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In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle.

This paper presents REDUCE, a free online tool designed to support decision-making processes by addressing inconsistency in multiplicative pairwise comparison (PC) matrices, a key element of many multi-criteria decision-making (MCDM) methods, including the analytic hierarchy process (AHP). AHP relies on pairwise comparisons to assign weights to decision criteria or alternatives, but human-generated PC matrices often exhibit inconsistencies. Consistency is evaluated using Saaty's consistency ratio ( C R ), where a value below 0.10 is considered acceptable. Higher inconsistency levels necessitate matrix corrections, which are challenging if the original expert is unavailable or revision constraints exist. REDUCE autonomously reduces inconsistency in PC matrices using two different algorithms that require no expert intervention. The tool accommodates different PC matrices, enabling users to specify the desired CR threshold (e.g., C R ≤ 0.10 ) and select the algorithm for adjustment. It ensures the resulting matrix is consistent while preserving the original preference structure to the greatest extent possible. Additionally, REDUCE calculates weights for the compared entities, making it a valuable tool for applications of AHP and related methodologies. Quantitative evaluations demonstrate that REDUCE can improve matrices with high inconsistency (e.g., C R = 0.25 ) to acceptable levels (e.g., C R = 0.08 ) while retaining up to 95% of the original preference integrity, depending on the chosen algorithm. By addressing the accessibility gap for small and medium enterprises (SMEs) that lack resources for costly decision-making software or expert consultants, REDUCE facilitates broader adoption of MCDM tools. This work highlights the potential of REDUCE to enhance decision-making reliability and accessibility in resource-constrained environments. [ABSTRACT FROM AUTHOR]

The existence of long-range dependencies in many natural systems was a very important discovery that introduced many interesting challenges and explanations about the systems behaviour. In the case of man-made systems such dependencies can also be visible, and one example is computer systems. Because the studies focused on long-range statistical dependencies in computer systems, particularly in the context of system performance counters, are not very common in the literature, this paper undertook an investigation of statistical long-range dependencies present in cache memory data represented as time series. Based on the time series collected during computer system processing by internal system tools, it will be seen that in the case of cache memory modelling, statistical models with long-term dependencies should be used. The following paper sections show how to collect data, analyse, and build an appropriate model. [ABSTRACT FROM AUTHOR]

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A case study based on the real data obtained from the Polish PSE System Operator of the highest voltages electrical energy network is shown. The data about the interconnection exchange and some complex networks (graphs) parameters were examined, after the removal of selected nodes. This allowed to test selected network parameters and to show that the breakdown of only three nodes in this network can cause significant drop of its average efficiency.

The article presents results of studies using simulations on computer network devices, designed to examine the effectiveness of routing protocols with the video streaming and generated traffic for Jperf applications. In order to demonstrate the effectiveness of the selected protocols several simulation scenarios were made using different sized UDP packets. The traffic was analyzed in terms of statistical self-similarity. Multifractal analysis has also been made, using two kinds of spectrums. The study determined the relationship between them. These tasks were designed to determine the multifractal and long-term relationship for a given process.

The problem of modeling different parts of computer systems requires accurate statistical tools. Cache memory systems is an inherent part of nowadays computer systems, where the memory hierarchical structure plays a key point role in behavior and performance of the whole system. In the case of Windows operating systems, cache memory is a place in memory subsystem where the I/O system puts recently used data from disk. In paper some preliminary results about statistical behavior of one selected system counter behavior are presented. Obtained results shown that the real phenomena, which have appeared during human-computer interaction, can be expressed in terms of non-extensive statistics that is related to Tsallis proposal of new entropy definition. [ABSTRACT FROM AUTHOR]

The paper will show the direct connections between q-Malthusian growth model, i.e. the classical exponential growth model generalized in Tsallis statistics, and the coalition growth model introduced by von Foerster in 1960. As it will turn out, the equations that have been taken into account when the coalition model was introduced, are closely related to the equations that describe the non-extensive generalization of entropy. [ABSTRACT FROM AUTHOR]

This paper presents a preliminary analysis of the system behavior that works far from the thermodynamical equilibrium states in the environment with limited resources. The examples of such systems are the real computer systems. Nowadays in such systems the runoff characteristic of the information flow is very turbulent in contradiction to the current existing laminar models. These systems work under constant overload, which means a permanent thermodynamical non-equilibrium (from the thermodynamical point of view). For such a situation the classical approach to their modeling is still based on Boltzmann-Gibbs (BG) thermodynamics,which is proper only for systems that are in equilibriumstate (sometimes called thermostatic) or very close to it. The changing number of tasks N in such systems and the limited resourcesK of the environment cause its chaotic behavior and generate the dependencies that have got a long-termproperty. Such processes degrade the system performance X and elongate the response time R; in other words degrade the Quality of Service (QoS). To understand the whole behavior of such systems one needs a proper thermodynamical basis that seems to be the Tsallis formula of the non-extensive entropy. [ABSTRACT FROM AUTHOR]

Areas of experience allow for the acquisition and consolidation of both existing knowledge and skills. These are significant factors in the training of staff members for companies in the Industry 4.0 area. One of the currently available modern tools used in the teaching process is virtual reality (VR) technology. This technology, due to its high level of immersion and involvement of the different senses, and the need to focus on the performed activities, allows one to develop skills in solving various tasks and problems. The extended VR environment enables the creation of diverse teaching scenarios adapted to the needs of industry. This paper presents the possibility of building training scenarios in the field of digital techniques. The software solution, developed and presented by the authors, uses elements of computer game mechanics and is designed to familiarize students with the idea of digital circuits, their construction, logical implementation and application. This paper also presents a comparison of the features of different forms of education used in teaching digital techniques, as well as a comparison of these forms, from the point of view of the student and his/her perceptions. [ABSTRACT FROM AUTHOR]