Estimating anisotropic pollen dispersal: a case study in Quercus lobata

The pollen dispersal distribution is an important element of the neighbourhood size of plant populations. Most methods aimed at estimating the dispersal curve assume that pollen dispersal is isotropic, but evidence indicates that this assumption does not hold for many plant species, particularly wind-pollinated species subject to prevailing winds during the pollination season. We propose here a method of detecting anisotropy of pollen dispersal and of gauging its intensity, based on the estimation of the differentiation of maternal pollen clouds (TWOGENER extraction), assuming that pollen dispersal is bivariate and normally distributed. We applied the new method to a case study in Quercus lobata, detecting only a modest level of anisotropy in pollen dispersal in a direction roughly similar to the prevailing wind direction. Finally, we conducted a simulation to explore the conditions under which anisotropy can be detected with this method, and we show that while anisotropy is detectable, in principle, it requires a large volume of data.     

Effect of sampling strategy on estimation of fine-scale spatial genetic structure in Androsace tapete (Primulaceae), an alpine plant endemic to Qinghai-Tibetan Plateau

The fine-scale spatial genetic structure (SGS) of alpine plants is receiving increasing attention, from which seed and pollen dispersal can be inferred. However, estimation of SGS may depend strongly on the sampling strategy,including the sample size and spatial sampling scheme. Here, we examined the effects of sample size and three spatial schemes, simple-random, line-transect, and random-cluster sampling, on the estimation of SGS in Androsace tapete, an alpine cushion plant endemic to Qinghai-Tibetan Plateau. Using both real data and simulated data of dominant molecular markers, we show that: (i) SGS is highly sensitive to sample strategy especially when the sample size is small (e.g., below 100); (ii) the commonly used SGS parameter (the intercept of the autocorrelogram) is more susceptible to sample error than a newly developed Sp statistic; and (iii) the random-cluster scheme is susceptible to obvious bias in parameter estimation even when the sample size is relatively large (e.g., above 200). Overall,the line-transect scheme is recommendable, in that it performs slightly better than the simple-random scheme in parameter estimation and is more efficient to encompass broad spatial scales. The consistency between simulated data and real data implies that these findings might hold true in other alpine plants and more species should be examined in future work.     

An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valves

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee–Sacks model is well-suited to reproduce the anisotropic stress–strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee–Sacks model that matches biaxial stress–strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee–Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.     

Mechanical characterization of anisotropic planar biological soft tissues using large indentation: a computational feasibility study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.     

Effect of sampling strategy on estimation of fine‐scale spatial genetic structure in Androsace tapete (Primulaceae), an alpine plant endemic to Qinghai‐Tibetan Plateau

Abstract The fine‐scale spatial genetic structure (SGS) of alpine plants is receiving increasing attention, from which seed and pollen dispersal can be inferred. However, estimation of SGS may depend strongly on the sampling strategy, including the sample size and spatial sampling scheme. Here, we examined the effects of sample size and three spatial schemes, simple‐random, line‐transect, and random‐cluster sampling, on the estimation of SGS in Androsace tapete, an alpine cushion plant endemic to Qinghai‐Tibetan Plateau. Using both real data and simulated data of dominant molecular markers, we show that: (i) SGS is highly sensitive to sample strategy especially when the sample size is small (e.g., below 100); (ii) the commonly used SGS parameter (the intercept of the autocorrelogram) is more susceptible to sample error than a newly developed Sp statistic; and (iii) the random‐cluster scheme is susceptible to obvious bias in parameter estimation even when the sample size is relatively large (e.g., above 200). Overall, the line‐transect scheme is recommendable, in that it performs slightly better than the simple‐random scheme in parameter estimation and is more efficient to encompass broad spatial scales. The consistency between simulated data and real data implies that these findings might hold true in other alpine plants and more species should be examined in future work.     

