Universal quantum computation requires precision control of the dynamics of qubits. Frequently accurate quantum control is impeded by systematic drifts and other errors. Compensating composite pulse sequences are a resource efficient technique for quantum error reduction. This work describes compensating sequences for ion-trap quantum computers. We introduce a Lie-algebraic framework which unifies all known fully-compensating sequences and admits a novel geometric interpretation where sequences are treated as vector paths on a dynamical Lie algebra. Using these techniques, we construct new narrowband sequences with improved error correction and reduced time costs. We use these sequences to achieve laser addressing of single trapped 40Ca+ ions, even if neighboring ions experience significant field intensity. We also use broadband sequences to achieve robust control of 171Yb+ ions even with inhomogeneous microwave fields. Further, we generalize compensating sequences to correct certain multi-qubit interactions. We show that multi-qubit gates may be corrected to arbitrary accuracy if there exists either two non-commuting controls with correlated errors or one error-free control. A practical ion-trap quantum computer must be extendible to many trapped ions. One solution is to employ microfabricated surface-electrode traps, which are well-suited for scalable designs and integrated systems. We describe two novel surface-electrode traps, one with on-chip microwave waveguides for hyperfine 171Yb+ qubit manipulations, and a second trap with an integrated high numerical aperture spherical micromirror for enhanced fluorescence collection.

We consider three problems in this dissertation, all under the unifying theme of random matrix products. The first and second problems are concerned with weak convergence in stochastic matrices and circulant matrices, respectively, and the third is concerned with the numerical calculation of the Lyapunov exponent associated with some random Fibonacci sequences. Stochastic matrices are nonnegative matrices whose row sums are all equal to 1. They are most commonly encountered as transition matrices of Markov chains. Circulant matrices, on the other hand, are matrices where each row after the first is just the previous row cyclically shifted to the right by one position. Like stochastic matrices, circulant matrices are ubiquitous in the literature.In the first problem, we study the weak convergence of the convolution sequence mu to the n, where mu is a probability measure with support S sub mu inside the space S of d by d stochastic matrices, d greater than or equal to 3. Note that mu to the n is precisely the distribution of the product X sub 1 times X sub 2 times and so on times X sub n of the mu distributed independent random variables X sub 1, X sub 2, and so on, X sub n taking values in S. In [CR] Santanu Chakraborty and B.V. Rao introduced a cyclicity condition on S sub mu and showed that this condition is necessary and sufficient for mu to the n to not converge weakly when d is equal to 3 and the minimal rank r of the matrices in the closed semigroup S generated by S sub mu is 2. Here, we extend this result to any d bigger than 3. Moreover, we show that when the minimal rank r is not 2, this result does not always hold.The second problem is an investigation of weak convergence in another direction, namely the case when the probability measure mu's support S sub mu consists of d by d circulant matrices, d greater than or equal to 3, which are not necessarily nonnegative. The resulting semigroup S generated by S sub mu now lacking the nice property of compactness in the case of stochastic matrices, we assume tightness of the sequence mu to the n to analyze the problem. Our approach is based on the work of Mukherjea and his collaborators, who in [LM] and [DM] presented a method based on a bookkeeping of the possible structure of the compact kernel K of S.The third problem considered in this dissertation is the numerical determination of Lyapunov exponents of some random Fibonacci sequences, which are stochastic versions of the classical Fibonacci sequence f sub (n plus 1) equals f sub n plus f sub (n minus 1), n greater than or equal to 1, and f sub 0 equal f sub 1 equals 1, obtained by randomizing one or both signs on the right side of the defining equation and or adding a "growth parameter." These sequences may be viewed as coming from a sequence of products of i.i.d. random matrices and their rate of growth measured by the associated Lyapunov exponent. Following techniques presented by Embree and Trefethen in their numerical paper [ET], we study the behavior of the Lyapunov exponents as a function of the probability p of choosing plus in the sign randomization.

The aim of this study is to look at the use of formulaic language, i.e. memorized and conventionalized combinations of words, in essays written by Swedish intermediate level students of English. Drawing on previous research (Cohen and Brooks -Carson 2001) this study will apply a method of “warming up” in Swedish (L1) before writing in English (L2). The primary material includes thirty essays written directly in English, and thirty essays starting from an outline in Swedish and then written in English, by the same students but on a different topic. Since there is evidence that native speakers always score the highest on amount of formulaic language in written discourse, the main hypothesis of this study is that by starting from an outline in Swedish and then writing in English the students will make use of more formulaic language than when writing directly in English. The first research question involves the quantity of formulaic language in the students’ essays. The second question concerns the distribution and use of the different categories of FSs (NPs, VPs etc) in the direct and indirect modes of writing. The last question addresses the erroneous attempts made by the students in forming FSs and the possible influence of transfer from L1 in the essays starting from an outline in Swedish compared to the essays written directly in English. The findings of this study lend support to the main hypothesis. Moreover, the analysis shows that there are significant differences in the distribution and use of the different categories of formulaic language in the direct and indirect modes of writing. Results are suggestive of a more conscious and less uncertain approach in the essays starting from an outline in Swedish, however the findings may be circumstantial. Furthermore, the results indicate that the method of “warming up” in Swedish may encourage the use of combinations of words that are more conventionalized and do not always interact with syntax in a regular way. The findings also indicate that transfer is not more salient in the essays starting from an outline in Swedish if compared to the essays written directly in English, at least not in relation to the erroneous FSs found in the students’ essays.

