The mapping class group and the Meyer function for plane curves

For each d>=2, the mapping class group for plane curves of degree d will be defined and it is proved that there exists uniquely the Meyer function on this group. In the case of d=4, using our Meyer function, we can define the local signature for 4-dimensional fiber spaces whose general fibers are non-hyperelliptic compact Riemann surfaces of genus 3. Some computations of our local signature will be given.Comment: 24 pages, typo adde

Benchmarking adaptive indexing

Ideally, realizing the best physical design for the current and all subsequent workloads would impact neither performance nor storage usage. In reality, workloads and datasets can change dramatically over time and index creation impacts the performance of concurrent user and system activity. We propose a framework that evaluates the key premise of adaptive indexing --- a new indexing paradigm where index creation and re-organization take place automatically and incrementally, as a side-effect of query execution. We focus on how the incremental costs and benefits of dynamic reorganization are distributed across the workload's lifetime. We believe measuring the costs and utility of the stages of adaptation are relevant metrics for evaluating new query processing paradigms and comparing them to traditional approaches

SZ and X-ray combined analysis of a distant galaxy cluster, RX J2228+2037.

We have performed a combined analysis of X-ray and Sunyaev-Zel'dovich data in the direction of the distant galaxy cluster, RX J2228+2037. Fitting a $\beta$-model to the high-resolution HRI data gives $r_c = 103 \pm 12 h_{70}^{-1}$ kpc and $\beta=0.54 \pm 0.03$. The dependency of the Sunyaev-Zel'dovich effect with respect to the gas temperature allows us, through the additional use of the 21 GHz data of the cluster, to determine $k_B T_e=10.4 \pm 1.8 h_{70}^{1/2}$ keV. Extrapolating the gas density profile out to the virial radius ($R_v=r_{178}=2.9$ Mpc), we derived a gas mass of $M_{g}(r<R_v)=(4.0\pm 0.2)\times 10^{14} h_{70}^{-5/2} \rm{M}_\odot$. Within the hypothesis of hydrostatic equilibrium, the corresponding extrapolated total mass for this source is: $M_{tot}(r<R_v)=(1.8 \pm 0.4)\times 10^{15} h^{-1} \rm{M}_\odot$, which corresponds to a gas fraction of $f_{gas}=0.22\pm 0.06 h_{70}^{-3/2}$. Our results on the temperature and on the cluster mass classify RX J2228+2037 among the distant, hot and very massive galaxy clusters. Our work highlights the power of the association of galaxy cluster mapping observations in X-ray and the SZ effect to derive the cluster's physical properties, even without X-ray spectroscopy.Comment: 7 pages, 4 figures, accepted for publication in A&

Probabilistic Search for Object Segmentation and Recognition

The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object probability, is introduced to infer an optimal sequence of object hypotheses to be evaluated for their match to the data. The truncated probability is partly determined by prior knowledge of the objects and partly learned from data. Some experiments on sequence quality and object segmentation and recognition from stereo data are presented. The article recovers classic concepts from object recognition (grouping, geometric hashing, alignment) from the probabilistic perspective and adds insight into the optimal ordering of object hypotheses for evaluation. Moreover, it introduces point-relation densities, a key component of the truncated probability, as statistical models of local surface shape.Comment: 18 pages, 5 figure

Star Formation in M51 Triggered by Galaxy Interaction

We have mapped the inner 360'' regions of M51 in the 158micron [CII] line at 55'' spatial resolution using the Far-infrared Imaging Fabry-Perot Interferometer (FIFI) on the Kuiper Airborne Observatory (KAO). The emission is peaked at the nucleus, but is detectable over the entire region mapped, which covers much of the optical disk of the galaxy. There are also two strong secondary peaks at ~43% to 70% of the nuclear value located roughly 120'' to the north-east, and south-west of the nucleus. These secondary peaks are at the same distance from the nucleus as the corotation radius of the density wave pattern. The density wave also terminates at this location, and the outlying spiral structure is attributed to material clumping due to the interaction between M51 and NGC5195. This orbit crowding results in cloud-cloud collisions, stimulating star formation, that we see as enhanced [CII] line emission. The [CII] emission at the peaks originates mainly from photodissociation regions (PDRs) formed on the surfaces of molecular clouds that are exposed to OB starlight, so that these [CII] peaks trace star formation peaks in M51. The total mass of [CII] emitting photodissociated gas is ~2.6x10^{8} M_{sun}, or about 2% of the molecular gas as estimated from its CO(1-0) line emission. At the peak [CII] positions, the PDR gas mass to total gas mass fraction is somewhat higher, 3-17%, and at the secondary peaks the mass fraction of the [CII] emitting photodissociated gas can be as high as 72% of the molecular mass.... (continued)Comment: 14 pages, 6 figures, Accepted in ApJ (for higher resolution figures contact the author

The Eastern Arm of M83 Revisited: High-Resolution Mapping of 12CO 1-0 Emission

We have used the Owens Valley Millimeter Array to map 12CO (J=1-0) along a 3.5 kpc segment of M83's eastern spiral arm at resolutions of 6.5"x3.5", 10", and 16". The CO emission in most of this segment lies along the sharp dust lane demarking the inner edge of the spiral arm, but beyond a certain point along the arm the emission shifts downstream from the dust lane to become better aligned with the young stars seen in blue and H-beta images. This morphology resembles that of the western arm of M100. Three possibilities, none of which is wholly satisfactory, are considered to explain the deviation of the CO arm from the dust lane: heating of the CO by UV radiation from young stars, heating by low-energy cosmic rays, and a molecular medium consisting of two (diffuse and dense) components which react differently to the density wave. Regardless, the question of what CO emission traces along this spiral arm is a complicated one. Strong tangential streaming is observed where the arm crosses the kinematic major axis of the galaxy, implying that the shear becomes locally prograde in the arms. Inferred from the streaming is a very high gas surface density of about 230 solar masses/pc**2 and an arm-interarm contrast greater than 2.3 in the part of the arm near the major axis. Using two different criteria, we find that the gas at this location is well above the threshold for gravitational instability -- much more clearly so than in either M51 or M100.Comment: Accepted for publication in ApJ. 25 pages, 5 figures. Manuscript in LaTeX, figures in pdf. Fig 3 in colo

Virtual and Soft Pair Corrections to Polarized Muon Decay Spectrum

Radiative corrections to the muon decay spectrum due to soft and virtual electron--positron pairs are calculated.Comment: 10pp, 2 PS figs, details of calculations are adde