The Hough Transform and Uncertainity

The paper deals with the generalisations of the Hough Transform making it the mean for analysing uncertainty. Some results related Hough Transform for Euclidean spaces are represented. These latter use the powerful means of the Generalised Inverse for description the Transform by itself as well as its Accumulator Function

Fuzzy sets: Abstraction Axiom, Statistical Interpretation, Observations of Fuzzy Sets

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities

Technology of Classification of Electronic Documents Based on the Theory of Disturbance of Pseudoinverse Matrices

Technology of classification of electronic documents based on the theory of disturbance of pseudoinverse matrices was proposed

Representation of Neural Networks by Dynamical Systems

Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered

UNCERTAINTY AND FUZZY SETS: CLASSIFYING THE SITUATION

Abstract: The so called "Plural Uncertainty Model" is considered, in which statistical, maxmin, interva

Dynamical Systems in Description of Nonlinear Recursive Regression Transformers

The task of approximation-forecasting for a function, represented by empirical data was investigated. Certain class of the functions as forecasting tools: so called RFT-transformers, – was proposed. Least Square Method and superposition are the principal composing means for the function generating. Besides, the special classes of beam dynamics with delay were introduced and investigated to get classical results regarding gradients. These results were applied to optimize the RFT-transformers. The effectiveness of the forecast was demonstrated on the empirical data from the Forex market

Generalizing of Neural Nets: Functional Nets of Special Type

Special generalizing for the artificial neural nets: so called RFT – FN – is under discussion in the report. Such refinement touch upon the constituent elements for the conception of artificial neural network, namely, the choice of main primary functional elements in the net, the way to connect them(topology) and the structure of the net as a whole. As to the last, the structure of the functional net proposed is determined dynamically just in the constructing the net by itself by the special recurrent procedure. The number of newly joining primary functional elements, the topology of its connecting and tuning of the primary elements is the content of the each recurrent step. The procedure is terminated under fulfilling “natural” criteria relating residuals for example. The functional proposed can be used in solving the approximation problem for the functions, represented by its observations, for classifying and clustering, pattern recognition, etc. Recurrent procedure provide for the versatile optimizing possibilities: as on the each step of the procedure and wholly: by the choice of the newly joining elements, topology, by the affine transformations if input and intermediate coordinate as well as by its nonlinear coordinate wise transformations. All considerations are essentially based, constructively and evidently represented by the means of the Generalized Inverse

Розробка моделі для навчання адаптивної системи розпізнавання кібератак для неоднорідних потоків запитів в інформаційних системах

The study presents results aimed at further development of models for intelligent and self-educational systems of recognising abnormalities and cyberattacks in mission-critical information systems (MCIS). It has been proven that the existing systems of cyberdefence still significantly rely on using models and algorithms of recognising cyberattacks, which allow taking into account information about the structure of incoming streams or the attackers’ change of the intensity of queries, the speed of the attack, and the duration of the impulse.A mathematical model has been suggested for the system module of intelligent identification of cyberattacks in heterogeneous flows of queries and network forms of cyberattacks. The model recognises heterogeneous incoming flows of queries and any possible change in the query intensity and other parameters of a targeted cyberattack aimed at a MCIS.Simulation models, which had been created in MATLAB and Simulink, were used to research the dynamics of changes in the states of the subsystem of blocking queries in the process of detecting cyberattacks in a MCIS. The probability of solving the problem of recognising cyberattacks in heterogeneous flows of queries and network forms of cyberattacks is 85–98 %, depending on the type of the cyberattack. The results of the modelling allow selection of ways to counter and neutralize the effects of the impact of such targeted attacks and help analyse more sophisticated cyberattacks.The suggested model of recognising complex cyberattacks if attackers use non-uniform flows of queries is more accurate, by 5–7 %, than the other existing models.The developed simulation models enable a 25–30 % decrease in the setup time for projects of cyberdefence systems, including SIRCA for CIS or MCIS.Предложена математическая модель для модуля системы интеллектуального распознавания кибератак для неоднородных потоков запросов и сетевых классов кибератак. Модель учитывает неоднородные входные потоки запросов и возможность изменения нападающими интенсивности запросов в информационных системах, позволяет осуществлять выбор способов противодействия и нейтрализации последствий их реализации, анализировать более сложные виды кибератак. С помощью имитационных моделей, созданных в MatLAB и Simulink, исследована динамика изменения состояний подсистемы блокировки запросов в процессе распознавания кибератак в критически важных компьютерных системах.Запропоновано математичну модель для модуля системи інтелектуального розпізнавання кібератак для неоднорідних потоків запитів та мережних класах кібератак. Модель враховує неоднорідні вхідні потоки запитів та можливість зміни нападниками інтенсивності запитів у інформаційних системах, що дозволяє здійснювати вибір способів протидії та нейтралізації наслідків від їх впливу, аналізувати більш складні види кібератак. За допомогою імітаційних моделей, створених у MatLAB та Simulink, досліджено динаміку зміни станів підсистеми блокування запитів в процесі розпізнавання кібератак у критично важливих комп’ютерних системах

Матричний метод найменших квадратів: приклади застосування в макроекономіці та телемедійному бізнесі

In the paper general framework of Least Square Method (LSM) on vectors and matrixes observation is represented. Also the results developing M-Ppi technique are submitted. Some principal examples are represented in the article. These examples illustrate the advantages of LSM in the case under consideration. General algorithm LSM with matrixes observations is proposed and described in step-by-step variant for linear and nonlinear scaled data. The examples of method applications in macroeconomics and TV-media business illustrate the advantages and capabilities of the method. Correspondent results are also represented below as well as illustration of its applications for predicting in macroeconomics of Ukraine and in estimating of TV audience. The proposed approach for finding predictive values indicators is competitive.В статье представлены общие основы метода наименьших квадратов (МНК) для случая векторных и матричных наблюдений. Также предложены примеры, которые демонстрируют преимущества использования МНК для прогнозирования показателей в макроэкономике и телемедийном бизнесе. Предложен пошаговый алгоритм использования МНК для матричных наблюдений с возможностью линейного и нелинейного масштабирования данных.У статті представлено загальні основи методу найменших квадратів (МНК) для випадків векторних та матричних спостережень. Також наведено деякі приклади, що демонструють перевагу застосування МНК для прогнозування показників у макроекономіці та телемедійному бізнесі. Запропоновано покроковий алгоритм застосування МНК до матричних спостережень з можливістю лінійного та нелінійного масштабування даних