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In this thesis we will analyze the k-Partition Problem. Specifically, we will analyze the five best algorithms for solving the Partition Problem, after which we will analyze five new algorithms for solving the k-Partition Problem. Two of these algorithms will be my contribution towards both problems. After we have understood how each algorithm works, we will test them among each other in order to figure out which algorithm is the fastest and why. We will also consider each algorithm's accuracy, since some algorithms trade their speed for precision. There will be a total of 70 test cases used throughout the testing phase. Some test cases will be random, and others specifically used as difficult test cases in regards to certain algorithms. Finally, we will shed light on the difference between theory and practice, that is, to the algorithms time complexities and their execution time. The goal of the thesis is not to find the fastest algorithm, but rather to analyze each of the algorithms and understand which of them is best suited for a given situation. V magisterskem delu bomo analizirali posplošeni problem razdelitve. Analizirali bomo pet najboljših algoritmov za reševanje problema razdelitve in pet novih algoritmov za reševanje posplošenega problema razdelitve. Dva izmed analiziranih algoritmov bosta prispevek k osnovnemu, pa tudi posplošenemu problemu razdelitve. Ko bomo razumeli, kako delujejo posamezni algoritmi, jih bomo testirali in paroma primerjali, da bi ugotovili, kateri je najhitrejši in zakaj. Upoštevali bomo tudi natančnost vsakega algoritma, saj nekateri algoritmi žrtvujejo svojo hitrost za natančnejšo rešitev. V fazi testiranja bo skupno uporabljenih 70 testnih primerov. Nekateri bodo naključni, nekateri pa specifično uporabljeni kot težki testni primeri za določene algoritme. Nazadnje bomo pokazali na razliko med teorijo in prakso med asimptotično časovno zahtevnostjo algoritmov in njihovo dejansko hitrostjo (v praksi). Cilj diplomske naloge ni najti najhitrejši algoritem, temveč analizirati vsakega od algoritmov in razumeti, kateri algoritem je najboljši za posamezno situacijo.

Področje stiskanja podatkov predstavlja eno izmed pomembnejših vej v informacijski teoriji. Stremi k reduciranju količine podatkov za zapis oziroma prenos neke informacije. V diplomski nalogi so na kratko predstavljeni osnovni algoritmi in principi stiskanja. Kasneje se osredotočimo na algoritem Lempel-Ziv-Welch, ki za stiskanje uporablja slovar in algoritem Huffman, ki za namene stiskanja uporablja statistiko. Oba našteta algoritma nato tudi implementiramo. Za izpeljavo tega uporabimo programski jezik C in operacijski sistem Linux. Da bi bila uporaba implementacije čim enostavnejša, s pomočjo odprtokodne knjižnice GTK ustvarimo preprost uporabniški vmesnik. V zaključni fazi algoritma preizkusimo na nekaj različnih primerih podatkov, npr. besedilo, slika, binarna datoteka, ipd., in vzporedno beležimo rezultate za kasnejšo analizo. Data compression represents one of the most important fields of information theory. It seeks to reduce the quantity of data used to store or transmit information. The thesis starts with a brief description of algorithms and principles used for data compression. Continues with the main focus on two algorithms – Lempel-Ziv-Welch and Huffman, where each one represents a different type of compression technique. Algorithms are then implemented in the C programming language. In order to make implementation simple to use, a graphical interface is designed with the help of the GTK open source library. Finally, both algorithms are tested on several types of files such as text, image, binary file, etc. Results are then used for a more in-depth analysis.

Herein, we report a computational algorithm that follows a spectroscopist-driven elucidation process of the structure of an organic molecule based on IR, $^1$H and $^{13}$C NMR, and MS tabular data. The algorithm is independent from database searching and is based on a bottom-up approach, building the molecular structure from small structural fragments visible in spectra. It employs an analytical combinatorial approach with a graph search technique to determine the connectivity of structural fragments that is based on the analysis of the NMR spectra, to connect the identified structural fragments into a molecular structure. After the process is completed, the interface lists the compound candidates, which are visualized by the WolframAlpha computational knowledge engine within the interface. The candidates are ranked according to the predefined rules for analyzing the spectral data. The developed elucidator has a user-friendly web interface and is publicly available (http://schmarnica. si).

Kakšna je prihodnost sodnih postopkov glede na vse hitrejši tehnološki napredek? Ali je širša mednarodna skupnost oblikovala pravne in etične standarde za uspešno in varno algoritemsko sodno odločanje in v katerih regulativnih dokumentih so zajeti? Kakšne so možne oblike uporabe orodij umetne inteligence v postopkih sodnega odločanja? Ali obstojijo primeri dobrih in slabih praks nadomestitve človeških sodnikov z robotskimi, katere lahko deležniki umetne inteligence uporabijo kot izhodišče za nadaljnji razvoj in uporabo tega tehnološkega orodja v sodnih dvoranah? Na varstvo katerih temeljnih človekovih pravic in svoboščin udeležencev postopka ter pravnih načel bodo vplivali robotski sodniki? Katere so ključne dileme, ki se porajajo ob misli na kibernetsko pravosodje? V magistrskem diplomskem delu podajam odgovore na zgoraj zastavljena vprašanja, ki privedejo do zaključka, da orodja umetne inteligence vsekakor ne bodo zmožna v popolnosti nadomestiti človeških odločevalcev, vendar pa bodo zaradi svojih karakteristik predstavljala še kako dobrodošlo dopolnilo in korekcijo pomanjkljivosti obstoječega načina sodnega odločanja. What is the future of judicial proceedings in the face of accelerating technological progress? Has the wider international community developed legal and ethical standards for successful and secure algorithmic adjudication, and what regulatory documents cover them? What are the possible applications of AI tools in judicial decision-making processes? Are there examples of good and bad practices of replacing human judges with robotic ones that AI stakeholders can use as a starting point for further development and use of this technological tool in courtrooms? Which fundamental human rights and freedoms of the participants in the proceedings and which legal principles robotic judges will affect? What are the key dilemmas that arise when thinking about cyber justice? In my Master's thesis, I provide answers to the above questions, which lead to the conclusion that AI tools will certainly not be able to fully replace human decision-makers, but their characteristics will make them a welcome complement and correction to the shortcomings of the existing way of judicial decision-making.

V zaključni nalogi bo predstavljena sestava in delovanje FPGA vezja, njegove prednosti in razlogi za uporabo v primerjavi z ostalimi vezji, postopek programiranja FPGA-ja in pa moˇznosti uporabe v industriji, s poudarkom na uporabi strojnega vida . Predstavljen bo tudi lasten enostaven primer uporabe FPGA-ja za namen strojnega vida in postopek kako lahko sami uporabimo FPGA vezje v namene tega. The thesis will present the composition and operations of the FPGA circuit, its advantages and reasons for use compared to other circuits, the FPGA programming process and the possibilities of use in industry, with an emphasis on the usage of machine vision. We will also present our own simple example of using FPGA for the purpose of machine vision and the process of how we can use the FPGA circuit for this purpose.

V tem diplomskem delu se bomo seznanili z osnovami anatomije in fiziologije električnega prevodnega sistema v človeškem srcu ter z umestitvijo in vlogo Hisovega snopa v njem. Seznanili se bomo tudi z načinom zajema unipolarnih in bipolarnih signalov električne aktivnosti srca – elektrokardiograma (EKG), ter znotrajsrčnega elektrograma (iEGM). Vse zbrane podatke za obdelavo tovrstnih signalov (s poudarkom na specifiki aktivnosti Hisovega snopa) bomo uporabili za razvoj in preizkus algoritma za detekcijo aktivnosti Hisovega snopa. Naloga tega diplomskega dela je detekcija trenutka aktivacije Hisovega snopa v posnetku znotrajsrčnega elektrograma (iEGM). Aktivnost Hisovega snopa ne moremo videti v katerem koli posnetku iEGM – vidi se samo v tistem, ki ga posnamemo v neposredni bližini Hisovega snopa znotraj srca. Pri tem načinu zajemanja iEGM lahko pride do različnih problemov, ker Hisov snop predstavlja majhen skup celic, in je njegova aktivnost zelo kratek pojav. Poleg tega je v tem signalu vedno prisotna električna aktivnost drugih delov srca, kar predstavlja motnjo in izziv za detekcijo aktivnosti Hisovega snopa. The thesis addresses basics of anatomy and physiology of electrical conduction system in the human heart and the placement and the role of the His bundle in it. We will also get acquainted with the method of capturing unipolar and bipolar signals of electrical activity of the heart - the electrocardiogram (ECG) and the intracardiac electrogram (iEGM). All data collected for the processing of such signals (with emphasis on the specifics of His bundle activity) will be used to develop and test an algorithm for detecting His bundle activity. The task of this thesis is the detection of the activation moment of the His bundle in the recording of the intracardiac electrogram (iEGM). His bundle activity cannot be seen in just any iEGM recording – it is only seen in the one taken in close proximity to the His bundle inside the heart. Various problems can arise with this method of iEGM capture because the His bundle represents a small set of cells and its activity is a very brief phenomenon. Electrical activity of other parts of the heart also appears in this signal, which is a disturbance and makes the detection of His bundle activity a challenge.

V tem dokumentu je predstavljeno zaključno diplomsko delo z naslovom: Uporaba hranilnikov električne energije za povečanje samooskrbe gospodinjstva. Namen diplomskega dela je predstaviti težave sončnih elektrarn, ki jih uporabljajo gospodinjstva, in ponuditi možne rešitve. V Sloveniji imamo velik delež sončnih elektrarn na strehi in v zadnjih letih se je povpraševanje za njih še povečalo. Za gospodinjstvo imamo na voljo dva različna sistema sončnih elektrarn. Način proizvodnje se ne spremeni, razlika je v načinu shranjevanja proizvedene energije. To sta otočno delovanje in delovanje po neto meritvah (v nadaljevanju net metering). Net metering sistem sončne elektrarne ne vsebuje lokalnega hranilnika električne energije. Presežek proizvedene električne energije zato pošilja v omrežje, kar pa povzroča dvigovanje napetosti na distribuciji in se nato odraža kot velik problem za operaterje omrežja, ki morajo vsem odjemalcem zagotavljati visoko kakovost oskrbe z električno energijo. Sončna elektrarna na princip delovanja net metering tako vpliva na celotno omrežje, saj je z njim povezana. Otočno delovanje je ločeno in ne povzroča teh problemov, vendar pa je potrebno pri samostojni proizvodnji in porabi električne energije imeti hranilnik energije, saj nimamo konstantne proizvodnje s sončnimi elektrarnami. Sončne elektrarne delujejo le podnevi ob določenih vremenskih pogojih, ki so ugodni za proizvodnjo – sončno vreme, brez oblačnosti in zmerne temperature. Previsoke temperature na proizvodnjo vplivajo negativno. Za ta namen sem izdelal algoritem, ki preračuna potrebno kapaciteto hranilnika, ki ga potrebujemo za samostojno obratovanje nekega gospodinjstva. Preko algoritma dokažemo, da se samooskrbno delovanje v Sloveniji za navadnega gospodinjskega odjemalca ekonomsko in tehnično ne izplača, je pa ekonomsko in tehnično izvedljivo delovanje v določenem času leta. This thesis describes the problem of having a big percentage of solar plants on the grid. It can cause problems like high saturating of the grid. It can create situations that forces grid operators to change and downgrade power of plants that are controllable. That results in change quality of electric energy. We can change this by changing these plants from Net metering to off grid plants. But for them to be able to work through all year we must know how much of batteries we must install. For that reason, I designed an algorithm that calculates this. It can calculate for whole year, and it can be changed to calculate for bigger or smaller time window. This thesis contain description why there is not economically speaking good to have off grid solar plant for one consumer. However, that fact there is one option where off grid is economical and even better than being connected to the grid. We can say with certain that having a solar panel is creating new challenges for energy engineer but there are solutions that are in place to prevent any big problem. In developing a high percentage of green energy production there must be place for solar plants.

Problemi pakiranja se pogosto uporabljajo v računalništvu, zaradi tega obstaja veliko načinov, na katerih jih je mogoče rešiti. Diplomska naloga se ukvarja z zelo specifičnim problemom pakiranja. Za toplotno obdelavo želimo optimalno spakirati določeno število mrež vijakov z uporabo natančnega števila škatel. Problem smo formalno zapisali dvonivojsko, kot problem pakiranja košev in problem več nahrbtnikov. Za njegovo reševanje sta uporabljena dva reševalnika OR-Toolsa. Prvi reševalnik je namenjen reševanju problema pakiranja košev, drugi reševanju problema več nahrbtnikov. Rezultate obeh reševalnikov smo glede časa izvajanja in števila optimalnih rešitev primerjali med seboj. Packing problems have many applications in computer science. For this reason, there are numerous ways in which they can be solved. This thesis concerns a very specific packing problem. We want to optimally pack several screw grids into a finite number of boxes. Firstly, the problem was written as a multiple knapsack problem and as a bin packing problem. Secondly, we used two OR-Tools solvers to solve it. One is designed for solving multiple knapsack problems and the other is for solving bin packing problems. Lastly, we compared the results in terms of their execution time and the number of optimal solutions.

