7 research outputs found
Full "Laplacianised" posterior naive Bayesian algorithm
BACKGROUND: In the last decade the standard Naive Bayes (SNB) algorithm has been widely employed in multiβclass classification problems in cheminformatics. This popularity is mainly due to the fact that the algorithm is simple to implement and in many cases yields respectable classification results. Using clever heuristic arguments βanchoredβ by insightful cheminformatics knowledge, Xia et al. have simplified the SNB algorithm further and termed it the Laplacian Corrected Modified Naive Bayes (LCMNB) approach, which has been widely used in cheminformatics since its publication. In this note we mathematically illustrate the conditions under which Xia et al.βs simplification holds. It is our hope that this clarification could help Naive Bayes practitioners in deciding when it is appropriate to employ the LCMNB algorithm to classify large chemical datasets. RESULTS: A general formulation that subsumes the simplified Naive Bayes version is presented. Unlike the widely used NB method, the Standard Naive Bayes description presented in this work is discriminative (not generative) in nature, which may lead to possible further applications of the SNB method. CONCLUSIONS: Starting from a standard Naive Bayes (SNB) algorithm, we have derived mathematically the relationship between Xia et al.βs ingenious, but heuristic algorithm, and the SNB approach. We have also demonstrated the conditions under which Xia et al.βs crucial assumptions hold. We therefore hope that the new insight and recommendations provided can be found useful by the cheminformatics community
Proposed algorithm for image classification using regression-based pre-processing and recognition models
Image classification algorithms can categorise pixels regarding to image attributes with the pre-processing of learnerβs trained samples. The precision and classification accuracy are complex to compute due to the variable size of pixels (different image width and height) and numerous characteristics of image per se. This research proposes an image classification algorithm based on regression-based pre-processing and the recognition models. The proposed algorithm focuses on an optimization of pre-processing results such as accuracy and precision. To evaluate and validate, recognition model is mapped in order to cluster the digital images which are developing the problem of a multidimensional state space. Simulation results show that compared to existing algorithms, the proposed method outperforms with the optimal number of precision and accuracy in classification as well as results higher matching percentage based upon image analytics
Granularity analysis of classification and estimation for complex datasets with MOA
Dispersed and unstructured datasets are substantial parameters to realize an exact amount of the required space. Depending upon the size and the data distribution, especially, if the classes are significantly associating, the level of granularity to agree a precise classification of the datasets exceeds. The data complexity is one of the major attributes to govern the proper value of the granularity, as it has a direct impact on the performance. Dataset classification exhibits the vital step in complex data analytics and designs to ensure that dataset is prompt to be efficiently scrutinized. Data collections are always causing missing, noisy and out-of-the-range values. Data analytics which has not been wisely classified for problems as such can induce unreliable outcomes. Hence, classifications for complex data sources help comfort the accuracy of gathered datasets by machine learning algorithms. Dataset complexity and pre-processing time reflect the effectiveness of individual algorithm. Once the complexity of datasets is characterized then comparatively simpler datasets can further investigate with parallelism approach. Speedup performance is measured by the execution of MOA simulation. Our proposed classification approach outperforms and improves granularity level of complex datasets
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Target Fishing: A Single-Label or Multi-Label Problem?
