Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

Observed adaptation to climate change: UK evidence of transition to a well-adapting society

This paper investigates whether and to what extent a wide range of actors in the UK are adapting to climate change, and whether this is evidence of a social transition. We document evidence of over 300 examples of early adopters of adaptation practice to climate change in the UK. These examples span a range of activities from small adjustments (or coping) to building adaptive capacity, implementing actions and creating deeper systemic change in public and private organisations in a range of sectors. We find that adaptation in the UK has been dominated by government initiatives and has principally occurred in the form of research into climate change impacts. These actions within government stimulate a further set of actions at other scales in public agencies, regulatory agencies and regional government (or in the devolved administrations), though with little real evidence of climate change adaptation initiatives trickling down to local government level. The water supply and flood defence sectors, requiring significant investment in large scale infrastructure such as reservoirs and coastal defences, have invested more heavily in identifying potential impacts and adaptations. Economic sectors that are not dependent on large scale infrastructure appear to be investing far less effort and resources in preparing for climate change. We conclude that while the government-driven top-down targeted adaptation approach has generated anticipatory action at low cost, it may also have created enough niche activities to allow for diffusion of new adaptation practices in response to real or perceived climate change. These results have significant implications for how climate policy can be developed to support autonomous adaptors in the UK and other countries.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Radial basis function classifier construction using particle swarm optimisation aided orthogonal forward regression

We develop a particle swarm optimisation (PSO) aided orthogonal forward regression (OFR) approach for constructing radial basis function (RBF) classifiers with tunable nodes. At each stage of the OFR construction process, the centre vector and diagonal covariance matrix of one RBF node is determined efficiently by minimising the leave-one-out (LOO) misclassification rate (MR) using a PSO algorithm. Compared with the state-of-the-art regularisation assisted orthogonal least square algorithm based on the LOO MR for selecting fixednode RBF classifiers, the proposed PSO aided OFR algorithm for constructing tunable-node RBF classifiers offers significant advantages in terms of better generalisation performance and smaller model size as well as imposes lower computational complexity in classifier construction process. Moreover, the proposed algorithm does not have any hyperparameter that requires costly tuning based on cross validation.

Electronic transitions and bonding properties in a series of five-coordinate “16-electron” complexes [Mn(CO)3(L2)]− (L2=chelating redox-active π-donor ligand)

In this article we present for the first time accurate density functional theory (DFT) and time-dependent (TD) DFT data for a series of electronically unsaturated five-coordinate complexes [Mn(CO)(3)(L-2)](-), where L-2 stands for a chelating strong pi-donor ligand represented by catecholate, dithiolate, amidothiolate, reduced alpha-diimine (1,4-dialkyl-1,4-diazabutadiene (R-DAB), 2,2'-bipyridine) and reduced 2,2'-biphosphinine types. The single-crystal X-ray structure of the unusual compound [Na(BPY)][Mn(CO)(3)(BPY)]center dot Et2O and the electronic absorption spectrum of the anion [Mn(CO)(3)(BPY)](-) are new in the literature. The nature of the bidentate ligand determines the bonding in the complexes, which varies between two limiting forms: from completely pi-delocalized diamagnetic {(CO)(3)Mn-L-2}(-) for L-2 = alpha-diimine or biphosphinine, to largely valence-trapped {(CO)(3)Mn-1-L-2(2-)}(-) for L-2(2-) = catecholate, where the formal oxidation states of Mn and L-2 can be assigned. The variable degree of the pi-delocalization in the Mn(L-2) chelate ring is indicated by experimental resonance Raman spectra of [Mn(CO)(3)(L-2)](-) (L-2=3,5-di-tBu-catecholate and iPr-DAB), where accurate assignments of the diagnostically important Raman bands have been aided by vibrational analysis. The L-2 = catecholate type of complexes is known to react with Lewis bases (CO substitution, formation of six-coordinate adducts) while the strongly pi-delocalized complexes are inert. The five-coordinate complexes adopt usually a distorted square pyramidal geometry in the solid state, even though transitions to a trigonal bipyramid are also not rare. The experimental structural data and the corresponding DFT-computed values of bond lengths and angles are in a very good agreement. TD-DFT calculations of electronic absorption spectra of the studied Mn complexes and the strongly pi-delocalized reference compound [Fe(CO)(3)(Me-DAB)] have reproduced qualitatively well the experimental spectra. Analyses of the computed electronic transitions in the visible spectroscopic region show that the lowest-energy absorption band always contains a dominant (in some cases almost exclusive) contribution from a pi(HOMO) -> pi*(LUMO) transition within the MnL2 metallacycle. The character of this optical excitation depends strongly on the composition of the frontier orbitals, varying from a partial L-2 -> Mn charge transfer (LMCT) through a fully delocalized pi(MnL2) -> pi*(MnL2) situation to a mixed (CO)Mn -> L-2 charge transfer (LLCT/MLCT). The latter character is most apparent in the case of the reference complex [Fe(CO)(3)(Me-DAB)]. The higher-lying, usually strongly mixed electronic transitions in the visible absorption region originate in the three lower-lying occupied orbitals, HOMO - 1 to HOMO - 3, with significant metal-d contributions. Assignment of these optical excitations to electronic transitions of a specific type is difficult. A partial LLCT/MLCT character is encountered most frequently. The electronic absorption spectra become more complex when the chelating ligand L-2, such as 2,2'-bipyridine, features two or more closely spaced low-lying empty pi* orbitals.

