Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements

A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda w_i(t)$ at the individual level with a global coupling through a constraint which does not allow the $w_i$'s to fall below a lower cutoff given by $c \cdot \bar w$, where $\bar w$ is their momentary average and $0<c<1$ is a constant. The dynamic variables $w_i$ are found to exhibit a power-law distribution of the form $p(w) \sim w^{-1-\alpha}$. The exponent $\alpha (c,N)$ is quite insensitive to the distribution $\Pi(\lambda)$ of the random factor $\lambda$, but it is non-universal, and increases monotonically as a function of $c$. The "thermodynamic" limit, N goes to infty and the limit of decoupled free multiplicative random walks c goes to 0, do not commute: $\alpha(0,N) = 0$ for any finite $N$ while $\alpha(c,\infty) \ge 1$ (which is the common range in empirical systems) for any positive $c$. The time evolution of ${\bar w (t)}$ exhibits intermittent fluctuations parametrized by a (truncated) L\'evy-stable distribution $L_{\alpha}(r)$ with the same index $\alpha$. This non-trivial relation between the distribution of the $w_i$'s at a given time and the temporal fluctuations of their average is examined and its relevance to empirical systems is discussed.Comment: 7 pages, 4 figure

Monthly sunspot number time series analysis and its modeling through autoregressive artificial neural network

This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p,q)). Based on minimization of AIC we find 3 and 1 as the best values of p and q respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).Comment: 17 pages, 4 figure

Shell evolution approaching the N=20 island of inversion : Structure of 26Na

The levels in 26Na with single particle character have been observed for the first time using the d(25Na, pγ) reaction at 5 MeV/nucleon. The measured excitation energies and the deduced spectroscopic factors are in good overall agreement with (0+1)hω shell model calculations performed in a complete spsdfp basis and incorporating a reduction in the N=20 gap. Notably, the 1p3/2 neutron configuration was found to play an enhanced role in the structure of the low-lying negative parity states in 26Na, compared to the isotone 28Al. Thus, the lowering of the 1p3/2 orbital relative to the 0f7/2 occurring in the neighbouring Z=10 and 12 nuclei - 25,27Ne and 27,29Mg - is seen also to occur at Z=11 and further strengthens the constraints on the modelling of the transition into the island of inversion

Towards a nanomechanical basis for temporary adhesion in barnacle cyprids (Semibalanus balanoides)

Cypris larvae of barnacles are able to use a rapidly reversible temporary adhesion mechanism for exploring immersed surfaces. Despite decades of research interest, the means by which cyprids maintain attachment with surfaces prior to permanent settlement remain poorly understood. Here, we present novel observations on the morphology of ‘footprints’ of a putative adhesive secretion deposited by cyprids during surface exploration. Atomic force microscopy (AFM) was used to image footprints at high resolution and to acquire measurements of interaction forces. R–CH3- and R–NH2-terminated glass surfaces were used for comparison of footprint morphology, and it was noted that on R–NH2 each footprint comprised three times the volume of material deposited for footprints on R–CH3. Direct scaling of adhesion forces derived from AFM measurements did not adequately predict the real attachment tenacity of cyprids, and it is suggested that a mixture of ‘wet’ and ‘dry’ adhesive mechanisms may be at work in cyprid adhesion. High-resolution images of cyprid footprints are presented that correlate well with the known morphology of the attachment structures

Issues of reliability and validity in the measurement of challenging behaviour (behavioural difficulties) in learning disability: a discussion of implications for nursing research and practice

Full text of this article is not available in the UHRAThe purpose of this paper is to contribute to the debate on issues related to the reliability and validity of measurement of challenging behaviour (behavioural difficulties) in learning disability. A number of practical, theoretical and methodological issues are discussed that have significance for the nurse both as practitioner and/or researcher in learning disability. These issues are equally important to both provider and purchaser of health care in order that resources can be most effectively targeted. The term 'challenging behaviour' would appear to be used both in literature and research synonymously with behavioural difficulties, this has implications for nurses in both their clinical practice and/or research. The author concludes by identifying a need to replace the term challenging behaviour, with 'behavioural difficulties'. It is argued that such a term is much more explicit in meaning and amenable to operational definition, thus enabling empirical study. Such a proposal will not be accepted by all as justifiable; this is because some might argue that adopting the term behavioural difficulties may be a retrograde step that perpetuates negative imagery and inappropriate labelling of people with a learning disability.Peer reviewe

Population consequences of mutual attraction between settling and adult barnacles

1. Spatial patterns of recruitment were compared between populations of the rocky shore barnacles (Crustacea: Cirripedia) Semibalanus balanoides, an obligate cross-fertilizer, and Chthamalus montagui, which can self-fertilize. We tested the hypothesis that recruitment depends on a behaviourally mediated interaction at settlement between the effects of adult background density and adult spacing, which limit free space for settlement and mating opportunities, respectively. Recruitment to patches of cleared rock (10- or 30-cm diameter) was compared between replicate shores with background densities of adult barnacles classed as low (?20 per 25 cm2) and high (&gt;4× low). Replicate patches were cleared of all barnacles surrounding a remnant cluster, comprising 0, 1, 2, 4, 8, 16 or 32 adults.2. For S. balanoides, settlement and subsequent recruitment over 5 months varied in direct proportion to remnant cluster size, except on the shore with the highest background density where recruitment was inversely proportional to cluster size. We interpret this inversion to indicate attraction to potential mates at low adult densities (positive density dependence, an Allee effect) switching to attraction to free space at high density (negative density dependence). The strengths and slopes of the regressions increased from shores with the lowest to the highest overall recruitment of barnacles, but retained significance over a five-fold range in recruitment. Positive effects of cluster size on recruitment were consistent between consecutive years, despite considerable variation in recruitment densities. In contrast, recruitment of C. montagui was generally more weakly proportional to cluster size, except for a strong positive correlation at the shore with the highest recruitment.3. Dispersion of recruits within treatment patches was accurately modelled by a computer simulation that allowed each barnacle to settle at random between fixed minimum and maximum distances from the nearest other settled barnacle. The model estimated threshold distances by maximum likelihood fit to observed recruitment into concentric annuli around the central adult cluster. Upper thresholds of separation corresponded to penis length for 65% of S. balanoides and 42% of C. montagui patches. Lower thresholds were ?2× cyprid length for 75% of S. balanoides patches, but were larger than this for C. montagui patches