Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm

The least-mean-fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially in sub-Gaussian noise environments. Recent work on normalised versions of the LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise environments. For example, the recently developed normalised LMF (XE-NLMF) algorithm is normalised by the mixed signal and error powers, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. In this work, a time-varying mixed-power parameter technique is introduced to overcome this dependency. A convergence analysis, transient analysis, and steady-state behaviour of the proposed algorithm are derived and verified through simulations. An enhancement in performance is obtained through the use of this technique in two different scenarios. Moreover, the tracking analysis of the proposed algorithm is carried out in the presence of two sources of nonstationarities: (1) carrier frequency offset between transmitter and receiver and (2) random variations in the environment. Close agreement between analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mean-square error is not a monotonically increasing function of the step size. (c) 2007 Elsevier B.V. All rights reserved.

Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

Convergence of bimodules over maximal abelian selfadjoint algebras

We prove a continuity result for the map sending a masa-bimodule to its support. We characterise the convergence of a net of weakly closed convex hulls of bilattices in terms of the convergence of the corresponding supports, and establish a lower-semicontinuity result for the map sending a support to the corresponding masa-bimodule.

Convergence of the iterative algorithm for a general Hammerstein system identification

The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters.

Convergence/Divergence: Party political discourse in Northern Ireland's transition from conflict

This paper illuminates the role of political language in a peace process through analysing the discourse used by political parties in Northern Ireland. What matters, it seems, is not whether party discourses converge or diverge but rather how, and in what ways, they do so. In the case of Northern Ireland, there remains strong divergence between discourses regarding the ethos of unionist and nationalist parties. As a consequence, core definitions of identity, culture, norms and principle remain common grounds for competition within nationalism and unionism. There has, however, been a significant shift towards convergence between unionist and nationalist parties in their discourses on power and governance, specifically among the now predominant (hardline) and the smaller (moderate) parties. The argument thus elaborated is that political transition from conflict need not necessarily entail the creation of a “shared discourse” between all parties. Indeed, points of divergence between parties’ discourses of power and ethos are as important for a healthy post-conflict democratic environment as the elements of convergence between them.

Community convergence and recruitment of keystone species as performance indicators of artificial reefs

An experimental artificial reefwas constructed in Strangford Lough, Northern Ireland as part of trials to regenerate damaged biogenic reefs formed by the horse mussel Modiolus modiolus. Experimental reef plots were constructed using Pecten maximus shell as cultch. Clumps of live adult M. modiolus were translocated from nearby natural reefs into cultchwith a high profile (elevated cultch), cultch with a lowprofile (flattened cultch), as well as directly into the seafloor. The aim of the study was to test the hypothesis that translocated mussel clumps would increase habitat complexity thus accelerating community succession and enhancing natural recruitment of M. modiolus spat. These effects were predicted to be greater on elevated cultch due to greater protection from
predators and increased accessibility to food resources. Within the artificial reef array the translocated clumps had a significant positive effect on recruitment compared to cultch without mussels with average densities of spat settled on the translocated M. modiolus clumps ranging from 100 to 200 individuals m-2 compared to 4 to 52 spat m-2 on cultch without mussels. Recruitment of M. modiolus spat was also significantly higher on translocated horse mussels when compared to natural reefs where densities of 8–36 spat m-2 were recorded.
Reef elevation appeared to provide some degree of protection from predators but differences in translocated M. modiolus survival on the different elevation treatments were not significant. In total, 223 taxa were recorded 12 months after reef construction. The presence of translocated clumps ofM. modiolus was the main driver of the increases in faunal diversity and species abundance. Application of objective criteria to assess the performance of artificial reefs suggested that translocation of M. modiolus clumps alone achieved most of the restoration objectives. Consequently this pilot study demonstrates a straightforward and realistic intervention technique that could be used to kick start the regeneration and expansion of impacted mussel and similar biogenic reefs elsewhere.

Compositional Divergence and Convergence in Local Communities and Spatially Structured Landscapes

Community structure depends on both deterministic and stochastic processes. However, patterns of community dissimilarity (e.g. difference in species composition) are difficult to interpret in terms of the relative roles of these processes. Local communities can be more dissimilar (divergence) than, less dissimilar (convergence) than, or as dissimilar as a hypothetical control based on either null or neutral models. However, several mechanisms may result in the same pattern, or act concurrently to generate a pattern, and much research has recently been focusing on unravelling these mechanisms and their relative contributions. Using a simulation approach, we addressed the effect of a complex but realistic spatial structure in the distribution of the niche axis and we analysed patterns of species co-occurrence and beta diversity as measured by dissimilarity indices (e.g. Jaccard index) using either expectations under a null model or neutral dynamics (i.e., based on switching off the niche effect). The strength of niche processes, dispersal, and environmental noise strongly interacted so that niche-driven dynamics may result in local communities that either diverge or converge depending on the combination of these factors. Thus, a fundamental result is that, in real systems, interacting processes of community assembly can be disentangled only by measuring traits such as niche breadth and dispersal. The ability to detect the signal of the niche was also dependent on the spatial resolution of the sampling strategy, which must account for the multiple scale spatial patterns in the niche axis. Notably, some of the patterns we observed correspond to patterns of community dissimilarities previously observed in the field and suggest mechanistic explanations for them or the data required to solve them. Our framework offers a synthesis of the patterns of community dissimilarity produced by the interaction of deterministic and stochastic determinants of community assembly in a spatially explicit and complex context.

Compositional divergence and convergence in arbuscular mycorrhizal fungal communities

In spite of the controversy that they have generated, neutral models provide ecologists with powerful tools for creating dynamic predictions about beta-diversity in ecological communities. Ecologists can achieve an understanding of the assembly rules operating in nature by noting when and how these predictions are met or not met. This is particularly valuable for those groups of organisms that are challenging to study under natural conditions (e.g., bacteria and fungi). Here, we focused on arbuscular mycorrhizal fungal (AMF) communities and performed an extensive literature search that allowed us to synthesize the information in 19 data sets with the minimal requisites for creating a null hypothesis in terms of community dissimilarity expected under neutral dynamics. In order to achieve this task, we calculated the first estimates of neutral parameters for several AMF communities from different ecosystems. Communities were shown either to be consistent with neutrality or to diverge or converge with respect to the levels of compositional dissimilarity expected under neutrality. These data support the hypothesis that divergence occurs in systems where the effect of limited dispersal is overwhelmed by anthropogenic disturbance or extreme biological and environmental heterogeneity, whereas communities converge when systems have the potential for niche divergence within a relatively homogeneous set of environmental conditions. Regarding the study cases that were consistent with neutrality, the sampling designs employed may have covered relatively homogeneous environments in which the effects of dispersal limitation overwhelmed minor differences among AMF taxa that would lead to environmental filtering. Using neutral models we showed for the first time for a soil microbial group the conditions under which different assembly processes may determine different patterns of beta-diversity. Our synthesis is an important step showing how the application of general ecological theories to a model microbial taxon has the potential to shed light on the assembly and ecological dynamics of communities.