Odjel za matematiku

Current projects

    • "GAMe-based learning in MAthematics-GAMMA", (Department of Mathematics, J. J. Strossmayer University of Osijek - Agency for Mobility and EU Programmes) - Project coordinator: Mirela Jukić Bokun

      Summary: In a modern world, there is a growing need for STEM (science, technology, engineering and mathematics) skills. This poses a great challenge to mathematics teachers and all educators involved. Teaching mathematics by using innovative, creative and modern methods is a way to decrease the number of students with insufficient skills in the field of mathematics, which is one of the goals of European Cooperation in Education and Training (ET 2020). Furthermore, this is a way to motivate students to choose a university in the STEM area, which is one of the priorities under Horizon 2020. Making better use of digital technology for teaching and learning and developing digital competences and skills are also priorities of the 2018 Digital Education Action Plan of the European Commission. Since students spend a lot of time in a digital environment, it is their natural environment. The aim of the project is to direct student knowledge of digital games and their connection thereto to enhance their mathematical skills. Since teachers should have a leading role in this process, we will develop educational materials which will be useful to all mathematics teachers who would like to use game-based learning (GBL) founded on digital technology. The main goal of the project is to create a GAMMA handbook for teachers, focused authoring systems (FAS) for the production of digital games, a teaching scenario template, eight teaching scenario examples and five games connected with them based on GBL for mathematics curriculum topics for students aged 14-18 years in all project countries. The target group are mathematics teachers who teach students of the said age. The aim of the project is to develop teacher competences in GBL and encourage them to use and apply digital technologies in their teaching practice. The consortium consists of partners from the following four countries: Croatia, Greece, the Netherlands and Finland. Those are countries with different achievements in the fields of mathematics and science according to PISA 2018 results (Finland and the Netherlands are countries with results above the average, and Croatia and Greece are countries with results under the average). One university, two schools and the Education and Teacher Training Agency (ETTA) are included from Croatia, one university and one school are included from each of the following two countries: Greece and Finland, while one university is included from the Netherlands. These nine institutions will work together on the creation of educational materials. Universities will be responsible for the creation of the handbook for teachers and FAS. During the training activities, participants from each project organisation will be trained on GBL and they will work on the development of a teaching scenario template, eight teaching scenario examples, and five games connected with them based on GBL for mathematics curriculum topics for students aged 14-18 years in all project countries. A scientific approach of universities and experience of schools and the ETTA in the teaching process will guarantee that we will develop high-quality teaching scenario examples and games connected with them. Around 40 educators from universities, schools and the ETTA will be included in the training activities. Teaching scenario examples will be piloted in the real context, i.e., in mathematics classrooms of participating schools and schools from the Netherlands. After the piloting phase, universities will adapt scenarios according to feedback obtained from schools. In local dissemination events in each partner country, we will train 120 school teachers on GBL founded on digital technology and motivate them to use GAMMA educational materials in their teaching process. The final conferences will be held in Croatia and Greece, and they will be used to disseminate the project intellectual outputs among the educational community and encourage teachers, as well as other educational stakeholders, to re-use the project outputs after the end of the project. Through project activities, partnerships between schools and higher education institutions will be developed not only at national, but also at EU level. During project activities, all educators from partner organisations will improve their digital skills and teaching competences. They will also gain insight into other European educational systems and they will develop their language skills. All prepared materials will be adapted to every participating country so that they can be used not only by partner schools, but also by other schools from participating countries. Since all materials will also be available in English, they can be translated to other languages and used in other EU countries. GBL is an upcoming and relevant subject for education in general, not only in mathematics. The GAMMA handbook for teachers can also be used as material which can introduce GBL in other subjects in EU schools.

