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neocortical neurons: regular-spiking (RS), Visual stimulation was consisted of intrinsically bursting (IB), fast spiking (FS), flashing light or dark circles (25 in diameter) fast repetitive bursting (FRB, also called 4- ۻ on black or light background, respectively.

Stimuli were presented on a computer monitor for 200 ms with the interstimulus interval of s.

Data analysis was performed using Plexon Offline Sorter and NeuroExplorer software. To resolve the spike waveforms associated with the individual neurons the spike detection was performed by using a threshold-crossing algorithm. Interspike Fig. 1. Waveform of the wide spike neuron. The interval histograms (ISIH) and perievent duration of the back edge is 350 s.

histograms with 1 ms bin for each neuron were computed to determine the time course of neuronal activity. The histograms were What concerned with our results was that the smoothed with 3 bin Gaussian window.

neurons of layer 4 generated as narrow as wide The neurons were classified based on a spikes. The duration of back edge of narrow wide variety of characteristics including a spikes was less than 300 s, whereas for wide distribution of spike width, interspike interval spikes it was more than 300 s. Some of the distribution, the mode of ISIH, frequency narrow spike neurons (6 cells) had unimodal discharge for RS and FS neurons, intraburst distribution of ISIs that was skewed on the and interburst frequency for burst generating right of the mode. These neurons were refered neurons, a refractory period, variability of to fast spiking (FS) neurons (Fig. 2). In spike amplitudes and interspike intervals in response to visual stimuli they generated trains bursts.

of spikes at the frequencies of 300-500 Hz.

The perievent histograms of these cells Results showed on- and off-responses to the stimulus presentation (Fig. 3).

Extracellular recording were obtained from 61 neurons in the area VI of anesthetized cats. All of the extracellular recorded spikes had the similar front edge (100-150 s), but differed in duration of the back edge (150600 s). Electrophysiological studies with simultaneously recorded extracellular and intracellular signals from hippocampal CApyramidal cells and interneurons [5] demonstrated that the front edge of the extracellular recorded signal corresponds to the width of rising depolarization phase of the intracellular action potential, whereas the back edge of the extracellular spike corresponds to the falling repolarization phase of the intracellular signal. The action potential repolarization phase is more variable in duration because of the ionic currents contributing to it [6] and is responsible for the short or wide duration of the action potential.

Fig. 2. Waveform and interspike interval histogram for Therefore we used the duration of the back FRB neuron recorded in 4 layer of visual cortex.

edge of the extracellular spike as a criterion of the action potential width (Fig. 1). In the intracellujar studies [1, 3] the action potential width is measured as the width at half height.

XVI (Fig. 6). The width of interspike intervals varied widely, with mode at 11-15 ms. The ISIHs of these cells showed a refractory period of 3-5 ms and center frequency of 88.5 Hz. In accordance with intracellular studies [1, 3], they were referred to regular-spiking (RS) neurons. 4 cells with the same ISIH distribution had narrow spikes with back edge less than 300 ms. The perievent histograms of RS neurons showed on-, off- and on-offresponses to the flashing circle.

Fig.3. Perievent histogram FRB neuron recorded in layer of visual cortex. The 99% confidence limit is presented by the dotted line.

The other cells with narrow spike showed the bimodal ISIHs (9 cells). The refractory period of these type neurons didn't exceed 2-3 ms. Neurons with bimodal ISIH could be referred to the fast repetitive bursting (FRB) type of activity (Fig.4). FRB cells generated bursts with intraburst frequency at 330-500 Hz in response to the flashing circle.

Fig. 5. Perievent histogram FS neuron recorded in The second mode was placed on 13-18 ms at layer of visual cortex. The 99% confidence limit is ISIHs that corresponded to the interval presented by the dashed line.

between bursts. The perievent histograms of cells of this group showed rhythmic fluctuation of activity in response to visual stimuli (Fig 5).

