**Link: **The optimization and statistical models and methods in recognizing properties of data sets measured with error

**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

**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 – 1 July 2022

**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 – 1 July 2022

**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

**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 – July 2022

**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

**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

**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

**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

**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

**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

**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

**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

**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

** 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

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

**Project duration:** 15 February 2017 – 31 July 2018

**Link: **TD COST Action TD1409

**Summary:** Mathematics underpins all of modern science and technology but advances in mathematical research are not always applied to maximum advantage in industry. The objective of this Action is to create a Europe-wide partnership to promote collaboration in, and the benefits of, industrial mathematics. The Actiom will run industry workshops, trainings weeks, and short-term scientific missions to both academic and industrial hosts, with the general aim of increasing the interaction between industry and academia. Exploiting the mathematical knowledge and methodologies af academics will provide European industry with a competitive advantage. Universities will benefit, as mathematicians are able to focus on practically relevant and cutting edge research problems. The training of Early-Career Investigators in particular will lead to a new generation with problem solving and communication skills and collaborative links that will be essential to maintain the goals of this Action in the future long after this funding has finished.

**Programme:** TD COST Action TD1409

**Project partners:**

Country | MC Member | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Austria | Dr Andreas BINDER | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Austria | Prof Ronny RAMLAU | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Belgium | Dr Patricia TOSSINGS | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Bosnia and Herzegovina | Dr Haris GAVRANOVIC | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Bosnia and Herzegovina | Dr Harun ŠILJAK | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Bulgaria | Mr Tihomir IVANOV | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Bulgaria | Prof Petar POPOV | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Croatia | Prof Anet REZEK JAMBRAK | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Croatia | Prof Kristian SABO | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Cyprus | Dr Katerina KAOURI | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Cyprus | Dr Margarita ZACHARIOU | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Denmark | Dr Poul HJORTH | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Denmark | Prof Maria Dolores ROMERO MORALES | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Estonia | Prof Peep MIIDLA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Estonia | Mr Jens HAUG | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Finland | Dr Simo ALI-LÖYTTY | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Finland | Dr Matylda JABLONSKA-SABUKA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

France | Dr Joost ROMMES | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

France | Ms Edwige GODLEWSKI | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

fYR Macedonia | Dr Tatjana ATANASOVA-PACHEMSKA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

fYR Macedonia | Dr Biljana JOLEVSKA-TUNESKA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Germany | Prof Dietmar HOEMBERG | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Germany | Prof Rene PINNAU | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Greece | Prof Vasileios KOSTOGLOU | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Greece | Dr Nikolaus PLOSKAS | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Hungary | Dr András BÁTKAI | Hungary | Prof Istvan FARAGO | Ireland | Dr Miguel BUSTAMANTE | Ireland | Dr William LEE | Israel | Dr Yirmeyahu KAMINSKI | Israel | Dr Aviv GIBALI | Italy | Prof Alessandra MICHELETTI | Italy | Dr Rada NOVAKOVIC | Lithuania | Prof Raimondas CIEGIS | Netherlands | Dr Vivi ROTTSCHAFER | Netherlands | Prof Wilhelmus SCHILDERS | Norway | Prof Elena CELLEDONI | Norway | Dr Svenn Anton HALVORSEN | Poland | Prof Wojciech OKRASINSKI | Poland | Dr Agnieszka WYLOMANSKA | Portugal | Prof Adérito ARAÚJO | Portugal | Ms Margarida PINA | Romania | Prof Costica MOROSANU | Romania | Dr Ionut PORUMBEL | Serbia | Prof Natasa KREJIC | Serbia | Prof Ivan OBRADOVIC | Slovakia | Dr Peter FROLKOVIC | Slovakia | Prof Karol MIKULA | Slovenia | Prof Janez POVH | Spain | Prof Tim MYERS | Spain | Prof Peregrina QUINTELA ESTÉVEZ | Sweden | Dr Hanifeh KHAYYERI | Sweden | Prof Johan HOFFMAN | Switzerland | Dr Joerg OSTERRIEDER | Switzerland | Prof Wolfgang BREYMANN | Turkey | Prof Enis KAYIS | United Kingdom | Dr Robert LEESE | United Kingdom | Dr Hilary OCKENDON |

