Vol 50, No 7 (2016)

Process mining is a new emerging discipline related to process management, formal process modelling, and data mining. One of the main tasks of process mining is model synthesis (discovery) based on event logs. A wide range of algorithms for process model discovery, analysis, and enhancement is developed. The real-life event logs often contain noise of different types. In this paper, we describe the main causes of noise in the event logs and study the effect of noise on the performance of process discovery algorithms. The experimental results of application of the main process discovery algorithms to artificial event logs with noise are provided. Specially generated event logs with noise of different types were processed using the four basic discovery techniques. Although modern algorithms can cope with some types of noise, in most cases, their use does not lead to obtaining a satisfactory result. Thus, there is a need for more sophisticated algorithms to deal with noise of different types.

Process mining is a new direction in the field of modeling and analysis of processes, where an important role is played by the use of information from event logs that describe the history of the system behavior. Methods and approaches used in process mining are often based on various heuristics, and experiments with large event logs are crucial for substantiating and comparing developed methods and algorithms. These experiments are very time consuming, so automation of experiments is an important task in the field of process mining. This paper presents the DPMine language developed specifically to describe and carry out process mining experiments. The basic concepts of the DPMine language as well as principles and mechanisms of its extension are described. Ways of integration of the DPMine language as dynamically loaded components into the VTMine modeling tool are considered. A sample experiment of building a fuzzy model of a process from a data log stored in a normalized database is given.

This paper presents a new infrastructure for creating specialized databases and database management systems (DBMSs). Some principles of this infrastructure are formulated based on an analysis of various NoSQL solutions. The main features of the proposed approach are: (a) a flexible system of type definitions that allows one to create data structures based on different paradigms and (b) different forms of supporting structured data and mapping them onto the file system. Experiments are carried out to implement RDF graphs, relational tables, name tables, and object-relational mappings. The proposed approach allows one to solve certain problems of developing new technologies for working with Big Data.

The article is devoted to an approach to constructing and verification of discrete PLC-programs by LTL-specification. This approach provides a possibility of analysing the correctness of PLCprograms by using the model checking method. The linear temporal logic LTL is used as a language of specification of the program behavior. The correctness analysis of LTL-specification is automatically performed by the symbolic model checking tool Cadence SMV. The article demonstrates the consistency of the approach to constructing and verification of PLC programs by LTL-specification from the point of view of Turing power. It is proved that in accordance with this approach for any Minsky counter machine an LTL-specification can be built, which is used for machine implementation in any PLC programming language of standard IEC 61131-3. Minsky machines are equipollent to Turing machines, and the considered approach also has the Turing power. The proof focuses on representation of a counter machine behavior in the form of a set of LTL-formulas and matching these formulas to constructions of ST and SFC languages. SFC is interesting as a specific graphical language. ST is considered as a basic language because the implementation of a counter machine on IL, FBD/CFC and LD languages is reduced to rewriting blocks of an ST-program. The idea of the proof is demonstrated by an example of a Minsky 3-counter machine, which implements a function of squaring.

In the article the problem of finding the maximum multiple flow in the network of any natural multiplicity k is studied. There are arcs of three types: ordinary arcs, multiple arcs and multi-arcs. Each multiple and multi-arc is a union of k linked arcs, which are adjusted with each other. The network constructing rules are described. The definitions of a divisible network and some associated subjects are stated. The important property of the divisible network is that every divisible network can be partitioned into k parts, which are adjusted on the linked arcs of each multiple and multi-arc. Each part is the ordinary transportation network. The main results of the article are the following subclasses of the problem of finding the maximum multiple flow in the divisible network. 1. The divisible networks with the multi-arc constraints. Assume that only one vertex is the ending vertex for a multi-arc in s network parts. In this case the problem can be solved in a polynomial time. 2. The divisible networks with the weak multi-arc constraints. Assume that only one vertex is the ending vertex for a multi-arc in k-1 network parts (1 ≤ s < k − 1) and other parts have at least two such vertices. In that case the multiplicity of the maximum multiple flow problem can be decreased to k - s. 3. The divisible network of the parallel structure. Assume that the divisible network component, which consists of all multiple arcs, can be partitioned into subcomponents, each of them containing exactly one vertex-beginning of a multi-arc. Suppose that intersection of each pair of subcomponents is the only vertex-network source x₀. If k=2, the maximum flow problem can be solved in a polynomial time. If k ≥ 3, the problem is NP-complete. The algorithms for each polynomial subclass are suggested. Also, the multiplicity decreasing algorithm for the divisible network with weak multi-arc constraints is formulated.