According to Cobanoglu et al and Murphy, it is now widely acknowledged that the single target paradigm (one protein or target, one disease, one drug) that has been the dominant premise in drug development in the recent past is untenable. More often than not, a drug-like compound (ligand) can be promiscuous - that is, it can interact with more than one target protein. In recent years, in in silico target prediction methods the promiscuity issue has been approached computationally in different ways. In this study we confine attention to the so-called ligand-based target prediction machine learning approaches, commonly referred to as target-fishing. With a few exceptions, the target-fishing approaches that are currently ubiquitous in cheminformatics literature can be essentially viewed as single-label multi-classification schemes; these approaches inherently bank on the single target paradigm assumption that a ligand can home in on one specific target. In order to address the ligand promiscuity issue, one might be able to cast target-fishing as a multi-label multi-class classification problem. For illustrative and comparison purposes, single-label and multi-label Naive Bayes classification models (denoted here by SMM and MMM, respectively) for target-fishing were implemented. The models were constructed and tested on 65,587 compounds and 308 targets retrieved from the ChEMBL17 database. SMM and MMM performed differently: for 16,344 test compounds, the MMM model returned recall and precision values of 0.8058 and 0.6622, respectively; the corresponding recall and precision values yielded by the SMM model were 0.7805 and 0.7596, respectively. However, at a significance level of 0.05 and one degree of freedom McNemar test performed on the target prediction results returned by SMM and MMM for the 16,344 test ligands gave a chi-squared value of 15.656, in favour of the MMM approach
ΠΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠΏΠ΅ΠΊΡΡΠΎΠ² Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Ρ ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ: Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΈ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΡ
oai:www.bmc-rm.org:article/4An essential characteristic of chemical compounds is their biological activity since its presence can become the basis for the use of the substance for therapeutic purposes, or, on the contrary, limit the possibilities of its practical application due to the manifestation of side action and toxic effects. Computer assessment of the biological activity spectra makes it possible to determine the most promising directions for the study of the pharmacological action of particular substances, and to filter out potentially dangerous molecules at the early stages of research. For more than 