The zero forcing number is a graph parameter first introduced as a tool for solving the minimum rank problem, which is: Given a simple, undirected graph G, and a field F, let S(F,G) denote the set of all symmetric matrices A=[a_{ij}] with entries in F such that a_{ij} doess not equal 0 if and only if ij is an edge in G. Find the minimum possible rank of a matrix in S(F,G). It is known that the zero forcing number Z(G) provides an upper bound for the maximum nullity of a graph. I investigate properties of the zero forcing number, including its behavior under various graph operations.

The presented text deals with designing of a multilingual application and its following implementation in the C++ language. The application encrypts disk volumes with Microsoft Windows system using symmetric cryptography and password authentication, where the password security strength is verified. Securing the sensitive data is one of the important security goals in area of information technology. The symmetric cryptography uses the same key for both the encryption and the decryption and due to its speed it is suitable for the data storage encryption. For the higher security it is possible to encrypt a whole disk volume with sensitive data.

<p>Tokom poslednje decenije efikasnost DC/DC konvertora, brzina odziva i snaga<br />koju mogu da isporuče ka potrošaču postali su značajan faktor prilikom<br />konstruisanja i izbora ovih kola. U mnogim istraživanjima je potvrđeno da<br />korišćenje višefaznih topologija, uzajamno sprezanje faza i simetrija faza<br />unutar kola igraju značajnu ulogu u unapređenju navedenih karakteristika DC/DC konvertora.<br />U ovoj disertaciji je predstavljen novi simetrični dizajn višefaznih<br />spregnutih induktora kod kojih svi namotaji dele jedno, zajedničko, feritno<br />jezgro. Projektovane strukture su analizirane u laboratorijskim uslovima u<br />frenkvencijskom opsegu od 50 kHz do 40 MHz, a merni rezultati su potvrđeni<br />simulacijama u specijalizovanom softveru. Uzorci su testirani u radnim<br />uslovima pomoću šestofaznog DC/DC buck konvertora. Rezultati testova su<br />pokazali da primena konstruisanih induktorskih struktura dovodi do<br />poboljšanja brzine odziva i porasta efikasnosti test kola.</p> / <p>In the last decade efficiency of DC/DC converters, transient response and<br />delivered power, become important factor in development and selecting<br />these circuits. Numerous researches confirm benefits of using multiphase<br />topologies, mutual coupling of phases and symmetry of phases in the circuit<br />of DC/DC converters.<br />In this dissertation, new symmetric designs of multiphase coupled inductors<br />placed in the same core have been presented. Designed structures have<br />been tested in laboratory conditions in frequency range from 50 kHz to 40<br />MHz, and results have been confirmed by simulations in specialized<br />software. Testing of samples in operating conditions have been performed<br />with six-phase buck converter circuit. These experiments confirm that<br />developed inductors improve transient response and efficiency of test circuit.</p>

The central objects of study in this thesis are metric measure spaces. These are metric spaces which are endowed with a reference measure and enriched with basic topological, geometric and measure theoretical properties. The objective of the first part of the work is to characterize metric measure spaces whose symmetry groups admit a differential structure making them Lie groups. The second part is concerned with the analysis of the induced geometry of spaces admitting non-trivial symmetries. More in detail, it is shown that in many cases synthetic notions of Ricci curvature lower bounds are inherited by quotient spaces.

In this thesis we explore if a proposed random binary sequence generation algorithm can be combined with a separately proposed symmetric key agreement protocol to provide usable security for communications in Wireless Body Area Networks (WBAN). Other previous works in this area fall short by only considering key generation between two of the same signals or allowing for key generation between two different types of signals but with the cost of a significant signal collection time requirement. We hoped to advance this area of research by making secure key generation more efficient with less signal collection time and allowing keys to be generated between two sensors that measure two different physiological signals. However, while the binary sequence generation algorithm and key agreement protocol perform well separately, they do not perform well together. The combined approach yields keys that have good properties for use in a WBAN, but the generation rate is low.

