The shape of two-dimensional space

Genomics, so fashionable today, is only half of the secret of life. The other half of the secret is shape, form, morphogenesis and metamorphosis. The gene may prescribe what is synthesised, but the proteins appear and operate in a pre-existing environment which they then change. The first step towards life is the appearance of a micelle, a spherical membrane, a surface which separates the world into inside and outside. We are here concerned with surfaces, with a particular subset of two-dimensional manifolds embedded in three-dimensional Euclidean space, namely the non-self-intersecting, periodic minimal surfaces of cubic symmetry, which separate the world into two regions as an infinite plane would do, but with much more complex topologies. Like the Platonic solids , these cubic surfaces are geometrical absolutes and have distinctive topologies but entail no arbitrary parameters . The objective is to enumerate at least some of these surfaces, for probably an infinite number answer to this description, to draw attention to their geometry and to point to some of their applications and occurrences on various scales between mega-engineering and nano-technology. These objects are solutions looking for problems

From “the dialectics of nature” to the inorganic gene

The concept of projection from one space to another, with a consequent loss of information, can be seen in the relationships of gene to protein and language description to real situation. Such a transformation can only be reversed if extra external information is re-supplied. The genetic algorithm embodying this idea is now used in applied mathematics for exploring a configuration space. Such a dialectic – transformation back and forth between two kinds of description – extends the traditional Hegelian concept used by Engels and others of change as resulting from a resolution of the conflict of two opposing tendencies and provides for evolution of the joint system

Periodic minimal surfaces of cubic symmetry

A survey of cubic minimal surfaces is presented, based on the concept of fundamental surface patches and their relation to the asymmetric units of the space groups. The software Surface Evolver has been used to test for stability and to produce graphic displays. Particular emphasis is given to those surfaces that can be generated by a finite piece bounded by straight lines. Some new varieties have been found and a systematic nomenclature is introduced, which provides a symbol (a ‘gene’) for each triply-periodic minimal surface that specifies the surface unambiguously

Factors which influence directional coarsening of Gamma prime during creep in nickel-base superalloy single crystals

Changes in the morphology of the gamma prime precipitate were examined as a function of time during creep at 982 C in 001 oriented single crystals of a Ni-Al-Mo-Ta superalloy. In this alloy, which has a large negative misfit of -0.80 pct., the gamma prime particles link together during creep to form platelets, or rafts, which are aligned with their broad faces perpendicular to the applied tensile axis. The effects of initial microstructure and alloy composition of raft development and creep properties were investigated. Directional coarsening of gamma prime begins during primary creep and continues well after the onset of second state creep. The thickness of the rafts remains constant up through the onset of tertiary creep a clear indication of the stability of the finely-spaced gamma/gamma prime lamellar structure. The thickness of the rafts which formed was equal to the initial gamma prime size which was present prior to testing. The single crystals with the finest gamma prime size exhibited the longest creep lives, because the resultant rafted structure had a larger number of gamma/gamma prime interfaces per unit volume of material. Reducing the Mo content by only 0.73 wt. pct. increased the creep life by a factor of three, because the precipitation of a third phase was eliminated

Sparse Graph Codes for Quantum Error-Correction

We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small: a constant number per quantum bit, independent of the blocklength. Third, sparse graph codes often offer great flexibility with respect to blocklength and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.Comment: Version 7.3e: 42 pages. Extended version, Feb 2004. A shortened version was resubmitted to IEEE Transactions on Information Theory Jan 20, 200

Serratia marcescens, the “Flame” Strain: The Genesis of a New Variant A Newly Described Strain with Prolific Pigment Produced at High Temperature

Serratia marcescens, a Gram-negative, rod-shaped, facultative anaerobe (Fig. 1), is ubiquitous in water, soil, and natural settings. It is easily grown in the lab and may serve as an ideal model for adaptation studies because of the natural color variation of S. marcescens (Gillen 2008). In this paper, we describe a new variant with prolific pigment (prodigiosin) production at high temperatures. In the wild and in buildings, S. marcescens is noted for the production of a bright red pigment called prodigiosin (Williams 1973). We have found a new strain that appears to have adapted to a relatively new pond system called Liberty Library Lake. It produces pigment up to 40°C without any enrichment to media. Most wild-type strains, like NIMA, produce pigment normally up to 30°C, but with extensive enrichment, wild-type strains can produce pigment up to 40°C. This new strain, called the “Flame” strain, not only produces prodigiosin to 39–40°C but also in higher abundance at 35°C and at a brighter hue. NIMA strains can produce pigment at 39–40°C with Serratia Synergy Agar (glycerol, peptone, agar) but not on TSA nor any common agar. It takes significant enhancement for any other Serratia marcescens strains to produce pigment even at 35°C. The Flame strain’s brief appearance in a local, small lake appears to be a phenotypic diversification and adaptation to an environmental perturbation this past school year. The environmental stress prior to its appearance was an autumn drought. Eventually, heavy rainfall occurred and the new strain was discovered. Its appearance coincided with an unusually high abundance of coliforms, avian Giardia, and Cryptosporidium, along with chemical treatment of the lake. The unusual conditions seem to favor a rapid phenotypic diversification and adaptation. The new strain still retains the pigment production at nearly 10°C higher for “normal” prodigiosin production by wild-type Serratia marcescens. This genesis of this new strain seems to have occurred as special conditions favored this new variant. It may be closer to a “proto-type” (ancestral) strain than to more common wild-type strains, like NIMA and BS303. It appears that most wild-type strains, like NIMA and BS303, may have lost this information over time since added enrichment is necessary to produce pigment at 39–40°C. The unusual conditions may have selected for this newly adapted strain to be common for a short time. Also as conditions returned to “normal,” a common wild-type strain reappeared at the local lake, and the Flame strain was no longer found. The objective of this article is to explain the mysterious origin of a new strain of Serratia marcescens that produces prodigiosin up to 40°C without any enrichment to media. This strain can naturally produce prolific pigment that is a bright, flame-red. Since Serratia marcescens offers protection from other microbes, UV light, and drought, it is a wonderful example of intelligent design commonly seen in the microbial world