Nenad Šuvak
Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia

Research Interests
 Diffusion processes
 Statistical analysis of stochastic processes
Degrees
 PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2010
 BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2004
Publications
Journal Publications
 N.N. Leonenko, Ž. Salinger, A. Sikorskii, N. Šuvak, M. Boivin, Generalized Gaussian time series model for increments of EEG data, Statistics and its Interface 16/1 (2023), 1729We propose a new strictly stationary time series model with marginal generalized Gaussian distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram (EEG) data collected from Ugandan children during coma from cerebral malaria. The model inherits its appealing properties from the strictly stationary strong mixing Markovian diffusion with invariant generalized Gaussian distribution (GGD). The GGD parametrization used in this paper comprises some famous lighttailed distributions (e.g., Laplace and Gaussian) and some well known and widely applied heavytailed distributions (e.g., Student). Two versions of this model fit to the data from each EEG channel. In the first model, marginal distributions is from the lighttailed GGD subfamily, and the distribution parameters were estimated using quasilikelihood approach. In the second model, marginal distributions is heavytailed (Student), and the tail index was estimated using the approach based on the empirical scaling function. The estimated parameters from models across EEG channels were explored as potential predictors of neurocognitive outcomes of these children 6 months after recovering from illness. Several of these parameters were shown to be important predictors even after controlling for neurocognitive scores immediately following cerebral malaria illness and traditional blood and cerebrospinal fluid biomarkers collected during hospitalization.
 N.N. Leonenko, A. Sikorskii, Ž. Salinger, M. Boivin, N. Šuvak, Multimodal diffusion model for increments of electroencephalogram data, Stochastic Environmental Research and Risk Assessement 37 (2023)We propose a new strictly stationary strong mixing diffusion model with marginal multimodal (threepeak) distribution and exponentially decaying autocorrelation function for modeling of increments of electroencephalogram data collected from Ugandan children during coma from cerebral malaria. We treat the increments as discretetime observations and construct a diffusion process where the stationary distribution is viewed as a mixture of three noncentral generalized Gaussian distributions and we state some important properties related to the moments of this mixture. We estimate the distribution parameters using the expectationmaximization algorithm, where the added shape parameter is estimated using the higher order statistics approach based on an analytical relationship between the shape parameter and kurtosis. The derived estimates are then used for prediction of subsequent neurodevelopment and cognition of cerebral malaria survivors using the elastic net regression. We compare different predictive models and determine whether additional information obtained from multimodality of the marginal distributions can be used to improve the prediction.
 J. Đorđević, M. Milošević, N. Šuvak, Nonlinear stochastic model for dopamine cycle, Chaos, Solitons & Fractals 1 (2023)Dopamine is a crucial neurotransmitter that plays a central role in various aspects of brain functions, including reward processing, motivation, learning, and movement control. Its intricate involvement in these biological processes has made it a subject of extensive research across multiple disciplines, ranging from neuroscience and psychology to computational modeling. In this paper the nonlinear stochastic model describing synthesis, storage, release, uptake and metabolism of dopamine in dopaminergic nerve terminal of the rat striatum is introduced. The model is driven by 9dimensional Brownian motion with constant coordinate intensities. Existence and uniqueness of a positive global solution on a corresponding timedomain are proved and lower and upper bounds for specific moments of coordinate processes are derived. These results are used for calculation of bounds for intensities of driving processes and time horizons ensuring that expected values of coordinate processes stay in the same timeinterval as the corresponding expected starting values. Furthermore, positivity preserving balance implicit method is used for simulation of coordinate processes in order to illustrate theoretical results.
 J. Đorđević, I. Papić, N. Šuvak, A two diffusion stochastic model for the spread of the new corona virus SARSCoV2, Chaos, Solitons & Fractals 148/110991 (2021)We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARSCov2, causing the COVID19 disease, taking into account the spread of the virus due to the regular infected individuals, hospitalized individuals and superspreaders. The model is constructed from the corresponding ordinary differential model by introducing two independent environmental white noises in transmission coefficients for above mentioned classes  one noise for infected and hospitalized individuals and the other for superspreaders. Therefore, the model is defined as a system of stochastic differential equations driven by two independent standard Brownian motions. Existence and uniqueness of the global positive solution is proven, and conditions under which extinction and persistence in mean hold are given. The theoretical results are illustrated via numerical simulations.