A square-planar nickel(II) monoradical complex with a bis(salicylidene)diamine ligand

The new square-planar Ni-II-N2O2 complex [Ni(L-Me)] (1(Me)), where L-Me, stands for the dianionic phenolato form of N,N'bis(3,5-di-tert-butyl-salicylidene)-4,5-dimethyl-1,2-phenyl- enediamine ((LH2)-L-Me), has been synthesised and fully characterised. X-ray crystallography was also used for the characterisation. The electrochemical one-electron oxidation of 1(Me) produces the thermally stable (within the temperature range 10-295 K) cationic species (1(Me))(+). The UV/Vis and X-band EPR experimental data, supported by DFT calculations, indicate that (1(Me))(+), is best described as a Ni-II monoradical complex and, thus, does NOT exist in a Ni-III ground state, in contrast to its demethylated counterpart [Ni(L-H)](+) (1(H))(+) below 170 K.

The International Urban Energy Balance Models Comparison Project: First Results from Phase 1

A large number of urban surface energy balance models now exist with different assumptions about the important features of the surface and exchange processes that need to be incorporated. To date, no com- parison of these models has been conducted; in contrast, models for natural surfaces have been compared extensively as part of the Project for Intercomparison of Land-surface Parameterization Schemes. Here, the methods and first results from an extensive international comparison of 33 models are presented. The aim of the comparison overall is to understand the complexity required to model energy and water exchanges in urban areas. The degree of complexity included in the models is outlined and impacts on model performance are discussed. During the comparison there have been significant developments in the models with resulting improvements in performance (root-mean-square error falling by up to two-thirds). Evaluation is based on a dataset containing net all-wave radiation, sensible heat, and latent heat flux observations for an industrial area in Vancouver, British Columbia, Canada. The aim of the comparison is twofold: to identify those modeling ap- proaches that minimize the errors in the simulated fluxes of the urban energy balance and to determine the degree of model complexity required for accurate simulations. There is evidence that some classes of models perform better for individual fluxes but no model performs best or worst for all fluxes. In general, the simpler models perform as well as the more complex models based on all statistical measures. Generally the schemes have best overall capability to model net all-wave radiation and least capability to model latent heat flux.

Strongly nucleophilic RhI centre in square-planar complexes with terdentate (κ3) 2,2′:6′,2′′-terpyridine ligands: crystallographic, electrochemical and density functional theoretical studies

Rh-I-terpyridine complexes have been unambiguously formed for the first time. The 2,21:6',2"-terpyridine (tpy), 4'-chloro-2,2':6',2"-terpyridine (4'-Cl-tpy) and 4'-(tert-butyldimethylsilyl-ortho-carboranyl)-2,2':6',2"-terpyridine (carboranyl-tpy) ligands were used for successful syntheses and characterisation of the corresponding Rh-I complexes with halide coligands, [Rh(X)(4'-Y-terpyridine)] (X = Cl, Y = H, Cl, carboranyl; X = Br, Y = H). All four neutral Rh-tpy complexes are square planar, with Rh-X bonds in the plane of the 4'-Y-terpyridine ligands. Full characterisation of these dark blue, highly air-sensitive compounds was hampered by their poor solubility in various organic solvents. This is mainly due to the formation of pi-stacked aggregates, as evidenced by the crystal structure of [Rh(Cl)(tpy)]; in addition, [Rh(Cl)(carboranyl-tpy)] merely forms discrete dimers. The (bonding) properties of the novel Rh-I-terpyridine complexes have been studied with single-crystal X-ray diffraction, (time-dependent) density functional theoretical (DFT) calculations, far-infrared spectroscopy, electronic absorption spectroscopy and cyclic voltammetry. From DFT calculations, the HOMO of the studied Rh-I-terpyridine complexes involves predominantly the metal centre, while the LUMO resides on the terpyridine ligand. Absorption bands of the studied complexes in the visible region (400-900 nm) can be assigned to MLCT and MLCT/XLCT transitions. The relatively low oxidation potentials of [Rh(X)(tpy)] (X = Cl, Br) point to a high electron density on the metal centre. This makes the Rh-I-terpyridine complexes strongly nucleophilic and (potentially) highly reactive towards various (small) substrate molecules containing carbon-halide bonds.