25 years, we have been developing and improving the computer program PASS (Prediction of Activity Spectra for Substances), designed to predict the biological activity spectrum of substance based on the structural formula of its molecules. The prediction is carried out by the analysis of structure-activity relationships for the training set, which currently contains information on structures and known biological activities for more than one million molecules. The structure of the organic compound is represented in PASS using Multilevel Neighborhoods of Atoms descriptors; the activity prediction for new compounds is performed by the naive Bayes classifier and the structure-activity relationships determined by the analysis of the training set. We have created and improved both local versions of the PASS program and freely available web resources based on PASS (http://www.way2drug.com). They predict several thousand biological activities (pharmacological effects, molecular mechanisms of action, specific toxicity and adverse effects, interaction with the unwanted targets, metabolism and action on molecular transport), cytotoxicity for tumor and non-tumor cell lines, carcinogenicity, induced changes of gene expression profiles, metabolic sites of the major enzymes of the first and second phases of xenobiotics biotransformation, and belonging to substrates and/or metabolites of metabolic enzymes.
The web resource Way2Drug is used by over 19 000 researchers from more than 100 countries around the world, which allowed them to obtain over 600 000 predictions and publish about 500 papers describing the obtained results. The analysis of the published works shows that in some cases the interpretation of the prediction results presented by the authors of these publications requires an adjustment. In this work, we provide the theoretical basis and consider, on particular examples, the opportunities and limitations of computer-aided prediction of biological activity spectra.ΠΠ°ΠΆΠ½ΠΎΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΎΠΉ Ρ
ΠΈΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΈΡ
Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠ°Ρ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ, ΠΏΠΎΡΠΊΠΎΠ»ΡΠΊΡ Π΅Π΅ Π½Π°Π»ΠΈΡΠΈΠ΅ ΠΌΠΎΠΆΠ΅Ρ ΡΡΠ°ΡΡ ΠΎΡΠ½ΠΎΠ²ΠΎΠΉ Π΄Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π²Π΅ΡΠ΅ΡΡΠ²Π° Π² ΡΠ΅ΡΠ°ΠΏΠ΅Π²ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅Π»ΡΡ
, Π»ΠΈΠ±ΠΎ, Π½Π°ΠΏΡΠΎΡΠΈΠ², ΠΎΠ³ΡΠ°Π½ΠΈΡΠΈΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ Π΅Π³ΠΎ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ Π²ΡΠ»Π΅Π΄ΡΡΠ²ΠΈΠ΅ ΠΏΡΠΎΡΠ²Π»Π΅Π½ΠΈΡ ΠΏΠΎΠ±ΠΎΡΠ½ΡΡ
