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A MACSYMA implementation of the Laplace transform for special functions is described. The generalized hypergeometric functions are used as a basis for the representation of approximately fifty special functions. Only a relatively small number of formulas that generally involve generalized hypergeometric functions are utilized for the integration stage. A sample of actual examples and their timing is provided.
Mutualisms are ubiquitous in natural systems, but less is known about how these positive interactions influence species distributions compared with antagonistic interactions, such as competition and predation. The niche concept is one useful approach for thinking about factors that shape species ranges, which we apply here towards understanding how the nature of plant-mycorrhizal symbioses change across large environmental gradients. We used a continuous niche mapping approach to examine how two ectomycorrhizal fungi (Thelephora terrestris, Suillus pungens) impact pine seedling growth across a two-dimensional soil nitrogen (N) and phosphorus (P) gradient. We found that ectomycorrhizal fungi improved plant growth most in nutrient addition treatments with highly imbalanced N:P ratios, demonstrating that mycorrhizal benefits depend on interactions between niche axes. Nevertheless, T. terrestris (highN:lowP) and S. pungens (lowN:highP) benefited plants most at opposite ends of the resource ratio spectrum, consistent with niche partitioning and functional specialization. While ectomycorrhizal fungi are often thought of as being most beneficial for nitrogen uptake, our results suggest that members of the Thelephoraceae may specialize in improving plant P uptake. Ectomycorrhizal colonization by a single fungus increased plant niche volume (calculated as convex hull volumes of plant growth response surfaces across N and P gradients) compared to non-mycorrhizal control plants and shows the overall positive effects of mutualisms on plant niche volume. Despite plant host benefits in S. pungens and T. terrestris single species treatments, the presence of both fungi together decreased plant niche volume. The lack of functional complementarity, despite functional specialization, indicates that in some environments, either fungal competition or the cost of maintaining a suboptimal mycorrhizal partner can limit the benefits of a higher quality partner. The niche mapping approach we present has the potential to answer fundamental questions about the dimensions of functional diversity in ectomycorrhizal fungi and the distributions of mycorrhizal symbioses.
We used surface-based representations to analyze functional specializations in the human cerebral cortex. A computerized reconstruction of the cortical surface of the Visible Man digital atlas was generated and transformed to the Talairach coordinate system. This surface was also flattened and used to establish a surface-based coordinate system that respects the topology of the cortical sheet. The linkage between two-dimensional and three-dimensional representations allows the locations of published neuroimaging activation foci to be stereotaxically projected onto the Visible Man cortical flat map. An analysis of two activation studies related to the hearing and reading of music and of words illustrates how this approach permits the systematic estimation of the degree of functional segregation and of potential functional overlap for different aspects of sensory processing.
This paper continues the previous work of the author and contains the results concerning the relations for a wide class of special functions related to multidimensional Poisson and polynomial random walks.
SUMMARY Xylan is the most abundant non‐cellulosic polysaccharide in grass cell walls, and it has important structural roles. The name glucuronoarabinoxylan (GAX) is used to describe this variable hemicellulose. It has a linear backbone of β‐1,4‐xylose (Xyl) residues that may be substituted with α‐1,2‐linked (4‐ O ‐methyl)‐glucuronic acid (GlcA), α‐1,3‐linked arabinofuranose (Ara f ), and sometimes acetylation at the O ‐2 and/or O ‐3 positions. The role of these substitutions remains unclear, although there is increasing evidence that they affect the way xylan interacts with other cell wall components, particularly cellulose and lignin. Here, we used substitution‐dependent endo‐xylanase enzymes to investigate the variability of xylan substitution in grass culm cell walls. We show that there are at least three different types of xylan: (i) an arabinoxylan with evenly distributed Ara f substitutions without GlcA (AXe); (ii) a glucuronoarabinoxylan with clustered GlcA modifications (GAXc); and (iii) a highly substituted glucuronoarabinoxylan (hsGAX). Immunolocalization of AXe and GAXc in Brachypodium distachyon culms revealed that these xylan types are not restricted to a few cell types but are instead widely detected in Brachypodium cell walls. We hypothesize that there are functionally specialized xylan types within the grass cell wall. The even substitutions of AXe may permit folding and binding on the surface of cellulose fibrils, whereas the more complex substitutions of the other xylans may support a role in the matrix and interaction with other cell wall components.
Adaptor enables mechanical and electrical connections made easily between special-purpose end effector and arm of robot or remote mainpulator. Use in prosthetic devices also contemplatd. With adaptor, hand changed quickly from device designed to grasp objects of various sizes and shapes to device intended to do specific task efficiently.
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This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Sections Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of computer codes that permit more accurate and efficient three-dimensional analyses of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components.
