The spatiotemporal context of individual specialization in resource use and environmental associations.

1. Individual niche specialization is widespread in natural populations and has key implications for higher levels of biological organization. This phenomenon, however, has been primarily quantified in resource niche axes, overlooking individual variation in environmental associations (i.e. abiotic conditions organisms experience). 2. Here, we explore what we can learn from a multidimensional perspective of individual niche specialization that integrates resource use and environmental associations into a common framework. 3. By combining predictions from theory and simple simulations, we illustrate how (i) multidimensional intraspecific niche variation and (ii) the spatiotemporal context of interactions between conspecifics scale up to shape emergent patterns of the population niche. 4. Contemplating individual specialization as a multidimensional, unifying concept across biotic and abiotic niche axes is a fundamental step towards bringing this concept closer to the n-dimensional niche envisioned by Hutchinson.

1. A especialização individual de nicho é prevalente em populações naturais e tem implicações importantes para níveis de organização biológica superiores. Esse fenômeno, entretanto, tem sido principalmente quantificado em eixos do nicho que representam o uso de recursos, negligenciando a variação individual em associações ambientais (i.e. as condições abióticas que organismos experimentam). 2. Aqui, exploramos o que podemos aprender a partir de uma perspectiva multidimensional da especialização individual que integra o uso de recursos e associações ambientais em uma abordagem única. 3. Ao combinar predições da teoria e simulações simples, ilustramos como (i) a variação intraespecífica multidimensional de nicho e (ii) o contexto espaço­temporal de interações entre conspecíficos podem moldar padrões emergentes do nicho de populações. 4. Encarar a especialização individual como um conceito multidimensional e unificador em eixos do nicho bióticos e abióticos é um passo fundamental na direção de aproximar esse conceito do nicho n­dimensional idealizado por Hutchinson.

Coupling spectral and resource-use complementarity in experimental grassland and forest communities.

Reflectance spectra provide integrative measures of plant phenotypes by capturing chemical, morphological, anatomical and architectural trait information. Here, we investigate the linkages between plant spectral variation, and spectral and resource-use complementarity that contribute to ecosystem productivity. In both a forest and prairie grassland diversity experiment, we delineated n-dimensional hypervolumes using wavelength bands of reflectance spectra to test the association between the spectral space occupied by individual plants and their growth, as well as between the spectral space occupied by plant communities and ecosystem productivity. We show that the spectral space occupied by individuals increased with their growth, and the spectral space occupied by plant communities increased with ecosystem productivity. Furthermore, ecosystem productivity was better explained by inter-individual spectral complementarity than by the large spectral space occupied by productive individuals. Our results indicate that spectral hypervolumes of plants can reflect ecological strategies that shape community composition and ecosystem function, and that spectral complementarity can reveal resource-use complementarity.

Non-Dimensional Star-Identification.

This study introduces a new "Non-Dimensional" star identification algorithm to reliably identify the stars observed by a wide field-of-view star tracker when the focal length and optical axis offset values are known with poor accuracy. This algorithm is particularly suited to complement nominal lost-in-space algorithms, which may identify stars incorrectly when the focal length and/or optical axis offset deviate from their nominal operational ranges. These deviations may be caused, for example, by launch vibrations or thermal variations in orbit. The algorithm performance is compared in terms of accuracy, speed, and robustness to the Pyramid algorithm. These comparisons highlight the clear advantages that a combined approach of these methodologies provides.

TReNDS-Software for reaction monitoring with time-resolved non-uniform sampling.

NMR spectroscopy, used routinely for structure elucidation, has also become a widely applied tool for process and reaction monitoring. However, the most informative of NMR methods-correlation experiments-are often useless in this kind of applications. The traditional sampling of a multidimensional FID is usually time-consuming, and thus, the reaction-monitoring toolbox was practically limited to 1D experiments (with rare exceptions, e.g., single-scan or fast-sampling experiments). Recently, the technique of time-resolved non-uniform sampling (TR-NUS) has been proposed, which allows to use standard multidimensional pulse sequences preserving the temporal resolution close to that achievable in 1D experiments. However, the method existed only as a prototype and did not allow on-the-fly processing during the reaction. In this paper, we introduce TReNDS: free, user-friendly software kit for acquisition and processing of TR-NUS data. The program works on Bruker, Agilent, and Magritek spectrometers, allowing to carry out up to four experiments with interleaved TR-NUS. The performance of the program is demonstrated on the example of enzymatic hydrolysis of sucrose.

ImageJ2: ImageJ for the next generation of scientific image data.