      Programme: Erasmus+, Key action: KA2 - Cooperation for innovation and the exchange of good practices, Action Type: KA201: Strategic Partnership for school education

      Project partner: Elektrotehnička i prometna škola Osijek, Croatia, Amsterdam University of Applied Sciences, Faculty of Education, Netherlands, Satakunta University of Applied Sciences, Finland, National and Kapodistrian University of Athens, School of Philosophy, Department of Educational Studies, Greece, First Senior High School of Peristeri Athens, Greece, Porin Lyseon lukio General Upper Secondary School, Finland, Srednja škola Markantuna de Dominisa Rab, Croatia i Agencija za odgoj i obrazovanje, Croatia

      Team members: Mirela Jukić Bokun, Dragana Jankov Maširević, Mihaela Ribičić Penava, Darija Marković, Ljerka Jukić Matić, i Mateja Đumić

      Project duration: 1 October 2020 - 1 October 2022

    • "Vibration Reduction in Mechanical Systems - Young Researchers' Career Development Project - Training of Doctoral Students", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatia Science Foundation) - Project coordinator: Zoran Tomljanović

      Summary: The main focus of scientific research is divided into four research themes distinguished by the external influence in linear time invariant systems. The first three research themes contain topics that are fundamental for vibration reduction: the homogeneous case, the case with a given external force, and the Multiple-Input Multiple-Output case (MIMO case). Since that the first three research themes have mutual connections and wide applications, we will include specific research theme IV that will aim to integrate the research themes I-III and various prominent applications. PhD student will be dedicated to the non-homogeneous case, which means that student will work on research themes that studies vibration reduction in case with a given external force and MIMO case. Also, since application of obtained results in practical examples is very important, PhD student will also study this kind of applications.

      Programme: Young Researchers' Career Development Project - Training of Doctoral Students

      Mentor's name and surname: Zoran Tomljanović

      PhD name and surname: Marinela Pilj Vidaković

      Project duration: 1 September 2020 - 1 September 2024

    • "Application of Generic Optimizer in Medical Imaging Classification Problem", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of science and Education and Deutscher Akademischer Austausch Dienst (DAAD)) - Project coordinator: Krešimir Burazin

      Summary: The main goal of this research collaboration between the Gene Center of LMU Munich and Department of Mathematics in Osijek is to try to better understand whether a standard generic solver such as a quasi-Newton method (L-BFGS-B) developed primarily for unconstrained smooth optimization problems combined with classical machine learning can compete with deep-learning in medical imaging classification problems. For that reason, the research group at the Gene Center will acquire a dataset of Magnetic Resonance Imaging (MRI) scans with corresponding diagnoses for training and testing purposes, as well as employ the CNN deep-learning techniques to automize the classification process. The research team in OSijek will work on the implementation of a L-BFGS-B method and will generalize it in order to built the solver for constrained optimization problems.

      Programme: The programme aimed at encouraging the exchange of project participants between the Ministry of Science and Education of the Republic of Croatia and the DAAD

      Project partner: Gene Center, Ludwig-Maximilians-Universität München

      Team members: Krešimir Burazin, Domagoj Matijević, Luka Borozan, Danijela Jaganjac, Mislav Blažević, Nathan Chappell, Stefan Canzar, Francisca Rojas Ringeling, Hoan Van Do, Pablo Monteagudo, Israa Al-Quassem, Shounak Chakraborty

      Project duration: January 2020 - December 2021

    • "Development and application of the advanced building materials for construction of healthy buildings: protection from non-ionizing radiation", (Faculty of Civil Engineering and Architecture, J. J. Strossmayer University of Osijek - European Regional Development Fund) - Project coordinator (MATHOS): Mirta Benšić

