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The examination of financial markets behaviour crucial part of the financial investments theory. The methods for analyzing the financial, markets established in the 1960's and 1970's, were valid only during periods of stable market conditions. They are based on the assumption that the financial market's behaviour is subject to the normal distribution law. In the nineties began to look at this problem from the point of view of fractal analysis. It was observed that financial time series have the property of self-similarity. In this paper, we have tested long memory property for the five biggest cryptocurrencies: Bitcoin, Ethereum, Binance Coin, XRP, and Cardano. This thesis studies persistence and volatility using R/S analysis was carried out. Our findings show that four out of five cryptocurrencies have a significant long memory, supporting the use of fractional Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) extensions as a suitable modeling technique. In this paper, the Fractionally Integrated GARCH (FIGARCH) models, with skewed student distribution, were produced and compared with GARCH models. Models were compared using Akaike information criteria, which indicated the improvement of the model's fitness. The paper ends with some concluding remarks and future directions of research.

Regression Analysis: The Research on International Citizens Migration. The aim of this Bachelor’s thesis is to analyze citizen's migration depending on the collected data from "osp.stat.gov.lt" and "stats.oecd.org" sites. In this final work, we were using one of the statistical methods - regression analysis. The results showed that migration is a complicated process, which depends on various aspects. Immigration and emigration, are closely correlated with the country's international trade, which indicates the economic situation of Lithuania. Also, we found out, that immigration is strongly correlated with tourism, but we still need to do a further investigation because of the lack of data. In the case of multiple regression, we could not found any good models, that would fulfill all assumptions and explain more data of the dependent variable.

This Bachelor’s thesis analyzses data strctures used for spatial index implementation as well as spatial data persistence and indexing support in relational database management systems. Space and data based tree data structures that are commonly used in spatial index implementation are analyzed. Four popular relatonal database management systems are discussed - SQL Server, Oracle, PostgreSQL along with the PostGIS module and SQLite along with the Spatialite module. An experiment was conducted with the goal of comparing the systems in practice by measuring the efectiveness of their spatial indexes when executing spatial search queries. The experiment was automated by creating a tool (console application). In the experiment 8 different datasets were used and the SELECT queries were formed by using two out out of multiple functions defined in the second part of the OGC SFA standard - ST_Within and ST_Intersects. [10] Three table join queries were also used in the experiment. The queries were executed in non-indexed and indexed databases to see how effective the spatial index is. The results show that spatial indexes do speed up the query execution most of the times, and that PostgreSQL with the PotsGIS module was the fastest when executing queries in indexed database, and Oracle was the slowest. Second fastest usually was SQLite with the Spatialite module, third - SQL Server. It was noticed that when executing queries on larger datasets spaial index in PostgreSQL slowed down the query excution. In the results of table join queries the patterns are even more noticable, the performance improvement that the index provides is even more significant. The query execution results are consistent accross all of the datasets used thus PostgreSQL with PostGIS module or SQLite with Spatialite module is recommended for working with spatial data.

In this thesis, the mathematical and computational models of bioreactors based on microbioreactors are considered. The aim of this thesis is set - to properly simulate and optimize microbioreactor-based bioreactor systems by proposing original mathematical and computational models. Generalizations of mathematical models are proposed by taking into account the additional layers of the microbioreactor and the initial and boundary conditions, as well as a new mathematical model of the microreactor with carbon-nanotubes is formulated and proposed. The proposed model was validated with experimental data. By analyzing the model approximations, an algorithm based on the homotopy perturbation method to find approximate analytical solutions for previously unexamined models was proposed, and the accuracy of the approximations in two-layer biocatalysis systems was evaluated. A numerical model for multi-task optimization is also developed, which allows searching for optimal bioreactor configurations. Large-scale system simulation of proposed open and closed bioreactor systems has been performed.

In this thesis, the mathematical and computational models of bioreactors based on microbioreactors are considered. The aim of this thesis is set - to properly simulate and optimize microbioreactor-based bioreactor systems by proposing original mathematical and computational models. Generalizations of mathematical models are proposed by taking into account the additional layers of the microbioreactor and the initial and boundary conditions, as well as a new mathematical model of the microreactor with carbon-nanotubes is formulated and proposed. The proposed model was validated with experimental data. By analyzing the model approximations, an algorithm based on the homotopy perturbation method to find approximate analytical solutions for previously unexamined models was proposed, and the accuracy of the approximations in two-layer biocatalysis systems was evaluated. A numerical model for multi-task optimization is also developed, which allows searching for optimal bioreactor configurations. Large-scale system simulation of proposed open and closed bioreactor systems has been performed.

This paper focuses on the methods of the data secrecy using SQL methods in relational database management systems (RDBMS). At the beginning, data secrecy, its features in relational databases and the goal of the secrecy assurance method are defined. The problem that data secrecy assurance methods vary between different databases and some RDBMS’s may lack some methods is covered. The focus is put on the table column encryption method which does not exist in some RDBMS’s. Many implementations of this method can be found, therefore some alternatives are covered and the decision of the chosen one are reasoned. This results in a methodology which defines the implementation of the method in any RDBMS and in any database schema. Features of the methodology are found through experiments, which can be repeated again to forecast exact features on another device. The main focus is on performance - how using the methodology affects the performance of simple SQL queries. One case is when a table has a fixed number of encrypted columns and different encryption algorithms are used and another case is when the same encryption algorithm is used on a table with a different number of encrypted columns. A dependency function is found in the results between the total SQL query execution time and the number of encrypted columns or used encryption algorithms.

Static code analysis examines program code and finds defects in programs before their run time. There are lots of tools based on static analysis, but there is a lack of information about these tools efficiency and effectiveness. A big part of static analysis tools use Java Modeling Language which is used to add specifications to Java code and validate the code using them. This paper describes a study using four different static analysis tools for the selected Java code which were analyzed and found the most effective tool — OpenJML. Tools analysis demonstrated that specific static analysis tools are efficient compared to static analysis performed by code compilers and that static analysis tools which use Java Modeling Language are more effective.

A UML diagram, such as a class diagram, is not advanced enough to provide all the important aspects of a specification. The OCL requirements language can be used to resolve uncertainties caused by additional model object constraints. This requirements language is usually used when the specification cannot be expressed in UML. The requirements language OCL only complements but does not replace UML diagrams. Meanwhile, to ensure the language of requirements in SQL statements, not all possibilities are always used. This paper investigates the provisioning of the requirements language OCL with SQL language statements, which are used to determine which requirements are not ensured. After finding out which requirements are not ensured, develop and test a methodology that can be used to ensure that the relevant OCL requirements are met by SQL statements.

This work describes how rows and values pattern matching is ensured in different relational databases and how to create similar pattern matching functions in those databases that do not have the same functionality as others. It includes analyzing rows and values pattern matching functions in different databases and comparing them with standard SQL pattern matching. During the analysis, all similarities and differences were found. Pattern matching functions and operators were chosen for implementation in order to apply them onto different databases based on the differences found. After writing those queries and functions it was discovered that in every chosen database it is possible to apply pattern matching functions that some other database has. Some of them are easier to apply, some of them not. As a result, pattern matching functions of chosen databases were implemented and applied to those that do not have that same functionality. This shows that if one database is in use, there is no need to choose another database just because it already has some better pattern matching functionalities. It is possible to achieve the same results with every database’s built in queries and functions.

One-dimensional model of biosensor with a perforated membrane that approximates two-dimensional model is presented in this work. The model is solved by using finite-difference method, explicit method. Modeling error was defined by computational modeling. The research was conducted with different parameter values of diffusion model, hole radius of perforated membrane and initial substrate concentration. The conditions to use a one-dimensional model instead of a two-dimensional biosensor with a perforated membrane model were found by computational modeling.

This paper analyzes suitability of one-dimensional modeling for biosensors based on an array of microreactors. A biosensor based on an array of right cylinders has been approximated from a two-dimensional model to a one-dimensional model using homogenization. Homogenization process has been performed using effective diffusion and reaction correction coefficients. Research findings show that in most cases homogenization has introduced an error less than 10%. It is concluded that one-dimensional modeling is well suited for researching biosensors based on an array of microreactors and chosen homogenization method is appropriate for merging enzyme and diffusion areas of such biosensors.

Biosensor is a device for detection and measurement of substrate concentration in analysed solution. It is a cheap and reliable device used in environment monitoring, food industry and medicine. In dissertation an artificial neural networks is applied to the biosensor to determine multiple substrate concentrations. The case of the multiple substrate is analysed. The biosensor model involves substrate interaction and the external (Nerst) diffusion layer. The response of the biosensor is used to determine multiple substrates concentrations. Moreover, the effect of the external diffusion layer is investigated. Furthermore, the determination of concentration of two substrates using two biosensor static currents is investigated and the effect of a diffusion module is analysed. In order to make good biosensor, the device should meet many contradictory requirements. Dissertation presents a method that combines mathematical modeling, multi-objective optimisation and multi-dimensional visualisation that is intended for the design and optimisation of amperometric biosensors. The approach for optimising parameters of biosensors are based on the availability of a mathematical model of a catalytic biosensor. A multi-objective visualisation of trade-off solutions and Pareto optimal decisions is applied to select of the most favorable decision by a human expert when designing biosensors. The multi-objective optimisation was applied to glucose and phenol biosensors.

Biosensor is a device for detection and measurement of substrate concentration in analysed solution. It is a cheap and reliable device used in environment monitoring, food industry and medicine. In dissertation an artificial neural networks is applied to the biosensor to determine multiple substrate concentrations. The case of the multiple substrate is analysed. The biosensor model involves substrate interaction and the external (Nerst) diffusion layer. The response of the biosensor is used to determine multiple substrates concentrations. Moreover, the effect of the external diffusion layer is investigated. Furthermore, the determination of concentration of two substrates using two biosensor static currents is investigated and the effect of a diffusion module is analysed. In order to make good biosensor, the device should meet many contradictory requirements. Dissertation presents a method that combines mathematical modeling, multi-objective optimisation and multi-dimensional visualisation that is intended for the design and optimisation of amperometric biosensors. The approach for optimising parameters of biosensors are based on the availability of a mathematical model of a catalytic biosensor. A multi-objective visualisation of trade-off solutions and Pareto optimal decisions is applied to select of the most favorable decision by a human expert when designing biosensors. The multi-objective optimisation was applied to glucose and phenol biosensors.