 J. Đorđević, B. Jovanović, J. Manojlović, N. Šuvak, Analysis of stability and sensitivity of deterministic and stochastic models for the spread of new corona virus SARSCoV2, Filomat 35/3 (2021), 10451063Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARSCoV2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the diseasefree equilibrium are derived and, in addition, conditions for existence of bifurcation state related to endemic equilibrium are established. For stochastic model, conditions for extinction and persistence in mean of the disease are derived. Complete sensitivity analysis of thresholds between the extinction and meanpersistence are performed for both the deterministic and the stochastic version of the model. Influence of variation in parameter values is illustrated for epidemics in Wuhan in early 2020.
Projects
Participation (as researcher) in work of the following projects:
 Application of shortrange and longrange dependent stochastic models (bilateral project with Faculty of Natural Sciences  Department of Mathematics, University of Niš, Serbia; Project leaders: Nenad Šuvak (University of Osijek) and Jasmina Đorđević (University of Niš); Project funded by Ministry of Science and Education of the Republic of Croatia and Ministry of Education, Science and Technology Development of the Republic of Serbia)
 Limiting behavior of intermittent processes and diffusions
Project runs in academic year 2019/2020. Project leader: Danijel Grahovac. Project funded by University of Osijek  RealForAll  Realtime measurements and forecasting for successful prevention and management of seasonal allergies in CroatiaSerbia crossborder region (2017  2019, project ID: HRRS151)
 Stochastic models with longrange dependence (Stohastički modeli s dugoročnom zavisnošću; 20172018), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
 Fractional Pearson Diffusions (Frakcionalne Pearsonove difuzije; 20152016), Department of Mathematics, J.J. Strossmayer University of Osijek, Leader: Nenad Šuvak (the project was funded by the J.J. Strossmayer University of Osijek)
 Statistical Aspects of Parameter Estimation in Nonlinear Parametric Models (Statistički aspekti procjene parametara u nelinearnim parametarskim modelima; 20072013), Department of Mathematic, University of Osijek, Leader: Prof. M. Benšić (the project was funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
 Models for Risk Assessment of the Company (Modeli za ocjenu rizičnosti poslovanja poduzeća; 20072013), Faculty of Economics, University of Osijek, Leader: Prof. N. Šarlija (the project was funded by the Ministry of Science, Education and Sports of the Republic of Croatia)
 Statistical Analysis of Diffusion Processes and their Applications in Economics and Finance (20092010)  this project was a collaborative project with Professor Nikolai N. Leonenko from School of Mathematics, Cardiff University, UK (the project was funded by the Croatian Science Foundation within the program for education of PhD students)
Grants
 ERASMUS grant for mobility of scientists (study visit to BabesBolyai University, ClujNapoca, Romania, 2016)
 ERASMUS grant for mobility of scientists (study visit to School of Mathematics, Cardiff University, UK, 2013)
 Grant of the AMACUK, United Kingdom Association of Alumni and Friends of Croatian Universities (study visit to School of Mathematics, Cardiff University, UK, 2011)
 Grant of the Croatian Ministry of Science, Education and Sports for specialization of croatian PhD students at the foreign Universities (study visit to School of Mathematics, Cardiff University, UK, 2008)
Professional Activities
Committee Memberships
 27th Young Statisticians Meeting, September 29  October 1, 2023., Osijek, Croatia
 Member of the International Program Committee, Book of Abstracts
 26th Young Statisticians Meeting, 30th of September  2nd of October 2022, Bohinj, Slovenia
 Member of the International Program Committee
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 2526 August 2022, Osijek, Croatia
 Member of the Organizing Committee
 25th Young Statisticians Meeting, 1517 October 2021, Monichwald/Vorau, Austria
 Member of the International Program Committee
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 2728 August 2020, Osijek, Croatia
 Chair of the Organizing Committee
 24th Young Statisticians Meeting, 1820 October 2019, Basovizza, Italy
 Member of the International Program Committee
 21st European Young Statisticians Meeting, July 29  August 2, 2019, Belgrade, Serbia
 Member of the International Organizing Committee/Scientific Program Committee
 23rd Young Statisticians Meeting, 1214 October 2018, Balatonfured, Hungary
 Member of the International Program Committee
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 3031 August 2018, Osijek, Croatia
 "Innovative Teaching of Mathematics"  National Meeting of Math Teachers, 2526 August 2016, Osijek, Croatia
 Chair of the Organizing Committee/Scientific Program Committee
 18th European Young Statisticians Meeting, 2630 August 2013, Osijek, Croatia
 Chair of the Local Organizing Committee
 17th European Young Statisticians Meeting, 59 September 2011, Lisbon, Portugal
