My publications list on:

## Current and past research

- Static deformation of rods and structures --- Applied Math
(pdf)*Tambača, Josip; Kosor, Mate; Čanić, Sunčica; Paniagua, David. Mathematical Modeling of Vascular Stents. // SIAM journal on applied mathematics. 70 (2010), 6; 1922-1952 (journal article).*We used linear rod model to model the strut, then joined many struts into a structure: stent that is used in medicine. The novel idea is to model a stent with 1D equations, as opposed to 3D models used before. This results in a much faster simulation, the execution time is order of the magnitude smaller. The model is static and because of the linearity the mathematical properties are classical for the theory of ordinary differential equations. Because of the linearity the model can be used for small deformations only.

(pdf)*Tambača, Josip; Čanić, Sunčica; Kosor, Mate; Fish, R. David; Paniagua, David. Mechanical Behavior of Fully Expanded Commercially Available Endovascular Coronary Stents. // Texas Heart Institute journal. 38 (2011), 5; 491-501 (journal article).*This paper shows the results of computer simulations that use the linear stent model in order to predict the mechanical properties of a stent design. We have studied few commercially available stents and the properties predicted by the model are in accord with clinical observations.

(pdf)*Kosor, Mate. Static model of stent based on the model of nonlinear hyperelastic rod. // Faculty of Science. University of Zagreb. 2014. (dissertation)*We developed a new, nonlinear stent model. Existing nonlinear rod model has been generalized to curves that lack smoothness. Then the new rod model has been applied to stents in a way similar our previous work. The new stent model can actually be applied to structures composed from rod like elements that can be found in various disciplines: for example to buildings. Because of the nonlinearity it is believed that for large deformations this new model is more accurate than the linear model. Nonlinearity also makes it mathematicaly nontrivial. We had to compile quite a few results (even some new) from distinct branches of mathematics in order to explain the properties if this model. The disertation is in Croatian language.

*Kosor, Mate; Tambača, Josip. Nonlinear bending-torsion model for curved rods with little regularity. // Mathematics and Mechanics of Solids. Published Online First*The article contains the generalization of the nonlinear rod model that I did as a part of my doctoral disertation.

- Economy of the public sector
(pdf)*Kosor, Mate. A review of the proposed motorway monetisation in Croatia. // Oeconomica Jadertina. 3 (2013), 2; 90-123 (preliminary note).*The article is published in Croatian, and English translation is provided in order to improve scholar visibility.

The Government of the Republic of Croatia requested from an advisor to carry out a study on the monetization of the public motorways. The stated reasons of the monetization are the raising of the funds for new state investments, the solving of the high indebtedness of the public motorways and the reduction of the public debt. The advisor suggested that the best option is to let highways to a private partner in a long-term concession. Apart from leasing the motorways under concession, the other options of monetization have not been thoroughly examined. We analyse the report of the monetization advisor and first point at the significant oversights that reduced the indicative amount of the monetization. The monetization cost was compared to the interest rate of the credit indebtedness. According to the comparable transactions, we list and evaluate some significant risks of the proposed model. In the second part, the operations of the motorways in Croatia and neighbouring countries are compared, thus showing that the operations can be run more efficiently. We indicate the significant financial potential and the value of the highways infrastructure. The financial state of the motorways is the consequence of bad investments and management and the proposed monetization model functions so that the current state of the government competence is projected in future and cemented for a long period. We offer a new model of motorways management.

- Other
*Goldstein, Pavle; Karaga, Maja; Kosor, Mate; Nižetić, Ivana; Tadić, Marija; Vlah, Domagoj. Hidden Markov Models and Multiple Alignments of Protein Sequences // Proceedings of the Conference Applied Mathematics and Scientific Computing / Drmač, Zlatko ; Marušić, Miljenko ; Tutek, Zvonimir (ur.). Berlin : Springer, 2005. (international peer-reviewed conference paper).*I was a part of this project as a student on the undergraduate level. We tried to model the proteins families according to the sequence of amino-acids in the chain. The goal was the method to group proteins in clusters and determine the "distance metric" among the proteins. We used the mathematical apparatus of Markov chains. My part in the project was to develop the computer program that was used for testing and tuning of the model.

(pdf)*Kosor, Mate. Orthogonal Projection of a Cone in Real Hilbert Spaces // Rad HAZU, Matematičke znanosti. 523=19 (2015); 13-26 (journal article)*Given the position of one vector and the angle, this investigates the angles between the components of the given vector and another unknown vector that closes the given angle with the given vector. As the given vector and the given angle define the cone, this can be recast as investigating the projection of the cone. In what is yet another interpretation of the same results, this is related to new contributions to Cauchy-Bunyakowski-Schwarz type inequalities.