      Summary: The Z2grade project will result in the development of advanced building materials whose application in buildings will allow for large absorption of EM radiation. Based on numerous studies of the effects of EMF on human health, many countries in the world have responded to new regulations and laws that limit EMF levels and introduce specific requirements for their sources. According to the World Health Organisation (WHO) classification, in 2011, radiofrequency electromagnetic fields were classified as a possible cause of brain cancer, and in its Resolution 1815 adopted in the same year, the Council of Europe called on all European governments to take all reasonable steps to reduce EMF exposure. What this resolution particularly emphasises is that special attention must be paid to vulnerable groups in society (children and young people). It also stresses that it is necessary to reduce indoor exposure to 0.6 V/m, aiming at 0.2 V/m. These advanced materials are the basis for the construction of residential, public and commercial buildings with an extremly weak electromagnetic field, which is reflected in an increased level of public health protection (EM radiation protection), especially of the most vulnerable groups: children, pregnant women, patients and the elderly. In the Republic of Croatia, this field is also legally regulated by the Non-Ionising Radiation Protection Act (Official Gazette No. 91/2010) and the Electromagnetic Field Protection Ordinance (Official Gazette No. 144/2014), which specify the limits of EMF exposure ranging to 300 GHz. The project is implemented through the phases of industrial and experimental development, and the result of the activities of both phases is new product design and development. As alredy stated, there is currently no similar product on the market, and this would both address this issue and represent great potential for patenting results. In the industrial research phase, testing will be carried out at the level of the key components of brick blocks (clay+TiO2, ferrite compounds, carbon nanotubes, fly ash) and mixed concrete with metamaterial. An integral part of this phase will be to develop prototypes that will demonstrate a sufficient level of mechanical resistance and stability for the use in construction. Based upon the previous phase and the economic analysis of the manufacturing costs of a new product, there will be a shift to experimental development, which will involve production of a new product on manufacturing assembly lines in a factory. Both phases will combine the final design of a 1:1 scale model made of a brick and reinforced concrete walls protype. In these models, measurements willl prove the basic hypothesis of the effectiveness of new materials in terms of EMF intesity reduction.

      Programme: Operational Programme Competitiveness and Cohesion 2014-2020 - European Regional Development Fund

      Project partners: Faculty of electrical engineering, computer science and information technology - J. J. Strossmayer University of Osijek, Department of Chemistry - J. J. Strossmayer University of Osijek, Department of Mathematics - J. J. Strossmayer University of Osijek and Faculty of civil engineering, architecture and geodesy - University of Split

      Team members: Damir Varevac, Ivana Miličević, Ksenija Čulo, Irena Ištoka Otković, Hrvoje Krstić, Tanja Kalman Šipoš, Davorin Penava, Filip Anić, Adriana Cerovečki, Slavko Rupčić, Snježana Rimac-Drlje, Vanja Mandrić Radivojević, Berislav Marković, Igor Đerđ, Tomislav Balić, Jelena Brdarić, Nikolina Filipović, Anamarija Stanković, Mirta Benšić, Boris Trogrlić, Dujmo Žižić, Hrvoje Bartulović i Petra Šunjić

      Project duration: December 2020 - December 2022

    • "The network framework of the "Ča-Kaj-Što"component of Croatian identity", (Department of Mathematics, J. J. Strossmayer University of Osijek - The Adris Foundation) - Project coordinator: Domagoj Ševerdija

      Summary: The project “Croatian in the Global Language Network Cloud” was carried out in 2018 with the support of the Adris Foundation, and it opens a new path for modern expansion of the identity of the Croatian language and Croatian cultural heritage. The first project (M. Orešković, PhD) created and tested an SSF dictionary/thesaurus of a standard language with about 1 million entries, which was integrated into the Linguistic Linked Open Data cloud. The new project will expand the same words with the Čakavian, Kajkavian and Štokavian dialects. Just like the first project, the thesaurus is accompanied by an appropriate corpus (digitised documents from which words are entered into the thesaurus), and in the new project the SSF will be expanded with many documents of the Croatian “Ča-Kaj-Što” trefoil (D. Štambuk). Since this is a continuation of the existing project, the course of the project is fully defined and clear: the project results have already been disseminated at national and international conferences, and one (to two) books containing direct outputs will be published, which will build the foundation for further work. After that, the algorithm and software related part of a network framework for audio recordings of individual words from any area of the Republic of Croatia and the surrounding area. A good solution sample (M. Essert et al.) has already been implemented as the Croatian Speech Sound Atlas (V. Piškorec, I. Kurtović Budja), but unlike the professional, segmented approach, it offers an online approach from any location (e.g., a local school that has Internet access) and of any size. Thus, in addition to the “Ča-Kaj-Što” audio recordings of words, the SSF thesaurus will also contain audio recordings of multiword expressions (idioms, proverbs, etc.) - a real treasure of a people, with a geolocation of the source. Digitised documents of all Croatian variants and dialects, as well as bibliographic data on the authors of printed or transcribed works will be saved (and optionally searched) on a timeline. The outcome and contribution of the project is reflected in the modern integration of the SSF network framework, digitised documents, sound recordings and programming foundations for other multimedia objects (image, video), all in spatial and temporal coordinates. By connecting with associations active in the local community and working to preserve the mother tongue, the project will achieve the most important goal of any heritage concern: connecting science and the bearer of cultural heritage.