 Member of the International Organizing Committee/Scientific Program Committee
Refereeing
 Scientific journals:
 Mathematical Communications, Glasnik matematički, Random Operators and Stochastic Equations, Journal of Classical Analysis, International Journal of Stochastic Analysis, Communication in Statistics  Simulation and Computation, Physical Communication, International Journal of Applied and Computational Mathematics, Mathematics, Applied Mathematical Modelling, Journal of Biological Physics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Applied Probability Journals
 Mathematical Communications, Glasnik matematički, Random Operators and Stochastic Equations, Journal of Classical Analysis, International Journal of Stochastic Analysis, Communication in Statistics  Simulation and Computation, Physical Communication, International Journal of Applied and Computational Mathematics, Mathematics, Applied Mathematical Modelling, Journal of Biological Physics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Applied Probability Journals
 Professional journals:
 Osijek Mathematical Gazette
Reviewing
 AMS Mathematical Reviews (20112020)
Conferences and Workshops
 Functional Analysis IX , June 2005, Dubrovnik, Croatia
 4th Croatian Mathematical Congress, June 17– 21, 2008, Osijek, Croatia (short communication)
 13th Young Statisticians Meeting, October 16–18, 2008, Balatonfured, Hungary (short communication)
 Croatian Quants Day, April 17, 2009, Department of Mathematics, Zagreb
 16th European Young Statisticians Meeting, August 2428, 2009, Bucharest, Romania (short communication)
 Workshop on Modern Interdisciplinary Applications of Powerful Techicques in Statistics (focus on Singular Spectrum Analysis (SSA) method), December 1, 2009, School of Mathematics, Cardiff University, Cardiff, UK
 "HighDimensional Data Analysis in Economics" Workshop, May 1920, 2010, Faculty of Economics, University of Zagreb, Croatia
 Croatian Quants Day, April 9, 2010, Department of Mathematics, Zagreb
 International Symposium on Business and Industrial Statistics, July 5  9, 2010, Portorose, Slovenia (invited speaker)
 Summer School in Financial Mathematics, August 22  September 2, 2011, Ljubljana, Slovenia
 Statistical Analysis of Financial Data Workshop, September 30  October 1, 2011, Opatija, Croatia (invited speaker)
 Spring School in Probability, April 2327, 2012, Dubrovnik, Croatia
 Croatian Quants Day, May 11, 2012, Department of Mathematics, Zagreb
 Workshop "Modern Trends in Markov Processes and Queuing Theory", February 15, 2013, Welsh Institute of Mathematical and Computational Sciences, Cardiff, UK (short communication)
 18th European Young Statisticians Meeting, August 2630, 2013, Osijek, Croatia
 Workshop on Quantitative Methods for Insurance and Finance, June 56, 2014, Zagreb, Croatia
 15th International Conference on Operational Research KOI 2014, September 2426, 2014, Osijek, Croatia (short communication)
 38th Conference on Stochastic Processes and their Applications, July 1317, 2015, University of Oxford, UK (short communication)
 6th Croatian Mathematical Congress, June 1417, 2016, Zagreb, Croatia (short communication)
 16th Conference on Operational Research KOI2016, September 2729, 2016, Osijek, Croatia (short communication)
 Mathematics for Big Data, May 31  June 1, 2017, Novi Sad, Serbia
 Korean Croatian Summer Probability Camp, July 36, 2017, Zagreb, Croatia
 39th Conference on Stochastic Processes and their Applications, July 2428, 2017, Moscow, Russia (short communication)
 21st European Young Statisticians Meeting, 1418 August 2017, Uppsala, Sweden (short communication with Ivan Papić)
 22nd Young Statisticians Meeting, October 1315, 2017. Zagreb, Croatia (short communication with Ivan Papić)
 ISSCRO'18 (2nd International Statistical Conference in Croatia), May 1011, Opatija, Croatia
 32nd European Meeting of Statisticians, July 2226, 2019, Palermo, Italy (short communication)
 ESPID  European Society for Paediatric Infectious Diseases, 39th Annual MeetingESPID  European Society for Paediatric Infectious Diseases, 39th Annual Meeting, Online Meeting and Hosted from Geneva, May 2429, 2021 (short communication with Ivana Valenčak Ignjatić, Universitiy Hospital for Infectious Diseases "Dr. Fran Mihaljević", Department for Pediatric Infectious Diseases, Zagreb, Croatia)
 22th European Young Statisticians Meeting, September 610, 2021, Greece (organized online, short communication with Željka Salinger)
 25th Young Statisticians Meeting, October 1517, 2021, Monichwald/Vorau, Austria (short communication with Željka Salinger)
 7th Croatian Mathematical Congress, June 1518, 2022, Split, Croatia (short communication)
 STORM Workshop, September 58, 2022, Oslo, Norway (invited lecture)
 12th Symposium Mathematics and Applications, December 23, 2022, Belgrade, Serbia (invited lecture)
 Applied Statistics, September 2426, 2023, Koper, Slovenia (short communication)
 27th Young Statisticians Meeting, September 29  October 1, 2023., Osijek, Croatia (organizer)
Lectures and Seminar talks
 Stohastički integral i Itova formula, Seminar za teoriju vjerojatnosti, PMFMatematički odjel, Zagreb, 2. i 9. svibnja 2006.
