Odjel za matematiku

Current projects

    • "Accelerated solution of optimal damping problems", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of science and Education and Deutscher Akademischer Austausch Dienst (DAAD)) - Project coordinator: Zoran Tomljanović

      Summary: In this project we plan to consider 6 research topics. In particular, we will consider: 1. Solve parametric Lyapunov equations using reduced basis techniques, 2. Exploitation of the structure and the use of Krylov subspaces, 3. Identification of dominant reachable and observable subspaces, 4. The use of tensor techniques for data-driven approaches, 5. The use of low-rank updates to Lyapunov solutions for optimization of damper locations, 6. The use of frequency-weighted damping via non-smooth optimization. Within this project the two research groups will share knowledge through joint work and discussions during visits to the guest institution, seminar talks and student lectures. Both groups are performing research within the area of systems and control theory, numerical linear algebra and scientific computing. Therefore, they have similar scientific interests, but their main scientific focus has been in different specializations. This project will create strong synergies for their research, since their general closeness ensures they speak a common scientific language, while their specialization ideally complement each other for the investigated tasks. The cooperation of the groups from Magdeburg and Osijek will result in new efficient approaches for damping optimization as well as the fruitful future collaboration between these two research groups and individual researchers.

      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: Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg

      Team members: Department of Mathematics, University of Osijek: Zoran Tomljanović, Ninoslav Truhar, Ivica Nakić, Suzana Miodragović, Matea Ugrica, Marinela Pilj Vidaković, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg: Jens Saak, Ion Victor Gosea, Pawan Goyal, Davide Palitta, Igor Pontes Duff, Jennifer Przybilla

      Project duration: January 2021 - December 2022

    • "Inter-institutional cooperation between Department of Mathematics at UNIOS and Department of Mathematics at Virginia Tech", (Department of Mathematics, J. J. Strossmayer University of Osijek - Agency for Mobility and EU Programmes) - Project coordinator: Zoran Tomljanović

      Summary: Both partners have working groups that have similar interests within their scientific research, this will mean that both partners will improve their knowledge and experience. Improving the quality of knowledge within scientific research will also have an impact on the quality of teaching process especially in courses within applied mathematics. Dissemination of their results will be performed through seminar and conference talks and the main results will be published in scientific papers cited in relevant scientific databases (CC, SCIE, mathscinet). Thus, from this cooperation both partners will have a strong mutual benefit.

      Programme: ERASMUS+ PROGRAMME - International Credit Mobility, KEY ACTION 1 - Learning mobility of Individuals between programme and partner country

      Project partner: Department of Mathematics, Virginia Tech, USA

      Team members: Zoran Tomljanović (Odjel za matematiku Sveučilišta u Osijeku), Serkan Gugercin (Department of Mathematics, Virginia Tech)

      Project duration: 2 November 2020 - 31 July 2022

    • "CA18232 Mathematical models for interacting dynamics on networks", (Department of Mathematics, J. J. Strossmayer University of Osijek - COST-European Cooperation in Science and Technology) - Project coordinator: Zoran Tomljanović

      Summary: Many physical, biological, chemical, financial or even social phenomena can be described by dynamical systems. It is quite common that the dynamics arises as a compound effect of the interaction between sub-systems in which case we speak about coupled systems. This Action shall study such interactions in particular cases from three points of view: 1. the abstract approach to the theory behind these systems, 2. applications of the abstract theory to coupled structures like network, neighbouring domains divided by permeable membranes, possibly non-homogeneous simplical complexes, etc., 3. modelling real-life situations within this framework. The purpose of this Action is to bring together leading groups in Europe working on a range of issues connected with modelling and analysing mathematical models for dynamical systems on networks. It aims to develop a semigroup approach to various (non-)linear dynamical systems on network as well as numerical methods based on modern variational methods and applying them to road traffic, biological systems, and further real-life models. The Action also explores the possibility of estimating solutions and long time behaviour of these systems by collecting basic combinatorial information about underlying networks.

