There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The flowering plant Arabidopsis thaliana is an important model system for identifying genes and determining their functions. Here we report the analysis of the genomic sequence of Arabidopsis. The sequenced regions cover 115.4 megabases of the 125-megabase genome and extend into centromeric regions. The evolution of Arabidopsis involved a whole-genome duplication, followed by subsequent gene loss and extensive local gene duplications, giving rise to a dynamic genome enriched by lateral gene transfer from a cyanobacterial-like ancestor of the plastid. The genome contains 25,498 genes encoding proteins from 11,000 families, similar to the functional diversity of Drosophila and Caenorhabditis elegans--the other sequenced multicellular eukaryotes. Arabidopsis has many families of new proteins but also lacks several common protein families, indicating that the sets of common proteins have undergone differential expansion and contraction in the three multicellular eukaryotes. This is the first complete genome sequence of a plant and provides the foundations for more comprehensive comparison of conserved processes in all eukaryotes, identifying a wide range of plant-specific gene functions and establishing rapid systematic ways to identify genes for crop improvement.

/pdf/analysis-of-the-genome-sequence-of-the-flowering-plant-3vizsb52m2.pdf

Analysis of the genome sequence of the flowering plant Arabidopsis thaliana.

Advances in next generation technologies have driven the costs of DNA sequencing down to the point that genotyping-by-sequencing (GBS) is now feasible for high diversity, large genome species. Here, we report a procedure for constructing GBS libraries based on reducing genome complexity with restriction enzymes (REs). This approach is simple, quick, extremely specific, highly reproducible, and may reach important regions of the genome that are inaccessible to sequence capture approaches. By using methylation-sensitive REs, repetitive regions of genomes can be avoided and lower copy regions targeted with two to three fold higher efficiency. This tremendously simplifies computationally challenging alignment problems in species with high levels of genetic diversity. The GBS procedure is demonstrated with maize (IBM) and barley (Oregon Wolfe Barley) recombinant inbred populations where roughly 200,000 and 25,000 sequence tags were mapped, respectively. An advantage in species like barley that lack a complete genome sequence is that a reference map need only be developed around the restriction sites, and this can be done in the process of sample genotyping. In such cases, the consensus of the read clusters across the sequence tagged sites becomes the reference. Alternatively, for kinship analyses in the absence of a reference genome, the sequence tags can simply be treated as dominant markers. Future application of GBS to breeding, conservation, and global species and population surveys may allow plant breeders to conduct genomic selection on a novel germplasm or species without first having to develop any prior molecular tools, or conservation biologists to determine population structure without prior knowledge of the genome or diversity in the species.

/pdf/a-robust-simple-genotyping-by-sequencing-gbs-approach-for-2orahkct9n.pdf

A Robust, Simple Genotyping-by-Sequencing (GBS) Approach for High Diversity Species

Nearly a century has been spent collecting and preserving genetic diversity in plants. Germplasm banks-living seed collections that serve as repositories of genetic variation-have been established as a source of genes for improving agricultural crops. Genetic linkage maps have made it possible to study the chromosomal locations of genes for improving yield and other complex traits important to agriculture. The tools of genome research may finally unleash the genetic potential of our wild and cultivated germplasm resources for the benefit of society.

http://www3.botany.ubc.ca/rieseberglab/plantevol/Tanksley%201997%20Seed%20banks%20and%20molecular%20maps.pdf

Seed Banks and Molecular Maps: Unlocking Genetic Potential from the Wild

Cytosine DNA methylation is important in regulating gene expression and in silencing transposons and other repetitive sequences. Recent genomic studies in Arabidopsis thaliana have revealed that many endogenous genes are methylated either within their promoters or within their transcribed regions, and that gene methylation is highly correlated with transcription levels. However, plants have different types of methylation controlled by different genetic pathways, and detailed information on the methylation status of each cytosine in any given genome is lacking. To this end, we generated a map at single-base-pair resolution of methylated cytosines for Arabidopsis, by combining bisulphite treatment of genomic DNA with ultra-high-throughput sequencing using the Illumina 1G Genome Analyser and Solexa sequencing technology. This approach, termed BS-Seq, unlike previous microarray-based methods, allows one to sensitively measure cytosine methylation on a genome-wide scale within specific sequence contexts. Here we describe methylation on previously inaccessible components of the genome and analyse the DNA methylation sequence composition and distribution. We also describe the effect of various DNA methylation mutants on genome-wide methylation patterns, and demonstrate that our newly developed library construction and computational methods can be applied to large genomes such as that of mouse.