**Team members (UNIOS):** Kristian Sabo, Krešimir Burazin

**Project duration:** 5 May 2015 – 4 May 2019

**Summary:** This project is devoted to second order mechanical systems which are described by a system of differential equations: M x”(t) + D x'(t)+ K x(t) =B f(t)+E w(t), x0=x(0), v0=x'(0), where M, D, K are semidefinite Hermitian large – scale matrices, dependent on one or more real parameters, while B and E are full rank matrices with p and q columns, respectively, much smaller than n. Although the above systems have been widely investigated, there are still many interest open problems from theoretical point of view, but also from the applications itself. One of such problems is optimization of a small rank damping of different kind (passive, viscose, semi-active) from which follow open problems as positioning of dampers, optimal number of dampers, optimal dampers characteristics, etc. The majority of the research within this project will therefore be focused to: optimization of active and passive damping and optimal control of parameter dependent mechanical systems with and without external force; describing the properties of eigenvalues and eigenvectors of the corresponding parameter-dependent quadratic eigenvalue problem as well as corresponding parameter-dependent nonlinear eigenvalue problems.

Within the problem of active and passive damping optimization and optimal control of parameter dependent mechanical systems with and without external force, we will develop a general theoretical framework which describe many important system properties, and we will construct the corresponding numerical algorithms for the calculation of desired quantites. These theoretical considerations will be related to the optimization of various damping parameters with respect to several different optimization criteria as e.g.: spectral abscissa optimization, optimization of total average energy of the system, optimization of average amplitude of displacement, optimization of average amplitude of energy and impulse response energy. Furthermore, within the stated objectives we will solve many numerical demanding problems, for example: mixed-integer nonlinear optimization problem, efficiently solving of large matrix equations (Lyapunov, Sylvester, Riccati), improving the optimization algorithms by dimension reduction. We will also consider theoretical and numerical aspects of optimization of semi-active damping problem and optimal control based on various criteria (minimization of H_2, H_infinity norms, etc.).

Within the problem of describing the behaviour of eigenvalues and eigenvectors of the parameter-dependent quadratic eigenvalue problems, we will develop perturbation theory for the corresponding quadratic problem where we will separately consider cases when M, D, K are semidefinite Hermitian matrices, and corresponding linearized pair is diagonalizable (this means that eigenvalues of quadratic eigenvalue problem can be complex) and so called overdamped case, i.e. the case when the corresponding linearized pair is definite. Further, we plan to generalize the obtained results on the parameter dependent nonlinear eigenvalue problem. For all cases we will develop perturbation theory which will contain perturbation bounds of absolute and relative type for the eigenvalues and associated eigenvectors i.e. subspaces.

Since the stated problems are closely related, insight into the behaviour of eigenvalues and corresponding eigenvectors will allow better understanding of the damping, or other parts of the mechanical systems, while the better understanding of optimal damping or parameters in mechanical system will clarify some important properties of mechanical systems, such as overdampness, stability etc.

**Programme:** Croatian Science Foundation

**Project partners:** Prof. dr. sc. Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

Prof. dr. sc. Ivan Slapničar, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split

Dr. sc. Nevena Jakovčević Stor, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split

Jonas Denißen, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

**Project members:** prof. dr. sc. Ninoslav Truhar, doc. dr. sc. Zoran Tomljanović, dr. sc. Ivana Kuzmanović, dr. sc. Suzana Miodragović

**Project duration:** 1. 7. 2015. – 30. 6. 2019.

**Summary:** Mechanical systems have been widely investigated, but there are still many interesting and important open problems from the theoretical point of view and also from the applications themselves. Within this project we plan to consider robust damping optimization. The criterion for damping optimization that we want to consider corresponds to the H-infinity system norm which, compared to other criteria such as the H-2 norm or the total average energy, provides better damping properties in terms of the system’s robustness. Thus, we plan to derive a new approach for efficient damping optimization and compare it to existing strategies.

