The norm of the saturation of a binomial ideal, with applications to Markov bases

Let B be a finite set of pure binomials in the variables xi, and write IB for the ideal generated by these binomials. We define a new measure of the complexity of the saturation of the ideal IB with respect to the product of the xi, which we call the norm of B. We give a bound on the norm in terms of easily computed invariants of B. We discuss statistical applications, both practical and theoretical.Analysis and StochasticsNumber theory, Algebra and Geometr

Quasi-compactness of Néron models, and an application to torsion points

We prove that Néron models of Jacobians of generically-smooth nodal curves over bases of arbitrary dimension are quasi-compact (hence of finite type) whenever they exist. We give a simple application to the orders of torsion subgroups of Jacobians over number fields.Number theory, Algebra and Geometr

Fields of definition of rational curves of a given degree

Number theory, Algebra and Geometr

Infinitesimal structure of the pluricanonical double ramification locus

We prove that a formula for the 'pluricanonical' double ramification cycle proposed by Janda, Pandharipande, Pixton, Zvonkine, and the second-named author is in fact the class of a cycle constructed geometrically by the first-named author. Our proof proceeds by a detailed explicit analysis of the deformation theory of the double ramification cycle, both to first and to higher order.NWOVI.Vidi.193.006Number theory, Algebra and Geometr

Asymptotics of the Néron height pairing

Number theory, Algebra and Geometr

Improving estimations of life history parameters of small animals in mesocosm experiments: a case study on mosquitoes

Mesocosm experiments enable researchers to study animal dynamics, but determining accurate estimates of survival and development rates of different life stages can be difficult, especially as the subjects may be hard to sample and mortality rates can be high. We propose a new methodology for estimating such parameters.We used an experimental set-up with 48 aquatic mesocosms, each with 20 first instar mosquito larvae and under 1 of 12 treatments with varying temperatures and nutrient concentrations. We took daily subsamples of the aquatic life stages as well as counting the emerging adults. We developed a method to estimate the survival and development probabilities at each life stage, based on optimising a matrix population model. We used two different approaches, one assuming the difference between predictions and observations was normally distributed, and the other using a combination of a normal and a multinomial distribution. For each approach, the resulting optimisation problem had around 100 parameters, making conventional gradient descent ineffective with our limited number of data points. We solved this by computing the formal derivatives of our matrix model.Both approaches proved effective in predicting mosquito populations over time, also when compared against a separate validation dataset, and the two approaches produced similar results. They also both predicted similar trends in the survival and development probabilities for each life stage, although there were some differences in the actual values. The approach which only used the normal distribution was considerably more computationally efficient than the mixed distribution approach.This is an effective approach for determining the survival and development rates of small animals in mesocosm experiments. We have not found any other reliable methodology for estimating these parameters, especially not from incomplete data or when there are many different experimental treatments. This methodology enables researchers to gain a much more detailed understanding of the life cycles of small animals, potentially leading to advances in a wide range of areas, for example in mosquito-borne disease risk or in considering the effects of biodiversity loss or climate change on different species.NWONWA.1160.1S.210Number theory, Algebra and Geometr

Chern-Weil and Hilbert-Samuel formulae for singular Hermitian line bundles

We show a Chern-Weil type statement and a Hilbert-Samuel formula for a large class of singular plurisubharmonic metrics on a line bundle over a smooth projective complex variety. For this we use the theory of b-divisors and the so-called multiplier ideal volume function. We apply our results to the line bundle of Siegel-Jacobi forms over the universal abelian variety endowed with its canonical invariant metric. This generalizes the results of [J. I. Burgos Gil et al., Lond. Math. Soc. Lect. Note Ser. 427, 45--77 (2016; Zbl 1378.14027)] to higher degrees.Number theory, Algebra and Geometr

Genome-enabled insights into the biology of thrips as crop pests

Background The western flower thrips,Frankliniella occidentalis(Pergande), is a globally invasive pest and plant virus vector on a wide array of food, fiber, and ornamental crops. The underlying genetic mechanisms of the processes governing thrips pest and vector biology, feeding behaviors, ecology, and insecticide resistance are largely unknown. To address this gap, we present theF. occidentalisdraft genome assembly and official gene set.Results We report on the first genome sequence for any member of the insect order Thysanoptera. Benchmarking Universal Single-Copy Ortholog (BUSCO) assessments of the genome assembly (size = 415.8 Mb, scaffold N50 = 948.9 kb) revealed a relatively complete and well-annotated assembly in comparison to other insect genomes. The genome is unusually GC-rich (50%) compared to other insect genomes to date. The official gene set (OGS v1.0) contains 16,859 genes, of which similar to 10% were manually verified and corrected by our consortium. We focused on manual annotation, phylogenetic, and expression evidence analyses for gene sets centered on primary themes in the life histories and activities of plant-colonizing insects. Highlights include the following: (1) divergent clades and large expansions in genes associated with environmental sensing (chemosensory receptors) and detoxification (CYP4, CYP6, and CCE enzymes) of substances encountered in agricultural environments; (2) a comprehensive set of salivary gland genes supported by enriched expression; (3) apparent absence of members of the IMD innate immune defense pathway; and (4) developmental- and sex-specific expression analyses of genes associated with progression from larvae to adulthood through neometaboly, a distinct form of maturation differing from either incomplete or complete metamorphosis in the Insecta.Conclusions Analysis of theF. occidentalisgenome offers insights into the polyphagous behavior of this insect pest that finds, colonizes, and survives on a widely diverse array of plants. The genomic resources presented here enable a more complete analysis of insect evolution and biology, providing a missing taxon for contemporary insect genomics-based analyses. Our study also offers a genomic benchmark for molecular and evolutionary investigations of other Thysanoptera species.Animal science

Néron models and the height jump divisor

Number theory, Algebra and Geometr

Positivity of the height jump divisor

We study the degeneration of semipositive smooth hermitian line bundles on open complex manifolds, assuming that the metric extends well away from a codimension two analytic subset of the boundary. Using terminology introduced by R. Hain, we show that under these assumptions the so-called height jump divisors are always effective. This result is of particular interest in the context of biextension line bundles on Griffiths intermediate jacobian fibrations of polarized variations of Hodge structure of weight −1⁠, pulled back along normal function sections. In the case of the normal function on M_g associated to the Ceresa cycle, our result proves a conjecture of Hain. As an application of our result we obtain that the Moriwaki divisor on M_g  has non-negative degree on all complete curves in M_g not entirely contained in the locus of irreducible singular curves.Number theory, Algebra and Geometr