The spectrum and convergence rates of exclusion and interchange processes on the complete graph

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a.\ random transpositions) on the complete graph. In the case of the exclusion process, this gives a simple closed form expression for all the eigenvalues and their multiplicities. This result is then used to give an exact expression for the distance in $L^2$ from stationarity at any time and upper and lower bounds on the convergence rate for the exclusion process. In the case of the interchange process, upper and lower bounds are similarly found. Our results strengthen or reprove all known results of the mixing time for the two processes in a very simple way.Comment: 16 page

Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 2: Appendices

There are no author-identified significant results in this report

Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone. Volume 1: Text

The author has identified the following significant results. Image interpretation and computer-assisted techniques were developed to analyze LANDSAT scenes in support of resource inventory and monitoring requirements for the Texas coastal region. Land cover and land use maps, at a scale of 1:125,000 for the image interpretation product and 1:24,000 for the computer-assisted product, were generated covering four Texas coastal test sites. Classification schemes which parallel national systems were developed for each procedure, including 23 classes for image interpretation technique and 13 classes for the computer-assisted technique. Results indicate that LANDSAT-derived land cover and land use maps can be successfully applied to a variety of planning and management activities on the Texas coast. Computer-derived land/water maps can be used with tide gage data to assess shoreline boundaries for management purposes

Development and Application of Operational Techniques for the Inventory and Monitoring of Resources and Uses for the Texas Coastal Zone

There are no author-identified significant results in this report

Development and application of operational techniques for the inventory and monitoring of resources and uses for the Texas coastal zone

The author has identified the following significant results. Four LANDSAT scenes were analyzed for the Harbor Island area test sites to produce land cover and land use maps using both image interpretation and computer-assisted techniques. When evaluated against aerial photography, the mean accuracy for three scenes was 84% for the image interpretation product and 62% for the computer-assisted classification maps. Analysis of the fourth scene was not completed using the image interpretation technique, because of poor quality, false color composite, but was available from the computer technique. Preliminary results indicate that these LANDSAT products can be applied to a variety of planning and management activities in the Texas coastal zone

Report of the Terrestrial Bodies Science Working Group. Volume 2: Mercury

The objectives and rationale for scientific investigation of Mercury are explored. Knowledge already obtained by astronomical observations and Mariner 10 spacecraft is reviewed and measurements required for the principal scientific goals are described. The use of low thrust propulsion systems is recommended so that maximum scientific return may be achieved and the reconnaissance phase of Mercury exploration may be completed in a single mission. Accelerated development is recommended on solar electric propulsion, solar sails, passive and active cooling mechanisms, and single rough landers

Wilson loops in the abelian lattice Higgs model

We consider the lattice Higgs model on $\mathbb{Z}^4$, with structure group given by $\mathbb{Z}_n$ for $n \geq 2$. We compute the expected value of the Wilson loop observable to leading order when the gauge coupling constant and hopping parameter are both sufficiently large. The leading order term is expressed in terms of a quantity arising from the related but much simpler $\mathbb{Z}_n$ model, which reduces to the Ising model when $n=2$. As part of the proof, we construct a coupling between the lattice Higgs model and the $\mathbb{Z}_n$ model.Comment: 56 pages, 8 figure

Wilson lines in the lattice Higgs model at strong coupling

We consider the 4D fixed length lattice Higgs model with Wilson action for the gauge field and structure group $\mathbb{Z}_n$. We study Wilson line observables in the strong coupling regime and compute their asymptotic behavior with error estimates. Our analysis is based on a high-temperature representation of the lattice Higgs measure combined with Poisson approximation. We also give a short proof of the folklore result that Wilson line (and loop) expectations exhibit perimeter law decay whenever the Higgs field coupling constant is positive.Comment: 48 pages, 6 figure

The Mars observer camera

A camera designed to operate under the extreme constraints of the Mars Observer Mission was selected by NASA in April, 1986. Contingent upon final confirmation in mid-November, the Mars Observer Camera (MOC) will begin acquiring images of the surface and atmosphere of Mars in September-October 1991. The MOC incorporates both a wide angle system for low resolution global monitoring and intermediate resolution regional targeting, and a narrow angle system for high resolution selective surveys. Camera electronics provide control of image clocking and on-board, internal editing and buffering to match whatever spacecraft data system capabilities are allocated to the experiment. The objectives of the MOC experiment follow

Poisson Representable Processes

Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our main focus is to determine which processes are representable in this way. Some of our results are as follows. (1) All positively associated Markov chains and a large class of renewal processes are so representable. (2) Whether an average of two product measures, with close densities, on $n$ variables, is representable is related to the zeroes of the polylogarithm functions. (3) Using (2), we show that a number of tree indexed Markov chains as well as the Ising model on $\mathbb{Z}^d ,$ $d\geq 2,$ for certain parameters are not so representable. (4) The collection of permutation invariant processes which are representable corresponds exactly to the set of infinitely divisible random variables on $[0,\infty]$ via a certain transformation. (5) The supercritical (low temperature) Curie-Weiss model is not representable for large $n$.Comment: 39 pages, 2 figure