      Programme: Creativity, Ecology, Heritage and Goodness -The Adris Foundation

      Team members: Domagoj Ševerdija, Mario Essert, Marko Orešković, Josip Užarević, Suzana Molčanov, Zrinka Jelaska, Ivana Kurtović Budja, Jasna Horvat, Marko Landeka, Krešimir Landeka, Milan Kranjčević

      Project duration: October 2019 - January 2021

    • "Vibration Reduction in Mechanical Systems - VIMS", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Zoran Tomljanović

      Summary: Vibration analysis and vibration reduction for mechanical systems are prominent problems in numerous research fields. Although the vibrations analysis is an intensively studied topic in recent decades, many problems still remain open. While the case without external excitation leads to the study of homogeneous systems, presence of an external forcing leads to the study of nonhomogeneous systems. Depending on the presence of an external excitation and applications, we will consider four different research themes. Within the first research theme, we will study theoretical results that are relevant for vibration reduction. We plan to develop theoretical results that characterize important properties of the quadratic eigenvalue problem (QEP) arising from vibration analysis of mechanical systems. Within the second research theme we develop new methods for frequency isolation and utilize methods which are based on algorithms for non-smooth optimization. For this case we will derive new algorithms that preserve the structure of the matrices and structural properties of the considered QEP. In the third research theme, we will consider vibration reduction based on criteria that use system norms (e.g. H2 and Hinf) for Multiple-Input Multiple-Output case. We will also study approaches for approximating the full-order model with a reduced-order model that retains the structure of parametric dependence. The new approaches will be well suited for computationally efficient parameter optimization and the study of important system properties. In the fourth research theme we will consider integrating research themes I-III and applications in real world examples. Moreover, we will apply obtained new approaches and algorithms in various academic examples, but also in real life examples that arise, e.g., in car industry (such as disc brake problem) and civil engineering (such as beams, civil buildings), etc. Therefore, the result from this project could have wide applications.

      Programme: Croatian Science Foundation

      Project members: Serkan Gugercin, Ivana Kuzmanović Ivičić, Suzana Miodragović

      Project duration: 1 January 2020 - 31 December 2023

    • "Machine learning in the analysis of MRI results", (Mono d.o.o.-HAMAG-BICRO)

      Summary: The goal of this project is to create a prototype of an online, Software-as-a-Service (SaaS) computer system for automated segmentation and classification of MR imaging in orthopaedics, with an emphasis placed on a knee MRI scan, using machine learning (ML) techniques. Algorithmics methods for MR analysis are divided into two main categories: classification and segmentation. Classification assigns labels to MRI batches (normal/abnormal, degree of severity of the problem, diagnosis). Segmentation is the process of delineating and marking the borders or contours of various tissues and the processes occurring within them. Our prototype will contain the functionality of both methods, with an emphasis on segmentation.

