Dimitrievska Ristovska, Vesna

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Dimitrievska Ristovska, Vesna

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Analysis and Visualization of Social Networks
(IEEE, 2022-12)
Limonka Koceva Lazarova
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Natasha Stojkovikj
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Aleksandra Stojanova Ilievska
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The huge development of social networks opens the need for their analysis. The visualization of social networks is an important and powerful tool for such kind of analysis. There are many software packages which can be used for visualization. In this paper we are using graph theory, Python, and the free software Gephi to make visualization of social networks. Particularly we have made visualization of social network Twitter in order to show the relations between its users. This visualization helps in the analysis of relations and interactions between social media users.
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Topological data analysis as a tool for classification of digital images
(University Goce Delchev, Shtip, 2022-12-27)
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Sekuloski, Petar
Topological data analysis, as a branch of applied mathematics, is one of the newer areas that enable data analysis. The basic tool of this field is persistent homology, the main method of topological data analysis and it is used to process the data set in this article. Persistent homology is a method that detects the topological features of a space reconstructed from a data set. The application is illustrated on simple synthetic generated sets. In this article, we proposed and evaluated a new model that includes topological features into the classification process in real data sets composed of digital images. We got results in which there are some improvements in most of the statistical values for the classification performance over a model that does not include these topological features.
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Classification of Digital Images using topological signatures – A Case Study
(Scientific Technical Union of Mechanical Engineering" Industry 4.0", 2022-12)
Petar Sekuloski
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Topological Data Analysis (TDA) is relatively new filed of Applied Mathematics that emerged rapidly last years. The main tool of Topological Data Analysis is Persistent Homology. Persistent Homology provides some topological characteristics of the datasets. In this paper we will discuss classification of digital images using their topological signatures computed with Persistent Homology. We will experiment on the Fashion-MNIST dataset. Using Topological Data Analysis, the classification was improved.
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Visualization of the nets of type of Zaremba−Halton constructed in generalized number system
(Faculty of Computer Science and Engineering, UKIM, Skopje, 2019)
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Vasil Grozdanov
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Tsvetelina Petrova
In the present paper a class of two-dimensional nets Z κ,µ B2,ν of type of Zaremba-Halton constructed in generalized B2−adic system is introduced. In order to show their very well uniform distribution, we made their visualization with mathematical software Mathematica. In our paper ”On the (Vil,B2; α; γ)−diaphony of the nets of type of Zaremba - Halton constructed in generalized number system” we constructed a class Z κ,µ,B2,ν of two-dimensional nets (throughout this paper the term net will denote finite sequence) of type of Zaremba Halton. Also, the (Vil,B2; α; γ)−diaphony which is based on using two-dimensional Vilenkin functions constructed in the same B2−adic system,of the nets of the class Zκ,µ,B2,ν is investigated. The obtained results have theoretical character and treat to the influence of the parameter α to the exact order of the (Vil,B2; α; γ)−diaphony of the nets from the class Zκ,µ,B2,ν. The purpose of this paper is to present in extended form the visualization of some concrete nets from the class Zκ,µ, B2,ν and to show the distribution of the points of these nets. In this sense the reader can understand the distribution properties of the considered nets. To construct nets of the class Zκ,µ,B2,ν we use the mathematical software Mathematica. Our interest for the importance of these types of sequences is implied from their usage in numerical integration, construction of random number generators e.t.c.
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Analysis, modeling, and simulation of emergency department
(Scientific Technical Union of Mechanical Engineering" Industry 4.0", 2022-12)
Natasha Stojkovik
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Limonka Koceva Lazarova
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Maja Kukuseva
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Aleksandra Stojanova Ilievska
Overcrowding in the Emergency Department (ED) is one of the most important issues in healthcare systems. Two major causes of this congestion are identified, the first one is unjustified Emergency Department visits and the second one a lack of downstream beds. The lack of downstream beds can deteriorate the quality of care for patients who need hospitalization after an ED visit. In this paper a generic simulation model is developed in order to analyse patient pathways from the ED to hospital discharge.
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On the (VilB2;α;γ)-diaphony of the nets of type of Zaremba-Halton constructed in generalized number system