BACKGROUND: ImageJ is an image analysis program extensively used in the biological sciences and beyond. Due to its ease of use, recordable macro language, and extensible plug-in architecture, ImageJ enjoys contributions from non-programmers, amateur programmers, and professional developers alike. Enabling such a diversity of contributors has resulted in a large community that spans the biological and physical sciences. However, a rapidly growing user base, diverging plugin suites, and technical limitations have revealed a clear need for a concerted software engineering effort to support emerging imaging paradigms, to ensure the software's ability to handle the requirements of modern science. RESULTS: We rewrote the entire ImageJ codebase, engineering a redesigned plugin mechanism intended to facilitate extensibility at every level, with the goal of creating a more powerful tool that continues to serve the existing community while addressing a wider range of scientific requirements. This next-generation ImageJ, called "ImageJ2" in places where the distinction matters, provides a host of new functionality. It separates concerns, fully decoupling the data model from the user interface. It emphasizes integration with external applications to maximize interoperability. Its robust new plugin framework allows everything from image formats, to scripting languages, to visualization to be extended by the community. The redesigned data model supports arbitrarily large, N-dimensional datasets, which are increasingly common in modern image acquisition. Despite the scope of these changes, backwards compatibility is maintained such that this new functionality can be seamlessly integrated with the classic ImageJ interface, allowing users and developers to migrate to these new methods at their own pace. CONCLUSIONS: Scientific imaging benefits from open-source programs that advance new method development and deployment to a diverse audience. ImageJ has continuously evolved with this idea in mind; however, new and emerging scientific requirements have posed corresponding challenges for ImageJ's development. The described improvements provide a framework engineered for flexibility, intended to support these requirements as well as accommodate future needs. Future efforts will focus on implementing new algorithms in this framework and expanding collaborations with other popular scientific software suites.

Nonrigid registration with corresponding points constraint for automatic segmentation of cardiac DSCT images.

BACKGROUND: Dual-source computed tomography (DSCT) is a very effective way for diagnosis and treatment of heart disease. The quantitative information of spatiotemporal DSCT images can be important for the evaluation of cardiac function. To avoid the shortcoming of manual delineation, it is imperative to develop an automatic segmentation technique for 4D cardiac images. METHODS: In this paper, we implement the heart segmentation-propagation framework based on nonrigid registration. The corresponding points of anatomical substructures are extracted by using the extension of n-dimensional scale invariant feature transform method. They are considered as a constraint term of nonrigid registration using the free-form deformation, in order to restrain the large variations and boundary ambiguity between subjects. RESULTS: We validate our method on 15 patients at ten time phases. Atlases are constructed by the training dataset from ten patients. On the remaining data the median overlap is shown to improve significantly compared to original mutual information, in particular from 0.4703 to 0.5015 ([Formula: see text]) for left ventricle myocardium and from 0.6307 to 0.6519 ([Formula: see text]) for right atrium. CONCLUSIONS: The proposed method outperforms standard mutual information of intensity only. The segmentation errors had been significantly reduced at the left ventricle myocardium and the right atrium. The mean surface distance of using our framework is around 1.73 mm for the whole heart.

N-dimensional hypervolumes to study stability of complex ecosystems.

Although our knowledge on the stabilising role of biodiversity and on how it is affected by perturbations has greatly improved, we still lack a comprehensive view on ecosystem stability that is transversal to different habitats and perturbations. Hence, we propose a framework that takes advantage of the multiplicity of components of an ecosystem and their contribution to stability. Ecosystem components can range from species or functional groups, to different functional traits, or even the cover of different habitats in a landscape mosaic. We make use of n-dimensional hypervolumes to define ecosystem states and assess how much they shift after environmental changes have occurred. We demonstrate the value of this framework with a study case on the effects of environmental change on Alpine ecosystems. Our results highlight the importance of a multidimensional approach when studying ecosystem stability and show that our framework is flexible enough to be applied to different types of ecosystem components, which can have important implications for the study of ecosystem stability and transient dynamics.

N-dimensional switch function for energy conservation in multiprocess reaction dynamics.

The MReaDy program was designed for studying Multiprocess Reactive Dynamic systems, that is, complex chemical systems involving different and concurrent reactions. It builds a global potential energy surface integrating a variety of potential energy surfaces, each one of them representing an elementary reaction expected to play a role in the chemical process. For each elementary reaction, energy continuity problems may happen in the transition between potential energy surfaces due to differences in the functional form for each of the fragments, especially if built by different authors. A N-dimensional switch function is introduced in MReaDy in order to overcome such a problem. As an example, results of a collision trajectory calculation for H2 + OH → H3 O are presented, showing smooth transition in the potential energy, leading to conservation in the total energy. Calculations for a hydrogen combustion system from 1000 K up to 4000 K shows a variation of 0.012% when compared to the total energy of the system. © 2016 Wiley Periodicals, Inc.