Use of a reduced Schiff-Base ligand to prepare novel chloro-bridged chains of rare Cu(II) trinuclear complexes with mixed azido/oxo and chloro/oxo bridges

Two mixed bridged one-dimensional (1D) polynuclear complexes, [Cu3L2(mu(1,1)-N-3)(2)(mu-Cl)Cl](n) (1) and {[Cu3L2(mu-Cl)(3)Cl]center dot 0.46CH(3)OH}(n), (2), have been synthesized using the tridentate reduced Schiff-base ligand HL (2-[(2-dimethylamino-ethylamino)-methyl]-phenol). The complexes have been characterized by X-ray structural analyses and variable-temperature magnetic susceptibility measurements. In both complexes the basic trinuclear angular units are joined together by weak chloro bridges to form a 1D chain. The trinuclear structure of 1 is composed of two terminal square planar [Cu(L)(mu(1,1)-N-3)] units connected by a central Cu(II) atom through bridging nitrogen atoms of end-on azido ligands and the phenoxo oxygen atom of the tridentate ligand. These four coordinating atoms along with a chloride ion form a distorted trigonal bipyramidal geometry around the central Cu(II). The structure of 2 is similar; the only difference being a Cl bridge replacing the mu(1,1)-N-3 bridge in the trinuclear unit. The magnetic properties of both trinuclear complexes can be very well reproduced with a simple linear symmetrical trimer model (H = JS(i)S(i+1)) with only one intracluster exchange coupling (J) including a weak intertrimer interaction (.j) reproduced with the molecular field approximation. This model provides very satisfactory fits for both complexes in the whole temperature range with the following parameters: g = 2.136(3), J = 93.9(3) cm(-1) and zj= -0.90(3) cm(-1) (z = 2) for 1 and g = 2.073(7), J = -44.9(4) cm(-1) and zJ = -1.26(6) cm(-1) (z = 2) for 2.

Use of the LMS adaptive signal processing technique to improve signal data rates from practical oil well logging equipment

The simulation and development work that has been undertaken to produce a signal equaliser used to improve the data rates from oil well logging instruments is presented. The instruments are lowered into the drill bore hole suspended by a cable which has poor electrical characteristics. The equaliser described in the paper corrects for the distortions that occur from the cable (dispersion and attenuation) with the result that the instrument can send data at 100 K.bits/second down its own suspension cable of 12 Km in length. The use of simulation techniques and tools were invaluable in generating a model for the distortions and proved to be a useful tool when site testing was not available.

Using modelling tools to optimise the calculation and subsequent reduction of cable distortion parameters with application to oil well logging systems

This paper discusses how the use of computer-based modelling tools has aided the design of a telemetry unit for use with oil well logging. With the aid of modern computer-based simulation techniques, the new design is capable of operating at data rates of 2.5 times faster than previous designs.

Adaptive least mean square CDMA detection with Gram–Schmidt pre-processing

The Gram-Schmidt (GS) orthogonalisation procedure has been used to improve the convergence speed of least mean square (LMS) adaptive code-division multiple-access (CDMA) detectors. However, this algorithm updates two sets of parameters, namely the GS transform coefficients and the tap weights, simultaneously. Because of the additional adaptation noise introduced by the former, it is impossible to achieve the same performance as the ideal orthogonalised LMS filter, unlike the result implied in an earlier paper. The authors provide a lower bound on the minimum achievable mean squared error (MSE) as a function of the forgetting factor λ used in finding the GS transform coefficients, and propose a variable-λ algorithm to balance the conflicting requirements of good tracking and low misadjustment.