Static program analysis and tools ensuring it (.NET)

In this paper 8 different methods for calculating apparent Michaelis constant are compared using computational modelling of biosensors. It has been experimentally determined that methods for calculating the values of Michaelis-Menten kinetic parameters can be used depending on the value of biosensor’s diffusion module. Research findings show that when the diffusion module does not exceed 1, all of the analyzed methods can be used to calculate approximate values of apparent Michaelis constant. It is concluded that Ridders’ method is the most effective at calculating apparent Michaelis constant with more precision, and the methods for calculating the values of Michaelis-Menten kinetic parameters are more effective at relatively rough estimations of apparent Michaelis constant.

Efficient event storage under high load

In this work approximation error of two-dimensional biosensor with rough surface model to one-dimensional model was analysed. Two-dimensional model was solved using altering directions implicit method, one-dimensional model - using implicit differences method. In order to decrease number of parameters in the analysing model, mathematical model of biosensor was changed to dimensionless mathematical model. Approximation error dependence of different enzyme surface geometries, enzyme layer thickness and initial substrate concentration was investigated.

Biosensors – devices, sensitive to certain materials, which are used to identify characteristics of that material. The model of a single enzyme amperometric biosensor, described in other works, is modified by changing plane electrode to carbon nanotubes based electrode in enzyme layer. Mathematical model was created together with a dimensionless mathematical model and numerical model. Numerical model was implemented in Matlab environment. After the research on biosensor sensitivity characteristics was performed and sensitivity was compared to classic biosensors with a plane electrode sensitivity, it can be stated that this biosensor with carbon nanotubes based electrode has approximately the same sensitivity characteristics.

Relational database as a Service

Ensuring JavaScript Object Notation in database management systems

The bachelor thesis analyzes how data integrity is enforced in NewSQL database management systems (DBMS) with respect to traditional relational DBMS. Data integrity was divided into four autonomous categories: entity, domain, referential and bussiness integrity and these were analyzed separately. It was identified what methods of relational DBMS are usually used to enforce integrity in different categories. In addition to that, thesis reviewed the fundamental similarities and differences between NewSQL and traditional relational DBMS, as well as identified potential problems that could arise when trying to enforce data integrity in NewSQL DBMS. The primary result of the thesis is a methodology of data integrity enforcement in NewSQL DBMS. The secondary result – practical adaptation of created methodology in specific database architecture using VoltDB and NuoDB DBMS. The thesis concludes that the created methodology is applicable in production, but since not all NewSQL DBMS support data integrity enforcement methods, which are usually used in traditional relational ones, sometimes we have to use alternative methods with certain drawbacks, such as loss of effectiveness or extra work required from developers.

In this work, a bacterial self-organization in a rounded container as detected by bioluminescence imaging is mathematically modelled. The pattern formation in a colony of luminous Escherichia coli is investigated in the whole container, on the top surface and the walls of the container and in pseudo-one dimension along the top three-phase contact line. The pattern formation is numerically simulated by the nonlinear reaction-advection-diffusion equations. Various model modifications are investigated in order to determine the most suitable for the modelling of a luminous E. coli colony. The impact of oxygen on pattern formation is investigated and a new model with the added equation describing oxygen dynamics is suggested. It is shown that this model becomes suitable for modelling pattern formation in a luminous E. coli colony in two and three dimensions of space in the case when a vessel with depth needs to be modelled. Moreover, model generalization to one, two and three dimensions is described and the investigation of pattern formation differences is carried out. It was determined that important changes in the patterns are observed when using models with the same parameter values in different dimensions.

Biosensors are sensing devices that transform a biological recognition into the detectable signal. In most cases biosensors are used to detect the concentration of the specific substance and are mostly applied in environmental, medicine and food industries. The enzyme is the most crucial and expensive part of the analysed biosensors, therefore decreasing the number of experiments performed in the laboratory is desired. One of the main reasons restricting wider use of the enzymatic amperometric biosensors is a relatively short linear range of the calibration curve. The application of intermediate substances to solve this kind of problem is analysed in this thesis. The mathematical models of two biosensors utilizing intermediate substances are presented and analysed. In general case, the models are solved numerically, by applying finite difference technique. Specific software is developed to solve the numerical models of the biosensors. The digital investigation process is automated by carrying out the calculations on the computational grid. The peculiarities of the biosensor with chemically modified electrode and biosensor with parallel substrates conversion are investigated by using developed software. The results of the investigation can be applied practically, as they describe the optimal configurations of the analysed biosensors. To solve the problems more efficiently, improvements to the mathematical and computational models as well as their accuracy are presented.

Biosensors are sensing devices that transform a biological recognition into the detectable signal. In most cases biosensors are used to detect the concentration of the specific substance and are mostly applied in environmental, medicine and food industries. The enzyme is the most crucial and expensive part of the analysed biosensors, therefore decreasing the number of experiments performed in the laboratory is desired. One of the main reasons restricting wider use of the enzymatic amperometric biosensors is a relatively short linear range of the calibration curve. The application of intermediate substances to solve this kind of problem is analysed in this thesis. The mathematical models of two biosensors utilizing intermediate substances are presented and analysed. In general case, the models are solved numerically, by applying finite difference technique. Specific software is developed to solve the numerical models of the biosensors. The digital investigation process is automated by carrying out the calculations on the computational grid. The peculiarities of the biosensor with chemically modified electrode and biosensor with parallel substrates conversion are investigated by using developed software. The results of the investigation can be applied practically, as they describe the optimal configurations of the analysed biosensors. To solve the problems more efficiently, improvements to the mathematical and computational models as well as their accuracy are presented.

Huge amounts of digital information are stored in the World today and the amount is increasing by quintillion bytes every day. Approximate data mining algorithms are very important to efficiently deal with such amounts of data due to the computation speed required by various real-world applications, whereas exact data mining methods tend to be slow and are best employed where the precise results are of the highest important. This thesis focuses on several data mining tasks related to analysis of big data: frequent pattern mining and visual representation. For mining frequent patterns in big data, three novel approximate methods are proposed and evaluated on real and artificial databases: • Random Sampling Method (RSM) creates a random sample from the original database and makes assumptions on the frequent and rare sequences based on the analysis results of the random sample. A significant benefit is a theoretical estimate of classification errors made by this method using standard statistical methods. • Multiple Re-sampling Method (MRM) is an improved version of RSM method with a re-sampling strategy that decreases the probability to incorrectly classify the sequences as frequent or rare. • Markov Property Based Method (MPBM) relies upon the Markov property. MPBM requires reading the original database several times (the number equals to the order of the Markov process) and then calculates the empirical frequencies using the Markov property. For visual representation... [to full text] Didžiuliai informacijos kiekiai yra sukaupiami kiekvieną dieną pasaulyje bei jie sparčiai auga. Apytiksliai duomenų tyrybos algoritmai yra labai svarbūs analizuojant tokius didelius duomenų kiekius, nes algoritmų greitis yra ypač svarbus daugelyje sričių, tuo tarpu tikslieji metodai paprastai yra lėti bei naudojami tik uždaviniuose, kuriuose reikalingas tikslus atsakymas. Ši disertacija analizuoja kelias duomenų tyrybos sritis: dažnų sekų paiešką bei vizualizaciją sprendimų priėmimui. Dažnų sekų paieškai buvo pasiūlyti trys nauji apytiksliai metodai, kurie buvo testuojami naudojant tikras bei dirbtinai sugeneruotas duomenų bazes: • Atsitiktinės imties metodas (Random Sampling Method - RSM) formuoja pradinės duomenų bazės atsitiktinę imtį ir nustato dažnas sekas, remiantis atsitiktinės imties analizės rezultatais. Šio metodo privalumas yra teorinis paklaidų tikimybių įvertinimas, naudojantis standartiniais statistiniais metodais. • Daugybinio perskaičiavimo metodas (Multiple Re-sampling Method - MRM) yra RSM metodo patobulinimas, kuris formuoja kelias pradinės duomenų bazės atsitiktines imtis ir taip sumažina paklaidų tikimybes. • Markovo savybe besiremiantis metodas (Markov Property Based Method - MPBM) kelis kartus skaito pradinę duomenų bazę, priklausomai nuo Markovo proceso eilės, bei apskaičiuoja empirinius dažnius remdamasis Markovo savybe. Didelio duomenų kiekio vizualizavimui buvo naudojami pirkėjų internetu elgsenos duomenys, kurie analizuojami naudojant... [toliau žr. visą tekstą]

