Neural network synthesis based on evolutionary optimization
The evolutionary approach for neural network structural synthesis is considered in this paper. The new method of multimodal evolutionary search with a chromosome clustering is offered. The developed method is based on the idea of simultaneous search of several optimums, thus chromosomes are grouped...
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Oliinyk, A.A. Subbotin, S.A. 2015-09-08T11:07:33Z 2015-09-08T11:07:33Z 2015 Neural network synthesis based on evolutionary optimization / A.A. Oliinyk, S.A. Subbotin // Системні дослідження та інформаційні технології. — 2015. — № 1. — С. 77-86. — Бібліогр.: 14 назв. — англ. 1681–6048 https://nasplib.isofts.kiev.ua/handle/123456789/86133 004.93 The evolutionary approach for neural network structural synthesis is considered in this paper. The new method of multimodal evolutionary search with a chromosome clustering is offered. The developed method is based on the idea of simultaneous search of several optimums, thus chromosomes are grouped in clusters on their arrangement in a search space. So stable subpopulations in different clusters are formed, diversity of search is provided, and convergence to different local minima is reached that allows to find closer to optimal architectures of neural networks. Software implementing proposed method is developed. The experiments with proposed method in practical problem solving were conducted. У статті розглянуто еволюційний підхід для структурного синтезу нейронних мереж. Запропоновано новий метод мультимодального еволюційного пошуку з кластеризацією хромосом. Розроблений метод заснований на ідеї одночасного пошуку декількох оптимумів, при якому хромосоми групуються у кластери за їхнім розташуванням у просторі пошуку. Таким чином формуються стабільні субпопуляції в різних кластерах, забезпечується різноманітність пошуку і досягається збіжність до різних локальних мінімумів , що дозволяє знайти архітектуру нейронної мережі, близьку до оптимальної. Розроблено програмне забезпечення, що реалізує запропонований метод, а також проведено експерименти з його дослідження при вирішенні практичних завдань. В статье рассмотрен эволюционный подход для структурного синтеза нейронных сетей. Предложен новый метод мультимодального эволюционного поиска с кластеризацией хромосом. Разработанный метод основан на идее одновременного поиска нескольких оптимумов, при котором хромосомы группируются в кластеры по их расположению в пространстве поиска. Таким образом формируются стабильные субпопуляции в различных кластерах, обеспечивается разнообразие поиска и достигается сходимость к различным локальным минимумам, что позволяет найти архитектуру нейронной сети, близкую к оптимальной. Разработано программное обеспечение, реализующее предложенный метод, а также проведены эксперименты по его исследованию при решении практических задач. en Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України Системні дослідження та інформаційні технології Проблемно і функціонально орієнтовані комп’ютерні системи та мережі Neural network synthesis based on evolutionary optimization Синтез нейронних мереж на основі еволюційної оптимізації Синтез нейронных сетей на основе эволюционной оптимизации Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Neural network synthesis based on evolutionary optimization |
| spellingShingle |
Neural network synthesis based on evolutionary optimization Oliinyk, A.A. Subbotin, S.A. Проблемно і функціонально орієнтовані комп’ютерні системи та мережі |
| title_short |
Neural network synthesis based on evolutionary optimization |
| title_full |
Neural network synthesis based on evolutionary optimization |
| title_fullStr |
Neural network synthesis based on evolutionary optimization |
| title_full_unstemmed |
Neural network synthesis based on evolutionary optimization |
| title_sort |
neural network synthesis based on evolutionary optimization |
| author |
Oliinyk, A.A. Subbotin, S.A. |
| author_facet |
Oliinyk, A.A. Subbotin, S.A. |
| topic |
Проблемно і функціонально орієнтовані комп’ютерні системи та мережі |
| topic_facet |
Проблемно і функціонально орієнтовані комп’ютерні системи та мережі |
| publishDate |
2015 |
| language |
English |
| container_title |
Системні дослідження та інформаційні технології |
| publisher |
Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України |
| format |
Article |
| title_alt |
Синтез нейронних мереж на основі еволюційної оптимізації Синтез нейронных сетей на основе эволюционной оптимизации |
| description |
The evolutionary approach for neural network structural synthesis is considered in this paper. The new method of multimodal evolutionary search with a chromosome clustering is offered. The developed method is based on the idea of simultaneous search of several optimums, thus chromosomes are grouped in clusters on their arrangement in a search space. So stable subpopulations in different clusters are formed, diversity of search is provided, and convergence to different local minima is reached that allows to find closer to optimal architectures of neural networks. Software implementing proposed method is developed. The experiments with proposed method in practical problem solving were conducted.