First of all the Internet pages presenting C++ Builder teaching material, are studied in the Master’s thesis. Applied themes are stressed the most of which is lacking in those pages. The aim of the work is – to describe the uses of C++ Builder tools that is - components of various format files (*.bmp, *.wmf, *.emf, *.ico, etc.) used to show images, graphic objects in the form of the program, which can show drawings, schemes, drafts; reading and drawing of random sequences, geometrical figures, function, drawing of analytically given functions and data presented by number sequences, the speech signals and other the sound files. Some examples of reading listening and viewing of the different sound files are also presented. The other important for applications subjects, as databases and programming of connections with databases, problem solutions in the form of algorithms, are also described The optimum algorithms “Division in half” and “Golden section” algorithms are realized in C++ Builder.

The constant demand for capacity increase, together with the foreseen saturation of the single-mode optical fiber, paved the way to technological breakthroughs that have completely changed the landscape of fiber-optic telecommunications. The most important advance was, undeniably, the practical implementation of a coherent detection with the help of high-speed electronics. This has, first, enabled the use of advanced modulation formats that allowed for a more efficient use of the fiber bandwidth, compared to the classical On-Off Keying, while adapted algorithms could not be used in order to mitigate the optical signal degradation. This thesis began a little after the advent of coherent detection and its main objective was to revisit the propagation effects in optical transmission systems using "Quadrature phase shift keying" (QPSK) modulation in the context of terrestrial systems, i.e. for transmission distances of up to about 2000 km. The manuscript is divided into two parts. The first part is dedicated to a study on the data sequences that need to be used in numerical simulations, when advanced modulation is involved. Fiber propagation, and in particular the interplay between chromatic dispersion and nonlinearities, usually introduce a nonlinear inter-symbol interference (ISI) to the transmitted signal. Since this ISI depends on the actual transmitted data pattern, it is obvious that the choice of the sequence used in our numerical simulations will have a direct influence on the estimated channel quality. Since, an infinite length, random sequence is impractical; we very commonly use pseudorandom" (PR) sequences, i.e. finite-length, deterministic sequences with balanced pattern statistics that seem to be random. In the first part we describe the method of generating M-level (with M>2) pseudorandom sequences and we detail their properties. In addition, we propose numerical tools to characterize the non-pseudorandom sequences that we use in numerical simulations, or we are sometimes forced to use in laboratory experiments. Finally, we present results of numerical simulations that quantify the necessity to use PR sequences as a function of our system parameters. After having established the "fairest possible" finite sequences, in the second part of the manuscript, we focus on the study of the nonlinear propagation, in the context of a transmission system using QPSK modulation and assuming a variable dispersion management and fiber type. Specifically, we numerically study the signal statistics due to the interplay of chromatic dispersion and nonlinear effects, neglecting all polarization or multi-wavelength effects and the amplifier noise. In this context, we were first interested in determining whether some empirical laws developed for OOK systems, can be also used in the case of QPSK modulation, such as the criterion of cumulative nonlinear phase (ΦNL) or laws that allow for a quick optimization of the dispersion management. Next we reveal the importance of a global phase rotation added to the initial signal constellation, as a parameter that can provide interesting information for the post-optimization of our system. We also discuss the fact that the constellation shape critically depends on the applied dispersion management, while there are generally 3 types of constellations, concerning the complex signal statistics: (1) the phase variance is higher than the amplitude variance (2) the amplitude variance is higher than the phase variance and (3) the received signal constellation resembles to a constellation of a signal under the influence of just an Additive White Gaussian Noise. Finally, we provide a phenomenological explanation of the constellations shapes revealing the fact that different data sub-sequences suffer from a different kind of signal degradation, while we also use this information to define a parameter that quantifies the potential benefit from a MAP (Maximum A Posteriori probability) correction algorithm

In this thesis we will consider divisibility properties of some recurrent sequences, Newman polynomials and computer calculations in those and related questions of number theory. / Čia nagrinėsime rekurenčiųjų sekų dalumo savybes, Niumano polinomus ir kompiuterių panaudojimąatliekant įvairius skaičiavimus, susijusius su minėtais skaičių teorijos klausimais.

Šioje disertacijoje bus nagrinėjamos rekurenčiųjų sekų dalumo savybės, Niumano polinomai ir kompiuterių panaudojimas atliekant įvairius matematinius skaiciavimus, susijusius su minėtais skaičių teorijos klausimais. / In this thesis we will consider divisibility properties of some recurrent sequences, Newman polynomials and computer calculations in those and related questions of number theory.

