Polyhedral Geometry and the Two-plane Parameterization

Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D function of light over the domain of directed lines. These systems use the intersection points of the lines on two planes to parameterize the lines in space. This paper explores the structure of the two-plane parameterization in detail. In particular we analyze the association between the geometry of the scene and subsets of the 4D data. The answers to these questions are essential to understanding the relationship between a lumigraph, and the geometry that it attempts to represent. This knowledge is potentially important for a variety of applications such as extracting shape from lumigraph data, and lumigraph compression.Engineering and Applied Science

Empirical regularities of opening call auction in Chinese stock market

We study the statistical regularities of opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in opening call auction and the closing price of last trading day, is asymmetric and that the distribution displays a sharp peak at zero relative price and a relatively wide peak at negative relative price. The detrended fluctuation analysis (DFA) method is adopted to investigate the long-term memory of relative order prices. We further study the statistical regularities of order sizes in opening call auction, and observe a phenomenon of number preference, known as order size clustering. The probability density function (PDF) of order sizes could be well fitted by a $q$-Gamma function, and the long-term memory also exists in order sizes. In addition, both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit-order book (LOB) established immediately after the opening call auction, and a price clustering phenomenon is observed.Comment: 11 pages, 6 figures, 3 table

Exploring complex networks via topological embedding on surfaces

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The local properties of the network are affected by the surface genus which, for example, produces significant changes in the degree distribution and in the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwoveness, changing the scaling properties from large-world-kind (small genus) to small- and ultra-small-world-kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description. Within such a framework, we study the properties of topologically-embedded graphs at high and low `temperatures' observing the formation of increasingly regular structures by cooling the system. We show that the cooling dynamics is strongly affected by the surface genus with the manifestation of a glassy-like freezing transitions occurring when the amount of topological disorder is low.Comment: 18 pages, 7 figure

High Resolution Chandra Spectroscopy of Gamma Cassiopeia (B0.5IVe)

gamma Cas has long been famous for its unique hard X-ray characteristics. We report herein on a 53 ks Chandra HETGS observation of this target. An inspection of our spectrum shows that it is quite atypical for a massive star, with abnormally weak Fe XXV, XXVI lines, Ly-alpha lines of H-like species from Fe XVII, XXIII, XXIV, S XVI, Si XIV, Mg XII, Ne X, O VII, VIII, and N VII. Also, line ratios of the rif-triplet of for a few He-like ions XVII are consistent with the dominance of collisional atomic processes. Yet, the presence of Fe and Si fluorescence K features indicates that photoionization also occurs in nearby cold gas. The line profiles indicate a mean velocity at rest and a broadening of 500 km/s. A global fitting analysis of the line and continuum spectrum finds that there are 3-4 plasma emission components. The dominant hot (12 keV) component and has a Fe abundance of 0.22 solar. Some fraction of this component (10-30%) is heavily absorbed. The other 2-3 components, with temperatures 0.1, 0.4, 3 keV, are "warm," have a nearly solar composition, a lower column absorption, and are responsible for most other emission lines. The strength of the fluorescence features and the dual-column absorption model for the hot plasma component suggest the presence near the hot sites of a cold gas structure with a column density of 10^23 cm^-2. Since this value is consistent with theoretical estimates of the vertical disk column of this star, these attributes suggest that the X-rays originate near the star or disk. It is possible that the Fe anomaly in the hot component is related to the First Ionization Potential effect found in coronal structures around active cool stars. This would be yet another indication that the X-rays -rays are produced in the immediate vicinity of the Be star.Comment: 32 pages, 4 figures (Fig. 3 colorized.) To be published in 01/10/04 Astrophysical Journal, Main Journal; included figures and updated formattin

CVM studies on the atomic ordering in complex perovskite alloys

The atomic ordering in complex perovskite alloys is investigated by the cluster variation method (CVM). For the 1/3\{111\}-type ordered structure, the order-disorder phase transition is the first order, and the order parameter of the 1:2 complex perovskite reaches its maximum near x=0.25. For the 1/2\{111\}-type ordered structure, the ordering transition is the second order. Phase diagrams for both ordered structures are obtained. The order-disorder line obeys the linear law.Comment: 10 pages, 6 figure

Star-planet magnetic interaction and activity in late-type stars with close-in planets

Late-type stars interact with their close-in planets through their coronal magnetic fields. We introduce a theory for the interaction between the stellar and planetary fields focussing on the processes that release magnetic energy in the stellar coronae. We consider the energy dissipated by the reconnection between the stellar and planetary magnetic fields as well as that made available by the modulation of the magnetic helicity of the coronal field produced by the orbital motion of the planet. We estimate the powers released by both processes in the case of axisymmetric and non-axisymmetric, linear and non-linear force-free coronal fields finding that they scale as v_r (B_s)^(4/3) (B_p)^(2/3) (R_p)^2, where v_r is the relative velocity between the stellar and planetary fields, B_s the mean stellar surface field, B_p the planetary field at the poles, and R_p the radius of the planet. A chromospheric hot spot or a flaring activity phased to the orbital motion of the planet are found only when the stellar field is axisymmetric. In the case of a non-axisymmetric field, the time modulation of the energy release is multiperiodic and can be easily confused with the intrinsic stellar variability. We apply our theory to the systems with some reported evidence of star-planet magnetic interaction finding a dissipated power at least one order of magnitude smaller than that emitted by the chromospheric hot spots. The phase lags between the planets and the hot spots are reproduced by our models in all the cases except for upsilon And. In conclusion, the chromospheric hot spots rotating in phase with the planets cannot be explained by the energy dissipation produced by the interaction between stellar and planetary fields as considered by our models and require a different mechanism.Comment: 16 pages, 3 figures, accepted by Astronomy and Astrophysic