A resistor interpretation of general anisotropic cardiac tissue

This paper describes a spatial discretization scheme for partial differential equation systems that contain anisotropic diffusion. The discretization method uses unstructured finite volumes, or the boxes, that are formed as a secondary geometric structure from an underlying triangular mesh. We show how the discretization can be interpreted as a resistive circuit network, where each resistor is assigned at each edge of the triangular element. The resistor is computed as an anisotropy dependent geometric quantity of the local mesh structure. Finally, we show that under certain conditions, the discretization gives rise to negative resistors that can produce non-physical hyperpolarizations near depolarizing stimuli. We discuss how the proper choice of triangulation (anisotropic Delaunay triangulation) can ensure monotonicity (i.e. all resistors are positive).     

Plant dispersal in the sub-Antarctic inferred from anisotropic genetic structure

Climatic conditions and landscape features often strongly affect species' local distribution patterns, dispersal, reproduction and survival and may therefore have considerable impacts on species' fine-scale spatial genetic structure (SGS). In this study, we demonstrate the efficacy of combining fine-scale SGS analyses with isotropic and anisotropic spatial autocorrelation techniques to infer the impact of wind patterns on plant dispersal processes. We genotyped 1304 Azorella selago (Apiaceae) specimens, a wind-pollinated and wind-dispersed plant, from four populations distributed across sub-Antarctic Marion Island. SGS was variable with Sp values ranging from 0.001 to 0.014, suggesting notable variability in dispersal distance and wind velocities between sites. Nonetheless, the data supported previous hypotheses of a strong NW-SE gradient in wind strength across the island. Anisotropic autocorrelation analyses further suggested that dispersal is strongly directional, but varying between sites depending on the local prevailing winds. Despite the high frequency of gale-force winds on Marion Island, gene dispersal distance estimates (σ) were surprisingly low (<10 m), most probably because of a low pollen dispersal efficiency. An SGS approach in association with isotropic and anisotropic analyses provides a powerful means to assess the relative influence of abiotic factors on dispersal and allow inferences that would not be possible without this combined approach.     

Cox Regression in Nested Case–Control Studies with Auxiliary Covariates

Summary Nested case–control (NCC) design is a popular sampling method in large epidemiological studies for its cost effectiveness to investigate the temporal relationship of diseases with environmental exposures or biological precursors. Thomas' maximum partial likelihood estimator is commonly used to estimate the regression parameters in Cox's model for NCC data. In this article, we consider a situation in which failure/censoring information and some crude covariates are available for the entire cohort in addition to NCC data and propose an improved estimator that is asymptotically more efficient than Thomas' estimator. We adopt a projection approach that, heretofore, has only been employed in situations of random validation sampling and show that it can be well adapted to NCC designs where the sampling scheme is a dynamic process and is not independent for controls. Under certain conditions, consistency and asymptotic normality of the proposed estimator are established and a consistent variance estimator is also developed. Furthermore, a simplified approximate estimator is proposed when the disease is rare. Extensive simulations are conducted to evaluate the finite sample performance of our proposed estimators and to compare the efficiency with Thomas' estimator and other competing estimators. Moreover, sensitivity analyses are conducted to demonstrate the behavior of the proposed estimator when model assumptions are violated, and we find that the biases are reasonably small in realistic situations. We further demonstrate the proposed method with data from studies on Wilms' tumor.     

An anisotropic internal-external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies

In this work, a complete internal-external bone-remodelling scheme is presented and implemented into a finite element code. This model uses a combination of an anisotropic internal remodelling model based on a new Continuum "Damage-Repair" theory and an external adaptation approach that follows the idea, early introduced by Mattheck et al., to simulate the growth behaviour of biological systems, known as CAO method. This combined scheme qualitatively resembles most of the main features of the bone adaptive behaviour, like the bone mass distribution (heterogeneity and porosity), the directional internal structure (anisotropy), the alignment of the microstructure with the constitutive principal directions and these with those of the stress tensor when permanently loaded by a unique stress state (Wolff's law). It is also thermodynamically consistent, fulfilling a principle of minimum mechanical dissipation. Finally, the comparison between the predicted results and the ones obtained by different experimental tests allows us to conclude that this model is able of reproducing qualitatively the global behaviour of bone tissue when subjected to external mechanical loads.     

