Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli diagram.

In 2010, Bezuglyi, Kwiatkowski, Medynets, and Solomyak [10] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence matrix determines a probability ergodic invariant measure. In this paper, we show that this result does not hold for stationary reducible generalized Bratteli diagrams. We consider classes of stationary and non -stationary reducible generalized Bratteli diagrams with infinitely many simple standard subdiagrams, in particular, with infinitely many odometers as subdiagrams. We characterize the sets of all probability ergodic invariant measures for such diagrams and study partial orders under which the diagrams can support a Vershik homeomorphism.

Generalized Bratteli diagrams with a countable set of vertices in every level are models for aperiodic Borel automorphisms. This paper is devoted to the description of all ergodic probability tail invariant measures on the path spaces of generalized Bratteli diagrams. Such measures can be identified with inverse limits of infinite-dimensional simplices associated with levels in generalized Bratteli diagrams. Though this method is general, we apply it to several classes of reducible generalized Bratteli diagrams. In particular, we explicitly describe all ergodic tail invariant probability measures for (i) the infinite Pascal graph and give the formulas for the values of such measures on cylinder sets, (ii) generalized Bratteli diagrams formed by a countable set of odometers, (iii) reducible generalized Bratteli diagrams with uncountable set of ergodic tail invariant probability measures. We also consider the method of measure extension by tail invariance from subdiagrams. We discuss the properties of the Vershik map defined on reducible generalized Bratteli diagrams.

Public clouds like AWS, Azure, GCP, and OCI offer a range of services including Container as a Service (CaaS) and Relational Database as a Service (RDBaaS). From the perspective of an IT system provider there is a notable lack of information on the overall performance that can be achieved when using specific configurations of these interdependent CaaS and RDBaaS services. To address this issue and avoid incorrect architectural assumptions, it was decided to empirically evaluate the combined performance offered by CaaS and RDBaaS services, considering their hardware configurations selected based on a predetermined cost constraint. The experiments were conducted in two stages. The first stage was aimed at narrowing down the set of investigated CaaS and RDBaaS services. Using the measurements collected in the second stage, a statistical analysis was performed, comparing the performance achieved in the cloud environments with the performance obtained in the on-premise environment, taking cost constraints into account. The experiments conducted for the cloud services provided insights into their limitations and performance, enabling informed architectural decisions during the design of complex IT systems. The results of the analysis confirmed that the performance obtained for the studied combinations of services and their associated costs significantly varied among the different cloud providers.

The primary network layer protocol on which theoperation of most computer networks is based, including the Internet is the Internet protocol version 4 (IPv4). Due to the limitations of this protocol, it is becoming increasingly widespread use of the Internet protocol version 6 (IPv6). The IPv6 implements some new features not available in IPv4. The paper provides a short overview of the key features of IPv6 and discussed the possible levels of network virtualization. The research environment to testing the level of support for IPv6 protocol by virtualization environments is proposed. The results of tests conducted using the proposed research environment for Hyper-V virtualizer are presented.

The implementation of parallel applications is always a challenge. It embraces many distinctive design decisions that are to be taken. The paper presents issues of parallel processing with use of .NET applications and popular Database Management Systems (DBMSes). In the paper, four design dilemmas are addressed: how efficient is the auto-parallelism implemented in the .NET TPL library, how do popular DBMSes differ in serving parallel requests, what is the optimal size of data chunks in the data parallelism scheme, and how the TPL auto-parallelism behaves in the public clouds. They are analyzed in the context of the typical and practical business case originated from IT solutions which are dedicated for the energy market participants. The paper presents the results of experiments conducted in a controlled, on-premises and cloud environments. The experiments allowed to compare the performance of the TPL auto-parallelism with a wide range of manually set numbers of worker threads. They also helped to evaluate four DBMSes: Oracle, MySQL, PostgreSQL, and MSSQL in the scenario of serving parallel queries. Finally, they showed the impact of data chunk sizes on the overall performance.

The paper concerns issues related to evaluation of processing in computational clouds while multiple services are run. The new approach for the cloud efficiency evaluation and the problem of selection the most suitable cloud configuration with respect to user demands on processing time and processing price cost is proposed. The base of proposed approach is defined the Relative Response Time RRT which is calculated for each service individually, for different loads, and for each tested configuration. The paper presents results of experiments performed in real clouds which enabled to evaluate processing at general and individual application levels. The experiments show the need of applying such type of metric for evaluation of cloud configurations if different types of services are to be delivered considering its response time and price cost. The presented approach with use of RRT enables for available cloud virtual machine configurations to choose suitable one to run the application with regard to considered demands.

For a Bratteli diagram B, we study the simplex M1(B) of probability measures on the path space of B which are invariant with respect to the tail equivalence relation. Equivalently, M1(B) is formed by probability measures invariant with respect to a homeomorphism of a Cantor set. We study relations between the number of ergodic measures from M1(B) and the structure and properties of the diagram B. We prove a criterion and find sufficient conditions of unique ergodicity of a Bratteli diagram, in which case the simplex M1(B) is a singleton. For a finite rank k Bratteli diagram B having exactly l≤k ergodic invariant measures, we explicitly describe the structure of the diagram and find the subdiagrams which support these measures. We find sufficient conditions under which: (i) a Bratteli diagram has a prescribed number (finite or infinite) of ergodic invariant measures, and (ii) the extension of a measure from a uniquely ergodic subdiagram gives a finite ergodic invariant measure. Several examples, including stationary Bratteli diagrams, Pascal-Bratteli diagrams, and Toeplitz flows, are considered.