      Programme: HAMAG-BICRO Proof of Innovation Concept Program (PoC7)

      Project members: Domagoj Matijević, Domagoj Ševerdija, Slobodan Jelić

      Project duration: 1 November 2018 - 1 May 2019

    • "Application of short-range and long-range dependent stohastic models", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science and Education ) - Project coordinator: Nenad Šuvak

      Summary: Standard models in probability and statistics usually rely on the assumption of independence or weak temporal dependence. On the other hand, numerous phenomena in applied sciences require temporal models in which the correlation between two events can decline very slowly causing time distance to increase. The purpose of research under this project is to gain a deeper understanding of the structure and properties of several classes of random processes with short- and long-term dependencies and to study their possible applications. Stochastic short-term dependency processes are known to be very widely used, e.g., in modelling biological and ecological phenomena, and in modelling phenomena in financial markets, where, for example, classical models for describing short-term interest rate fluctuations are well-known Vasiček and Cox-Ingersoll-Ross models that belong to a wider class of processes that will be studied within the framework of this project, i.e., the Pearson diffusions, for which we want to find new applications or make use of known concepts of applications. Furthermore, applications of stochastic processes with long-term dependence are a very modern field of research that is currently in full swing. Such processes are used, for example, in Internet traffic modelling, in hydrology to model the temporal component of jamming in pollutant particle motion through a porous medium, and in finance, where such processes with a positive set of values are an important stochastic volatility model. In these areas, it is also interesting to apply forward-backward stochastic differential equations as continuous-time stochastic models. One of the project goals is to analyse the available data (financial, biological, epidemiological, hydrological, etc.), incorporate the data into existing stochastic models and extend the theoretical analysis and application of stochastic differential equations from the following aspects: a) study of different types of backward stochastic differential equations (BSDEs), stochastic analysis of optimal control problems (in finance and biological systems) and the contribution of the application of theoretical results to concrete problems from the aforementioned applied sciences, b) study of the impact of white noise, coloured noise, jump processes and delays on the behaviour of solutions of different population and epidemiological models, examination of conditions under which survival or extinction of a population (disease) occurs, c) consideration of various analytical and numerical methods to provide insight into the behaviour of systems described by stochastic differential equations (SDEs) in order to determine the conditions under which exact (theoretical) and approximate (numerical) solutions have common features, such as almost sure exponential or polynomial stability and convergence in probability, and d) statistical inference (parameter estimation and testing of various statistical hypotheses of interest in applications) of the aforementioned stochastic processes.

      Programme: The program of scientific-technological cooperation between the Republic of Croatia and the Republic of Serbia, Ministry of Science, Education and Sports

      Project members: Nenad Šuvak, Jasmina Đorđević, Danijel Grahovac, Miljana Jovanović, Ivan Papić, Marija Milošević, Una Radojičić, Marija Krstić, Dušan Đorđević

      Project duration: 1 January 2019 - 31 December 2020

    • "Croatian in the Global Language Network Cloud - Creativity, Ecology, Heritage and Goodness", (Department of Mathematics, J. J. Strossmayer University of Osijek - The Adris Foundation ) - Project coordinator: Domagoj Ševerdija

      Summary: The project goal is to integrate the Croatian language as the foundation of Croatian cultural heritage into the Linguistic Linked Open Data cloud (LLOD, http://linguistic-lod.org/llod-cloud), which means to position the Croatian language the inter-European and world languages, in a modern and interoperable way. All steps of inclusion in the LLOD cloud have already been made as part of Marko Orešković’s PhD thesis (https://old.datahub.io/dataset/ssf-lexicon) so that there are already 60,000 - unfortunately unverified - data in the cloud (words and their grammatical and semantic features), which would be checked and supplemented with new ones in this project (about 740,000 words, i.e., 100,000 lemmas are awaiting verification. This project is a continuation of many years of work of Dr. Mario Essert, Full Professor, and his associates on the construction of an integrated thesaurus of the Croatian language, which has been accomplished and internationally recognized without any support of institutions and foundations (in Oxford Q1 journals: IGPL and IJL, as well as at international conferences: Vienna: Semantics 2015, Rome: CombiLex 2016, Tbilisi: EURALEX 2017). Moreover, an invitation to cooperate with the Oxford University Press (Mr Sandro Cirulli, OUP) was received, i.e., to include project results in their world dictionaries (https://www.oxforddictionaries.com/). Project results was disseminated in all relevant places (Institute of Croatian Language and Linguistics, Matica Hrvatska, Faculty of Humanities and Social Sciences in Zagreb, Croatian Ministry of Science and Education/Agency for Science and Higher Education), but the project was neither understood not supported. Finally, the Department of Mathematics (http://www.mathos.hr) recognised its importance and became involved. In the “Computational Linguistics” course, students majoring in Mathematics and Computer Science were also involved in project development. It remains to include Croatian language teachers to help us check existing and enter new content. For their work, the project leader and collaborators will write all necessary programme modules. This project does not provide “one more” dictionary of the Croatian language as an outcome, but rather an online database linked to other words of the world languages, and given the features entered (e.g., a morpheme and syllable dictionary, an MWE dictionary), it represents the basis for a syntactic and semantic analysis of digital documents in Croatian. Some applications (e.g., distinguishing between the types of dependent clauses or recognising metonymy and metaphor in texts) have already been demonstrated at linguistic conferences (6th Croatian Syntactic Days, The Third International Symposium on Figurative Thought and Language).

