International Year of Planet Earth 6. Biosignatures: Interpreting Evidence of the Origins and Diversity of Life

Biosignatures are molecular, mineral or isotopic patterns that can be unambiguously interpreted as evidence of life and so provide the means for us to address our most fundamental questions about the origins and evolution of life. Biosignatures of microbial life are especially important to our understanding of early Earth history, and can be recorded in magnetic mineral traces, various carbon compounds, and stable isotope ratios of many elements. These signatures, preserved in the geologic record, represent the primary means by which we gain insight into the early history of life on Earth, including the timing of the origins of life and major interactions of life with its environment, such as the oxidation of the Earth’s atmosphere. In addition, microbial biosignatures are also considered one of the most likely targets in the search for life beyond Earth. However, identifying and interpreting geochemical biosignatures of microbial life is challenging and involves careful differentiation between signatures of biological processes and those of abiological processes. Canada is playing an important role in biosig-nature research, both through the geologic record of life preserved in our ancient rocks, and through many examples of microbial life in extreme environments. The latter provide the modern understanding required to interpret the biosignature record from early Earth and perhaps one day from another planet. SOMMAIRE Les biosignatures sont ces arrangements moléculaires, minéraux et isotopiques qui sont des preuves évidentes de l’existence de vie organique, et qui sont donc autant de moyens nous permettant de tenter de répondre aux questions fondamentales sur l’origine et l’évolution de la vie. Les biosig-natures microbiennes sont particulièrement importantes pour la compréhension des premiers stades de l’histoire de la Terre; elles sont constituées de traces de minéraux magnétiques, de composés organiques divers, ou de ratios particuliers d’isotopes stables de nombreux éléments. Ces signatures conservées dans la roche sont des indicateurs de première importance nous permettant de déchiffrer les premiers stades de l’histoire de la vie sur Terre, incluant la chronologie des origines de la vie et des grandes interactions de la vie avec l’environnement, comme l’oxydation de l’atmosphère terrestre. De plus, on considère que les biosignatures microbiennes sont l’un des indicateurs les plus probables de la présence de vie extraterrestre. Cela dit, l’identification et l’interprétation de biosignatures géochimiques microbiennes est délicate; il faut pouvoir distinguer les biosignatures de processus biologiques de celles de processus abiologiques. Le Canada joue un rôle important dans la recherche sur les biosignatures, à la fois par les traces de vie préservées dans les roches anciennes de son histoire géologique, et du fait des exemples de vie microbienne dans des environnements extrêmes de son territoire. Les recherches en milieux extrêmes nous permettent d’acquérir les connaissances nécessaires pour interpréter les biosignatures des premiers stades de l’histoire géologique de la Terre, et peut-être un jour d’une autre planète

Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PT's) of the associated 4 x 4 density matrices). But the full implementation of the test--requiring that the determinant of the PT be nonnegative for separability to hold--appears to be, at least presently, computationally intractable. So, we have previously implemented--using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/{135 pi^2} =0.76854$. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a still further improved upper bound of 1129/2100 = 0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESF's that comes close to reproducing our numerical estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the end are correcte

Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence

The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional and 15-dimensional in nature, respectively. The total volumes of the spaces they occupy with respect to the Hilbert-Schmidt and Bures metrics are obtainable as special cases of formulas of Zyczkowski and Sommers. We claim that if one could determine certain metric-independent 3-dimensional "eigenvalue-parameterized separability functions" (EPSFs), then these formulas could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes occupied by only the separable two-qubit states (and hence associated separability probabilities). Motivated by analogous earlier analyses of "diagonal-entry-parameterized separability functions", we further explore the possibility that such 3-dimensional EPSFs might, in turn, be expressible as univariate functions of some special relevant variable--which we hypothesize to be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical results we obtain are rather closely supportive of this hypothesis. Both the real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude roughly 50% at C=1/2, as well as a number of additional matching discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.

Electron corrected Lorentz forces in solids and molecules in magnetic field

We describe the effective Lorentz forces on the ions of a generic insulating system in an magnetic field, in the context of Born-Oppenheimer ab-initio molecular dynamics. The force on each ion includes an important contribution of electronic origin, which depends explicitly on the velocity of all other ions. It is formulated in terms of a Berry curvature, in a form directly suitable for future first principles classical dynamics simulations based {\it e.g.,} on density functional methods. As a preliminary analytical demonstration we present the dynamics of an H$_2$ molecule in a field of intermediate strength, approximately describing the electrons through Slater's variational wavefunction.Comment: 5 pages, 2 figures; to appear in Phys. Rev.