Didžiuliai informacijos kiekiai yra sukaupiami kiekvieną dieną pasaulyje bei jie sparčiai auga. Apytiksliai duomenų tyrybos algoritmai yra labai svarbūs analizuojant tokius didelius duomenų kiekius, nes algoritmų greitis yra ypač svarbus daugelyje sričių, tuo tarpu tikslieji metodai paprastai yra lėti bei naudojami tik uždaviniuose, kuriuose reikalingas tikslus atsakymas. Ši disertacija analizuoja kelias duomenų tyrybos sritis: dažnų sekų paiešką bei vizualizaciją sprendimų priėmimui. Dažnų sekų paieškai buvo pasiūlyti trys nauji apytiksliai metodai, kurie buvo testuojami naudojant tikras bei dirbtinai sugeneruotas duomenų bazes: • Atsitiktinės imties metodas (Random Sampling Method - RSM) formuoja pradinės duomenų bazės atsitiktinę imtį ir nustato dažnas sekas, remiantis atsitiktinės imties analizės rezultatais. Šio metodo privalumas yra teorinis paklaidų tikimybių įvertinimas, naudojantis standartiniais statistiniais metodais. • Daugybinio perskaičiavimo metodas (Multiple Re-sampling Method - MRM) yra RSM metodo patobulinimas, kuris formuoja kelias pradinės duomenų bazės atsitiktines imtis ir taip sumažina paklaidų tikimybes. • Markovo savybe besiremiantis metodas (Markov Property Based Method - MPBM) kelis kartus skaito pradinę duomenų bazę, priklausomai nuo Markovo proceso eilės, bei apskaičiuoja empirinius dažnius remdamasis Markovo savybe. Didelio duomenų kiekio vizualizavimui buvo naudojami pirkėjų internetu elgsenos duomenys, kurie analizuojami naudojant... [toliau žr. visą tekstą] Huge amounts of digital information are stored in the World today and the amount is increasing by quintillion bytes every day. Approximate data mining algorithms are very important to efficiently deal with such amounts of data due to the computation speed required by various real-world applications, whereas exact data mining methods tend to be slow and are best employed where the precise results are of the highest important. This thesis focuses on several data mining tasks related to analysis of big data: frequent pattern mining and visual representation. For mining frequent patterns in big data, three novel approximate methods are proposed and evaluated on real and artificial databases: • Random Sampling Method (RSM) creates a random sample from the original database and makes assumptions on the frequent and rare sequences based on the analysis results of the random sample. A significant benefit is a theoretical estimate of classification errors made by this method using standard statistical methods. • Multiple Re-sampling Method (MRM) is an improved version of RSM method with a re-sampling strategy that decreases the probability to incorrectly classify the sequences as frequent or rare. • Markov Property Based Method (MPBM) relies upon the Markov property. MPBM requires reading the original database several times (the number equals to the order of the Markov process) and then calculates the empirical frequencies using the Markov property. For visual representation... [to full text]

In many important real world applications the initial representation of the data is inconvenient, or even prohibitive for further analysis. For example, in image analysis, text analysis and computational genetics high-dimensional, massive, structural, incomplete, and noisy data sets are common. Therefore, feature extraction, or revelation of informative features from the raw data is one of fundamental machine learning problems. Efficient feature extraction helps to understand data and the process that generates it, reduce costs for future measurements and data analysis. The representation of the structured data as a compact set of informative numeric features allows applying well studied machine learning techniques instead of developing new ones.. The dissertation focuses on supervised and semi-supervised feature extraction methods, which optimize the dependence structure of features. The dependence is measured using the kernel estimator of Hilbert-Schmidt norm of covariance operator (HSIC measure). Two dependence structures are investigated: in the first case we seek features which maximize the dependence on the dependent variable, and in the second one, we additionally minimize the mutual dependence of features. Linear and kernel formulations of HBFE and HSCA are provided. Using Laplacian regularization framework we construct semi-supervised variants of HBFE and HSCA. Suggested algorithms were investigated experimentally using conventional and multilabel classification data... [to full text] Daugelis praktiškai reikšmingu sistemu mokymo uždaviniu reikalauja gebeti panaudoti didelio matavimo, strukturizuotus, netiesinius duomenis. Vaizdu, teksto, socialiniu bei verslo ryšiu analize, ivairus bioinformatikos uždaviniai galetu buti tokiu uždaviniu pavyzdžiais. Todel požymiu išskyrimas dažnai yra pirmasis žingsnis, kuriuo pradedama duomenu analize ir nuo kurio priklauso galutinio rezultato sekme. Šio disertacinio darbo tyrimo objektas yra požymiu išskyrimo algoritmai, besiremiantys priklausomumo savoka. Darbe nagrinejamas priklausomumas, nusakytas kovariacinio operatoriaus Hilberto-Šmidto normos (HSIC mato) branduoliniu ivertiniu. Pasiulyti šiuo ivertiniu besiremiantys HBFE ir HSCA algoritmai leidžia dirbti su bet kokios strukturos duomenimis, bei yra formuluojami tikriniu vektoriu terminais (tai leidžia optimizavimui naudoti standartinius paketus), bei taikytini ne tik prižiurimo, bet ir dalinai prižiurimo mokymo imtims. Pastaruoju atveju HBFE ir HSCA modifikacijos remiasi Laplaso reguliarizacija. Eksperimentais su klasifikavimo bei daugiažymio klasifikavimo duomenimis parodyta, jog pasiulyti algoritmai leidžia pagerinti klasifikavimo efektyvuma lyginant su PCA ar LDA.

The field of the dissertation research is features of computer network packet traffic, the impact of network node features on traffic service, methods of real-time analysis of network traffic features and their application for dynamic prognostication of computer network packet traffic variance. The object of the research is the features of computer network packet traffic, the impact of network node features on computer network traffic service, methods of real-time network traffic features analysis and their application for dynamic prognostication of network traffic variances. The aim of work is to investigate fractal processes in computer networks, grounding on the results obtained to select methods suitable for real-time analysis of network traffic and to work out methods for real-time measurement of self-similarity as well as to apply it for perfection of computer networks service quality. Possibilities for mathematical modelling of network components, computer network packet traffic models and models using service theory instruments have been analysed. The package of network traffic features analysis has been worked out; it was used for analysis, assessment and comparison of methods for computer networks fractality and self-similarity research. For assessment of self-similarity of the network traffic time lines analysis, frequency/wave feature estimates, self-similarity analysis methods based on time line stability parameters estimators and assessed by the chaos theory means have been studied. The package of real-time network traffic self-similarity analysis has been worked out; by using it for real-time measurement of self-similarity the robust regression method and IR statistics were selected. Software for simulation of fractal processes was analysed. After applying a stochastically limited network communication model and algebra plus means, the GI/G/10//N computer network node is described. The simulation system of computer network self-similar and Poisson traffics was created and, by using it, the impact of network node features on quality of network traffic service was investigated. The worked methods were applied for perfection of computer network service quality. Methods for computer network traffic self-similarity real-time measurement have been worked out; they recurrently form a queue, calculate its statistical parameters and stored results in a temporal memory. These methods differ from others by real-time aggregation of network traffic by applying the method of smoothing moving means or the sum of transmitted data traffic during a time interval, the formed queue is stored in a temporal memory, recurrently calculates self-similarity parameters of a dynamically formed queue calculating α-stability index, IR estimator and Hurst coefficient, stores the calculations results in a temporal or/and permanent memory for further analysis. The method has been patented at the State Patent Bureau of the Republic of Lithuania, patent No. LT20011099. By using the method real-time analysis of computer network packet traffic self-similarity, an open network node control model including feedback has been worked out. Research results have been presented and discussed in two international conferences, one international seminar, two national conferences and three national seminars. Two articles have been published in foreign scholarly publications included into the Institute’s of Scientific Information list of main journals with the citation index, one published in international conference proceedings included into the Institute’s of Scientific Information list and four appeared in reviewed Lithuanian and foreign publications.

Disertaciniame darbe nagrinėjamas diskretaus laiko rizikos modelis su skirtingai pasiskirsčiusiomis žalomis. Šis modelis aprašo draudimo įmonės turtą įtakojančius veiksnius: pradinį kapitalą, gaunamas įmokas, išmokamas žalas. Išvedamos rekursinės formulės, kurių pagalba galima tiksliai ir greitai rasti baigtinio laiko bankroto tikimybių ir Gerber-Shiu funkcijos vertes. Rekursinės formulės taip pat pateikiamos ir begalinio laiko rizikos matams, tačiau nevienodai pasiskirsčiusių žalų atveju iškyla papildomų sunkumų randant bankroto tikimybę ir Gerber-Shiu funkciją, kai pradinis kapitalas lygus 0. Tam įrodoma atskira teorema, tačiau nedarant jokių prielaidų apie žalų pasiskirstymus, apskaičiuoti vertes lengva tikrai nėra. Kaip išeitis pasiūloma cikliškai pasiskirsčiusių žalų struktūra ir pateikiami algoritmai, leidžiantys teoremas pritaikyti praktiškai. Demonstruojant teoremų ir rekursinių formulių veikimą, pateikiami skaitiniai pavyzdžiai su grafinėmis iliustracijomis bei programų kodai. Galiausiai nagrinėjamas atskiras diskretaus laiko rizikos modelio atvejis, kai žalos pasiskirsčiusios skirtingai pagal geometrinį dėsnį. Disertacijoje taip pat yra nagrinėjamas diskretaus laiko rizikos modelis su skirtingai pasiskirsčiusiomis žalomis, kurios įgyja racionalias reikšmes, bei kintančiomis įmokomis ir pradiniu kapitalu, taip pat įgyjančiais racionalias reikšmes su tam tikra sąlyga. Įrodomos dvi teoremos kaip rasti tokio modelio baigtinio laiko bankroto tikimybę ir keli... [toliau žr. visą tekstą] In this thesis, the discrete time risk model with inhomogeneous claims is considered. This model is used for describing the insurer‘s capital and its components: initial capital, premiums received, and claims paid. The main risk measures, ruin probabilities and Gerber-Shiu function, are investigated and recursive formulas are obtained. These formulas give fast and accurate evaluation of the finite time ruin probabilities and Gerber-Shiu function. However, the infinite time investigations require that the Gerber-Shiu function's values for the initial capital equal to 0 must be known. This is slightly more difficult due to the claim inhomogeneity and for this reason a theorem with explicit expression of the infinite time Gerber-Shiu function for a zero initial capital is proposed. However, for the calculation of the infinite time values, some assumption about underlying claim structure must be made. As a solution the cyclically distributed claims are proposed, the algorithms for application of the theorems are given and numerical examples with graphical output are presented. Finally, a special case of discrete time risk model with inhomogeneous claims distributed according geometric law is investigated. In addition to the main results, another discrete time risk model with inhomogeneous claims acquiring rational values is investigated. Two theorems for evaluation of the finite time ruin probabilities are proved and some examples are presented.

