Spatial distribution of invasive species: an extent of occurrence approach

Ecological Risk Assessment faces the challenge of determining the impact of invasive species on biodiversity conservation. Although many statistical methods have emerged in recent years in order to model the evolution of the spatio-temporal distribution of invasive species, the notion of extent of occurrence, formally defined by the International Union for the Conservation of Nature, has not been properly handled. In this work, a novel and flexible reconstruction of the extent of occurrence from occurrence data will be established from nonparametric support estimation theory. Mathematically, given a random sample of points from some unknown distribution, we establish a new data-driven method for estimating its probability support S in general dimension. Under the mild geometric assumption that S is $$r-$$ r - convex, the smallest $$r-$$ r - convex set which contains the sample points is the natural estimator. A stochastic algorithm is proposed for determining an optimal estimate of r from the data under regularity conditions on the density function. The performance of this estimator is studied by reconstructing the extent of occurrence of an assemblage of invasive plant species in the Azores archipelago.

Weyl Law on Asymptotically Euclidean Manifolds

We study the asymptotic behaviour of the eigenvalue counting function for self-adjoint elliptic linear operators defined through classical weighted symbols of order (1, 1), on an asymptotically Euclidean manifold. We first prove a two-term Weyl formula, improving previously known remainder estimates. Subsequently, we show that under a geometric assumption on the Hamiltonian flow at infinity, there is a refined Weyl asymptotics with three terms. The proof of the theorem uses a careful analysis of the flow behaviour in the corner component of the boundary of the double compactification of the cotangent bundle. Finally, we illustrate the results by analysing the operator $$Q=(1+|x|^2)(1-\varDelta )$$ Q = ( 1 + | x | 2 ) ( 1 - Δ ) on $$\mathbb {R}^d$$ R d .

Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping

In this paper, we analyze the longtime behavior of the wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-diff-calculus, we obtain a Carleman estimate, and then establish an estimate on the corresponding resolvent operator. As a result, we show the logarithmic decay rate for energy of the system without any geometric assumption on the subdomain on which the damping is effective.

The impact of different geometric assumption of mitral annulus on the assessment of mitral regurgitation volume by Doppler method

Background: Mitral regurgitation volume (MRvol) by quantitative pulsed Doppler (QPD) method previously recommended suffers from geometric assumption error because of circular geometric assumption of mitral annulus (MA). Therefore, the aim of this study was to evaluate the impact of different geometric assumption of MA on the assessment of MRvol by two-dimensional transthoracic echocardiographic QPD method. Methods: This study included 88 patients with varying degrees of mitral regurgitation (MR). The MRvol was evaluated by QPD method using circular or ellipse geometric assumption of MA. MRvol derived from effective regurgitant orifice area by real time three-dimensional echocardiography (RT3DE) multiplied by MR velocity-time integral was used as reference method. Results: Assumption of a circular geometry of MA, QPD-MAA4C and QPD-MAPLAX overestimated the MRvol by a mean difference of 10.4 ml (P ＜ 0.0001) and 22.5 ml (P ＜ 0.0001) compared with RT3DE. Assumption of a ellipse geometry of MA, there was no significant difference of MRvol (mean difference = 1.7 ml, P = 0.0844) between the QPD-MAA4C+A2C and the RT3DE. Conclusions: Assuming that the MA was circular geometry previously recommended, the MRvol by QPD-MAA4C was overestimated compared with the reference method. However, assuming that the MA was ellipse geometry, the MRvol by the QPD-MAA4C+A2C has no significant difference with the reference method.