У статті розглянуто еволюційний підхід для структурного синтезу нейронних мереж. Запропоновано новий метод мультимодального еволюційного пошуку з кластеризацією хромосом. Розроблений метод заснований на ідеї одночасного пошуку декількох оптимумів, при якому хромосоми групуються у кластери за їхнім розташуванням у просторі пошуку. Таким чином формуються стабільні субпопуляції в різних кластерах, забезпечується різноманітність пошуку і досягається збіжність до різних локальних мінімумів , що дозволяє знайти архітектуру нейронної мережі, близьку до оптимальної. Розроблено програмне забезпечення, що реалізує запропонований метод, а також проведено експерименти з його дослідження при вирішенні практичних завдань.
В статье рассмотрен эволюционный подход для структурного синтеза нейронных сетей. Предложен новый метод мультимодального эволюционного поиска с кластеризацией хромосом. Разработанный метод основан на идее одновременного поиска нескольких оптимумов, при котором хромосомы группируются в кластеры по их расположению в пространстве поиска. Таким образом формируются стабильные субпопуляции в различных кластерах, обеспечивается разнообразие поиска и достигается сходимость к различным локальным минимумам, что позволяет найти архитектуру нейронной сети, близкую к оптимальной. Разработано программное обеспечение, реализующее предложенный метод, а также проведены эксперименты по его исследованию при решении практических задач.
|
| issn |
1681–6048 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/86133 |
| citation_txt |
Neural network synthesis based on evolutionary optimization / A.A. Oliinyk, S.A. Subbotin // Системні дослідження та інформаційні технології. — 2015. — № 1. — С. 77-86. — Бібліогр.: 14 назв. — англ. |
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AT oliinykaa neuralnetworksynthesisbasedonevolutionaryoptimization AT subbotinsa neuralnetworksynthesisbasedonevolutionaryoptimization AT oliinykaa sintezneironnihmerežnaosnovíevolûcíinoíoptimízacíí AT subbotinsa sintezneironnihmerežnaosnovíevolûcíinoíoptimízacíí AT oliinykaa sintezneironnyhseteinaosnoveévolûcionnoioptimizacii AT subbotinsa sintezneironnyhseteinaosnoveévolûcionnoioptimizacii |
| first_indexed |
2025-11-27T02:12:24Z |
| last_indexed |
2025-11-27T02:12:24Z |
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| fulltext |
© A.A. Oliinyk, S.A. Subbotin, 2015
Системні дослідження та інформаційні технології, 2015, № 1 77
UDC 004.93
NEURAL NETWORK SYNTHESIS
BASED ON EVOLUTIONARY OPTIMIZATION
A.A. OLIINYK, S.A. SUBBOTIN
The evolutionary approach for neural network structural synthesis is considered in
this paper. The new method of multimodal evolutionary search with a chromosome
clustering is offered. The developed method is based on the idea of simultaneous
search of several optimums, thus chromosomes are grouped in clusters on their
arrangement in a search space. So stable subpopulations in different clusters are
formed, diversity of search is provided, and convergence to different local minima is
reached that allows to find closer to optimal architectures of neural networks. Soft-
ware implementing proposed method is developed. The experiments with proposed
method in practical problem solving were conducted.
INTRODUCTION
Nowadays neural networks, with their ability to derive meaning from complicated
or imprecise data, are widely used to extract patterns and detect trends that are too
complex to be noticed by either humans or other computer techniques [1, 2].
It is known that the architecture of a neural network determines its informa-
tion processing capability [3]. So architecture design has become one of the most
important tasks in neural network research and application.