Magistrsko diplomsko delo obravnava predstavitev pojma umetne inteligence, njeno vedno pogostejšo uporabo na najrazličnejših področjih, med drugim tudi na področju prava, natančneje pri razlagi pravnih aktov. V navezavi z navedenim so opisana teoretična izhodišča razlage pravnih aktov, in sicer s poudarkom na vrstah in metodah razlage. Nadalje so navedeni in opisani sistemi umetne inteligence, ki se danes že uporabljajo kot pomožno orodje pri razlagi pravnih aktov, kot sta algoritmski sistem in strojno učenje, pri čemer so predstavljeni tudi razlogi in pomisleki, zakaj umetna inteligenca sama (vsaj zaenkrat) še ne more biti uporabljena kot samostojen subjekt razlage, na osnovi česar bi lahko generirala samostojno sprejeto pravno zavezujočo odločitev. V zadnjem delu je obravnavana uporaba umetne inteligence pri razlagi pravnih aktov skozi prizmo etičnih načel in človekovih pravic, prav tako tudi vprašanje zadostitve potrebe po zagotavljanju ustrezno podane obrazložitve sprejetih odločitev. Ker so osnova za delovanje sistemov umetne inteligence najrazličnejše in obsežne baze podatkov, je izpostavljena tudi potreba po ustrezni obdelavi in hrambi osebnih podatkov, ki jih njeni sistemi uporabljajo, pri čemer je opravljena analiza ustreznih pravnih aktov, ki slednje urejajo na nacionalni in mednarodni ravni. Na osnovi v celoti pojasnjenega so v zaključku podane sklepne ugotovitve o pomenu ustrezno izluščene razlage pravnih aktov, dejanski uporabnosti umetne inteligence na področju razlage pravnih aktov, kot tudi na širšem področju prava v praksi in vpliva, ki ga bo umetna inteligenca imela na pravniške poklice v prihodnosti. This thesis presents the concept of artificial intelligence, its increasingly frequent use in a wide variety of fields, including in the field of law and in the interpretation of legal acts. In connection with the above, the theoretical starting points of the interpretation of legal acts are described, namely with an emphasis on the types and methods of interpretation. Furthermore, artificial intelligence systems are listed and described, which are already used today as an auxiliary tool in the interpretation of legal acts, such as algorithmic systems and machine learning, while also presenting the reasons and concerns why artificial intelligence alone (at least for the time being) cannot yet be used as an independent subject of interpretation which could generate an independently adopted legally binding decision. The last part deals with the use of artificial intelligence in the interpretation of legal acts through the prism of ethical principles and human rights, as well as the issue of meeting the need to provide an adequately explained rationale for the decisions made. Since the basis for the operation of artificial intelligence systems are the most diverse and extensive databases, the need for appropriate processing and storage of personal data used by its systems is also highlighted, with an analysis of the relevant legal acts that regulate the latter, both nationally and international level. The conclusion is about the importance of an adequately extracted interpretation of legal acts, the actual usefulness of artificial intelligence in the field of interpretation of legal acts, as well as in the wider field of law in practice and the impact that artificial intelligence will have on the legal professions in the future.

V diplomski nalogi je opisan postopek razvijanja algoritmov, ki napovedujejo prekritost sonca z oblaki. V času ogromnega naraščanja števila elektrarn na omrežju, ki jih poganjajo obnovljivi viri, postaja izjemno pomembno tudi kratkoročno napovedovanje proizvodnje električne energije. Prav tako pa je kratkoročno napovedovanje temelj za trgovanje z energenti, predvsem na krajši rok. V nalogi iščemo rešitev specifično za sončne elektrarne, ki za omrežje, v večjem številu, predstavljajo veliko obremenitev. Program pa najde svoje mesto tudi pri trgovcih z energenti. Naloga detajlno opisuje vsak del algoritma. Prvo opisujemo postopek kalibracije kamere oz. pridobivanje parametrov za namen preslikave iz polkrogle, ki jo predstavlja nebo na ravno površino. Naslednji korak pri izdelavi programa je bilo izkustveno določanje barvnih kriterijev, pod katere spadajo oblaki in Sonce za namen programskega zaznavanja njihovih centrov. Preko zaznanih centrov oblakov in Sonca je nato nastal algoritem za sledenje objektom na nebu, preko njihovih koordinat centrov. Iz dveh zaporednih slik lahko program namreč razbere, kateri centri pripadajo istemu zaznanemu objektu, na podlagi Evklidove razdalje. Ko program zajame šest zaporednih posnetkov zaslona iz videoposnetka, program prične z napovedjo pozicij oblakov in Sonca. Medtem, ko program izvaja branje neba se koordinate centrov vseh zaznanih oblakov in Sonca shranjujejo (vsak šesti shranjeni nabor koordinat se z novim posnetkom zaslona osveži), z namenom, da te podatke naprej poda algoritmu, ki je najbolj primeren za iskanje krivulje, ki opisuje potovanje centrov oblaka ali Sonca. Opisana je tudi primerjava metod za napovedovanje, med drugimi: ARIMA, eksponentno glajenje, polinomska regresija in metoda, ki temelji na povprečju razdalj med vsemi zgodovinskimi nabori koordinat. Za najboljšo, se je po prilagoditvi njenih parametrov izkazala metoda z eksponentnim glajenjem, ki je v večini primerov lahko napovedala koordinato na piksel natančno za korak naprej (ena minuta). Program po izračunih napovedi, na posnetek zaslona nariše Sonce na napovedano koordinato in šele nato nariše še oblake na napovedane pozicije. Sonce preslika z neko barvo, ki pa se nujno razlikuje od barv, s katerimi program preslika oblake. Program na koncu preveri koliko pikslov v barvah Sonca je prisotnih in na podlagi tega izračuna prekritost. Na koncu pa program preveri še barvna razmerja pikslov oblakov, ki prekrivajo Sonce. Glede na barvna razmerja program razvrsti piksle v razred, ki procentualno opisuje ali gre za temen, delno temen ali svetel del oblaka. Prozornost oblaka pa je povprečje vseh teh vrednosti. Opisan je tudi postopek izdelave uporabniškega vmesnika. This thesis describes the development of algorithms, which can forecast the coverage of the Sun by the clouds. In times of increased renewable source installements on the grid, the importance of short term forecasting is becoming more relevant by the day, for production of electricity. It also represents the basis on which short term energy traders work on. In this diploma tehsis we are trying to find a solution spcifically for solar plants, which are capable of stressing the power grid in case of weather changes. Likewise, the program could also be useful to energy traders. This literature describes every step of the development. Firstly, camera calibration or gathering of extrinsic parameters of the camera is described, which is done to help the program remap the objects on the sky from a semicircle onto a flat surface. Next step in the development of the program was to set thresholds of HSV values for cloud and sun centre detecting purposes. With detected centres the development could then be focused on a tracking algortihms. With two consecutive screenshots of the sky, the program is able to guess which centres on both screenshots belong to the same detected object, based on Euclidian formula for distance. When the program detects and saves six consecutive collections of centres it can then start with the position forecasting of the sun and the clouds. While program is reading the video of the sky, all the centres of clouds and the sun are being recorded (every sixth list of coordinates is being updated upon arrival of new frames of the sky), for forecasting method data feeding purposes. Forecasting method was chosen based on the best curve fitting capability. Comparison of a few forecasting methods is also described, among those are: ARIMA, exponential smoothing, polynomial regression and a method which is based on the average distance between the collection of corresponnding coordinates. Best among those methods proved to be Exponential Smoothing (DES), which was able to predict the coordinates most accurately based on a one-step ahead (1 minute) test. After all the forecasting, the program draws a sun and after that it draws all the clouds onto a screenshot of the sky. Sun is drawn with a color that must be different from the colors with which the clouds are being drawn with. Program then checks how many pixels are left with the same color as the sun, to then calculate the coverage by the clouds. At the end program also iterates through every pixel that represents the clouds over the sun and calculates their color ratios. Based on those ratios it puts every pixel into one of three classes that descirbe the transparency of the cloud. One of the classes describe dark pixel, another one describes semi dark and the last one represents the light ones.Transparency is the average of all those pixels. Front-end development of the program is also described towards the end of the paper.

Umetna inteligenca vedno bolj kroji naša življenja. Zagon, ki ga prinaša pandemija COVID-19 in inflacija novih tehnologij, se prenašata tudi v sodne sisteme. Vprašanje, ki si ga upravičeno lahko zastavimo, je, ali bo umetna inteligenca sodniku samo v pomoč ali pa ga bo tudi nadomestila. Nekateri vidiki sodnega odločanja so v bolj razvitih državah na tem področju že nadomeščeni z umetno inteligenco. Zato si moramo posledice tega dobro pogledati in uvesti umetno inteligenco na tak način, da zmanjšamo negativne posledice, ki bodo nedvomno nastale. Iz aktivnosti Evropske unije je opazno, da se na vstop tehnologij umetne inteligence dobro pripravljamo, vendar konkretnejša pravila še ne obstajajo. V bližnji prihodnosti bodo algoritmi umetne inteligence gotovo pomagali sodnikom pri njihovem odločanju, vendar nadomestili človeškega sodnika najbrž še ne bodo. Obstaja veliko etičnih in praktičnih vidikov, ki to zaenkrat še preprečujejo. V daljno prihodnost seveda ne moremo videti, še težje lahko predvidimo razvoj novih tehnologij, zato bo popolna nadomestitev človeškega sodnika, tema, ki se ji tudi v prihodnosti ne bomo mogli izogniti. Važno je, da zastavimo zakonodajo že danes, da negativne lastnosti umetne inteligence izničimo ali vsaj bistveno zmanjšamo, saj gre za sodni sistem, ki mora biti učinkovit in pravičen, saj si brez tega ne moremo predstavljati moderne in bistveno bolj pomembno, družbe prihodnosti. Artificial intelligence is increasingly shaping our lives. The momentum of new technologies brought upon by the COVID-19 pandemic and the inflation are transferring over to judicial systems. The main question we should be asking ourselves at this point is, whether artificial intelligence will only help our judges or also replace them. Some aspects of judicial decision-making have already been replaced by artificial intelligence in some developed countries. We must therefore take a good look at the consequences of this phenomenon and introduce artificial intelligence in such a way as to minimize the negative consequences that will undoubtedly arise. It is evident from the European Union's activities that we are preparing for the entry of artificial intelligence technologies, but there are no concrete rules as of yet. Soon, artificial intelligence algorithms will surely help judges in their decision-making, but they will not yet replace them. There are many ethical and practical considerations preventing this from happening as of now. We have yet to see future endeavours in the field of artificial intelligence unfold, so the complete replacement of the human judge will be a topic that we will not be able to avoid in the future. It is important that we recognize, legislate and reduce negative features of artificial intelligence today so the judicial system remains efficient and fair for generations to come. Without it, there is no modern society.

