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151	Lösungsoperatoren für Delaysysteme und Nutzung zur Stabilitätsanalyse Gehre, Nico 06 April 2018 (has links) In diese Dissertation werden lineare retardierte Differentialgleichungen (DDEs) und deren Lösungsoperatoren untersucht. Wir stellen eine neue Methode vor, mit der die Lösungsoperatoren für autonome und nicht-autonome DDEs bestimmt werden. Die neue Methode basiert auf dem Pfadintegralformalismus, der aus der Quantenmechanik und von der Analyse stochastischer Differentialgleichungen bekannt ist. Es zeigt sich, dass die Lösung eines Delaysystems zum Zeitpunkt t durch die Integration aller möglicher Pfade von der Anfangsbedingung bis zur Zeit t gebildet werden kann. Die Pfade bestehen dabei aus verschiedenen Schritten unterschiedlicher Längen und Gewichte. Für skalare autonome DDEs können analytische Ausdrücke des Lösungsoperators in der Literatur gefunden werden, allerdings existieren keine für nicht-autonome oder höherdimensionale DDEs. Mithilfe der neuen Methode werden wir die Lösungsoperatoren der genannten DDEs aufstellen und zusätzlich auf Delaysysteme mit mehreren Delaytermen erweitern. Dabei bestätigen wir unsere Ergebnisse sowohl analytisch wie auch numerisch. Die gewonnenen Lösungsoperatoren verwenden wir anschließend zur Stabilitätsanalyse periodischer Delaysysteme. Es werden zwei neue Verfahren präsentiert, die mithilfe des Lösungsoperators den transformierten Monodromieoperator des Delaysystems nähern und daraus die Stabilität bestimmen können. Beide neue Verfahren sind spektrale Methoden für autonome sowie nicht-autonome Delaysysteme und haben keine Einschränkungen wie bei der bekannten Chebyshev-Kollokationsmethode oder der Chebyshev-Polynomentwicklung. Die beiden bisherigen Verfahren beschränken sich auf Delaysysteme mit rationalem Verhältnis zwischen Periode und Delay. Außerdem werden wir eine bereits bekannte Methode erweitern und zu einer spektralen Methode für periodische nicht-autonome Delaysysteme entwickeln. Wir bestätigen alle drei neue Verfahren numerisch. Damit werden in dieser Dissertation drei neue spektrale Verfahren zur Stabilitätsanalyse periodischer Delaysysteme vorgestellt. / In this thesis linear delay differential equations (DDEs) and its solutions operators are studied. We present a new method to calculate the solution operators for autonomous and non-autonomous DDEs. The new method is related to the path integral formalism, which is known from quantum mechanics and the analysis of stochastic differential equations. It will be shown that the solution of a time delay system at time t can be constructed by integrating over all paths from the initial condition to time t. The paths consist of several steps with different lengths and weights. Analytic expressions for the solution operator for scalar autonomous DDEs can be found in the literature but no results exist for non-autonomous or high dimensional DDEs. With the help of the new method we can calculate the solution operators for such DDEs and for time delay systems with several delay terms. We verify our results analytically and numerically. We use the obtained solution operators for the stability analysis of periodic time delay systems. Two new methods will be presented to approximate the transformed monodromy operator with the help of the solution operator and to get the stability. Both new methods are spectral methods for autonomous and non-autonomous delay systems and have no limitations like the known Chebyshev collocation method or Chebyshev polynomial expansion. Both previously known methods are limited to time delay systems with a rational relation between period and delay. Furthermore we will extend a known method to a spectral method for non-autonomous time delay systems. We verify all three new methods numerically. Hence, in this thesis three new spectral methods for the stability analysis of periodic time delay systems are presented. info:eu-repo/classification/ddc/530 ddc:530
152	Studying the effectiveness of dynamic analysis for fingerprinting Android malware behavior / En studie av effektivitet hos dynamisk analys för kartläggning av beteenden hos Android malware Regard, Viktor January 2019 (has links) Android is the second most targeted operating system for malware authors and to counter the development of Android malware, more knowledge about their behavior is needed. There are mainly two approaches to analyze Android malware, namely static and dynamic analysis. Recently in 2017, a study and well labeled dataset, named AMD (Android Malware Dataset), consisting of over 24,000 malware samples was released. It is divided into 135 varieties based on similar malicious behavior, retrieved through static analysis of the file classes.dex in the APK of each malware, whereas