**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 partners:** Technische Universität Berlin (Matthias Voigt, Volker Mehrmann and Philipp Schulze)

**Team members (UNIOS):** Ninoslav Truhar and Matea Puvača

**Project duration:** 1 January 2017 – 31 December 2018

**Link: **TD COST Action TD1307

**Summary:** This network will connect large groups in Europe working on model reduction strategies used in many domains of science and technology. The growing complexity of mathematical models used to predict real systems, such as climate problems or problems of the human cardiovascular system, lead to the need for model reduction. Therefore, it is necessary to develop algorithms that replace complex models with much simpler ones that approximate the system well and contain the most important phenomena observed in a given model. Emphasis shall be placed on several topics:

1. Design, optimization and control theory in real-time applications in engineering.

2. Data assimilation, recording geometry and parameter estimation with a particular focus on real-time computing in biomedical engineering and computational physics.

3. Visualisation in real-time physically based simulations in computer science.

4. Studying the problem of large dimensions in the state space, physical space and industrial problems or the parameter space.

5. Interaction between reduction model approaches that use dimension reduction.

The focus of the network is methodology; however, a large number of complex scientific and industrial problems is designed to motivate, simulate, and finally demonstrate the importance and efficiency of the network. The main goal is to significantly accelerate computer programs in order to be more realistic for industrial, scientific, economic and social models, which will be achieved by means of reduction models.

**Programme:** TD COST Action TD1307

**Partners in the project:**

Country | MC Member |

Belgium | Prof Karl MEERBERGEN |

Belgium | Prof Benjamin DEWALS |

Croatia | Prof Ninoslav TRUHAR |

France | Prof Francisco CHINESTA |

Germany | Prof Peter BENNER |

Germany | Prof Bernard HAASDONK |

Ireland | Dr Patrick BRADLEY |

Italy | Dr Gianluigi ROZZA |

Luxembourg | Prof Andreas ZILIAN |

Luxembourg | Prof Stéphane BORDAS |

Netherlands | Prof Wil SCHILDERS |

Netherlands | Prof Jacquelien SCHERPEN |

Portugal | Prof Nuno POMBO |

Portugal | Prof Luis Miguel SILVEIRA |

Romania | Prof Daniel IOAN |

Romania | Dr Alexandra Raluca STEFANESCU |

Spain | Prof Antonio FALCO |

Spain | Mr Enrique S. QUINTANA-ORTI |

Sweden | Prof Elias JARLEBRING |

Switzerland | Prof Alfio QUARTERONI |

United Kingdom | Dr Mark OPMEER |

Country | MC Substitute |

Germany | Prof Heike FASSBENDER |

Germany | Prof Tatjana STYKEL |

Netherlands | Prof Siep WEILAND |

Netherlands | Prof Arjan VAN DER SCHAFT |

Switzerland | Prof Jan HESTHAVEN |

**Project members:** Ninoslav Truhar, Zoran Tomljanović

**Project duration:** 14 November 2013 – 14 November 2017

**Summary:** Common scientific interests were identifed through previous cooperation and planned cooperation activities in this project are planned to be realized through joint work on the following topics:

a) Optimal control, optimal design, generalized solutions and homogenization. Within the framework of this topic, we plan to study a linear quadratic problem in Friedrich’s systems, with an emphasis placed on applications to specfic initial boundary phenomena. Furthermore, we would study the role of two-phase multi-state optimal design for the stationary diffusion equation, aiming to minimize the weighted sum of energy functionals in all blends of two isotropic materials. Here the objective is to explicitly calculate a solution to the relaxed task, at least in the spherically symmetric case. It would be interesting to see whether linearized elasticity can fit into the setting of Friedrich’s systems, and we also plan to research characterization of H-distribution, with special attention to the issue of relations between H-distribution or H-measure carriers and wavefront.

b) Optimization problems of specific structure. A class of optimization problems of special structure will be described, in which the objective function is shown in the form of a sum a large number of the so-called loss functions. We are particulary interested in the problems where direct minimization of the objective function determined on the basis of the set of all data (due to its size) is not possible. To reduce the cost of the iterative optimization procedures, we will consider the methods in which the number of local functions losses is variable in each iteration. In doing so, the objective functions is approximated based on the sample size, for which second-order methods are considered to be particularly interesting. Bearing in mind the aim to reduce dimension of large amounts of data, we will develop incremental and adaptive methods based on spectral relaxation that are used for searching for an approximately globally optimal partition.

