial markets analysis.

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There are a lot of different extrapolation algorithms. However, despite their vari -ety, a necessity of the fast, robust, and most precision algorithms and devices is still ur-gent today and in the future.

In the context of the current work, a sum of the constant component S0, the linear trend Kt, and a finite number n of periodic arbitrarily-shaped components (which can be modulated by a periodic function or linear trend) is used as a model of the time-series which is extrapolated. An additive white noise N(t) with a normal distribution and finite energy is introduced into the model to make the problem statement closer to actual situ -ations.

Thus, the analytical representation of the model of the studied class of time series is as follows:

S(t)=S0 +Kt +Pi(i t +i) + N (t) , i=1…n

It seems promising to use a polyharmonic extrapolation algorithm (PEA) for pre-diction of time series represented by such a model. This algorithm consists in revealing harmonic components of the input time series, determining their amplitudes and phases, as well as trends of their changes and linear extrapolation of their values for each har-monic of the process. After the inverse Fourier transformation of the found spectrum, we get a new time series which comprises a part of the known past history of the time series and a part of the previously unknown values of the time series.

A polyharmonic extrapolation algorithm of the time series which contains a signif-icant number of quasi-periodic components is based on the well-known postulate of the theory of forecasting that any forecast will be close to the truth only if the patterns which are working in the forecast interval are the same as the patterns in the past his-tory interval. Hence, only those periodic components can be effectively extrapolated which completely fill the past history interval as well as the future interval.

The analytical representation of the PEA in the conventional notation is as follows:

,

where SI, SII, and SIII are partly overlapped segments of the processed time series. The beginning of SI corresponds to the beginning of the past history of the time series. The end of SII corresponds to the end of the past history. The third segment SIII includes a part of known data and a part of unknown data which is an estimation of the future val -ues of the time series, based on the assumption that dynamic trends of the time series are permanent (or slowly fluctuating).

This algorithm can also be extended to two-dimensional data, which allows one to process a set of more than one of one-dimensional time series and take dependence be-tween time series into account, while making a forecast as well.

In this paper, we have investigated several properties of this algorithm such as the extrapolation errors dependent on forecast intervals and periods of oscillations of a sin-gle sinusoid. We have also investigated the extrapolation error dependent on the signal-

272


to-noise ratio. The main attention has been paid to analisis of the results of this algo-rithm concerning two-dimensional data.

Analysis of the results of computer-aided modeling allowed us to state that this al -gorithm is able to work with the above-mentioned class of time series and is preferable for some situations against other well-known extrapolation algorithms.

It is necessary to mention some cases where the precision of extrapolation is sig-nificantly decreased and this algorithm works worse compared with conventional algo -rithms. First of all, it is the case where dominant components having length of the order of 2-5 sizes of the Fourier-transform window are present in the past history of the pro-cessed time series.

Another loosing case appears when the signal-to-noise ratio of the input data ap-proaches unity. According to analytical equations, this ratio approaches the value 0.5 in the extrapolated (output) data.

For extrapolation of two-dimensional data, the use of a two-dimensional Fourier transform as the main analysis tool enables easy accounting of correlation coupling along any of 2 directions for complicated combinations of time series similar to the one-dimensional case.

The polyharmonic extrapolation algorithm has a short and fixed time of computing a forecast for given cases.

DOPPLER RATEMETER (EXPERIMENTAL DATA FOR DIGITAL SIGNAL PROCESSING TRAINING COURSE)

S.Yu. Lupov, E.P. FradkinaNizhniy Novgorod State University

In laboratory works on the “Digital Signal Processing” training course, the Marple test sequence [1] is usually used as a signal for spectral estimation of super-resolution algorithms. The sequence contains several frequency components at fixed frequencies and Gaussian noise. Such a signal does not have properties of actual signals, for exam-ple, harmonics at multiple frequencies, the presence of frequency-modulated compo-nents, and quantization noise appearing after analog-digital transformation.

We propose to obtain the signal under consideration in a laboratory setup (Fig. 1).

The laboratory setup for study-ing different estimation methods consists of a pendulum with a metallic well sound reflective plate, the speakers, a microphone, and a computer. A microphone and the speakers are connected to the suit-able computer inputs. A micro-

Fig. 1

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phone is situated between radiating sinusoidal signal speakers and a pendulum so as the sound emitted by the speakers be reflected from a swinging plate and hit upon it. A sig-nal from the microphone is recorded on a computer disk as a file by using a sound adapter.The obtained signal is interesting for us due to the fact that along with a refer -ence frequency component of a signal radiated by the speakers, there is a weaker fre-quency component of a Doppler-shifted sound signal reflected from a swinging plate. The Doppler frequency shift can be obtained from the formula

,

where is the sound wavelength ( 75 mm for a frequency of 4410 Hz) and V is the rate of metallic plate motion. The Doppler frequency shift is no more than 15 Hz at the reference signal frequency 4410 Hz. There is also quantization noise, harmonics caused by nonlinear nature of a computer sound adapter, and interfering sound signals.

Our purposes are signal obtaining and processing and estimation of instantaneous speed of a swinging plate, using different methods of time-frequency estimation.

Fig. 2

A time-frequency distribution obtained by using the Sig2Prony program for the signal is presented in Fig. 2. The program has been developed at the Radioengineering Division of the University of Nizhny Novgorod and is based on time-frequency estima-tion by the Prony method in a running window.

Time in readouts is indicated on the horizontal axis (8.28 sec.). The Doppler fre -quency from -20 to 20 Hz is indicated on the vertical axis, which corresponds to the speed of motion of a plate from -0.75 m/s to +0.75 m/s.

Two frequency components are well seen in the distribution. One of them corre-sponds to the frequency of the signal from the speakers (4410 Hz), and the other, to the frequency of the signal reflected from a moving plate.

The following conclusions can be drawn: A signal derived from the laboratory setup is more complicated than the Marple test

sequence, but it has all the properties which actual signals have. The laboratory setup has simple design and it can easily be assembled at home. The performed study is useful for the “Digital Signal Processing” training course.

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[1] Marple S.L. Digital Spectral Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1987.

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