/pdf/shotgun-bisulphite-sequencing-of-the-arabidopsis-genome-4vsc5rypad.pdf

Shotgun bisulphite sequencing of the Arabidopsis genome reveals DNA methylation patterning

Random Processes and Random Fields Optical Turbulence in the Atmosphere Free-Space Propagation of Gaussian-Beam Waves Classical Theory of Optical Wave Propagation Line-of-Sight Propagation - Weak Fluctuation Theory, Part 1 Line-of-Sight Propagation - Weak Fluctuation Theory, Part 2 Propagation Through Random Phase Screens Laser Satellite Communication Systems Propagation Through Complex Paraxial ABCD Optical Systems Doublepassage Problems - Laser Radar Systems Line-of-Sight Propagation - Strong Fluctuation Theory Appendices - Special Functions Integral Table Tables of Beam Statistics Mathematica Programmes.

Laser beam propagation through random media

Optical Wave Propagation In Random Media - Background Review Optical Scintillation Modelling Theory Of Scintillation - Plane Wave Model Theory Of Scintillation - Spherical Wave Model Theory Of Scintillation - Gaussian-Beam Wave Model Aperture Averaging Optical Communication Systems Fade Statistics For Lasercom Systems Laser Radar Systems - Scintillation Of Return Waves Laser Radar Systems - Imaging Through Turbulence.

Laser Beam Scintillation with Applications

We develop a model for the probability density function (pdf) of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The model is a two-parameter distribution that is based on a doubly stochastic theory of scintillation that assumes that small-scale irradiance fluctuations are modulated by large-scale irradi- ance fluctuations of the propagating wave, both governed by indepen- dent gamma distributions. The resulting irradiance pdf takes the form of a generalized K distribution that we term the gamma-gamma distribution. The two parameters of the gamma-gamma pdf are determined using a recently published theory of scintillation, using only values of the refractive-index structure parameter C n (or Rytov variance) and inner scale l 0 provided with the simulation data. This enables us to directly calculate various log-irradiance moments that are necessary in the scaled plots. We make a number of comparisons with published plane wave and spherical wave simulation data over a wide range of turbu- lence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simu- lation data in nearly all cases tested. © 2001 Society of Photo-Optical Instrumen-

/pdf/mathematical-model-for-the-irradiance-probability-density-12lphyjf63.pdf

Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

Plant Regeneration from Tissue Cultures of Maize1

Plants regenerated from relatively undifferentiated callus cultures possess a vast array of genetic changes. Such variations can result in useful agricultural and horticultural products. For other purposes, however, variations in traits other than those of interest may be undesirable--for example, using cultured cells for genetic engineering. Any steps made toward understanding the basis of tissue culture-induced genetic variation should be helpful in developing a more stable and manipulatable somatic cell system. This review provides a glimpse at the specific kinds of genetic changes encountered among regenerated plants and their progeny. Included among these variations are cytosine methylation alterations of the genome. The repeat-induced point mutation (RIP) phenomenon, reported for filamentous fungi, is invoked to provide a framework to consider the origin of variation in plant tissue cultures.

https://www.pnas.org/content/pnas/91/12/5222.full.pdf

Ronald L. Phillips

Papers

Laser beam propagation through random media

Laser Beam Scintillation with Applications

Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

Plant Regeneration from Tissue Cultures of Maize1

Genetic instability of plant tissue cultures: breakdown of normal controls