On Metric Dimension of Functigraphs

The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid v=f(u)\}$. We study how metric dimension behaves in passing from $G$ to $C(G,f)$ by first showing that $2 \le \dim(C(G, f)) \le 2n-3$, if $G$ is a connected graph of order $n \ge 3$ and $f$ is any function. We further investigate the metric dimension of functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure

PinR mediates the generation of reversible population diversity in Streptococcus zooepidemicus

Opportunistic pathogens must adapt to and survive in a wide range of complex ecosystems. Streptococcus zooepidemicus is an opportunistic pathogen of horses and many other animals, including humans. The assembly of different surface architecture phenotypes from one genotype is likely to be crucial to the successful exploitation of such an opportunistic lifestyle. Construction of a series of mutants revealed that a serine recombinase, PinR, inverts 114 bp of the promoter of SZO_08560, which is bordered by GTAGACTTTA and TAAAGTCTAC inverted repeats. Inversion acts as a switch, controlling the transcription of this sortase-processed protein, which may enhance the attachment of S. zooepidemicus to equine trachea. The genome of a recently sequenced strain of S. zooepidemicus, 2329 (Sz2329), was found to contain a disruptive internal inversion of 7 kb of the FimIV pilus locus, which is bordered by TAGAAA and TTTCTA inverted repeats. This strain lacks pinR and this inversion may have become irreversible following the loss of this recombinase. Active inversion of FimIV was detected in three strains of S. zooepidemicus, 1770 (Sz1770), B260863 (SzB260863) and H050840501 (SzH050840501), all of which encoded pinR. A deletion mutant of Sz1770 that lacked pinR was no longer capable of inverting its internal region of FimIV. The data highlight redundancy in the PinR sequence recognition motif around a short TAGA consensus and suggest that PinR can reversibly influence the wider surface architecture of S. zooepidemicus, providing this organism with a bet-hedging solution to survival in fluctuating environments

Effect of positron-atom interactions on the annihilation gamma spectra of molecules

Calculations of gamma spectra for positron annihilation on a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The annihilation gamma spectra characterise the momentum distribution of the electron-positron pair at the instant of annihilation. The contribution to the gamma spectra from individual molecular orbitals is obtained from electron momentum densities calculated using modern computational quantum chemistry density functional theory tools. The calculation, in its simplest form, effectively treats the low-energy (thermalised, room-temperature) positron as a plane wave and gives annihilation gamma spectra that are about 40% broader than experiment, although the main chemical trends are reproduced. We show that this effective "narrowing" of the experimental spectra is due to the action of the molecular potential on the positron, chiefly, due to the positron repulsion from the nuclei. It leads to a suppression of the contribution of small positron-nuclear separations where the electron momentum is large. To investigate the effect of the nuclear repulsion, as well as that of short-range electron-positron and positron-molecule correlations, a linear combination of atomic orbital description of the molecular orbitals is employed. It facilitates the incorporation of correction factors which can be calculated from atomic many-body theory and account for the repulsion and correlations. Their inclusion in the calculation gives gamma spectrum linewidths that are in much better agreement with experiment. Furthermore, it is shown that the effective distortion of the electron momentum density, when it is observed through positron annihilation gamma spectra, can be approximated by a relatively simple scaling factor.Comment: 26 pages, 12 figure

Interrelation of structural and electronic properties of InGaN/GaN quantum dots using an eight-band k.p model

We present an eight-band k.p model for the calculation of the electronic structure of wurtzite semiconductor quantum dots (QDs) and its application to indium gallium nitride (InGaN) QDs formed by composition fluctuations in InGaN layers. The eight-band k.p model accounts for strain effects, piezoelectric and pyroelectricity, spin-orbit and crystal field splitting. Exciton binding energies are calculated using the self-consistent Hartree method. Using this model, we studied the electronic properties of InGaN QDs and their dependence on structural properties, i.e., their chemical composition, height, and lateral diameter. We found a dominant influence of the built-in piezoelectric and pyroelectric fields, causing a spatial separation of the bound electron and hole states and a redshift of the exciton transition energies. The single-particle energies as well as the exciton energies depend heavily on the composition and geometry of the QDs

A simulation model of the Kenya national economy and its use as a guide to economic policy

This paper describes a simulation model of the Kenya national economy. The aim is to present a novel way of identifying, discussing and analysing a fairly wide spectrum of development problems facing Kenya. The model consists of a nine-sector input/output production component linked to a consumption component composed of four rural and five urban income classes. One of the main features of this model is that it is demand driven. Thus, growth rates in the productive sectors are generated endogenously as a function of demand. The model also deals with questions of income distribution, rural-urban migration and inflation. An overview is presented of the Kenyan economic and planning environment and the development and applications of the Kenya Simulation Model (KENSIM). The structure as well as the computational sequences of the model are described. A more detailed description of the model, including the overall structure (as reported in Slater and Walsham 1975) the set of economic assumptions and equations, the fortran computer programme, and the details of the data sources are reported in a forthcoming book by Slater, Walsham and Shah(l977). The paper goes on to discuss the application of KENSIM as a forecasting tool and for the simulation of alternative policy options, giving the example of rural-urban migration. The scope for further application and development of KENSIM is wide, and some of the major areas of current interest are identified. Some lessons and experiences are also included concerning co-operation between decision-makers and 'model-builders', which is essential if simulation models are to be used effectively for development planning