This work analyzes firstly the theoretical background of dynamical motion primitives, their intended purpose, motivation, possibilities, and pros and cons, later going into a specific application of dynamical motion primitives for generating a trajectory for a seven joint redundant robotic manipulator. The work’s purpose is to provide insight into the field of flexible trajectory generation based on demonstrated and learned motions while trying to stay readable and understandable to a wider audience for future practical purposes. Initially, motion primitives (the two kinds, kinematic and dynamic) are defined and analyzed in detail as constructive components, or rather, building blocks of muscular motion, observed from the standpoints of biorobotics and system design. We observe the way that motion primitives may present themselves as mathematical descriptions of the way biological entities, such as vertebrates and invertebrates, perform motions. The underlying principles of motion primitives, such as the relationships between the learning of the skill to the actual reproduction of the motion are analyzed. Motor learning and the construction of mathematical representations for the purposes of generalizing motion-based tasks are observed. Differences between discrete motion primitives and rhythmic motion primitives are outlined, as well as their individual points of importance. Following is a description of the procedures used to record a demonstration of a motion. An algorithm for encoding the discrete dynamical motion primitive based upon Gaussian basis functions and locally weighted regression is described in detail. Point attractor dynamics pertaining to the manner in which dynamical motion primitives generate a trajectory are defined, described, and visualized. A method used to modify the trajectory generation algorithm with the goal of a timely approach to the necessary goal point is outlined, with the necessary mathematical formulation. We define the specifics and the peculiarities of the task upon which the method is tested and used. The robotic manipulator performed the task of localizing bacterial colonies located on a Petri dish with the use of a camera affixed to its end-effector, and used the pre-recorded and encoded dynamical motion primitives to extract the desired bacteria colony from the dish, using a needle probe affixed to the end-effector, and place the bacteria colony onto a target plate. Given the minuscule dimensions of the bacteria colonies (with respect to the dimensions of the robotic manipulator), with many visible bacteria colonies on a scale of a third of a millimeter, a high dose of precision was required, both by the trajectory generation algorithm and by the robot’s control system. In the first chapter, we introduced the problem of achieving a generalized method of robot planning and control, that could rely on a recording of a motion but that could also generalize this motion to different scenarios. We explained the origins and the motivations of such a method in the form of dynamic motion primitives (DMPs). We introduced the task at hand, bacterial colony extraction for which high accuracy was required (below a millimeter along each of the X, Y and Z axes). We described the equipment used for the task, in the form of a 7-DOF robot manipulator with an industrial-grade imaging device and colony extraction needle affixed to its end-effector. In the second chapter, we go into detail about how DMPs are formulated, and the dynamical foundations upon which the approach is based. We explain the physics of attractors on a model of a realistic pendulum, going into state-space to model one of the possible attractors of the system, which is the central resting point of the pendulum. We go in detail about the dynamical equations which form the DMPs. We explain the primary transformation system that guides each degree of freedom according to the forcing functions and the beginning and goal values. The canonical system is introduced as the driving mechanism behind the dynamical equations, and as a method of forming the phase variable which controls the forcing functions of the DMP mechanism. Lastly, we explained in detail the derivations behind the forcing functions and the mathematical foundations upon which they rest. We did so by referring to the pendulum model example. In the third chapter, we introduced an initial implementation of DMPs on the robot manipulator. The testing task comprised of contacting each of the points on a 3D printed model. The model consisted of five tips with well-known dimensions and offsets that could be used as contact points for the end-effector needle. We explained the recording of the contacting (approach) DMP and the creation of the retracting DMP. We expounded on the setup of the robot manipulator scenario and performed the offline testing of the algorithm. We then performed a real life test of the algorithm, with a brief explanation of how the Simulink model was formed, primarily with respect to the dynamical equations contained within the DMP. The architecture of the control model was explained, and the second-order filter introduced as a way of guaranteeing a precise approach to the end of the motion. The results of the motion were displayed and briefly analyzed. In the fourth chapter, we went into detail about the task of bacterial colony extraction. The motivation for the task was explained, as well as the logistics of extracting bacteria colonies from a Petri dish. The full setup of the task was explained and the steps were delineated one by one. The recordings of the picking procedure and the depositing procedure were performed and the offline performance of the DMP algorithm was shown for each procedure. Finally, the real life execution of the algorithm was performed and displayed (with pictures), and the results of the DMPs’ accuracy displayed and analyzed. In the fifth and final chapter, we summed up the work and presented a brief overview for the reader. Magistrska naloga analizira teoretično ozadje dinamičnih primitivov gibanja, njihov predvideni namen, motivacijo, možnosti, prednosti in slabosti ter preučuje specifično uporabo dinamičnih primitivov gibanja za generiranje trajektorije za sedem sklepov redundantnega robotskega manipulatorja. Namen dela je zagotoviti vpogled v področje fleksibilnega generiranja trajektorije, ki temelji na demonstriranih in naučenih gibih. Sprva so primitivi gibanja (kinematični in dinamični) opredeljeni in podrobno analizirani kot konstruktivni sestavni deli oziroma gradniki mišičnega gibanja, opazovani s stališč biorobotike in načrtovanja sistemov. Ugotavljamo, kako se primitivi gibanja lahko predstavijo kot matematični opis izvajanja gibov živih bitij, kot so vretenčarji in nevretenčarji. Analiziramo osnovna načela primitivov gibanja, kot so razmerja med učenjem spretnosti in dejansko reprodukcijo giba. Opazujemo motorično učenje in konstruiranje matematičnih predstav za posploševanje gibalnih nalog. Opisane so razlike med primitivi diskretnega gibanja in primitivmi ritmičnega gibanja ter njihov pomen. Sledi opis postopkov, ki jih uporabljamo za učenje z demonstracijo. Podrobno je opisan algoritem za kodiranje diskretnega dinamičnega primitiva gibanja, ki temelji na Gaussovih bazičnih funkcijah in lokalno uteženi regresiji. Dinamika točkovnega atraktorja, ki se nanaša na način, na katerega dinamični primitivi gibanja generirajo trajektorijo, je definirana, opisana in vizualizirana. Opisana in matematično formulirana je metoda za prilagajanje algoritma generiranja trajektorije s ciljem pravočasnega doseganja ciljne točke. V nadaljevanju predstavimo posebnosti naloge, na kateri se metoda preizkuša in uporablja. Robotski manipulator s pomočjo kamere, pritrjene na vrh robota, izvede lokalizacijo kolonij bakterij, ki se nahajajo v petrijevki. S pomočjo predhodno demonstriranih in kodiranih dinamičnih primitivov gibanja nato robot z uporabo igelne sonde zajame želeno kolonijo bakterij ter jo prenese na ciljno ploščo za analizo. Glede na majhne dimenzije kolonij bakterij (v primerjavi z dimenzijo robotskega manipulatorja), je za manipulacijo bakterij potrebna visoka stopnja natančnosti, tako algoritma generiranja trajektorije kot tudi robotskega regulacijskega sistema. V prvem poglavju smo predstavili problem načrtovanja trajektorij in vodenja robota, ki se opira na demonstracijo gibanja in lahko to gibanje tudi posploši na različne scenarije. Pojasnili smo izvor in motivacijo uporabe metode v obliki dinamičnih primitivov gibanja (DMP). Predstavili smo nalogo, ekstrakcije kolonij bakterij, za katero je bila potrebna visoka stopnja natančnosti (manjša od milimetra vzdolž vseh treh kartezičnih osi). Opisali smo opremo, ki je bila uporabljena za nalogo, in jo sestavljajo robotski manipulator ter industrijska kamera, linijski laserski skener in igla za ekstrakcijo kolonije, ki so združeni v obliko orodja na vrhu manipulatorja. V drugem poglavju podrobno obravnavamo zasnovo DMP in temelje dinamike, na kateri temelji pristop. Fiziko atraktorjev razložimo na modelu nihala, ki ga obravnavamo v prostoru stanj. Modeliramo enega od možnih atraktorjev sistema, ki je osrednja točka mirovanja nihala. Podrobno obravnavamo dinamične enačbe, ki tvorijo DMP. Razložimo sistem transformacij, ki vodi vsako stopnjo prostosti robotskega mehanizma glede na nelinearne aktivacijske funkcije ter začetne in ciljne vrednosti. Kanonični sistem je predstavljen kot gonilni mehanizem za dinamične enačbe in kot metoda oblikovanja fazne spremenljivke, ki nadzoruje nelinearne aktivacijske funkcije mehanizma DMP. Nazadnje smo podrobno razložili izpeljave nelinearnih aktivacijskih funkcij in matematične temelje, na katerih so osnovane. To smo storili s sklicevanjem na primer modela nihala. V tretjem poglavju smo predstavili začetno implementacijo DMP na robotskem manipulatorju. Testna naloga je obsegala stik vrha robota s točkami na 3D tiskanem modelu. Model je vseboval pet konic z dobro znanimi dimenzijami in odmiki, ki smo jih uporabili kot točke dotika za iglo na vrhu robotskega manipulatorja. Pojasnili smo demonstracijo gibanja za učenje DMP, ki omogoča približevanje koloniji bakterij, in generiranje DMP za odmik. Razložili smo nastavitve robotskega manipulatorja in opravili testiranje algoritma v simulaciji. Nato smo izvedli preizkus algoritma na dejanskem robotu z implementacijo dinamičnih enačb DMP v obliki Simulink modela. Pojasnjena je arhitektura modela vodenja in predstavljen je filter drugega reda, ki zagotavlja natančno približevanje končni ročki. Rezultati gibanja so prikazani in na kratko analizirani. V četrtem poglavju smo podrobno obravnavali nalogo ekstrakcije bakterijskih kolonij. Razloženi sta motivacija za nalogo, pa tudi logistika pridobivanja kolonij bakterij iz petrijevke. Pojasnjena je celotna postavitev naloge. Razčlenjeni so posamezni koraki izvedbe. Prikazane so trajektorije postopkov zajema in odlaganja bakterijskih kolonij. Za vsak postopek je prikazana zmogljivost algoritma DMP. Nazadnje je izveden in prikazan algoritem na dejanskem robotu. Prikazani in analizirani so rezultati natančnosti vodenja robota z uporabo DMP. V petem in zadnjem poglavju smo delo povzeli in bralcu predstavili kratek pregled.

V diplomski nalogi skušam orisati postopne mutacije sodobne umetnosti v relaciji do njenih tehnoloških okoliščin, pri čemer se posebej osredotočam predvsem na implikacije algoritmov in nevronskih mrež. Prek primerov nekaterih nedavnih umetnostnih praks ter z njimi povezanih teoretizacij ponazorim sodobne strategije mišljenja in izvajanja kulturne produkcije, ki se prilagajajo medijski krajini sedanjosti in prihodnosti, pri čemer spreminjajo odnos do avtorstva, inovacije, reprezentacije, politike in umetnostnega trga. Po kratki razlagi tehnologije nevronskih mrež v zaključku predstavim tudi svojo avtorsko prakso in načrt za samostojno razstavo, v katerem ponazorim aplikacije predlaganih strategij. In my dissertation I try to outline the gradual mutations of contemporary art in relation to its technological circumstances, with a special focus on the implications of algorithms and neural networks. Through examples of some recent art practices and related theorizations, I illustrate contemporary strategies of thinking and performing cultural production that adapt to the media landscape of the present and the future while changing attitudes towards authorship, innovation, representation, politics and the art market. After a brief explanation of neural network technology, I present my practice and a plan for a solo exhibition through which I illustrate some applications of the proposed strategies.

Algoritme in tehnike reševanja problema interpolacije v eni spremenljivki lahko razširimo na reševanje v več spremenljivkah z različnimi posplošitvami in nadgradnjami le-teh. Obliko Newtonove baze in algoritem deljenih diferenc za iskanje pripadajočih koeficientov lahko neposredno posplošimo za interpolacijo na mrežnih točkah. Ta posplošitev je tenzorska ali pa v obliki omejitve skupne stopnje. Pri tej posplošitvi uporabljamo multiindeksno notacijo za sklicevanje na interpolacijske točke. Množicam interpolacijskih točk, za katere se uporablja tenzorski prostor, imenujemo polne množice. Sem sodijo t. i. škatlaste množice točk in trikotne množice točk. Poljubno izbrane interpolacijske točke ne zagotavljajo enolične interpolacije, vendar v nekaterih primerih s posplošitvijo baze, ki jo imenujemo Newton-Sauerjeva baza, pridemo do preprostega trikotnega linearnega sistema, ki vrne ustrezne koeficiente interpolacijskega polinoma. Za ustrezno število paroma različnih interpolacijskih točk nam algoritem, ki temelji na Gaussovih eliminacijah, vrne Newton-Sauerjevo bazo ali pa polinom, ki ima vrednost 0 na vseh interpolacijskih točkah, kar nam pove, da enolična interpolacija ni mogoča. Algoritem lahko uporabimo tudi, da za dan nabor interpolacijskih podatkov konstruiramo polinomski podprostor minimalne stopnje, kjer je enolična interpolacija vedno mogoča. Techniques and algorithms for finding univariate Newton interpolating polynomials can be extended to multivariate data points by different generalizations. The Newton basis format and divided-difference algorithm for coefficients can be generalized in a straightforward way when interpolating at nodes on a grid. Two different approaches, the tensor product case or the triangular case, are usually considered. The multi-index notation is used to refer to nodes. Node configurations where the tensor product case applies are called lower sets, and they include $n$-dimensional rectangles and triangles. Arbitrary distinct nodes do not ensure unique interpolating polynomials but, when possible, a different basis generalization, which we call Newton--Sauer basis, results in a nice triangular linear system for the coefficients. For the right number of distinct nodes, an algorithm based on Gaussian elimination produces either this Newton--Sauer basis or a polynomial that is zero on all nodes, showing that unique interpolation is impossible. The algorithm may also be used on any distinct nodes to produce a polynomial subspace of minimal degree where unique interpolation is possible.

