Mathematical Research Seminar - Archive
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This paper discusses the political donations - public procurement interplay. It rests on a unique and comprehensive hand-collected firm-by-tender micro-level dataset that enables the assessment of partisan favouritism in procuring goods, services and work by the Croatian government in the 2012-2018 period. Main results show that (i) political donations pay off and a ten percent increase in political donations leads to an increase in public procurement revenues of 5.7%; (ii) political disloyalty, i.e. switching donations from centre-right to centre-left parties or vice versa, does not reimburse; (iii) big firms in Croatia are big enough to bid lower prices and/or contract better terms, such that they don’t need favouritism in public procurement awards; and (iv) political contributions ex-post election (2016-2018) increase procurement revenues of donating firms by 27%, and firms connected to the losing party exhibit a drop in procurement revenues of more than 12% compared to the ex-ante elections.
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For a graph G, and two distinct vertices u and v of G, let nG(u,v) be the number of vertices of G that are closer in G to u than to v. Miklavi\v{c} and \v{S}parl (arXiv:2011.01635v1) define the distance-unbalancedness {uB}(G) of G as the sum of |nG(u,v)-nG(v,u)| over all unordered pairs of distinct vertices u and v of G. For positive integers n up to 15, they determine the trees T of fixed order n with the smallest and the largest values of { uB}(T), respectively. While the smallest value is achieved by the star K1,n-1 for these n, the structure of the trees maximizing the distance-unbalancedness remained unclear. For n up to 15 at least, all these trees were subdivided stars. Contributing to problems posed by Miklavi\v{c} and \v{S}parl, we show that stars minimize distance-unbalancedness among all trees of a given order, that
and that
where S(n1,…,nk) is the subdivided star such that removing its center vertex leaves paths of orders n1,…,nk.
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Computer-aided geometric design (CAGD) deals with the mathematical description, and computational aspects of geometric objects, such as parametric curves and surfaces. It is a field of mathematical nature with relevant use in computer science and engineering. Approximation theory studies the process of approximating general functions by simple functions such as polynomials or splines. Therefore, it plays a central role in the analysis of numerical methods, particularly in approximation of partial differential equations. During the lecture, I will show how my research interests connect the fields of Computer-aided geometric design and Approximation theory. The following two research topics, in which I have been most active in the last decade, will be briefly presented. Parameterization of curves and surfaces are basic concepts in CAGD. In several applications, it is desirable for these curves and surfaces to have some particular properties, such as polynomial arc-length and rational offsets. A special class of curves that satisfies these requirements are Pythagorean-hodograph curves, of which the first part of my talk will be devoted. In the second part, we will get acquainted with a recent method for numerical solution of partial differential equations, i.e., Isogeometric Analysis. The main advantage of this method is in the use of the same standard CAGD spline functions both for describing the geometry and for the numerical simulation of partial differential equations. The increased smoothness of the spline functions compared to traditional finite elements allows for improved stability and convergence properties.
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We often observe that people help strangers in real life. Such altruistic behaviour is puzzling for economics and biology because it promotes the welfare of another person at a cost to oneself. It is also difficult to explain it by long-term strategic motivations when the recipient is a stranger who may not be able to return a favour. Real-life evidence does not offer many opportunities to learn about the motivations behind individual altruism, unfortunately.
In this project, we instead investigate reciprocal altruism in a laboratory experiment with people playing a long-term economic game of indirect reciprocity. This experiment provides sufficiently detailed data about motivations for altruism to facilitate the classification of almost 90% of participants into several theoretically feasible strategies. For this, we apply a recently developed statistical method to our indirect reciprocity experiment. We compare the resulting classification to the classifications of three other existing methods in the literature and demonstrate that it is the closest to a consensus measure. We then show how the other three existing methods ignore a learning strategy that is used by almost half of the subjects in one of our experimental treatments. Finally, we compare the strategy classification to people's self-reports and show that these are a very unreliable source of data about individual motivations for altruism.
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