**Current projects**

- "Real-time measurements and forecasting for successful prevention and management of seasonal allergies in Croatia-Serbia cross-border region", (Odjel za matematiku, Sveučilište u Osijeku - Interreg IPA CBC Croatia - Serbia 2014-2020) - koordinator projekta: Kristian Sabo
**Sažetak:**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.**Program:**Interreg IPA Cross-border Cooperation Programme Croatia - Serbia 2014-2020**Partneri na projektu:**Institut BioSens - Istraživačko razvojni institut za informacione tehnologije biosistema (Lead Beneficiary), Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu and Grad Osijek**Suradnici na projektu:**Kristian Sabo, Krešimir Burazin, Nenad Šuvak and Slobodan Jelić**Trajanje projekta:**15 July 2017 - 14 January 2020 - "Stochastic models with long-range dependence", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Nenad Šuvak
**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 - "Robustness optimization of damped mechanical systems", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science and Education and Deutscher Akademischer Austanschdienst (DAAD)) - Project coordinator: Zoran Tomljanović
**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 - "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 - "Calculus of variations, optimisation and applications", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science, Education and Sports) - Project coordinator: Krešimir Burazin
**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 - "Mathematics for industry network (MI-NET) (TD COST Action TD1409 ), (Department of Mathematics, J. J. Strossmayer University of Osijek - COST - European Cooperation in Science and Technology) - Project coordinator: Kristian Sabo
**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 - "Optimization of parameter dependent mechanical systems", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Ninoslav Truhar
**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. - "European Model Reduction Network (EU-MORNET) (TD COST Action TD1307)", (Department of Mathematics, University of Osijek - COST - European Cooperation in Science and Technology) - project coordinator: Ninoslav Truhar
**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