      Programme: Creativity, Ecology, Heritage and Goodness - The Adris Foundation

      Project members: Domagoj Ševerdija, Ana Mikić Čolić, Mario Essert, Suzana Molčanov, Marko Orešković i Juraj Benić

      Project duration: October 2018 - January 2020

    • "Application of optimization methods in biomedicine", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science and Education ) - Project coordinator: Slobodan Jelić

      Summary: Optimisation models in biological networks. The subnetwork extraction method can solve important problems in biomedicine. Metabolic and genetic networks are highlighted in the first place. There are different approaches to the construction of metabolic networks, the most common approach being weighted (un)directed graphs with a set of vertices consisting of compounds and reactions between them. Genetic networks describe the interaction of genes in controlling cellular processes. Mutations block certain signalling pathways, which may disrupt essential cellular processes. Finding such signalling pathways contributes to early detection of the risk of cancer. One of the goals is to study possible representations of biological networks, and to consider different optimisation models for extracting their subnetworks. Here, we particularly emphasise the NP-heavy network design problems, such as the (un)directed group Steiner tree problem and the isomorphic subgraph problem.

      Programme: The program of scientific-technological cooperation between the Republic of Croatia and the Republic of Serbia, Ministry of Science, Education and Sports

      Project members: Slobodan Jelić, Dušan Jakovetić, Domagoj Ševerdija, Tatjana Davidović, Snježana Majstorović, Irena Jovanović, Luka Borozan, Nataša Krejić, Mateja Đumić, Nataša Krklec Jerinkić, Rebeka Čorić, Luka Matijević, Marija Mioč

      Project duration: 1 January 2019 - 31 December 2020

    • "Computer managed corpus linguistics - UNIOS - ZUP 2018 - Youth Research Projects", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Domagoj Ševerdija

      Summary: Corpus linguistics investigate languages by using samples from given real-world texts. As a digitalized data source, it brings great possibilities for computer processing of corpus data inorder to help making corpus-based judgments. Most digitalized corpora today usually encompass a framework where one can make a linguistic-specific analysis. In this project, a unique network as a web application will be realized which will enable linguistic researchers to form their own corpora having at its disposal a set of tools for corpora analytics. This framework will be used for several case studies which are mostly investigated by theoretical linguistics approach. Our approach will be based on corpus data classification with respect to morphological and semantic features using standard corpus-based classification methods and recursive/recurrent neural network deep learning methods.

      Programme: UNIOS - ZUP 2018 - Youth Research Projects

      Project members: dr. sc. Ana Mikić Čolić, Assistant Professor (Faculty of Philosophy, Josip Juraj Strossmayer University of Osijek) i dr. sc. Mario Essert, Full Professor (Faculty of Mechanical Engineering and Naval Arcitecture of the University of Zagreb)

      Project duration: 18 month

    • "Isolation of the unwanted part of the spectrum in the quadratic eigenvalue problem - UNIOS - ZUP 2018 - Youth Research Projects", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Suzana Miodragović

      Summary: Some important properties of vibrational systems can be described by the corresponding quadratic eigenvalue problem. In the case when the eigenvalues of the mechanical system are close to the frequency of the external force this system undergo large oscillations. This is the phenomenon of so-called resonance. This acting of the system can be avoid by isolating the part of the eigenvalues in corresponding quadratic eigenvalue problem. If we define so-called resonance band in which we do not want eigenvalues, then the idea is to slightly modify damping matrix in order to obtain a new system whose eigenvalues are outside the resonance band. This problem will be obtained for the hyperbolic and also for gyroscopic quadratic eigenvalue problems.