The architecture of a neural network includes its topological structure, the
transfer and discriminant function of each node in the network.
Before present times architecture design is still a human expert’s job. It de-
pends heavily on the expert experience and a tedious trial-and-error process.
There is no systematic way to design a near-optimal architecture for a given task
automatically.
The synthesis of neural network is concerned with the optimization of some
criterion like a sum of squared error. However, solving of this optimization task is
engaged with problems caused by high dimension of training sample, multiextre-
meness of criterion function, nondifferentiability of activation functions [2], that
complicates or makes impossible application of traditional optimization
methods [1].
Research on constructive and destructive algorithms represents an effort to-
wards the automatic design of architectures. A constructive algorithm starts with
a minimal network (network with minimal number of hidden layers, nodes, and
connections) and adds new layers, nodes, and connections when necessary during
training while a destructive algorithm does the opposite, i.e., starts with the
maximal network and deletes unnecessary layers, nodes, and connections during
training. However, such structural hill climbing methods are susceptible to be-
A.A. Oliinyk, S.A. Subbotin
ISSN 1681–6048 System Research & Information Technologies, 2015, № 1 78
coming trapped at structural local optima. In addition, they only investigate
restricted topological subsets rather than the complete class of network architec-
tures [3].
For the synthesis of neural network it is expedient to use methods of evolu-
tionary search that are a family of computational models inspired by evolution.
These methods differ from more traditional optimization techniques in that they
involve a search from a population of solutions, not from a single point. Each
iteration of an evolutionary method involves a competitive selection that weeds
out poor solutions. The solutions with high fitness are recombined with other
solutions by swapping parts of a solution with another [4].
However, the result of evolutionary optimization is the set of equal or few
distinguished decisions. Therefore, the optimum structure of neural network can
be not found because classical evolutionary methods can not uniformly cover
search space, and large areas in space of variables can appear not investigated for
the limited amount of iterations.
Therefore, the purpose of this work is a development of a multimodal
method of evolutionary search which raises a diversity of a population and allows
to cover in regular more intervals space of search which result is a set of various
decisions (structures of neural network), that allows to choose architecture of neu-
ral network, in the best way satisfying external criteria.
PROBLEM STATEMENT
Let A be a maximal allowable quantity of neurons in the network, >< YX , is
a sample of training data, where }{ iXX = is a set of feature values describing
considered object or process; }{ pyY = is a set of target values; }{ ipi xX = is an
i-th feature in the sample, ;,,2,1 Li K= ipx is a value of i-th feature for p-th ob-
servation of the sample, ;,,2,1 mp K= py represents the value of the predicted
parameter for p-th observation of the sample; L is a quantity of features in the
sample; m is a quantity of observations.
So the problem of structural synthesis of neural network )(CNNNN = can
be formulated as a search problem opt),,( →= YXNNξ in architecture space,
where ),( ALCC = is a matrix determining presence or absence of the connec-
tions between elements in the network ,NN ),,( YXNN=ξ is an optimality cri-
teria, e.g., lowest training error, lowest network complexity, etc.
STRUCTURAL SYNTHESIS OF NEURAL NETWORK BASED ON
EVOLUTIONARY OPTIMIZATION
For application of evolutionary search for neural network synthesis it is necessary
to determine a scheme of representation of network structure in a chromosome
and to choose a fitness-function for estimation of chromosomes.
Neural network synthesis based on evolutionary optimization
Системні дослідження та інформаційні технології, 2015, № 1 79
There are following methods of encoding of the information on neural net-
work structure in chromosomes [3]: direct encoding, parametric representation,
developmental rule representation, fractal representation, etc. One of the most
effective encoding method is a direct encoding at which presence of each possible
connection is directly described in a binary matrix of connections ,C where value
ij
c corresponds to presence )1( =ijc or absence )0( =ijc of connection from i-th
to j-th neuron. Thus, the neural network is represented as a connectivity matrix.
The chromosome (Fig. 1) in direct encoding scheme is represented by the bit
line containing the information about presence of connections.
Chromosome decoding to the structure of neural network occurs as follows.
