The return of the Andromedids meteor shower

The Andromedid meteor shower underwent spectacular outbursts in 1872 and 1885, producing thousands of visual meteors per hour and described as `stars fell like rain' in Chinese records of the time. The shower originates from comet 3D/Biela whose disintegration in the mid-1800's is linked to the outbursts, but the shower has been weak or absent since the late 19th Century. This shower returned in December 2011 with a zenithal hourly rate of approximately 50, the strongest return in over a hundred years. Some 122 probable Andromedid orbits were detected by the Canadian Meteor Orbit Radar. The shower outburst occurred during 2011 Dec 3-5. The radiant at RA +$18\degree$ and Dec +$56\degree$ is typical of the `classical' Andromedids of the early 1800's, whose radiant was actually in Cassiopeia. The orbital elements indicate that the material involved was released before 3D/Biela's breakup prior to 1846. The observed shower in 2011 had a slow geocentric speed (16 km s$^{-1}$) and was comprised of small particles: the mean measured mass from the radar is $\sim5 \times 10^{-7}$ kg corresponding to radii of 0.5 mm at a bulk density of 1000 kg/m$^3$. Numerical simulations of the parent comet indicate that the meteoroids of the 2011 return of the Andromedids shower were primarily ejected during 3D/Biela's 1649 perihelion passage. The orbital characteristics, radiant, timing as well as the absence of large particles in the streamlet are all consistent with simulations. Predictions are made regarding other appearances of the shower in the years 2000-2047 based on our numerical model. We note that the details of the 2011 return can, in principle, be used to better constrain the orbit of 3D/Biela prior to the comets first recorded return in 1772.Comment: submitted to the Astronomical Journal Sep 22 201

Positivity and nonstandard graded Betti numbers

A foundational principle in the study of modules over standard graded polynomial rings is that geometric positivity conditions imply vanishing of Betti numbers. The main goal of this paper is to determine the extent to which this principle extends to the nonstandard graded case. In this setting, the classical arguments break down, and the results become much more nuanced. We introduce a new notion of Castelnuovo-Mumford regularity and employ exterior algebra techniques to control the shapes of nonstandard graded minimal free resolutions. Our main result reveals a unique feature in the nonstandard graded case: the possible degrees of the syzygies of a graded module in this setting are controlled not only by its regularity, but also by its depth. As an application of our main result, we show that, given a simplicial projective toric variety and a module M over its coordinate ring, the multigraded Betti numbers of M are contained in a particular polytope when M satisfies an appropriate positivity condition.Comment: 12 page

Linear syzygies of curves in weighted projective space

We develop analogues of Green's $N_p$-conditions for subvarieties of weighted projective space, and we prove that such $N_p$-conditions are satisfied for high degree embeddings of curves in weighted projective space. A key technical result links positivity with low degree (virtual) syzygies in wide generality, including cases where normal generation fails.Comment: 29 page

Minimal free resolutions of differential modules

We propose a notion of minimal free resolutions for differential modules, and we prove existence and uniqueness results for such resolutions. We also take the first steps toward studying the structure of minimal free resolutions of differential modules. Our main result in this direction explains a sense in which the minimal free resolution of a differential module is a deformation of the minimal free resolution of its homology; this leads to structural results that mirror classical theorems about minimal free resolutions of modules.Comment: 20 page

Tate resolutions on toric varieties

We develop an analogue of Eisenbud-Floystad-Schreyer's Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier- Mukai transform, works quite generally and provides a new perspective on the relationship between Tate resolutions and Beilinson's resolution of the diagonal. We also develop a Beilinson-type resolution of the diagonal for toric varieties.Comment: 31 pages. To appear in the Journal of the European Mathematical Society (JEMS

A short proof of the Hanlon-Hicks-Lazarev Theorem

We give a short, new proof of a recent result of Hanlon-Hicks-Lazarev about toric varieties. As in their work, this leads to a proof of a conjecture of Berkesch-Erman-Smith on virtual resolutions and to a resolution of the diagonal in the simplicial case.Comment: 5 pages. The title has changed from "Results on virtual resolutions for toric varieties

Ancestral sequence alignment under optimal conditions

BACKGROUND: Multiple genome alignment is an important problem in bioinformatics. An important subproblem used by many multiple alignment approaches is that of aligning two multiple alignments. Many popular alignment algorithms for DNA use the sum-of-pairs heuristic, where the score of a multiple alignment is the sum of its induced pairwise alignment scores. However, the biological meaning of the sum-of-pairs of pairs heuristic is not obvious. Additionally, many algorithms based on the sum-of-pairs heuristic are complicated and slow, compared to pairwise alignment algorithms. An alternative approach to aligning alignments is to first infer ancestral sequences for each alignment, and then align the two ancestral sequences. In addition to being fast, this method has a clear biological basis that takes into account the evolution implied by an underlying phylogenetic tree. In this study we explore the accuracy of aligning alignments by ancestral sequence alignment. We examine the use of both maximum likelihood and parsimony to infer ancestral sequences. Additionally, we investigate the effect on accuracy of allowing ambiguity in our ancestral sequences. RESULTS: We use synthetic sequence data that we generate by simulating evolution on a phylogenetic tree. We use two different types of phylogenetic trees: trees with a period of rapid growth followed by a period of slow growth, and trees with a period of slow growth followed by a period of rapid growth. We examine the alignment accuracy of four ancestral sequence reconstruction and alignment methods: parsimony, maximum likelihood, ambiguous parsimony, and ambiguous maximum likelihood. Additionally, we compare against the alignment accuracy of two sum-of-pairs algorithms: ClustalW and the heuristic of Ma, Zhang, and Wang. CONCLUSION: We find that allowing ambiguity in ancestral sequences does not lead to better multiple alignments. Regardless of whether we use parsimony or maximum likelihood, the success of aligning ancestral sequences containing ambiguity is very sensitive to the choice of gap open cost. Surprisingly, we find that using maximum likelihood to infer ancestral sequences results in less accurate alignments than when using parsimony to infer ancestral sequences. Finally, we find that the sum-of-pairs methods produce better alignments than all of the ancestral alignment methods

Arabidopsis accelerated cell death 11, ACD11, is a ceramide-1-phosphate transfer protein and intermediary regulator of phytoceramide levels

The accelerated cell death 11 (acd11) mutant of Arabidopsis provides a genetic model for studying immune response activation and localized cellular suicide that halt pathogen spread during infection in plants. Here, we elucidate ACD11 structure and function and show that acd11 disruption dramatically alters the in vivo balance of sphingolipid mediators that regulate eukaryotic-programmed cell death. In acd11 mutants, normally low ceramide-1- phosphate (C1P) levels become elevated, but the relatively abundant cell death inducer phytoceramide rises acutely. ACD11 exhibits selective intermembrane transfer of C1P and phyto-C1P. Crystal structures establish C1P binding via a surface-localized, phosphate headgroup recognition center connected to an interior hydrophobic pocket that adaptively ensheaths lipid chains via a cleft-like gating mechanism. Point mutation mapping con- firms functional involvement of binding site residues. A p helix (p bulge) near the lipid binding cleft distinguishes apo-ACD11 from other GLTP folds. The global two-layer, a-helically dominated, ‘‘sandwich’’ topology displaying C1P-selective binding identifies ACD11 as the plant prototype of a GLTP fold subfamily