An improved sufficient condition for absence of limit cycles in digital filters

It is known that if the state transition matrix A of a digital filter structure is such that D - A^{dagger}DA is positive definite for some diagonal matrix D of positive elements, then all zero-input limit cycles can be suppressed. This paper shows that positive semidefiniteness of D - A^{dagger}DA is in fact sufficient. As a result, it is now possible to explain the absence of limit cycles in Gray-Markel lattice structures based only on the state-space viewpoint

On factorization of a subclass of 2-D digital FIR lossless matricesfor 2-D QMF bank applications

The role of one-dimensional (1-D) digital finite impulse response (FIR) lossless matrices in the design of FIR perfect reconstruction quadrature mirror filter (QMF) banks has been explored previously. Structures which can realize the complete family of FIR lossless transfer matrices, have also been developed, with QMF application in mind. For the case of 2-D QMF banks, the same concept of lossless polyphase matrix has been used to obtain perfect reconstruction. However, the problem of finding a structure to cover all 2-D FIR lossless matrices of a given degree has not been solved. Progress in this direction is reported. A structure which completely covers a well-defined subclass of 2-D digital FIR lossless matrices is obtained

Low-complexity RLS algorithms using dichotomous coordinate descent iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of O(N-2) operations per sample; N being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3N multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2N multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented

The robust selection of predictive genes via a simple classifier

Identifying genes that direct the mechanism of a disease from expression data is extremely useful in understanding how that mechanism works. This in turn may lead to better diagnoses and potentially can lead to a cure for that disease. This task becomes extremely challenging when the data are characterised by only a small number of samples and a high number of dimensions, as it is often the case with gene expression data. Motivated by this challenge, we present a general framework that focuses on simplicity and data perturbation. These are the keys for the robust identification of the most predictive features in such data. Within this framework, we propose a simple selective na¨ıve Bayes classifier discovered using a global search technique, and combine it with data perturbation to increase its robustness to small sample sizes. An extensive validation of the method was carried out using two applied datasets from the field of microarrays and a simulated dataset, all confounded by small sample sizes and high dimensionality. The method has been shown capable of identifying genes previously confirmed or associated with prostate cancer and viral infections

Multigrid solver for axisymmetrical 2D fluid equations

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigrid method with respect to the number of grid points allowed us to use $256\times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids(the initial solution on $256\times 256$ grid was extrapolated steady solution from $128\times 128$ grid which allowed using "long" integration time steps). The fluid solver may be used as the basis for hybrid codes for DC discharges.Comment: preliminary version; presented at 28 ICPIG, July 15-20, 2007, Prague, Czech Republi

Effect of impurity substitution on band structure and mass renormalization of the correlated FeTe0.5_{0.5}Se0.5_{0.5} superconductor

Using angle-resolved photoemission spectroscopy (ARPES), we studied the effect of the impurity potential on the electronic structure of FeTe$_{0.5}$Se$_{0.5}$ superconductor by substituting 10\% of Ni for Fe which leads to an electron doping of the system. We could resolve three hole pockets near the zone center and an electron pocket near the zone corner in the case of FeTe$_{0.5}$Se$_{0.5}$, whereas only two hole pockets near the zone center and an electron pocket near the zone corner are resolved in the case of Fe$_{0.9}$Ni$_{0.1}$Te$_{0.5}$Se$_{0.5}$, suggesting that the hole pocket having predominantly the $xy$ orbital character is very sensitive to the impurity scattering. Upon electron doping, the size of the hole pockets decrease and the size of the electron pockets increase as compared to the host compound. However, the observed changes in the size of the electron and hole pockets are not consistent with the rigid-band model. Moreover, the effective mass of the hole pockets is reduced near the zone center and of the electron pockets is increased near the zone corner in the doped Fe$_{0.9}$Ni$_{0.1}$Te$_{0.5}$Se$_{0.5}$ as compared to FeTe$_{0.5}$Se$_{0.5}$. We refer these observations to the changes of the spectral function due to the effect of the impurity potential of the dopants.Comment: 8 pages, 3 figure

Ultraviolet photonic crystal laser

We fabricated two dimensional photonic crystal structures in zinc oxide films with focused ion beam etching. Lasing is realized in the near ultraviolet frequency at room temperature under optical pumping. From the measurement of lasing frequency and spatial profile of the lasing modes, as well as the photonic band structure calculation, we conclude that lasing occurs in the strongly localized defect modes near the edges of photonic band gap. These defect modes originate from the structure disorder unintentionally introduced during the fabrication process.Comment: 4 pages, 4 figure