Step 1. Generate connectivity matrix (Fig. 1, b) of neural network, corre-
sponding to a chromosome (Fig. 1, a).
Step 2. Construct a graph (Fig. 1, c) based on the connectivity matrix.
Step 3. Synthesize a neural network (Fig. 1, d) on the basis of the graph con-
structed on the previous step, having removed thus neurons, not having target
connections with neurons of the subsequent layers.
In case of need a choice of neuron activation function at structural synthesis
it is possible to enter in a chromosome the additional genes containing the infor-
mation of a kind of activation function for each neuron.
Structural synthesis of neural network based on the evolutionary approach
can be executed as the following sequence of steps [5–8].
Step 1. Generate the initial population of chromosomes containing the in-
formation of network’s structure.
Step 2. Compute the fitness of each chromosome in the current population.
Step 2.1. Decode each chromosome in the population into architecture of the
neural network.
Step 2.2. Train each neural network by the chosen rule using the data from
training sample.
Step 2.3. Calculate value of the fitness-function considering a training error
and complexity of constructed neural network.
Fig. 1. An example of a chromosome and its decoding: a — chromosome, b — connec-
tivity matrix, c — graph (architecture), d — synthesized neural network
⎟
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0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1
a
A.A. Oliinyk, S.A. Subbotin
ISSN 1681–6048 System Research & Information Technologies, 2015, № 1 80
Step 3. Check up search termination criteria. In the case of their satisfaction
go to a step 7.
Step 4. Select the most fitted chromosomes for their crossing and mutation.
Step 5. Execute crossover and mutation operators on chromosomes selected
earlier.
Step 6. Create new generation from the chromosomes obtained on the previ-
ous step and the elite chromosomes of the current generation. Go to a step 2.
Step 7. End.
A MULTIMODAL EVOLUTIONARY METHOD FOR STRUCTURAL
SYNTHESIS OF NEURAL NETWORKS
It is shown in [3] that the surface of performance function for neural networks
structural synthesis is nondiferentiable, noisy, complex and multimodal since dif-
ferent architectures may have similar performance.
The result of usage of classical evolutionary methods is the population of
a few distinguished solutions therefore the found decision can appear a local op-
timum of multiextreme function. Such a decision (structure of neural network), as
a rule, is inefficient at its usage in practice.
Therefore, for structural synthesis of neural networks it is expedient to use
evolutionary methods capable to find several suboptimum decisions. The main
problem of usage of traditional evolutionary methods for optimization of multi-
modal functions is a premature convergence to a local optimum. For overcoming
this problem two groups of methods are developed: avoid strategies and repair
strategies [9–13].
In avoid strategies method, the main idea is to prevent premature conver-
gence to a local optimum [9–12]. The algorithms attempting to slow down genetic
convergence aim at maintaining the population’s diversity for a longer period and
thereby avoid stagnation in a local optimum. Algorithms in this category either
use a replacement scheme for updating the population or try to reduce the spread
of genes by introducing a spatial population topology. The strategies trying to
prevent overlap of solutions using penalty functions for reduction of the probabil-
ity of occurrence in a population of similar solutions that attracts necessity of
penalty function calculation for each chromosome in the population, hence, con-
siderably slows down process of evolutionary search.
In repair strategies method, algorithms either maintain diversity by mass ex-
tinction techniques or by introducing new genetic material when population con-
vergence is detected, that also demands significant time expenses [9, 13].
In the developed method of multimodal evolutionary search with chromo-
some clustering it is offered to group solutions (chromosome) in cluster on their
arrangement in a search space.
The suggested method during evolutionary search defines the groups of
similar chromosomes and raises a variety of a population by reducing the of fit-
ness function values of chromosomes depending on a closeness to the center of
their group.
Neural network synthesis based on evolutionary optimization
Системні дослідження та інформаційні технології, 2015, № 1 81
The developed polymodal evolutionary search with the chromosome cluster-
ing assumes the execution of the following steps.
