Composite lacunary polynomials and the proof of a conjecture of Schinzel

Let $g(x)$ be a fixed non-constant complex polynomial. It was conjectured by Schinzel that if $g(h(x))$ has boundedly many terms, then h(x)\in \C[x] must also have boundedly many terms. Solving an older conjecture raised by R\'enyi and by Erd\"os, Schinzel had proved this in the special cases $g(x)=x^d$; however that method does not extend to the general case. Here we prove the full Schinzel's conjecture (actually in sharper form) by a completely different method. Simultaneously we establish an "algorithmic" parametric description of the general decomposition $f(x)=g(h(x))$, where $f$ is a polynomial with a given number of terms and $g,h$ are arbitrary polynomials. As a corollary, this implies for instance that a polynomial with $l$ terms and given coefficients is non-trivially decomposable if and only if the degree-vector lies in the union of certain finitely many subgroups of $\Z^l$.Comment: 9 page

4q32-q35 and 6q16-q22 are valuable candidate regions for split hand/foot malformation

On the basis of the Human Cytogenetic Database, a computerized catalog of the clinical phenotypes associated with cytogenetically detectable human chromosome aberrations, we collected from the literature 102 cases with chromosomal aberrations and split hand/foot malformation or absent fingers/toes. Statistical analysis revealed a highly significant association (P<0.001) between the malformation and the chromosomal bands 4q32-q35, 5q15, 6q16-q22 and 7q11.2-q22 (SHFM1). Considering these findings, we suggest additional SHFM loci on chromosome 4q, 6q and probably 5q. The regions 4q and 6q have already been discussed in the literature as additional SHFM loci. We now show further evidence. In the proposed regions, there are interesting candidate genes such as, on 4q: HAND2, FGF2, LEF1 and BMPR1B; on 5q: MSX2, FLT4, PTX1 and PDLIM7; and on 6q: SNX3, GJA1, HEY2 and Tbx18.European Journal of Human Genetics advance online publication, 18 February 2009; doi:10.1038/ejhg.2009.11

Screening for UBE3A gene mutations in a group of Angelman syndrome patients selected according to non-stringent clinical criteria

Abstract.: The Angelman syndrome (AS) is caused by genetic abnormalities affecting the maternal copy of chromosome region 15q12. Until recently, the molecular diagnosis of AS relied on the detection of either a deletion at 15q11-13, a paternal uniparental disomy (UPD) for chromosome 15 or imprinting mutations. A fourth class of genetic defects underlying AS was recently described and consists of mutations of the UBE3A gene. The vast majority of mutations reported so far are predicted to cause major disruptions at the protein level. It is unclear whether mutations with less drastic consequences for the gene product could lead to milder forms of AS. We report on our results obtained by screening 101 clinically diagnosed AS patients for mutations in the UBE3A gene. Non-stringent clinical criteria were purposely applied for inclusion of AS patients in this study. The mutation search was carried out by single-strand conformation polymorphism (SSCP), and SSCP/restriction fragment length polymorphism (RFLP) analyses and revealed five novel UBE3A gene mutations as well as three different polymorphisms. All five mutations were detected in patients with typical features of AS and are predicted to cause frameshifts in four cases and the substitution of a highly conserved residue in the fifth. The results we obtained add to the as yet limited number of reports concerning UBE3A gene mutations. Important aspects that emerge from the data available to date is that the four classes of genetic defects known to underlie AS do not appear to cover all cases. The genetic defect underlying approximately 10% of AS cases, including some familial cases, remains unknow

Monitoring the Sky with the Prototype All-Sky Imager on the LWA1

We present a description of the Prototype All-Sky Imager (PASI), a backend correlator and imager of the first station of the Long Wavelength Array (LWA1). PASI cross-correlates a live stream of 260 dual-polarization dipole antennas of the LWA1, creates all-sky images, and uploads them to the LWA-TV website in near real-time. PASI has recorded over 13,000 hours of all-sky images at frequencies between 10 and 88 MHz creating opportunities for new research and discoveries. We also report rate density and pulse energy density limits on transients at 38, 52, and 74 MHz, for pulse widths of 5 s. We limit transients at those frequencies with pulse energy densities of $>2.7\times 10^{-23}$, $>1.1\times 10^{-23}$, and $>2.8\times 10^{-23}$ J m$^{-2}$ Hz$^{-1}$ to have rate densities $<1.2\times10^{-4}$, $<5.6\times10^{-4}$, and $<7.2\times10^{-4}$ yr$^{-1}$ deg$^{-2}$Comment: 27 pages, 10 Figures, 1 Tabl

More Discriminants with the Brezing-Weng Method

The Brezing-Weng method is a general framework to generate families of pairing-friendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endomorphism rings with small class number

Radio and gamma-ray follow-up of the exceptionally high activity state of PKS 1510-089 in 2011

We investigate the radio and gamma-ray variability of the flat spectrum radio quasar PKS 1510-089 in the time range between 2010 November and 2012 January. In this period the source showed an intense activity, with two major gamma-ray flares detected in 2011 July and October. During the latter episode both the gamma-ray and the radio flux density reached their historical peak. Multiwavelength analysis shows a rotation of about 380 deg of the optical polarization angle close in time with the rapid and strong gamma-ray flare in 2011 July. An enhancement of the optical emission and an increase of the fractional polarization both in the optical and in radio bands is observed about three weeks later, close in time with another gamma-ray outburst. On the other hand, after 2011 September a huge radio outburst has been detected, first in the millimeter regime followed with some time delay at centimeter down to decimeter wavelengths. This radio flare is characterized by a rising and a decaying stage, in agreement with the formation of a shock and its evolution, as a consequence of expansion and radiative cooling. If the gamma-ray flare observed in 2011 October is related to this radio outburst, then this strongly indicates that the region responsible for the gamma-ray variability is not within the broad line, but a few parsecs downstream along the jet.Comment: 14 pages, 12 figures, accepted for publication in MNRA

Observations of Giant Pulses from Pulsar PSR B0950+08 using LWA1

We report the detection of giant pulse emission from PSR B0950+08 in 24 hours of observations made at 39.4 MHz, with a bandwidth of 16 MHz, using the first station of the Long Wavelength Array, LWA1. We detected 119 giant pulses from PSR B0950+08 (at its dispersion measure), which we define as having SNRs at least 10 times larger than for the mean pulse in our data set. These 119 pulses are 0.035% of the total number of pulse periods in the 24 hours of observations. The rate of giant pulses is about 5.0 per hour. The cumulative distribution of pulse strength $S$ is a steep power law, $N(>S)\propto S^{-4.7}$, but much less steep than would be expected if we were observing the tail of a Gaussian distribution of normal pulses. We detected no other transient pulses in a dispersion measure range from 1 to 90 pc cm$^{-3}$, in the beam tracking PSR B0950+08. The giant pulses have a narrower temporal width than the mean pulse (17.8 ms, on average, vs. 30.5 ms). The pulse widths are consistent with a previously observed weak dependence on observing frequency, which may be indicative of a deviation from a Kolmogorov spectrum of electron density irregularities along the line of sight. The rate and strength of these giant pulses is less than has been observed at $\sim$100 MHz. Additionally, the mean (normal) pulse flux density we observed is less than at $\sim$100 MHz. These results suggest this pulsar is weaker and produces less frequent giant pulses at 39 MHz than at 100 MHz.Comment: 27 pages, 12 figures, typos correcte