      Programme: UNIOS - ZUP 2018 - Youth Research Projects

      Project members: Ninoslav Truhar (Department of Mathematics, J. J. Strossmayer University of Osijek), Zoran Tomljanović (Department of Mathematics, J. J. Strossmayer University of Osijek), Matea Puvača (Department of Mathematics, J. J. Strossmayer University of Osijek), Fernando de Teran (Universidad Carlos III de Madrid, Math. Department)

      Project duration: 18 months

    • "Limiting behavior of intermittent processes and diffusions - UNIOS - ZUP 2018 - Youth Research Projects", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Danijel Grahovac

      Summary: The inference in statistics and probability theory is largely based on limiting results that describe the stochastic properties of different models when time tends to infinity. For example, the central limit theorem guarantees that under some conditions the arithmetic mean has approximately a normal Gaussian distribution. Today it is quite clear that such results cannot describe the complexity of natural phenomena. Among other things, it is not possible to explain the fact that some phenomena show different behavior in small and large time scales (e.g. turbulent fluid flow, value of the financial asset, etc.). In this project the limiting properties of stochastic models will be studied. Emphasis will be placed on models that have the property of intermittency and on the implications that this property has on the stochastic nature of the model. In addition, the class of diffusion models will be studied, the limiting behavior of estimators of unknown parameters in these models, and the approximation of their transition density functions.

      Programme: UNIOS - ZUP 2018 - Youth Research Projects

      Project members: Nenad Šuvak (Department of Mathematics, J. J. Strossmayer University of Osijek), Ivan Papić (Department of Mathematics, J. J. Strossmayer University of Osijek), Nikolai N. Leonenko (School of Mathematics, Cardiff University), Murad S. Taqqu (Department of Mathematics and Statistics, Boston University), Una Radojčić (Department of Mathematics, J. J. Strossmayer University of Osijek) i Mirta Benšić (Department of Mathematics, J. J. Strossmayer University of Osijek)

      Project duration: 18 months

    • "The optimization and statistical models and methods in recognizing properties of data sets measured with errors- Young Researchers' Career Development Project - Training of Doctoral Students", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Mirta Benšić

      Summary: The PhD student will deal with the methods of nonlinear regression and classification. Emphasis is placed on understanding, developing and applying nonparametric methods including neural networks. The specific purpose of this PhD education programme is to contribute to mathematical understanding of statistical and algorithmic properties of multilayer neural networks and related methods with a tendency to find expressions for the approximation of errors, complexity, statistical risk and time of calculation. Theoretically the results will be supported by simulations and applied to real problems. The PhD student is planned to enrol in the Joint Postgraduate Doctoral Study Programme in Mathematics of the universities of Osijek, Rijeka, Split and Zagreb, to specialise in the field of probability and mathematical ststistics and to further educate and train at the University of Yale (led by Prof. Andrew Barron).

      Programme: Young Researchers' Career Development Project - Training of Doctoral Students

      Mentor's name and surname: Mirta Benšić

      PhD name and surname: Una Radojičić

      Project duration: 1 March 2017 - 28 February 2021

    • "Optimization of parameter dependent mechanical systems - Young Researchers' Career Development Project - Training of Doctoral Students", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Ninoslav Truhar

      Summary: The doctoral student will deal with the optimization of active and passive damping of mechanical systems with and without external force. For this purpose, it will be necessary to develop a general theoretical framework that describes many important system properties and to construct adequate numerical algorithms for calculating the desired sizes. The doctoral candidate is planned to enroll in the Joint university postgraduate doctoral study program in mathematics at the universities of Osijek,Rijeka, Split and Zagreb and specialize in the field of control and optimization theory, i.e. ordinary differential equations and dynamic systems.