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

**Project partners:** Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad

**Team members (UNIOS):** Kristian Sabo, Ivana Vuksanović, Jelena Jankov

**Project duration:** 1 January 2016 – 31 December 2017

**Summary:** Standard models in probability and statistics tend to rely on the assumption of independence or weak dependence between temporally close events. On the other hand, a number of phenomena in applied sciences require temporal models where the correlation between the two events may decay very slowly with time. Research activities in this project cover several types of long-range dependent stochastic processes, their construction and properties. The following topics will be studied: correlated random walks and their connection with fractional Pearson diffusions, trawl processes and their intermittency property and processes obtained by the time-change of the autoregressive process in continuous time.

**Programme:** IZIP-2016

**Guest researcher:** Professor Nikolai N. Leonenko (School of Mathematics, Cardiff University, UK)

**Team members (UNIOS):** Danijel Grahovac (Department of Mathematics, University of Osijek, Croatia) and Ivan Papić (Department of Mathematics, University of Osijek, Croatia)

**Project duration:** March 2017 – March 2018

**Summary:** This project is dedicated to the study of nonlinear parameter dependent eigenvalue problems, where the special emphasis is on the behavior of the eigenvalues and eigenvectors of the parameter dependent quadratic eigenvalue problems *(ʎ(p)²M(p)+ʎ(p)C(p)+K(p))x(p)=0*, where *M, C, K* Hermitian matrices, *ʎ* is eigenvalues, *x* is eigenvector and *p* is some parameter. Characteristics of the parameter dependent eigenvalues and eigenvectors will be used to derive perturbation bounds(absolute and relative type) for the case whan *M, C, K* are arbitrary Hermitian matrices. The new results are planned to be generalized to other parameter dependent eigenproblems, such as the rational and polynomial problem.

**Programme:** Guest researcher (INGI-2015) Josip Juraj Strossmayer University of Osijek

**Guest researcher:** Rafikul Alam

**Project partners:** Department of Mathematics, Indian Institute of Technology Guwahati, India

**Team members (UNIOS):** Ivana Kuzmanović, Suzana Miodragović, Zoran Tomljanović, Matea Puvača

**Project duration:** 10 June 2016 – 10 July 2016

**Summary:** The visitor and a group of researchers from the Department of Mathematics, University of Osijek, will explore clustering optimization problems focusing on the optimization of likelihood initialized with tensor-based moment methods. The team will also explore efficiency of nonlinear least squares fit of empirical distributions in certain parametric estimation problems.

**Programme:** Guest researcher (INGI-2015) Josip Juraj Strossmayer University of Osijek

**Guest researcher:** Andrew R. Barron

**Project partners:** Department of Statistics, Yale University, USA

**Team members (UNIOS):** Kristian Sabo; Danijel Grahovac; Ivan Papić

**Project duration:** March 2016 – November 2016

**Summary:** The overall objective of the project is to contribute to the further implementation of the Croatian Qualifications Framework in the field of teacher training and education. A draft proposal of occupational and qualification standards will be developed for informatics, engineering, biology, chemistry, physics and mathematics teachers, which should contribute to the modernisation of study programmes for training and educating teachers inthe aforementioned fields, and based upon the Croatian Qualifications Framework by developing learning outcomes.

Specific objectives of the project are to develop 6 occupational standards, 6 qualification standards and 10 study programmes/curricula based on learning outcomes.

In the first part of the implementation of project activities, strategic documents, sector profiles, as well as the demand and supply for these occupations, will be analysed and an occupational standard survey will be carried out.

In the second part, key jobs and competencies in these positions will be established through roundtables of working groups in each of these fields, as well as the sets of learning outcomes required to achieve these competencies.

In the final stage, roundtables will be held to harmonise the qualifying study programmes with occupational and qualification standards for informatics, engineering, biology, chemistry, physics and mathematics teachers developed previously, as well as workshops on curriculum development in line with the approach based on learning outcomes.

**Programme:** Grant for projects financed by the European Social Fund as part of Human Resources Development 2007-2013

**Project partners:** Faculty of Philosophy in Zagreb, Faculty of Philosophy in Rijeka, University of Rijeka, Josip Juraj Strossmayer University of Osijek, III High School in Split and the Education and Teacher Training Agency. The project will also include representatives of key stakeholders in the education of the aforementioned staff as a target group.