Stiffness characterization of anisotropic trabecular meshwork

Elevation of intraocular pressure has been correlated to changes in stiffness of trabecular meshwork (TM) in glaucomatous eyes although mechanical properties of the TM remain to be quantitatively determined. Data in the literature suggest that the TM cannot be considered mechanically as a uniform layer of isotropic elastic material, because the value of its Young’s modulus depends on the methods of measurements and can vary up to five orders of magnitude. To this end, we proposed a new theoretical framework for mechanical analysis of the TM, in which the inner wall of Schlemm’s canal and the juxtacanalicular tissue in the TM were treated as a uniform layer of isotropic elastic material, and the rest of the TM, i.e., the uveal and corneoscleral meshworks, were modeled as a uniform layer of transversely isotropic material. Using the model, we demonstrated that the large discrepancy in the apparent Young’s modulus reported in the literature could be caused by the anisotropy of the meshwork that was significantly stiffer in the longitudinal direction than in the transverse direction. The theoretical framework could be used to integrate existing data of the stiffness, investigate anisotropic behaviors of the tissues, and develop new methods to measure mechanical properties of the TM.     

Processing of ND NMR spectra sampled in polar coordinates: a simple Fourier transform instead of a reconstruction

In order to reduce the acquisition time of multidimensional NMR spectra of biological macromolecules, projected spectra (or in other words, spectra sampled in polar coordinates) can be used. Their standard processing involves a regular FFT of the projections followed by a reconstruction, i.e. a non-linear process. In this communication, we show that a 2D discrete Fourier transform can be implemented in polar coordinates to obtain directly a frequency domain spectrum. Aliasing due to local violations of the Nyquist sampling theorem gives rise to base line ridges but the peak line-shapes are not distorted as in most reconstruction methods. The sampling scheme is not linear and the data points in the time domain should thus be weighted accordingly in the polar FT; however, artifacts can be reduced by additional data weighting of the undersampled regions. This processing does not require any parameter tuning and is straightforward to use. The algorithm written for polar sampling can be adapted to any sampling scheme and will permit to investigate better compromises in terms of experimental time and lack of artifacts.     

Optimizing the trade‐off between spatial and genetic sampling efforts in patchy populations: towards a better assessment of functional connectivity using an individual‐based sampling scheme

Genetic data are increasingly used in landscape ecology for the indirect assessment of functional connectivity, that is, the permeability of landscape to movements of organisms. Among available tools, matrix correlation analyses (e.g. Mantel tests or mixed models) are commonly used to test for the relationship between pairwise genetic distances and movement costs incurred by dispersing individuals. When organisms are spatially clustered, a population‐based sampling scheme (PSS) is usually performed, so that a large number of genotypes can be used to compute pairwise genetic distances on the basis of allelic frequencies. Because of financial constraints, this kind of sampling scheme implies a drastic reduction in the number of sampled aggregates, thereby reducing sampling coverage at the landscape level. We used matrix correlation analyses on simulated and empirical genetic data sets to investigate the efficiency of an individual‐based sampling scheme (ISS) in detecting isolation‐by‐distance and isolation‐by‐barrier patterns. Provided that pseudo‐replication issues are taken into account (e.g. through restricted permutations in Mantel tests), we showed that the use of interindividual measures of genotypic dissimilarity may efficiently replace interpopulation measures of genetic differentiation: the sampling of only three or four individuals per aggregate may be sufficient to efficiently detect specific genetic patterns in most situations. The ISS proved to be a promising methodological alternative to the more conventional PSS, offering much flexibility in the spatial design of sampling schemes and ensuring an optimal representativeness of landscape heterogeneity in data, with few aggregates left unsampled. Each strategy offering specific advantages, a combined use of both sampling schemes is discussed.     

Evolving anisotropy and degree of elastolytic insult in abdominal aortic aneurysms: Potential clinical relevance?