No description available.

Partial exchangeability is the fundamental building block in the subjective approach to the probability of multi-type sequences which replaces the independence concept of the objective theory. The aim of this thesis is to present some theory for partially exchangeable sequences of random variables based on well-known results for exchangeable sequences. The reader is introduced to the concepts of partially exchangeable events, partially exchangeable sequences of random variables and partially exchangeable o-fields, followed by some properties of partially exchangeable sequences of random variables. Extending de Finetti's representation theorem for exchangeable random variables to hold for multi-type sequences, we obtain the following result to be used throughout the thesis: There exists a o-field, conditional upon which, an infinite partially exchangeable sequence of random variables behaves like an independent sequence of random variables, identically distributed within types. Posing (i) a stronger requirement (spherical symmetry) and (ii) a weaker requirement (the selection property) than partial exchangeability on the infinite multi-type sequence of random variables, we obtain results related to de Finetti's representation theorem for partially exchangeable sequences of random variables. Regarding partially exchangeable sequences as mixtures of independent and identically distributed (within types) sequences, we (i) give three possible expressions for the directed random measures of the partially exchangeable sequence and (ii) look at three possible expressions for the o-field mentioned in de Finetti's representation theorem. By manipulating random measures and using de Finetti's representation theorem, we point out some concrete ways of constructing partially exchangeable sequences. The main result of this thesis follows by extending de Finetti's represen. tation theorem in conjunction with the Chatterji principle to obtain the following result: Given any a.s. limit theorem for multi-type sequences of independent random variables, identically distributed within types, there exists an analogous theorem satisfied by all partially exchangeable sequences and by all sub-subsequences of some subsequence of an arbitrary dependent infinite multi-type sequence of random variables, tightly distributed within types. We finally give some limit theorems for partially exchangeable sequences of random variables, some of which follow from the above mentioned result. / Thesis (Ph.D.)-University of Natal, Durban, 1991.

The ß-lactam antibiotics are the most important antibacterial agents in the treatment of infectious diseases. A severe problem in ß-lactam therapy is the emergence of ß-lactam resistant bacteria. Clinical ß-lactam resistance is most often due to the production of ß-lactamases. ß-lactamase genes reside either on plasmids or on the chromosome. The aim of this study was to acquire an understanding of organisation and regulation of chromosomal ß- lactamase genes in different Gram negative species and to elucidate the mechanisms for ampC hyperproduction in the in vivo situation. By DNA hybridization with an ampC probe from Escherichia coli K-12 it was shown that other Gram negative bacteria contained an artpC like chromosomal gene, suggesting a common evolutionary origin. Furthermore, the preceding frd operon that overlaps the ampC gene in E. coli K-12 was found to be much more conserved than the ampC gene in the bacterial species investigated. The ampC and frd opérons in Shigella sonnei and Citrobacter freundii were cloned and characterized by physical mapping. The respective maps were compared to the ampC and frd region in E. coli K-12. The physical map of Sh. sonnei was almost identical to the E. coli K-12 map, whereas in C. freundii only the frd region exhibited any considerable homology. Moreover, in C. freundii, the anpC and frd regions were separated by 1100 basepairs. It is suggested that this DNA is involved in the induction of ß-lactamase production in this organism. A hypothesis for the evolution of the anpC operon in enterobacteria is presented. By isolating and characterizing six ß-lactam resistant clinica], isolates of E. coli hyperproducing the dhrcmosomal ß-lactamase, genetic mechanisms for in vivo evolved resistance was aimed at. These isolates exhibited a 24-48 fold increase in ß-lactamase production. The ß-lactamase produced was found to be biochemically and immunologically identical to the ß-lactamase produced by E. coli K-12. The ampC control region of these six E. coli isolates was DNA-seqenced. The cause of ß-lactamase hyperproduction in five of the clinical E. coli isolates, identical in the DNA segment sequenced, was due to a strong novel ampC promoter displaced 5 bp upstream of the ampC promoter defined in E. coli K-12. The ß-lactamase hyperproduction in the sixth clinical isolate was shown to be caused by two mutations affecting both the promoter and the attenuator in the regulatory region defined by E. coli K- 12. The obtained changes were sufficient to explain the increase in ampC ß- 1 act ama se expression exhibited in these clinical E. coli isolates. Sequence analysis of the ampC control region in Sh. sonnei revealed that it was, with one exception, identical to the one found in the five clinical E. coli ß-lactamase hyperproducers. The only difference was in a position that creates the strong novel ampC promoter in the E. coli hyperproducers. By isolating spontaneous Sh. sonnei mutants with a 40-fold increase in ß-lactamase production carrying the same novel ampC promoter as the clinical E. coli isolates it was concluded that this DNA segment has been transferred in vivo frcm Shigella to E. coli across the species barrier. / <p>Diss. (sammanfattning) Umeå : Umeå universitet, 1983; Härtill 5 uppsatser</p> / digitalisering@umu