In this thesis, the discrete time risk model with inhomogeneous claims is considered. This model is used for describing the insurer‘s capital and its components: initial capital, premiums received, and claims paid. The main risk measures, ruin probabilities and Gerber-Shiu function, are investigated and recursive formulas are obtained. These formulas give fast and accurate evaluation of the finite time ruin probabilities and Gerber-Shiu function. However, the infinite time investigations require that the Gerber-Shiu function's values for the initial capital equal to 0 must be known. This is slightly more difficult due to the claim inhomogeneity and for this reason a theorem with explicit expression of the infinite time Gerber-Shiu function for a zero initial capital is proposed. However, for the calculation of the infinite time values, some assumption about underlying claim structure must be made. As a solution the cyclically distributed claims are proposed, the algorithms for application of the theorems are given and numerical examples with graphical output are presented. Finally, a special case of discrete time risk model with inhomogeneous claims distributed according geometric law is investigated. In addition to the main results, another discrete time risk model with inhomogeneous claims acquiring rational values is investigated. Two theorems for evaluation of the finite time ruin probabilities are proved and some examples are presented. Disertaciniame darbe nagrinėjamas diskretaus laiko rizikos modelis su skirtingai pasiskirsčiusiomis žalomis. Šis modelis aprašo draudimo įmonės turtą įtakojančius veiksnius: pradinį kapitalą, gaunamas įmokas, išmokamas žalas. Išvedamos rekursinės formulės, kurių pagalba galima tiksliai ir greitai rasti baigtinio laiko bankroto tikimybių ir Gerber-Shiu funkcijos vertes. Rekursinės formulės taip pat pateikiamos ir begalinio laiko rizikos matams, tačiau nevienodai pasiskirsčiusių žalų atveju iškyla papildomų sunkumų randant bankroto tikimybę ir Gerber-Shiu funkciją, kai pradinis kapitalas lygus 0. Tam įrodoma atskira teorema, tačiau nedarant jokių prielaidų apie žalų pasiskirstymus, apskaičiuoti vertes lengva tikrai nėra. Kaip išeitis pasiūloma cikliškai pasiskirsčiusių žalų struktūra ir pateikiami algoritmai, leidžiantys teoremas pritaikyti praktiškai. Demonstruojant teoremų ir rekursinių formulių veikimą, pateikiami skaitiniai pavyzdžiai su grafinėmis iliustracijomis bei programų kodai. Galiausiai nagrinėjamas atskiras diskretaus laiko rizikos modelio atvejis, kai žalos pasiskirsčiusios skirtingai pagal geometrinį dėsnį. Disertacijoje taip pat yra nagrinėjamas diskretaus laiko rizikos modelis su skirtingai pasiskirsčiusiomis žalomis, kurios įgyja racionalias reikšmes, bei kintančiomis įmokomis ir pradiniu kapitalu, taip pat įgyjančiais racionalias reikšmes su tam tikra sąlyga. Įrodomos dvi teoremos kaip rasti tokio modelio baigtinio laiko bankroto tikimybę ir keli... [toliau žr. visą tekstą]

Software systems are permanently changed in order to meet new requirements and to adapt them to permanently changing technology. Design modularity decouples design concerns that probably can be changed and in this way facilitates further system changes. Unfortunately, some design concerns, called crosscutting concerns, cannot be modularized using traditional modularization methods and techniques. Modularization of crosscutting concerns is the research subject of the new emerging software engineering paradigm, aspect-oriented analysis and design. However, this paradigm is still not enough mature. It is still unknown, which design patterns developed in the object-oriented paradigm can be adapted for aspect-oriented paradigm and how to transform them from one paradigm to another in a systematic way. Despite the fact that some attempts have been done to solve this problem, the proposed solutions only eliminate crosscutting concerns in object-oriented design patterns, but do not generate pure aspect-oriented patterns. The thesis defines the class of object-oriented design patterns which can be transformed into pure aspect-oriented ones, proposes a systematic procedure for such transformation and investigates properties of resulting patterns from the viewpoint of their applicability in the design of aspect-oriented domain frameworks. This is the main contribution of the research work. The case study methodology has been used for the experimental research of the properties of... [to full text] Programų sistemos yra dažnai keičiamos, siekiant jas pritaikyti prie pasikeitusių reikalavimų ir dėl nuolat kintančių technologijų. Modulinė sistemos architektūra įgalina nepriklausomus dalykinius turinius realizuoti nepriklausomais ar nedaug vienas nuo kito priklausomais moduliais, kuriuos galima keisti nepriklausomai vienas nuo kito. Tačiau esamomis priemonėmis galima atskirti ne visus turinius. Kai kurie dalykiniai turiniai yra susipynę tarpusavyje ir jų negalima realizuoti savarankiškais moduliais. Šiai problemai spręsti buvo pasiūlyta nauja programų sistemų inžinerijos paradigma – aspektinė paradigma. Tačiau sistemų projektavimo technologija joje kol kas dar nėra pakankamai brandi. Vis dar nėra žinoma, kuriuos objektinio projektavimo šablonus galima panaudoti aspektinėje paradigmoje ir kaip juos transformuoti, keliant iš vienos paradigmos į kitą. Nors keliuose darbuose yra parodoma, kaip objektinių šablonų realizacijas perrašyti aspektinėmis programavimo kalbomis, nė viename iš jų šablonų transformavimo klausimai nebuvo nagrinėti sistemiškai. Šioje disertacijoje nagrinėjami grynieji aspektinio projektavimo šablonai, kurie buvo transformuoti iš objektinių projektavimo šablonų, apibrėžiama sistemiška tokio transformavimo procedūra ir analizuojamas tokių šablonų taikymas aspektiniams dalykiniams karkasams projektuoti. Atskiro atvejo analizės tyrimo metodas disertacijoje yra naudojamas, siekiant išsiaiškinti, kokį poveikį grynieji aspektiniai šablonai padaro aspektinių... [toliau žr. visą tekstą]

In practice, optimization problems are often multiple criteria. The criteria are usually contradictory, so the final decision depends on a decision maker. When the problem is solved interactively, the decision maker can change his/her preferences in decision process. Moreover, it is important to obtain solutions from the whole Pareto front. A decision support system adapted to the specific of the problem is essential for solving multiple criteria optimization problems interactively. The objects of research are multiple criteria optimization problems, interactive methods for solving these problems, interactive decision support systems, and application of parallel computing in decision support systems. Multiple criteria optimization methods are analyzed in the dissertation. The focus of attention is the methods for a uniform distribution of solutions on the Pareto front as well as the interactive methods. An interactive way for solving multicriteria optimization problems, which finds alternative solutions uniformly distributed on the Pareto front is proposed and investigated in this dissertation. An interactive decision support system which integrates the created interactive solving way, the decision process visualization and parallelization for multiple criteria optimization is developed. The solving strategies, when a multiple criteria optimization problem is solved interactively, using a computer cluster are developed and compared experimentally. The time required for a... [to full text] Praktikoje dažnai tenka spręsti sudėtingus daugiakriterinius optimizavimo uždavinius, kai kriterijai būna prieštaringi, o galutinis apsisprendimas priklauso nuo sprendimų priėmėjo. Kai sprendimų priėmėjas dalyvauja sprendimo procese interaktyviai, tai jis gali koreguoti prioritetus ir siekiamus tikslus uždavinio sprendimo eigoje, kas įgalina spęsti uždavinius, turinčius daug kriterijų ir apribojimų. Be to, sprendimo priėmėjui svarbu gauti sprendinius iš visos Pareto aibės. Interaktyviam uždavinių sprendimui būtina sprendimų paramos sistema, kurios grafinė sąsaja yra pritaikyta sprendžiamam uždaviniui. Šio darbo tyrimų sritis yra interaktyvus daugiakriterinių optimizavimo uždavinių sprendimas bei sprendimų paramos sistemos. Disertacijoje nagrinėjant daugiakriterinio optimizavimo metodus, didesnis dėmesys skirtas metodams, užtikrinantiems gaunamų sprendinių tolygų pasiskirstymą Pareto aibėje bei interaktyviems metodams. Pasiūlytas ir ištirtas daugiakriterinių optimizavimo uždavinių sprendimo būdas, leidžiantis spręsti daugiakriterinius optimizavimo uždavinius interaktyviai ir užtikrinantis gaunamų sprendinių tolygų pasiskirstymą Pareto aibėje. Sukurta ir ištirta interaktyvi daugiakriterinių optimizavimo uždavinių sprendimų paramos sistemą, apjungianti pasiūlytą optimizavimo uždavinių sprendimo būdą, sprendimo proceso vizualizavimą ir jo lygiagretinimą. Taip pat pasiūlyta sprendimo strategija, pagal kurią sprendžiant daugiakriterinį optimizavimo uždavinį pasitelkiamas... [toliau žr. visą tekstą]