Accurately estimating patient-specific rupture risk remains a primary challenge in timing interventions for abdominal aortic aneurysms (AAAs). By re-analyzing published biaxial mechanical testing data from surgically repaired human AAAs, material anisotropy emerged as a potentially important determinant of patient-specific lesion progression. That is, based on a new classification scheme, we discovered that anisotropic aneurysmal specimens correlated with increased patient age at surgery when compared with more isotropic specimens (79.7 vs. 70.9 years, p<0.002), despite no significant difference in maximum diameter. Furthermore, using an idealized axisymmetric, finite-element growth and remodeling model of AAA progression, we found that both the initial axial extent of elastin loss and ongoing damage to elastin in the shoulder region of the AAA directly affected the degree of anisotropy as the lesion evolved, with more extensive insults increasing the anisotropy. This effect appeared to be mediated by alterations in axial loading and subsequent differences in orientation of deposited collagen fibers. While the observed increased age before surgical intervention may suggest a potential benefit of anisotropic remodeling, future biaxial tests coupled with pre-surgical data on expansion rates and detailed theoretical analyses of the biostability of a lesion as a function of anisotropy will be required to verify its clinical relevance to patient-specific rupture risk.     

The terminology and use of species–area relationships: a response to Dengler (2009)

Dengler ( Journal of Biogeography , 2009, 36 , 728–744) addresses issues regarding species–area relationships (SARs), but fails to settles those issues. He states that only certain types of sampling schemes should be used to construct SARs, but is not consistent in the criteria that he uses to include some sampling schemes but not others. He argues that a sampling scheme of contiguous plots will be more accurate in extrapolating beyond the sampled area, but logic tells us that a dispersed sampling scheme is likely to be more accurate. Finally, he concludes that the 'true' SAR is a power function, but this conclusion is inconsistent with his results and with the results of others. Rather than defining a narrow framework for SARs, we need to recognize that the relationship between area and species richness is scale- and system-dependent. Different sampling schemes serve different purposes, and a variety of functional relationships are likely to hold. Further theoretical and empirical work is needed to resolve these issues fully.     

Multivariate denoising methods combining wavelets and principal component analysis for mass spectrometry data

The identification of new diagnostic or prognostic biomarkers is one of the main aims of clinical cancer research. In recent years, there has been a growing interest in using mass spectrometry for the detection of such biomarkers. The MS signal resulting from MALDI‐TOF measurements is contaminated by different sources of technical variations that can be removed by a prior pre‐processing step. In particular, denoising makes it possible to remove the random noise contained in the signal. Wavelet methodology associated with thresholding is usually used for this purpose. In this study, we adapted two multivariate denoising methods that combine wavelets and PCA to MS data. The objective was to obtain better denoising of the data so as to extract the meaningful proteomic biological information from the raw spectra and reach meaningful clinical conclusions. The proposed methods were evaluated and compared with the classical soft thresholding denoising method using both real and simulated data sets. It was shown that taking into account common structures of the signals by adding a dimension reduction step on approximation coefficients through PCA provided more effective denoising when combined with soft thresholding on detail coefficients.     

Sequential sampling: a novel method in farm animal welfare assessment

Lameness in dairy cows is an important welfare issue. As part of a welfare assessment, herd level lameness prevalence can be estimated from scoring a sample of animals, where higher levels of accuracy are associated with larger sample sizes. As the financial cost is related to the number of cows sampled, smaller samples are preferred. Sequential sampling schemes have been used for informing decision making in clinical trials. Sequential sampling involves taking samples in stages, where sampling can stop early depending on the estimated lameness prevalence. When welfare assessment is used for a pass/fail decision, a similar approach could be applied to reduce the overall sample size. The sampling schemes proposed here apply the principles of sequential sampling within a diagnostic testing framework. This study develops three sequential sampling schemes of increasing complexity to classify 80 fully assessed UK dairy farms, each with known lameness prevalence. Using the Welfare Quality herd-size-based sampling scheme, the first ‘basic’ scheme involves two sampling events. At the first sampling event half the Welfare Quality sample size is drawn, and then depending on the outcome, sampling either stops or is continued and the same number of animals is sampled again. In the second ‘cautious’ scheme, an adaptation is made to ensure that correctly classifying a farm as ‘bad’ is done with greater certainty. The third scheme is the only scheme to go beyond lameness as a binary measure and investigates the potential for increasing accuracy by incorporating the number of severely lame cows into the decision. The three schemes are evaluated with respect to accuracy and average sample size by running 100 000 simulations for each scheme, and a comparison is made with the fixed size Welfare Quality herd-size-based sampling scheme. All three schemes performed almost as well as the fixed size scheme but with much smaller average sample sizes. For the third scheme, an overall association between lameness prevalence and the proportion of lame cows that were severely lame on a farm was found. However, as this association was found to not be consistent across all farms, the sampling scheme did not prove to be as useful as expected. The preferred scheme was therefore the ‘cautious’ scheme for which a sampling protocol has also been developed.     