(BOKU-University of Natural Resources and Applied Life Sciences (Vienna, Austria) and Institute of Mathematics of the Slovak Academy of Sciences, (Bratislava, Slovakia), 2020)
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Vasil Grozdanov
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Tsvetelina Petrova
In the present paper the so-called (VilBs ; α; γ)-diaphony as a quantitative measure for the distribution of sequences and nets is considered. A class of two-dimensional nets Zκ,μ, B2,ν of type of Zaremba-Halton constructed in a generalized B2-adic system or Cantor system is introduced and the (VilB2 ; α; γ)-diaphony of these nets is studied. The influence of the vector α = (α1, α2) of exponential parameters to the exact order of the (VilB2 ; α; γ)-diaphony of the nets Zκ,μ,B2,ν is shown. If α1 = α2, then the following holds: if 1 < α2 < 2 the exact order is O(√log N/(N^(1−ε))) for some ε > 0, if α2 = 2 the exact order is O (√log N/N) and if α2 > 2 the exact order is O(√log N/N^(1+ε)) for some ε > 0. If α1 > α2, then the following holds: if 1 < α2 < 2 the exact order is O(1/N^(1−ε)) for some ε > 0, if α2 = 2 the exact order is O(1/N) and if α2 > 2 the exact order is O(1/N^(1+ε)) for some ε > 0. Here N = Bν , where Bν denotes the number of the points of the nets Zκ,μ,B2,ν.
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A novel model for image classification based on Persistent Homology
(International Journal of Science and Research (IJSR), 2022-12)
Petar Sekuloski
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Vassil Grozdanov
Topological Data Analysis (TDA) is relatively new field of Applied Mathematics that emerged rapidly last years. The main tool of Topological Data Analysis is Persistent Homology. Persistent Homology tracks the topological features of datasets. In this paper we will introduce a novel model for image classification based on Persistent Homology. In the experimental part we the introduced new novel on real medical dataset. Using this model, the classification was improved.
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Teaching and Examination Process of Some University Courses before vs during the Corona Crisis
(Vilnius University Press, 2021-06-01)
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Sekuloski, Petar
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The newly emerged corona crisis in our country, but also much broader – on the entire planet, caused by the pandemic scale of COVID-19 virus, dictated the need for adjustment of the teaching and examination process of many university courses. At our institution, Faculty of Computer Science and Engineering (FCSE) in Skopje, starting from March 17, 2020, until today (March 2021), classes and exams are completely realized through distance learning systems, i.e. using the BigBlueButton video conferencing system, implemented in the Courses and Exams student services – the official FCSE websites on the Moodle e-learning platform. For all faculty courses, lectures, auditory and laboratory exercises, colloquia and exams, all take place via a video conferencing system for distance education. In this paper we present a comparative analysis of the conduction of some courses at FCSE in classical conditions, as opposed to the conditions with distance education. We have considered the analysis mainly from the aspect of the approach to teaching, as well as from the aspect of exam conduction and achieved exam results. The analysis of those aspects leads us to conclusions about several positive and negative sides that we noticed in distance education compared to the classical conditions of classes and exams. Our findings also may apply on the organization of online contests, especially in informatics.
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Check for updates Image Classification Using Deep Neural Networks and Persistent Homology
(Springer Nature, 2024)
Sekuloski, Petar
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Persistent Homology (PH), a key tool in Topological Data Analysis (TDA), has gained significant traction in Machine Learning and Data Science applications in recent years. By combining techniques from algebraic topology, statistics, and computer science, PH captures the topological characteristics of datasets. This study aims to propose new classification models that integrate deep learning and Persistent Homology, exploring the impact of PH on model performance. Additionally, a transfer learning approach incorporating pre-trained networks and topological signatures is evaluated. Real-world datasets are used to assess the effectiveness of these models. The findings contribute to understanding the role of Persistent Homology in improving classification models, bridging the gap between deep learning, topological analysis, and practical data analysis. The performance of the models that include topological signatures showed better performance than the models that do not.
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MAPPER ALGORITHM AND IT’S APPLICATIONS
(Scientific Technical Union of Mechanical Engineering" Industry 4.0", 2019)
Sekuloski, Petar
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In this paper we analyze and apply one of the main algorithms of TDA (Topological Data Analysis), Mapper, on some real data sets. We use Mapper for visualization of a data sets, and we tend to get some insights if some key characteristics of the data are captured by the visualization and how they are connected with human perception of the data. Also, we will discuss if the visualization can make progress in further work.

Dimitrievska Ristovska, Vesna

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