Minimax Estimation of Nonregular Parameters and Discontinuity in Minimax Risk

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the nondifferentiable transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is two fold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk

When virulence originates from non-agricultural hosts: New insights into plant breeding

Monogenic plant resistance breakdown is a model for testing evolution in action in pathogens. As a rule, plant pathologists argue that virulence – the allele that allows pathogens to overcome resistance – is due to a new mutation at the avirulence locus within the native/endemic population that infects susceptible crops. In this article, we develop an alternative and neglected scenario where a given virulence pre-exists in a non-agricultural host and might be accidentally released or introduced on the matching resistant cultivar in the field. The main difference between the two scenarios is the divergence time expected between the avirulent and the virulent populations. As a consequence, population genetic approaches such as genome scans and Approximate Bayesian Computation methods allow explicit testing of the two scenarios by timing the divergence. This review then explores the fundamental implications of this alternative scenario for plant breeding, including the invasion of virulence or the evolution of more aggressive hybrids, and proposes concrete solutions to achieve a sustainable resistance

Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

Complete intersections: Moduli, Torelli, and good reduction

We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.Comment: 37 pages. Typo's fixed. Expanded Section 2.

Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks

This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this problem. We use this formula and the mark specific cumulative hazard function of Huang and Louis (1998) to obtain the almost sure limit of the MLE. This result leads to necessary and sufficient conditions for consistency of the MLE which imply that the MLE is inconsistent in general. We show that the inconsistency can be repaired by discretizing the marks. Our theoretical results are supported by simulations.Comment: 27 pages, 4 figure

Draft Genome Sequence of the Human-Pathogenic Fungus Scedosporium boydii

The opportunistic fungal pathogen Scedosporium boydii is the most common Scedosporium species in French patients with cystic fibrosis. Here we present the first genome report for S. boydii, providing a resource which may enable the elucidation of the pathogenic mechanisms in this species

Magic traits drive the emergence of pathogens

An important branch of evolutionary biology strives to understand how divergent selection for an ecologically important trait can foster the emergence of new species specialized on different niches. Such ecological speciation is usually difficult to achieve because recombination between different subsets of a population that are adapting to different environments counteracts selection for locally adapted gene combinations. Traits pleiotropically controlling adaptation to different environments and reproductive isolation are therefore the most favourable for ecological speciation, and are thus called “magic traits”. We used genetic markers and cross-inoculations to show that pathogenicity-related loci are responsible for both host adaptation and reproductive isolation in emerging populations of Venturia inaequalis, the fungus causing apple scab disease. Because the fungus mates within its host and because the pathogenicity-related loci prevent infection of the non-host trees, host adaptation pleiotropically maintains genetic differentiation and adaptive allelic combinations between sympatric populations specific to different apple varieties. Such “magic traits” are likely frequent in fungal pathogens, and likely drive the emergence of new diseases.