Species divergence and trait convergence in experimental plant community assembly

Despite decades of research, it remains controversial whether ecological communities converge towards a common structure determined by environmental conditions irrespective of assembly history. Here, we show experimentally that the answer depends on the level of community organization considered. In a 9-year grassland experiment, we manipulated initial plant composition on abandoned arable land and subsequently allowed natural colonization. Initial compositional variation caused plant communities to remain divergent in species identities, even though these same communities converged strongly in species traits. This contrast between species divergence and trait convergence could not be explained by dispersal limitation or community neutrality alone. Our results show that the simultaneous operation of trait-based assembly rules and species-level priority effects drives community assembly, making it both deterministic and historically contingent, but at different levels of community organization.

The development of convergence and accommodation

Aim: To review current literature on the development of convergence and accommodation. The accommodation and vergence systems provide the foundation upon which bifoveal binocular single vision develops. Deviations from their normal development not only are implicated in the aetiology of convergence anomalies, accommodative anomalies and strabismus, but may also be implicated in failure of the emmetropisation process. Method: This review considers the problems of researching the development of accommodation and vergence in infants and how infant research has had to differ from adult methods. It then reviews and discusses the implications of current research into the development of both systems and their linkages. Results: Vergence and accommodation develop rapidly in the first months of life, with accommodation changing from relatively fixed myopic focus in the neonatal period to adult-like responses by 4 months of age. Vergence develops gradually and becomes more accurate after 4 months of age, but has been demonstrated in infants well before the age that binocular disparity detection mechanisms are thought to develop. Hypotheses for this early vergence mechanism are discussed. The relationship between accommodation and vergence shows much more variability in infants than adult literature has found, but this apparent adult/infant difference may be partly attributed to methodological differences rather than maturational change alone. Conclusions: Variability and flexibility characterise infant responses. This variability may enable infants to develop a flexible and robust binocular system for later life. Studies of infant visual cue use may give clues to the aetiology of strabismus and refractive error.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Minimum stable convergence criteria for stochastic diffusion search

An analysis of Stochastic Diffusion Search (SDS), a novel and efficient optimisation and search algorithm, is presented, resulting in a derivation of the minimum acceptable match resulting in a stable convergence within a noisy search space. The applicability of SDS can therefore be assessed for a given problem.

Convergence analysis of stochastic diffusion search

In this paper we present a connectionist searching technique - the Stochastic Diffusion Search (SDS), capable of rapidly locating a specified pattern in a noisy search space. In operation SDS finds the position of the pre-specified pattern or if it does not exist - its best instantiation in the search space. This is achieved via parallel exploration of the whole search space by an ensemble of agents searching in a competitive cooperative manner. We prove mathematically the convergence of stochastic diffusion search. SDS converges to a statistical equilibrium when it locates the best instantiation of the object in the search space. Experiments presented in this paper indicate the high robustness of SDS and show good scalability with problem size. The convergence characteristic of SDS makes it a fully adaptive algorithm and suggests applications in dynamically changing environments.

Convergence analysis of chip- and fractionally spaced LMS adaptive multiuser CDMA detectors

This paper analyzes the convergence behavior of the least mean square (LMS) filter when used in an adaptive code division multiple access (CDMA) detector consisting of a tapped delay line with adjustable tap weights. The sampling rate may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally spaced (FS) detection, respectively. It is shown that CS and FS detectors with the same time-span exhibit identical convergence behavior if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). This phenomenon is carefully explained with reference to the eigenvalues of the correlation matrix when the input signal is not perfectly bandlimited. The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of the transient behavior and the influence of the initial tap weight vector on convergence speed are highlighted. Specifically, a initialization within the signal subspace or to the origin leads to very much faster convergence compared with initialization in the a noise subspace.