Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Polymerase chain reaction tests for the identification of Ross River, Kunjin and Murray Valley encephalitis virus infections in horses

Objective To develop and validate specific, sensitive and rapid diagnostic tests using RT-PCR for the detection of Ross River virus (RRV), Kunjin virus (KV) and Murray Valley encephalitis virus (MVEV) infections in horses. Methods Primer sets based on nucleotide sequence encoding the envelope glycoprotein E2 of RRV and on the nonstructural protein 5 (NS5) of KV and MVEV were designed and used in single round PCRs to test for the respective viruses in infected cell cultures and, in the case of RRV, in samples of horse blood and synovial fluid. Results The primer pairs designed for each of the three viruses amplified a product of expected size from prototype viruses that were grown in cell culture. The identity of each of the products was confirmed by nucleotide sequencing indicating that in the context used the RT-PCRs were specific. RRV was detected in serums from 8 horses for which there were clinical signs consistent with RRV infection such that an acute-phase serum sample was taken and submitted for RRV serology testing. The RRV RT-PCR was analytically sensitive in that it was estimated to detect as little as 50 TCID50 of RRV per mL of serum and was specific in that the primer pairs did not amplify other products from the 8 serum samples. The RRV primers also detected virus in three independent mosquito pools known to contain RRV by virus isolation in cell culture. Samples from horses suspected to be infected with KV and MVEV were not available. Conclusion Despite much anecdotal and serological evidence for infection of horses with RRV actual infection and associated clinical disease are infrequently confirmed. The availability of a specific and analytically sensitive RT-PCR for the detection of RRV provides additional opportunities to confirm the presence of this virus in clinical samples. The RTPCR primers for the diagnosis of KV and MVEV infections were shown to be specific for cell culture grown viruses but the further validation of these tests requires the availability of appropriate clinical samples from infected horses.

Synthesis and characterization of mono- and bis-ligand zinc(II) and cadmium(II) complexes of the di-2-pyridylketone Schiff base of S-benzyl dithiocarbazate (Hdpksbz) and the X-ray crystal structures of the [Zn(dpksbz)2] and [Cd(dpksbz)NCS]2 complexes

New mono- and bis-chelated zinc(II) and cadmium(II) complexes of formula, [M(dpksbz)NCS] (dpksbz = anionic form of the di-2-pyridylketone Schiff base of S-benzyldithiocarbazate) and [M(dpksbz)(2)] (M = Zn-II, Cd-II) have been prepared and characterized. The structure of the bis-ligand complex, [Zn(dpksbZ)(2)] has been determined by X-ray diffraction. The complex has a distorted octahedral geometry in which the ligands are coordinated to the zinc(II) ion as uninegatively charged tridentate chelates via the thiolate sulfur atoms, the azomethine nitrogen atoms and the pyridine nitrogen atoms. The distortion from a regular octahedral geometry is attributed to the restricted bite angles of the Schiff base ligands. X-ray structural analysis shows that the [Cd(dpksbz)NCS](2) complex is a centrosymmetric dimer in which each of the cadmium(II) ions adopts a five-coordinate, approximately square-pyramidal configuration with the Schiff base acting as a tetradentate chelating agent coordinating a cadmium(II) ion via one of the pyridine nitrogen atoms, the azomethine nitrogen atom and the thiolate sulfur atom; the second pyridine nitrogen atom is coordinated to the other cadmium(II) ion of the dimer. The fifth coordination position around each cadmium(II) is occupied by an N-bonded thiocyanate ligand. (C) 2003 Elsevier Science Ltd. All rights reserved.

The preparation of zinc(II) and cadmium(II) complexes of the pentadentate N3S2 ligand formed from 2,6-diacetylpyridine and S-benzyldithiocarbazate (H2SNNNS) and the X-ray crystal structure of the novel dimeric [Zn2(SNNNS)2] complex

The pentadentate chelating agent, 2,6-diacetylpyridinebis(S-benzyldithiocarbazate) (H2SNNNS) reacts with zinc(II) and cadmium(II) ions forming stable complexes of empirical formula, [M(SNNNS)] (M=Zn2+, Cd2+; SNNNS2 =doubly deprotonated anionic form of the Schiff base). These complexes have been characterized by a variety of physico-chemical techniques. IR and H-1 NMR spectral evidence indicate that the Schiff base coordinates to the zinc(II) and cadmium(II) ions via the pyridine nitrogen atoms, the azomethine nitrogen atoms and the mercaptide sulfur atoms. The crystal and molecular structure of the zinc(II) complex has been determined by X-ray diffraction. The complex is a dimer in which the pyridine nitrogen atom,the azomethine nitrogen atom and the thiolate sulfur atom from one ligand coordinate to one of the zinc(II) ions whereas the azomethine and thiolate sulfur atoms from another ligand complete pentacoordination around the zinc(II) ion, the ligands being coordinated in their deprotonated forms. The coordination geometry about each zinc(II) can be considered as intermediate between a square-pyramid and trigonal-bipyramid. The cadmium(II) complex is also assigned with a dimeric structure. (C) 2003 Elsevier Ltd. All rights reserved.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.