Praktikoje dažnai tenka spręsti sudėtingus daugiakriterinius optimizavimo uždavinius, kai kriterijai būna prieštaringi, o galutinis apsisprendimas priklauso nuo sprendimų priėmėjo. Kai sprendimų priėmėjas dalyvauja sprendimo procese interaktyviai, tai jis gali koreguoti prioritetus ir siekiamus tikslus uždavinio sprendimo eigoje, kas įgalina spęsti uždavinius, turinčius daug kriterijų ir apribojimų. Be to, sprendimo priėmėjui svarbu gauti sprendinius iš visos Pareto aibės. Interaktyviam uždavinių sprendimui būtina sprendimų paramos sistema, kurios grafinė sąsaja yra pritaikyta sprendžiamam uždaviniui. Šio darbo tyrimų sritis yra interaktyvus daugiakriterinių optimizavimo uždavinių sprendimas bei sprendimų paramos sistemos. Disertacijoje nagrinėjant daugiakriterinio optimizavimo metodus, didesnis dėmesys skirtas metodams, užtikrinantiems gaunamų sprendinių tolygų pasiskirstymą Pareto aibėje bei interaktyviems metodams. Pasiūlytas ir ištirtas daugiakriterinių optimizavimo uždavinių sprendimo būdas, leidžiantis spręsti daugiakriterinius optimizavimo uždavinius interaktyviai ir užtikrinantis gaunamų sprendinių tolygų pasiskirstymą Pareto aibėje. Sukurta ir ištirta interaktyvi daugiakriterinių optimizavimo uždavinių sprendimų paramos sistemą, apjungianti pasiūlytą optimizavimo uždavinių sprendimo būdą, sprendimo proceso vizualizavimą ir jo lygiagretinimą. Taip pat pasiūlyta sprendimo strategija, pagal kurią sprendžiant daugiakriterinį optimizavimo uždavinį pasitelkiamas... [toliau žr. visą tekstą] In practice, optimization problems are often multiple criteria. The criteria are usually contradictory, so the final decision depends on a decision maker. When the problem is solved interactively, the decision maker can change his/her preferences in decision process. Moreover, it is important to obtain solutions from the whole Pareto front. A decision support system adapted to the specific of the problem is essential for solving multiple criteria optimization problems interactively. The objects of research are multiple criteria optimization problems, interactive methods for solving these problems, interactive decision support systems, and application of parallel computing in decision support systems. Multiple criteria optimization methods are analyzed in the dissertation. The focus of attention is the methods for a uniform distribution of solutions on the Pareto front as well as the interactive methods. An interactive way for solving multicriteria optimization problems, which finds alternative solutions uniformly distributed on the Pareto front is proposed and investigated in this dissertation. An interactive decision support system which integrates the created interactive solving way, the decision process visualization and parallelization for multiple criteria optimization is developed. The solving strategies, when a multiple criteria optimization problem is solved interactively, using a computer cluster are developed and compared experimentally. The time required for a... [to full text]

Savaime susidarančių lokalizuotų struktūrų valdymas deterministiškai (reguliariai) arba stochastiškai (atsitiktinai) osciliuojančiais laukais, kurių vidutinė vertė yra nulis, yra plačiai paplitęs įvairiose terpėse. Disertacijoje nagrinėjami savame susidarantys bistabilūs frontai disipatyviose sistemose, kurios aprašomos netiesinėmis parabolinėmis diferencialinėmis lygtimis su dalinėmis išvestinėmis. Disertacijos tikslas yra ištirti kryptingo bistabilių frontų dreifo valdymo nuliniais laukais galimybes, taikant kompiuterinį modeliavimą bei analitinius metodu. Tikslui pasiekti buvo sudaryti matematinis bei skaitinis modeliai, sukurta programinė įranga ir skaitiškai ištirtos savaiminių bistabilių frontų valdymo galimybės, naudojant periodinius, kvaziperiodinius ir stochastinius nulinius laukus. Spatio-temporal control of the self-ordered structures by use of the time-dependent oscillatory fields of zero-time average, either deterministic (temporally regular) or noisy (temporally irregular) ones, has today become a fundamental field of multidisciplinary research in a wide variety of the highly nonlinear systems of the different physical origin. The self-ordered bistable fronts in the essentially dissipative systems of the reaction-diffusion type, that are formulated by parabolic partial differential equations, are investigated in the dissertation. The objective of the research is to investigate new possibilities of controlling the directed net motion of the self-ordered bistable fronts by the deterministic and stochastic zero-mean ac forces using computer modeling and analytic tools. In order to achieve the objective mathematical and numerical models were applied, computer software was created and new possibilities of controlling the directed net motion of bistable fronts by use of the zero-average periodic, quasi-periodic and bounded noise fields were investigated.

Biosensors are analytical devices made up of a combination of a biological entity, usually an enzyme, that recognizes a specific analyte (substrate) and the transducer that translates the biorecognition event into a signal. In order to create new types of biosensors the corresponding experimental studies are necessary. Computational experiments could very well replace very expensive physical ones. However, the multi-step character of a chemical reaction scheme must be considered and modeled accordingly. In this thesis such reaction schemes were studied in great details. Original mathematical models were developed for optical peroxidase-based and amperometric laccase-based biosensors. The deterministic nature of model construction allows the automated models to be built. Based on this assumption flexible model for computational modeling of different practical multistep biosensors was developed. In order to optimize the numerical solution of the reaction-diffusion type equations common finite difference schemes were compared. The comparison shows that the fastest schemes to achieve the required relative error are implicit and Hopscotch schemes. For the problems where accuracy is not a significant factor but the speed is, the simplest explicit scheme should be used. Applying the new flexible model a computational modeling of the multi-step biosensors were produced. The modeling of laccase biosensor explained and confirmed the synergistic effect. The computational modeling of the... [to full text] Biojutikliai yra analitiniai įtaisai sudaryti iš biologiškai aktyvios bei selektyviai atpažįstančios substratą medžiagos, dažniausiai fermento, ir keitiklio formuojančio makroskopinį fizinį signalą. Naujų įtaisų kūrimui būtini lygiagretūs eksperimentiniai tyrimai. Skaitiniai eksperimentai gali patikimai pakeisti fizinius. Modeliuojant tokius biojutiklius, būtina atsižvelgti į juose vykstančių procesų daugiapakopį pobūdį. Šiame darbe nuodugniai ištirtos tokių reakcijų schemų savybės. Sudaryti originalūs matematiniai modeliai optiniam peroksidaziniam bei amperometriniam lakaziniam daugiapakopiams biojutikliams. Deterministinė modelių sudarymo proceso prigimtis leidžia jį automatizuoti. Remiantis šiuo principu sukurtas bendras įrankis kompiuteriniam daugiapakopių biojutiklių modeliavimui. Siekiant optimizuoti skaitinį sprendimą palygintos dažniausiai naudojamos baigtinių skirtumų skaitinio sprendimo schemos sprendžiant reakcijos - difuzijos lygtis. Pastarasis palyginimas parodė, kad greičiausiai reikiamas sprendinio tikslumas pasiekiamas taikant neišreikštinę bei Hopscotch schemas. Uždaviniams, kuriems sparta svarbesnė už tikslumą, turėtų būti taikoma išreikštinė schema. Taikant naują įrankį atliktas kompiuterinis daugiapakopių biojutiklių modeliavimas. Kompiuterinis lakazinio biojutiklio modeliavimas teoriškai paaiškino eksperimentiškai stebėtą sinergetinę mediatoriaus įtaką biojutiklio atsakui. Peroksidazinio biojutiklio kompiuterinio modeliavimo rezultatai parodė, kad plataus... [toliau žr. visą tekstą]

Biojutikliai yra analitiniai įtaisai sudaryti iš biologiškai aktyvios bei selektyviai atpažįstančios substratą medžiagos, dažniausiai fermento, ir keitiklio formuojančio makroskopinį fizinį signalą. Naujų įtaisų kūrimui būtini lygiagretūs eksperimentiniai tyrimai. Skaitiniai eksperimentai gali patikimai pakeisti fizinius. Modeliuojant tokius biojutiklius, būtina atsižvelgti į juose vykstančių procesų daugiapakopį pobūdį. Šiame darbe nuodugniai ištirtos tokių reakcijų schemų savybės. Sudaryti originalūs matematiniai modeliai optiniam peroksidaziniam bei amperometriniam lakaziniam daugiapakopiams biojutikliams. Deterministinė modelių sudarymo proceso prigimtis leidžia jį automatizuoti. Remiantis šiuo principu sukurtas bendras įrankis kompiuteriniam daugiapakopių biojutiklių modeliavimui. Siekiant optimizuoti skaitinį sprendimą palygintos dažniausiai naudojamos baigtinių skirtumų skaitinio sprendimo schemos sprendžiant reakcijos - difuzijos lygtis. Pastarasis palyginimas parodė, kad greičiausiai reikiamas sprendinio tikslumas pasiekiamas taikant neišreikštinę bei Hopscotch schemas. Uždaviniams, kuriems sparta svarbesnė už tikslumą, turėtų būti taikoma išreikštinė schema. Taikant naują įrankį atliktas kompiuterinis daugiapakopių biojutiklių modeliavimas. Kompiuterinis lakazinio biojutiklio modeliavimas teoriškai paaiškino eksperimentiškai stebėtą sinergetinę mediatoriaus įtaką biojutiklio atsakui. Peroksidazinio biojutiklio kompiuterinio modeliavimo rezultatai parodė, kad plataus... [toliau žr. visą tekstą] Biosensors are analytical devices made up of a combination of a biological entity, usually an enzyme, that recognizes a specific analyte (substrate) and the transducer that translates the biorecognition event into a signal. In order to create new types of biosensors the corresponding experimental studies are necessary. Computational experiments could very well replace very expensive physical ones. However, the multi-step character of a chemical reaction scheme must be considered and modeled accordingly. In this thesis such reaction schemes were studied in great details. Original mathematical models were developed for optical peroxidase-based and amperometric laccase-based biosensors. The deterministic nature of model construction allows the automated models to be built. Based on this assumption flexible model for computational modeling of different practical multistep biosensors was developed. In order to optimize the numerical solution of the reaction-diffusion type equations common finite difference schemes were compared. The comparison shows that the fastest schemes to achieve the required relative error are implicit and Hopscotch schemes. For the problems where accuracy is not a significant factor but the speed is, the simplest explicit scheme should be used. Applying the new flexible model a computational modeling of the multi-step biosensors were produced. The modeling of laccase biosensor explained and confirmed the synergistic effect. The computational modeling of the... [to full text]

