Quantifying the Morphologies and Dynamical Evolution of Galaxy Clusters. I. The Method

We describe and test a method to quantitatively classify clusters of galaxies according to their projected morphologies. This method will be subsequently used to place constraints on cosmological parameters ($\Omega$ and the power spectrum of primordial fluctuations on scales at or slightly smaller than that of clusters) and to test theories of cluster formation. We specifically address structure that is easily discernible in projection and dynamically important to the cluster. The method is derived from the two-dimensional multipole expansion of the projected gravitational potential and yields dimensionless {\it power ratios} as morphological statistics. If the projected mass profile is used to characterize the cluster morphology, the power ratios are directly related to the cluster potential. However, since detailed mass profiles currently exist for only a few clusters, we use the X-ray--emitting gas as an alternative tracer of cluster morphology. In this case, the relation of the power ratios to the potential is qualitatively preserved. We demonstrate the feasibility of the method by analyzing simulated observations of simple models of X-ray clusters using the instrument parameters of the ROSAT PSPC. For illustrative purposes, we apply the method to ROSAT PSPC images of A85, A514, A1750, and A2029. These clusters, which differ substantially in their X-ray morphologies, are easily distinguished by their respective power ratios. We discuss the suitability of this method to address the connection between cluster morphology and cosmology and to assess whether an individual cluster is sufficiently relaxed for analysis of its intrinsic shape using hydrostatic methods. Approximately 50 X-ray observations of Abell clusters with the PSPC will be amenable to morphological analysis using the method of this paper.Comment: To appear in ApJ October 20, 1995. 29 pages (7 figures missing), PostScrip

Noncanonical Amino Acids in the Interrogation of Cellular Protein Synthesis

Proteins in living cells can be made receptive to bioorthogonal chemistries through metabolic labeling with appropriately designed noncanonical amino acids (ncAAs). In the simplest approach to metabolic labeling, an amino acid analog replaces one of the natural amino acids specified by the protein’s gene (or genes) of interest. Through manipulation of experimental conditions, the extent of the replacement can be adjusted. This approach, often termed residue-specific incorporation, allows the ncAA to be incorporated in controlled proportions into positions normally occupied by the natural amino acid residue. For a protein to be labeled in this way with an ncAA, it must fulfill just two requirements: (i) the corresponding natural amino acid must be encoded within the sequence of the protein at the genetic level, and (ii) the protein must be expressed while the ncAA is in the cell. Because this approach permits labeling of proteins throughout the cell, it has enabled us to develop strategies to track cellular protein synthesis by tagging proteins with reactive ncAAs. In procedures similar to isotopic labeling, translationally active ncAAs are incorporated into proteins during a “pulse” in which newly synthesized proteins are tagged. The set of tagged proteins can be distinguished from those made before the pulse by bioorthogonally ligating the ncAA side chain to probes that permit detection, isolation, and visualization of the labeled proteins. Noncanonical amino acids with side chains containing azide, alkyne, or alkene groups have been especially useful in experiments of this kind. They have been incorporated into proteins in the form of methionine analogs that are substrates for the natural translational machinery. The selectivity of the method can be enhanced through the use of mutant aminoacyl tRNA synthetases (aaRSs) that permit incorporation of ncAAs not used by the endogenous biomachinery. Through expression of mutant aaRSs, proteins can be tagged with other useful ncAAs, including analogs that contain ketones or aryl halides. High-throughput screening strategies can identify aaRS variants that activate a wide range of ncAAs. Controlled expression of mutant synthetases has been combined with ncAA tagging to permit cell-selective metabolic labeling of proteins. Expression of a mutant synthetase in a portion of cells within a complex cellular mixture restricts labeling to that subset of cells. Proteins synthesized in cells not expressing the synthetase are neither labeled nor detected. In multicellular environments, this approach permits the identification of the cellular origins of labeled proteins. In this Account, we summarize the tools and strategies that have been developed for interrogating cellular protein synthesis through residue-specific tagging with ncAAs. We describe the chemical and genetic components of ncAA-tagging strategies and discuss how these methods are being used in chemical biology

Design of a lattice-based faceted classification system

We describe a software reuse architecture supporting component retrieval by facet classes. The facets are organized into a lattice of facet sets and facet n-tuples. The query mechanism supports precise retrieval and flexible browsing

Modular Forms on the Double Half-Plane

We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.Comment: 17 pages: Minor corrections in text (due to a helpful referee), updated affiliations. Accepted for publication in the International Journal for Number Theory (IJNT

Halo abundances within the cosmic web

We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of cosmological theory, allowing mass-dependent biasing to be understood via the peak-background split. On the assumption of a Gaussian density field, this analysis can be extended to ask how the mass function depends on the geometrical environment: clusters, filaments, sheets and voids, as classified via the tidal tensor (the Hessian matrix of the gravitational potential). In linear theory, the problem can be solved exactly, and the result is attractively simple: the conditional mass function has no explicit dependence on the local tidal field, and is a function only of the local density on the filtering scale used to define the tidal tensor. There is nevertheless a strong implicit predicted dependence on geometrical environment, because the local density couples statistically to the derivatives of the potential. We compute the predictions of this model and study the limits of their validity by comparing them to results deduced empirically from $N$-body simulations. We have verified that, to a good approximation, the abundance of haloes in different environments depends only on their densities, and not on their tidal structure. In this sense we find relative differences between halo abundances in different environments with the same density which are smaller than 13%. Furthermore, for sufficiently large filtering scales, the agreement with the theoretical prediction is good, although there are important deviations from the Gaussian prediction at small, non-linear scales. We discuss how to obtain improved predictions in this regime, using the 'effective-universe' approach.Comment: 14 pages, 6 figures. Revision matching journal versio