Communicability across evolving networks

Many natural and technological applications generate time ordered sequences of networks, defined over a fixed set of nodes; for example time-stamped information about ‘who phoned who’ or ‘who came into contact with who’ arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural definition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by time’s arrow is captured naturally through the non-mutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction.

Liquid ultraviolet matrix-assisted laser desorption/ionization - mass spectrometry for automated proteomic analysis

We have combined several key sample preparation steps for the use of a liquid matrix system to provide high analytical sensitivity in automated ultraviolet -- matrix-assisted laser desorption/ionisation -- mass spectrometry (UV-MALDI-MS). This new sample preparation protocol employs a matrix-mixture which is based on the glycerol matrix-mixture described by Sze et al. The low-femtomole sensitivity that is achievable with this new preparation protocol enables proteomic analysis of protein digests comparable to solid-state matrix systems. For automated data acquisition and analysis, the MALDI performance of this liquid matrix surpasses the conventional solid-state MALDI matrices. Besides the inherent general advantages of liquid samples for automated sample preparation and data acquisition the use of the presented liquid matrix significantly reduces the extent of unspecific ion signals in peptide mass fingerprints compared to typically used solid matrices, such as 2,5-dihydroxybenzoic acid (DHB) or alpha-cyano-hydroxycinnamic acid (CHCA). In particular, matrix and low-mass ion signals and ion signals resulting from cation adduct formation are dramatically reduced. Consequently, the confidence level of protein identification by peptide mass mapping of in-solution and in-gel digests is generally higher.

Liquid ultraviolet matrix-assisted laser desorption/ionization mass spectrometry for automated proteomic analysis

We have combined several key sample preparation steps for the use of a liquid matrix system to provide high analytical sensitivity in automated ultraviolet - matrix-assisted laser desorption/ ionisation - mass spectrometry (UV-MALDI-MS). This new sample preparation protocol employs a matrix-mixture which is based on the glycerol matrix-mixture described by Sze et al. U. Am. Soc. Mass Spectrom. 1998, 9, 166-174). The low-ferntomole sensitivity that is achievable with this new preparation protocol enables proteomic analysis of protein digests comparable to solid-state matrix systems. For automated data acquisition and analysis, the MALDI performance of this liquid matrix surpasses the conventional solid-state MALDI matrices. Besides the inherent general advantages of liquid samples for automated sample preparation and data acquisition the use of the presented liquid matrix significantly reduces the extent of unspecific ion signals in peptide mass fingerprints compared to typically used solid matrices, such as 2,5-dihydrox-ybenzoic acid (DHB) or alpha-cyano-hydroxycinnamic acid (CHCA). In particular, matrix and lowmass ion signals and ion signals resulting from cation adduct formation are dramatically reduced. Consequently, the confidence level of protein identification by peptide mass mapping of in-solution and in-gel digests is generally higher.

Chalcogenide-halides of niobium (V). 1. Gas-phase structures of NbOBr3, NbSBr3, and NbSCl3. 2. Matrix infrared spectra and vibrational force fields of NbOBr3, NbSBr3, NbSCl3, and NbOCl3

The molecular structures of NbOBr3, NbSCl3, and NbSBr3 have been determined by gas-phase electron diffraction (GED) at nozzle-tip temperatures of 250 degreesC, taking into account the possible presence of NbOCl3 as a contaminant in the NbSCl3 sample and NbOBr3 in the NbSBr3 sample. The experimental data are consistent with trigonal-pyramidal molecules having C-3v symmetry. Infrared spectra of molecules trapped in argon or nitrogen matrices were recorded and exhibit the characteristic fundamental stretching modes for C-3v species. Well resolved isotopic fine structure (Cl-35 and Cl-37) was observed for NbSCl3, and for NbOCl3 which occurred as an impurity in the NbSCl3 spectra. Quantum mechanical calculations of the structures and vibrational frequencies of the four YNbX3 molecules (Y = O, S; X = Cl, Br) were carried out at several levels of theory, most importantly B3LYP DFT with either the Stuttgart RSC ECP or Hay-Wadt (n + 1) ECP VDZ basis set for Nb and the 6-311 G* basis set for the nonmetal atoms. Theoretical values for the bond lengths are 0.01-0.04 Angstrom longer than the experimental ones of type r(a), in accord with general experience, but the bond angles with theoretical minus experimental differences of only 1.0-1.5degrees are notably accurate. Symmetrized force fields were also calculated. The experimental bond lengths (r(g)/Angstrom) and angles (angle(alpha)/deg) with estimated 2sigma uncertainties from GED are as follows. NbOBr3: r(Nb=O) = 1.694(7), r(Nb-Br) = 2.429(2), angle(O=Nb-Br) = 107.3(5), angle(Br-Nb-Br) = 111.5(5). NbSBr3: r(Nb=S) = 2.134(10), r(Nb-Br) = 2.408(4), angle(S=Nb-Br) = 106.6(7), angle(Br-Nb-Br) = 112.2(6). NbSCl3: Nb=S) = 2.120(10), r(Nb-Cl) = 2.271(6), angle(S=Nb-Cl) = 107.8(12), angle(Cl-Nb-Cl) = 111.1(11).

The philosophy of W. Ross Ashby and its relationship to 'The Matrix'

Ashby was a keen observer of the world around him, as per his technological and psychiatrical developments. Over the years, he drew numerous philosophical conclusions on the nature of human intelligence and the operation of the brain, on artificial intelligence and the thinking ability of computers and even on science in general. In this paper, the quite profound philosophy espoused by Ashby is considered as a whole, in particular in terms of its relationship with the world as it stands now and even in terms of scientific predictions of where things might lead. A meaningful comparison is made between Ashby's comments and the science fiction concept of 'The Matrix' and serious consideration is given as to how much Ashby's ideas lay open the possibility of the matrix becoming a real world eventuality.

Spectrum of a Feinberg-Zee random hopping matrix

This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.

Importance of oceanic resolution and mean state on the extra-tropical response to El Niño in a matrix of coupled models

The extra-tropical response to El Niño in configurations of a coupled model with increased horizontal resolution in the oceanic component is shown to be more realistic than in configurations with a low resolution oceanic component. This general conclusion is independent of the atmospheric resolution. Resolving small-scale processes in the ocean produces a more realistic oceanic mean state, with a reduced cold tongue bias, which in turn allows the atmospheric model component to be forced more realistically. A realistic atmospheric basic state is critical in order to represent Rossby wave propagation in response to El Niño, and hence the extra-tropical response to El Niño. Through the use of high and low resolution configurations of the forced atmospheric-only model component we show that, in isolation, atmospheric resolution does not significantly affect the simulation of the extra-tropical response to El Niño. It is demonstrated, through perturbations to the SST forcing of the atmospheric model component, that biases in the climatological SST field typical of coupled model configurations with low oceanic resolution can account for the erroneous atmospheric basic state seen in these coupled model configurations. These results highlight the importance of resolving small-scale oceanic processes in producing a realistic large-scale mean climate in coupled models, and suggest that it might may be possible to “squeeze out” valuable extra performance from coupled models through increases to oceanic resolution alone.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.