Biojutikliai yra įrenginiai, skirti medžiagoms aptikti bei jų koncentracijoms matuoti. Siekiant sumažinti biojutiklių gamybos kaštus yra pasitelkiamas matematinis biojutikliuose vykstančių procesų modeliavimas. Disertacijoje nagrinėjami matematiniai ir kompiuteriniai biojutiklių modeliai, aprašantys biojutiklių, sudarytų iš kelių, skirtingas savybes turinčių dalių, veikimą. Nagrinėjami modeliai yra formuluojami vienmatėje bei dvimatėje erdvėse, aprašomi diferencialinėmis lygtimis dalinėmis išvestinėmis su netiesiniais nariais ir yra sprendžiami skaitiškai, naudojant baigtinių skirtumų metodą. Skaitiniai modeliai yra įgyvendinami kompiuterine programa. Disertacijoje pateikiamas originalus matematinis modelis biojutikliui su anglies nanovamzdelių elektrodu, nustatyti kriterijai, apibrėžiantys, kada biojutiklį su perforuota membrana galima modeliuoti vienmačiu modeliu. Darbe susisteminti elementai, naudojami biojutiklių modelių formulavimui, pagrindinį dėmesį skiriant biojutiklio struktūrinėms savybėms modeliuoti. Apibrėžta biojutiklių modelių aprašo kalba ir sukurta programinė įranga, leidžianti modeliuoti biojutiklių veikimą vienmačiais modeliais arba modeliais, formuluojamais stačiakampėje dvimatės erdvės srityje. Taikant sukurtą biojutiklių modeliavimo programinę įrangą, ištirtas biojutiklio su anglies nanovamzdelių elektrodu modelio adekvatumas ir struktūrinių bei geometrinių savybių įtaka biojutiklio elgsenai. Biosensors are analytical devices mainly used to detect analytes and measure their concentrations. Mathematical modeling is widely used for optimizing and analyzing an operation of biosensors for reducing price of development of new biosensors. The object of this research is mathematical and computer models, describing an operation of biosensors, made of several parts with different properties. The dissertation covers models, formulated in one and two-dimensional spaces by partial differential equations with non-linear members, and solved numerically, using the method of finite differences. The numerical models are implemented by a computer program. An original mathematical model for a biosensor with a carbon nanotube electrode is presented in the dissertation. The conditions at which the one-dimensional mathematical model can be used instead of two-dimensional one for accurate prediction of the biosensor response are investigated. Elements, used to build models of biosensors with a complex structure, were systemized. The biosensor description language is proposed and the computer software, simulating an operation of biosensors in the one-dimensional space and a rectangular domain of the two-dimensional space, is developed. An adequateness of the model for the biosensor with the carbon nanotube electrode and the impact of structural and geometrical properties on a response of the biosensor were investigated, performing computer experiments using the developed software.

Biosensors are analytical devices mainly used to detect analytes and measure their concentrations. Mathematical modeling is widely used for optimizing and analyzing an operation of biosensors for reducing price of development of new biosensors. The object of this research is mathematical and computer models, describing an operation of biosensors, made of several parts with different properties. The dissertation covers models, formulated in one and two-dimensional spaces by partial differential equations with non-linear members, and solved numerically, using the method of finite differences. The numerical models are implemented by a computer program. An original mathematical model for a biosensor with a carbon nanotube electrode is presented in the dissertation. The conditions at which the one-dimensional mathematical model can be used instead of two-dimensional one for accurate prediction of the biosensor response are investigated. Elements, used to build models of biosensors with a complex structure, were systemized. The biosensor description language is proposed and the computer software, simulating an operation of biosensors in the one-dimensional space and a rectangular domain of the two-dimensional space, is developed. An adequateness of the model for the biosensor with the carbon nanotube electrode and the impact of structural and geometrical properties on a response of the biosensor were investigated, performing computer experiments using the developed software. Biojutikliai yra įrenginiai, skirti medžiagoms aptikti bei jų koncentracijoms matuoti. Siekiant sumažinti biojutiklių gamybos kaštus yra pasitelkiamas matematinis biojutikliuose vykstančių procesų modeliavimas. Disertacijoje nagrinėjami matematiniai ir kompiuteriniai biojutiklių modeliai, aprašantys biojutiklių, sudarytų iš kelių, skirtingas savybes turinčių dalių, veikimą. Nagrinėjami modeliai yra formuluojami vienmatėje bei dvimatėje erdvėse, aprašomi diferencialinėmis lygtimis dalinėmis išvestinėmis su netiesiniais nariais ir yra sprendžiami skaitiškai, naudojant baigtinių skirtumų metodą. Skaitiniai modeliai yra įgyvendinami kompiuterine programa. Disertacijoje pateikiamas originalus matematinis modelis biojutikliui su anglies nanovamzdelių elektrodu, nustatyti kriterijai, apibrėžiantys, kada biojutiklį su perforuota membrana galima modeliuoti vienmačiu modeliu. Darbe susisteminti elementai, naudojami biojutiklių modelių formulavimui, pagrindinį dėmesį skiriant biojutiklio struktūrinėms savybėms modeliuoti. Apibrėžta biojutiklių modelių aprašo kalba ir sukurta programinė įranga, leidžianti modeliuoti biojutiklių veikimą vienmačiais modeliais arba modeliais, formuluojamais stačiakampėje dvimatės erdvės srityje. Taikant sukurtą biojutiklių modeliavimo programinę įrangą, ištirtas biojutiklio su anglies nanovamzdelių elektrodu modelio adekvatumas ir struktūrinių bei geometrinių savybių įtaka biojutiklio elgsenai.

Often there is a need to establish and understand the structure of multidimensional data: their clusters, outliers, similarity and dissimilarity. One of solution ways is a dimensionality reduction and visualization of the data. If a huge datasets is analyzed, it is purposeful to reduce the number of the data items before visualization. The area of research is reduction of the number of the data analyzed and mapping the data in a plane. In the dissertation, vector quantization methods, based on artificial neural networks, and visualization methods, based on a dimensionality reduction, have been investigated. The consecutive and integrated combinations of neural gas and multidimensional scaling have been proposed here as an alternative to combinations of self-organizing maps and multidimensional scaling. The visualization quality is estimated by König’s topology preservation measure, Spearman’s rho and MDS error. The measures allow us to evaluate the similarity preservation quantitatively after a transformation of multidimensional data into a lower dimension space. The ways of selecting the initial values of two-dimensional vectors in the consecutive combination and the first training block of the integrated combination have been proposed and the ways of assigning the initial values of two-dimensional vectors in all the training blocks, except the first one, of the integrated combination have been developed. The dependence of the quantization error on the values of training... [to full text] Dažnai iškyla būtinybė nustatyti ir giliau pažinti daugiamačių duomenų struktūrą: susidariusius klasterius, itin išsiskiriančius objektus, objektų tarpusavio panašumą ir skirtingumą. Vienas iš sprendimų būdų – duomenų dimensijos mažinimas ir jų vizualizavimas. Kai analizuojamos didelės duomenų aibės, tikslinga prieš vizualizavimą sumažinti ne tik dimensiją, bet ir duomenų skaičių. Šio darbo tyrimų sritis yra daugiamačių duomenų skaičiaus mažinimas ir duomenų atvaizdavimas plokštumoje. Disertacijoje nagrinėjami dirbtiniais neuroniniais tinklais grindžiami vektorių kvantavimo ir dimensijos mažinimu pagrįsti vizualizavimo metodai. Kaip alternatyva saviorganizuojančių neuroninių tinklų ir daugiamačių skalių junginiams, darbe pasiūlyti nuoseklus neuroninių dujų ir daugiamačių skalių junginys bei integruotas, atsižvelgiantis į neuroninių dujų metodo mokymosi eigą ir leidžiantis gauti tikslesnę daugiamačių vektorių projekciją plokštumoje. Junginiais gautų vaizdų kokybės vertinimui pasirinkti Konigo matas, Spirmano koeficientas bei MDS paklaida. Šie matai leidžia kiekybiškai įvertinti panašumų išlaikymą po daugiamačių duomenų transformavimo į mažesnės dimensijos erdvę. Taip pat pasiūlyti dvimačių vektorių pradinių koordinačių parinkimo būdai nuosekliame junginyje ir integruoto junginio pirmame mokymo bloke bei koordinačių reikšmių priskyrimo būdai integruoto junginio kituose mokymo blokuose. Eksperimentiškai nustatyta kvantavimo paklaidos priklausomybė nuo neuroninių dujų tinklo... [toliau žr. visą tekstą]

The aim of master thesis is to model amperometric biosensor with chemically modified electrode, introducing into existing model one more additional mediator layer. Mediator concentration inside the layer is changing during the biosensor action. Master thesis content consists of: enzyme kinetics introduction, biosensor modeling peculiarities exploration, chemically modified electrode information, biosensor action aspects description. Following chapter concentrates on mathematical modeling of particular biosensor type. Mathematical model represents differential equations with partial derivatives describing the reactions and diffusion inside biosensor. Next, numerical model is formulated. The explicit method technique was used. Based on numerical model software was made and validated. Using software the biosensor action was simulated in order to investigate biosensor properties and characteristics. In this work several properties were analyzed: impact of substrate and mediator concentrations, size of mediator, enzyme and diffusion layers, mediator layer diffusion coefficient on biosensor response. This model was compared with previous introduced model and it was shown that there is some difference between them and there is a reason to use new model.

