Flexible MMSE DFE using length and LAG adaptation

This paper investigates how to choose the optimum tap-length and decision delay for the decision feedback equalizer (DFE). Although the feedback filter length can be set as the channel memory, there is no closed-form expression for the feedforward filter length and decision delay. In this paper, first we analytically show that the two dimensional search for the optimum feedforward filter length and decision delay can be simplified to a one dimensional search, and then describe a new adaptive DFE where the optimum structural parameters can be self-adapted.

Self-assembled molecular complexes and coordination polymers of CdII, hexamine, and monocarboxylates: structural analysis and theoretical studies of supramolecular interactions

Four new cadmium(II) complexes [Cd-2(bz)(4)(H2O)(4)(mu 2-hmt)]center dot Hbz center dot H2O (1), [Cd-3(bz)(6)(H2O)(6)(mu 2-hmt)(2)]center dot 6H(2)O (2), [Cd(pa)(2)(H2O)(mu(2)-hmt)](n) (3), and {[Cd-3(ac)(6)(H2O)(3)(mu(3)-hmt)(2)]center dot 6H(2)O}(n) (4) with hexamine (hmt) and monocarboxylate ions, benzoate (bz), phenylacetate (pa), or acetate (ac) have been synthesized and characterized structurally. Structure determinations reveal that 1 is dinuclear, 2 is trinuclear, 3 is a one-dimensional (1D) infinite chain, and 4 is a two-dimensional (2D) polymer with fused hexagonal rings consisting of Cd-II and hmt. All the Cd-II atoms in the four complexes (except one CdII in 2) possess seven-coordinate pentagonal bipyramidal geometry with the various chelating bidentate carboxylate groups in equatorial sites. One of the CdII ions in 2, a complex that contains two monodentate carboxylates is in a distorted octahedral environment. The bridging mode of hmt is mu 2- in complexes 1-3 but is mu 3- in complex 4. In all complexes, there are significant numbers of H-bonds, C-H/pi, and pi-pi interactions which play crucial roles in forming the supramolecular networks. The importance of the noncovalent interactions in terms of energies and geometries has been analyzed using high level ab initio calculations. The effect of the cadmium coordinated to hmt on the energetic features of the C-H/pi interaction is analyzed. Finally, the interplay between C-H/pi and pi-pi interactions observed in the crystal structure of 3 is also studied.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

A new floating model level scheme for the assimilation of boundary layer top inversions: the univariate assimilation of temperature.

The assimilation of observations with a forecast is often heavily influenced by the description of the error covariances associated with the forecast. When a temperature inversion is present at the top of the boundary layer (BL), a significant part of the forecast error may be described as a vertical positional error (as opposed to amplitude error normally dealt with in data assimilation). In these cases, failing to account for positional error explicitly is shown t o r esult in an analysis for which the inversion structure is erroneously weakened and degraded. In this article, a new assimilation scheme is proposed to explicitly include the positional error associated with an inversion. This is done through the introduction of an extra control variable to allow position errors in the a priori to be treated simultaneously with the usual amplitude errors. This new scheme, referred to as the ‘floating BL scheme’, is applied to the one-dimensional (vertical) variational assimilation of temperature. The floating BL scheme is tested with a series of idealised experiments a nd with real data from radiosondes. For each idealised experiment, the floating BL scheme gives an analysis which has the inversion structure and position in agreement with the truth, and outperforms the a ssimilation which accounts only for forecast a mplitude error. When the floating BL scheme is used to assimilate a l arge sample of radiosonde data, its ability to give an analysis with an inversion height in better agreement with that observed is confirmed. However, it is found that the use of Gaussian statistics is an inappropriate description o f t he error statistics o f t he extra c ontrol variable. This problem is alleviated by incorporating a non-Gaussian description of the new control variable in the new scheme. Anticipated challenges in implementing the scheme operationally are discussed towards the end of the article.

Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Structural variations in self-assembled coordination complexes of Zn(II) with hexamethylenetetramine and isomeric 2-, 3- and 4-nitrobenzoates

Three new zinc(II)-hexamethylenetetramine (hmt) complexes [Zn-2(4-nbz)(4)(mu(2)-hmt)(OH2)(hmt)] (1). [Zn-2(2-nbz)(4)(mu(2)-hmt)(2)](n) (2) and [Zn-3(3-nbz)(4)(mu(2)-hmt)(mu(2)-OH)(mu(3)-OH)](n) (3) with three isomeric nitrobenzoate, [4-nbz = 4-nitrobenzoate, 2-nbz = 2-nitrobenzoate and 3-nbz = 3-nitrobenzoate] have been synthesized and structurally characterized by X-ray crystallography. Their identities have also been established by elemental analysis: IR, NMR, UV-Vis and mass spectral studies. 1 is a dinuclear complex formed by bridging hmt with mu(2) coordinating mode. The geometry around the Zn centers in 1 is distorted tetrahedral. Paddle-wheel centrosymmetric Zn-2(2-nbz)(4) units of complex 2 are interconnected by mu(2)-hmt forming a one-dimensional chain with square-pyramidal geometries around the Zn centers. Compound 3 contains a mu(2)/mu(3)-hydroxido and mu(2)-hmt bridged 1D chain. In this complex, varied geometries around the Zn centers are observed viz, tetrahedral, square pyramidal and trigonal bipyramidal. Various weak forces, i.e. lone pair-pi, pi-pi and CH-pi interactions, play a key role in stabilizing the observed structures for complexes 1,2 and 3. This series of complexes demonstrates that although the nitro group does not coordinate to the metal center, its presence at the 2-, 3- or 4-position of the phenyl ring has a striking effect on the dimensionality as well as the structure of the resulted coordination polymers, probably due to the participation of the nitro group in 1.p.center dot center dot center dot pi and/or C-H center dot center dot center dot pi interactions.

Host–guest supramolecular interactions in the coordination compounds of 4,4′-azobis(pyridine) with MnX2(X = NCS–, NCNCN–, and PF6–): structural analyses and theoretical study

Three new Mn(II) coordination compounds {[Mn(NCNCN)2(azpy)]·0.5azpy}n (1), {[Mn(NCS)2(azpy)(CH3OH)2]·azpy}n (2), and [Mn(azpy)2(H2O)4][Mn(azpy)(H2O)5]·4PF6·H2O·5.5azpy (3) (where azpy = 4,4'-azobis-(pyridine)) have been synthesized by self-assembly of the primary ligands, dicyanamide, thiocyanate, and hexafluorophosphate, respectively, together with azpy as the secondary spacer. All three complexes were characterized by elemental analyses, IR spectroscopy, thermal analyses, and single crystal X-ray crystallography. The structural analyses reveal that complex 1 forms a two-dimensional (2D) grid sheet motif These sheets assemble to form a microporous framework that incorporates coordination-free azpy by host-guest pi center dot center dot center dot pi. and C-H center dot center dot center dot N hydrogen bonding interactions. Complex 2 features azpy bridged one-dimensional (ID) chains of centrosymmetric [Mn(NCS)(2)(CH3OH)(2)} units which form a 2D porous sheet via a CH3 center dot center dot center dot pi supramolecular interaction. A guest azpy molecule is incorporated within the pores by strong H-bonding interactions. Complex 3 affords a 0-D motif with two monomeric Mn(II) units in the asymmetric unit. There exist pi center dot center dot center dot pi, anion center dot center dot center dot pi, and strong hydrogen bonding interactions between the azpy, water, and the anions. Density functional theory (DFT) calculations, at the M06/6-31+G* level of theory, are used to characterize a great variety of interactions that explicitly show the importance of host-guest supramolecular interactions for the stabilization of coordination compounds and creation of the fascinating three-dimensional (3D) architecture of the title compounds.

A very rare self-assembled ribbon of fused cyclic water pentamers encapsulated in a Cu-II based metal-organic framework

A metal organic framework of Cu-II, tartarate (tar) and 2,2'-bipyridyl (2,2'-bipy)], {[Cu(tar)(2,2'-bipy)]center dot 5H(2)O}(n)} (1) has been synthesized at the mild ambient condition and characterized by single crystal X-ray crystallography. In the compound, the Cu(2,2'-bipy) entities are bridged by tartarate ions which are coordinated to Cu-II by both hydroxyl and monodentate carboxylate oxygen to form a one-dimensional chain. The non-coordinated water molecules form ID water chains by edge-sharing cyclic water pentamers along with dangling water dimers. It shows reversible water expulsion upon heating. The water chains join the ID coordination polymeric chains to a 31) network through hydrogen-bond interactions.