Že davno v zgodovini, pred novim štetjem, so ljudje začeli množiti števila. Razvile so se različne metode množenja, a v današnjih časih je najbolj znan način osnovnošolskega množenja. Ta algoritem je prepočasen, da bi ga uporabljali v računalništvu, saj je uporaba velikih števil z razvojem računalništva in Interneta rasla. Zaradi tega je leta 1960 Karatsuba izumil algoritem, ki je bil hitrejši. Kmalu po njegovi objavi sta se razvila algoritma Toom-Cook-k (ATC-k) in Schönhage-Strassen (ASS). Leta 2019 smo se spoznali z do sedaj teoretično najbolj hitrim algoritmom za množenje števil, ki sta ga objavila znanstvenika Harvey in Hoeven. V diplomskem delu smo pregledali, kako delujejo zgoraj našteti algoritmi, pri čemer smo se poglobili v algoritma ATC-k in ASS. Na koncu pa smo še na kratko opisali algoritem Harvey-Hoeven (AHH) in predstavili implementacijo algoritma ATC-3. A long time ago in the ancient history, before our time, people began to multiply numbers. Various methods of multiplication have been developed, but nowadays the most well-known method is the one that is taught in primary school. This algorithm, however, is too slow to be used in computer science, as the use of large numbers has grown together with the development of computer science and Internet. Due to this problem, in 1960 Karatsuba invented an algorithm that was faster. Shortly after its publication, the Toom-Cook-k (ATC-k) and Schönhage-Strassen (ASS) algorithms were developed. In 2019, we were introduced to the theoretically fastest number multiplication algorithm ever, published by scientists Harvey and Hoeven. In the dissertation, we reviewed how the algorithms listed above work, delving into ATC-k and ASS. Furthermore the ending briefly describes algorithm Harvey-Hoeven (AHH) and presents the implementation of ATC-3.

Konveksno ovojnico množice točk v ravnini si lahko predstavljamo kot najmanjši konveksen poligon, ki obdaja celotno množico. Računanje konveksne ovojnice je v praksi pogosta operacija in ima uporabo na številnih področjih stroke. V tem diplomskem delu so predstavljeni in analizirani številni tradicionalni in moderni algoritmi za izračun konveksne ovojnice v dvodimenzionalnem Evklidskem prostoru, ki so nato ovrednoteni na podlagi različnih praktičnih performančnih testov. Bolj podrobno je predstavljen algoritem Ordered hull, ki se je izkazal za bistveno hitrejšega od algoritma Quickhull, ki je dolgo časa veljal za najhitrejšega. The convex hull of a planar point set is the smallest convex polygon enclosing the entire set. Computing the convex hull is a fundamental operation with uses in several different fields of research. In this thesis, we explore several different traditional and modern algorithms for computing the convex hull in two dimensional Euclidean space. The algorithms are then evaluated through several different practical performance tests. Algorithm Ordered hull is described in greater detail, as it proved to be significantly faster than Quickhull, which is commonly regarded as the fastest algorithm for the problem.

Trikotniki v grafu so podgrafi, sestavljeni iz treh povezanih vozlišč. Število trikotnikov je računsko zahtevna statistika, ki se pogosto uporablja v analizi velikih omrežij in v raznih primerih uporabe, kot so recimo odkrivanje skupnosti v omrežju, zaznavanje vsiljive vsebine, odkrivanje skritih tematskih struktur. Cilj diplomskega dela je pregled in primerjava algoritmov za štetje trikotnikov. Na začetku predstavimo problem, definicije in nekaj primerov uporabe štetja trikotnikov. Nato predstavimo algoritme za točno štetje trikotnikov, zatem pa še algoritme za približno štetje. Na koncu sledi še primerjava hitrosti in kratek zaključek. Triangles in a graph are subgraphs composed of three connected nodes. The number of triangles is a computationally intensive statistic that is often used in the analysis of large networks and in various use cases, such as discovering communities in a network, detecting spam, discovering hidden thematic structures. The aim of the thesis is to review and compare algorithms for counting triangles. At the beginning we present the problem, definitions and some examples of the use of counting triangles. Then we present algorithms for exact counting of triangles, and then algorithms for approximate counting. Finally, there is a comparison of speed and a short conclusion.

V diplomski nalogi predstavljamo interaktivno aplikacijo, ki vizualizira delovanje nekaterih algoritmov za iskanje najkrajših poti na grafih. Iz precej širokega nabora algoritmov smo izbrali Dijkstrov, Bellman-Fordov, Floyd-Warshallov, D'Esopo-Papeov in Fredman-Tarjanov algoritem. V besedilu teoretično predstavljamo njihovo delovanje in uporabo na različnih področjih, navajamo pa tudi njihovo psevdokodo. Predstavljamo tudi delovanje aplikacije in primere delovanja za posamezne algoritme. Aplikacijo smo izdelali kot didaktički pripomoček, namenjen tako učiteljem kot študentom. In this diploma thesis, we present an interactive application for visualizing algorithms for finding shortest paths in graphs. From a fairly large set of algorithms, we selected the Dijkstra, Bellman-Ford, Floyd-Warshall, D'Esopo-Pape, and Fredman-Tarjan algorithm. We describe them informally and in pseudocode. Tha application was designed as a didactic tool, both for teachers and for students.

Cilj diplomske naloge je opredelitev storitvenega modela, ki zajema storitve za izvajanje algoritmov na zahtevo. Poleg tega želimo izdelati programsko rešitev, ki zagotavlja takšno storitev. V ta namen najprej na kratko predstavimo področje računalništva v oblaku, storitvene modele in nekaj sorodnih rešitev. Sledi predstavitev problemov in predlog storitvenega modela, ki jih rešuje. Nato predstavimo načrtovanje in izvedbo programske rešitve za zagotavljanje storitve. Ta je zasnovana kot REST API in izdelana v programskem jeziku Go. Dodana je spletna aplikacija, ki služi enostavnejši uporabi rešitve. Na koncu rešitev ovrednotimo. Rezultati testiranj kažejo na zadovoljivo delovanje. The objective of this thesis is to define a service model, which includes services that offer algorithm execution on request. Furthermore, we aim to create a software solution that provides such a service. Firstly, we briefly describe the field of cloud computing, service models and a few similar solutions. Next, we define the main problems and our solution in the form of a service model. Then, we present the planning and implementation of a software solution that provides our service. It is designed as a REST API and built using the Go programming language. We add a web application, which serves to simplify the use of our solution. Lastly, we assess our solution. The results show adequate performance.

Seznanili se bomo s pojmom notranjega obsega ravninskega grafa in predstavili algoritem za njegov izračun s časovno zahtevnostjo O(nlog n) ter del algoritma z linearno zahtevnostjo. Podrobneje si bomo ogledali še povezavo med notranjim obsegom in najmanjšim prerezom ravninskih grafov. After acquainting ourselves with the girth of a planar graph, we first examine an algorithm for computing it in time O(nlog n). Second, we take a look at another procedure that runs in linear time and finally, we examine the connection between the girth and the minimum cut in planar graphs.

V nalogi je predstavljen algoritem DEM (Distance estimation method), ki omogoča učinkovito grafično prikazovanje fraktaličnih množic. Algoritem sodi na področje kompleksne dinamike, ki preučuje obnašanje iteracij kompleksnih preslikav. Začetek te veje matematike sega v obdobje med leti 1917 in 1919, ko so bile objavljene prve raziskave na temo iteracij kompleksnih racionalnih funkcij ene spremenljivke, s strani francoskih matematikov Gastona Juliaja in Pierre Fatouja. Sledilo je obdobje daljšega mirovanja teorije, ki pa ga je prekinil razvoj numerične matematike in posledično tudi fraktalne geometrije. Tako je področje znova postalo zelo popularno tako med matematiki kot med umetniki. V središču naloge bo eden izmed najbolj znanih objektov te teorije, tako imenovana Mandelbrotova množica. Gre za podmnožico kompleksne ravnine, ki na svojevrsten način ilustrira družino kvadratnih polinomov s povezano Juliajevo množico. V nalogi bomo podali njeno definicijo in dokazali nekaj njenih topoloških lastnosti. V ospredju bo dokaz njene povezanosti, ki nam bo v zadnjem poglavju omogočil izpeljavo algoritma DEM, s katerim bomo to množico tudi učinkovito grafično prikazali. In this paper we study the DEM (Distance estimation method) algorithm, which enables effective graphical representation of fractal sets. The algorithm is based on the theory of complex dynamics, which studies complex function's behavior under repeated iterations. This branch of mathematics had its beginnings between the years of 1917 and 1919, when the first research about iteration of complex rational function of one variable was published by French mathematicians Gaston Julia and Pierre Fatou. There followed multiple years of inactivity, until it was disrupted by the progress in the field of computer science and hence fractal geometry. Thus the field became immensely popular amidst mathematicians and artists alike. In the midst of this paper we will study one of the most recognizable objects of the theory, the so called Mandelbrot set. The name belongs to a subset of the complex plane, which in its own way illustrates the family of quadratic polynomials with a connected Julia set. We will define this set and prove some of its topological characteristics. The main proof being its connectedness, which will allow us to derive the DEM algorithm in the last section, using which we will be able to effectively represent the set graphically.

V svetu programiranja je urejanje podatkov zelo pomembno. Sčasoma so ljudje implementirali veliko različnih algoritmov, ki rešujejo ta problem ali pa izboljšujejo že obstoječe. Diplomsko delo obravnava problem urejanja podatkov na podlagi manj znanih algoritmov. Implementirani in analizirani so naslednji: sodo-liho urejanje (Odd-even sort), comb sort, ciklično urejanje (Cycle sort), pigeonhole sort, urejanje z drevesom (Tree sort) in timsort. Primerjava algoritmov je izvedena na podlagi prostorske in časovne zahtevnosti, dejanskega časa izvajanja, števila primerjav, števila prireditev in števila rekurzivnih klicev (če jih imajo). Da bi bila analiza realna, so vsi algoritmi analizirani na podlagi podobnih testnih podatkov, ki zajemajo večino možnih scenarijev pri urejanju. In the world of programming, sorting is very important. Over time, people have implemented many different algorithms that solve this problem or improve existing ones. The diploma thesis deals with the problem of data sorting using less known algorithms. Some of them have been implemented and analyzed: Odd-even Sort, Comb sort, Cycle sort, Pigeonhole sort, Tree sort, and Tim sort. The comparison of algorithms is based on the time and space complexity, the actual execution time, the number of comparisons, the number of assignments, and the number of recursive calls (if any). To make the analysis realistic, all algorithms are analyzed on similar test data. The test data cover most of the possible scenarios that could occur during sorting.

In this thesis we will focus on different algorithms for solving the Partition Problem. First, we will explain what the Partition Problem is and why it has been causing so many difficulties even in its simplest form. Then we will focus on different methods and algorithms for solving this problem that were published in the last few decades. We will explain their underlying ideas, positive and negative properties, asymptotic time complexities, and their actual speed. We will also present an algorithm that is based on our own ideas. All the algorithms will be experimentally evaluated on a set of problem instances. The goal of this work is not to find the best algorithm for the problem of partitioning, but rather to explain various algorithms for solving it, emphasize their positive and negative sides, thus allowing the user to pick the most appropriate algorithm for the scenario/problem instance at hand. V delu se bomo osredotočili na razne algoritme za rešavanje Problema Razdelitve. Najprej bomo pojasili, kaj je problem razdelitve in zakaj je v preteklosti povzročil - celo v svoji najenostavnejši različici - toliko preglavic. Nato se bomo posvetili raznim metodam in algoritmom za rešavanje tega problema, ki so bili objavljeni v zadnjem desetletju. Razložili bomo njihove zamisli, prednosti in slabosti, njihove asimptotične časovne zahtevnosti in dejanske hitrosti. Predstavili bomo tudi algoritem, ki smo ga zasnovali sami. Vse algoritme bomo eksperimentalno ovrednotili, na množici primerov problema. Cilj našega dela ni poiskati najboljši algoritem za problem razdelitve, pač pa razložiti delovanje takšnih algoritmov, izpostaviti njihove prednosti in slabosti, in tako omogočiti uporabniku, da izbere tistega, ki je za rešitev njegove situacije/primera problema, najprimernejši.

