Syntheses of new binucleating heterocyclic ligands

The syntheses of five new mixed azine–azole binucleating ligands are described

Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets

An identifying code of a (di)graph $G$ is a dominating subset $C$ of the vertices of $G$ such that all distinct vertices of $G$ have distinct (in)neighbourhoods within $C$. In this paper, we classify all finite digraphs which only admit their whole vertex set in any identifying code. We also classify all such infinite oriented graphs. Furthermore, by relating this concept to a well known theorem of A. Bondy on set systems we classify the extremal cases for this theorem

Partitions with Prescribed Hook Differences

We investigate partition identities related to off-diagonal hook differences. Our results generalize previous extensions of the Rogers—Ramanujan identities. The identity of the related polynomials with constructs in statistical mechanics is discussed

Theory for Metal Hydrides with Switchable Optical Properties

Recently it has been discovered that lanthanum, yttrium, and other metal hydride films show dramatic changes in the optical properties at the metal-insulator transition. Such changes on a high energy scale suggest the electronic structure is best described by a local model based on negatively charged hydrogen (H$^-$) ions. We develop a many-body theory for the strong correlation in a H$^-$ ion lattice. The metal hydride is described by a large $U$-limit of an Anderson lattice model. We use lanthanum hydride as a prototype of these compounds, and find LaH$_3$ is an insulator with a substantial gap consistent with experiments. It may be viewed either as a Kondo insulator or a band insulator due to strong electron correlation. A H vacancy state in LaH$_3$ is found to be highly localized due to the strong bonding between the electron orbitals of hydrogen and metal atoms. Unlike the impurity states in the usual semiconductors, there is only weak internal optical transitions within the vacancy. The metal-insulator transition takes place in a band of these vacancy states.Comment: 18 pages, 16 figures and 6 tables. Submitted to PR

Anomalous Dynamics of Forced Translocation

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N^2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (sub-diffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N^2 and N^{1+\nu}, respectively, where \nu is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).Comment: 13 pages, RevTeX4, 16 eps figure

The Oedipal Paradigm in Group Development

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68383/2/10.1177_104649647300400302.pd

Conformal Invariance, Dark Energy, and CMB Non-Gaussianity

In addition to simple scale invariance, a universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is due to the mathematical isomorphism between the conformal group of certain 3 dimensional slices of de Sitter space and the de Sitter isometry group SO(4,1). In the standard homogeneous isotropic cosmological model in which primordial density perturbations are generated during a long vacuum energy dominated de Sitter phase, the embedding of flat spatial sections in de Sitter space induces a conformal invariant perturbation spectrum and definite prediction for the shape of the non-Gaussian CMB bispectrum. In the case in which the density fluctuations are generated instead on the de Sitter horizon, conformal invariance of the horizon embedding implies a different but also quite definite prediction for the angular correlations of CMB non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic to the symmetries of de Sitter space and in that sense, independent of specific model assumptions. Each is different from the predictions of single field slow roll inflation models which rely on the breaking of de Sitter invariance. We propose a quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise to these non-Gaussianities without a slow roll inflaton field, and argue that conformal invariance also leads to the expectation for the relation n_S-1=n_T between the spectral indices of the scalar and tensor power spectrum. Confirmation of this prediction or detection of non-Gaussian correlations in the CMB of one of the bispectral shape functions predicted by conformal invariance can be used both to establish the physical origins of primordial density fluctuations and distinguish between different dynamical models of cosmological vacuum dark energy.Comment: 73 pages, 9 figures. Final Version published in JCAP. New Section 4 added on linearized scalar gravitational potentials; New Section 8 added on gravitational wave tensor perturbations and relation of spectral indices n_T = n_S -1; Table of Contents added; Eqs. (3.14) and (3.15) added to clarify relationship of bispectrum plotted to CMB measurements; Some other minor modification

Tight-binding parameters for charge transfer along DNA

We systematically examine all the tight-binding parameters pertinent to charge transfer along DNA. The $\pi$ molecular structure of the four DNA bases (adenine, thymine, cytosine, and guanine) is investigated by using the linear combination of atomic orbitals method with a recently introduced parametrization. The HOMO and LUMO wavefunctions and energies of DNA bases are discussed and then used for calculating the corresponding wavefunctions of the two B-DNA base-pairs (adenine-thymine and guanine-cytosine). The obtained HOMO and LUMO energies of the bases are in good agreement with available experimental values. Our results are then used for estimating the complete set of charge transfer parameters between neighboring bases and also between successive base-pairs, considering all possible combinations between them, for both electrons and holes. The calculated microscopic quantities can be used in mesoscopic theoretical models of electron or hole transfer along the DNA double helix, as they provide the necessary parameters for a tight-binding phenomenological description based on the $\pi$ molecular overlap. We find that usually the hopping parameters for holes are higher in magnitude compared to the ones for electrons, which probably indicates that hole transport along DNA is more favorable than electron transport. Our findings are also compared with existing calculations from first principles.Comment: 15 pages, 3 figures, 7 table

‘O sibling, where art thou?’ – a review of avian sibling recognition with respect to the mammalian literature

Avian literature on sibling recognition is rare compared to that developed by mammalian researchers. We compare avian and mammalian research on sibling recognition to identify why avian work is rare, how approaches differ and what avian and mammalian researchers can learn from each other. Three factors: (1) biological differences between birds and mammals, (2) conceptual biases and (3) practical constraints, appear to influence our current understanding. Avian research focuses on colonial species because sibling recognition is considered adaptive where ‘mixing potential’ of dependent young is high; research on a wider range of species, breeding systems and ecological conditions is now needed. Studies of acoustic recognition cues dominate avian literature; other types of cues (e.g. visual, olfactory) deserve further attention. The effect of gender on avian sibling recognition has yet to be investigated; mammalian work shows that gender can have important influences. Most importantly, many researchers assume that birds recognise siblings through ‘direct familiarisation’ (commonly known as associative learning or familiarity); future experiments should also incorporate tests for ‘indirect familiarisation’ (commonly known as phenotype matching). If direct familiarisation proves crucial, avian research should investigate how periods of separation influence sibling discrimination. Mammalian researchers typically interpret sibling recognition in broad functional terms (nepotism, optimal outbreeding); some avian researchers more successfully identify specific and testable adaptive explanations, with greater relevance to natural contexts. We end by reporting exciting discoveries from recent studies of avian sibling recognition that inspire further interest in this topic