Summary presents self-service networks operational performance improvement and management system, which is adapted to manage the supply of ATMs’ cash flows. The system is created using multi-agent technologies and artificial neural networks. Adaptive neural network model has been created for the forecast of ATMs’ cash demand. Flexibility of the network is regulated in real time mode by limiting neural network weights, depending on process complexity, therefore such network better forecasts in real life situations. Evaluation and process improvement methodology has been created to optimize productivity of self-service systems, which includes: value-based self-service quality and performance criteria’s, and performance evaluation models. Using these models is possible to increase productivity of self-service systems. Using theoretical studies results a computer program enabling real-time monitoring and management of ATM cash flows was created. Analysis of high and low intensity of ATM network profitability showed that the created flexible neural network forecast method is more superior than classical methods of time series forecast (moving average, Holt, Winters, and ARMA), and is able to quite accurately forecast various time series of ATM cash demand. Based on studies found that using the created ANN method and optimization procedure, ATM cash management productivity may be approximately increased by 33 percent. Santraukoje pristatoma savitarnos tinklų veiklos našumo didinimo ir valdymo intelektinė sistema, pritaikyta valdyti bankomatų grynųjų pinigų tiekimo srautus. Sistema sukurta naudojant multi-agentų technologijas ir neuroninius tinklus. Bankomatų grynųjų pinigų poreikiui prognozuoti sudarytas adaptyvus neuroninis tinklas. Šio tinklo lankstumas reguliuojamas realiu laiku apribojant neuroninių tinklų svorius, priklausomai nuo proceso sudėtingumo, todėl toks tinklas gali geriau prognozuoti realiose situacijose. Savitarnos sistemų našumui optimizuoti sukurta vertinimo ir procesų tobulinimo metodika apimanti: verte pagrįstus savitarnos kokybės ir našumo kriterijus bei našumo vertinimo ir procesų tobulinimo modelius. Naudojant šiuos modelius galima užtikrinti našesnį savitarnos sistemų darbą. Teorinių tyrimų pagrindu buvo sukurta kompiuterinė programa, leidžianti realiu laiku stebėti ir valdyti bankomatų grynųjų pinigų srautus. Šios programos panaudojimas leidžia sumažinti tinklo valdymo kaštus ir padidinti paslaugų prieinamumą. Atlikus didelio ir mažo intensyvumo bankomatų tinklų pelningumo analizę nustatyta, kad sukurtas lankstus neuroninių tinklų prognozavimo metodas yra pranašesnis už klasikinius laiko eilučių prognozavimo metodus (slankiųjų vidurkių, Holto, Vinterio, ARMA), ir gali pakankamai tiksliai prognozuoti įvairias bankomatų grynųjų pinigų poreikio laiko eilutes. Remiantis atliktais tyrimais nustatyta, kad pritaikius sukurtą ANN metodą ir optimizavimo procedūrą, bankomatų... [toliau žr. visą tekstą]

Penkiose disertacijos darbo dalyse nagrinėjamos asmens identifikavimo pagal pirštų atspaudus ir balsą problemos ir siūlomi jų sprendimai. Pirštų atspaudų požymių išskyrimo algoritmų kokybės įvertinimo problemą siūloma spręsti panaudojant sintezuotus pirštų atspaudus. Darbe siūlomos žinomo pirštų atpaudų sintezės algoritmo modifikacijos, kurios leidžia sukurti piršto atspaudo vaizdą su iš anksto nustatytomis charakteristikomis ir požymiais bei pagreitina sintezės procesą. Pirštų atspaudų požymių palyginimo problemos yra aptartos ir naujas palyginimo algoritmas yra siūlomas deformuotų pirštų palyginimui. Algoritmo kokybė yra įvertinta naudojant viešai prieinamas ir vidines duomenų bazes. Naujas asmens identifikavimo pagal balsą metodas remiantis tiesinės prognozės modelio grupinės delsos požymiais ir tų požymių palyginimo metrika kokybės prasme lenkia tradicinius asmens identifikavimo pagal balsą metodus. Pirštų ir balso įrašų nepriklausomumas yra irodytas ir asmens atpažinimas pagal balsą ir pirštų atspaudus kartu yra pasiūlytas siekiant išspręsti bendras biometrinių sistemų problemas. This dissertation focuses on person identification problems and proposes solutions to overcome those problems. First part is about fingperprint feaures extraction algorithm performance evaluaiton. Modifications to a known synthesis algorithm are proposed to make it fast and suitable for performance evaluation. Matching of deformed fingerprints is discussed in the second part of the work. New fingerprint matching algorithm that uses local structures and does not perform fingerprint alignment is proposed to match deformed fingerprints. The use of group delay features of linear prediciton model for speaker identification is proposed in the third part of the work. New similarity metric that uses group delay features is described. It is demonstrated that automatic speaker identification system with proposed features and similarity metric outperforms traditional speaker identification systems. Multibiometrics using fingerprints and voice is adressed in the last part of the dissertation.

This dissertation focuses on person identification problems and proposes solutions to overcome those problems. First part is about fingerprint features extraction algorithm performance evaluation. Modifications to a known synthesis algorithm are proposed to make it fast and suitable for performance evaluation. Matching of deformed fingerprints is discussed in the second part of the work. New fingerprint matching algorithm that uses local structures and does not perform fingerprint alignment is proposed to match deformed fingerprints. The use of group delay features of linear prediction model for speaker recognition is proposed in the third part of the work. New similarity metric that uses group delay features is described. It is demonstrated that automatic speaker recognition system with proposed features and similarity metric outperforms traditional speaker identification systems . Multibiometrics using fingerprints and voice is addressed in the last part of the dissertation. Penkiose disertacijos darbo dalyse nagrinėjamos žmogaus identifikavimo pagal pirštų atspaudus ir balsą problemos ir siūlomi jų sprendimai. Pirštų atspaudų požymių išskyrimo algoritmų kokybės įvertinimo problemą siūloma spręsti panaudojant sintezuotus pirštų atspaudus. Darbe siūlomos žinomo pirštų atpaudų sintezės algoritmo modifikacijos, kurios leidžia sukurti piršto atspaudo vaizdą su iš anksto nustatytomis charakteristikomis ir požymiais bei pagreitina sintezės procesą. Pirštų atspaudų požymių palyginimo problemos yra aptartos ir naujas palyginimo algoritmas yra siūlomas deformuotų pirštų palyginimui. Algoritmo kokybė yra įvertinta ant viešai prieinamų ir vidinių duomenų bazių. Naujas asmens identifikavimo pagal balsą metodas remiantis tiesinės prognozės modelio grupinės delsos požymiais ir tų požymių palyginimo metrika kokybės prasme lenkia tradicinius asmens identifikavimo pagal balsą metodus. Pirštų ir balso įrašų nepriklausomumas yra irodytas ir asmens atpažinimas pagal balsą ir pirštų atspaudus kartu yra pasiūlytas siekiant išspręsti bendras biometrinių sistemų problemas.

There are plenty of solutions for the task of multi-class recognition. Unfortunately, these solutions are not always unanimous. Most of them are based on empirical experiments while statistical data features consideration is often omitted. That’s why questions like when and which method should be used, what the reliability of any chosen method is for solving a multi-class recognition task arise. In this dissertation two-stage multi-class decision methods are analyzed. Pair-wise classifiers able to better exploit statistical data features are used in the first stage of such methods. In the second stage a particular fusion rule of the first stage results is used to fuse the first stage results in order to produce the final classification decision. Complexity issues of pair-wise classifiers, training data size and precision of method quality estimation are pointed out in the research. The precision of algorithm highly depends on the data and the number of experiments performed (data permutation, division into training and testing data). It is shown that the declared superiority of some known algorithms is not reliable due to low precision of estimation. A detailed comparison of well known multi-class classification methods is performed and a new pair-wise classifier fusion method based on similar method used in multi-class classifier fusion is presented. The recommendations for multi-class classification task designer are provided. Methods which allow reducing classification... [to full text] Daugelio klasių atpažinimo uždaviniams spręsti yra sukurta aibė sprendimų ir ne visada vieningų rekomendacijų. Dauguma jų paremta empiriniais bandymais, retai atsižvelgiama į statistines duomenų savybes. Dėl to sprendžiant daugelio klasių klasifikavimo uždavinį kyla klausimų, kurį metodą ir kada geriausia naudoti, koks vieno ar kito metodo patikimumas. Disertacijoje nagrinėjami dviejų pakopų sprendimo priėmimo metodai, kai pirmame etape sudaromi klasifikatoriai poroms (angl. pair-wise), sugebantys geriau išnaudoti klasių tarpusavio statistines savybes, o kitame etape yra atliekamas klasifikatorių poroms rezultatų apjungimas. Tyrime ypatingas dėmesys yra skiriamas klasifikatorių poroms sudėtingumui, mokymo duomenų kiekiui bei algoritmų kokybės įvertinimo tikslumui. Tikslumas labai priklauso nuo duomenų bei atliktų eksperimentų kiekio (duomenų permaišymo klasėse, juos skirstant į mokymo ir testavimo). Parodyta, jog dėl žemo įvertinimo tikslumo kai kurių publikuotų algoritmų deklaruojamas pranašumas prieš žinomus algoritmus nėra patikimas. Darbe atliktas detalus žinomų metodų palyginimas bei pristatytas naujai sukurtas klasifikatorių poroms apjungimo algoritmas, kuris yra paremtas analogišku algoritmu daugelio klasių klasifikatorių rezultatų apjungimui. Pateiktos bendros rekomendacijos, kaip projektuotojui elgtis daugelio klasių atveju. Pasiūlyti metodai, leidžiantys sumažinti klasifikavimo klaidą atliekant klasifikatorių poroms apjungimo koregavimą, kad algoritmas nebūtų... [toliau žr. visą tekstą]

