Comparison of regulatory regions in the mitochondrial genomes of grasses

Abstract only availableRegulation of transcription in plant mitochondria is not well understood. The recent sequencing of the mitochondrial genomes of 10 closely related grasses allowed a comparative analysis of regulatory regions. To look for conserved regions and potential “swapped” regulatory regions, we have performed a comparative analysis of the upstream and downstream regions of all of the protein-coding genes in the mitochondrial genomes of eleven grasses: five mitochondrial types of maize (two fertile and three cytoplasmic male sterile), three other taxa within the genus (Zea mays ssp. parviglumis, Z. luxurians, Z. perennis), two close relatives (Tripsacum dactyloides, Sorghum bicolor), and an outgroup, rice. These genomes contain an average of 35 protein-coding genes, composed of 40 transcriptional units. Our analyses examined 1000 base pairs (bp) upstream of the first exon of each transcriptional unit and 1000 bp downstream of its last exon. The reference genome was NB, the most common fertile maize mitochondrial genotype. Compared with the genes from NB, more than half of the mitochondrial genes in the other genomes contain sequences that flank different genes in NB; we refer to these as “swapped” regions. More than 25% of the translocated sequences are longer than 100 bp, and 21 are greater than 500 bp. The longer sequences are more likely to have a regulatory function. In addition, some of these regions were found multiple times: 12 of the translocated gene-flanking regions were found flanking five or more other genes; four had sequences that were flanking ten or more. Furthermore, in Z. luxurians, Z. perennis and T. dactyloides, the co-transcribed 18S and 5S ribosomal RNA genes have been translocated immediately upstream of the start of cox1, with the 5S rRNA 3' end only 80 bp from the start of cox1 exon 1. This is a position that is difficult to rectify with the divergent transcriptional needs of the two types of genes.Plant Genomics Internship @ M

On the Localization of One-Photon States

Single photon states with arbitrarily fast asymptotic power-law fall-off of energy density and photodetection rate are explicitly constructed. This goes beyond the recently discovered tenth power-law of the Hellwarth-Nouchi photon which itself superseded the long-standing seventh power-law of the Amrein photon.Comment: 7 pages, tex, no figure

Time delay for one-dimensional quantum systems with steplike potentials

This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with a potential $V(x)$ converging to different limits $V_{\ell}$ and $V_{r}$ as $x \to -\infty$ and $x \to +\infty$ respectively. Due to the anisotropy they exhibit a two-channel structure. We first establish the existence and properties of the channel wave and scattering operators by using the modern Mourre approach. We then use scattering theory to show the identity of two apparently different representations of time delay. The first one is defined in terms of sojourn times while the second one is given by the Eisenbud-Wigner operator. The identity of these representations is well known for systems where $V(x)$ vanishes as $|x| \to \infty$ ($V_\ell = V_r$). We show that it remains true in the anisotropic case $V_\ell \not = V_r$, i.e. we prove the existence of the time-dependent representation of time delay and its equality with the time-independent Eisenbud-Wigner representation. Finally we use this identity to give a time-dependent interpretation of the Eisenbud-Wigner expression which is commonly used for time delay in the literature.Comment: 48 pages, 1 figur

Rigged Hilbert Space Approach to the Schrodinger Equation

It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to handle unbounded Schrodinger Hamiltonians whose spectrum has a continuous part are disclosed. Those difficulties are overcome by using an appropriate Rigged Hilbert Space (RHS). The RHS is able to associate an eigenket to each energy in the spectrum of the Hamiltonian, regardless of whether the energy belongs to the discrete or to the continuous part of the spectrum. The collection of eigenkets corresponding to both discrete and continuous spectra forms a basis system that can be used to expand any physical wave function. Thus the RHS treats discrete energies (discrete spectrum) and scattering energies (continuous spectrum) on the same footing.Comment: 27 RevTex page

Dynamical approach to chains of scatterers

Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the transport through the chain to the spectral properties of individual scatterers. For a single-scattering channel case some new light is shed on known transport properties of disordered and noisy chains, whereas translationally invariant case can be studied analytically in terms of a simple deterministic dynamical map. The many-channel case was studied numerically by examining the statistical properties of scatterers that correspond to a certain type of transport of the chain i.e. ballistic or (partially) localised.Comment: 16 pages, 7 figure

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Human Impacts on Forest Biodiversity in Protected Walnut-Fruit Forests in Kyrgyzstan

We used a spatially explicit model of forest dynamics, supported by empirical field data and socioeconomic data, to examine the impacts of human disturbances on a protected forest landscape in Kyrgyzstan. Local use of 27 fruit and nut species was recorded and modeled. Results indicated that in the presence of fuelwood cutting with or without grazing, species of high socioeconomic impor- tance such as Juglans regia, Malus spp., and Armeniaca vulgaris were largely eliminated from the landscape after 50–150 yr. In the absence of disturbance or in the presence of grazing only, decline of these species occurred at a much lower rate, owing to competi- tive interactions between tree species. This suggests that the current intensity of fuelwood harvesting is not sustainable. Conversely, cur- rent grazing intensities were found to have relatively little impact on forest structure and composition, and could potentially play a positive role in supporting regeneration of tree species. These results indicate that both positive and negative impacts on biodiversity can arise from human populations living within a protected area. Potentially, these could be reconciled through the development of participatory approaches to conservation management within this reserve, to ensure the maintenance of its high conservation value while meeting human needs

Scattering from Singular Potentials in Quantum Mechanics

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r variable. The present paper extends those early results to an arbitrary number of spatial dimensions. The Hill-type equation which leads, in principle, to the evaluation of the polydromy parameter, is obtained from the Hill equation for a two-dimensional problem by means of a simple change of variables. The asymptotic forms of the wave function as r tends to zero and as r tends to infinity are also derived. The Darboux technique of intertwining operators is then applied to obtain an algorithm that makes it possible to solve the Schrodinger equation with a singular potential containing many negative powers of r, if the exact solution with even just one term is already known.Comment: 19 pages, plain Tex. In this revised version, the analysis of Eq. (5.29) has been amended, and an appendix has been added for completenes

In and around: identifying predictors of theft within and near to major mass underground transit systems

This article identifies factors that encourage or reduce pick-pocketing at underground rail stations through a case study analysis of the London Underground. Negative binomial Poisson regression models found predictor variables of pick-pocketing selected from the internal characteristics of stations and features of their nearby surroundings. Factors that increased risk were those associated with greater congestion inside stations including lifts, waiting rooms and fewer platforms; and increased levels of accessibility near stations, more paths and roads. Features that reduced risk were those likely to encourage detection and guardianship; stations with more personal validators, staffing levels and shop rentals; and the presence of more domestic buildings nearby. Station type was also influential; those that were ‘attractors’ of crime and those frequently used by tourists were at greater risk. The findings suggest a transmission of theft risk between the internal settings of underground stations and their nearby surroundings