We developed and validated an automated routine for the fitting of I-V curve data to the single diode model according to an exact analytical solution. Our fitting routine was validated to show good noise immunity and high accuracy usingsimulated values from LTSPICE. We are thus able to automate parameter extraction from a dataset or arbitrary size. This parameterization allows for better simulation of performance of real cells and arrays and provides utility for a host of applications relevant to space arrays. We will use this methodology to determine the array performance of radiated cells over time, and simulate the performance of the arrays with bypass diodes and power electronics.
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Advanced 3-D inelastic structural/stress analysis methods and solution strategies for more accurate yet more cost-effective analysis of components subjected to severe thermal gradients and loads in the presence of mechanical loads, with steep stress and strain gradients are being developed. Anisotropy, time and temperature dependent plasticity and creep effects are also addressed. The approach is to develop four different theories, one linear and three higher order theories (polynomial function, special function, general function). The theories are progressively more complex from linear to general function in order to provide streamlined analysis capability with increasing accuracy for each hot section component and for different parts of the same component according to the severity of the local stress, strain and temperature gradients associated with hot spots, cooling holes and surface coating cracks. To further enhance the computational effectiveness, the higher order theories will have embedded singularities (cooling passages, for example) in the generic modeling region. Each of the four theories consists of three formulation models derivable from independent theoretical formulations. These formulation models are based on: (1) mechanics of materials; (2) special finite elements; and (3) an advanced formulation to be recommended by the contractor.
In this report, the application of the acoustical holography (AH) technique for projecting near-field acoustic data to the far field is discussed. Test problems will be used to showcase the accuracy and utility of this technique and to demonstrate its superiority over the more common technique of spherical spreading projection. Three versions of the technique will be presented: planar, cylindrical, and spherical. Depending on the nature of the acoustic field, one or more of these versions may be useful and practical to use. Since the cylindrical and spherical versions depend on the accurate numerical computations of certain special functions, such as the Hankel functions and the associated Legendre polynomials, the implementation of the high-precision numerical computation of the required special functions on a computer are included in the appendixes at the end of the report. In some cases, the material presented in these appendixes represents a substantial extension of the results previously published in the open literature. As appropriate, special considerations associated with the use of the AH technique in practical situations are discussed.
This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.
Significance Evidence suggests that the brain is arranged in functionally specialized modules to form a network of networks (NoN). Understanding how functionality emerges from the integration of such modular architectures is one of the greatest scientific challenges. We introduce a model of brain NoN, which is robust against random node failures, captures the integration of functionally specialized modules in the brain, and provides falsifiable predictions about the locations of the most influential nodes, called neural collective influencers, in the brain network—predictions that are impossible in existing but fragile models of interdependent NoN. If confirmed by experiment, our results may pave the way for applications of clinical interest.
Integrals of products of error functions with other functions are presented, taking into account a combination of the error function with powers, a combination of the error function with exponentials and powers, a combination of the error function with exponentials of more complicated arguments, definite integrals from Laplace transforms, and a combination of the error function with trigonometric functions. Other integrals considered include a combination of the error function with logarithms and powers, a combination of two error functions, and a combination of the error function with other special functions.
A method is being developed that provides for an artificial-intelligence system to learn a user's preferences for sets of objects and to thereafter automatically select subsets of objects according to those preferences. The method was originally intended to enable automated selection, from among large sets of images acquired by instruments aboard spacecraft, of image subsets considered to be scientifically valuable enough to justify use of limited communication resources for transmission to Earth. The method is also applicable to other sets of objects: examples of sets of objects considered in the development of the method include food menus, radio-station music playlists, and assortments of colored blocks for creating mosaics. The method does not require the user to perform the often-difficult task of quantitatively specifying preferences; instead, the user provides examples of preferred sets of objects. This method goes beyond related prior artificial-intelligence methods for learning which individual items are preferred by the user: this method supports a concept of setbased preferences, which include not only preferences for individual items but also preferences regarding types and degrees of diversity of items in a set. Consideration of diversity in this method involves recognition that members of a set may interact with each other in the sense that when considered together, they may be regarded as being complementary, redundant, or incompatible to various degrees. The effects of such interactions are loosely summarized in the term portfolio effect. The learning method relies on a preference representation language, denoted DD-PREF, to express set-based preferences. In DD-PREF, a preference is represented by a tuple that includes quality (depth) functions to estimate how desired a specific value is, weights for each feature preference, the desired diversity of feature values, and the relative importance of diversity versus depth. The system applies statistical concepts to estimate quantitative measures of the user s preferences from training examples (preferred subsets) specified by the user. Once preferences have been learned, the system uses those preferences to select preferred subsets from new sets. The method was found to be viable when tested in computational experiments on menus, music playlists, and rover images. Contemplated future development efforts include further tests on more diverse sets and development of a sub-method for (a) estimating the parameter that represents the relative importance of diversity versus depth, and (b) incorporating background knowledge about the nature of quality functions, which are special functions that specify depth preferences for features.