An information geometrical evaluation of Shannon information metrics on a discrete n-dimensional digital manifold.

The definition and nature of information have perplexed scientists due to its dual nature in measurements. The information is discrete and continuous when evaluated on a metric scale, and the Laplace-Beltrami operator and Gauss-Bonnet Theorem can map one to another. On the other hand, defining the information as a discrete entity on the surface area of an n-dimensional discrete digital manifold provides a unique way of calculating the entropy of a manifold. The software simulation shows that the surface area of the discrete n-dimensional digital manifold is an effectively computable function. Moreover, it also provides the information-geometrical evaluation of Shannon information metrics.

Algebraic structure and basics of analysis of n-dimensional quaternionic space.

In this study, we focused on n-dimensional quaternionic space H n . To create the module structure, first part is devoted to define a metric depending on the product order relation of R n . The set of H n has been rewritten with a different representation of n-vectors. Using this notation, formulations corresponding to the basic operations in H n are obtained. By adhering these representations, module structure of H n over the set of real ordered n-tuples is given. Afterwards, we gave limit, continuity and the derivative basics of quaternion valued functions of a real variable.

A fast algorithm to find reduced hyperplane unit cells and solve N-dimensional Bézout's identities.

Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180° rotation. Thus, crystallographic models of twinning require the determination of the short unit cells attached to the planes, or hyperplanes for dimensions higher than 3. Here, a method is presented to find them. Equivalently, it gives the solutions of the N-dimensional Bézout's identity associated with the Miller indices of the hyperplane.

Higher dimensional Bianchi type-I string cosmological model in f(R) theory of gravity.

In this paper, we have studied Bianchi type-I string cosmological model by combining Kaluza-Klein (KK) theory and f ( R ) theory of gravity which is an extension of 5-dimensional KK string cosmological models. We have used equation of state in the form of p-string or Takabayasi string given by ρ = ( 1 + ω ) λ , where ρ and λ denote the rest density of energy cloud of strings, and the tension density of the system of strings, respectively and ω is a constant. In order to get physically significant and viable solution various forms of the function f ( R ) are assumed, in this paper we assume f ( R ) = R + α R 2 (e.g. Astashenok et al. (2017) [1]), where α is real number. Some physical and geometrical properties of the model are also discussed.

n-Dimensional (S,N)-implications.

The n-dimensional fuzzy logic (n-DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n-DFL provides a consolidated logical strategy for applied technologies since the ordered evaluations provided by decision makers impact not only by selecting the best solutions for a decision making problem, but also by enabling their comparisons. In such context, this paper studies the n-dimensional fuzzy implications (n-DI) following distinct approaches: (i) analytical studies, presenting the most desirable properties as neutrality, ordering, (contra-)symmetry, exchange and identity principles, discussing their interrelations and exemplifications; (ii) algebraic aspects mainly related to left- and right-continuity of representable n-dimensional fuzzy t-conorms; and (iii) generating n-DI from existing fuzzy implications. As the most relevant contribution, the prospective studies in the class of n-dimensional interval (S,N)-implications include results obtained from t-representable n-dimensional conorms and involutive n-dimensional fuzzy negations. And, these theoretical results are applied to model approximate reasoning of inference schemes, dealing with based-rule in n-dimensional interval fuzzy systems. A synthetic case-study illustrates the solution for a decision-making problem in medical diagnoses.

A preliminary study on constructing a high-dimensional asynchronous spectrum to analyze bilinear data.

A novel approach to constructing high-dimensional asynchronous spectra (nD-Asyn) is proposed. Three theorems relevant to 1D slices of nD-Asyn are revealed. nD-Asyn is used to analyze bilinear data from mixtures containing multiple components obtained via hyphenated techniques. The spectral contribution of different components can be removed in a stepwise manner by increasing the dimensions of asynchronous spectra. As a result, the spectra of different components can be faithfully recovered even if the time-related profiles of different components severely overlap. Moreover, correct results can still be obtained via the nD-Asyn even if a considerable level of noise and baseline drift are present. The nD-Asyn approach is compared with MCR-ALS using different constraints in analyzing the data for a simulated and also for a real system. The nD-Asyn produced correct spectrum of every component. Only when complete constraints obtained from nD-Asyn method is utilized in the MCR-ALS calculation, correct spectra of all the components can be obtained. Thus, nD-Asyn can be used alone or in conjunction with MCR-ALS to analyze bilinear data containing contributions of multiple components.

An integrated phenotypic trait-network in thermo-Mediterranean vegetation describing alternative, coexisting resource-use strategies.

