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Mistletoes are considered keystone species on woodlands and savannas worldwide, providing a food resource for a diversified fauna, as well as a nutrient-enriched litter. Infections can be large (∼1–3 m) and, in some parts of the Amazonian savannas, parasitize up to 70% of hosts locally. Despite these facts, biomass of mistletoes is rarely investigated. Here we constructed allometric models to predict the biomass stock of the shrubby mistletoe Psittacanthus plagiophyllus in an Amazonian savanna. In addition, we determined whether host size could be used as a proxy for mistletoe biomass. Finally, we compared the biomass of mistletoes with that of trees, to evaluate their relative importance. We have shown that: (1) biomass of leaves (46.1% ± 13.5%) are as important as of stems (47.8% ± 13.5%), and relative contribution of stems increases as plant grows; (2) the model including width, breadth and vertical depth was the best (SE = 0.39, R2 = 0.9) for predicting individual mistletoe biomass; (3) mistletoe load and biomass per host had a positive, but weak (R2 = 0.11 and 0.09, respectively), relationship with host size, and thus such host information is a poor predictor of mistletoe biomass; and (4) in comparison with trees, mistletoes constituted less than 0.15% (0.5–22 kg ha−1) of the total above-ground biomass, suggesting that this life-form is irrelevant to the local biomass stock despite its unequivocal biological importance.
Consanguineous marriages potentially play an important role in the transmission of β-thalassaemia in many communities. This study aimed to determine the rate and socio-demographic associations of consanguineous marriages and to assess the influence on the prevalence of β-thalassaemia in Sri Lanka. Three marriage registrars from each district of Sri Lanka were randomly selected to prospectively collect data on all couples who registered their marriage during a 6-month period starting 1st July 2009. Separately, the parents of patients with β-thalassaemia were interviewed to identify consanguinity. A total of 5255 marriages were recorded from 22 districts. The average age at marriage was 27.3 (±6.1) years for males and 24.1 (±5.7) years for females. A majority (71%) of marriages were ‘love’ marriages, except in the Moor community where 84% were ‘arranged’ marriages. Overall, the national consanguinity rate was 7.4%. It was significantly higher among ethnic Tamils (22.4%) compared with Sinhalese (3.8%) and Moors (3.2%) (p < 0.001). Consanguinity rates were also higher in ‘arranged’ as opposed to ‘love’ marriages (11.7% vs 5.6%, p < 0.001). In patients with β-thalassaemia, the overall consanguinity rate was 14.5%; it was highest among Tamils (44%) and lowest among Sinhalese (12%). Parental consanguinity among patients with β-thalassaemia was double the national average. Although consanguinity is not the major factor in the transmission of the disease in the country, emphasis should be given to this significant practice when conducting β-thalassaemia prevention and awareness campaigns, especially in high-prevalence communities.
Despite recent advancements on cloud-enabled and human-in-the-loop cyber-physical systems, there is still a lack of understanding of how infrastructure-related quality of service (QoS) issues affect user-perceived quality of experience (QoE). This work presents a pilot experiment over a cloud-enabled mobility assistive device providing a guidance service and investigates the relationship between QoS and QoE in such a system. In our pilot experiment, we employed the CloudWalker, a system linking smart walkers and cloud platforms, to physically interact with users. Different QoS conditions were emulated to represent an architecture in which control algorithms are performed remotely. Results point out that users report satisfactory interaction with the system even under unfavorable QoS conditions. We also found statistically significant data linking QoE degradation to poor QoS conditions. We finalize discussing the interplay between QoS requirements, the human-in-the-loop effect, and the perceived QoE in healthcare applications.