Magistrsko delo opisuje izdelavo merilnika temperature z algoritmom za varčevanje energije za uporabo v internetu stvari. Izdelava merilnika temelji na algoritmu, ki s pomočjo Newtonove interpolacije predvideva naslednjo izmerjeno temperaturo. Opisan je tudi algoritem na podlagi interpolacije z zlepki, ki ga uporabimo, če temperature ne prikazujemo v realnem času. Cilj je izdelati prototip merilnika, ki je kompakten, učinkovit, cenovno ugoden in ponuja čim daljšo življenjsko dobo baterije. Poleg teoretičnega ozadja in opisa izdelave merilnika je v magistrsko delo vključen še zajeten eksperimentalni del. This master's thesis describes the making of a temperature meter with an energy-saving algorithm for use in the internet of things. Making of the meter is based on an algorithm, which predicts the next measured temperature, using Newton's interpolation. An algorithm with spline-based interpolation is also described. It is used if the temperature is not needed to be displayed in real-time. The goal is to create a prototype meter that is compact, efficient, affordable, and offers the longest possible battery life. In addition to the theoretical background and description of the meter, a comprehensive experimental part is included in this thesis.

Namen dela je seznaniti bralca o algoritmih za iskanje največjega pretoka v omrežjih. Opisuje tri vrste algoritmov, njihovo delovanje in analizo. Prvi algoritem je Ford-Fulkersonov algoritem, ki je bil eden izmed prvih algoritmov za iskanje največjega pretoka. Drugi algoritem je zaporedni potisni in preimenuj, ki je eden izmed najhitrejših zaporednih algoritmov v današnjem času. Tretji algoritem je vzporedni potisni in preimenuj algoritem, ki je vzporedna pohitritev zaporednega potisni in preimenuj algoritma. Poleg algoritmov je v drugem poglavju opisana teorija omrežij, za lažje razumevanje delovanja algoritmov. V petem poglavju so zajeti vsi rezultati. Na začetku je časovna primerjava vseh treh algoritmov. V nadaljevanju se rezultati osredotočijo zgolj na vzporedni potisni in preimenuj algoritem, saj nas je zanimala pohitritev zaporednega potisni in preimenuj algoritma z vzporednim procesiranjem ter vplivom števila procesorjev na izvajanje vzporednega potisni in preimenuj algoritma. Pohitritev zaporednega algoritma se je kljub počasnejšemu delovanju na omrežjih z manj vozlišči izkazala za uspešno. Na omrežjih z velikim številom vozlišč smo zaporedni potisni in preimenuj algoritem pohitrili do 4-krat. Vzporedni potisni in preimenuj algoritem bi lahko še bolje optimizirali in s tem še dodatno pohitrili izvajanje, vendar to ni cilj te diplomske naloge. The purpose of the work is to acquaint the reader about algorithms for finding the maximum flow in networks. It describes three types of algorithms, their implementations and analysis. First algorithm is Ford-Fulkerson which was one of the first algorithms for finding maximum flow in networks. Second algorithm is sequential push-relabel algorithm which is one of the fastest sequential algorithms for finding maximum flow in networks at the time. Third algorithm is parallel push-relabel algorithm which is parallel speed up of sequential push-relabel algorithm. In addition to algorithms, Chapter 2 describes network theory to help understand how algorithms work. Chapter 5 covers all the results. In the beginning, there is a time comparison of all three algorithms. Then the results focus only on the parallel push-relabel algorithm, since we were interested in speeding up the sequential push-relabel by parallel processing and the impact of the number of processors on running the parallel push-relabel algorithm. Speeding up the sequential algorithm has proven to be successful, despite slower performance on networks with fewer nodes. On networks with many nodes, the sequential push-relabel algorithm was speeded up to 4 times. The parallel push-relabel algorithm could be further optimized to better speed up imprementation, but this was not the goal of this thesis.

V okviru tega diplomskega dela predstavimo ozadje in koncepte kolutnih iger na srečo, ter opišemo izziv vrednotenja dobitkov pri teh igrah. Predstavimo in implementiramo preproste algoritme za tri načine vrednotenja, nato pa te algoritme nadgradimo tako, da pospešimo njihovo izvajanje ali podpremo kakšno dodatno funkcionalnost. In this thesis we present the background and basic concepts of slot games, and describe the challenge of win evaluation. We present and implement simple algorithms for three evaluation modes and then upgrade them to optimize for shorter run-time or support a more complex functionality.

Nove tehnologije prinašajo nove izzive tudi v pravni sistem. Umetna inteligenca je sodobna tehnologija, ki spreminja delovanje različnih družbenih panog. Pojavlja se vprašanje, ali lahko umetna inteligenca popolnoma in samostojno nadomesti sodnika, ali pa mu lahko le pomaga pri odločitvah. Vpeljava umetne inteligence v procese kazenskega postopka lahko predstavlja tako prednost kot slabost za posameznika glede na obstoječe pravice. Vplive je potrebno podrobno analizirati, spremljati in ustrezno ukrepati - preprečiti je potrebno morebitne negativne posledice. V Združenih državah Amerike uporabljeni sistemi umetne inteligence niso skladni s smernicami Sveta Evrope. Omenjeni sistemi lahko povzemajo in dodatno okrepijo človeške predsodke ter diskriminacijo posameznika (verska, rasna, spolna usmeritev). Tudi v Evropi se pojavljajo poskusi vpeljave sistemov umetne inteligence, vendar rezultati niso prepričljivi. V prihodnosti bodo takšni algoritmi umetne inteligence vsekakor predstavljali pomoč sodnikom pri sprejemanju odločitev, v nekaterih primerih bodo lahko avtomatizirali manj zahtevne procesne naloge. Odločanje o krivdi posameznika s sistemi umetne inteligence trenutno še ni možno. Bodoči razvoj tovrstnih sistemov pa lahko močno spremeni celotni pravni sistem. New technologies also bring new challenges to the legal system. Artificial intelligence is a modern technology that changes the functioning of different social sectors. The question is whether artificial intelligence can completely and independently replace a judge, or whether it can only help him make decisions. The introduction of artificial intelligence into criminal justice processes can be both an advantage and a disadvantage for an individual over existing rights. Impacts need to be thoroughly analyzed, monitored and action taken - any negative consequences should be avoided. In the United States, artificial intelligence systems used are not in line with Council of Europe guidelines. These systems can summarize and further enhance human prejudice and discrimination against individuals (based on religion, race, sexual orientation). There are also attempts to introduce artificial intelligence systems in Europe, but the results are not convincing. In the future, such artificial intelligence algorithms will certainly help judges make decisions, in some cases being able to automate less demanding process tasks. Deciding if an individual is guilty with artificial intelligence systems is not possible yet. The future development of such systems can, however, greatly alter the overall legal system.

Že tisočletja poznamo problem razpoznavanja praštevil, vendar je to včasih veljalo za bolj teoretičen problem. Šele v 20. stoletju so znanstveniki ugotovili, kako zelo pomemben je ta problem tudi za praktične namene, saj so bili kriptografski sistemi zasnovani na podlagi velikih praštevil. Razvili so se polinomski verjetnosti algoritmi, ki so v praksi zelo uporabni in zadostni za potrebe varnih kriptografskih sistemov, vendar pri izvajanju verjetnostnih algoritmov vedno obstaja majhna možnost, da podajo nepravilen rezultat. Še vedno je obstajalo vprašanje, ali obstaja polinomski deterministični algoritem za razpoznavanje praštevilskosti. Tak algoritem so leta 2002 predstavili trije indijski znanstveniki Agrawal, Kayal in Saxena. V diplomski nalogi smo pregledali najbolj znane algoritme za dan problem in podrobno opisali prvi polinomski deterministični algoritem AKS ter ga dokazali. Predstavljena je tudi implementacija tega algoritma. We have known the problem of prime numbers recognition for thousands of years, but it has been considered a more theoretical problem. It was not until the twentieth century that scientists realized the importance of this problem for practical purposes as well, since cryptographic systems were designed on the basis of large prime numbers. Scientists developed randomized polynomial algorithms, which are in practice very useful and sufficient for the needs of secure cryptographic systems. There was still open question of whether there was a polynomial deterministic algorithm for testing primes. Such an algorithm was introduced in 2002 by three Indian scientists Agrawal, Kayal and Saxena. In the thesis we examined the most known algorithms for the given problem and described the first polynomial deterministic algorithm AKS and proved it. We also presented an implementation of algorithm AKS.

V delu obravnavamo antitrikotni razcep za simetrične nedefinitne matrike, znan tudi kot Batmanov razcep, katerega obstoj tudi dokažemo. Obravnavamo algoritem, ki z množenjem z ortogonalnimi matrikami pretvori vhodno matriko v bločno antitrikotno matriko, iz katere lažje razberemo inercijo in ocenimo lastne vrednosti. Omenjena dejstva so podprta tudi s primeri. V delo je vključena tudi analiza časovne zahtevnosti algoritma, ki lahko pri različnih vhodnih podatkih močno varira. In this work the antitriangular decomposition for symmetric matrices, also known as the Batman decomposition, is examined and it's existence is proved. An algorithm which uses the multiplication by orthogonal matrices to transform the input matrix to a block antitriangular matrix is presented. This algorithm allows us to determine the inertia and estimate the eigenvalues more efficiently. This claim is supported by examples. Also included in the work is the analysis of time complexity of the algorithm, which can variate strongly depending on the input data.

Pisanje je ključni del uporabe računalnika, pri tem pa glavno vlogo igra tipkovnica. Standardna razporeditev tipk (Qwertz) se po določenih kriterijih izkaže za neidealno. V diplomski nalogi razvijemo program, ki lahko s podanimi fizičnimi parametri neke tipkovnice in vzorcem besedila, kakršen bi se na dani tipkovnici pisal, išče optimalno postavitev črk na razpoložljivih tipkah. To dosežemo z uporabo genetskega algoritma. Ta za svojo ocenitveno funkcijo simulira uporabo tipkovnice na danih vzorcih besedil. Nova postavitev ima potencialno prednost pred klasično razporeditvijo Qwertz v več pogledih: hitrost pisanja, zmanjšanje števila napak pri pisanju, zmanjšanje napora mišic v rokah. V diplomski nalogi se osredotočimo predvsem na iskanje razporeditve za pisanje v slovenščini, vendar pa je program zmožen poiskati ureditve za kateri koli jezik, vključno s specializiranimi jeziki, kot so na primer programski jeziki. S programom poiščemo dve različni razporeditvi in jih statistično primerjamo s Qwertz, kot tudi nekaterimi drugimi uveljavljenimi alternativami. Z obema izvedemo še krajšo primerjalno študijo z razporeditvijo Qwertz. Writing is a key part of using a computer. The standard keyboard layout (Qwerty/Qwertz) is less than ideal under certain criteria. In this thesis we develop a program which can search for an optimal character layout for a given physical keyboard model based on samples of text that are expected to be written on it. The resulting layout has many advantages over a Qwerty/Qwertz layout such as: typing speed, lowering the number of writing errors, lessening the strain on hand muscles. We achieve that by using a genetic algorithm. The genetic algorithm simulates the use of the keyboard on the given text for its fitness function. We focus on searching for a layout for typing in Slovene, however the program is capable of finding layouts for any given language as well as specialized languages as say programming. Using the program, we find two new keyboard layouts. We compare them to Qwerty/Qwertz and some other established alternatives using certain statistical methods. We also run a short comparative study between them and Qwerty/Qwertz.

V tem magistrskem delu obravnavamo algoritem za hidromehaniko zglajenih delcev v 2D prostoru. Algoritem je bil sprva razvit za probleme na področju astrofizike, kasneje pa se je uveljavil kot algoritem za simulacije tekočin. Glavna lastnost algoritma je interpolacija veličin simuliranega fizikalnega pojava s sistemi delcev. S tem se razlikuje od algoritmov, ki simulirajo fizikalne pojave s topološkimi mrežami. Predstavimo teoretično podlago algoritma v 2D prostoru in izvedbo na praktičnem primeru simulacije tekočine v 2D prostoru. In this master's thesis we present smoothed particle hydrodnymics (SPH) algorithm in 2D space. SPH was originaly developed for problems in astrophysics and later gained traction in fluid simulation comunity. The main property of the algorithm is the smoothing of physical quantities of the underlying simulated problem with system of particles. This is also the main difference between SPH and other set of algorithms which solve simulation problem with mesh topology. In this thesis we will provide theoretical description of the algorithm in 2D space and practiclal demostration of 2D fluid simulation.

