This diploma thesis is focused on the description and implementation of the user interface for the analysis of local DNA structures as a web application in the Vue.js framework. The local structure can be described as an alternative DNA structure which arises in a specific DNA sequence that occurs in important regions of the genome. The first part of the thesis is theoretical and examines the field of DNA research and a description of selected technologies. The second part deals with the implementation and testing of the user interface on specific DNA sequences.

<p>In the thesis we are concerned with actual problems on palindromic subwords and palindromic factors of finite and infinite words. The main course of the research are the ways of determining which of two given words is &ldquo;more palindromic&rdquo; than the other one, that is, defining a measure for the degree of &ldquo;palindromicity&rdquo; of a word. Particularly, we pay attention to two actual approaches: the so-called MP-ratio and the so-called <em>palindromic defect</em>, and answer several open questions about them.<br /><br />Namely, concerning the MP-ratio, a few plausible-looking question have been asked in the literature, which would have, if answered positively, made computations of MP-ratios significantly simpler. We add one more related question to these ones, and then show that, rather unexpectedly, all these questions have negative answer.<br /><br />Concerning the palindromic defect, the main result of this work is a construction of an infinite class of infinite words that have several properties that were sought after in some recent works in this area. Among the most interesting facts is that that all these words are aperiodic words of a finite positive defect, having the set of factors closed under reversal---in some recent works, the construction of even a single word having these properties turned out to be quite hard. Using these words, which we are calling <em>highly potential words</em>, we check the validity of several open&nbsp; conjectures, and for several of them we find out that they are false.</p> / <p> U tezi razmatramo aktuelne probleme u vezi s palindromskim podrečima i palindromskim faktorima konačnih i beskonačnih reči. Glavni pravac istraživanja jesu kriterijumi za određivanje koja od dve date reči je &bdquo;palindromičnija&ldquo; od druge, tj. određivanje stepena &bdquo;palindromičnosti&ldquo; date reči. Akcenat stavljamo na dva aktuelna pristupa: tzv. <em>MP-razmeru</em> i tzv. <em>palindromski defekt</em>, i odgovaramo na vi&scaron;e otvorenih pitanja u vezi s njima.<br /> <br /> Naime, u vezi sa MP-razmerom u literaturi je postavljeno vi&scaron;e pitanja, intuitivno uverljivih, koja bi, u slučaju pozitivnog razre&scaron;enja, znatno pojednostavila izračunavanje MP-razmere. Ovim pitanjima dodajemo jo&scaron; jedno srodno, a zatim pokazujemo da, prilično neočekivano, sva ova pitanja imaju negativan odgovor.<br /> <br /> U vezi s palindromskim defektom, glavni rezultat rada je konstrukcija beskonačne klase beskonačnih reči koje imaju vi&scaron;e osobina za kojima je iskazana potreba u skora&scaron;njim radovima iz ove oblasti. Među najzanimljivije spada činjenica da su sve aperiodične reči konačnog pozitivnog defekta, i da im je skup faktora zatvoren za preokretanje &ndash; u nekim skora&scaron;njim radovima konstrukcija makar jedne reči s ovim osobinama pokazala se kao prilično te&scaron;ka. Pomoću ovih reči, koje nazivamo <em>visokopotencijalne reči</em>, ispitujemo validnost vi&scaron;e otvorenih hipoteza, i za vi&scaron;e njih ustanovljavamo da nisu validne.</p>

<p>We focus on two complexity measures of words that are invariant under the operation of reversal of a word: the palindromic defect and the MP-ratio.The palindromic defect of a given word w is dened by jwj + 1&nbsp;&nbsp; jPal(w)j, where jPal(w)j denotes the number of palindromic factors of w. We study innite words, to which this de&nbsp; nition can be naturally extended. There are many results in the literature about the so- called rich words (words&nbsp; of defect 0), while words of nite positive defect have been studied signicantly less; for some time (until recently) it was not known whether there even exist such words that additionally are aperiodic and have their set of factors closed under reversal. Among the rst examples that appeared were the so-called highly potential words. In this&nbsp; thesis we present a much more general construction,which gives a wider class of words, named generalized highly potential words, and analyze their signicance within the frames of combinatorics on words.The MP-ratio of a given n-ary&nbsp; word w is dened as the quotient jrwsj jwj ,where r and s are words such that the word rws is minimal- palindromic and that the length jrj + jsj is minimal possible; here, an n-ary word is called minimal-palindromic if it does not contain palindromic subwords of length greater than jwj n . In the binary case, it was proved that the MP-ratio is well-dened and that it is bounded from above by 4, which is the best possible upper bound. The question of well- denedness of the MP-ratio for larger alphabets was left open. In this thesis we solve that&nbsp; question in the ternary case: we show that the MP-ratio is indeed well-dened in the ternary case, that it is bounded from above by the constant 6 and that this is the best possible upper bound.</p> / <p>Izucavamo dve mere slozenosti reci koje su invarijantne u odnosu na operaciju preokretanja reci: palindromski defekt i MP-razmeru date reci.Palindromski defekt reci w denise se kao jwj + 1&nbsp;&nbsp; jPal(w)j, gde jPal(w)j predstavlja broj palindromskih faktora reci w. Mi izucavamo beskonacne reci, na koje se ova denicija moze prirodno prosiriti. Postoje mnogobrojni rezultati u vezi sa tzv. bogatim recima (reci cije je defekt 0), dok se o recima sa konacnim pozitivnim defektom relativno malo zna; tokom jednog perioda (donedavno) nije bilo poznato ni da li uopste postoje takve reci koje su,dodatno, aperiodi cne i imaju skup faktora zatvoren za preokretanje. Medu prvim primerima koji su se pojavili u literaturi su bile tzv. visokopotencijalne reci. U disertaciji cemo predstaviti znatno opstiju konstrukciju, kojom se dobija znacajno sira klasa reci, nazvanih uop stene visokopotencijalne reci, i analiziracemo njihov znacaj u okvirima kombinatorike na recima.MP-razmera date n-arne reci w denise se kao kolicnik jrwsj jwj , gde su r i s takve da je rec rws minimalno-palindromicna, i duzina jrj + jsj je najmanja moguca; ovde, za n-arnu rec kazemo da je minimalno-palindromicna ako ne sadrzi palindromsku podrec duzine vece od&nbsp; jwj n&nbsp; . U binarnom slucaju dokazano je da je MP-razmera dobro&nbsp; denisana i da je ogranicena odozgo konstantom 4, sto je i najbolja moguca granica. Dobra denisanost MP-razmere za vece alfabete je ostavljena kao otvoren problem. U ovoj tezi resavamo taj problem u ternarnom slucaju: pokazacemo da MP- razmera jeste dobro de-nisana u ternarnom slucaju, da je ogranicena odozgo sa 6, i da se ta granica ne moze poboljsati.<br />&nbsp;</p>