In 2017, dicamba-resistant (DR) soybean was commercially available to farmers in the United States. In August and September of 2017, a survey of 312 farmers from 60 Nebraska soybean-producing counties was conducted during extension field days or online. The objective of this survey was to understand farmers’ adoption and perceptions regarding DR soybean technology in Nebraska. The survey contained 16 questions and was divided in three parts: (1) demographics, (2) dicamba application in DR soybean, and (3) dicamba off-target injury to sensitive soybean cultivars. According to the results, 20% of soybean hectares represented by the survey were planted to DR soybean in 2017, and this number would probably double in 2018. Sixty-five percent of survey respondents own a sprayer and apply their own herbicide programs. More than 90% of respondents who adopted DR soybean technology reported significant improvement in weed control. Nearly 60% of respondents used dicamba alone or glyphosate plus dicamba for POST weed control in DR soybean; the remaining 40% added an additional herbicide with an alternative site of action (SOA) to the POST application. All survey respondents used one of the approved dicamba formulations for application in DR soybean. Survey results indicated that late POST dicamba applications (after late June) were more likely to result in injury to non-DR soybean compared to early POST applications (e.g., May and early June) in 2017. According to respondents, off-target dicamba movement resulted both from applications in DR soybean and dicamba-based herbicides applied in corn. Although 51% of respondents noted dicamba injury on non-DR soybean, 7% of those who noted injury filed an official complaint with the Nebraska Department of Agriculture. Although DR soybean technology allowed farmers to achieve better weed control during 2017 than previous growing seasons, it is apparent that off-target movement and resistance management must be addressed to maintain the viability and effectiveness of the technology in the future.
Borderline personality disorder (BPD) is characterized by a heterogeneous clinical phenotype that emerges from interactions among genetic, biological, neurodevelopmental, and psychosocial factors. In the present family study, we evaluated the familial aggregation of key clinical, personality, and neurodevelopmental phenotypes in probands with BPD (n = 103), first-degree biological relatives (n = 74; 43% without a history of psychiatric disorder), and non-psychiatric controls (n = 99).
Methods
Participants were assessed on DSM-IV psychiatric diagnoses, symptom dimensions of emotion dysregulation and impulsivity, ‘big five’ personality traits, and neurodevelopmental characteristics, as part of a larger family study on neurocognitive, biological, and genetic markers in BPD.
Results
The most common psychiatric diagnoses in probands and relatives were major depression, substance use disorders, post-traumatic stress disorder, anxiety disorders, and avoidant personality disorder. There was evidence of familial aggregation for specific dimensions of impulsivity and emotion dysregulation, and the big five traits neuroticism and conscientiousness. Both probands and relatives reported an elevated neurodevelopmental history of attentional and behavioral difficulties.
Conclusions
These results support the validity of negative affectivity- and impulse-spectrum phenotypes associated with BPD and its familial risk. Further research is needed to investigate the aggregation of neurocognitive, neural and genetic factors in families with BPD and their associations with core phenotypes underlying the disorder.
This contribution covers the topic of my talk at the 2016-17 Warwick-EPSRC Symposium: 'PDEs and their applications'. As such it contains some already classical material and some new observations. The main purpose is to compare several avatars of the Kato criterion for the convergence of a Navier-Stokes solution, to a regular solution of the Euler equations, with numerical or physical issues like the presence (or absence) of anomalous energy dissipation, the Kolmogorov 1/3 law or the Onsager C^{0,1/3} conjecture. Comparison with results obtained after September 2016 and an extended list of references have also been added.
We investigate existence, uniqueness and regularity of time-periodic solutions to the Navier-Stokes equations governing the flow of a viscous liquid past a three-dimensional body moving with a time-periodic translational velocity. The net motion of the body over a full time-period is assumed to be non-zero. In this case, the appropriate linearization is the time-periodic Oseen system in a three-dimensional exterior domain. A priori L^q estimates are established for this linearization. Based on these "maximal regularity" estimates, existence and uniqueness of smooth solutions to the fully nonlinear Navier-Stokes problem is obtained by the contraction mapping principle.
