Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.

Identification of linear systems in the presence of piecewise polynomial disturbances

The paper proposes a method of performing system identification of a linear system in the presence of bounded disturbances. The disturbances may be piecewise parabolic or periodic functions. The method is demonstrated effectively on two example systems with a range of disturbances.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Extracellular release of a heterologous phytase from roots of transgenic plants: does manipulation of rhizosphere biochemistry impact microbial community structure?

To maintain the sustainability of agriculture, it is imperative that the reliance of crops on inorganic phosphorus (P) fertilizers is reduced. One approach is to improve the ability of crop plants to acquire P from organic sources. Transgenic plants that produce microbial phytases have been suggested as a possible means to achieve this goal. However, neither the impact of heterologous expression of phytase on the ecology of microorganisms in the rhizosphere nor the impact of rhizosphere microorganisms on the efficacy of phytases in the rhizosphere of transgenic plants has been tested. In this paper, we demonstrate that the presence of rhizosphere microorganisms reduced the dependence of plants oil extracellular secretion of phytase from roots when grown in a P-deficient soil. Despite this, the expression of phytase in transgenic plants had little or no impact on the microbial community structure as compared with control plant lines, whereas soil treatments, such as the addition of inorganic P, had large effects. The results demonstrate that soil microorganisms are explicitly involved in the availability of P to plants and that the microbial community in the rhizosphere appears to be resistant to the impacts of single-gene changes in plants designed to alter rhizosphere biochemistry and nutrient cycling.

Moderate drought alters biomass and depth distribution of fine roots in Norway spruce

A rain shelter experiment was conducted in a 90-year-old Norway spruce stand, in the Kysucké Beskydy Mts (Slovakia). Three rain shelters were constructed in the stand to prevent the rainfall from reaching the soil and to reduce water availability in the rhizosphere. Fine root biomass and necromass were repeatedly measured throughout a growing season by soil coring. We established the quantities of fine root biomass (live) and necromass (dead) at soil depths of 0-5, 5-15, 15-25, and 25-35 cm. Significant differences in soil moisture contents between control and drought plots were found in the top 15 cm of soil after 20 weeks of rainfall manipulation (lasting from early June to late October). Our observations show that even relatively light drought decreased total fine root biomass from 272.0 to 242.8 g m-2 and increased the amount of necromass from 79.2 to 101.2 g m-2 in the top 35 cm of soil. Very fine roots, i.e. those with diameter up to 1 mm, were more affected than total fine roots defined as 0-2 mm. The effect of reduced water availability was depth-specific, as a result we observed a modification of vertical distribution of fine roots. More roots in drought treatment were produced in the wetter soil horizons at 25-35 cm depth than at the surface. We conclude that fine and very fine root systems of Norway spruce have the capacity to re-allocate resources to roots at different depths in response to environmental signals, resulting in changes in necromass to biomass ratio.

Measuring variation in potato roots in both field and glasshouse: the search for useful yield predictors and a simple screen for root traits

Aims Potatoes have an inadequate rooting system for efficient acquisition of water and minerals and use disproportionate amounts of irrigation and fertilizer. This research determines whether significant variation in rooting characteristics of potato exists, which characters correlate with final yield and whether a simple screen for rooting traits could be developed. Methods Twenty-eight genotypes of Solanum tuberosum groups Tuberosum and Phureja were grown in the field; eight replicate blocks to final harvest, while entire root systems were excavated from four blocks. Root classes were categorised and measured. The same measurements were made on these genotypes in the glasshouse, 2 weeks post emergence. Results In the field, total root length varied from 40 m to 112 m per plant. Final yield was correlated negatively with basal root specific root length and weakly but positively with total root weight. Solanum tuberosum group Phureja genotypes had more numerous roots and proportionally more basal than stolon roots compared with Solanum tuberosum, group Tuberosum genotypes. There were significant correlations between glasshouse and field measurements. Conclusions Our data demonstrate that variability in rooting traits amongst commercially available potato genotypes exists and a robust glasshouse screen has been developed. By measuring potato roots as described in this study, it is now possible to assess rooting traits of large populations of potato genotypes.

Contributions of roots and rootstocks to sustainable, intensified crop production

Sustainable intensification is seen as the main route for meeting the world’s increasing demands for food and fibre. As demands mount for greater efficiency in the use of resources to achieve this goal, so the focus on roots and rootstocks and their role in acquiring water and nutrients, and overcoming pests and pathogens, is increasing. The purpose of this review is to explore some of the ways in which understanding root systems and their interactions with soils could contribute to the development of more sustainable systems of intensive production. Physical interactions with soil particles limit root growth if soils are dense, but root–soil contact is essential for optimal growth and uptake of water and nutrients. X-ray microtomography demonstrated that maize roots elongated more rapidly with increasing root–soil contact, as long as mechanical impedance was not limiting root elongation, while lupin was less sensitive to changes in root–soil contact. In addition to selecting for root architecture and rhizosphere properties, the growth of many plants in cultivated systems is profoundly affected by selection of an appropriate rootstock. Several mechanisms for scion control by rootstocks have been suggested, but the causal signals are still uncertain and may differ between crop species. Linkage map locations for quantitative trait loci for disease resistance and other traits of interest in rootstock breeding are becoming available. Designing root systems and rootstocks for specific environments is becoming a feasible target.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Polynomial-based noise variance estimation for MIMO-SCBT systems

In this paper, we present a polynomial-based noise variance estimator for multiple-input multiple-output single-carrier block transmission (MIMO-SCBT) systems. It is shown that the optimal pilots for noise variance estimation satisfy the same condition as that for channel estimation. Theoretical analysis indicates that the proposed estimator is statistically more efficient than the conventional sum of squared residuals (SSR) based estimator. Furthermore, we obtain an efficient implementation of the estimator by exploiting its special structure. Numerical results confirm our theoretical analysis.