Traditional network architecture is inflexible and complex. This observation has led to a paradigm shift toward software-defined networks (SDNs), in which the network control level is separated from the data link layer. This change became possible because of the control plane transfer from switching equipment to software modules that run on a dedicated server called a controller (or a network operating system) or to network applications that work with this controller. Methods of presentation, storage, and communication interfaces with network topology elements available to SDN controller users are the most important aspects of network operating systems because the operation of some key controller modules depends heavily on the internal representation of the network topology. Firewall and routing modules can be cited as examples of these modules. This paper considers the methods used to represent and store the network topology, as well as communication interfaces with corresponding modules of the Floodlight controller. An alternative algorithm for exchanging messages on the changes in the network topology between the controller and network applications has been proposed and developed. The algorithm makes it possible to issue notifications based on a subscription to relevant events. An API for the module of interacting with applied programs of the SDN controller has been developed. The Topology Tracker module has been designed based on this algorithm and API. In active mode, this module can inform network applications about the changes in the network topology and store its compact representation for the interaction acceleration.

The problem about local dynamics of the logistic equation with a rapidly oscillating timeperiodic piecewise constant coefficient of delay has been considered. It has been shown that the averaged equation is a logistic equation with two delays. A stability criterion for equilibrium points has been obtained. The dynamical properties of the original equation are considered provided that the critical case of the equilibrium point stability problem has been implemented. It has been found that an increase of delay coefficient oscillation frequency may lead to an unlimited process of steady-mode birth and death.

A system of two logistic equations with delay coupled by delayed control has been considered. It has been shown that, in the case of a fairly large delay control coefficient, the problem of the dynamics of the initial systems has been reduced to investigating the nonlocal dynamics of special families of partial differential equations that do not contain small and large parameters. New interesting dynamic phenomena are discovered based on the results of numerical analysis. Systems of three logistic delay equations with two types of diffusion relations have been considered. Special families of partial differential equations that do not contain small and large parameters have also been constructed for each of these systems. The research results for the dynamic properties of the original equations have been presented. It has been shown that the difference in the dynamics of the considered systems of three equations may be of a fundamental nature.

In this paper, a first-order equation with state-dependent delay and a nonlinear right-hand side is considered. The conditions of the existence and uniqueness of the solution of the initial value problem are supposed to be executed.The task is to study the behavior of solutions of the considered equation in a small neighborhood of its zero equilibrium. The local dynamics depends on real parameters, which are coefficients of the right-hand side decomposition in a Taylor series.The parameter, which is a coefficient at the linear part of this decomposition, has two critical values that determine the stability domain of the zero equilibrium. We introduce a small positive parameter and use the asymptotic method of normal forms in order to investigate local dynamics modifications of the equation near each two critical values. We show that the stability exchange bifurcation occurs in the considered equation near the first of these critical values, and the supercritical Andronov–Hopf bifurcation occurs near the second of these values (provided the sufficient condition is executed). Asymptotic decompositions according to correspondent small parameters are obtained for each stable solution. Next, a logistic equation with state-dependent delay is considered to be an example. The bifurcation parameter of this equation has the only critical value. A simple sufficient condition of the occurrence of the supercritical Andronov–Hopf bifurcation in the considered equation near a critical value has been obtained as a result of applying the method of normal forms.

We consider a second-order linear differential equation of with a small factor at the highest derivative. We study the asymptotic behavior of eigenvalues of the first boundary-value problem (the Dirichlet problem) under the assumption that turning points (points where the coefficient at the first derivative equals to zero) exist. It has been shown that only the behavior of coefficients of the equation in a small neighborhood of the turning points is essential. The main result is a theorem on the limit values of the eigenvalues of the first boundary-value problem.