ΠΈ ΡΠΎΠΊΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΠ΅ΠΊΡΠΎΠ². ΠΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½Π°Ρ ΠΎΡΠ΅Π½ΠΊΠ° ΡΠΏΠ΅ΠΊΡΡΠ° Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π΄Π°Π΅Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΠΏΠ΅ΡΡΠΏΠ΅ΠΊΡΠΈΠ²Π½ΡΠ΅ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π΄Π»Ρ ΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ°ΡΠΌΠ°ΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄Π΅ΠΉΡΡΠ²ΠΈΡ ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠ½ΡΡ
Π²Π΅ΡΠ΅ΡΡΠ² ΠΈ ΠΎΡΡΠ΅ΡΡΡ ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»ΡΠ½ΠΎ ΠΎΠΏΠ°ΡΠ½ΡΠ΅ ΠΌΠΎΠ»Π΅ΠΊΡΠ»Ρ Π½Π° ΡΠ°Π½Π½ΠΈΡ
ΡΡΠ°Π΄ΠΈΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ. Π‘Π²ΡΡΠ΅ 25 Π»Π΅Ρ Π½Π°ΠΌΠΈ ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ° ΠΈ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠΉ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ PASS (Prediction of Activity Spectra for Substances), ΠΏΡΠ΅Π΄Π½Π°Π·Π½Π°ΡΠ΅Π½Π½ΠΎΠΉ Π΄Π»Ρ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΏΠ΅ΠΊΡΡΠ° Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π²Π΅ΡΠ΅ΡΡΠ²Π° ΠΏΠΎ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΡΠΎΡΠΌΡΠ»Π΅ Π΅Π³ΠΎ ΠΌΠΎΠ»Π΅ΠΊΡΠ». ΠΡΠΎΠ³Π½ΠΎΠ· ΠΎΡΡΡΠ΅ΡΡΠ²Π»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π½Π°Π»ΠΈΠ·Π° Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Β«ΡΡΡΡΠΊΡΡΡΠ°-Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΡΒ» Π΄Π»Ρ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ ΠΎΠ±ΡΡΠ°ΡΡΠ΅ΠΉ Π²ΡΠ±ΠΎΡΠΊΠΈ, Π² Π½Π°ΡΡΠΎΡΡΠ΅Π΅ Π²ΡΠ΅ΠΌΡ ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠ΅ΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡ ΠΎ ΡΡΡΡΠΊΡΡΡΠ°Ρ
ΠΈ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
Π²ΠΈΠ΄Π°Ρ
Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π±ΠΎΠ»Π΅Π΅ ΡΠ΅ΠΌ Π΄Π»Ρ ΠΌΠΈΠ»Π»ΠΈΠΎΠ½Π° ΠΌΠΎΠ»Π΅ΠΊΡΠ». ΠΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΡΡΡΠΊΡΡΡΡ ΠΌΠΎΠ»Π΅ΠΊΡΠ» ΠΎΡΠ³Π°Π½ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡ ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Π½ΠΎ Π² PASS ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ Π΄Π΅ΡΠΊΡΠΈΠΏΡΠΎΡΠΎΠ² Π°ΡΠΎΠΌΠ½ΡΡ
ΠΎΠΊΡΠ΅ΡΡΠ½ΠΎΡΡΠ΅ΠΉ (Multilevel Neighborhoods of Atoms), ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ Π΄Π»Ρ Π½ΠΎΠ²ΡΡ
ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΠΉ Π²ΡΠΏΠΎΠ»Π½ΡΠ΅ΡΡΡ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠΌ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Β«Π½Π°ΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΠ°ΠΉΠ΅ΡΠΎΠ²ΡΠΊΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π°Β» ΠΈ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠ΅ΠΉ Β«ΡΡΡΡΠΊΡΡΡΠ°-Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΡΒ», Π²ΡΡΠ²Π»ΡΠ΅ΠΌΡΡ