Adaptation-induced collective dynamics of a single-cell protozoan

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

Groundwater residence time distributions in peatlands: implications for peat decomposition and accumulation

Peat soils consist of poorly decomposed plant detritus, preserved by low decay rates, and deep peat deposits are globally significant stores in the carbon cycle. High water tables and low soil temperatures are commonly held to be the primary reasons for low peat decay rates. However, recent studies suggest a thermodynamic limit to peat decay, whereby the slow turnover of peat soil pore water may lead to high concentrations of phenols and dissolved inorganic carbon. In sufficient concentrations, these chemicals may slow or even halt microbial respiration, providing a negative feedback to peat decay. We document the analysis of a simple, one-dimensional theoretical model of peatland pore water residence time distributions (RTDs). The model suggests that broader, thicker peatlands may be more resilient to rapid decay caused by climate change because of slow pore water turnover in deep layers. Even shallow peat deposits may also be resilient to rapid decay if rainfall rates are low. However, the model suggests that even thick peatlands may be vulnerable to rapid decay under prolonged high rainfall rates, which may act to flush pore water with fresh rainwater. We also used the model to illustrate a particular limitation of the diplotelmic (i.e., acrotelm and catotelm) model of peatland structure. Model peatlands of contrasting hydraulic structure exhibited identical water tables but contrasting RTDs. These scenarios would be treated identically by diplotelmic models, although the thermodynamic limit suggests contrasting decay regimes. We therefore conclude that the diplotelmic model be discarded in favor of model schemes that consider continuous variation in peat properties and processes.

Structural and magnetic studies of Schiff base complexes of nickel(ii) nitrite: change in crystalline state, ligand rearrangement and a very rare μ-nitrito-1κO:2κN:3κO′ bridging mode

Four new nickel(II) complexes, [Ni2L2(NO2)2]·CH2Cl2·C2H5OH, 2H2O (1), [Ni2L2(DMF)2(m-NO2)]ClO4·DMF (2a), [Ni2L2(DMF)2(m-NO2)]ClO4 (2b) and [Ni3L¢2(m3-NO2)2(CH2Cl2)]n·1.5H2O (3) where HL = 2-[(3-amino-propylimino)-methyl]-phenol, H2L¢ = 2-({3-[(2-hydroxy-benzylidene)-amino]-propylimino}-methyl)-phenol and DMF = N,N-dimethylformamide, have been synthesized starting with the precursor complex [NiL2]·2H2O, nickel(II) perchlorate and sodium nitrite and characterized structurally and magnetically. The structural analyses reveal that in all the complexes, NiII ions possess a distorted octahedral geometry. Complex 1 is a dinuclear di-m2-phenoxo bridged species in which nitrite ion acts as chelating co-ligand. Complexes 2a and 2b also consist of dinuclear entities, but in these two compounds a cis-(m-nitrito-1kO:2kN) bridge is present in addition to the di-m2-phenoxo bridge. The molecular structures of 2a and 2b are equivalent; they differ only in that 2a contains an additional solvated DMF molecule. Complex 3 is formed by ligand rearrangement and is a one-dimensional polymer in which double phenoxo as well as m-nitrito-1kO:2kN bridged trinuclear units are linked through a very rare m3-nitrito-1kO:2kN:3kO¢ bridge. Analysis of variable-temperature magnetic susceptibility data indicates that there is a global weak antiferromagnetic interaction between the nickel(II) ions in four complexes, with exchange parameters J of -5.26, -11.45, -10.66 and -5.99 cm-1 for 1, 2a, 2b and 3, respectively

Standardized test to evaluate numerical weather prediction algorithms

In order to assist in comparing the computational techniques used in different models, the authors propose a standardized set of one-dimensional numerical experiments that could be completed for each model. The results of these experiments, with a simplified form of the computational representation for advection, diffusion, pressure gradient term, Coriolis term, and filter used in the models, should be reported in the peer-reviewed literature. Specific recommendations are described in this paper.