Abstract:
The language of gene expression displays topological symmetry. An important step during gene expression is the binding of transcriptional proteins to DNA promoters adjacent to a gene. Some proteins bind to many promoters in a genome, defining a regulon of genes wherein each promoter might vary in DNA sequence relative to the average consensus. Here we examine the linguistic organization of gene promoter networks, wherein each node in the network represents a promoter and links between nodes represent the extent of base pair-sharing. Prior work revealed a fractal nucleus in several σ-factor regulons from Escherichia coli. We extend these findings to show fractal nuclei in gene promoter networks from three bacterial species, E. coli, Bacillus subtilis, and Pseudomonas aeruginosa. We surveyed several non-σ transcription factors from these species and found that many contain a nucleus that is both visually and numerically fractal. Promoter footprint size scaled as a negative power-law with both information entropy and fractal dimension, while the latter two parameters scaled positively and linearly. The fractal dimension of the diffuse networks (dB = ~1.7) was close to that expected of a diffusion limited aggregation process, confirming prior predictions as to a possible mechanism for development of this structure.

Abstract:
Much is known regarding the structure and logic of genetic regulatory networks. Less understood is the contextual organization of promoter signals used during transcription initiation, the most pivotal stage during gene expression. Here we show that promoter networks organize spontaneously at a dimension between the 1-dimension of the DNA and 3-dimension of the cell. Network methods were used to visualize the global structure of E. coli sigma (σ) recognition footprints using published promoter sequences (RegulonDB). Footprints were rendered as networks with weighted edges representing bp-sharing between promoters (nodes). Serial thresholding revealed phase transitions at positions predicted by percolation theory, and nuclei denoting short steps through promoter space with geometrically constrained linkages. The network nuclei are fractals, a power-law organization not yet described for promoters. Genome-wide promoter abundance also scaled as a power-law. We propose a general model for the development of a fractal nucleus in a transcriptional grammar.

Abstract:
Much is known regarding the structure and logic of genetic regulatory networks. Less understood is the contextual organization of promoter signals used during transcription initiation, the most pivotal stage during gene expression. Here we show that promoter networks organize spontaneously at a dimension between the 1-dimension of the DNA and 3-dimension of the cell. Network methods were used to visualize the global structure of E. coli sigma (σ) recognition footprints using published promoter sequences (RegulonDB). Footprints were rendered as networks with weighted edges representing bp-sharing between promoters (nodes). Serial thresholding revealed phase transitions at positions predicted by percolation theory, and nuclei denoting short steps through promoter space with geometrically constrained linkages. The network nuclei are fractals, a power-law organization not yet described for promoters. Genome-wide promoter abundance also scaled as a power-law. We propose a general model for the development of a fractal nucleus in a transcriptional grammar.

The different forms of duality in Robert Ulanowicz’s (2009) book A Third Window are compared to the notion of neo-duality found in Logan and Schumann (2005). The influence of Heraclitus on the formulation Ulanowicz’ duality is described. It is argued that the origin of language, which led to conceptualization and emotional intelligence, also gave rise to human spirituality, cooperation and altruism all of which contributed to human survival. The four mysteries of the existence of 1) matter/energy, 2) life, 3) human intelligence, and 4) human spirituality are identified. It is suggested that physics and chemistry deal with mystery number one; that Ulanowicz’s process ecology describes mystery number two and the relation of life to energy/matter. Mystery number three entails process ecology and consideration of the effects of language. The emergence of the fourth mystery of spirituality and/or a belief in God is shown to have emerged from two uniquely human attributes, namely the abstract form of language-based intelligence and altruism. It is suggested rather than as an agent that influences events in the universe God, an idea that arises in the minds of humankind as a metaphor of all that is good in humankind.

Abstract:
A completely non-perturbative estimate is given for gA using both quenched and unquenched O(a) improved Wilson fermions. Particular attention is paid to the determination of the axial renormalisation constant, ZA, using the Ward identity for the propagator. For the quenched case, we have results at three lattice spacings allowing a continuum extrapolation.

Abstract:
Some aspects of recent QCDSF-UKQCD nucleon moments of structure function computations (both quenched and unquenched) are reviewed in an effort to explore the light quark mass regime, lattice spacing effects and quenching artefacts.

Abstract:
In 1940 Fisher famously showed that if there exists a non-trivial $(v,k,\lambda)$-design then $\lambda(v-1) \geq k(k-1)$. Subsequently Bose gave an elegant alternative proof of Fisher's result. Here, we show that the idea behind Bose's proof can be generalised to obtain new bounds on the number of blocks in $(v,k,\lambda)$-coverings and -packings with $\lambda(v-1)

Abstract:
We prove that a complete bipartite graph can be decomposed into cycles of arbitrary specified lengths provided that the obvious necessary conditions are satisfied, the length of each cycle is at most the size of the smallest part, and the longest cycle is at most three times as long as the second longest. We then use this result to obtain results on incomplete even cycle systems with a hole and on decompositions of complete multipartite graphs into cycles of uniform even length.

Abstract:
It was proved in 2009 that any partial Steiner triple system of order $u$ has an embedding of order $v$ for each admissible integer $v\geq 2u+1$. This result is best-possible in the sense that, for each $u\geq 9$, there exists a partial Steiner triple system of order $u$ that does not have an embedding of order $v$ for any $v<2u+1$. Many partial Steiner triple systems do have embeddings of orders smaller than $2u+1$, but little has been proved about when these embeddings exist. In this paper we construct embeddings of orders less than $2u+1$ for partial Steiner triple systems with few triples. In particular, we show that a partial Steiner triple system of order $u \geq 62$ with at most $\frac{u^2}{50}-\frac{11u}{100}-\frac{116}{75}$ triples has an embedding of order $v$ for each admissible integer $v \geq \frac{8u+17}{5}$.

Abstract:
A numerical calculation of the lattice staggered renormalisation constants at $\beta = 5.35$, $m = 0.01$ is presented. It is seen that there are considerable non-perturbative effects present. As an application the vector decay constant $f_\rho$ is estimated. (LAT92 contribution, one LATEX file with 3 postscript figures appended.)