Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight

In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the pth graded component of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W for groups of rank seven and eight. For classical Coxeter groups, these characters are given using a formula that is expected to hold in all ranks.Comment: Minor changes; final versio

Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group $W$ acting on the $p$th graded component of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of $W$. Our refined conjecture relates the character above to a component of a decomposition of the regular character of $W$ related to Solomon's descent algebra of $W$. The refined conjecture has been proved for symmetric and dihedral groups, as well as finite Coxeter groups of rank three and four. In this paper, the second in a series of three dealing with groups of rank up to eight (and in particular, all exceptional Coxeter groups), we prove the conjecture for finite Coxeter groups of rank five and six, further developing the algorithmic tools described in the previous article. The techniques developed and implemented in this paper provide previously unknown decompositions of the regular and Orlik-Solomon characters of the groups considered.Comment: Final Version. 17 page

Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms

We present numerical relativity simulations of nine-orbit equal-mass binary neutron star covering the quasicircular late inspiral and merger. The extracted gravitational waveforms are analyzed for convergence and accuracy. Second order convergence is observed up to contact, i.e. about 3-4 cycles to merger; error estimates can be made up to this point. The uncertainties on the phase and the amplitude are dominated by truncation errors and can be minimized to 0.13 rad and less then 1%, respectively, by using several simulations and extrapolating in resolution. In the latter case finite-radius extraction uncertainties become a source of error of the same order and have to be taken into account. The waveforms are tested against accuracy standards for data analysis. The uncertainties on the waveforms are such that accuracy standards are generically not met for signal-to-noise ratios relevant for detection, except for some best cases using extrapolation from several runs. A detailed analysis of the errors is thus imperative for the use of numerical relativity waveforms from binary neutron stars in quantitative studies. The waveforms are compared with the post-Newtonian Taylor T4 approximants both for point-particle and including the analytically known tidal corrections. The T4 approximants accumulate significant phase differences of 2 rad at contact and 4 rad at merger, underestimating the influence of finite size effects. Tidal signatures in the waveforms are thus important at least during the last six orbits of the merger process.Comment: Physical Review D (Vol.85, No.10) 201

Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group $W$ afforded by the homogeneous components of its Orlik-Solomon algebra as sums of characters induced from linear characters of centralizers of elements of $W$. Our refined conjecture also relates the Orlik-Solomon characters above to the terms of a decomposition of the regular character of $W$ related to the descent algebra of $W$. A consequence of our conjecture is that both the regular character of $W$ and the character of the Orlik-Solomon algebra have parallel, graded decompositions as sums of characters induced from linear characters of centralizers of elements of $W$, one for each conjugacy class of elements of $W$. The refined conjecture has been proved for symmetric and dihedral groups. In this paper we develop algorithmic tools to prove the conjecture computationally for a given finite Coxeter group. We use these tools to verify the conjecture for all finite Coxeter groups of rank three and four, thus providing previously unknown decompositions of the regular characters and the Orlik-Solomon characters of these groups.Comment: Final version. 20 pages, 6 tables. To appear in J. Symbolic Compu

Autumn destabilization of deep porewater CO2 store in a northern peatland driven by turbulent diffusion

The CO2 stored in deep peat porewater is viewed as a fixed component of peatland C cycling. Here, the authors reveal a hitherto unknown hydro-physical process that results in sudden losses from this CO2 store every autumn.The deep porewater of northern peatlands stores large amounts of carbon dioxide (CO2). This store is viewed as a stable feature in the peatland CO2 cycle. Here, we report large and rapid fluctuations in deep porewater CO2 concentration recurring every autumn over four consecutive years in a boreal peatland. Estimates of the vertical diffusion of heat indicate that CO2 diffusion occurs at the turbulent rather than molecular rate. The weakening of porewater thermal stratification in autumn likely increases turbulent diffusion, thus fostering a rapid diffusion of deeper porewater CO2 towards the surface where net losses occur. This phenomenon periodically decreases the peat porewater CO2 store by between 29 and 90 g C m(-2) throughout autumn, which is comparable to the peatland's annual C-sink. Our results establish the need to consider the role of turbulent diffusion in regularly destabilizing the CO2 store in peat porewater

Can Authorship Representation Learning Capture Stylistic Features?

Automatically disentangling an author's style from the content of their writing is a longstanding and possibly insurmountable problem in computational linguistics. At the same time, the availability of large text corpora furnished with author labels has recently enabled learning authorship representations in a purely data-driven manner for authorship attribution, a task that ostensibly depends to a greater extent on encoding writing style than encoding content. However, success on this surrogate task does not ensure that such representations capture writing style since authorship could also be correlated with other latent variables, such as topic. In an effort to better understand the nature of the information these representations convey, and specifically to validate the hypothesis that they chiefly encode writing style, we systematically probe these representations through a series of targeted experiments. The results of these experiments suggest that representations learned for the surrogate authorship prediction task are indeed sensitive to writing style. As a consequence, authorship representations may be expected to be robust to certain kinds of data shift, such as topic drift over time. Additionally, our findings may open the door to downstream applications that require stylistic representations, such as style transfer.Comment: appearing at TACL 202

Wintertime phytoplankton bloom in the subarctic Pacific supported by continental margin iron

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 20 (2006): GB1006, doi:10.1029/2005GB002557.Heightened biological activity was observed in February 1996 in the high-nutrient low-chlorophyll (HNLC) subarctic North Pacific Ocean, a region that is thought to be iron-limited. Here we provide evidence supporting the hypothesis that Ocean Station Papa (OSP) in the subarctic Pacific received a lateral supply of particulate iron from the continental margin off the Aleutian Islands in the winter, coincident with the observed biological bloom. Synchrotron X-ray analysis was used to describe the physical form, chemistry, and depth distributions of iron in size fractionated particulate matter samples. The analysis reveals that discrete micron-sized iron-rich hot spots are ubiquitous in the upper 200 m at OSP, more than 900 km from the closest coast. The specifics of the chemistry and depth profiles of the Fe hot spots trace them to the continental margins. We thus hypothesize that iron hot spots are a marker for the delivery of iron from the continental margin. We confirm the delivery of continental margin iron to the open ocean using an ocean general circulation model with an iron-like tracer source at the continental margin. We suggest that iron from the continental margin stimulated a wintertime phytoplankton bloom, partially relieving the HNLC condition.This work was supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research (KP1202030) to J. K. B and by NSFATM-9987457 to I. F. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Division of Chemical Sciences, Geosciences, and Biosciences of the U.S. Department of Energy at Lawrence Berkeley National Laboratory under contract DE-AC03-76SF00098