Quaternions, octonions and Bell-type inequalities

Multipartite Bell-type inequalities are derived for general systems. They involve up to eight observables with arbitrary spectra on each site. These inequalities are closely related to the algebras of quaternions and octonions.Comment: 4 pages, no figure

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

A NASA high-power space-based laser research and applications program

Applications of high power lasers are discussed which might fulfill the needs of NASA missions, and the technology characteristics of laser research programs are outlined. The status of the NASA programs or lasers, laser receivers, and laser propulsion is discussed, and recommendations are presented for a proposed expanded NASA program in these areas. Program elements that are critical are discussed in detail

Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

Myelin pathology: Involvement of molecular chaperones and the promise of chaperonotherapy

The process of axon myelination involves various proteins including molecular chaperones. Myelin alteration is a common feature in neurological diseases due to structural and functional abnormalities of one or more myelin proteins. Genetic proteinopathies may occur either in the presence of a normal chaperoning system, which is unable to assist the defective myelin protein in its folding and migration, or due to mutations in chaperone genes, leading to functional defects in assisting myelin maturation/migration. The latter are a subgroup of genetic chaperonopathies causing demyelination. In this brief review, we describe some paradigmatic examples pertaining to the chaperonins Hsp60 (HSPD1, or HSP60, or Cpn60) and CCT (chaperonin-containing TCP-1). Our aim is to make scientists and physicians aware of the possibility and advantages of classifying patients depending on the presence or absence of a chaperonopathy. In turn, this subclassification will allow the development of novel therapeutic strategies (chaperonotherapy) by using molecular chaperones as agents or targets for treatment

Preliminary design and cost of a 1-megawatt solar-pumped iodide laser space-to-space transmission station

A preliminary conceptual design of a space-based solar pumped iodide laser emitting 1 megawatt of laser power for space-to-space power transmission is described. A near parabolic solar collector focuses sunlight onto the t-C4F9I (perfluoro-t butyl iodide) lasant within a transverse flow optical cavity. Using waste heat, a thermal system was designed to supply compressor and auxiliary power. System components were designed with weight and cost estimates assigned. Although cost is very approximate, the cost comparison of individual system components leads to valuable insights for future research. In particular, it was found that laser efficiency was not a dominant cost or weight factor, the dominant factor being the laser cavity and laser transmission optics. The manufacturing cost was approx. two thirds of the total cost with transportation to orbit the remainder. The flowing nonrenewable lasant comprised 20% of the total life cycle cost of the system and thus was not a major cost factor. The station mass was 92,000 kg without lasant, requiring approx. four shuttle flights to low Earth orbit where an orbital transfer vehicle will transport it to the final altitude of 6378 km

On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine

We consider the relationship between the conjectured uniqueness of the Moonshine Module, ${\cal V}^\natural$, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible $Z_n$ meromorphic orbifold constructions of ${\cal V}^\natural$ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster group $M$ together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that ${\cal V}^\natural$ is unique, we then consider meromorphic orbifoldings of ${\cal V}^\natural$ and show that Monstrous Moonshine holds if and only if the only meromorphic orbifoldings of ${\cal V}^\natural$ give ${\cal V}^\natural$ itself or the Leech theory. This constraint on the meromorphic orbifoldings of ${\cal V}^\natural$ therefore relates Monstrous Moonshine to the uniqueness of ${\cal V}^\natural$ in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0

Weak Disorder in Fibonacci Sequences

We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1-epsilon, but follow a different recursion rule with a small probability epsilon. We focus on the weak disorder limit and obtain the Lyapunov exponent, that characterizes the typical growth of the sequence elements, using perturbation theory. The limiting distribution for the ratio of consecutive sequence elements is obtained as well. A number of variations to the basic Fibonacci recursion including shift, doubling, and copying are considered.Comment: 4 pages, 2 figure

COLA. III. Radio Detection of Active Galactic Nucleus in Compact Moderate Luminosity Infrared Galaxies

We present results from 4.8 GHz Very Large Array (VLA) and global very long baseline interferometry (VLBI) observations of the northern half of the moderate FIR luminosity (median L_(IR) = 10^(11.01) L_☉) COLA sample of star-forming galaxies. VLBI sources are detected in a high fraction (20/90) of the galaxies observed. The radio luminosities of these cores (~10^(21) W Hz^(–1)) are too large to be explained by radio supernovae or supernova remnants and we argue that they are instead powered by active galactic nuclei (AGNs). These sub-parsec scale radio cores are preferentially detected toward galaxies whose VLA maps show bright 100-500 parsec scale nuclear radio components. Since these latter structures tightly follow the FIR to radio-continuum correlation for star formation, we conclude that the AGN-powered VLBI sources are associated with compact nuclear starburst environments. The implications for possible starburst-AGN connections are discussed. The detected VLBI sources have a relatively narrow range of radio luminosity consistent with models in which intense compact Eddington-limited starbursts regulate the gas supply onto a central supermassive black hole. The high incidence of AGN radio cores in compact starbursts suggests little or no delay between the starburst phase and the onset of AGN activity