To date, a huge amount of data on organisms diversity has been accumulated. Databases help to store and use these data for scientific purposes. There exists several dozens of databases for storing biodiversity data that were described in publications. Each has an original structure which badly correlates with the structures of other databases. This complicates data exchange and the formation of big biodiversity data array. The cause of this situation is the lack of the formal definitions of universal data components, which allow to build the database with any data on the diversity of organisms. The analysis of publications and author’s experience show that such universal components are present in the characteristics of any organisms. For example, it is an organism taxonomic name and a location where it was found. There are six such components and they answer to one of the six questions: what, where, when, who, where from and where to. What determines the name of an organism; where determines the location where it was found; when indicates the date of finding; who enumerates the persons, who found and analyzed an organism; where from refers to publications, where data about an organism are extracted or published; where to shows in which biological collection an organism is put in. Each component corresponds to a separate database table. These tables are linked to the table with data about organism (individual) and they are not linked with each other. Attributes of the links between the organism table and the component tables are stored in intermediate tables. They are used, for example, to store bibliographic facts, descriptions of collection items or geographical points. They also act as docking stations to which tables with any other information are attached. The creation of any database about the diversity of living organisms begins with the definition of the table of organism specimens. It must be used even if there is no explicit data on organisms. In that case virtual organisms should be introduced and the other components should be linked with them by means of intermediate tables. The latter are docked to other data. Minimal structures of all the tables, links between them and examples of databases construction are described in the work.
Reliability, survivability, and stability analysis tasks are typical not only for telecommunications, but also for systems whose components are subject to one or more types of failures, such as transport, power, mechanical systems, integrated circuits, and even software. The logical approach involves the decomposition of the system into a number of small functional elements, and within telecommunications networks they are usually separate network devices (switches, routers, terminals, etc.), as well as communication lines between them (copper-core, fiber-optic, coaxial cables, wireless media, and other transmission media). Functional relationships also define logical relationships between the failures of individual elements and the failure of the network as a whole. The assumption is also used that device failures are relatively less likely than communication line failures, which implies using the assumption of absolute stability (reliability, survivability) of these devices. Model of a telecommunication network in the form of the generalized model of Erdos–Renyi is presented. In the context of the stability of the telecommunications network, the analyzed property is understood as the connectivity of the network in one form or another. Based on the concept of stochastic connectivity of a network, as the correspondence of a random graph of the connectivity property between a given set of vertices, three connectivity measures are traditionally distinguished: two-pole, multi-pole, and all-pole. The procedures for forming an arbitrary structure of sets of paths and trees for networks are presented, as well as their generalization of multipolar trees. It is noted that multipolar trees are the most common concept of relatively simple chains and spanning trees. Solving such problems will allow us to proceed to calculating the probability of connectivity of graphs for various connectivity measures.
Event-driven software systems, belonging to the class of systems with complex behavior in the scientific literature, are reactive systems, which react to the same input effect in different ways depending on their state and background. It is convenient to describe such systems using state-transition models utilizing special language tools, both graphical and textual. Methodology for automated development of systems with complex behavior using the designed CIAO language (Cooperative Interaction of Automata Objects), which allows formally specifying the required behavior based on an informal description of the reacting system, is presented. An informal description of a reacting system can be provided verbally in a natural language or in another way adopted in a specific domain. Further, according to this specification in the CIAO language, a software system for interacting automata in the C++ programming language is generated with a special system. The generated program implements a behavior guaranteed to correspond to a given specification and original informal description. CIAO provides both graphical and textual notation. Graphic notation is based on an extended notation of state machine diagrams and component diagrams of the unified modeling language UML, which are well established in describing the behavior of event-driven systems. The text syntax of the CIAO language is described by context-free grammar in regular form. Automatically generated C++ code allows using of both library and any external functions written manually. At the same time, the evident correspondence of the formal specification and the generated code is preserved on conditions that the external functions conform to their specifications. As an example, an original solution to D. Knut's problem of a responsive elevator control system is proposed. The effectiveness of the proposed methodology is demonstrated, since the automaton-converter generating the C++ code is presented as a responsive system, is specified in the CIAO language and implemented by the bootstrapping. The proposed methodology is compared with other well-known formal methods for describing systems with complex behavior.
A problem of reducing a linear time-invariant dynamic system is considered as a problem of approximating its initial rational transfer function with a similar function of a lower order. The initial transfer function is also assumed to be rational. The approximation error is defined as the standard integral deviation of the transient characteristics of the initial and reduced transfer function in the time domain. The formulations of two main types of approximation problems are considered: a) the traditional problem of minimizing the approximation error at a given order of the reduced model; b) the proposed problem of minimizing the order of the model at a given tolerance on the approximation error. Algorithms for solving approximation problems based on the Gauss-Newton iterative process are developed. At the iteration step, the current deviation of the transient characteristics is linearized with respect to the coefficients of the denominator of the reduced transfer function. Linearized deviations are used to obtain new values of the transfer function coefficients using the least-squares method in a functional space based on Gram-Schmidt orthogonalization. The general form of expressions representing linearized deviations of transient characteristics is obtained. To solve the problem of minimizing the order of the transfer function in the framework of the least squares algorithm, the Gram-Schmidt process is also used. The completion criterion of the process is to achieve a given error tolerance. It is shown that the sequence of process steps corresponding to the alternation of coefficients of polynomials of the numerator and denominator of the transfer function provides the minimum order of transfer function. The paper presents an extension of the developed algorithms to the case of a vector transfer function with a common denominator. An algorithm is presented with the approximation error defined in the form of a geometric sum of scalar errors. The use of the minimax form for error estimation and the possibility of extending the proposed approach to the problem of reducing the irrational initial transfer function are discussed. Experimental code implementing the proposed algorithms is developed, and the results of numerical evaluations of test examples of various types are obtained.
A phase enlargement of semi-Markov systems that does not require determining stationary distribution of the embedded Markov chain is considered. Phase enlargement is an equivalent replacement of a semi-Markov system with a common phase state space by a system with a discrete state space. Finding the stationary distribution of an embedded Markov chain for a system with a continuous phase state space is one of the most time-consuming and not always solvable stage, since in some cases it leads to a solution of integral equations with kernels containing sum and difference of variables. For such equations there is only a particular solution and there are no general solutions to date. For this purpose a lemma on a type of a distribution function of the difference of two random variables, provided that the first variable is greater than the subtracted variable, is used. It is shown that the type of the distribution function of difference of two random variables under the indicated condition depends on one constant, which is determined by a numerical method of solving the equation presented in the lemma. Based on the lemma, a theorem on the difference of a random variable and a complicated recovery flow is built up. The use of this method is demonstrated by the example of modeling a technical system consisting of two series-connected process cells, provided that both cells cannot fail simultaneously. The distribution functions of the system residence times in enlarged states, as well as in a subset of working and non-working states, are determined. The simulation results are compared by the considered and classical method proposed by V. Korolyuk, showed the complete coincidence of the sought quantities.
