Relational information represented by graphs can be found in various areas. Understanding completely connected groups of items is useful in studying relational information. However, when displayed in the form of a graph drawing, completely connected graphs contain quadratically many edges relative to the number of their vertices. This may increase the difficulty in identifying useful information, such as maximal cliques, in the graph. This thesis attempts to display the maximal cliques and the cliques contained in two or more maximal cliques in a given graph in an explicit and clear fashion. In order to achieve the goal, the thesis defines two models, the clique-star and the reduced-clique-star, that represent given input graphs. Both representations reduce the number of edges of the original graphs while maintaining the information about the maximal cliques. This thesis shows that six classes of graphs that can be represented by planar clique-star representations, and four classes of graphs that can be represented by planar reduced-clique-star representations. It also empirically shows that small graphs or either very sparse or very dense graphs maybe beneficially represented by planar clique-star or planar reduced-clique-star representations.

Abstract The Purchasing power parity ¡]PPP¡^ theory was originally developed by a Swidish economist, Gustav Cassel, in 1916. It is a method using the long-run equilibrium exchange rate of two currencies to measure the currencies' purchasing power. It is based on the law of one price, the idea that, in an efficient market, identical goods must have only one price internationally. This parity is a central building block of many theoretical and empirical models of exchange rate determination, since most are relied on PPP as the basis for long-run real exchange rates. While the literature on the PPP hypothesis is voluminous today and still growing, the doctrine has not found well. The validity of PPP can be examined by testing the stationary of real exchange rates. Most of the empirical evidences relied mainly on using linear structure to explore PPP in the past. By using traditional unit root test, the PPP is hard to hold in the long run. There is a growing consensus that previous empirical research reflects the poor power of the tests rather necessarily against PPP. Therefore, the use of more powerful tests is needed. Recently, an alternative point of view based on the presence of market frictions that impede commodity trade has arisen. The adjustment of real exchange rates is perhaps described more appropriately as a nonlinear process once market frictions are taken into account. There are several reasons that theoretically explain why the adjustment process of deviations from PPP is nonlinear, such as transactions and transportation costs and tariffs and non-tariff barriers to international trade. Therefore, the analysis of real exchange rate should be conducted under the nonlinear structure. This study uses the STAR methodology proposed by Granger & Teräsvirta (1993) and Teräsvirta (1994) to examine whether the deviation of PPP is a nonlinear dynamic adjustment among the following countries: Australia, Denmark, Italy, Japan, Luxembourg, Norway, Spain, Sweden and the United Kingdom. If the linear hypothesis was rejected, then to distinguish if the model of STAR is LSTAR or ESTAR. This study finds that the deviations from equilibrium exchange rates show strong evidence of nonlinear properties. The deviations of exchange rates for all countries can be explained by the LSTAR model. In conclusion, this study finds the real exchange rates exhibit the property of nonlinear mean reversion for most countries.

Every (convex) star polygon with n vertices can be associated with a permutation on {1,2, . . . , n } . It is known that the sum of interior angles of the polygon is solely determined by £». In this thesis, we give an exact formula to calculate the sum of interior angles in term of £». We make use of this formula to derive a recurrence relation concerning the number of star polygons having a particular value of sums of interior angles.

Gonads are distinct organs in organisms with complicated reproductive systems, and they have specific locations in the body. The gonads of crinoids, however, are scattered in numerous genital pinnules of their arms. We studied seven species of feather stars, Comatella maculata (Carpenter, 1888), Comatella nigra (Carpenter, 1888), Comaster multifidus (M􀎏ller, 1841), Comaster distinctus (Carpenter, 1881), Comanthus parvicirrus (M􀎏ller, 1841), Colobometra perspinosa (Carpenter,1881) and Himerometra magnipinna Clark, 1908 collected at Kenting, southern Taiwan in 2007. The purpose is to explore if the distribution patterns of gonads are adaptative. With bimonthly samplings in a year, it is discovered that the spawning seasons of the species are not synchronized in a particular season. Three models of relationships between maximum arm lengths and numbers of arms exist in the seven species, i.e., constant arm numbers, linear, and quadratic with an asymptote of arm numbers. Therefore, the maximum arm length is more appropriate than arm number as a size index of feather stars. Evidence of bigger mature than immature individuals is found in Comatella maculata, Comaster distinctus and Comaster multifidus, and there is no size difference between males and females. The gonads of feather stars are distributed in the proximal end of arms. The proportion of arms represented by genital pinnules within individuals were constant except in Comanthus parvicirrus where a negative correlation was found. Except the 2 cave-dwelling species, Comatella maculata and Comanthus parvicirrus, most regenerating arms of 5 other species had breakage points occurred near the proximal ends of the arms. Distal breakage may regenerate too fast to recognize. The arms obviously do not grow so fast as to limit gonad development to the proximal ends of arms. Habitat difference may cause variation in genital pinnule widths, but not in the number of genital pinnules as suggested by comparsions of specimens between 2 sites. The cave-dwelling Comanthus parvicirrus has special congregated long arms, which are extended outside. Moreover, these arms have higher probability of breakage, and smaller ranges of genital pinnules than short arms. This phenomenon supports that the limited gonad distribution is adaptive for reducing loss upon arm breakage.