We give a survey of recent results on weak-strong uniqueness for compressible and incompressible Euler and Navier-Stokes equations, and also make some new observations. The importance of the weak-strong uniqueness principle stems, on the one hand, from the instances of nonuniqueness for the Euler equations exhibited in the past years; and on the other hand from the question of convergence of singular limits, for which weak-strong uniqueness represents an elegant tool.
By their use of mild solutions, Fujita-Kato and later on Giga-Miyakawa opened the way to solving the initial-boundary value problem for the Navier-Stokes equations with the help of the contracting mapping principle in suitable Banach spaces, on any smoothly bounded domain
$$\Omega \subset \R^n, n \ge 2$$
, globally in time in case of sufficiently small data. We will consider a variant of these classical approximation schemes: by iterative solution of linear singular Volterra integral equations, on any compact time interval J, again we find the existence of a unique mild Navier-Stokes solution under smallness conditions, but moreover we get the stability of each (possibly large) mild solution, inside a scale of Banach spaces which are imbedded in some
$$C^0 (J, L^r (\Omega))$$
,
$$1 < r < \infty$$
.
We address the decay and the quantitative uniqueness properties for solutions of the elliptic equation with a gradient term,
$$\Delta u=W\cdot \nabla u$$
. We prove that there exists a solution in a complement of the unit ball which satisfies
$$|u(x)|\le C\exp (-C^{-1}|x|^2)$$
where
$$W$$
is a certain function bounded by a constant. Next, we revisit the quantitative uniqueness for the equation
$$-\Delta u= W \cdot \nabla u$$
and provide an example of a solution vanishing at a point with the rate
$${\rm const}\Vert W\Vert_{L^\infty}^2$$
. We also review decay and vanishing results for the equation
$$\Delta u= V u$$
.
This paper reviews and summarizes two recent pieces of work on the Rayleigh-Taylor instability. The first concerns the 3D Cahn-Hilliard-Navier-Stokes (CHNS) equations and the BKM-type theorem proved by Gibbon, Pal, Gupta, & Pandit (2016). The second and more substantial topic concerns the variable density model, which is a buoyancy-driven turbulent flow considered by Cook & Dimotakis (2001) and Livescu & Ristorcelli (2007, 2008). In this model $\rho^* (x, t)$ is the composition density of a mixture of two incompressible miscible fluids with fluid densities
$$\rho^*_2 > \rho^*_1$$
and
$$\rho^*_0$$
is a reference normalisation density. Following the work of a previous paper (Rao, Caulfield, & Gibbon, 2017), which used the variable
$$\theta = \ln \rho^*/\rho^*_0$$
, data from the publicly available Johns Hopkins Turbulence Database suggests that the L2-spatial average of the density gradient
$$\nabla \theta$$
can reach extremely large values at intermediate times, even in flows with low Atwood number At =
$$(\rho^*_2 - \rho^*_1)/(\rho^*_2 + \rho^*_1) = 0.05$$
. This implies that very strong mixing of the density field at small scales can potentially arise in buoyancy-driven turbulence thus raising the possibility that the density gradient
$$\nabla \theta$$
might blow up in a finite time.
The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
In this contribution we focus on a few results regarding the study of the three-dimensional Navier-Stokes equations with the use of vector potentials. These dependent variables are critical in the sense that they are scale invariant. By surveying recent results utilising criticality of various norms, we emphasise the advantages of working with scale-invariant variables. The Navier-Stokes equations, which are invariant under static scaling transforms, are not invariant under dynamic scaling transforms. Using the vector potential, we introduce scale invariance in a weaker form, that is, invariance under dynamic scaling modulo a martingale (Maruyama-Girsanov density) when the equations are cast into Wiener path-integrals. We discuss the implications of this quasi-invariance for the basic issues of the Navier-Stokes equations.