Podatek o časovni porazdelitvi padavin znotraj padavinskega dogodka je za hidrološko modeliranje in za določevanje projektnih pretokov izrednega pomena, saj ima razporeditev padavin pomemben vpliv na čas nastopa visokovodne konice. Najbolj zanesljive določitve te porazdelitve pa so tiste, ki temeljijo na podatkih za daljše časovno obdobje. V prvem delu magistrske naloge smo izdelali in predstavili algoritem v programskem jeziku C#, ki analizira 5-minutne zapise ombrografa in loči posamezne padavinske dogodke. Izdelali smo tudi algoritem v programskem jeziku R, ki izdela Huffove krivulje in naredi dodatne statistične analize padavinskih dogodkov. Oba algoritma se lahko uporabita za katerokoli padavinsko postajo. V drugem delu naloge smo z uporabo obeh algoritmov naredili analizo dolgoletnih nizov meritev za 30 padavinskih postaj v Sloveniji in ugotovili, da prihaja do velikih razlik v časovni porazdelitvi padavin znotraj padavinskega dogodka. Iz rezultatov je razvidna tudi geografska odvisnost časovne porazdelitve padavin. Ugotavljali smo tudi razlike med letnimi časi in ugotovili, da prihaja do določenih razlik tako v časovni porazdelitvi padavin znotraj padavinskega dogodka, kot tudi v številu teh dogodkov. Na koncu smo preverili še vpliv podnebne spremenljivosti na časovno porazdelitev padavin za padavinsko postajo Ljubljana-Bežigrad in ugotovili, da bistvenega vpliva ni. Temporal rainfall distribution within each individual rainfall event is very important for hydrological modelling and for developing of design flows. This is because temporal rainfall distribution plays crucial role on appearance of time of peak flow rate. Most dependable methods for determination of temporal rainfall distribution are those, which rely on data from long periods of precipitation measurements. In the first part of the master thesis we developed algorithm in programming language C# which analyses 5 minute data obtained from rain gauge and divides each individual rainfall events. We also developed algorithm in programming language R that develops Huff curves and performs additional statistical analysis of rainfall events. Both algorithms can be used on data based from every rain gauge. In the second part of the thesis we performed analysis of data obtained form 30 rain gauges in Slovenia and concluded that significant differences in temporal rainfall distribution within rainfall events are occurring among them. The results show that geographical location plays significant role in temporal rainfall distribution within rainfall events. We also tried to identify differences among seasons and concluded that there are significant differences in temporal rainfall distributions within rainfall events and even in number of rainfall events in different season. We also tried to identify impact of climate change on temporal rainfall distribution within rainfall events using data for rain gauge in Ljubljana-Bežigrad and concluded that there is no significant change to be observed.

Endometrioza in rak endometrija sta hormonsko odvisni, pogosti ženski ginekološki bolezni. Endometrioza predstavlja eno najpogostejših kroničnih benignih ginekoloških bolezni, ki je značilna predvsem za ženske pred menopavzo in je najpogostejši vzrok neplodnosti. Rak endometrija pa je značilen predvsem za ženske po menopavzi in je v Sloveniji na petem mestu najpogostejših malignih obolenj, v svetovnem merilu pa na šestem mestu. Obe bolezni povezuje hormonska odvisnost, kjer je povečana koncentracija estrogenov in/ali zmanjšana koncentracija progesterona dejavnik tveganja za nastanek obeh bolezni. Diagnosticiranje endometrioze trenutno poteka z invazivnimi metodami, saj biokemijski označevalci, ki bi omogočili zanesljivo neinvazivno postavitev diagnoze, še niso znani. Namen naših študij na področju endometrioze je identifikacija biokemijskih označevalcev, ki skupaj s kliničnimi podatki bolnic predstavljajo osnovo za statistično analizo, modeliranje in izgradnjo diagnostičnih modelov, ki bi jih lahko prenesli v klinično prakso. Pri bolnicah z rakom endometrija pa je namen naših študij identifikacija tako diagnostičnih kot tudi prognostičnih biokemijskih označevalcev. Diagnostični biokemijski označevalci endometrioze in raka endometrija bi omogočili zgodnejše odkritje bolezni, kar bi vodilo v zgodnejše zdravljenje in bi tako preprečilo napredovanje bolezni, s pomočjo prognostičnih biokemijskih označevalcev raka endometrija pa bi lahko identificirali bolnice z bolj ali manj agresivno obliko bolezni in temu ustrezno prilagodili obseg in vrsto operativnega pristopa. Biokemijske označevalce endometrioze in raka endometrija smo iskali med posameznimi proteini (o. p. CA-125, HE4, ARX) ter s pristopi tarčne »omike« v naboru številnih proteinov (o. p. od 40 do 900 različnih proteinov) in metabolitov (o. p. od 163 do 188 različnih metabolitov). V prvem delu doktorske disertacije smo tako na osnovi predhodne transkriptomske študije preverili potencial ARX (angl. Aristaless-related homeobox) kot možnega biokemijskega označevalca endometrioze. Ugotovili smo, da ARX ni biokemijski označevalec endometrioze, saj izvira iz strome jajčnika in ne iz endometriotičnih epitelnih ali stromalnih celic. Glede na prisotnost ARX-a v celicah, ki izvirajo iz ovarijske strome, pa smo predpostavili, da bi lahko predstavljal označevalca sex cord-stromalne diferenciacije pri tumorjih jajčnikov. V sodelovanju z Ginekološko kliniko Univerzitetnega kliničnega centra v Ljubljani in Ginekološko kliniko Medicinske univerze na Dunaju smo zbrali krvne vzorce bolnic z endometriozo, rakom endometrija in dveh kontrolnih skupin bolnic. Na osnovi izmerjenih serumskih koncentracij dveh tumorskih označevalcev (o. p. CA-125 in HE4), zbranih kliničnih podatkov in s pristopi logistične regresije smo postavili več različnih diagnostičnih modelov za bolnice z endometriozo in diagnostičen model za bolnice z rakom endometrija. Ugotovili smo tudi, da ima HE4 v primerjavi s CA-125 pri raku endometrija boljše prognostične karakteristike, vendar prognostičnega modela nismo uspeli postaviti. V sodelovanju z inštitutom Helmholtz Zentrum München (Institute of Experimental Genetics, Genome Analysis Centre, Nueherberg, Nemčija) smo s pomočjo komercialno dostopnih kompletov in z uporabo tekočinske kromatografije, sklopljene s tandemsko masno spektrometrijo, v plazmi bolnic z endometriozo in rakom endometrija določili koncentracije 188 oz. 163 različnih metabolitov lipidov. Preliminarni rezultati študije metabolitov kot potencialnih biokemijskih označevalcev endometrioze so pokazali, da je med bolnicami z različnimi oblikami endometrioze in kontrolno skupino bolnic več statistično značilno spremenjenih metabolitov, kar nam je predstavljalo izhodišče za izgradnjo diagnostičnega modela. Pri bolnicah z rakom endometrija smo identificirali tri posamezne metabolite in 341 razmerij koncentracij metabolitov, ki predstavljajo potencialne diagnostične biokemijske označevalce. Postavili smo tudi diagnostičen model, ki vključuje tri različna razmerja metabolitov in dodani podatek o statusu kajenja. Postavili smo štiri različne prognostične modele za napoved prisotnosti globoke invazije v miometrij in model za napoved prisotnosti limfovaskularne invazije pri bolnicah z rakom endometrija. Z uporabo proteinskih mikromrež smo na manjšem številu vzorcev plazme bolnic s peritonealno endometriozo in plazme kontrolne skupine bolnic iz nabora 900 različnih proteinov identificirali 24 potencialnih biokemijskih označevalcev, med katerimi smo koncentracije treh proteinov določili na večjem številu vzorcev bolnic z različnimi oblikami endometrioze. Z uporabo visoko zmogljive imunološke metode, imenovane »Luminex«, smo v plazmi bolnic z endometriozo in plazmi kontrolne skupine bolnic določili koncentracije 40 različnih citokinov in kemokinov. Na osnovi plazemskih koncentracij teh vnetnih dejavnikov in z uporabo ustreznih statističnih pristopov diagnostičnega modela, ki bi ločeval bolnice z endometriozo od kontrolne skupine bolnice, ni bilo mogoče postaviti. Z navedenimi študijami smo tako prispevali k identifikaciji biokemijskih označevalcev endometrioze in raka endometrija. Pokazali smo, da lahko na osnovi izmerjenih vrednosti določenih proteinov in/ali metabolitov, zbranih kliničnih podatkov ter z ustreznimi statističnimi pristopi postavimo modele z dobrimi diagnostičnimi in/ali prognostičnimi karakteristikami, ki bi jih lahko, po dodatnih validacijskih študijah, prenesli v klinično prakso. Endometriosis and endometrial cancer are hormone-dependent gynecological diseases. Endometriosis is one of the most common chronic benign gynecological diseases it is predominantly prevalent in pre-menopausal women, and is the most common cause of infertility. Endometrial cancer is particularly prevalent in post-menopausal women, and it is the fifth most common malignant disease in Slovenia, and the sixth in the world. As hormone-dependent diseases, increased estrogen levels and/or decreased progesterone levels are a risk factor for the emergence of both endometriosis and endometrial cancer. Diagnosis of endometriosis is currently performed through an invasive surgical approach, as to date there are no biomarkers known that can provide reliable non-invasive diagnosis. One aim of our studies on endometriosis and endometrial cancer is thus the identification of biomarkers that can be combined with clinical data of patients as the starting point for statistical analysis and construction of diagnostic models that can be translated into clinical practice. Diagnostic biomarkers of endometriosis and endometrial cancer will enable their earlier detection, allowing earlier treatment to prevent progression of these diseases. Similarly, we aim to identify prognostic biomarkers of endometrial cancer, through which it will be possible to better define the aggressive nature of these cancers, and hence to adjust the treatment approaches for these patients accordingly. We searched for biomarkers of endometriosis and endometrial cancer among individual proteins (i. e. CA-125, HE4, ARX) as well as in a panel of proteins (i. e. from 40 to 900 different proteins) and metabolites (i. e. from 163 to 188 different metabolites). In the first part of this project for my doctoral thesis, and on the basis of a previous transcriptomic study, we investigated the Aristaless-related homeobox (ARX) protein as a biomarker of endometriosis. However, this was not the case, as ARX originates from the ovarian stroma rather than the endometriotic epithelial or stromal cells. Therefore, as ARX is found in the ovarian stroma and cells derived from the ovarian stroma, and also in all types of sex-cord stromal tumors of the ovary, we hypothesize that it represents a marker for sex-cord stromal differentiation in ovarian tumours. We collected blood samples from patients with endometriosis and endometrial cancer, and also from control groups of patients, in collaboration with the Department of Obstetrics and Gynaecology at the University Medical Centre Ljubljana (Ljubljana, Slovenia) and with the Medical University (Vienna, Austria). On the basis of the serum concentrations of two tumor markers, CA-125 and HE4, and the collected patient clinical data and our logistic regression analysis, several diagnostic models were constructed for patients with endometriosis, and a diagnostic model was constructed for patients with endometrial cancer. Here, we showed that serum HE4 levels have superior prognostic value compared to serum CA-125 levels, although we did not succeed in establishing a suitable prognostic model. In a further collaboration with Helmholtz Zentrum München (Institute of Experimental Genetics, Genome Analysis Centre, Nueherberg, Germany), we used commercially available analytical kits and liquid chromatography–tandem mass spectrometry to define the plasma concentrations of 188 and 163 different lipid metabolites in patients with endometriosis and endometrial cancer, respectively. Our preliminary analysis of these metabolites as biomarkers of endometriosis indicated several different statistically significant metabolic variables between patients with different types of endometriosis and the control group. This provided the starting point for the construction of a diagnostic model. In the metabolic study for patients with endometrial cancer, three individual metabolites and 341 metabolite ratios were identified as potential diagnostic biomarkers. We thus constructed a diagnostic model using three metabolite ratios and with the addition of smoking status. For these patients with endometrial cancer, we also constructed four different prognostic models for the presence of deep myometrial invasion, plus a model for the presence of lymphovascular invasion. Using plasma samples collected from patients with peritoneal endometriosis and a control group of patients, we also used proteomics aporoch with antibody microarrays to define 24 potential biochemical markers from a set of 900 different proteins. Although this was carried out on a relatively small number of plasma samples, one of these biochemical markers was also confirmed for a larger number of samples from patients with different types of endometriosis. We also used a high-performance immunological method known as ‘Luminex’ to determine the concentrations of 40 different cytokines and chemokines in plasma samples from patients with endometriosis and from a control group of patients. Through the appropriate statistical approaches, the aim was to define a diagnostic model here to separate the patients with endometriosis from the control group of patients however, such a model could not be established on the basis of the plasma concentrations of these inflammatory factors. These studies have contributed to the identification of biomarkers of endometriosis and endometrial cancer. We have demonstrated that on the basis of the levels of certain proteins and/or metabolites, the collected clinical data of the patients, and the appropriate statistical approaches, models with good diagnostic and/or prognostic characteristics can be defined. Following additional validation studies, the aim is to transfer these to clinical practice.