the labeled features were determined by manual inspection of three samples in each variety. However, static analysis is known to be weak against obfuscation techniques, such as repackaging or dynamic loading, which can be exploited to avoid the analysis. In this study the second approach is utilized and all malware in the dataset are analyzed at run-time in order to monitor their dynamic behavior. However, analyzing malware at run-time has known weaknesses as well, as it can be avoided through, for instance, anti-emulator techniques. Therefore, the study aimed to explore the available sandbox environments for dynamic analysis, study the effectiveness of fingerprinting Android malware using one of the tools and investigate whether static features from AMD and the dynamic analysis correlate. For instance, by an attempt to classify the samples based on similar dynamic features and calculating the Pearson Correlation Coefficient (r) for all combinations of features from AMD and the dynamic analysis. The comparison of tools for dynamic analysis, showed a need of development, as most popular tools has been released for a long time and the common factor is a lack of continuous maintenance. As a result, the choice of sandbox environment for this study ended up as Droidbox, because of aspects like ease of use/install and easily adaptable for large scale analysis. Based on the dynamic features extracted with Droidbox, it could be shown that Android malware are more similar to the varieties which they belong to. The best metric for classifying samples to varieties, out of four investigated metrics, turned out to be Cosine Similarity, which received an accuracy of 83.6% for the entire dataset. The high accuracy indicated a correlation between the dynamic features and static features which the varieties are based on. Furthermore, the Pearson Correlation Coefficient confirmed that the manually extracted features, used to describe the varieties, and the dynamic features are correlated to some extent, which could be partially confirmed by a manual inspection in the end of the study. Android malware dynamic analysis droidbox cuckoodroid droidscope mobsf malware behavior correlation pearson correlation cosine similarity euclidean distance chebyshev distance mahalanobis distance similarity analysis static features dynamic features tf-idf AMD Android malware dataset malware dataset UpDroid EC2 Computer and Information Sciences Data- och informationsvetenskap
153	Prime number races Haddad, Tony 08 1900 (has links) Sous l’hypothèse de Riemann généralisée et l’hypothèse d’indépendance linéaire, Rubinstein et Sarnak ont prouvé que les valeurs de x > 1 pour lesquelles nous avons plus de nombres premiers de la forme 4n + 3 que de nombres premiers de la forme 4n + 1 en dessous de x ont une densité logarithmique d’environ 99,59%. En général, l’étude de la différence #{p < x : p dans A} − #{p < x : p dans B} pour deux sous-ensembles de nombres premiers A et B s’appelle la course entre les nombres premiers de A et de B. Dans ce mémoire, nous cherchons ultimement à analyser d’un point de vue numérique et statistique la course entre les nombres premiers p tels que 2p + 1 est aussi premier (aussi appelés nombres premiers de Sophie Germain) et les nombres premiers p tels que 2p − 1 est aussi premier. Pour ce faire, nous présentons au préalable l’analyse de Rubinstein et Sarnak pour pouvoir repérer d’où vient le biais dans la course entre les nombres premiers 1 (mod 4) et les nombres premiers 3 (mod 4) et émettons une conjecture sur la distribution des nombres premiers de Sophie Germain. / Under the Generalized Riemann Hypothesis and the Linear Independence Hypothesis, Rubinstein and Sarnak proved that the values of x which have more prime numbers less than or equal to x of the form 4n + 3 than primes of the form 4n + 1 have a logarithmic density of approximately 99.59%. In general, the study of the difference #{p < x : p in A} − #{p < x : p in B} for two subsets of the primes A and B is called the prime number race between A and B. In this thesis, we will analyze the prime number race between the primes p such that 2p + 1 is also prime (these primes are called the Sophie Germain primes) and the primes p such that 2p − 1 is also prime. To understand this, we first present Rubinstein and Sarnak’s analysis to understand where the bias between primes that are 1 (mod 4) and the ones that are 3 (mod 4) comes from and give a conjecture on the distribution of Sophie Germain primes. Courses de nombres premiers Biais de Chebyshev Formule explicite Fonctions L Nombres premiers de Sophie Germain Crible de Selberg Modèle de Cramér Méthode du cercle Théorie analytique des nombres Prime number races Chebyshev's bias Explicit formula L-functions Sophie Germain primes Selberg sieve Cramér's model Circle method Analytic number theory
