<abstract xmlns="http://www.w3.org/1999/xhtml">

Let A and S be the adjacency and the Seidel matrix of a graph G respectively. A-energy is the ordinary energy E(G) of a graph G defined as the sum of the absolute values of eigenvalues of A. Analogously, S-energy is the Seidel energy ES(G) of a graph G defined to be the sum of the absolute values of eigenvalues of the Seidel matrix S. In this article, certain class of A-equienergetic and S-equienergetic graphs are presented. Also some linear relations on A-energies and S-energies are given.
</abstract>

On A-energy and S-energy of certain class of graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">

In recent years, community detection in dynamic networks has received great interest. Due to its importance, many surveys have been suggested. In these surveys, the authors present and detail a number of methods that identify a community without taking into account the incremental methods which, in turn, also take an important place in dynamic community detection methods. In this survey, we provide a review of incremental approaches to community detection in both fully and growing dynamic networks. To do this, we have classified the methods according to the type of network. For each type of network, we describe three main approaches: the first one is based on modularity optimization; the second is based on density; finally, the third is based on label propagation. For each method, we list the studies available in the literature and state their drawbacks and advantages.
</abstract>

Incremental methods for community detection in both fully and growing dynamic networks

<abstract xmlns="http://www.w3.org/1999/xhtml">

Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R×. In this paper, we determine the Laplacian and signless Laplacian eigenvalues for the unitary Cayley graph of a commutative ring. Also, we compute the Laplacian and signless Laplacian energy of the graph GR and its line graph.
</abstract>

On Laplacian spectrum of unitary Cayley graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">

Cryptocurrencies are digital assets that can be stored and transferred electronically. Bitcoin (BTC) is one of the most popular cryptocurrencies that has attracted many attentions. The BTC price is considered as a high volatility time series with non-stationary and non-linear behavior. Therefore, the BTC price forecasting is a new, challenging, and open problem. In this research, we aim the predicting price using machine learning and statistical techniques. We deploy several robust approaches such as the Box-Jenkins, Autoregression (AR), Moving Average (MA), ARIMA, Autocorrelation Function (ACF), Partial Autocorrelation Function (PACF), and Grid Search algorithms to predict BTC price. To evaluate the performance of the proposed model, Forecast Error (FE), Mean Forecast Error (MFE), Mean Absolute Error (MAE), Mean Squared Error (MSE), as well as Root Mean Squared Error (RMSE), are considered in our study.
</abstract>

Department of Information Technology Engineering

Bitcoin daily close price prediction using optimized grid search method

<abstract xmlns="http://www.w3.org/1999/xhtml">

We investigated the predictability of mean reverting portfolios and the VAR(1) model in several aspects. First, we checked the dependency of the accuracy of VAR(1) model on different data types including the original data itself, the return of prices, the natural logarithm of stock and on the log return. Then we compared the accuracy of predictions of mean reverting portfolios coming from VAR(1) with different generative models such as VAR(1) and LSTM for both online and o ine data. It was eventually shown that the LSTM predicts much better than the VAR(1) model. The conclusion is that the VAR(1) assumption works well in selecting the mean reverting portfolio, however, LSTM is a better choice for prediction. With the combined model a strategy with positive trading mean profit was successfully developed. We found that online LSTM outperforms all VAR(1) predictions and results in a positive expected profit when used in a simple trading algorithm.
</abstract>

Budapest University of Technology and Economics

Department of Networked Systems and Services

Trading sparse, mean reverting portfolios using VAR(1) and LSTM prediction

<abstract xmlns="http://www.w3.org/1999/xhtml">

The intersection of surfaces is a fundamental process in computational geometry and computer-aided design applications to build and interrogate complex shapes in the computer. This paper presents a novel and simple dual quaternion-based osculating circle DQOC algorithm to find the intersection curve of two regular surfaces based on the osculating circle concept and dual quaternions. Additionally, we expressed the natural equations of the intersection curve. We have also demonstrated the superiority of our method through numerical examples.
</abstract>

Dual quaternion-based osculating circle algorithm for finding intersection curves

<abstract xmlns="http://www.w3.org/1999/xhtml">

This paper presents results for some vertex stress related parameters in respect of specific subfamilies of Kneser graphs. Kneser graphs for which diam(KG(n, k)) = 2 and k ≥ 2 are considered. The note establishes the foundation for researching similar results for Kneser graphs for which diam(KG(n, k)) ≥ 3. In addition some important vertex stress related properties are stated. Finally some results for specific bipartite Kneser graphs i.e. BK(n, 1), n ≥ 3 will be presented. In the conclusion some worthy research avenues are proposed.
</abstract>

Vertex stress related parameters for certain Kneser graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">

<sec><h3>Context</h3>It is crucial to understand how reproducible the measurement results in the scientific publications are, as reproducibility is one of the cornerstones of engineering.</sec>
<sec><h3>Objective</h3>The goal of this study is to investigate the scientific publications presented at the premier technical debt conferences by understanding how reproducible the reported findings are.</sec>
<sec><h3>Method</h3>We conducted a systematic literature review of 135 unique papers published at the “International Workshop on Managing Technical Debt” and the “International Conference on Managing Technical Debt”, the premier scientific conference series on technical debt.</sec>
<sec><h3>Results</h3>Only 44 of the investigated 135 papers presented numerical evidence and only 5 papers listed the tools, the availability of the tools, and the version of the tools used. For the rest of the papers additional information would have been needed for the potential reproducibility. One of the published papers even referred to a pornographic site as a source of a toolset for empirical research.</sec>
</abstract>

Reproducibility in the technical debt domain

<abstract xmlns="http://www.w3.org/1999/xhtml">

Dynamic programming (DP) is a widely used optimization method with several applications in various fields of science. The DP problem solving process can be divided in two phases: mathematical part and programming part. There are a number of researchers for whom the mathematical part is available, but they are not familiar with computer programming. In this paper we present a software tool that automates the programming part of DP and allows users to solve problems based only on their mathematical approach. The application builds up the “d-graph model” of the problem to be solved and applies the “d-variant” of the corresponding single source shortest path algorithm. In addition, we report experimental results regarding the e ciency of the tool relative to the Matlab implementation.
</abstract>

Sapientia Hungarian University of Transylvania

Department of Mathematics and Informatics Tirgu Mures

DP-solver: automating dynamic programming

<abstract xmlns="http://www.w3.org/1999/xhtml">

The quark-gluon plasma is written by the non-Abelian gauge theory. The dynamics of the gauge SU(2) are given by the Hamiltonian function, which contains the quadratic part of the field strength tensor 
<inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausi-2021-0018_ineq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mtext>F</mtext><mrow><mi>μ</mi><mi>v</mi></mrow><mtext>a</mtext></msubsup></mrow></math>
<tex-math>{\rm{F}}_{\mu v}^{\rm{a}}</tex-math>
</alternatives>
</inline-formula>
 expressed in Minkowski space. The homogeneous Yang-Mills equations are solved on lattice Nd considering classical approximation, which exhibits chaotic dynamics. We research the time-dependent entropy-energy relation, which can be shown by the energy spectrum of Kolmogorov-Sinai entropy and the spectra of the statistical complexity.
</abstract>

Nonlinearity of the non-Abelian lattice gauge field theory according to the spectrum of Kolmogorov-Sinai entropy and complexity

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