      Programme: Young Researchers' Career Development Project - Training of Doctoral Students

      Mentor's name and surname: Ninoslav Truhar

      PhD name and surname: Matea Puvača

      Project duration: 20 September 2016 - 20 September 2020

    • "Real-time measurements and forecasting for successful prevention and management of seasonal allergies in Croatia-Serbia cross-border region", (Department of Mathematics, J. J. Strossmayer University of Osijek - Interreg IPA CBC Croatia - Serbia 2014-2020) - Project coordinator: Kristian Sabo

      Summary: Allergen avoidance is important for managing allergy. Knowledge about when certain pollen types are likely to be in the air helps allergy sufferers to plan activities and medication use. Since airborne pollen is transported by air masses it can easily cross the border resulting an increased risk for allergy symptoms in sensitive population. Airborne allergens are routinely monitored in cross-border area. However, applied methodology is time consuming and results are disseminated to end users with a delay which limits the impact of collected data in every day health management. The project will modernize public health service and notably enhance the quality and applicative value of the information they provide in cross-border area: by introducing real time monitoring of airborne allergens, by developing models for prediction exposure and by creating a joint platform for instantaneous dissemination of these information. In addition the project will make an effort to educate end users on the benefits from using information for prevention and management of allergy symptoms coming from the information public health services will provide following the implementation of this project. The project will focus on three major pollen allergens (i.e. Birch, Grass, Ambrosia) and thus, having in mind overall prevalence of seasonal allergies in the Croatia-Serbia cross-border region, its results will enhance public health services needed for 15-30% of the population. Particular attention will be given to introduction of developed services to vulnerable groups i.e. children and elderly people for which it can help to plan travelling, outdoor activities, start of the therapy, self assessment of the therapy effectiveness etc. Joint approach for dissemination of measurements and forecasts will improve information flow for people travelling from one side of the border to another but also for visitors coming from other regions.

      Programme: Interreg IPA Cross-border Cooperation Programme Croatia - Serbia 2014-2020

      Project partners: Institut BioSens - Istraživačko razvojni institut za informacione tehnologije biosistema (Lead Beneficiary), Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu and Grad Osijek

      Project members: Kristian Sabo, Krešimir Burazin, Nenad Šuvak and Slobodan Jelić

      Project duration: 15 July 2017 - 14 January 2020

    • "The optimization and statistical models and methods in recognizing properties of data sets measured with errors", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Rudolf Scitovski

      Summary: As a part of an attractive and active area of research known as big data analysis, optimization and statistical aspects of recognizing data sets properties will be analyzed. Research will be focused on clustering problems, deconvolution models and applications. The assumption is that the observed data sets represent the measured values of the variables to be analyzed but also that they contain a measurement error. In large data sets it is often appropriate to cluster data sets on the basis of certain characteristics and then apply models for each group that can describe variable properties such as relationship among them, possibility of separation, edges, specific form of the set of values, dimensions (length, surface or volume) of the set of values or general parameter vector which determines them. The problem in many practical situations can be formulated as an optimization problem for which the objective functions is generally neither differentiable nor convex. In order to solve such problems effectively, rapid and accurate numerical procedures will be developed. Also, due to errors in the data,in order to understand and correctly interpret the results, statistical models will be used and important statistical properties will be characterized.

      Programme: Croatian Science Foundation (IP-06-2016)

      Team members (UNIOS): Andrew Barron (Yale University, USA), Mirta Benšić (Department of Mathematics, University of Osijek, Croatia), Dragan Jukić (Department of Mathematics, University of Osijek, Croatia), Karlo Emmanuel Nyarko (Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, University of Osijek, Croatia), Safet Hamedović (Faculty of Metallurgy and Materials, University of Zenica, BiH), Kristian Sabo (Department of Mathematics, University of Osijek, Croatia), Petar Taler (Department of Mathematics, University of Osijek, Croatia)

      Project duration: 1 March 2017 - 28 February 2021