Step 1. Set: the quantity of optimums (the quantity optimum architectures of
neural network) k which is required to be found during evolutionary search;
N represents the quantity of chromosomes in a population, .kN >>
Step 2. Set the counter of iterations: .1=t
Step 3. Set the quantity of elite chromosomes: .kke =
Step 4. Initialize an initial population with chromosomes iH ),,2,1( Nj K=
with length L (the quantity of features).
Step 5. Calculate the fitness function value )( jHf for each chromo-
some .jH
Step 6. Group chromosomes in k clusters based on their fitness function
values and an arrangement in an architecture space.
Step 6.1. For each chromosome jH calculate Hamming distance [2] to all
other chromosomes in a population. Hamming distance d between chromosomes
jH and lH is calculated by the formula:
,||
1
∑
=
−=
L
u
luju hhd
where juh and luh are the values of genes of chromosomes jH and ,lH respec-
tively
Step 6.2. Set the counter of generated clasters: .1=m
Step 6.3. Choose a chromosome with the best fitness function value as the
center of m-th cluster. Thus the chromosomes which yet have been not grouped in
clusters are considered.
Step 6.4. Add in cluster )1/( −kN chromosomes nearest on Hamming dis-
tance to a chromosome, being the center of current m-th cluster.
Step 6.5. If km = then go to a step 7.
Step 6.6. Set: .1+= mm Go to a step 6.3.
Step 7. Reduce fitness function values of the chromosomes which are not
being the best in cluster using the formula:
,
max,
, j
s
j
j
jn f
d
d
f ⎟
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=
where jf is the fitness function value before j-th chromosome changing; jnf , is
a new fitness function value of j-th chromosome; jd is a Hamming distance from
j-th chromosome to the center of its group; jdmax, is a maximal Hamming dis-
tance in the cluster of j-th chromosome; s is the parameter determining a degree
of fitness function reduction of chromosomes, not being the centers of cluster,
.1≥s
Step 8. Apply crossover and mutation operators.
A.A. Oliinyk, S.A. Subbotin
ISSN 1681–6048 System Research & Information Technologies, 2015, № 1 82
Step 9. Generate new population. Thus the best (elite) chromosomes in
every cluster are guaranteed pass in the new generation.
Step 10. If Tt = (T is the maximum possible quantity of iterations), then
go to a step 13.
Step 11. Set: .1+= tt
Step 12. Go to a step 5.
Step 13. Estimate each of k the chromosomes being the centers of clusters,
with the help of the data of test sample. Choose the best chromosome. Neural
network, corresponding to such chromosome, is the solution.
Step 14. End.
The developed method of multimodal evolutionary search with chromosome
clustering raises a variety of a population and allows to cover in regular more in-
tervals search space, raising thus an opportunity of search of a global optimum
and increasing probability of successful execution of estimation procedure of the
founded solutions with the help of the external criteria on test sample.
EXPERIMENTS AND RESULTS
The suggested method of multimodal evolutionary search with the chromosome
clustering has been realised as computer program. The experimental research of
the offered method of neural network synthesis was carried out based on the deci-
sion of a vehicle classification problem by 2d gray-scale images.
The initial sample contained the transformed graphic representations of ve-
hicles received from video cameras at streets in Zaporozhye, Ukraine. Sample
consisted of 1062 vehicle images, each of which was characterized by 4096 fea-
tures representing normalized values of the image points intensity projected on
a sensor matrix of 64×64 pixels. Using these 4096 features there were calculated
26 generalizing features. Vehicles were classified on cars, minibuses, motorcy-
cles, trucks and buses. For each class of transport the model was constructed.
Thus the problem has consisted in synthesis of four classification models of each
type of vehicles based on 26 generalizing features [14].
The coding of a potential solution was performed like at Fig. 1. There are
evolutionary operators were used: roulette wheel selection, uniform crossover,
simple mutation. The initial parameters of all evolutionary methods were estab-
lished by the following: population size ;100=N crossover probability
;8,0=crp mutation rate .02,0=rm Stopping criteria: maximum number of itera-
tions ;100=T achievement of comprehensible value of the fitness function equal
to .01.0
The purpose of the experiments was to synthesize the optimal neural network
model. The maximal allowable sum of squared error on this model for training data
and test sample is 0,01 and 0,02, respectively. Results of experiments for different
quantity of clusters are presented in the table 1 lsSSE( represents a sum of squared
error for learning sample, tsSSE is a sum of squared error for test sample, n repre-
sents the quantity of the obtained models providing sufficient value of sum of
squared error for test sample).