Thermal entanglement of Hubbard dimers in the nonextensive statistics

The thermal entanglement of the Hubbard dimer (two-site Hubbard model) has been studied with the nonextensive statistics. We have calculated the auto-correlation ($O_q$), pair correlation ($L_q$), concurrence ($\Gamma_q$) and conditional entropy ($R_q$) as functions of entropic index $q$ and the temperature $T$. The thermal entanglement is shown to considerably depend on the entropic index. For $q < 1.0$, the threshold temperature where $\Gamma_q$ vanishes or $R_q$ changes its sign is more increased and the entanglement may survive at higher temperatures than for $q=1.0$. Relations among $L_q$, $\Gamma_q$ and $R_q$ are investigated. The physical meaning of the entropic index $q$ is discussed with the microcanonical and superstatistical approaches. The nonextensive statistics is applied also to Heisenberg dimers.Comment: 28 pages, 6 figures; the final version accepted in Physica

High-Resolution Chandra Spectroscopy Of Gamma Cassiopeiae (B0.5e)

gamma Cas is the prototypical classical B0.5e star and is now known to be the primary in a wide binary system. It has long been famous for its unique hard X-ray characteristics, among which are variations that correlate with changes in a number of optical light and UV line and continuum properties. These peculiarities have led to a picture in which processes on or near the Be star produce the observed X-ray emission. In this paper we report on a 53 ks Chandra High Energy Transmission Grating Spectrometer observation of this target. An inspection of our spectrum shows that it is quite atypical for a massive star. The emission lines appear weak because of a strong short-wavelength continuum that arises from a hot plasma with kT = 11-12 keV. The spectrum exhibits many lines, the strongest of which are Lyalpha features of H-like species from Fe through the even-Z intermediate elements (S, Si, Mg, and Ne), down to O and N. Line ratios of the rif triplet for a variety of He-like ions and of Fe XVII are consistent with the dominance of collisional atomic processes. However, the presence of Fe and Si fluorescence K features indicates that photoionization also occurs in nearby cold gas. The line profiles indicate a mean velocity at rest with an rms line broadening of 500 km s(-1) and little or no asymmetry. An empirical global-fitting analysis of the line and continuum spectrum suggests that there are actually three or four plasma emission components. The first is the dominant hot ( 12 keV) component, of which some fraction (10%-30%) is heavily absorbed, while the remainder is affected by a much lower column density of only 3 x 10(21) cm(-2). The hot component has a Fe abundance of only 0.22 +/- 0.05 solar. The other two or three major emission components are warm and are responsible for most other emission lines. These components are dominated by plasma having temperatures near 0.1, 0.4, and 3 keV. Altogether, the warm components have an emission measure of about 14% of the hot component, a low column density, and a more nearly solar composition. The 100 eV component is consistent with X-ray temperatures associated with a wind in a typical early B star. Nonetheless, its emission measure is a few times higher than would be expected from this explanation. The strength of the fluorescence features and the dual-column absorption model for the hot plasma component suggest the presence near the hot sites of a cold gas structure with a column density of similar to10(23) cm(-2). Because this is also the value determined by Millar and Marlborough for the vertical column of the Be disk of gamma Cas, these attributes suggest that the X-ray emitting sources could be close to the disk and hence to the Be star. Finally, we discuss the probably related issues of the origin of the warm emission components, as well as the puzzling deficient Fe abundance in the hot component. It is possible that the latter anomaly is related to the FIP (abundance fractionation) effect found in certain coronal structures on the Sun and RS CVn stars. This would be yet another indication that the X-rays are produced in the immediate vicinity of the Be star

Spintessence! New Models for Dark Matter and Dark Energy

We investigate a class of models for dark matter and/or negative-pressure, dynamical dark energy consisting of ``spintessence,'' a complex scalar field $\phi$ spinning in a U(1)-symmetric potential $V(\phi)=V(|\phi|)$. As the Universe expands, the field spirals slowly toward the origin. The internal angular momentum plays an important role in the cosmic evolution and fluctuation dynamics. We outline the constraints on a cosmic spintessence field, describing the properties of the potential necessary to sustain a viable dark energy model, making connections with quintessence and self-interacting and fuzzy cold dark matter. Possible implications for the coincidence problem, baryogenesis, and cosmological birefringence, and generalizations of spintessence to models with higher global symmetry and models in which the symmetry is not exact are also discussed.Comment: 4 pages. To appear in Phys. Lett.