Synthesis and X-ray crystal and molecular structure of tetrakis(2,2-dimethyl-1-phenylethenyl)chromium(IV), the first structurally-characterised homoleptic alkenyl compound of a transition metal

The title compound, the first homoleptic Group 6A metal alkenyl, has been prepared from CrCl3·3(thf), and its properties, including X-ray crystal structure determination, are reported.

From matron to matrix: gender, authority and (dis)embodiment in Beckett’s Theatre

An examination of Samuel Beckett's representation of women in a selection of his plays for stage and radio.

Formation of atypical podosomes in extravillous trophoblasts regulates extracellular matrix degradation

Throughout pregnancy the cytotrophoblast, the stem cell of the placenta, gives rise to the differentiated forms of trophoblasts. The two main cell lineages are the syncytiotrophoblast and the invading extravillous trophoblast. A successful pregnancy requires extravillous trophoblasts to migrate and invade through the decidua and then remodel the maternal spiral arteries. Many invasive cells use specialised cellular structures called invadopodia or podosomes in order to degrade extracellular matrix. Despite being highly invasive cells, the presence of invadapodia or podosomes has not previously been investigated in trophoblasts. In this study these structures have been identified and characterised in extravillous trophoblasts. The role of specialised invasive structures in trophoblasts in the degradation of the extracellular matrix was compared with well characterised podosomes and invadopodia in other invasive cells and the trophoblast specific structures were characterised by using a sensitive matrix degradation assay which enabled visualisation of the structures and their dynamics. We show trophoblasts form actin rich protrusive structures which have the ability to degrade the extracellular matrix during invasion. The degradation ability and dynamics of the structures closely resemble podosomes, but have unique characteristics that have not previously been described in other cell types. The composition of these structures does not conform to the classic podosome structure, with no distinct ring of plaque proteins such as paxillin or vinculin. In addition, trophoblast podosomes protrude more deeply into the extracellular matrix than established podosomes, resembling invadopodia in this regard. We also show several significant pathways such as Src kinase, MAPK kinase and PKC along with MMP-2 and 9 as key regulators of extracellular matrix degradation activity in trophoblasts, while podosome activity was regulated by the rigidity of the extracellular matrix.

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.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

A matrix iteration for dynamic network summaries

We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at non-uniform points in time. We illustrate the new approach on synthetic and real data.

Equol: a comparison of the effects of the racemic compound with that of the purified S-enantiomer on the growth, invasion, and DNA integrity of breast and prostate cells in vitro

It has been postulated that the R- and S-equol enantiomers have different biological properties given their different binding affinities for the estrogen receptor. S-(-)equol is produced via the bacterial conversion of the soy isoflavone daidzein in the gut. We have compared the biological effects of purified S-equol to that of racemic (R and S) equol on breast and prostate cancer cells of varying receptor status in vitro. Both racemic and S-equol inhibited the growth of the breast cancer cell line MDA-MB-231 (> or = 10 microM) and the prostate cancer cell lines LNCaP (> or = 5 microM) and LAPC-4 (> or = 2.5 microM). The compounds also showed equipotent effects in inhibiting the invasion of MDA-MB-231 and PC-3 cancer cells through matrigel. S-equol (1, 10, 30 microM) was unable to prevent DNA damage in MCF-7 or MCF-10A breast cells following exposure to 2-hydroxy-4-nonenal, menadione, or benzo(a)pyrene-7,8-dihydrodiol-9,10-epoxide. In contrast, racemic equol (10, 30 microM) prevented DNA damage in MCF-10A cells following exposure to 2-hydroxy-4-nonenal or menadione. These findings suggest that racemic equol has strong antigenotoxic activity in contrast to the purified S-equol enantiomer implicating the R-, rather than the S-enantiomer as being responsible for the antioxidant effects of equol, a finding that may have implications for the in vivo chemoprotective properties of equol.

Variability in fecal water genotoxicity, determined using the Comet assay, is independent of endogenous N-nitroso compound formation attributed to red meat consumption

Red meat consumption causes a dose-dependent increase in fecal apparent total N-nitroso compounds (ATNC). The genotoxic effects of these ATNCs were investigated using two different Comet assay protocols to determine the genotoxicity of fecal water samples. Fecal water samples were obtained from two studies of a total of 21 individuals fed diets containing different amounts of red meat, protein, heme, and iron. The first protocol incubated the samples with HT-29 cells for 5 min at 4 degrees C, whereas the second protocol used a longer exposure time of 30 min and a higher incubation temperature of 37 degrees C. DNA strand breaks were quantified by the tail moment (DNA in the comet tail multiplied by the comet tail length). The results of the two Comet assay protocols were significantly correlated (r = 0.35, P = 0.003), however, only the second protocol resulted in detectable levels of DNA damage. Inter-individual effects were variable and there was no effect on fecal water genotoxicity by diet (P > 0.20), mean transit time (P = 0.588), or weight (P = 0.705). However, there was a highly significant effect of age (P = 0.019). There was no significant correlation between concentrations of ATNCs in fecal homogenates and fecal water genotoxicity (r = 0.04, P = 0.74). ATNC levels were lower in fecal water samples (272 microg/kg) compared to that of fecal homogenate samples (895 microg/kg) (P < 0.0001). Failure to find dietary effects on fecal water genotoxicity may therefore be attributed to individual variability and low levels of ATNCs in fecal water samples.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

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.

Effect of a methyl group on the spontaneous resolution of a square-pyramidal coordination compound: crystal packing and conglomerate formation

Reaction of [Cu(pic)2]·2H2O (where pic stands for 2-picolinato) with 2-({[2-(dimethylamino)ethyl]amino}methyl)phenol (HL1) produces the square-pyramidal complex [CuL1(pic)] (1), which crystallizes as a conglomerate (namely a mixture of optically pure crystals) in the Sohncke space group P212121. The use of the methylated ligand at the benzylic position, i.e. (±)-2-(1-{[2-(dimethylamino)ethyl]amino}ethyl)phenol (HL2), yields the analogous five-coordinate complex [CuL2(pic)] (2) that crystallizes as a true racemate (namely the crystals contain both enantiomers) in the centrosymmetric space group P21/c. Density functional theory (DFT) calculations indicate that the presence of the methyl group indeed leads to a distinct crystallization behaviour, not only by intramolecular steric effects, but also because its involvement in non-covalent C–H···π and hydrophobic intermolecular contacts appears to be an important factor contributing to the crystal-lattice (stabilizing) energy of 2