There has been many recent observations in the area of star formation. High-resolution observations of other galaxies enabled a study of extragalactic star formation in more detailed while large scale surveys of the Milky Way enabled a more comprehensive study of Galactic star formation. The main goal of this thesis is to use multi-wavelength, large-scale observations of the Milky Way to connect Galactic to extragalactic star formation and to study star formation regulation in molecular clouds. We tested the use of extragalactic star formation rate tracers on nearby molecular clouds and found that the total infrared and 24 μm luminosity underestimate star formation rates of nearby molecular clouds by a large factor, indicating a problem of using extragalactic tracers of star formation on small regions and regions with low mass or low star formation rates. We studied the relation between star formation and molecular gas distribution in a 11 square degree of the Galactic Plane on various spatial scales starting from a clump scale of around few parsecs to a scale of ≈ 200 parsec. The result shows a good correlation between molecular gas and star formation on a scale above ≈ 5 − 8′. The star formation relation that is seen on disk-averaged scales in other galaxies shows a large scatter on the small scales. We built a catalog of Galactic molecular clouds with measured star formation rates and studied the relations between properties of molecular clouds and star formation. We tested several models of star formation on the catalog of molecular clouds. We found that the dense gas mass shows significant correlations with star formation rates but the depletion time of dense gas varies with other properties of the clouds. We found that the free- fall efficiency is higher in dense gas compared to the general molecular gas of the clouds.

Stars form from collapsing massive clouds of gas and dust. The UV and optical light emitted by a forming or recently-formed star is absorbed by the surrounding cloud and is re-radiated thermally at infrared and submillimetre wavelengths. Observations in the submillimetre spectrum are uniquely sensitive to star formation in the early Universe, as the peak of the thermal emission is redshifted to submillimetre wavelengths. The coolest objects in star forming regions in our own Galaxy, including heavily-obscured proto-stars and starless gravitationally-bound clumps, are also uniquely bright in the submillimetre spectrum. The Earth's atmosphere is mostly opaque at these wavelengths, however, limiting the spectral coverage and sensitivity achievable from ground-based observatories. The Balloon-borne Large Aperture Submillimeter Telescope (BLAST) observes the sky from an altitude of 40 km, above 99.5% of the atmosphere, using a long-duration scientific balloon platform. BLAST observes at 3 broad-band wavelengths spanning 250-500 micron, taking advantage of detector technology developed for the space-based instrument SPIRE, scheduled for launch in 2008. The greatly-enhanced atmospheric transmission at float altitudes, increased detector sensitivity and large number of detector elements allow BLAST to survey much larger fields in a much smaller time than can be accomplished with ground-based instruments. It is expected that in a single 10-day flight, BLAST will detect ~10000 extragalactic sources, ~100 times the number detected in 10 years of ground-based observations, and 1000s of Galactic star-forming sources, a large fraction of which are not seen by infrared telescopes. The instrument has performed 2 scientific flights, in the summer of 2005 and winter of 2006, for a total of 16 days of observing time. This thesis discusses the design of the instrument, performance of the flights, and presents the analysis of 2 of the fields observed during the first flight. A failure in the optical system during the first flight precluded sensitive extragalactic observations, so the majority of the flight was spent observing Galactic targets. We anticipate exciting extragalactic and Galactic results from the 2006 data.

Twenty-one sites were surveyed for star-nosed mole (Condylura cristata) activity during May-October, 2001 and 2002. Star-nosed moles were live-trapped and their habitat characteristics were quantified and compared to habitat characteristics at nonuse sites, as well as capture sites of three other small mammal species: the short-tailed shrew (Blarina brevicauda), the whitefooted mouse (Peromyscus leucopus) and the meadow vole (Microtus pennsylvanicus). Star-nosed moles were captured at sites characterized by moist, clay-loam soils with a slightly acidic pH, prominent horizontal cover, and a nearby water source. Starnosed mole habitat was similar to that of short-tailed shrews and white-footed mice, but differed from that of meadow voles. / Department of Biology

No description available.