154	Introduction to Probability Theory Chen, Yong-Yuan 25 May 2010 (has links) In this paper, we first present the basic principles of set theory and combinatorial analysis which are the most useful tools in computing probabilities. Then, we show some important properties derived from axioms of probability. Conditional probabilities come into play not only when some partial information is available, but also as a tool to compute probabilities more easily, even when partial information is unavailable. Then, the concept of random variable and its some related properties are introduced. For univariate random variables, we introduce the basic properties of some common discrete and continuous distributions. The important properties of jointly distributed random variables are also considered. Some inequalities, the law of large numbers and the central limit theorem are discussed. Finally, we introduce additional topics the Poisson process. Chebyshev¡¦s inequality central limit theorem Poisson process Markov¡¦s inequality multivariate normal distribution multinomial distribution F distribution t distribution chi-square distribution lognormal distribution Beta distribution Cauchy distribution Weibull distribution gamma distribution exponential distribution normal distribution discrete uniform distribution uniform distribution hypergeometric distribution geometric distribution negative binomial distribution Poisson distribution binomial distribution Bernoulli distribution Bayes theorem theorem of total probability axioms of probability multinomial theorem inclusion-exclusion principle set
155	Laboratorní úloha zaměřená na obvody se spínanými kapacitory / Laboratory device focused on the switched capacitor circuits Urban, Lukáš January 2009 (has links) This Master`s thesis is focused on through acquaintance of principles of the function circuits with switched capaticors and posibility of their application mainly in frequency filters or signal generators. The origin of the switched capacitor circuits is mentioned at the beginning of the work. There are references to the first scientific work and scientists who have dealt with this issue. Maxwell`s idea: lossy element (resistor) replace with lossless element (switched capacitor) in electric circuit, is further described. In the next chapter of this work are listed types of switching capacitors and their use in simple RC filters and in structures of inverted or noninverted integrators and their application in more complex higher order filters. The advantages and disadvantages of SC circuits versus circuit composed of discrete components are shown. It is also listed a simple low-pass switched RC filter implemented with analogue multiplexer 4053. Using the LTC1043 integrated circuit, which structure and properties are described and analyzed in detail in the work, the 1st order aktive or pasive low and high pass filters were designed and subsequently simulated in the computer simulator OrCAD PSpice v.10. Another chapter deals with the integrated circuits higher order filters, structure and properties of the integrated filter LTC1060 are further analyzed here. Except this IC there are mentioned integrated filters commercially less available from the corporations Linear Technology and Maxim. The main objective of thesis was to propose and establish laboratory device and laboratory measurment focused on the switched capacitor circuits. The laboratory device has been designed with integrated circuits LTC1043 and LTC1060, which is demonstrated by using passive and active integrator, 2nd order band-pass and 4th order band-pass with Chebyshevovou approximation.
156	Feigenbaum Scaling Sendrowski, Janek January 2020 (has links) In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive. Feigenbaum Feigenbaum constant Feigenbaum point superstable self-similarity fractals final-state diagram logistic map period-doubling operator linearized period-doubling operator Cantor set Sharkovsky sequence Chebyshev interpolation stable manifold unstable manifold orbits fixed points scaling factor pitchfork bifurcation cobweb plot renormalization iterates one-hump map unimodal map bifurcation cascade Feigenbaum universality chaos theory spectrum generalized Feigenvalues bifurcation points superstable points fixed function universal function eigenvalues eigenvectors eigenfunctions universality conditions Schwarzian derivative Newton’s method power method Arnoldi’s method attractive fixed point repellent fixed point Banach fixed-point theorem collocation method functional analysis topology Mathematical Analysis Matematisk analys Other Mathematics Annan matematik Computational Mathematics Beräkningsmatematik

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