Research Interests

Numerical and applied mathematics

Degrees

1998 PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia

1994 MSc in Mathematics, Department of Mathematics, University of Zagreb

1987 BSc in Mathematics and Physics, University of Osijek, Croatia

Publications

1. T. Marošević, J. Miletić, On some quantitative indicators of a few features of electoral systems, Croatian Operational Research Review 15 (2024), 119-130
   Abstract

   Electoral systems can be analyzed by means of their numerous properties. Some quantitative indicators of a few technical features of electoral systems are considered. With respect to the effective number of parties in a electoral system, one can observe some known indicators (e.g., fractionalization of vote shares, the Laakso-Taagepera index, the Wildgen index, the Molinar index). With regard to the government stability, one can look at the indicator which is called the expectation of government stability. These indicators are examined from the empirical point of view, i.e., in relation of elections in different countries.
2. T. Marošević, J. Miletić, M. Miloloža Pandur, The bounds of votes of divisor electoral methods, Central European Journal of Operations Research 31 (2023), 1265-1280
3. D. Jukić, T. Marošević, An existence level for the residual sum of squares of the power-law regression with an unknown location parameter, Mathematica Slovaca 71/4 (2021), 1019-1026
   Abstract

   In a recent paper Jukic [1], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.
4. T. Marošević, I. Soldo, Modified indices of political power: a case study of a few parliaments, Central European Journal of Operations Research 26/3 (2018), 645-657
   Abstract

   According to yes–no voting systems, players (e.g., parties in a parliament) have some influence on making some decisions. In formal voting situations, taking into account that a majority vote is needed for making a decision, the question of political power of parties can be considered. There are some well-known indices of political power e.g., the Shapley–Shubik index, the Banzhaf index, the Johnston index, the Deegan–Packel index. In order to take into account different political nature of the parties, as the main factor for forming a winning coalition i.e., a parliamentary majority, we give a modification of the power indices. For the purpose of comparison of these indices of political power from the empirical point of view, we consider the indices of power in some cases, i.e., in relation to a few parliaments.
5. T. Marošević, The Hausdorff distance between some sets of points, Mathematical Communications 23 (2018), 247-257
   Abstract

   Hausdorff distance can be used in various areas, where the problems of shape matching and comparison appear. We look at the Hausdorff distance between two hyperspheres in $mathbb{R}^n$. With respect to different geometric objects, the Hausdorff distance between a segment and a hypersphere in $mathbb{R}^n$ is given, too. Using the Mahalanobis distance, a modified Hausdorff distance between a segment and an ellipse in the plane, and generally between a segment and a hyper-ellipsoid in $mathbb{R}^n$ is adopted. Finally, the modified Hausdorff distance between ellipses is obtained.
6. R. Scitovski, T. Marošević, Multiple circle detection based on center-based clustering, Pattern Recognition Letters 52 (2015), 9-16
   Abstract

   The multiple circle detection problem has been considered in the paper on the basis of given data point set $mathcal{A}subset  Rn$. It is supposed that all data points from the set $mathcal{A}$ come from $k$ circles that should be reconstructed or detected. The problem has been solved by the application of center-based clustering of the set $mathcal{A}$, i.e. an optimal $k$-partition is searched for, whose clusters are determined by corresponding circle-centers. Thereby, the algebraic distance from a point to the circle is used. First, an adaptation of the well-known $k$-means algorithm is given in the paper. Also, the incremental algorithm for searching for an approximate globally optimal $k$-partition is proposed. The algorithm locates either a globally optimal $k$-partition or a locally optimal k-partition close to the global one. Since optimal partitions with 2, 3, ... clusters are determined successively in the algorithm, several well-known indexes for determining an appropriate number of clusters in a partition are adopted for this case. Thereby, the Hausdorff distance between two circles is used and adopted. The proposed method and algorithm are illustrated and tested on several numerical examples.
7. T. Marošević, R. Scitovski, Multiple ellipse fitting by center-based clustering, Croatian Operational Research Review 6/1 (2015), 43-53
   Abstract