High resolution observations have been made of a number of southern Cepheids to make an observational and theoretical study of Cepheid variables using radial velocities. The stars studied were part of a long term programme to observe southern variable stars, from which a valuable database of radial velocities gathered over a long period were available. Sixteen échelle spectrograph orders in the wavelength region 5400 - 8600Å were used, which included a number of absorption lines covering a range of species and excitation potentials. The line bisector technique was used to measure stellar and telluric lines and to obtain radial velocities. To improve the precision of the radial velocities we used telluric lines to calibrate the observations to a common reference frame. The radial velocities have a precision of ~300ms⁻¹ allowing the detection of velocity differences of ~1 kms⁻¹ with confidence. The radial velocity data obtained at Mount John University Observatory (MJUO) was combined with data from various sources to determine the orbits of any Cepheids exhibiting orbital motion. The various orbital parameters were determined for a number of systems and where radial velocities for the companions exist, some estimate of the mass was made. The precision of the radial velocities obtained from MJUO also allowed us to search for line level effects for a number of species among the Cepheid spectra. A number of IAU standard stars were observed to calibrate the radial velocities obtained at MJUO to the IAU standard scale. The radial velocities from MJUO were found not to differ significantly from the IAU values. Binary Cepheids are particularly useful in the determination of Cepheid masses, which are still an active topic for astronomical research. The value of the MJUO data was that it provided a consistent set of data against which other sources of data could be compared. For 8 of the Cepheids new or improved orbital solutions were found. They are Y Car, YZ Car, AX Cir, BP Cir, S Mus, V636 Sco, V350 Sgr, W Sgr and T Mon. Of these 8 systems, 3 had radial velocities for their respective companions which allowed the determination of the mass of the Cepheids. Masses were determined for the 9 day Cepheid S Mus (6.0±0.4M⊙), the double mode Cepheid Y Car (4.5±1.8 M⊙) and the 5 day Cepheid V350 Sgr (6.0±0.9 M⊙). New results presented here include the first orbital solution for the binary Cepheid AX Cir, a completely revised orbital solution for the binary Cepheid YZ Car which established its eccentricity, and orbital motion. The binary Cepheid BP Cir however was found to require a new pulsation period of 2.39819d to fit the observed pulsational velocities. Observations of the suspected binary Y Oph show it to be an unusual Cepheid with no evidence of binarity (~0.5 kms⁻¹) in our data. Finally, the 5 day Cepheid W Sgr was observed to have the lowest orbital amplitude measured. We discussed the line level effects found in our observations, where a number of spectral lines were observed to show departures from the Fei velocity curve. Line level effects were observed in H⍺, CaⅡ, BaⅡ, FeⅡ, SiⅠ and SiⅡ. Most of the Cepheids were observed to show the same progression of line level effects, with the best example being the bright Cepheid β Dor. The SiⅡ velocities indicate that these lines have the lowest velocity amplitude and form deeper in the atmosphere than the FeⅠ, where as the CaⅡ and H⍺ lines were all observed to have much greater velocity amplitudes with the peak of these velocity curves occurring later, in pulsational phase. These observations are consistent with the lines forming at different depths as a density wave propagates through the atmosphere. X Sgr is peculiar due to its interesting spectra which at certain phases show line doubling and at most other phases the lines were asymmetric. These observations are interpreted to support the idea that X Sgr has strong shock waves present and that X Sgr has greater atmospheric transparency in the spectral region near 6000Å. We also present the results of dynamical modelling of a pulsating Cepheid. Using a non-linear radiative hydrodynamic code developed by A. Fokin, we have modelled two Cepheids, AX Cir and YZ Car. These models have then been compared with the observations obtained here. After extensive modelling using the latest OP opacities, it has been determined that the Cepheid AX Cir can be modelled using parameters L = 2050 L⊙, M = 4.8 M⊙ and Teff = 5900K. The model reproduced the observed stellar characteristics, such as the photometric amplitude and pulsational period. Comparison between the observations and the model for the selected spectral lines, FeⅠ 5576Å, SiⅡ 6347Å, BaⅡ 5853Å and CaⅡ 8542Å show good agreement with similar amplitudes and velocity curves. With no strong shock waves being produced by the model, the observed line level effects can be explained by a density wave. The 18 day Cepheid YZ Car was chosen to explore the capabilities of the radiative hydrodynamic code for a long period Cepheid. The best model developed that reproduced the observed stellar characteristics had parameters L = 9350 L⊙, M = 7.7 M⊙ and Teff = 5590K. The period was 18.314 days and the bolometric light curve agreed well with the observed visual light curve. Comparison of the theoretical and observed radial velocities showed good agreement.

University of Chicago, 1898, Thesis (Ph. D.) / Includes bibliographical references (p. iii-xxii). - OCLC, 32164936. - Reproduction of original from Harvard Law School Library