Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on Bargmann-Segal-Fock spaces.Comment: 48 pages, LaTeX file, to appear in J. Math. Phy

Polymorphic organization in a planktonic graptoloid (Hemichordata: Pterobranchia) colony of Late Ordovician age

Graptolites are common fossils in Early Palaeozoic strata, but little is known of their soft-part anatomy. However, we report a long-overlooked specimen of Dicranograptus aff. ramosus from Late Ordovician strata of southern Scotland that preserves a strongly polymorphic, recalcitrant, organic-walled network hitherto unseen in graptoloid graptolites. This network displays three morphologies: proximally, a strap-like pattern, likely of flattened tubes; these transform distally into isolated, hourglass-shaped structures; then, yet more distally, revert to a (simpler) strap-like pattern. The network most likely represents a stolon-like system, hitherto unknown in graptoloids, that connected individual zooids. Its alternative interpretation, as colonial xenobionts that infested a graptoloid colony and mimicked its architecture, is considered less likely on taphonomic and palaeobiological grounds. Such polymorphism is not known in non-graptolite pterobranchs, which are less diverse and morphologically more conservative: a division of labour between graptoloid zooids for such functions as feeding, breeding and rhabdosome construction may have been the key to their remarkable evolutionary success

The Large-scale J=3-2 and J=2-1 CO Emission from M17 and its Implications for Extragalactic CO Observations

We observed a 10x20 pc region of the molecular cloud M17 in the 12CO and 13CO J=3-2 and J=2-1 transitions to determine their global behavior and to assess the reliability of using ratios of CO line intensities integrated over an entire cloud to determine the physical conditions within the cloud. Both the 12CO/13CO J=2-1 and J=3-2 line ratios correlate with the 13CO integrated intensity, with smaller line ratios observed at locations with large integrated intensities. This correlation is likely due to variations in the column density from one position to another within M17. The 12CO and 13CO (J=3-2/J=2-1) line ratios show no significant variation from place to place within M17, even on the peak of the photon-dominated region. A Large Velocity Gradient analysis of globally averaged line ratios gives results in reasonable agreement with the results obtained for individual lines-of-sight through the cloud, which suggests that the typical physical conditions in a molecular cloud can be determined using CO line ratios integrated over the entire cloud. There appears to be a clear trend of increasing 12CO/13CO J=2-1 and J=3-2 line ratios as one moves from Galactic molecular cloud cores to entire Galactic molecular clouds to normal galaxies. The most likely explanation of the high line ratios for normal galaxies is a significant contribution to the CO emission by low column density material, such as diffuse molecular clouds or the outer envelopes of giant molecular clouds.Comment: 26 pages, 6 figures, 2 tables. Accepted for publication in Ap

Microwave Sinterator Freeform Additive Construction System (MS-FACS)

The harmful properties of lunar dust, such as small size, glass composition, abnormal surface area, and coatings of imbedded nanophase iron, lead to a unique coupling of the dust with microwave radiation. This coupling can be exploited for rapid sintering of lunar soil for use as a construction material that can be formed to take on an infinite number of shapes and sizes. This work describes a system concept for building structures on the lunar surface using lunar regolith (soil). This system uses the ATHLETE (All-Terrain Hex- Limbed Extra-Terrestrial Explorer) mobility system as a positioning system with a microwave print head (similar to that of a smaller-scale 3D printer). A processing system delivers the lunar regolith to the microwave print head, where the microwave print head/chamber lays down a layer of melted regolith. An arm on the ATHLETE system positions the layer depending on the desired structure

A simple approach to counterterms in N=8 supergravity

We present a simple systematic method to study candidate counterterms in N=8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D^{2k} R^n +... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n>4, we find that R^n, D^2 R^n, D^4 R^n, and D^6 R^n are excluded as counterterms of MHV amplitudes, while only R^n and D^2 R^n are excluded at the NMHV level. As a consequence, for loop order L<7, there are no independent D^{2k}R^n counterterms with n>4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D^4 R^6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/allowed candidate counterterms is summarized in a colorful chart.Comment: 25 pages, 1 figure, published versio

Stringy KLT relations, global symmetries, and E_7(7) violation

We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi) R^4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'^3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R^4 is incompatible with continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R^4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.Comment: 23 pages, published versio

Two-Loop Renormalization Group Equations for Soft Supersymmetry-Breaking Couplings

We compute the two-loop renormalization group equations for all soft supersymmetry-breaking couplings in a general softly broken N=1 supersymmetric model. We also specialize these results to the Minimal Supersymmetric Standard Model.Comment: 26 pages. [v4: Signs of equations (4.2) and (4.3) are fixed.

Large N Gauge Theory -- Expansions and Transitions

We use solvable two-dimensional gauge theories to illustrate the issues in relating large N gauge theory to string theory. We also give an introduction to recent mathematical work which allows constructing master fields for higher dimensional large N theories. We illustrate this with a new derivation of the Hopf equation governing the evolution of the spectral density in matrix quantum mechanics. Based on lectures given at the 1994 Trieste Spring School on String Theory, Gauge Theory and Quantum Gravity.Comment: RU-94-72 (LaTeX with espcrc2.sty and epsf.sty, 26 pp., 6 figures. References added and other improvements.

Scalable Syriac Paleography using Interactive Visualization

Syriac (a dialect of Aramaic) was the primary language spoken in the late ancient Middle East between the second and eighth centuries AD, and continues to be a language of Christian scholarship and liturgy up to the present day. There are approximately 20,000 known surviving Syriac manuscripts. Among early manuscripts, only around 10% include a scribal note that provides information regarding when, where, and by whom a given manuscript was written. For the remaining 90%, close examination of subtle differences in the handwritten script remains the primary tool for determining provenance. Prior to this study, scholars classified early Syriac manuscripts into two divergent script styles: Estrangela and Serto. In this paper, we present a case study of historians’ analysis of this collection of manuscripts supported by visual analytic tools. This approach uncovered major inaccuracies in this dichotomous model, resulting in profound disruption to the dominant understanding of the development of these texts

Detectors for the James Webb Space Telescope Near-Infrared Spectrograph I: Readout Mode, Noise Model, and Calibration Considerations

We describe how the James Webb Space Telescope (JWST) Near-Infrared Spectrograph's (NIRSpec's) detectors will be read out, and present a model of how noise scales with the number of multiple non-destructive reads sampling-up-the-ramp. We believe that this noise model, which is validated using real and simulated test data, is applicable to most astronomical near-infrared instruments. We describe some non-ideal behaviors that have been observed in engineering grade NIRSpec detectors, and demonstrate that they are unlikely to affect NIRSpec sensitivity, operations, or calibration. These include a HAWAII-2RG reset anomaly and random telegraph noise (RTN). Using real test data, we show that the reset anomaly is: (1) very nearly noiseless and (2) can be easily calibrated out. Likewise, we show that large-amplitude RTN affects only a small and fixed population of pixels. It can therefore be tracked using standard pixel operability maps.Comment: 55 pages, 10 figure