**Team members (UNIOS):** Ljerka Jukić Matić (mathematics), Tomislav Marošević (mathematics), Darija Marković (mathematics), Domagoj Ševerdija (informatics), Domagoj Matijević (informatics)

**Project duration:** 18 July 2015 – 18 September 2016

**Summary:** The problem we will consider is devoted to damping optimization, in particular, the problem is to determine dampers’ position and viscosities for a vibrational system. A criterion in the optimization problem is to minimize the total energy for a vibrational system over all initital states of unit energy, and all dampers’ position and its viscosities. In general this is a Mixed Integer Nonlinear Program (MINLP) as viscosities represent real numbers, while position are given as coordinates in the network, indexed by nonnegative integers.

The main drawback in damping optimization is the combinatorial explosion of the total number of damping combinations. Therefore, we would like to use recent advances in MINLP.

Furthemore, we would like to address the linearization of the MINLP, which in this case is possible since the product of variables can be expressed as separable functions. Hence, we end up with an Integer Program (IP).

In this setting, we would like to discuss and compare the result from the MINLP and IP approaches with the prevously investigated and abovely mentioned discrete to continous approaches.

Furthemore, we would like to consider a new damping optimization problem when a mechanical system is excited by an external force. In this case we consider a new criterion which is based on the amplitude, such as average energy amplitude and average displacement amplitude criterion.

With the knowledge of damping based on total energy we will derive explicit formulas for particular case studies. In the general setting we will propose approaches in which the objectives functions can be efficiently calculated. Moreover, in this optimization problem we would like to employ MINLP as well in order to determine optimal damping efficiently.

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

**Partners in the project:** Max Planck Institute for Dynamics of Complex Technical Systems (Peter Benner, Yao Yue, Xin Liang, Jonas Denissen, Manuela Hund)

**Project members:** Ninoslav Truhar, Zoran Tomljanović, Suzana Miodragović

**Project duration:** 1 January 2015 – 31 December 2016

**Summary:** The goal of this project is to investigate irreducible subquotients and to determine the composition series of induced representations which play an important role in the unitary and non-unitary duals of classical groups over non-Archimedean local fields. Mostly, we plan to study the composition series of certain generalized principal series, representation induced from those of segment type and representations induced from several irreducible essentially square integrable ones on the general linear part and strongly positive discrete series on the classical-group part. We plan to generalize applications of intertwining operator methods and Jacquet modules method, starting inductively from known descriptions of Jacquet modules.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Ivan Matić (coordinator), Ljerka Jukić Matić, Darija Brajković

**Project duration:** 2 May 2015 – 2 May 2016

**Summary:** The research will be focused on the fractional Pearson diffusion (FPD), more specifically on the study of the construction techniques and probabilistic properties of special types of this class of fractional diffusions: Ornstein-Uhlenbec and Cox-Ingersol-Ross fractional diffusion. We will focus on two main problems: 1. construction of the FPD 2. the analysis of the spectrum of the infinitesimal generator of the FPD and the use of the known structure of its spectrum and corresponding eigenfunctions for deriving the transition density functions of some special cases of FPD.

For Ornstein-Uhlenbeck and Cox-Ingersol-Ross FPD studied in more details we will investigate theirphysical interpretation and possible applications in other sciences.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:**Nenad Šuvak (coordinator); Danijel Grahovac; Ivan Papić; Mirta Benšić (consultant)

**Project duration:** 2 May 2015 – 2 May 2016

**Summary:** This project is devoted to damping optimization which is a very important issue since prevents undesirable effects in vibrations of systems.

We consider the case when a system is excited by an external force which has an important influence on system behavior. Optimization procedure will be based on the minimization of the average displacement and the average energy amplitude.

Since the optimization process is a very demanding we will develop several methods and algorithms for the efficient damping optimization. In particular, we will consider models with internal damping, different dampers viscosities and the influence of various external functions on system behavior

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Zoran Tomljanović (coordinator), Ivana Vuksanović, Jelena Jankov

**Project duration:** 2 May 2015 – 1 May 2016

**Summary:** In real physical systems which possess elasticity and mass, dangerous vibrations are a typical phenomenon which have been widely studied in the past. But also nowadays this is an intensively investigated phenomenon. For the majority of engineering applications, resonance and sustained oscillations can cause structural damage. The way to reduce dangerous vibrations is through damping.