   This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is represented by the corresponding Mahalanobis circle-center. The distance from a point a∈R^2 to the Mahalanobis circle is based on the algebraic criterion. The well-known k-means algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circle-centers. Several numerical examples are used to illustrate the proposed algorithm.
8. T. Marošević, Data clustering for circle detection, Croatian Operational Research Review 5/1 (2014), 15-24
   Abstract

   This paper considers multiple-circle detection problem on the basis of given data. The problem is being solved by application of center-based clustering method. For the purpose of searching a locally optimal partition, modeled on a well-known $k$-means algorithm, $k$-closest circles algorithm has been constructed. The method has been illustrated with several numerical examples.
9. T. Marošević, K. Sabo, P. Taler, A mathematical model for uniform distribution voters per constituencies, Croatian Operational Research Review 4 (2013), 63-64
   Abstract

   This paper presents two different approaches on the basis of which it is possible to generate constituencies. The first one is based on cluster analysis by means of which one can get compact constituencies having an approximately equal number of voters. An optimal number of constituencies can be obtained by using this method. The second approach is based on partitioning the country to several areas with respect to territorial integrity of bigger administrative units. Natural units obtained in this way will represent constituencies which do not necessarily have to have an approximately equal number of voters. Each constituency is associated with a number of representatives that is proportional to its number of voters, so the problem is reduced to the integer approximation problem. Finally, these two approaches are combined and applied on the Republic of Croatia.
10. T. Marošević, R. Scitovski, An application of a few inequalities among sequences in electoral systems, Applied mathematics and computation 194 (2007), 480-485
    Abstract

    We look at the concept of ‘favouring large states’ for divisor methods in proportional electoral systems, which is based on the comparison of the ratios of divisors. We show that it is possible in the ordered way to insert new divisor methods between any two divisor methods which have the property that one ‘favours large states’ over the other. It follows from a few sequences’ inequalities of the harmonic, geometric, arithmetic and quadratic means.
11. T. Marošević, Over- and Underrepresentation in Proportional Electoral Systems - an Empirical Study, Mathematical Communications - Supplement 1 (2001), 33-41
12. D. Jukić, T. Marošević, R. Scitovski, Discrete total lp-norm approximation problem for the exponential function, Applied mathematics and computation 94/2-3 (1998), 137-143
    Abstract

    In this paper we consider the total lp-norm (p > 0) approximation problem for the exponential function. We give sufficient conditions which guarantee the existence of such optimal parameters.
13. T. Marošević, D. Jukić, Least orthogonal absolute deviations problem for exponential function, Student 2/2 (1997), 131-138
    Abstract

    We consider the existence problem of the optimal parameters for the exponential function, in the sense of the least orthogonal absolute deviations, and prove the existence of such optimal parameters for monotic data.
14. T. Marošević, Least orthogonal absolute deviations problem for generalized logistic function, Mathematical Communications 2 (1997), 135-141

1. D. Jukić, T. Marošević, Least squares fitting problem for the power-law regression with a location parameter, 18th International Conference on Operational Research, KOI 2020, Šibenik, 2020
2. T. Marošević, J. Miletić, M. Miloloža Pandur, Use of several inequalities in the comparison of proportional electoral methods, Book of Abstracts 17th International Conference on Operational Research, KOI 2018, Zadar, Croatia, 2018
3. T. Marošević, On directional bias of the Lp-norm, Conference on Applied Mathematics and Scientific Computing 2001, Dubrovnik, 2003, 229-235
4. T. Marošević, D. Šterc, On estimating distances by means of Lp-norms, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 195-199
5. T. Marošević, Estimation of optimal parameters of generalized logistic model--function in the discrete Lp norm, 7th International Conference on Operational Research KOI 1998, Rovinj, 1999, 247-256
6. T. Marošević, I. Bašić, Primjena dviju inačica metode najmanjih kvadrata u ispitivanju električnih strojeva, 6th International Conference on Operational Research KOI 1996, Rovinj, 1996, 69-74
7. R. Scitovski, T. Marošević, D. Jukić, Estimation of the optimal initial conditions in mathematical model, 17th Int. Conf. Information Technology Interfaces, Cavtat, 1995, 475-480
8. R. Galić, R. Scitovski, T. Marošević, D. Jukić, Problem optimalnih početnih uvjeta u matematičkom modelu, 5th Conference on Operational Research KOI 1995, Rab, 1995, 62-71
9. R. Galić, R. Scitovski, T. Marošević, Primjena pomične metode najmanjih kvadrata za rješavanje problema identifikacije parametara u matematičkom modelu, 4th Conference on Operational Research KOI 1994, Rab, 1994, 181-191
10. D. Sobol, T. Marošević, Procjena nula u dijagramu zračenja adaptivnih antenskih sustava, 33. Simpozij ETAN u pomorstvu, Zadar, 1991, 283-286