Pri procesu nanašanja fitofarmacevtskega sredstva, pomešanega z vodo (škropilna brozga) v predpisani koncentraciji, s klasičnimi pršilniki za kemično varstvo krošenj dreves v sadovnjaku se uporabljajo standardni modeli za izražanje odmerkov fitofarmacevtskega sredstva in se pri tem ne upoštevajo karakteristične lastnosti krošenj dreves v sadovnjaku. Rezultat takšnih modelov je nekontrolirano krmiljenje količine škropilne brozge skozi posamezne šobe na krošnjo drevesa. V doktorski disertaciji predstavljamo avtonomni sistem, ki omogoča nadzorovano krmiljenje količin brozge skozi šobe na različnih segmentih krošnje drevesa. Avtonomni sistem temelji na mehkem odločitvenem modelu, v katerega smo, zaradi preciznejšega krmiljenja količin brozge, vključili informacijo o ocenjeni vrednosti listne površine. Ocenjeno vrednost listne površine na segmentih krošnje drevesa smo ovrednotili na osnovi ročnih meritev, laserskega merilnega sistema in programskega algoritma, s katerim smo omogočili tridimenzionalno rekonstrukcijo krošnje drevesa. V eksperimentu v sadovnjaku smo za ovrednotenje listne površine zajeli različne starosti in sorte jablan ('zlati delišes', 'jonagold' in 'gala'). Z uporabo regresijske metode smo ocenili zvezo med dvema odvisnima spremenljivkama (digitalno število zadetkov odbitih laserskih žarkov in digitalna prostornina krošnje drevesa) in eno neodvisno spremenljivko (listna površina, ročno izmerjena). Glede na razmerje med številom oblakov točk in listne površine smo ugotovili, da znaša maksimalna vrednost korelacijskega koeficienta 0,878. Sestavni del mehkega odločitvenega modela je predstavljal mehki logični algoritem za krmiljenje tripoložajnih elektromagnetnih ventilov v pulznoširinskem načinu, ki smo jih namestili na prototip aksialnega pršilnika. Rezultati so pokazali, da lahko z mehkim odločitvenim modelom omogočimo krmiljenje količin škropilne brozge v točno določenem območju glede na ocenjeno vrednost listne površine, zato bo ta model v bližnji prihodnosti predstavljal močno orodje pri zmanjševanju porabe fitofarmacevtskih sredstev za varstvo rastlin. In the process of applying a plant protection product mixed with water (spray mixture) at the prescribed concentration with conventional sprayers for chemical protection of tree canopies in an orchard, standard models are used to express the dose rate of the plant protection product. Characteristic properties of the tree canopy in an orchard are not taken into consideration. Such models result in uncontrolled quantities of spray mixture sprayed through individual nozzles into a tree canopy. In the doctoral thesis an autonomous system is presented, which ensures a controlled quantity of spray mixture sprayed through the nozzles into different tree canopy segments. The autonomous system is based on a fuzzy decision-making model that includes information about the estimated leaf area value to ensure a more precise spray mixture control. The estimated value of the leaf area at canopy segments was evaluated using manual measurements, the laser LIDAR measuring method and a software algorithm for a three-dimensional reconstruction of the canopy. In the experiment, in an orchard, the leaf area of various ages and apple cultivars ('golden delicious', 'jonagold', 'gala') was captured for evaluation. Based on the regression approach, the relationship was assessed between two dependent variables (the digital number of hits of laser beams and the digital volume of the canopy) and an independent variable (canopy leaf area, manually measured). Based on the ratio between the number of point clouds and the leaf surface, it was established that the maximum value of the correlation coefficient was 0,878. An integral part of the fuzzy decision-making model is represented by a fuzzy logic controller for controlling three-position electromagnetic valves in the pulse width mode the valves were installed in the axial sprayer prototype. The results showed that with the fuzzy decision-making model it was possible to control the quantity of spray mixture in the specific range depending on the estimated value of the leaf area. Consequently, this model will represent a powerful tool for reducing the quantity of spray mixture for plant protection in the near future.

Digitalna tehnologija je postala nepogrešljiv del vseh področij in vidikov tako zasebnega kot javnega življenja in posega tako v prosti čas kot v sfero podjetništva. Takšne avtomatizirane sisteme uporabljajo banke, delodajalci, zdravstvene ustanove, podjetja idr. Posamezniki so vse pogosteje podvrženi avtomatizaciji, vprašanje pa je, v kolikšni meri se tega zavedajo. Z vnosom zahtevanih podatkov v posamezne obrazce npr. na banki, računalnik sam na podlagi algoritmov odloči o tem, ali je nekdo upravičen da pridobi kredit ali ne. Pri tem se zastavlja vprašanje, v kolikšni meri lahko pride pri takšnem odločanju do diskriminacije na podlagi posameznih vnešenih podatkov, ki jih algoritem ovrednoti različno. Razvoj avtomatizacije in umetne inteligence pa gre celo tako daleč, da lahko pričakujemo avtomatizacijo tudi na sodiščih, vprašanje pa je, v kolikšni meri lahko do tega pride. Mnogi so pri tem zaskrbljeni, kaj avtomatizacija odločanja pomeni za pravnike in ali lahko ogrozi poklic pravnika, saj npr. v nekaterih odvetniških pisarnah v Združenih državah Amerike že uporabljajo sistem algoritmov, ki stranki preko izpolnjenega spletnega obrazca sporoči, ali je v določeni zadevi primeren posvet pri odvetniku in pravno postopanje ali ne. Splošna uredba o varstvu podatkov (GDPR - General Data Protection Regulation), ki je bila sprejeta 27. aprila 2016 in se je pričela uporabljati 25. maja 2018, vsebuje pomembne določbe, ki urejajo področje avtomatiziranega odločanja. Oddelek 4 drugega poglavja ima naslov Pravica do ugovora in avtomatizirano sprejemanje posameznih odločitev, ki v členih 21 in 22 določa, kdaj lahko posameznik ugovarja obdelavi osebnih podatkov in kdaj je mogoče avtomatizirano sprejemanje posameznih odločitev, vključno z oblikovanjem profilov. V skladu z 22. členom Splošne uredbe o varstvu podatkov ima posameznik, na katerega se nanašajo osebni podatki, pravico, da zanj ne velja odločitev, ki temelji zgolj na avtomatizirani obdelavi, vključno z oblikovanjem profilov, ki ima pravne učinke v zvezi z njim ali na podoben način nanj znatno vpliva. Nadalje pa je določeno, da se omejitev iz prvega odstavka ne uporablja, če veljajo določene izjeme. Moja magistrska naloga bo napisana na podlagi predhodno opravljene raziskave o tem, kako se avtomatizacija in avtomatizirano odločanje uporablja v praksi, kje se že uporablja in v katerih postopkih se že uporablja, kakšne so njene prednosti in slabosti, kakšne spremembe na tem področju lahko pričakujemo po pričetku uporabe Splošne uredbe o varstvu podatkov in ali je možna avtomatizacija odločanja na sodiščih ter v kolikšni meri. Digital technology has become significant part in all aspects of both private and public life, not just in leisure but also in business. Automated-decision making systems are used in banking system, healthcare system, in business etc. Individuals are often subject to automated decision-making and the question is to what extent they are aware of it. By entering the required data into individual forms, for example in the bank, the computer itself decides on the basis of algorithm whether someone is entitled to get a loan or not. This raises the question of the extent in which such a decision can lead to discrimination based on individual’s data entered that algorithm evaluates differently. The development of automation and artificial intelligence is even so far that automation can be expected on the courts, but the question is to what extent is this possible. Some people are worried about the impact automated decision-making will have for lawyers and whether it can jeopardise the profession of a lawyer. In some law firms in the United States they are already using algorithmic systems to inform a client, through a completed online form, whether or not a consultation with a lawyer and legal action is appropriate in particular case. The General Data Protection Regulation (GDPR) was adopted on 27 April 2016 and applied on 25 May 2018. GDPR contains important provisions governing the field of automated decision-making. Section 4 of the second chapter has a title “Right to object and automated decision-making” which in Articles 21 and 22 determines when an individual have the right object to the processing of personal data concerning him/her and when the data subject can be subject to a decision reached in automated decision-making. In accordance with Article 22 of the GDPR the data subject has the right not to be subject to the decision based solely on automated processing, including profiling, which produces legal effects concerning him or her or similarly significantly affects him or her. Furthermore, it is provided that the restriction referred to in paragraph 1 shall not apply in certain exceptions. The master’s thesis focus on the previously conducted research on how automation and automated decision-making are used in practice, where this kind of system is already used and in which procedures. Furthermore, it focus on advantages and disadvantages of such automated decision-making systems and what changes can be expected in this field after the application of the GDPR and whether automated decision-making is possible on the courts and to what extent.

V diplomski nalogi bomo predstavili reševanje in ustvarjanje uganke sudoku. Spoznali bomo osnovne gradnike vsake sudoku uganke. Obravnavali bomo problem natančnega pokritja množice in kako se sudoku uganka preslika na problem natančnega pokritja. Razložili bomo prevedbo zapisa sudoku uganke v računalniški zapis (matriko pokritja), nad katero se izvaja naš program. Pri reševanju sudokuja smo uporabili algoritem X, ki je implementiran v jeziku Java. Spoznali bomo drugi način implementacije algoritma X, metodo plesočih povezav, ki je žal nismo implementirali. Primerjali bomo oba načina reševanja sudoku mrež s pomočjo časovne in prostorske analize ter si podrobneje ogledali omejitve naše implementacije. Sledi predstavitev postopka sestavljanja poljubne sudoku mreže iz več sudokujev ter težave, s katerimi se srečamo, ko sestavljamo poljuben sudoku. Na koncu si bomo ogledali še primer vmesnika, ki nam omogoča sestavljanje poljubnih sudokujev. Za vmesnik smo uporabili tehnologiji HTML in javascript. The goal of the thesis is to study how to create and solve a sudoku puzzle. We will look into the individual components which every sudoku puzzle contains. Furthermore, we will take a closer look into the exact set cover problem and how sudoku puzzle can be represented as one. We will present how to represent a sudoku puzzle so that our program can use it for solving. Sudoku solver was created using "Algorithm X'', using Java programming language. We will get better acquainted with an alternative way to implement "Algorithm X'', the "Dancing Links'' method which unfortunately was not implemented. With the help of time and space complexity analysis we will compare both implementations and also have a closer look at the limitations of our implementation. After that, we will have a look at how to create a custom sudoku grid which consists of multiple other sudoku grids. We also mention problems which we can encounter during the creation. Lastly, a simple user interface proposal will be introduced, using HTML and javascript, which enables users to create any kind of sudoku they wish.

