Solving the 100 Swiss Francs Problem

Sturmfels offered 100 Swiss Francs in 2005 to a conjecture, which deals with a special case of the maximum likelihood estimation for a latent class model. This paper confirms the conjecture positively

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Limits to Quantum Gravity Effects from Observations of TeV Flares in Active Galaxies

We have used data from the TeV gamma-ray flare associated with the active galaxy Markarian 421 observed on 15 May 1996 to place bounds on the possible energy-dependence of the speed of light in the context of an effective quantum gravitational energy scale. The possibility of an observable time dispersion in high energy radiation has recently received attention in the literature, with some suggestions that the relevant energy scale could be less than the Planck mass and perhaps as low as 10^16 GeV. The limits derived here indicate this energy scale to be in excess of 4x10^16 GeV at the 95% confidence level. To the best of our knowledge, this constitutes the first convincing limit on such phenomena in this energy regime.Comment: 6 pages, including 2 figure

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

Complex Spectral Variability from Intensive Multi-wavelength Monitoring of Mrk421 in 1998

We conducted a multi-frequency campaign for the TeV blazar Mrk~421 in 1998 April. The campaign started from a pronounced high amplitude flare recorded by SAX and Whipple; ASCA observation started three days later. In the X-ray data, we detected multiple flares, occuring on time scales of about one day. ASCA data clearly reveal spectral variability. The comparison of the data from ASCA, EUVE and RXTE indicates that the variability amplitudes in the low energy synchrotron component are larger at higher photon energies. In TeV Gamma-rays, large intra-day variations -- which were correlated with the X-ray flux -- were observed when results from three Cherenkov telescopes are combined. The RMS variability of TeV Gamma--rays was similar to that observed in hard X-rays, above 10 keV. The X-ray light curve reveals flares which are almost symmetric for most of cases, implying the dominant time scale is the light crossing time through the emitting region. The structure function analysis based on the continuous X-ray light curve of seven days indicates that the characteristic time scale is ~0.5 day. The analysis of ASCA light curves in various energy bands appears to show both soft (positive) and hard (negative) lags. These may not be real, as systematic effects could also produce these lags, which are all much smaller than an orbit. If the lags of both signs are real, these imply that the particle acceleration and X-ray cooling time scales are similar.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter

Constraints on Gamma-ray Emission from the Galactic Plane at 300 TeV

We describe a new search for diffuse ultrahigh energy gamma-ray emission associated with molecular clouds in the galactic disk. The Chicago Air Shower Array (CASA), operating in coincidence with the Michigan muon array (MIA), has recorded over 2.2 x 10^{9} air showers from April 4, 1990 to October 7, 1995. We search for gamma rays based upon the muon content of air showers arriving from the direction of the galactic plane. We find no significant evidence for diffuse gamma-ray emission, and we set an upper limit on the ratio of gamma rays to normal hadronic cosmic rays at less than 2.4 x 10^{-5} at 310 TeV (90% confidence limit) from the galactic plane region: (50 degrees < l < 200 degrees); -5 degrees < b < 5 degrees). This limit places a strong constraint on models for emission from molecular clouds in the galaxy. We rule out significant spectral hardening in the outer galaxy, and conclude that emission from the plane at these energies is likely to be dominated by the decay of neutral pions resulting from cosmic rays interactions with passive target gas molecules.Comment: Astrophysical Journal, submitted, 11 pages, AASTeX Latex, 3 Postscript figure

BeppoSAX Observations of Markarian 501 in June 1999

We present the preliminary results of a long BeppoSAX observation of the BL Lac object Mkn501 carried out in June 1999. The source was fainter than found during the BeppoSAX pointings of 1997 and 1998, but is still detected with a good signal-to-noise ratio up to ~40 keV. The X-ray spectrum in the energy range 0.1-40 keV, produced through synchrotron radiation, is steeper than in the previous years, it is clearly curved, and peaks (in nu*F_nu) at ~0.5 keV. This energy is much lower than those at which the synchrotron component was found to peak in 1997 and 1998. Some intraday variability suggests that activity of the source on small time scales accompanies the large long time scale changes of brightness and spectrum.Comment: 4 pages, Latex, 2 PostScript figures, to appear in the Proceedings of the Conference "X-ray Astronomy '999: Stellar Endpoints, AGNs, and the Diffuse X-ray Background" (Bologna, 6-10 September 1999

The 5q31 variants associated with psoriasis and Crohn's disease are distinct

Predisposition to psoriasis is known to be affected by genetic variation in HLA-C, IL12B and IL23R, but other genetic risk factors also exist. We recently reported three psoriasis-associated single nucleotide polymorphisms (SNPs) in the 5q31 locus, a region of high linkage disequilibrium laden with inflammatory pathway genes. The aim of this study was to assess whether other variants in the 5q31 region are causal to these SNPs or make independent contributions to psoriasis risk by genotyping a comprehensive set of tagging SNPs in a 725 kb region bounded by IL3 and IL4 and testing for disease association. Ninety SNPs, capturing 86.4% of the genetic diversity, were tested in one case–control sample set (467 cases/460 controls) and significant markers (Pallelic < 0.05) (n = 9) were then tested in two other sample sets (981 cases/925 controls). All nine SNPs were significant in a meta-analysis of the combined sample sets. Pair-wise conditional association tests showed rs1800925, an intergenic SNP located just upstream of IL13 (Mantel–Haenszel Pcombined = 1.5 × 10−4, OR = 0.77 [0.67–0.88]), could account for observed significant association of all but one other SNP, rs11568506 in SLC22A4 [Mantel–Haenszel Pcombined = 0.043, OR = 0.68 (0.47–0.99)]. Haplotype analysis of these two SNPs showed increased significance for the two common haplotypes (rs11568506–rs1800925: GC, Pcombined = 5.67 × 10−6, OR = 1.37; GT, Pcombined = 6.01 × 10−5, OR = 0.75; global haplotype P = 8.93 × 10−5). Several 5q31-region SNPs strongly associated with Crohn's disease (CD) in the recent WTCCC study were not significant in the psoriasis sample sets tested here. These results identify the most significant 5q31 risk variants for psoriasis and suggest that distinct 5q31 variants contribute to CD and psoriasis risk