1. T. Marošević, M. Šarić, O indeksima snage u sustavima glasovanja da-ne, Math.e : hrvatski matematički elektronski časopis 36/1 (2019), 1-12
   Abstract

   U sustavima glasovanja da-ne, ”igrači” (primjerice, stranke u parlamentu) imaju određeni utjecaj na donošenje nekih odluka. U tim situacijama glasovanja, kod kojih je potrebna većina glasova za prihvaćanje odluke, može se razmatrati pitanje snage pojedinih stranaka (odnosno ”igrača”). Postoji više različitih indeksa snage, od kojih nekoliko poznatih opisujemo u ovom članku, primjerice Shapley-Shubik indeks, Banzhaf indeks, Johnston indeks, Deegan-Packel indeks. Radi ilustracije, promatramo te indekse snage u nekoliko primjera i u slučaju Europskog parlamenta.
2. T. Marošević, I. Soldo, Kako se mjeri snaga stranaka u parlamentu (2016)
   Abstract

   U članku su prikazani neki kvantitativni (brojčani) pokazatelji političke snage u sustavu glasovanja DA-NE : Shapley-Shubik indeks, Banzhaf indeks i Deegan-Packel indeks. Za ilustraciju tih indeksa navedeno je nekoliko primjera. Web strana: www.glas-slavonije.hr/sglasnik/sveucilisni-glasnik-18.pdf
3. T. Marošević, O metodama raspodjele mjesta u razmjernim izbornim sustavima, Osječki matematički list 1 (2001), 29-33
4. T. Marošević, A choice of norm in discrete approximation, Mathematical Communications 1 (1996), 147-152
5. T. Marošević, Nonparametric Regression -- Some Approaches, Mathematical Communications 1 (1996), 43-50
6. T. Marošević, Verižni razlomci i fizika, Matka 5 (1996), 7-11
7. T. Marošević, O metodama za rješavanje rijetkih nelinearnih sustava jednadžbi, Tehnički vjesnik 2/3-4 (1995), 33-40
8. T. Marošević, Verižni razlomci, Matka 4 (1995), 127-132

Projects

• Parameter estimation in mathematical models (0235001)       Project leader: prof.dr.sc. Rudolf Scitovski, Dept. of Mathematics, University of Osijek (Ministry of Science, Education and Sport of the Republic of Croatia, 2002-2006), investigator

• Parameter identification problems in mathematical models (165021) (Department of Mathematics, University of Osijek; – Ministry of Science and Technology), investigator

• Application of numerical and finite mathematics                                         (1-01-129)  (Faculty of Electrical Engineering, University of Osijek;  – Ministry of Science, Technology and Computing), investigator

Professional Activities

• Osječki matematički list

• Mathematical Reviews

• Osječki matematički list

Teaching

Konzultacije (Office Hours): ponedjeljak (Mon) u 10:45 – 11:30 . Također, konzultacije su moguće i po dogovoru.

Teme diplomskih radova:    pdf

Nastava u akad.god. 2023./2024.:

Povijest matematike

Primjene diferencijalnog i integralnog računa II

Matematički aspekti izbornih sustava

Diferencijalni račun   (Odjel za fiziku  Sveučilišta u Osijeku)

Matematika III  (Fakultet elektrotehnike, računarstva i informacijskih tehnologija u Osijeku)

Matematika II  (Prehrambeno-tehnološki fakultet u Osijeku)