Fig. 6. Waveform and interspike interval histogram for RS neuron recorded in 4 layer of visual cortex In the infragranular layers we recorded Fig 4. Waveform and interspike interval histogram for neurons with wide spikes more often than with FS neuron recorded in 4 layer of visual cortex narrow ones. They had unimodal and bimodal distribution of ISIHs. Neurons with wide Neurons with wide spikes (3 cells) action potential and unimodal ISIH were were characterized by unimodal symmetrical classified as regular spiking (17 cells). RS or skewed on the right distribution of ISIs 4- ۻ cells from deep layers fired at lower frequency Conclusion than RS cells from 4 layer and had spike Electrophysiological properties and the frequency approximately 61 Hz.

resulting firing patterns of neocortical neurons Neurons with wide action potential and are uniform enough during intracellular and bimodal ISIH (15 cells) were classified as extracellular recording in response to current bursting neurons with intrinsically bursting pulses and visual stimuli, respectively. That type activity (Fig. 7). They were characterized allows using described here criteria for the by averaged intraburst spike frequency of definition of electrophysiological classes of Hz and refractory period of 2-3 ms. Their the extracellular recorded cells in multichannel intraburst interval was slowly increasing to the recording behavioral experiments.

end of the burst. The interburst interval was The examples illustrated here point to a widely varied (20-38 ms). 3 cells recorded in crucial role played by the biophysical 5-6 layers showed ISIH distributions similar to properties of single neurons in the dynamics of that of IB neurons, yet they exhibited shortlocal circuit networks. The classification of duration action potential. In response to the cells into electrophysiological classes based on flashing circle IB neurons showed on-, off- their firing pattern and spike width allows the and on-off-responses (Fig. 8).

construction of models of local networks that take into account the different dynamics of the individual cells. There are no circuits in cortex formed by neurons with similar morphological characteristics that have common pattern of activity. Therefore, understanding the details of network including single cells with their temporal pattern of spike firing are required for description of neocortical operations and information processing in neocortex.

The work is supported by A.B.

Kogans grant from A.B.Kogan Research Institute of Neurocybernetics SFedU.

References 1. Connors BW, Gutnick MJ, Prince DA Electrophysiological properties of neocortical neurons in vitro// J Neurophysiology. 1982. 48: 1302-1320.

2. McCormick DA, Connors BW, Lighthall JW, Prince DA Comparative electrophysiology of pyramidal Fig. 7. Waveform and interspike interval histogram for and sparsely spiny stellate neurons of the neocortex// J.

IB neuron recorded in 5 layer of visual cortex.

Neurophysiol. 1985.54: 782-806.

3. Nowak LG, Azoun R, Sanchez-Vives MV, Gray CM, McCormick DA. Electrophysiological Classes of Cat Primary Visual Cortical Neurons In Vivo as Revealed by Quantitative Analyses// J. Neurophysiol.

2003. 89: 1541-1566.

4. Steriade M, Neocortical cell classes are flexible entities// Nature Reviews. Neuroscience. 2004. 5: 121134.

5. Henze DA, Borhegyi Z, Csicsvari J, Mamiya A, Harris KD, Buzsaki G, Intracellular features predicted by extracellular recordings in the hippocampus in vivo// J Neurophysiol. 2000. 84(1):390-400.

6. Chen W, Zhang J., Hu GY, Wu CP Different mechanisms underlying the repolarization of narrow and wide action potentials in pyramidal cells and Fig. 8. Perievent histogram IB neuron recorded in interneurons of cat motor cortex// Neuroscience. 1996.

layer of visual cortex. The 99% confidence limit is 73(1):57-68.

presented by the dotted line.