Our goal is to develop efficient approaches for solving problems which appear in damping optimization but also in closely connected issues such as optimality of the solution of the linear systems, stability via Lyapunov and optimal control.

The usage of model order reduction approaches is investigated for this task and additionally, we will derive a theory which will describe the geometry of the corresponding eigenspaces as well as the relative perturbation bounds for corresponding eigenvalues.

We also consider the feedback stabilization we will also consider the case of active damping with direct velocity feedback, since one can obtain almost the same second order system as with passive damping.

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

**Partners in the project:** Max Planck Institute for Dynamics of Complex Technical Systems (Peter Benner, Jonas Denissen, Patrick Kürschner, Matthias Voigt, Andre Schneider)

**Project members:** Ninoslav Truhar, Zoran Tomljanović

**Project duration:** 1 January 2013 – 31 December 2014

**Summary:** Knowledge of composition series of induced representations of p-adic groups is one of the most interesting and most important unsolved problems in the whole representation theory. A particulary important case of induced represenations are the so-called generalised principal series, i.e., representations induced from maximal parabolic subgroups of a discrete series located on the classical part. Although reducibility points of generalized principal series were obtained and presented by Goran Muić, irreducible subquotients of such representations are known only in the case of induction of a strictly positive representation. The aim of this project is to expand knowledge to the generalised principal series induced from more general types of discrete series, where the emphasis is placed on the detection of necessary and sufficient conditions to have a generalized discrete series contain a subquotient in a discrete series. We also plan to prove that in this case the induced representation must also contain a subrepresentation in a discrete series.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Dr. Ljerka Jukić Matić, Darija Brajković MMath

**Project duration:** 25 September 2013 – 25 September 2014

**Summary:** The theoretical part of research deals with various aspects of the problem of parameter estimation in a special family of nonlinear two-parameter mathematical models. Emphasis is placed on the existence problems of optimal parameters in a predefined parameter space, the problem of choosing a numerical minimization method and the problem of determining a good initial approximation. The problems are formulated and solved in different l_p standards (1≤ p≤∞), and in addition to the classical methods of optimisation, numerical analysis and approximation theory, the classical Ordinary Least Squares Method is particulary used in the research. As part of research, special attention is given to all aforementioned aspects of the parameter estimation problem in some mathematical models which are widely used in applied research (agriculture, economics, electrical engineering, biology, biotechnology, medicine, such as a two-parameter exponential regression model, a two-parameter power regression model, Fox`s model, Cobb-Douglas model, Schumacher equation and others.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Darija Marković, Dragana Jankov Maširević, Dragan Jukić, Luka Borozan(student)

**Project duration:** 25 September 2013 – 24 September 2014

**Summary:** By designing fast parallel algorithms we want to approximately solve a (mixed) packing and covering problem. By modifying the existing algorithms and comparing their performance we want to determine the most appropriate algorithm for the parallel CUDA computing model. The project result will significantly contribute to approximate solution of many NP-hard combinatorial optimisation problems which have important applications in robotics and telecommunications. For example, the SIMPLEX method solves an LP problem with 5,000 variables and 5,000 conditions in two hours by using a computer with one modern CPU. The objective is to efficiently solve the problem with the number of variables and parameters up to 50,000 by using modern graphics NVIDIA chips.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Domagoj Matijević, Domagoj Ševerdija, Slobodan Jelić

**Project duration:** 1 October 2013 – 1 October 2014

**Summary:** Friedrichs systems are a broad class of linear PDEs which includes many seemingly significantly different equations in a unique enviroment. In the last ten years, significant progress was made in their development, new results were obtained that refer to well established tasks for stationary Friedrichs systems and new numerical schemes were developed, which has motivated their further study. In this project, we will study nonstationary, i.e., evolutionary Friedrichs systems (in which the time variable occurs), and their possible applications, which naturally imposes further development of some well-known methods used in the study of PDEs.

More precisely, our goal is to study under which assumptions the initial-boundary task for the evolutionary Friedrichs system is well posed in the weak sense, to explore the possibility of practical applications, as well as the possible generalisations of the existing compactness theory by compensation in the L^p-L^q case.