Neural network synthesis based on evolutionary optimization
Системні дослідження та інформаційні технології, 2015, № 1 83
T a b l e 1 . Results of Experiments
Quantity of clusters lsSSE tsSSE n
1 0,0098 0,0272 0
2 0,0095 0,0227 0
3 0,0096 0,0183 1
4 0,0094 0,0142 1
5 0,0095 0,0137 2
The example of running different evolutionary methods for the decision of
a vehicles classification problem is shown in Fig. 2.
The comparison of the proposed method with other evolutionary methods is
presented in the table 2 (τ represents a time for evolutionary optimisation, countf
is the quantity of fitness function calculation).
The best solution (neural network structure) found by the proposed method
is shown in Fig. 3.
T a b l e 2 . Comparison of Evolutionary Methods
Method τ countf lsSSE tsSSE
Canonical genetic algorithm 709,3 9619 0,0098 0,0272
Avoid strategies method 587,9 8018 0,0095 0,0191
Repair strategies method 629,8 8714 0,0097 0,0158
Multimodal evolutionary search 521,7 7092 0,0095 0,0137
Fig. 2. An example of evolutionary methods running
A.A. Oliinyk, S.A. Subbotin
ISSN 1681–6048 System Research & Information Technologies, 2015, № 1 84
The weight matrix of synthesized neural network is presented in the table 3,
where μ represents the number of layer in the network; ρ is the number of neuron
in the layer; b is the value of bias; node is the first node in the connection; w is the
value of weight.
The experiments have shown that as a result of application of multimodal
evolutionary search with the chromosome clustering stable subpopulations are
formed in different clusters, heterogeneity of search is provided, and also conver-
gence to different local minima is reached.
CONCLUSION
The new method of multimodal evolutionary search with a chromosome cluster-
ing is offered in this paper. The developed method is based on idea of simultane-
ous search of several optimums, thus solutions (architectures) are grouped in clus-
ters on their arrangement in architecture space that results in more uniform
covering of search space. Comparison of the results obtained with the help of the
developed method with results of application of classical evolutionary methods
shows that the offered method allows to synthesize closer to optimum neural net-
works because of more uniform covering of search space. Thus, the suggested
method can be recommended for application in practice for solving different
problems in pattern recognition and computational diagnosis.
Fig. 3. The best solution (neural network structure)
x1
x7
x10
x12
x2
x5
x6
x20
x23
x7
x8
x11
x15
x5
x6
x18
x23
x2
x10
x25
9
y
Neural network synthesis based on evolutionary optimization
Системні дослідження та інформаційні технології, 2015, № 1 85
Table 3. The Weight Matrix of Synthesized Neural Network
μ ρ b node w
feature х1 –1,7264
feature х7 2,2621
feature х10 0,8386
1 – 0,1852
feature х12 – 0,1721
feature х2 – 0,7502
feature х5 – 1,1064
feature х6 2,1628
feature х20 1,8531
2 – 0,5291
feature х23 1,0372
feature х7 0,8580
feature х8 – 0,6082
feature х11 – 0,5810
3 1,2674
feature х15 – 1,1310
feature х5 0,5502
feature х16 1,3051
feature х18 1,2109
4 – 0,9620
feature х23 – 2,0945
feature х2 1,0845
feature х10 – 1,6093
1
5 0,4281
feature х25 0,8803
neuron 1 0,7726 6 –1,6528
neuron 3 – 0,6190
neuron 2 – 1,5278
neuron 3 – 1,7429 7 2,9381
neuron 4 0,9726
neuron 3 0,7904
neuron 4 0,4086
2
8 0,7804
neuron 5 – 1,0462
neuron 6 0,8054
neuron 7 – 1,7960 3 9 0,3174
neuron 8 0,9467
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Received 14.02.2014
From the Editorial Board: the article corresponds completely to submitted manuscript.
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