ΠΏΡΠΈ Π°Π½Π°Π»ΠΈΠ·Π΅ ΠΎΠ±ΡΡΠ°ΡΡΠ΅ΠΉ Π²ΡΠ±ΠΎΡΠΊΠΈ. ΠΠ°ΠΌΠΈ ΡΠΎΠ·Π΄Π°Π½Ρ ΠΈ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΡΡΡΡΡ ΠΊΠ°ΠΊ Π»ΠΎΠΊΠ°Π»ΡΠ½ΡΠ΅ Π²Π΅ΡΡΠΈΠΈ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ PASS, ΡΠ°ΠΊ ΠΈ ΡΠ²ΠΎΠ±ΠΎΠ΄Π½ΠΎ Π΄ΠΎΡΡΡΠΏΠ½ΡΠ΅ Π² ΠΠ½ΡΠ΅ΡΠ½Π΅Ρ Π²Π΅Π±-ΡΠ΅ΡΡΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ PASS (http://way2drug.com): ΠΏΡΠΎΠ³Π½ΠΎΠ· Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΡ
ΡΡΡΡΡ Π²ΠΈΠ΄ΠΎΠ² Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ (ΡΠ°ΡΠΌΠ°ΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΡΠ΅ΠΊΡΡ, ΠΌΠΎΠ»Π΅ΠΊΡΠ»ΡΡΠ½ΡΠ΅ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΡ Π΄Π΅ΠΉΡΡΠ²ΠΈΡ, ΡΠΏΠ΅ΡΠΈΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΎΠΊΡΠΈΡΠ½ΠΎΡΡΡ ΠΈ ΠΏΠΎΠ±ΠΎΡΠ½ΠΎΠ΅ Π΄Π΅ΠΉΡΡΠ²ΠΈΠ΅, ΠΌΠ΅ΡΠ°Π±ΠΎΠ»ΠΈΠ·ΠΌ, Π° ΡΠ°ΠΊΠΆΠ΅ Π²Π»ΠΈΡΠ½ΠΈΠ΅ Π½Π° Π½Π΅ΠΆΠ΅Π»Π°ΡΠ΅Π»ΡΠ½ΡΠ΅ ΠΌΠΈΡΠ΅Π½ΠΈ, ΠΌΠΎΠ»Π΅ΠΊΡΠ»ΡΡΠ½ΡΠΉ ΡΡΠ°Π½ΡΠΏΠΎΡΡ, Π³Π΅Π½Π½ΡΡ ΡΠΊΡΠΏΡΠ΅ΡΡΠΈΡ), ΠΏΡΠΎΠ³Π½ΠΎΠ· ΡΠΈΡΠΎΡΠΎΠΊΡΠΈΡΠ½ΠΎΡΡΠΈ Π΄Π»Ρ ΠΎΠΏΡΡ
ΠΎΠ»Π΅Π²ΡΡ
ΠΈ Π½Π΅ΠΎΠΏΡΡ
ΠΎΠ»Π΅Π²ΡΡ
ΠΊΠ»Π΅ΡΠΎΡΠ½ΡΡ
Π»ΠΈΠ½ΠΈΠΉ, ΠΏΡΠΎΠ³Π½ΠΎΠ· ΠΊΠ°Π½ΡΠ΅ΡΠΎΠ³Π΅Π½Π½ΠΎΡΡΠΈ, ΠΏΡΠΎΠ³Π½ΠΎΠ· ΠΈΠ½Π΄ΡΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΎΡΠ³Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½ΠΈΡΠΌΠΈ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ ΠΏΡΠΎΡΠΈΠ»Π΅ΠΉ ΡΠΊΡΠΏΡΠ΅ΡΡΠΈΠΈ Π³Π΅Π½ΠΎΠ², ΠΏΡΠΎΠ³Π½ΠΎΠ· Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ Ρ ΡΠ΅ΡΠΌΠ΅Π½ΡΠ°ΠΌΠΈ ΠΌΠ΅ΡΠ°Π±ΠΎΠ»ΠΈΠ·ΠΌΠ° Π»Π΅ΠΊΠ°ΡΡΡΠ², Π² ΡΠΎΠΌ ΡΠΈΡΠ»Π΅ ΠΏΡΠΎΠ³Π½ΠΎΠ· ΡΠ°ΠΉΡΠΎΠ² ΠΌΠ΅ΡΠ°Π±ΠΎΠ»ΠΈΠ·ΠΌΠ°, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΎΠ³Π½ΠΎΠ· ΠΏΡΠΈΠ½Π°Π΄Π»Π΅ΠΆΠ½ΠΎΡΡΠΈ ΠΊ ΡΡΠ±ΡΡΡΠ°ΡΠ°ΠΌ ΠΈ/ΠΈΠ»ΠΈ ΠΌΠ΅ΡΠ°Π±ΠΎΠ»ΠΈΡΠ°ΠΌ ΡΡΠΈΡ
ΡΠ΅ΡΠΌΠ΅Π½ΡΠΎΠ².
ΠΠ΅Π±-ΡΠ΅ΡΡΡΡ Way2Drug ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡ ΡΠ²ΡΡΠ΅ 19 ΡΡΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ Π±ΠΎΠ»Π΅Π΅ ΡΠ΅ΠΌ ΠΈΠ· 100 ΡΡΡΠ°Π½ ΠΌΠΈΡΠ°, ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΠ»ΠΎ ΠΈΠΌ ΠΎΡΡΡΠ΅ΡΡΠ²ΠΈΡΡ ΡΠ²ΡΡΠ΅ 600 ΡΡΡΡΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΎΠ² ΠΈ ΠΎΠΏΡΠ±Π»ΠΈΠΊΠΎΠ²Π°ΡΡ ΠΎΠΊΠΎΠ»ΠΎ 500 ΡΠ°Π±ΠΎΡ Ρ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ΠΌ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ². ΠΠ½Π°Π»ΠΈΠ· ΠΎΠΏΡΠ±Π»ΠΈΠΊΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ°Π±ΠΎΡ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Π΅Ρ, ΡΡΠΎ Π² Π½Π΅ΠΊΠΎΡΠΎΡΡΡ
ΡΠ»ΡΡΠ°ΡΡ
ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΠΌΠ°Ρ Π°Π²ΡΠΎΡΠ°ΠΌΠΈ ΡΡΠΈΡ
ΠΏΡΠ±Π»ΠΈΠΊΠ°ΡΠΈΠΉ ΠΈΠ½ΡΠ΅ΡΠΏΡΠ΅ΡΠ°ΡΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΠΏΡΠΎΠ³Π½ΠΎΠ·Π° ΡΡΠ΅Π±ΡΠ΅Ρ ΠΊΠΎΡΡΠ΅ΠΊΡΠΈΡΠΎΠ²ΠΊΠΈ. Π ΡΠ°ΠΌΠΊΠ°Ρ
Π½Π°ΡΡΠΎΡΡΠ΅ΠΉ ΡΠ°Π±ΠΎΡΡ ΠΌΡ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΠΈΠΌ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΈ ΡΠ°ΡΡΠΌΠΎΡΡΠΈΠΌ Π½Π° ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠ½ΡΡ
ΠΏΡΠΈΠΌΠ΅ΡΠ°Ρ
Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΈ ΠΎΠ³ΡΠ°Π½ΠΈΡΠ΅Π½ΠΈΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΏΠ΅ΠΊΡΡΠΎΠ² Π±ΠΈΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