XVI REGULARIZATION OF NEURAL NETWORK MODELS WITH DISTORTED INFORMATION ATTRIBUTE SPACE AND OBSERVATIONS DEFICIENCY S.A. Gorbatkov1, D.V. PolupanovA branch of Federal State Budgetary Educational Institution of Higher Professional Education All-Russian Distance Institute of Finance and Economics, in the city of Ufa, Russia sgorbatkov@mail.ru Federal State Budgetary Educational Institution of Higher Professional Education Bashkir State University, city of Ufa, Russia demetrious@mail.ru Procedures of pre-regularizing and Bayesian plans of field tax audits and also taxpayers regularizing neural network models are proposed in clustering with an aim to take a decision as to tax tasks of approximating and clustering economic systems regulation. The approach proposed creates with strong data distortion. An in-depth analysis of the background for enhancing automation, fairness selected procedures effectiveness was carried out, the procedures were tested on a large series of and efficiency of tax aurthorities work.

computational experiments and a comparison with Practical confirmation of the regulation natural experiments of field audits.

procedure proposed was carried out for a group of 24 agricultural enterprises [3], for The work treats issues of regularizing neural which 16 specific indicators analogous to ones network models (NNM) in the conditions of used for economic analysis in the work [5].

distortion, up to intentional one, of source data and deficiency of observations. We viewed Approximation tasks methods of data regularization and preprocessing for building up NNMs of a According to data of taxpayers it is generalized production function of economic necessary to build up a Bayesian group of NNM objects in [1]. NNM regularization for cases of in the framework of a metahypothesis H (a source data correspondence to Gaussian multilayer perceptron) and to obtain an optimal mixtures of distribution of probability density plan of field audits on its base. It is supposed that was explored by S.A.Shumsky [2]. However data contain both accidental distortion and there is a class of applied problems where this intentional distortion. NNM is presented as requirement is not fulfilled due to a strong = [F o F o F ](x). Here x is a vector of input 3 2 distortion of source data and a scarce data values, y is is an output value, is its calculated volume. The issue of Bayesian NNM value. Functionals F1, F2, F3 carry out regularization in the conditions of missing procedures of enhancing data homogeneity and certain information about distortion distribution informativeness such as source database, formed law has not been explored before. We offer clusters clearing, repair of seperate columns, estimations of posterior probability {P(h | H)} of q erasing erratic lines [2]. Neural network (NN) selected hypotheses {h } H of NNM group q organization and a type of activation functions in differing in the framework of a metahypothesis hidden layers varied in hypotheses space {hq} :

H (a neural network paradigm) with a number of - hypothesis h1 is a NN with one hidden hidden layers, a number of neural processing layer with a function of sigmoids activation:

elements in them and a kind of activation functions in case of an approximation task; f (s) =,a > 0;

learning speed and neighborhood of neural 1+ e-as processing element interaction with training - hypothesis h2 is a NN with two hidden sampling vector in case of a clustreing task. The layers with a function of sigmoids activation in application issue of the work is related to the both layers;

technologies of tax control and management [3- hypothesis h3 is a NN with two hidden 4]. The work treats restoring multifactorial layers with an activation function in the first curvilinear relationships hidden in data of layer and a hyperbolic tangent:

declarations with an aim to construct optimal 4- ۻ Clustering task f ( s ) = th( bs ),b > in the second layer;

- hypothesis h4 is a NN with one hidden A posterior filtration of trained layer with with an activation function of a hypotheses is carried out according to a hyperbolic tangent;

criterion estimating the clustering quality both - hypothesis h5 is a NN with two hidden in objects group density around clusters layers with an activation function of centers and in clusters distance from each hyperbolic tangent in the both layers;


Nm - hypothesis h6 is a NN with two hidden (xim m) d ;xc layers with an activation function of m=1 i=q =.

hyperbolic tangent in the first layer and a M sigmoid in the second layer.

(xc m) d ;xc i CM j=1 i= j+ It is proposed to use a frequency probability as an estimation of a posterior P = (N / N) q q Here q =1,2,...,Q, with Nm being a number of probability; is a number of "good" points for N q elements grouped in a mth cluster; d(xim ;xc m) the qth hypothesis, a deviation = - y / y g g g g being the Euclidean distance from the explored between a declared value and a calculated value object xim to the center of its cluster xc ; q m does not exceed the expert set level, N is a total being a hypothesis number in a set, M being the number of points produced for a trained NNM.

number of clusters; d (xc ;xcm) being the Further on a -criterion of selection is built-up i for field audits [3] considering a deviation, a distance between ith and mth clusters, M being prehistory and a scale for a gth taxpayer:

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