 Dokazi nepotpunosti bez dijagonalne leme, Seminar za logiku i osnove matematike, PMFMatematički odjel, Zagreb, 3. travnja 2007.
 Statistical analysis of Pearson diffusions with heavytailed marginal distributions, OR and Statistics Seminar, School of Mathematics, Cardiff University, UK, November 10, 2009
 Statistička analiza Pearsonovih difuzija s marginalnim distribucijama koje imaju teške repove, Seminar za optimizaciju i primjene, Odjel za matematiku, Osijek, 16. prosinca 2009.
 Statistička analiza Pearsonovih difuzija s marginalnim distribucijama koje imaju teške repove I, II, III, Seminar za teoriju vjerojatnosti, PMFMatematički odjel, Zagreb, 16. i 23. veljače, 30. ožujka 2010.
 Testiranje hipoteza za FisherSnedecorovu difuziju, Matematički kolokvij, Odjel za matematiku, Osijek, 19. travnja 2012.
 Bertrandov paradoks  nastavni izazovi, Geometrijska škola Stanka Bilinskog, SŠ Isidora Kršnjavoga, Našice, 8. travnja 2017.
 Mjere zavisnosti  svojstva i zamke, Statistički seminar, Odjel za matematiku, Osijek, 14. prosinca 2017.
 Modeliranje koncentracije peludi ambrozije, Statistički seminar, Odjel za matematiku, Osijek, 8. studenog 2018.
 Statistical analysis of Pearson diffusions with heavytailed marginal distributions, Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Niš, Serbia, February 14, 2020.
 Stochastic models for SARSCoV2 epidemics, Statistički seminar, Odjel za matematiku, Osijek, 3. veljače 2022.
Study visits
 School of Mathematics, Cardiff University, UK (study visits lasting 26 weeks in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2016 and 2018)
Service Activities
 President of the Osijek Mathematical Society (20172021)
 Cochair of the Statistical seminar of the Department of Mathematics (since January 2017)
 Member of the Higher Education Quality Assurance Board at the Department of Mathematics (since 2006)
Teaching
Konzultacije (Office Hours):
 Srijedom u 12:00, ured 18 na katu Odjela za matematiku
 Po dogovoru emailom, konzultacije su moguće i u drugim terminima.
Teme završnih i diplomskih radova:
 teme završnih radova (ak. god. 2023./2024.)
 teme diplomskih radova (ak. god. 2023./2024.)
Courses:
 Matematičke financije (Mathematical Finance), MATHOS (winter semester)
 Slučajni procesi II (Stochastic Processes II), MATHOS (spring semester)
 Stručna praksa (Professional practice), MATHOS
 Primijenjena i inženjerska matematika (Applied and Engineering Mathematics), PTFOS (winter semester)
 Matematika i statistika (Mathematics and Statistics), Mechanical Engineering Faculty, University of Slavonski Brod
Courses taught:
 Selected Applications of Probability, Stochastic Processes I, Probability, Introduction to Probability and Statistics, StatLab, Elementary Mathematics I and II, Introduction to Probability and Statistics, Introduction to Computer Science, Web Programming (Department of Mathematics, University of Osijek)
 Mathematics IV (Department of Physics, University of Osijek)
 Statistics (Faculty of Education, University of Osijek)
 Mathematics (Faculty of Agriculture, University of Osijek)
 Probability and Statistics (Faculty of Civil Engineering, University of Osijek)
 Statistics (Faculty of Food Technology, University of Osijek)