Кафедра "Комп'ютерна математика і аналіз даних"

Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/7570

Офіційний сайт кафедри http://web.kpi.kharkov.ua/kmmm

Кафедра "Комп'ютерна математика і аналіз даних" заснована в 2002 році.

Кафедра входить до складу Навчально-наукового інституту комп'ютерних наук та інформаційних технологій Національного технічного університету "Харківський політехнічний інститут", забезпечує підготовку бакалаврів і магістрів за проектно-орієнтованою освітньою програмою за напрямом науки про дані "DataScience".

У складі науково-педагогічного колективу кафедри працюють: 3 доктора наук: 1 – технічних, 1 – фізико-математичних, 1 – педагогічних; 15 кандидатів наук: 10 – технічних, 4 – фізико-математичних, 1 – педагогічних; 3 співробітників мають звання професора, 9 – доцента.

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Фільтри

2018 - 20192

Налаштування

Автор: search.filters.author.Sira, OksanaКлючові слова: search.filters.subject.перетворення Лапласа

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  • Ескіз
    Документ
    Development of graphic-­analytical models for the software security testing algorithm
    (Technology center PC, 2018) Semenov, Serhii; Sira, Oksana; Kuchuk, Nina
    An analysis of one of the main types of software testing, namely security testing has been made. It was established that there are a number of specific features associated with the possibility of negative manipulation with software products. A graphic-analytical model of the algorithm of testing software security was developed. The model based on the theory of semi-Markov processes provides an adequate structural description of the actual testing process. However, accuracy of this model essentially depends on accuracy of reproduction of densities of distribution of duration of the system residence in each of the possible states. An alternative model that uses the method of probability-time graphs is less demanding. For its implementation, it is sufficient to know the mean values of duration of residence in each of the states and the probability of transitions from one state to another. Correlations were obtained for calculating statistical characteristics and density of distribution of the mean time of execution of the software security testing algorithm. The model can be used to study basic stages of software security testing. Application of this model will reduce software vulnerability and improve security of the IT project as a whole. Also, the model is applicable when developing new methods, algorithms, and procedures for managing the IT projects.
  • Ескіз
    Документ
    Methodology of probabilistic analysis of state dynamics of multi­dimensional semi­-Markov dynamic systems
    (Technology center PC, 2019) Meleshko, Yelyzaveta; Raskin, Lev; Semenov, Serhii; Sira, Oksana
    The problem of probabilistic analysis of a complex dynamic system, which in the process of functioning passes from one state to another at random times, is considered. The methodology for calculating the conditional probabilities of the system getting into a given state at a given time t, provided that at the initial time the system was in any of the possible states is proposed. The initial data for analysis are a set of experimentally obtained values of the duration of the system stay in each of the states before transition to another state. Approximation of the resulting histograms using the Erlang distribution gives a set of distribution densities of the duration of the system stay in possible states before transition to other states. At the same time, the choice of the proper Erlang distribution order provides an adequate description of the semi-Markov processes occurring in the system. The mathematical model that relates the obtained distribution densities to the functions determining the probabilistic dynamics of the system is proposed. The model describes a random process of system transitions from any possible initial state to any other state during a given time interval. Using the model, a system of integral equations for the desired functions describing the probabilistic transition process is obtained. To solve these equations, the Laplace transform is used. As a result of solving the system of integral equations, functions are obtained that specify the probability distribution of the system states at any time t. The same functions also describe the asymptotic probability distribution of states. An illustrative example of solving the problem for the case when the distribution densities of the lengths of the system stay in possible states are described by the second-order Erlang distributions is given. The solution procedure is described in detail for the most natural special case, when the initial state is H₀.