The paper concerns issues related to evaluation of processing in computational clouds. The effectiveness of the computational clouds depends on many factors and different metrics can be used to asses effects of processing. In this work potentiality for evaluation of processing in cloud virtual machines that takes into account also financial cost constraints is investigated. There are considered KVM and Hyper–V based cloud platform configurations. In the paper the APPI index (Application Performance and Price Index) that can be used for selection of recommended configuration considering acceptable price of processing is defined. Presented experiments show the impact of use of the proposed metric on the choice of recommended platform for processing.

Writing efficient general-purpose programs for Graphics Processing Units (GPU’s) is a complex task. In order to be able to program these processors efficiently, one has to understand their intricate architecture, memory subsystem as well as the interaction with the Central Processing Unit (CPU). The paper presents the GAP - an automatic parallelizer designed to translate sequential ANSI C code to parallel CUDA C programs. The general processing architecture of GAP is presented. Developed and implemented compiler was tested on the series of ANSI C programs. The generated code performed very well, achieving significant speed-ups for the programs that expose high degree of data-parallelism. The results show that the idea of applying the automatic parallelization for generating the CUDA C code is feasible and realistic.

Writing efficient general-purpose programs for Graphics Processing Units (GPU) is a complex task. In order to be able to program these processors efficiently, one has to understand their intricate architecture, memory subsystem as well as the interaction with the Central Processing Unit (CPU). The paper presents the GAP - an automatic parallelizer designed to translate sequential ANSI C code to parallel CUDA C programs. Developed and implemented compiler was tested on the series of ANSI C programs. The generated code performed very well, achieving significant speed-ups for the programs that expose high degree of data-parallelism. Thus, the idea of applying the automatic parallelization for generating the CUDA C code is feasible and realistic.

We study ergodic finite and infinite measures defined on the path space $X_{B}$ of a Bratteli diagram $B$ which are invariant with respect to the tail equivalence relation on $X_{B}$ . Our interest is focused on measures supported by vertex and edge subdiagrams of $B$ . We give several criteria when a finite invariant measure defined on the path space of a subdiagram of $B$ extends to a finite invariant measure on $B$ . Given a finite ergodic measure on a Bratteli diagram $B$ and a subdiagram $B^{\prime }$ of $B$ , we find the necessary and sufficient conditions under which the measure of the path space $X_{B^{\prime }}$ of $B^{\prime }$ is positive. For a class of Bratteli diagrams of finite rank, we determine when they have maximal possible number of ergodic invariant measures. The case of diagrams of rank two is completely studied. We also include an example which explicitly illustrates the proven results.

Video motion magnification (VMM) allows to amplify hardly visible changes in the video input sequence. It is possible to amplify breathing motion of hospital patients or oscillations of some mechanical element without need to connect measuring devices. On the other hand modified VMM algorithm can be used to extinguish motion before processing with another method. Unfortunately, algorithm in its full, but slowest version uses new pyramids instead laplacian ones and requires remarkable computational power in each stage of processing and that problem is solved by GPU-based implementation of basic operations using CUDA technology and scheduling them by CPU. That approach lets to run all computations on GPU. Additionally in comparison with previous studies temporal filter was changed to butterworth one. Although testing hardware was only able to run low resolution in real time, there are no doubts that better GPU would be able to run 640 × 480 resolution in real time.

Image enhancement is a challenging problem in the world of digital technology. Currently, producers of video cameras, are providing devices working with increasingly higher frequencies and resolutions of acquired video frames. However, that creates a need of development of methods used in image enhancement. Furthermore, real time processing of a significant amount of data require utilization of parallel processing. The paper presents the results of research on the problem of real time histogram stretching. Proposed solution utilizes parallel processing, supported by FPGA (Field Programmable Gate Array). The problem of histogram stretching is closely associated with thermal imaging, in which, in most of the cases, the range of measured infrared radiation, in the observed scene, is generally narrow, in relation to total possible range of radiation measured by IRFPA (Infrared Focal Plane Array), which results in narrow histogram and thus low contrast of the acquired image. The proposed solution can be used in every branch of contemporary industry, wherever video cameras are used. Real time operating hardware implementation, eliminates a need of further post-processing, and may be considered as useful and eligible in many modern applications.

In the recent years it can be observed increasing popularity of parallel processing using multi-core processors, local clusters, GPU and others. Moreover, currently one of the main requirements the IT users is the reduction of maintaining cost of the computer infrastructure. It causes that the performance evaluation of the parallel applications becomes one of the most important problem. Then obtained results allows efficient use of available resources. In traditional methods of performance evaluation the results are based on wall-clock time measurements. This approach requires consecutive application executions and includes a time-consuming data analysis. In the paper an alternative approach is proposed. The decomposition of parallel application execution time onto computation time and overheads related to parallel execution is use to calculate the granularity of application and then determine its efficiency. Finally the application scalability can be evaluates.

Nowadays wireless services are a part of the everyday life of billions of people around the world. To decrease not only their design and maintenance costs but also to enhance user comfort there is a high demand for specialized software that helps during theirs designing. Unfortunately commonly available and used software is demanding in terms of computing power in order for receiving the results in the reasonable time. The aim of the presented research is verification whether using GPU it is possible accelerate computation in reasonable way. The paper presents a study of possible parallelization of algorithms used for signal power simulation as well as algorithms that optimize placement of routers. The main goal of the paper is to show the impact of GPU usage on different stages of wireless network planning process. The first received results are very promising, the speedup received is even up to 46 for simulation algorithm and up to 15 for optimization algorithms.