Regularity criteria for solutions of the three-dimensional Navier-Stokes equations are derived in this paper. Let
$$\Omega(t, q) := \left\{x:|u(x,t)| > C(t,q)\normVT{u}_{L^{3q-6}(\mathbb{R}^3)}\right\} \cap\left\{x:\widehat{u}\cdot\nabla|u|\neq0\right\}, \tilde\Omega(t,q) := \left\{x:|u(x,t)| \le C(t,q)\normVT{u}_{L^{3q-6}(\mathbb{R}^3)}\right\} \cap\left\{x:\widehat{u}\cdot\nabla|u|\neq0\right\},$$
where
$$q\ge3$$
and
$$C(t,q) := \left(\frac{\normVT{u}_{L^4(\mathbb{R}^3)}^2\normVT{|u|^{(q-2)/2}\,\nabla|u|}_{L^2(\mathbb{R}^3)}}{cq\normVT{u_0}_{L^2(\mathbb{R}^3)} \normVT{p+\mathcal{P}}_{L^2(\tilde\Omega)}\normVT{|u|^{(q-2)/2}\, \widehat{u}\cdot\nabla|u|}_{L^2(\tilde\Omega)}}\right)^{2/(q-2)}.$$
Here
$$u_0=u(x,0)$$
,
$$\mathcal{P}(x,|u|,t)$$
is a pressure moderator of relatively broad form,
$$\widehat{u}\cdot\nabla|u|$$
is the gradient of
$$|u|$$
along streamlines, and
$$c=(2/\pi)^{2/3}/\sqrt{3}$$
is the constant in the inequality
$$\normVT{f}_{L^6(\mathbb{R}^3)}\le c\normVT{\nabla f}_{L^2(\mathbb{R}^3)}$$
.
The aim of this paper is to prove energy conservation for the incompressible Euler equations in a domain with boundary. We work in the domain
$$\TT^2\times\R_+$$
, where the boundary is both flat and has finite measure; in this geometry we do not require any estimates on the pressure, unlike the proof in general bounded domains due to Bardos & Titi (2018). However, first we study the equations on domains without boundary (the whole space
$$\R^3$$
, the torus
$$\mathbb{T}^3$$
, and the hybrid space
$$\TT^2\times\R$$
). We make use of some arguments due to Duchon & Robert (2000) to prove energy conservation under the assumption that
$$u\in L^3(0,T;L^3(\R^3))$$
and
$${|y|\to 0}\frac{1}{|y|}\int^T_0\int_{\R^3} |u(x+y)-u(x)|^3\,\d x\,\d t=0$$
or
$$\int_0^T\int_{\R^3}\int_{\R^3}\frac{|u(x)-u(y)|^3}{|x-y|^{4+\delta}}\,\d x\,\d y\,\d t<\infty,\qquad\delta>0$$
, the second of which is equivalent to
$$u\in L^3(0,T;W^{\alpha,3}(\R^3))$$
,
$$\alpha>1/3$$
.
This article offers a modern perspective that exposes the many contributions of Leray in his celebrated work on the three-dimensional incompressible Navier-Stokes equations from 1934. Although the importance of his work is widely acknowledged, the precise contents of his paper are perhaps less well known. The purpose of this article is to fill this gap. We follow Leray's results in detail: we prove local existence of strong solutions starting from divergence-free initial data that is either smooth or belongs to
$$H^1$$
or
$$L^2 \cap L^p$$
(with
$$p \in (3,\infty]$$
), as well as lower bounds on the norms
$$\| \nabla u (t) \|_2$$
and
$$\| u(t) \|_p$$
(
$$p\in(3,\infty]$$
) as t approaches a putative blow-up time. We show global existence of a weak solution and weak-strong uniqueness. We present Leray's characterisation of the set of singular times for the weak solution, from which we deduce that its upper box-counting dimension is at most 1/2. Throughout the text we provide additional details and clarifications for the modern reader and we expand on all ideas left implicit in the original work, some of which we have not found in the literature. We use some modern mathematical tools to bypass some technical details in Leray's work, and thus expose the elegance of his approach.