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

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

Challenging the Estrangela / Serto Divide: Why the Standard Model of Syriac Scripts Just Doesn\u27t Work

As part of a larger digital paleography project, our team has assembled a database of tens of thousands of individual Syriac letters and letter data from 96% of extant early Syriac manuscripts that have a secure composition date. Long term, such data can help scholars develop more accurate ways to classify Syriac scripts. In the present article we use this data to illustrate just how frequently the most common way of categorizing Syriac scripts as either Estrangela or Serto does not accurately convey the ways early scribes actually wrote. In addition to challenging this “Standard Model” of Syriac scripts, the project illustrates how large data sets, digital analysis, and visual analytics can help researchers address key philological and historical problems

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

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

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

Atmospheric Retrieval of L Dwarfs: Benchmarking Results and Characterizing the Young Planetary Mass Companion HD 106906 b in the Near-infrared

© 2023. The Author(s). Published by the American Astronomical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0We present model constraints on the atmospheric structure of HD 106906 b, a planetary-mass companion orbiting at a ∼700 au projected separation around a 15 Myr old stellar binary, using the APOLLO retrieval code on spectral data spanning 1.1–2.5 μm. C/O ratios can provide evidence for companion formation pathways, as such pathways are ambiguous both at wide separations and at star-to-companion mass ratios in the overlap between the distributions of planets and brown dwarfs. We benchmark our code against an existing retrieval of the field L dwarf 2MASSW J2224–0158, returning a C/O ratio consistent with previous fits to the same JHK s data, but disagreeing in the thermal structure, cloud properties, and atmospheric scale height. For HD 106906 b, we retrieve C/O =0.53−0.25+0.15 , consistent with the C/O ratios expected for HD 106906's stellar association and therefore consistent with a stellar-like formation for the companion. We find abundances of H2O and CO near chemical equilibrium values for a solar metallicity but a surface gravity lower than expected, as well as a thermal profile with sharp transitions in the temperature gradient. Despite high signal-to-noise ratio and spectral resolution, more accurate constraints necessitate data across a broader wavelength range. This work serves as preparation for subsequent retrievals in the era of JWST, as JWST's spectral range provides a promising opportunity to resolve difficulties in fitting low-gravity L dwarfs and also underscores the need for simultaneous comparative retrievals on L-dwarf companions with multiple retrieval codes.Peer reviewe

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