Results on lattice vector quantization with dithering

The statistical properties of the error in uniform scalar quantization have been analyzed by a number of authors in the past, and is a well-understood topic today. The analysis has also been extended to the case of dithered quantizers, and the advantages and limitations of dithering have been studied and well documented in the literature. Lattice vector quantization is a natural extension into multiple dimensions of the uniform scalar quantization. Accordingly, there is a natural extension of the analysis of the quantization error. It is the purpose of this paper to present this extension and to elaborate on some of the new aspects that come with multiple dimensions. We show that, analogous to the one-dimensional case, the quantization error vector can be rendered independent of the input in subtractive vector-dithering. In this case, the total mean square error is a function of only the underlying lattice and there are lattices that minimize this error. We give a necessary condition on such lattices. In nonsubtractive vector dithering, we show how to render moments of the error vector independent of the input by using appropriate dither random vectors. These results can readily be applied for the case of wide sense stationary (WSS) vector random processes, by use of iid dither sequences. We consider the problem of pre- and post-filtering around a dithered lattice quantifier, and show how these filters should be designed in order to minimize the overall quantization error in the mean square sense. For the special case where the WSS vector process is obtained by blocking a WSS scalar process, the optimum prefilter matrix reduces to the blocked version of the well-known scalar half-whitening filter

Cyclic LTI systems in digital signal processing

Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the past. In this paper, we introduce the fundamentals of cyclic multirate systems and filter banks, presenting several important differences between the cyclic and noncyclic cases. Cyclic systems with allpass and paraunitary properties are studied. The paraunitary interpolation problem is introduced, and it is shown that the interpolation does not always succeed. State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited. It is shown that unlike in traditional linear systems, these two notions are not related to the system minimality in a simple way. Throughout the paper, a number of open problems are pointed out from the perspective of the signal processor as well as the system theorist

Results on optimal biorthogonal filter banks

Optimization of filter banks for specific input statistics has been of interest in the theory and practice of subband coding. For the case of orthonormal filter banks with infinite order and uniform decimation, the problem has been completely solved in recent years. For the case of biorthogonal filter banks, significant progress has been made recently, although a number of issues still remain to be addressed. In this paper we briefly review the orthonormal case, and then present several new results for the biorthogonal case. All discussions pertain to the infinite order (ideal filter) case. The current status of research as well as some of the unsolved problems are described

Rigorous Calculations of Non-Abelian Statistics in the Kitaev Honeycomb Model

We develop a rigorous and highly accurate technique for calculation of the Berry phase in systems with a quadratic Hamiltonian within the context of the Kitaev honeycomb lattice model. The method is based on the recently found solution of the model which uses the Jordan-Wigner-type fermionization in an exact effective spin-hardcore boson representation. We specifically simulate the braiding of two non-Abelian vortices (anyons) in a four vortex system characterized by a two-fold degenerate ground state. The result of the braiding is the non-Abelian Berry matrix which is in excellent agreement with the predictions of the effective field theory. The most precise results of our simulation are characterized by an error on the order of $10^{-5}$ or lower. We observe exponential decay of the error with the distance between vortices, studied in the range from one to nine plaquettes. We also study its correlation with the involved energy gaps and provide preliminary analysis of the relevant adiabaticity conditions. The work allows to investigate the Berry phase in other lattice models including the Yao-Kivelson model and particularly the square-octagon model. It also opens the possibility of studying the Berry phase under non-adiabatic and other effects which may constitute important sources of errors in topological quantum computation.Comment: 27 pages, 9 figures, 3 appendice

Analysis of agreement among definitions of metabolic syndrome in nondiabetic Turkish adults: a methodological study

İstanbul Bilim Üniversitesi, Tıp Fakültesi.Abstract Background: We aimed to explore the agreement among World Health Organization (WHO), European Group for the Study of Insulin Resistance (EGIR), National Cholesterol Education Program (NCEP), American College of Endocrinology (ACE), and International Diabetes Federation (IDF) definitions of the metabolic syndrome. Methods: 1568 subjects (532 men, 1036 women, mean age 45 and standard deviation (SD) 13 years) were evaluated in this cross-sectional, methodological study. Cardiometabolic risk factors were determined. Insulin sensitivity was calculated by HOMA-IR. Agreement among definitions was determined by the kappa statistic. ANOVA and post hoc Tukey's test were used to compare multiple groups. Results: The agreement between WHO and EGIR definitions was very good (kappa: 0.83). The agreement between NCEP, ACE, and IDF definitions was substantial to very good (kappa: 0.77–0.84). The agreement between NCEP or ACE or IDF and WHO or EGIR definitions was fair (kappa: 0.32–0.37). The age and sex adjusted prevalence of metabolic syndrome was 38% by NCEP, 42% by ACE and IDF, 20% by EGIR and 19% by WHO definition. The evaluated definitions were dichotomized after analysis of design, agreement and prevalence: insulin measurement requiring definitions (WHO and EGIR) and definitions not requiring insulin measurement (NCEP, ACE, IDF). One definition was selected from each set for comparison. WHO-defined subjects were more insulin resistant than subjects without the metabolic syndrome (mean and SD for log HOMA-IR, 0.53 ± 0.14 vs. 0.07 ± 0.23, respectively, p 0.05), but lower log HOMA-IR values (p < 0.05). Conclusion: The metabolic syndrome definitions that do not require measurement of insulin levels (NCEP, ACE and IDF) identify twice more patients with insulin resistance and increased Framingham risk scores and are more useful than the definitions that require measurement of insulin levels (WHO and EGIR)

Quantum Transport with Spin Dephasing: A Nonequilibrium Green's Function Approach

A quantum transport model incorporating spin scattering processes is presented using the non-equilibrium Green's function (NEGF) formalism within the self-consistent Born approximation. This model offers a unified approach by capturing the spin-flip scattering and the quantum effects simultaneously. A numerical implementation of the model is illustrated for magnetic tunnel junction devices with embedded magnetic impurity layers. The results are compared with experimental data, revealing the underlying physics of the coherent and incoherent transport regimes. It is shown that small variations in magnetic impurity spin-states/concentrations could cause large deviations in junction magnetoresistances.Comment: NEGF Formalism, Spin Dephasing, Magnetic Tunnel Junctions, Magnetoresistanc