Representation theory and projective geometry

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.Comment: 37 pages with picture

Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time

Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood estimators. This paper intends to fill this gap. Specifically, we prove the consistency of the maximum likelihood estimators and derive their asymptotic distributions. The maximum likelihood estimators are shown to be semiparametrically efficient.Comment: Published at http://dx.doi.org/10.1214/009053605000000480 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Series of nilpotent orbits

We organize the nilpotent orbits in the exceptional complex Lie algebras into series using the triality model and show that within each series the dimension of the orbit is a linear function of the natural parameter a=1,2,4,8, respectively for f_4,e_6,e_7,e_8. We also obtain explicit representatives in a uniform manner. We observe similar regularities for the centralizers of nilpotent elements in a series and graded components in the associated grading of the ambient Lie algebra. More strikingly, for a greater than one, the degrees of the unipotent characters of the corresponding Chevalley groups, associated to these series through the Springer correspondance are given by polynomials which have uniform expressions in terms of a.Comment: 20 pages, revised version with more formulas for unipotent character

Modeling intraseasonal features of 2004 North American monsoon precipitation

This study examines the capabilities and limitations of the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) in predicting the precipitation and circulation features that accompanied the 2004 North American monsoon (NAM). When the model is reinitialized every 5 days to restrain the growth of modeling errors, its results for precipitation checked at subseasonal time scales (not for individual rainfall events) become comparable with ground- and satellite-based observations as well as with the NAM's diagnostic characteristics. The modeled monthly precipitation illustrates the evolution patterns of monsoon rainfall, although it underestimates the rainfall amount and coverage area in comparison with observations. The modeled daily precipitation shows the transition from dry to wet episodes on the monsoon onset day over the Arizona-New Mexico region, and the multiday heavy rainfall (>1 mm day-1) and dry periods after the onset. All these modeling predictions agree with observed variations. The model also accurately simulated the onset and ending dates of four major moisture surges over the Gulf of California during the 2004 monsoon season. The model reproduced the strong diurnal variability of the NAM precipitation, but did not predict the observed diurnal feature of the precipitation peak's shift from the mountains to the coast during local afternoon to late night. In general, the model is able to reproduce the major, critical patterns and dynamic variations of the NAM rainfall at intraseasonal time scales, but still includes errors in precipitation quantity, pattern, and timing. The numerical study suggests that these errors are due largely to deficiencies in the model's cumulus convective parameterization scheme, which is responsible for the model's precipitation generation. © 2007 American Meteorological Society

Crystalline Electric Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO4_4

We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb$^{3+}$ crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO$_4$. Three CEF excitations from the ground-state Kramers doublet are centered at the energies $\hbar \omega$ = 39, 61, and 97\,meV in agreement with the effective \mbox{spin-1/2} $g$-factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg$^{2+}$ and Ga$^{3+}$ giving rise to a distribution of Yb--O distances and orientations and, thus, of CEF parameters that account for the peculiar energy profile of the CEF excitations. The CEF randomness gives rise to a distribution of the effective spin-1/2 $g$-factors and explains the unprecedented broadening of low-energy magnetic excitations in the fully polarized ferromagnetic phase of YbMgGaO$_4$, although a distribution of magnetic couplings due to the Mg/Ga disorder may be important as well.Comment: Accepted in Phys. Rev. Let

Tackling the technical history of the textiles of El-Deir, Kharga Oasis, the Western Desert of Egypt

The site of El-Deir is situated north of Kharga in the “Great Oasis” of the Egyptian Western Desert (fig. 1). The site was occupied between the 6th century BC and the 6th century AD. A complex history emerged with the influence of many cultures: Persian, Greek, Roman and early Christian. Archaeological finds in both El-Deir and the oasis itself (the site of Dush and the temple of Darius in Hibis, a city north of Kharga) confirm that the Great Oasis was a wealthy region. This is also substantiated by texts from Ain Manawir and Dakhleh. The presence of an artesian aquifer, a great economic asset, further underpinned the prosperity of the area, which was a crossroads for numerous routes from the earliest dynasties. There are currently three different sources of textiles on the site (fig. 2): the six cemeteries (five polytheistic and one Christian), the workshop of the embalmers, and the Roman fortress with adjacent temple. Most of the textiles have been found in a funerary context. The study of the textiles takes place within an oasis, a circumscribed setting with a specific geography and climate, and over a long continuous period. Such conditions are favourable for emphasising traditions and changes. Before briefly mentioning the material from El-Deir, we feel it is important to underline that comparisons with other textile studies are difficult. The majority of the necropoleis of the site are Ptolemaic and very few studies have concentrated on this period. In consequence, any possible comparisons must be made with recourse to Pharaonic textiles. On the other hand, the examples of textiles retrieved from the soundings in the fortress can be easily placed due to studies conducted in the Eastern Desert. Likewise, material from the Christian cemetery finds parallels in the numerous sites in Egypt that date to the Byzantine era. Technical and aesthetic criteria of the textiles from the site are important for the study of the social status of the buried individuals and provide an assessment of the local standard of living. The study of textiles can also help in reconstructing, at least partially, the textile industry of the oasis. Textiles can also shed new light on religious, cultural and economic life. Lastly, they can serve as a comparative tool for other sites. How does one deal with the diversity and quantity of textiles found in such a specific oasis site? Four hundred pieces of textile were selected in the field, entered into a database and then analysed. An essential step in the first instance was to choose, on-site, representative textiles according to quantity and quality, archaeological context, per individual, per tomb or en masse. These were in the great majority mere fragments, the site having been looted many times in the not too distant past. Once the textiles had been sorted, the second step involved a technical examination stretching from fibre to fabric, in order to shed light, for each, on the characteristics, the techniques used to transform them and, when possible, the tools used to do so. Only a few examples, which illustrate the diversity of the site, will be presented in this article, while focus shall remain on the raw material. We have chosen to present, one by one, the three textile fibres found on the site: linen, cotton and wool

Phase separation of polymer solutions. The calculation of the cloudpoint curve with a concentration and temperature-dependent free energy correction parameter

The free enthalpy correction parameter g in the Flory-Huggins equation for the Gibbs free enthalpy of mixing in polymer solutions is considered generally as a concentration- and temperature-independent parameter. It has been extended here with linear concentration- and temperature-dependent terms. With these parameters, six different types of cloudpoint curves can be predicted. Using the experimental cloudpoint curve for solutions of poly(2,6-dimethyl-1,4-phenylene oxide) in toluene up to about 70 per cent by weight of polymer, a set of g-parameters is obtained, accounting for concentration and temperature dependence. With the parameters thus obtained, the melting point curve has been calculated which agrees very well with the experimental melting points for this system