The impact of different geometric assumption of mitral annular on the assessment of mitral regurgitation volume by Doppler method

Background Mitral regurgitation volume (MRvol) by quantitative pulsed Doppler (QPD) method previously recommended suffers from geometric assumption error because of circular geometric assumption of mitral annulus (MA). Therefore, the aim of this study was to evaluate the impact of different geometric assumption of MA on the assessment of MRvol by two-dimensional transthoracic echocardiographic QPD method.Methods This study included 88 patients with varying degrees of mitral regurgitation (MR). The MRvol was evaluated by QPD method using circular or ellipse geometric assumption of MA. MRvol derived from effective regurgitant orifice area by real time three-dimensional echocardiography (RT3DE) multiplied by MR velocity-time integral was used as reference method.Results Assumption of a circular geometry of MA, QPD-MAA4C and QPD-MAPLAX overestimated the MRvol by a mean difference of 10.4 ml ( P < 0.0001) and 22.5 ml ( P < 0.0001) compared with RT3DE. Assumption of a ellipse geometry of MA, there was no significant difference of MRvol (mean difference = 1.7 ml, P = 0.0844) between the QPD-MAA4C+A2C and the RT3DE.Conclusions Assuming that the MA was circular geometry previously recommended, the MRvol by QPD-MAA4C was overestimated compared with the reference method. However, assuming that the MA was ellipse geometry, the MRvol by the QPD-MAA4C+A2C has no significant difference with the reference method.

An unusual cause of lacunar infarcts: Lambl’s excrescences on aortic valve shown in detail by 3D transesophageal echocardiography

Lambl’s excrescences (LE) are rare cardiac structures. They are associated with catastrophic thromboembolic and coronary events. Despite resulting in such important events, 2D echocardiographic imaging modalities may overlook LE owing to very thin cardiac structures. So, 3D echocardiographic imaging modalities may fully offer this cardiac mass and provide us to more accurately guess the complication rate related to LE due to the fact that 3D echocardiographic imaging techniques have higher spatial resolution and are not based on the geometric assumption. Indeed, another benefit of 3D echocardiographic imaging modalities in this population is that these imaging modalities clearly provide the relationship to adjacent structures of LE and its movement over a cardiac cycle in 3D space. In our case report, we aim to present the usefulness of 3D echocardiography as a modality to clearly offer all features of LE, furthermore to give valuable information about management in patients with thromboembolic events leading to LE.

Enumerating coloured partitions in 2 and 3 dimensions

We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a conjecture concerning a basic factorisation property of the generating function of coloured plane partitions that can be thought of as an orbifold analogue of a conjecture of Maulik et al., now a theorem, in three-dimensional Donaldson–Thomas theory. We study natural quantisations of the generating functions arising from geometry, discuss a quantised version of our conjecture, and prove a positivity result for the quantised coloured plane partition function under a geometric assumption.

Conical geodesic bicombings on subsets of normed vector spaces

We establish existence and uniqueness results for conical geodesic bicombings on subsets of normed vector spaces. Concerning existence, we give a first example of a convex geodesic bicombing that is not consistent. Furthermore, we show that under a mild geometric assumption on the norm a conical geodesic bicombing on an open subset of a normed vector space locally consists of linear geodesics. As an application, we obtain by the use of a Cartan–Hadamard type result that if a closed convex subset of a Banach space has non-empty interior, then it admits a unique consistent conical geodesic bicombing, namely the one given by the linear segments.

Extremal spectral gaps for periodic Schrödinger operators

The spectrum of a Schrödinger operator with periodic potential generally consists of bands and gaps. In this paper, for fixed m, we consider the problem of maximizing the gap-to-midgap ratio for the mth spectral gap over the class of potentials which have fixed periodicity and are pointwise bounded above and below. We prove that the potential maximizing the mth gap-to-midgap ratio exists. In one dimension, we prove that the optimal potential attains the pointwise bounds almost everywhere in the domain and is a step-function attaining the imposed minimum and maximum values on exactly m intervals. Optimal potentials are computed numerically using a rearrangement algorithm and are observed to be periodic. In two dimensions, we develop an efficient rearrangement method for this problem based on a semi-definite formulation and apply it to study properties of extremal potentials. We show that, provided a geometric assumption about the maximizer holds, a lattice of disks maximizes the first gap-to-midgap ratio in the infinite contrast limit. Using an explicit parametrization of two-dimensional Bravais lattices, we also consider how the optimal value varies over all equal-volume lattices.