      Programme: Cost Action 18232

      Project partners:

      Country

      MC Member

      Albania

      Dr Besiana ÇOBANI

      Albania

      Dr Valma PRIFTI

      Austria

      Prof András BÁTKAI

      Austria

      Prof Jussi BEHRNDT

      Belgium

      Prof Alexandre MAUROY

      Belgium

      Prof Wim VANROOSE

      Bosnia and Herzegovina

      Dr Miralem MEHIC

      Bosnia and Herzegovina

      Prof Dženan GUŠIĆ

      Bulgaria

      Dr Zlatinka DIMITROVA

      Bulgaria

      Prof Nikolay VITANOV

      Croatia

      Prof Ivica NAKIĆ

      Croatia

      Prof Nelida CRNJARIC-ZIC

      Cyprus

      Dr Demetris HADJILOUCAS

      Cyprus

      Dr Marios CHARALAMBIDES

      Czech Republic

      Prof Dalibor BIOLEK

      Czech Republic

      Prof David KREJCIRIK

      Denmark

      Dr Cumhur ERKUT

      Denmark

      Prof Sanja LAZAROVA-MOLNAR

      Estonia

      Dr Andres UDAL

      Finland

      Dr Lassi PAUNONEN

      France

      Dr Paola GOATIN

      France

      Prof Serge NICAISE

      Germany

      Prof Balint FARKAS

      Germany

      Prof Delio MUGNOLO

      Greece

      Prof Ioannis KIOUTSIOUKIS

      Hungary

      Dr Petra CSOMÓS

      Hungary

      Mr István LADJÁNSZKI

      Ireland

      Dr Brendan HAYES

      Ireland

      Dr Harun ŠILJAK

      Israel

      Prof Ram BAND

      Israel

      Prof Yosi KELLER

      Italy

      Prof Abdelaziz RHANDI

      Italy

      Prof Rinaldo M. COLOMBO

      Latvia

      Dr Juris VIKSNA

      Lithuania

      Prof Ricardas KRIKSTOLAITIS

      Luxembourg

      Dr Matteo POLETTINI

      Malta

      Dr Kenneth SCERRI

      Moldova

      Mr Lilian GOLBAN

      Montenegro

      Prof Nevena MIJAJLOVIĆ

      Montenegro

      Prof Vladimir JACIMOVIC

      Netherlands

      Prof Ming CAO

      North Macedonia

      Dr Martin LUKAREVSKI

      North Macedonia

      Prof Miroslav MIRCHEV

      Norway

      Prof Helge HOLDEN

      Norway

      Prof Nils Henrik RISEBRO

      Poland

      Dr Aleksandra PUCHALSKA

      Poland

      Prof Adam BOBROWSKI

      Portugal

      Dr James KENNEDY

      Portugal

      Dr Pedro ANTUNES

      Romania

      Dr Ligia Adriana MUNTEANU

      Romania

      Prof Rodica IOAN

      Serbia

      Dr Milana COLIC

      Serbia

      Mr Igor MARINOVIĆ

      Slovakia

      Dr Roman HRIC

      Slovenia

      Dr Irena STRNAD

      Slovenia

      Prof Aleksey KOSTENKO

      Spain

      Prof María Santos BRUZÓN GALLEGO

      Spain

      Prof Sergio GÓMEZ

      Sweden

      Prof Mats-Erik PISTOL

      Sweden

      Prof Pavel KURASOV

      Switzerland

      Prof Daniel KRESSNER

      Switzerland

      Prof Gianluca RIZZO

      Turkey

      Dr Emre MENGI

      Turkey

      Dr Hamdullah YÜCEL

      United Kingdom

      Dr David SEIFERT

      United Kingdom

      Prof Ginestra BIANCONI

      Team members: Zoran Tomljanović (Department of Mathematics, University of Osijek)

      Project duration: 4 October 2019 - 3 October 2023

    • "Inter-institutional cooperation between Department of Mathematics at UNIOS and Department of Mathematics at Virginia Tech", (Department of Mathematics, J. J. Strossmayer University of Osijek - Agency for Mobility and EU Programmes) - Project coordinator: Zoran Tomljanović

      Summary: Both partners have working groups that have similar interests within their scientific research, this will mean that both partners will improve their knowledge and experience. Improving the quality of knowledge within scientific research will also have an impact on the quality of teaching process especially in courses within applied mathematics. Dissemination of their results will be performed through seminar and conference talks and the main results will be published in scientific papers cited in relevant scientific databases (CC, SCIE, mathscinet). Thus, from this cooperation both partners will have a strong mutual benefit.

      Programme: ERASMUS+ PROGRAMME - International Credit Mobility, KEY ACTION 1 - Learning mobility of Individuals between programme and partner country

      Project partner: Department of Mathematics, Virginia Tech, USA

      Team members: Zoran Tomljanović (Department of Mathematics, University of Osijek), Serkan Gugercin (Department of Mathematics, Virginia Tech)

      Project duration: 15 February 2017 - 31 July 2018

    • "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

    • "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

    • "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

    • "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