Mathematical Sciences
Subcommunities within this community
Collections in this community
Recent Submissions

Alshafah, Samira (Beograd , 2018)[more][less]
Abstract: Proteins with intrinsically disordered regions are involved in large number of key cell processes including signaling, transcription, and chromatin remodeling functions . On the other side, such proteins have been observed in people suffering from neurological and cardiovascular diseases, as well as various malignancies. Process of experimentally determining disordered regions in proteins is a very expensive and long  term process. As a consequence, a various computer programs for predicting position of disordered regions in proteins have been developed and constantly improved. In this thesis a new method for determining Amino acid sequences that characterize ordered/disordered regions is presented. Material used in research includes 4076 viruses wit h more than 190000 proteins. Proposed method is based on defining correspondence between n grams (including both repeats and palindromic sequence s) characteristics and their belonging to ordered/disordered protein regions. Positions of ordered/disordered regions are predicted using three different predictors. The features of the repetitive strings used in the research include mol e fractions, fract ional differences, and z values. Also, data mining techniques association rules and classification were applied on both repeats and palindromes. The results obtained by all techniques show a high level of agreement for a short length of less than 6, while the level of agreement grows up to the maximum with increasing the length of the sequences. The high reliability of the results obtained by the data mining techniques shows that there are n grams, both repeating sequences and palindromes, which uniquely ch aracterize the disordered/ ordered regions of the proteins . The obtained results were verified by comparing with the results based on n grams from the DisProt database which contain s the positions of experimentally verified disordered regions of the protein. Results can be used both for the fast localization of disordered/ordered regions in proteins as well as for further improving existing programs for their prediction. URI: http://hdl.handle.net/123456789/4746 Files in this item: 1
ThesisSamira_Alshafah.pdf ( 3.106Mb ) 
Makragić, Milica (Beograd , 2018)[more][less]
Abstract: This doctoral dissertation comprises two parts. Trigonometric polynomial rings are the central topic of the first part of the dissertation. It is presented that the ring of complex trigonometric polynomials, C [cos x, sin x ], is a unique factorization domain, and that the ring of real trigonometric polynomials, R [cos x, sin x ], is not a unique factorization domain. Necessary and sufficient conditions for the case when in the ring C [cos x, sin x ], unlike the ring R [cos x, sin x ], the degree of the product of two trigonometric polynomials is not equal to the sum of degrees of its factors, are given. The theory of trigonometric polynomials is extended to hyperbolictrigonometric polynomials, or HTpolynomials for short, which are defined similarly to trigonome tric polynomials. Real or complex HTpolynomials form a ring and even an integral domain R [cosh x, sinh x ], or C [cosh x, sinh x ]. Factorization in these domains is con sidered, and it is shown that these are unique factorization domains. The irreducible elements, as well as the form of the maximal ideals of both these domains are deter mined. The algorithms for dividing, factoring, computing greatest common divisors, as well as the algorithms for simplifying ratios of two HTpolynomials are considered over the field of rational numbers. In the second part of the dissertation, related to applications, two methods of proving inequalities of the form f ( x ) > 0 are described over the given finite in terval ( a,b ) ⊂ R , a ≤ 0 ≤ b , which by using the finite Maclaurin series expan sion generate polynomial approximations, when the function f ( x ) is element of the ring extension of R [cos x, sin x ], or R [cosh x, sinh x ], denoted by R [ x, cos x, sin x ], or R [ x, cosh x, sinh x ]. The completeness of the presented methods is proved and the concrete results of these methods are illustrated through examples of proving actual inequalities. URI: http://hdl.handle.net/123456789/4745 Files in this item: 1
Disertacija_Milica_Makragic.pdf ( 2.169Mb ) 
Đenić, Aleksandar (Beograd , 2018)[more][less]
Abstract: This pap er considers two discrete lo cation problems: Bus Terminal Lo cation Problem (BTLP) and Longterm Care Facility Lo cation Problem (LTCFLP). Vari able Neighb orho o d Search (VNS) metho d for solving BTLP and LTCFLP is pre sented in this pap er. VNS is a singlesolution based metaheuristic based on system atic change of neighb orho o ds while searching for optimal solution of the problem. It consists two main phases: shake phase and lo cal search phase. BTLP is a discrete lo cation problem which considers lo cating bus terminals in order to provide the highest p ossible quality of public service to the clients. Clients are presented as public transp ortation stations, such as bus or metro stations. VNS algorithm is used for solving BTLP. This algorithm uses improved lo cal search based on e cient neighb orho o d interchange. VNS is parallelized (PVNS) which leads to signi cant time improvement in function of the pro cessor core count. Computa tional results show that prop osed PVNS metho d improves existing results from the literature in terms of quality. Larger instances, based on instances from the Trav eling Salesman Problem library, are presented and computational results for those instances are rep orted. LTCFLP is created as a part of health care infrastructure planning in South Korea. Clients are considered as groups of patients with a need of longterm health care, while established facilities present lo cations where the centers that provide health care services should b e built. Prede ned are n lo cations where centers are to b e established. This problem seeks at most K lo cations to establish health centers so they are to b e equally loaded with clients demand. For solving LTCFLP, by using VNS algorithm, data structure based on fast interchange is presented. It reduces the time complexity of one iteration of lo cal search algorithm to O ( n · max( n,K 2 )) comparing to the known time complexity from the literature O ( K 2 · n 2 ) . Reduced time complexity of the presented VNS leads to b etter quality solutions, due to larger numb er of VNS iterations that can b e p erformed in less computational time. This pap er presents computational results that outp erform the b est known results from the literature. URI: http://hdl.handle.net/123456789/4744 Files in this item: 1
Aleksandar_Djenic_phd.pdf ( 2.183Mb ) 
Acketa, D,; Tošić, R.; Batagalj, V,; Cvetković, D.; Torgašev, A.; Doob, M.; Gutman, I.; Radosavljević, Z.; Djoković, D. Ž.; Farrell, E. J.; Harary, F.; Schmidt, R.; Katona, G. C. H.; Mohar, B.; Pisanski, T.; Petkovšek, M. (Mathematical Institute Novi Sad , 1984)[more][less]

Paunić, Đura; Tošić, Ratko (Mathematical Institute Novi Sad , 1992)[more][less]