V disertaciji vpeljemo nov algebraičen pristop k analizi časovnih omrežij, ki temelji na časovnih količinah nad ustreznim polkolobarjem. Definiramo polkolobarje za analizo časovnih omrežij brez potovalnega in čakalnega časa in polkolobarje za analizo časovnih omrežij, ko potovalni in čakalni časi niso ničelni. Za omrežja brez potovalnih in čakalnih časov razvijemo algoritme za učinkovito računanje s časovnimi količinami in za izbrane mere pomembnosti, ki so posplošitve mer za analizo statičnih omrežij. Opišemo izračun stopnje vozlišč, nakopičenosti, dostopnosti in vmesnosti ter rekurzivnih mer pomembnosti. Razdelamo postopke za izračun mere pomembnosti glede na lastne vektorje sosednostne matrike omrežja, Katzove pomembnosti in Bonacichevih pomembnosti ▫$alpha$▫ in ▫$(alpha,beta)$▫. Opišemo tudi postopka HITS (kazala in viri) in pageRank. Definiramo dejavnost in privlačnost vozlišč. Mere pomembnosti nam omogočajo identifikacijo skupine najpomembnejših vozlišč omrežja in z njihovim pregledom / primerjavo vpogled v spreminjanje njihove vloge skozi čas. Povemo, kako izračunamo ovojnico nad absorpcijskimi polkolobarji in z njeno uporabo časovno dosegljivost. S pomočjo dosegljivosti izračunamo časovno razbitje na šibke in krepke komponente. Opisani pristop lahko uporabimo za analizo skupin, ki so določene s poljubno drugo časovno ekvivalenčno relacijo na danem omrežju. Opisani postopki so dostopni kot Pythonska knjižnica TQ. Algoritme preizkusimo na realnih omrežjih, Franzosijevem omrežju nasilja v Italiji in omrežju Reutersovih novic o terorističnem napadu 11. septembra. In the thesis we describe a new algebraic approach to the temporal network analysis based on the notion of temporal quantities. We define semirings for the analysis of temporal networks with zero latency and zero waiting time and semirings for the analysis of temporal networks where the latency is given. For temporal networks with zero latency and zero waiting time we present algorithms for the efficient operations with temporal quantities and for the computation of chosen centrality measures that are generalized cases of centrality measures for static networks. We describe the computation of degree, clustering coefficients, closeness, betweenness and recursive measures of centrality. We explain the eigenvector centrality, the Katz centrality measure, the Bonacich ▫$alpha$▫ and ▫$(alpha,beta)$▫ centralities, the HITS (hubs and authorities) centrality, and the pageRank centrality. We define activity and attraction coefficients in temporal networks. Centrality measures allow us to identify groups of important vertices. With a review / comparison of the vertices from the groups we get an insight into their roles through time. We present the algorithm for computing the closure of a temporal network over an absorptive semiring and for computing the temporal reachability of nodes. We also describe the procedure for computing temporal weak and strong connectivity components using the appropriate closure. This approach can also be used for the analysis of groups that are determined by other equivalence relations on the given network. The described procedures are available as a Python library TQ. We tested the algorithms on real networks, the Franzosi's violence network and the Reuters terror news network.

V magistrski nalogi smo se posvetili realizaciji alternativne analitično-numerične metode izračuna magnetnih razmer v zračni reži motorja s površinsko nameščenimi magneti. Metoda opisuje algoritme za izračune gostote magnetnih pretokov v zračni reži zaradi vzbujanja magnetov in zaradi vpliva toka statorskega navitja. V nadaljevanju realiziramo in opišemo kompleksno permeančno funkcijo, dodamo vpliv relativne permeabilnosti magnetov h gostoti magnetnega pretoka. Iz vseh dobljenih vrednosti nato izračunamo inducirano napetost, elektromagnetni in samodržni navor. Analitično metodo primerjamo še z metodo končnih elementov, kjer upoštevamo linearno B-H karakteristiko železa. Ugotovimo ujemanje gostot magnetnih pretokov in inducirane napetosti, slabše pa je ujemanje navorov zaradi izbrane analitične metode izračuna navorov. Na koncu dodamo še nelinearno B-H karakteristiko feromagnetnega materiala k izračunu z metodo končnih elementov in ugotovimo, da se poteki gostot magnetnega pretoka v zračni reži in potek inducirane napetosti ujemajo. Vrednosti elektromagnetnega navora pa so nekoliko manjše v tako predstavljenem stroju. Prikazana je še uporaba analitično-numerične metode, kjer smo s poskusi iskali minimalno vrednost samodržnega navora. Metoda je uporabna, dovolj natančna za osnovno optimizacijo in hitrejša od metode končnih elementov. Za nadaljnjo optimizacijo električnega stroja se nato uporablja metodo končnih elementov. The primary objective of the master thesis was to calculate and analyse magnetic conditions within the surface mounted permanent magnet electric motors. More precisely, the distribution of magnetic flux density within the air-gap and the resulting physical quantities such as the induced voltage, the electromagnetic torque and the cogging torque were calculated and analysed. The analysis was based on an analytical-numerical model of the surface mounted permanent magnet electric motor. First, the algorithms for calculation of magnetic flux density in the air gap were developed. Second, the complex permeance function for stator slotting is defined and calculated and the relative peremeance of the rotor magnets is added into the algorithm. The developed algorithm enables calculation of radial and tangential components of magnetic flux densities produced by both the rotor permanent magnets and stator current. Based on the resulting magnetic flux densities the algorithm enables the calculation of the induced voltage, electromagnetic and cogging torque. The results obtained with the analytical-numerical model were compared with a finite element based numerical model with linear B-H characteristic of feromagnetic material. A good agreement for the magnetic flux density and the induced voltage was obtained between the two models. However, the electromagnetic and cogging torque differs due to the chosen analytical method. Therefore, the finite element model was improved with the nonlinear B-H characteristic of the feromagnetic material. The new comparison showed a difference only in electromagnetic torques due to magnetic saturation of the motor core. Finally, the applicability of the developed algorithm was tested and demonstrated for different geometries of the surface mounted permanent magnet electric motors.

This research demonstrates the basic elements of a prototype automated orchard sprayer which delivers pesticide spray selectively with respect to the characteristics of the targets. The density of an apple tree canopy was detected by PROWAVE 400EP250 ultrasound sensors controlled by a Cypress PSOC CY8C29466 microcontroller. The ultrasound signal was processed with an embedded computer built around a LPC1343 microcontroller and fed in real time to electro-magnetic valves which open/close spraying nozzles in relation to the canopy structure. The analysis focuses on the detection of appropriate thresholds on 15 cm ultrasound bands, which correspond to maximal response to tree density, and this was selected for accurate spraying guidance. Evaluationof the system was performed in an apple orchard by detecting deposits of tartrazine dye (TD) on apple leaves. The employment of programmable microcontrollers and electro-magnetic valves decreased the amountof spray delivered by up to 48.15%. In contrast, the reduction of TD wasonly up to 37.7% at some positions within the tree crown and 65.1% in the gaps between trees. For all these reasons, this concept of precise orchard spraying can contribute to a reduction of costs and environmental pollution, while obtaining similar or even better leaf deposits.

This paper presents the synthesis of an optimal robust controller with the use of pole placement technique. The presented method includes solving a polynomial equation on the basis of the chosen fixed characteristic polynomial and introduced parametric solutions with a known parametric structure of the controller. Robustness criteria in an unstructured uncertainty description with metrics of norm ℋ∞ are for a more reliable and effective formulation of objective functions for optimization presented in the form of a spectral polynomial with positivity conditions. The method enables robust low-order controller design by using plant simplification with partial-fraction decomposition, where the simplification remainder is added to the performance weight. The controller structure is assembled of well-known parts such as disturbance rejection, and reference tracking. The approach also allows the possibility of multiobjective optimization of robust criteria, application of mixed sensitivity problem, and other closed-loop limitation criteria, where the common criteria function can be composed from different unrelated criteria. Optimization and controller design are performed with iterative evolution algorithm.

A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law.

Diplomska naloga rešuje problem zalog pri izbrani prostočasni dejavnosti, ki se ukvarja z ročno izdelavo zvezkov. Pri izbrani prostočasni dejavnosti je težava vodenje zalog, s tem povezan pa je tudi (pre)počasen odziv izvajalca prostočasne dejavnosti na povpraševanje kupca. Zaradi omenjenega prihaja pri kupcih do nejevolje ter kasnejšega nezanimanja za sicer prvotno kupcu zanimiv izdelek. Namen zaključnega dela je bil poiskati primerno aplikacijo za nadzor zalog pri prostočasnih dejavnostih. V ta namen je bila najprej raziskana ponudba na trgu prostodostopnih aplikacij za nadzor zalog, katere bi lahko bile primerne za izbrano prostočasno dejavnost. Ugotovljeno je bilo, da je na trgu veliko prostodostopnih aplikacij za nadzor zaloge, vendar pa le-te niso v celoti ustrezale našim zahtevam, kot so npr. upravljanje zalog preko mobilnih telefonov, platforma aplikacije povezana z Gmail računom zaradi registracije, vnos želenih informacij, vpis sodelavcev, ki bi imeli dostop do vpogleda zalog itd. Na podlagi teh ugotovitev smo izdelali algoritem in grafično oblikovali videz nove prostodostopne aplikacije, ki bo primerna za izbrano prostočasno dejavnost, prav tako pa bo dostopna širšemu trgu. In my thesis, I have created a solution in how to store items in complementary work of making handmade notebooks. In this handcrafting action, there is a slower response rate for buyers command and a problem with managing the inventory of the notebooks. There is a delay with the answer because of it and the buyers lose interest in an item they wanted to buy beforehand. The main purpose of my study is to find the right application, which could manage the inventory items in the handcraft business. We made an inquiry about the apps on the market, which are free of access. We made a conclusion that every free application lacked a specific that we required. For example managing stock on the mobile phone, platform of the app required your g-mail account to register, some of the needed information was missing, the entry of co-workers, who could access the database. We established an algorithm and a graphic design and created a new application that will be suitable for any handcraft business and will be widely accessible on the market.

V doktorski disertaciji predstavimo nov algoritem za klasifikacijo vegetacije v podatkih LiDAR. Klasifikacijski postopek povzamemo z dvema korakoma: analiza porazdelitve točk ter analiza njihovega konteksta. Poglavitna značilnost točk vegetacije je namreč statistično visoka razpršenost višin, zato jih lahko učinkovito razpoznamo v odvisnosti od napak pri prileganju ravnin. Klasifikacijo dodatno izboljšamo z uvedbo treh kontekstnih filtrov, ki obravnavajo povezane objekte (na primer zidove, dimnike, balkone), razraščeno vegetacijo in majhne objekte (na primer avtomobile, ograje, kipe). Pokazali smo, da lahko s predlaganim algoritmom vegetacijo razpoznamo neodvisno od tipa vegetacije (listavci in iglavci), okolja (gorsko, gozdnato, urbano) in nivoja olistanosti. V postopku validacije algoritma smo namreč v povrečju dosegli 97,9% rezultat F1 v neurbanih območjih in 91% v urbanih, ki iz vidika težavnosti klasifikacije veljajo za zahtevnejša. Pri klasifikaciji uporabljamo samo geometrijske podatke oblaka točk, kar predstavlja prednost algoritma pred drugimi, katerih uspešnost je v veliki meri odvisna od lastnosti, kot so visoka gostota točk in zanesljivost (ali prisotnost) drugih informacij. Analiza treh vhodnih parametrov je prav tako pokazala, da so le-ti stabilni in robustni. Predlagani algoritem zato omogoča uporabniško interakcijo ter nadzor razmerja celovitosti in pravilnosti klasifikacije. In this Doctoral dissertation, we introduce a new algorithm for the classification of vegetation points within LiDAR data. The classification procedure can be outlined with two steps: An analysis of the distribution of points and an analysis of the context in which they are located. Vegetation points are, namely, characterised by their non-linear distributions and they can, therefore, be recognised effciently in relation to the large plane fitting errors. The classification is improved further by introducing three contextual filters, which deal with attached objects (e.g. walls, chimneys, balconies), overgrown vegetation and small objects (e.g. vehicles, fences, statues). We have shown that the proposed algorithm is able to classify vegetation despite of the different vegetation types (deciduous and coniferous), enviroments (mountain, forested,urban), and different levels of leaf conditions. An average F1 score of 97.9% was achieved for non-urban areas and 91% for urban areas, which are, in terms of classification difficulty, considered to be more difficult. The algorithm uses only the geometrical information of points, which presents an advantage when compared with the methods which rely on point clouds with high point density and reliability (or the presence) of other information. The parameter sensitivity analysis has also shown that the three used input parameters are stable and robust. They, therefore, provide an efficient way to regulate the ratio between completeness and correctness.

V diplomskem delu je obravnavan problem izboljšave slik videonadzornih kamer v namene forenzičnih raziskav. V forenziki se tehniki pogosto srečujejo s problemom premajhne ločljivosti oziroma prevelike oddaljenosti nekega ključnega objekta na videoposnetku. V delu so predstavljeni obstoječa programska oprema za izboljšavo slik ter osnovni filtri in tehnike izboljšav, ki so lahko v pomoč. Diplomsko delo se nato osredotoči na bolj zapleteno metodo superresolucije. Problem se je skušal rešiti z algoritmi superresolucije, bolj natančno z bikubičnim in bilinearnim interpolacijskim pristopom. Proučevano je bilo, koliko superresolucija lahko pomaga v različnih primerih. In this thesis the problem of enhancing images of video surveillance cameras for purposes of forensic investigation will be addressed. In forensics technicians often come across the problem of low resolution, or the key subject being too far away on the video or image. First the software that allows technicians to process images and the basic filters and processing techniques will be presented. After that the thesis will focus on a more complex method called super-resolution. The problem of low resolution will try to be solved with super-resolution algorithms, more specifically using bicubic interpolation approach and bilinear interpolation approach. The main point of this thesis, is to learn how much the super-resolution can help in different scenarios.