Whenever we make a prediction we will make an error of a varying degree. What is worse,positive errors or negative ones? This question is important to answer before estimating amodel. When estimating a model a loss function is chosen, a function that gives an instruction of how to transform a particular error. Previous research hints at applications whereasymmetric loss functions provide more optimal models than using symmetric loss functions.Through a simulation study, this thesis highlights the consequences of using symmetric andasymmetric loss functions when assuming the actual problem is asymmetric. This thesis isconducted to cover a gap in literature as well as to correct a common statistical misunderstanding. Our core findings are that the models that take the asymmetry into account havethe lowest prediction errors, while also demonstrating that the larger the degree of asymmetry leads to a greater difference in performance between asymmetric and symmetric modelsin favour of the models estimated with asymmetric loss functions. This confirms what isdemonstrated in existing literature and what can be found in statistical theory.

We have found an operation between permutations in the symmetric group Sn upon which we have experimentally derived results that can be linked to desirable properties in cryptography, mainly in the domain of one-way functions. From it, we have implemented a beta version of an algorithm for a hashing function by exploiting the operation’s low computational cost for speed and its properties for security. Its design makes it resistant to length extension attacks and the encoding of blocks into permutations suggests that any differential cryptanalysis technique that is based on bit conditions should be useless against it. More precisely, when measuring the evolution of differences in the compression function, bit-based distances such as the exclusive-or distance should be replaced by another type of distance, still to be determined in future research. In this work we will present the algorithm and introduce a new framework of cryptanalysis for collision and preimage attacks in order to somehow measure its security. Once this is done, we will run comparison tests against MD5 and SHA256 in order to externally evaluate our algorithm in terms of speed, weaknesses and strength.

The consequences of substituting the denominator Q 3(p) - Q 1(p) by Q 2 - Q 1(p) in Groeneveld's class of quantile measures of kurtosis (γ 2(p)) for symmetric distributions, are explored using the symmetric influence function. The relationship between the measure γ 2(p) and the alternative class of kurtosis measures κ2(p) is derived together with the relationship between their influence functions. The Laplace, Logistic, symmetric Two-sided Power, Tukey and Beta distributions are considered in the examples in order to discuss the results obtained pertaining to unimodal, heavy tailed, bounded domain and U-shaped distributions.

Union-free families of subsets of [n] = {1, . . ., n} have been studied in Frankl and Füredi (Eur J Combin 5:127-131, 1984). In this paper, we provide a complete characterization of maximal symmetric difference-free families of subsets of [n].

This dissertation consists of three essays studying employer learning and statistical discrimination of young workers in the U.S. labor market. The first chapter outlines the dissertation by discussing the motivations, methods, and research findings.<br /><br />Chapter two develops a framework that nests both symmetric and asymmetric employer learning, and derives testable hypotheses on racial statistical discrimination under different processes of employer learning. Testing the model with data from the NLSY79, we find that employers statistically discriminate against black workers on the basis of both education and race in the high school market where learning appears to be mostly asymmetric. In the college market, employers directly observe most parts of the productivity of potential employees and learn very little over time.<br /><br />In chapter three, we investigate how the process of employer learning and statistical discrimination varies over time and across employers. The comparison between the NLSY79 and the NLSY97 cohorts reveals that employer learning and statistical discrimination has became stronger over the past decades. Using the NLSY97 data, we identify three employer- specific characteristics that influencing employer learning and statistical discrimination, the supervisor-worker race match, supervisor\'s age, and firm size. Black high school graduates face weaker employer learning and statistical discrimination if they choose to work for a black supervisor, work for an old supervisor, or work in a firm of small size.<br /><br />In the last chapter, we are interested in the associations between verbal and quantitative skills and individual earnings as well as the employer learning process of these two specific types of skills. There exist significant differences in both the labor market rewards and employer learning process of verbal and quantitative skills between high school and college graduates. Verbal skills are more important than quantitative skills for high school graduates, whereas college-educated workers benefit greatly from having high quantitative skills but little from having high verbal skills. In addition, employers directly learn verbal skills and continuously learn quantitative skills in the high school market, but almost perfectly observe quantitative skills in the college market. / Ph. D.