Vascular plants have been found to align along globally-recognised resource-allocation trade-offs among specific functional traits. Genetic constrains and environmental pressures limit the spectrum of viable resource-use strategies employed by plant species. While conspecific plants have often been described as identical, intraspecific variation facilitates species coexistence and evolutionary potential. This study attempts to link an individual's phenotype to its environmental tolerance and ecosystem function. We hypothesised that: (1) seasonal variation in water availability has selected for tight phenotypic integration patterns that shape Mediterranean vegetation; however, (2) coexisting species employ alternative resource-use strategies to avoid competitive exclusion; specifically (3) species with smaller climatic niches (i.e. potential distributions) display higher functional diversity. We examined the interdependence among and the sources of variation within 11 functional traits, reflecting whole-plant economics (e.g. construction costs, hydraulics, defences, water storage capacity), from nine dominant, thermo-Mediterranean species measured across a wide environmental and geographic gradient. Furthermore, we delineated the phenotypic and climatic hypervolumes of each studied species to test for climatic niche overlap and functional distinctiveness. By adopting this multidimensional trait-based approach we detected fundamental phenotypic integration patterns that define thermo-Mediterranean species regardless of life history strategy. The studied traits emerged intercorrelated shaping a resource-allocation spectrum. Significant intraspecific variability in most measured traits allowed for functional distinctiveness among the measured species. Higher functional diversity was observed in species restricted within narrower climatic niches. Our results support our initial hypotheses. The studied functional traits collectively formed an integrated space of viable phenotypic expressions; however, phenotypic plasticity enables functionally distinctive species to succeed complementary in a given set of environmental conditions. Functional variability among coexisting individuals defined species' climatic niches within the trait-spectrum permitted by Mediterranean conditions. Ultimately, a species establishment in a locality depends on the extent that it can shift its trait values.

Combining Bayesian genetic clustering and ecological niche modeling: Insights into wolf intraspecific genetic structure.

The distribution of intraspecific genetic variation and how it relates to environmental factors is of increasing interest to researchers in macroecology and biogeography. Recent studies investigated the relationships between the environment and patterns of intraspecific genetic variation across species ranges but only few rigorously tested the relation between genetic groups and their ecological niches. We quantified the relationship of genetic differentiation (F ST) and the overlap of ecological niches (as measured by n-dimensional hypervolumes) among genetic groups resulting from spatial Bayesian genetic clustering in the wolf (Canis lupus) in the Italian peninsula. Within the Italian wolf population, four genetic clusters were detected, and these clusters showed different ecological niches. Moreover, different wolf clusters were significantly related to differences in land cover and human disturbance features. Such differences in the ecological niches of genetic clusters should be interpreted in light of neutral processes that hinder movement, dispersal, and gene flow among the genetic clusters, in order to not prematurely assume any selective or adaptive processes. In the present study, we found that both the plasticity of wolves-a habitat generalist-to cope with different environmental conditions and the occurrence of barriers that limit gene flow lead to the formation of genetic intraspecific genetic clusters and their distinct ecological niches.

Global realized niche divergence in the African clawed frog Xenopus laevis.

Although of crucial importance for invasion biology and impact assessments of climate change, it remains widely unknown how species cope with and adapt to environmental conditions beyond their currently realized climatic niches (i.e., those climatic conditions existing populations are exposed to). The African clawed frog Xenopus laevis, native to southern Africa, has established numerous invasive populations on multiple continents making it a pertinent model organism to study environmental niche dynamics. In this study, we assess whether the realized niches of the invasive populations in Europe, South, and North America represent subsets of the species' realized niche in its native distributional range or if niche shifts are traceable. If shifts are traceable, we ask whether the realized niches of invasive populations still contain signatures of the niche of source populations what could indicate local adaptations. Univariate comparisons among bioclimatic conditions at native and invaded ranges revealed the invasive populations to be nested within the variable range of the native population. However, at the same time, invasive populations are well differentiated in multidimensional niche space as quantified via n-dimensional hypervolumes. The most deviant invasive population are those from Europe. Our results suggest varying degrees of realized niche shifts, which are mainly driven by temperature related variables. The crosswise projection of the hypervolumes that were trained in invaded ranges revealed the south-western Cape region as likely area of origin for all invasive populations, which is largely congruent with DNA sequence data and suggests a gradual exploration of novel climate space in invasive populations.

A general theorem on the stability of a class of functional equations including quadratic-additive functional equations.

We prove a general stability theorem of an n-dimensional quadratic-additive type functional equation [Formula: see text]by applying the direct method.

Existence and global exponential stability of periodic solutions for n-dimensional neutral dynamic equations on time scales.

In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).