The present dissertation deals with one of the speech synthesizer components – automatic stressing of a text and two other goals relating to it – homographs (words that can be stressed in several ways) disambiguation and a search for clitics (unstressed words). The method, which by means of decision trees finds sequences of letters that unambiguously define the word stressing, was applied to stress a Lithuanian text. Decision trees were created using large corpus of stressed words. Stressing rules based on sequences of letters at the beginning, ending and in the middle of a word have been formulated. The algorithm proposed reaches the accuracy of about 95.5%. The homograph disambiguation algorithm proposed by the present author is based on frequencies of lexemes and morphological features, that were obtained from corpus containing about one million words. Such methods were not used for Lithuanian language so far. The proposed algorithm enables to select the correct variant of stressing within the accuracy of 85.01%. Besides the author proposes methods of four types to search for the clitics in a Lithuanian text: methods based on recognising the combinational forms, based on statistical stressed/unstressed frequency of a word, grammar rules and stressing of the adjacent words. It is explained how to unite all the methods into a single algorithm. 4.1% of errors was obtained for the testing data among all the words, and the ratio of errors and unstressed words accounts for 18... [to full text] Disertacijoje nagrinėjama viena iš kalbos sintezatoriaus sudedamųjų dalių – teksto automatinis kirčiavimas, bei su kirčiavimu susiję kiti uždaviniai: vienodai rašomų, bet skirtingai tariamų, žodžių (homografų) vienareikšminimas bei prie gretimo žodžio prišlijusių bekirčių žodžių (klitikų) paieška. Teksto kirčiavimui pritaikytas metodas, kuris naudodamas sprendimų medžius randa raidžių sekas, vienareikšmiai nusakančias žodžio kirčiavimą. Sprendimo medžiams sudaryti buvo naudojamas didelies apimties sukirčiuotų žodžių tekstynas. Buvo sudarytos kirčiavimo taisyklės remiantis raidžių sekomis žodžių pradžioje, pabaigoje ir viduryje. Pasiūlytas kirčiavimo algoritmas pasiekia apie 95,5% tikslumą. Homografams vienareikšminti pritaikyti iki šiol lietuvių kalbai nenaudoti metodai, pagrįsti leksemų ir morfologinių pažymų vartosenos dažniais, gautais iš vieno milijono žodžių tekstyno. Darbe parodyta, kad morfologinių pažymų dažniai yra svarbesni už leksemų dažnius. Pasiūlyti metodai leido homografus vienareikšminti 85,01% tikslumu. Klitikų paieškai pasiūlyti metodai, kurie remiasi: 1) samplaikinių formų atpažinimu, 2) statistiniu žodžio kirčiavimo/nekirčiavimo dažniu, 3) kai kuriomis gramatikos taisyklėmis bei 4) gretimų žodžių kirčių pasiskirstymu (ritmika). Paaiškinta, kaip visus metodus sujungti į vieną algoritmą. Pritaikius šį algoritmą testavimo duomenims, klaidų ir visų žodžių santykis buvo 4,1%, o klaidų ir nekirčiuotų žodžių santykis – 18,8%.

Sequent calculi for BDI logics is a research object of the thesis. BDI logics are widely used for agent system description and implementation. Agents are autonomous systems, those acts in some environment and aspire to achieve preassigned goals. Implementation of the decision making is the main and the most complicated part in agent systems implementation. Logic calculi may be used for the decision making implementation. In this thesis, there are researched sequent calculi for BDI logics. Sequent calculi for BDI logics, like sequent calculi for other modal logics, use loop-check technique to get decidability. Inefficient loop-check takes a major part of the resources used for the derivation. For some modal logics, there are known loop-check free sequent calculi or calculi with an efficient loop-check. In this thesis, there is presented loop-check free sequent calculus for KD45 logic, which is the main fragment of the BDI logics. Introduced calculus not only eliminates loop-check, but also simplifies sequent derivation. For the branching time logic (another BDI logic fragment) there is presented sequent calculus with an efficient loop-check. Obtained results are adapted for creation sequent calculi for monoagent and multiagent BDI logics. Introduced calculi use only restricted loop-check. Moreover, loop-check is totally eliminated for some types of the loops. These results enables to create more efficient agent systems, those are based on the BDI logics. Darbe nagrinėjami sekvenciniai skaičiavimai BDI logikoms. BDI logikos yra plačiai naudojamos agentinių sistemų aprašymui ir realizavimui. Agentai yra autonomiškos sistemos, kurios veikia kažkurioje aplinkoje ir siekia įvykdyti iš anksto apibrėžtus tikslus. Sprendimų priėmimo realizavimas yra svarbiausia ir sudėtingiausia dalis realizuojant agentines sistemas. Sprendimo priėmimo realizavimui gali būti naudojami logikos skaičiavimai. Šiame darbe ir yra nagrinėjami sekvenciniai skaičiavimai BDI logikoms. BDI logikose, kaip ir kitose modalumo logikose, yra naudojama ciklų paieška išsprendžiamumui gauti. Neefektyvi ciklų paieška užima didesnę išvedimų paieškos resursų dalį. Kai kurioms modalumo logikoms yra žinomi becikliai skaičiavimai ar skaičiavimai naudojantys efektyvią ciklų paiešką. Šiame darbe yra pateikiamas beciklis sekvencinis skaičiavimas KD45 logikai, kuri yra esminis BDI logikų fragmentas. Pateiktas skaičiavimas ne tik eliminuoja ciklų paiešką, bet ir supaprastina patį sekvencijos išvedimą. Skaidaus laiko logikai (kitam BDI logikų fragmentui) yra pateikiamas sekvencinis skaičiavimas naudojantis efektyvią ciklų paiešką. Gauti rezultatai yra pritaikyti sukuriant sekvencinius skaičiavimus vianaagentinei ir daugiaagentinei BDI logikoms. Pristatyti skaičiavimai naudoja tik apribotą ciklų paiešką. Be to, kai kurių tipų ciklus eliminuoja visiškai. Šie rezultatai įgalina kurti efektyvesnes agentines sistemas, paremtas BDI logikomis.

Matematinis ir skaitinis biojutiklių modeliavimas yra svarbus uždavinys, kuriant naujus ir tobulinant esamus biojutiklius. Disertacijos tyrimo objektas – matematiniai bei skaitiniai modeliai, aprašantys naujoviškų lipazės aktyvumo nustatymo biojutiklių bei teorinio biojutiklio, padengto valdoma membrana, veikimą. Tyrimo tikslai – nustatyti, kokie matematiniai ir skaitiniai modeliai geriausiai tinka lipazės aktyvumo nustatymo biojutikliams aprašyti, taip pat nustatyti, kokiais parametrais pasižymėtų biojutiklis, turintis valdomą membraną, kokiomis sąlygomis išryškėtų jo privalumai ir trūkumai. Nustatyta, kad lipazės aktyvumo matavimo biojutiklio modeliavimui klasikinį modelį reikia papildyti netiesiniu nariu. Biojutiklis su valdoma membrana pasiteisintų, jei fiziškai neištraukiant jutiklio iš darbinės aplinkos, reikėtų perjunginėti jo darbo režimą iš difuzinio į kinetinį ir atvirkščiai. Biosensor mathematical and computer modeling is an important task for the development of new biosensors and for the improvement of the existing ones. Objects of this study are mathematical and numerical models which describe operation of novel lipase activity assessment biosensors and theoretical biosensor with controllable permeability membrane. Specific aims of this thesis are to identify what mathematical and numerical models are best suited for modeling specific lipase activity assessment biosensors and to identify what parameters of operation are specific for biosensor with controllable membrane. Also to identify the conditions which would reveal the positive and negative features of controllable membrane. It was discovered that in the case of lipase activity assessment biosensor the classic mathematical model should be extended with a non-linear term (in respect to substrate). Also, it was discovered that biosensor with controllable membrane would be useful in cases when biosensor cannot be physically removed from the operating environment, but still needs to be reconfigured for operation in the kinetic or diffusion mode.

Biosensor mathematical and computer modeling is an important task for the development of new biosensors and for the improvement of the existing ones. Objects of this study are mathematical and numerical models which describe operation of novel lipase activity assessment biosensors and theoretical biosensor with controllable permeability membrane. Specific aims of this thesis are to identify what mathematical and numerical models are best suited for modeling specific lipase activity assessment biosensors and to identify what parameters of operation are specific for biosensor with controllable membrane. Also to identify the conditions which would reveal the positive and negative features of controllable membrane. It was discovered that in the case of lipase activity assessment biosensor the classic mathematical model should be extended with a non-linear term (in respect to substrate). Also, it was discovered that biosensor with controllable membrane would be useful in cases when biosensor cannot be physically removed from the operating environment, but still needs to be reconfigured for operation in the kinetic or diffusion mode. Matematinis ir skaitinis biojutiklių modeliavimas yra svarbus uždavinys, kuriant naujus ir tobulinant esamus biojutiklius. Disertacijos tyrimo objektas – matematiniai bei skaitiniai modeliai, aprašantys naujoviškų lipazės aktyvumo nustatymo biojutiklių bei teorinio biojutiklio, padengto valdoma membrana, veikimą. Tyrimo tikslai – nustatyti, kokie matematiniai ir skaitiniai modeliai geriausiai tinka lipazės aktyvumo nustatymo biojutikliams aprašyti, taip pat nustatyti, kokiais parametrais pasižymėtų biojutiklis, turintis valdomą membraną, kokiomis sąlygomis išryškėtų jo privalumai ir trūkumai. Nustatyta, kad lipazės aktyvumo matavimo biojutiklio modeliavimui klasikinį modelį reikia papildyti netiesiniu nariu. Biojutiklis su valdoma membrana pasiteisintų, jei fiziškai neištraukiant jutiklio iš darbinės aplinkos, reikėtų perjunginėti jo darbo režimą iš difuzinio į kinetinį ir atvirkščiai.

The purpose of this master thesis was to develop a methodology, which would assure an efficient way to use computing grids for computer models modeling biocatalytic processes. After researching possibilities to use computing grids for modeling of such processes, a methodology was presented, which can be used independently of grid middleware. Methodology was implemented on BalticGrid. By applying this methodology biocatalytic processes in biosensors were investigated. Operation of biosensor is described with mathematical model, which in general case is solved with computer model. Computer models of biosensors are commonly parameterized, and in most cases same problem is being solved only with different set of parameters. Such processes can be solved by using computational grids. Methodology presented in this paper was used to compare quasi steady state and detailed models of chemically modified biosensors. After examining methodology presented in this paper it was proved that this methodology can be used efficiently to research biocatalytic processes. Effectiveness of applying this methodology in concrete computational grid was estimated and suggestions were presented how to apply this methodology in an efficient way.