Revealing biogeographical patterns by nonlinear ordinations and derived anisotropic spatial filters

Aim Spatial floristic and faunistic data bases promote the investigation of biogeographical gradients in relation to environmental determinants on regional to continental scales. Our aim was to extract major gradients in the distribution of vascular plant species from a grid‐based inventory (the German FLORKART data base) and relate them to long‐term precipitation and temperature records as well as soil conditions. We present an ordination technique capable of coping with this complex data array. The goal was also to sort out the influence of spatial autocorrelation, assuming floristic autocorrelation is anisotropic. Location Germany, at a spatial resolution of 6′ × 10′. Methods Isometric feature mapping (Isomap) was applied as a nonlinear ordination method. Isomap was coupled to ‘eigenvector‐based filters’ for generating spatial reference models representing spatial autocorrelation. What is novel here is that the derived filters are not based on the assumption of equidirectional autocorrelation. Instead, the so‐called ‘principal coordinates of anisotropic neighbour matrices’ build filters to test the influence of geographical vicinity in directions of high similarity among observations. Results The Isomap ordination of floristic data explained more than 95% of the data variance in six dimensions. The leading two dimensions (representing about 80% of the FLORKART data variance) revealed clear spatial gradients that could be related to independent effects of temperature, precipitation and soil observations. By contrast, the third and higher FLORKART dimensions were dominated by an antagonism of anisotropic spatial autocorrelation and soil conditions. A subsequent cluster analysis of the floristic Isomap coordinates educed the spatial organization of the floristic survey, indicating a considerable sampling bias. Conclusions We showed that Isomap provides a consistent methodical framework for both ordination and derived spatial filters. The technique is useful for tracing the often nonlinear features of species occurrence data to environmental drivers, taking into account anisotropic spatial autocorrelation. We also showed that sampling biases are a conspicuous source of variance in a frequently used floristic data base.     

Second-order susceptibilities of anisotropic liquid-crystal thin films

Using optical second-harmonic generation, we have measured the anisotropic orientation behavior of liquid crystal (LC) molecules in thin films. A high degree of in-plane anisotropy was obtained by depositing the LC films onto rubbed polyimide-covered substrates. The analysis with respect to the relevant second-order susceptibility tensor components is based upon the experimental results obtained in transmission geometry using different angles of incidence for the separation of isotropic and anisotropic contributions.     

An Improvement of Robust Biometrics-Based Authentication and Key Agreement Scheme for Multi-Server Environments Using Smart Cards

In multi-server environments, user authentication is a very important issue because it provides the authorization that enables users to access their data and services; furthermore, remote user authentication schemes for multi-server environments have solved the problem that has arisen from user’s management of different identities and passwords. For this reason, numerous user authentication schemes that are designed for multi-server environments have been proposed over recent years. In 2015, Lu et al. improved upon Mishra et al.’s scheme, claiming that their remote user authentication scheme is more secure and practical; however, we found that Lu et al.’s scheme is still insecure and incorrect. In this paper, we demonstrate that Lu et al.’s scheme is vulnerable to outsider attack and user impersonation attack, and we propose a new biometrics-based scheme for authentication and key agreement that can be used in multi-server environments; then, we show that our proposed scheme is more secure and supports the required security properties.