Density Distribution Sunflower Plots

Density distribution sunflower plots are used to display high-density bivariate data. They are useful for data where a conventional scatter plot is difficult to read due to overstriking of the plot symbol. The x-y plane is subdivided into a lattice of regular hexagonal bins of width w specified by the user. The user also specifies the values of l, d, and k that affect the plot as follows. Individual observations are plotted when there are less than l observations per bin as in a conventional scatter plot. Each bin with from l to d observations contains a light sunflower. Other bins contain a dark sunflower. In a light sunflower each petal represents one observation. In a dark sunflower, each petal represents k observations. (A dark sunflower with p petals represents between /2-pk k and /2+pk k observations.) The user can control the sizes and colors of the sunflowers. By selecting appropriate colors and sizes for the light and dark sunflowers, plots can be obtained that give both the overall sense of the data density distribution as well as the number of data points in any given region. The use of this graphic is illustrated with data from the Framingham Heart Study. A documented Stata program, called sunflower, is available to draw these graphs. It can be downloaded from the Statistical Software Components archive at http://ideas.repec.org/c/boc/bocode/s430201.html . (Journal of Statistical Software 2003; 8 (3): 1-5. Posted at http://www.jstatsoft.org/index.php?vol=8 .)

Noncontacting devices to indicate deflection and vibration of turbopump internal rotating parts

Published report discusses feasibility of ultrasonic techniques; neutron techniques; X-radiography; optical devices; gamma ray devices; and conventional displacement sensors. Use of signal transmitters in place of slip rings indicated possible improvement and will be subject of futher study

Noncontacting device to indicate deflection of turbopump internal rotating parts

Phase 2 (development) which was concluded for the ultrasonic Doppler device and the light-pipe-reflectance device is reported. An ultrasonic Doppler breadboard system was assembled which accurately measured runout in the J-2 LOX pump impeller during operation. The transducer was mounted on the outside of the pump volute using a C-clamp. Vibration was measured by conducting the ultrasonic wave through the volute housing and through the fluid in the volute to the impeller surface. The impeller vibration was also measured accurately using the light-pipe probe mounted in an elastomeric-gland fitting in the pump case. A special epoxy resin developed for cryogenic applications was forced into the end of the fiber-optic probe to retain the fibers. Subsequently, the probe suffered no damage after simultaneous exposure to 2150 psi and 77 F. Preliminary flash X-radiographs were taken of the turbine wheel and the shaft-bearing-seal assembly, using a 2-megavolt X-ray unit. Reasonable resolution and contrast was obtained. A fast-neutron detector was fabricated and sensitivity was measured. The results demonstrated that the technique is feasible for integrated-time measurements requiring, perhaps, 240 revolutions to obtain sufficient exposure at 35,000 rpm. The experimental verification plans are included

Direct Dark Matter Detection with Velocity Distribution in the Eddington approach

Exotic dark matter together with the vacuum energy (associated with the cosmological constant) seem to dominate the Universe. Thus its direct detection is central to particle physics and cosmology. Supersymmetry provides a natural dark matter candidate, the lightest supersymmetric particle (LSP). One essential ingredient in obtaining the direct detection rates is the density and the velocity distribution of the LSP in our vicinity. In the present paper we study simultaneously density profiles and velocity distributions in the context of the Eddington approach. In such an approach, unlike the commonly assumed Maxwell-Boltzmann (M-B) distribution, the upper bound of the velocity arises naturally from the potential.Comment: 21 LaTex pages, 27 figure

Capturing Hiproofs in HOL Light

Hierarchical proof trees (hiproofs for short) add structure to ordinary proof trees, by allowing portions of trees to be hierarchically nested. The additional structure can be used to abstract away from details, or to label particular portions to explain their purpose. In this paper we present two complementary methods for capturing hiproofs in HOL Light, along with a tool to produce web-based visualisations. The first method uses tactic recording, by modifying tactics to record their arguments and construct a hierarchical tree; this allows a tactic proof script to be modified. The second method uses proof recording, which extends the HOL Light kernel to record hierachical proof trees alongside theorems. This method is less invasive, but requires care to manage the size of the recorded objects. We have implemented both methods, resulting in two systems: Tactician and HipCam

On the Core of a Graph†

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135576/1/plms0305.pd