Research will be carried out by using semigroup theory, Galerkin method, and the vanishing viscosity method, while compactness by compensation will be explored by using pseudodifferential operators.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Krešimir Burazin, Marin Mišur, Ivana Vuksanović

**Project duration:** 25 September 2013 – 25 September 2014

**Summary:** In many physical and engineering models, dangerous vibrations can damage or even break the resonant system, therefore optimal systems control has a wide range of applications.

Research into damping optimisation is a very challenging problem that often leads to problems for which the numerical solution takes a lot of time, mathematical operations and computer memory. Therefore, in this project, we want to develop optimisation approaches that will effectively count the approximation of the solution to the considered optimisation problem.

In this project, special emphasis will be placed on the problem of optimising semi-active damping. In the above system, the basic problem is to minimise the impact of input to output such that we optimise the coefficients in the damping matrix. The impact of input to output can be measured by impulse response energy. This criterion leads to the resolution of the corresponding Lyapunov equation.

The goal is also to theoretically justify approximation algorithms. In this sense, we want to develop and apply perturbation theory that studies the eigenvalue square problem corresponding to the resonant problem.

**Programme:** Internal project of J. J. Strossmayer University of Osijek

**Project members:** Zoran Tomljanović, Suzana Miodragović

**Project duration:** 1 January 2014 – 31 December 2014

**Summary:** Geometric and other representations of graphs or graph-based structures have important applications in mathematics, computer science, social networks, chemistry, bioinformatics, etc. The main goal of the project is to develop a coherent theory of graph representations, mostly of symmetric or almost symmetric structures and products. The knowledge acquired by the researches will be applied to geometrically interesting combinatorial structures like configurations, maps and polytopes, as well as to large partially symmetric networks. The project will consist of the following parts:

1. representation and enumeration of highly symmetric graphs;

2. almost symmetric graph structures;

3. representation of large networks;

4. representations and configurations of symmetric maps and polytopes;

5. graph representations in mathematical chemistry and bioinformatics.

The individual goal of the project is to apply graph theory in the fields of chemistry, bioinformatics, sociological research and graph products.

**Partners in the project:**

Faculty of Mathematics and Physics, Koper, Slovenia,

Faculty of Mathematics and Physics, Ljubljana, Slovenia,

Faculty of Arts and Sciences, Istanbul, Turkey,

Faculty of Mathematics, Natural Sciences and Information Technologies, Koper, Slovenia,

Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia,

Faculty of Mathematics and Computer Science, Leipzig, Germany,

Montanuniversitaet Leoben, Leoben, Austria

Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek

**Programme:** EUROCORES “Graphs in Geometry and Algorithms (Euro GIGA)” European Science Foundation

**Project members:**: Snježana Majstorović (J.J. Strossmayer University of Osijek, Department of Mathematics), Damir Vukičević, Jelena Sedlar, Tanja Vojković (University of Split, Faculty of Science)

**Project duration:** 1 May 2011 – 30 April 2014

“Fast and efficient kinetic spanners” (J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science, Education and Sports – Deutscher Akademischer Austauschdienst (DAAD)) – Project coordinator: Domagoj Matijević

2007 – 2013 “Nonlinear parameter estimation problems in mathematical models” (235-2352818-1034) (J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science, Education and Sports) – Project coordinator: Dragan Jukić

2007 – 2013 “Statistical aspects of estimation problem in nonlinear parametric models” (235-2352818-1039) (J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science, Education and Sports) – Project coordinator: Mirta Benšić

2007 – 2013 “Passive control of mechanical models” (235-2352818-1042)” (J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science, Education and Sports) – Project coordinator: Ninoslav Truhar

2001 – 2006 “Parameter estimation in mathematical models” (0235001)” (J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science and Technology) – Principal investigator: Rudolf Scitovski

2001 – 2006 “Statistical aspects of parameter estimators in mathematical models” (0235002)” (J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science and Technology) – Principal investigator: Mirta Benšić

1996 – 2000 “Parameter identification problems in mathematical models” (165021)”(J.J. Strossmayer University of Osijek, Department of Mathematics – Ministry of Science and Technology) – Principal investigator: Rudolf Scitovski

1991 – 1995 “Application of numerical and finite mathematics” (1-01-129)” (J.J. Strossmayer University of Osijek, Faculty of Electrical Engineering – Ministry of Science and Technology) – Principal investigator: Rudolf Scitovski