A novel repair model for imperfect maintenance

Commonly used repair rate models for repairable systems in the reliability literature are renewal processes, generalised renewal processes or non-homogeneous Poisson processes. In addition to these models, geometric processes (GP) are studied occasionally. The GP, however, can only model systems with monotonously changing (increasing, decreasing or constant) failure intensities. This paper deals with the reliability modelling of failure processes for repairable systems where the failure intensity shows a bathtub-type non-monotonic behaviour. A new stochastic process, i.e. an extended Poisson process, is introduced in this paper. Reliability indices are presented, and the parameters of the new process are estimated. Experimental results on a data set demonstrate the validity of the new process.

Modelling: promoting creativity whilst forging links between science education and design and technology education

Educational reforms in many countries currently call for the development of knowledge-based societies. In particular, emphasis is placed on the promotion of creativity, especially in the areas of science education and of design and technology education. In this paper, perceptions of the nature of creativity and of the conditions for its realization are discussed. The notion of modelling as a creative act is outlined and the scope for using modelling as a bridge between science education and design and technology education explored. A model for the creative act of modelling is proposed and its major aspects elaborated upon. Finally, strategies for forging links between the two subjects are outlined.

Depression, confidence, and decision: evidence against depressive realism

This research examined how retrospective self-assessments of performance are affected by major depression. To test the validity of the depressive realism versus the selective processing hypotheses, aggregate posttest performance estimates (PTPEs) were obtained from clinically depressed patients and an age-matched comparison group across 4 decision tasks (object recognition, general knowledge, social judgment, and line-length judgment). As expected on the basis of previous findings, both groups were underconfident in their PTPEs, consistently underestimating the percentage of questions they had answered correctly. Contrary to depressive realism, and in partial support of the selective processing account, this underconfidence effect was not reduced but modestly exacerbated in the depressed patients. Further, whereas the PTPEs of the comparison group exceeded that expected on the basis of chance alone those of the depressed individuals did not. The results provide no support for the depressive realism account and suggest that negative biases contribute to metacognitive information processing in major depression.

Input constraints handling in an MPC/feedback linearization scheme

The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real time MPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.

The locally twisted cubes

This paper introduces a new variant of the popular n-dimensional hypercube network Q(n), known as the n-dimensional locally twisted cube LTQ(n), which has the same number of nodes and the same number of connections per node as Q(n). Furthermore. LTQ(n) is similar to Q(n) in the sense that the nodes can be one-to-one labeled with 0-1 binary sequences of length n. so that the labels of any two adjacent nodes differ in at most two successive bits. One advantage of LTQ(n) is that the diameter is only about half of the diameter of Q(n) We develop a simple routing algorithm for LTQ(n), which creates a shortest path from the source to the destination in O(n) time. We find that LTQ(n) consists of two disjoint copies of Q(n) by adding a matching between their nodes. On this basis. we show that LTQ(n) has a connectivity of n.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Models for evolving networks: with applications in telecommunication and online activities

Driven by a range of modern applications that includes telecommunications, e-business and on-line social interaction, recent ideas in complex networks can be extended to the case of time-varying connectivity. Here we propose a general frame- work for modelling and simulating such dynamic networks, and we explain how the long time behaviour may reveal important information about the mechanisms underlying the evolution.

Linear-wavelet networks

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.

Circulating insulin-like factor 3 (INSL3) in healthy and infertile women

STUDY QUESTION: How does insulin-like factor 3 (INSL3) concentration in blood vary across the menstrual cycle in women? SUMMARY ANSWER: INSL3 is secreted by the theca interna cells of growing antral follicles and is phasic in its expression. WHAT IS KNOWN ALREADY: The relaxin-like hormone INSL3 is known to be expressed in follicles of several mammal species, and was recently shown in cows to be specifically secreted into the bloodstream by growing antral follicles, corresponding to follicular waves. In males INSL3 is known to be acutely independent of the hormones of the hypothalamic-pituitary-gonadal axis, suggesting that in women INSL3 might be a novel biomarker for antral follicle recruitment and development. STUDY DESIGN, SIZE, DURATION: Two cohorts of women were studied. First, 18 healthy women of reproductive age were followed longitudinally for one and a half cycles, with blood sampling and hormone measurement every 2-3 days. A second cohort comprised a cross-sectional study of 909 women attending an infertility clinic, with a single blood sample taken at entry, together with other clinical and hormonal parameters. PARTICIPANTS/MATERIALS, SETTING, METHODS: Blood samples from both retrospective cohorts were analyzed for INSL3 using a highly sensitive time-resolved fluorescent immunoassay, and data were analyzed in comparison with other clinical and hormonal parameters. MAIN RESULT AND THE ROLE OF CHANCE: For young healthy women of reproductive age, we showed a phasic expression of INSL3 corresponding to antral follicle growth in both the follicular and luteal phases of the cycle, which was significantly (P < 0.05) elevated compared with that during menses. For women attending an infertility clinic, those with diagnosed polycystic ovarian syndrome indicated significantly (P < 0.0005) greater circulating INSL3 levels and those with low ovarian reserve showed significantly (P < 0.002) decreased INSL3 values. LIMITATIONS, REASONS FOR CAUTION: These were retrospective studies and the results were obtained from natural cycles only, with their inherent variability. WIDER IMPLICATIONS OF THE FINDINGS: We show for the first time that INSL3 in women does vary across the menstrual cycle, and appears to reflect the number of growing antral follicles recruited within both follicular and luteal phases. STUDY FUNDING/COMPETING INTEREST(S): The present retrospective study was largely supported by departmental funds. There were no competing interests.

Chess endgame news

This note defines what it means by the 'chess endgame' and looks at the frequency of sub-n-man and 'FinalGen' positions in games and studies and in the FIDE 2013 World Cup. It includes the exposition of the DTM-minimaxing line from one of the three DTM-deepest known (KQPKRBN) positions. It refines the definitions of 'longest game' and 'bionic game'. The games of the FIDE 2013 World Cup and the longest known decisive game are available here.

Transreal calculus

Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal tangent function and extend continuity and limits from the real domain to the transreal domain. With this preparation, we extend the real derivative to the transreal derivative and extend proper integration from the real domain to the transreal domain. Further, we extend improper integration of absolutely convergent functions from the real domain to the transreal domain. This demonstrates that transreal calculus contains real calculus and operates at singularities where real calculus fails.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Investigating relationships within and between category networks in Wikipedia

This work maps and analyses cross-citations in the areas of Biology, Mathematics, Physics and Medicine in the English version of Wikipedia, which are represented as an undirected complex network where the entries correspond to nodes and the citations among the entries are mapped as edges. We found a high value of clustering coefficient for the areas of Biology and Medicine, and a small value for Mathematics and Physics. The topological organization is also different for each network, including a modular structure for Biology and Medicine, a sparse structure for Mathematics and a dense core for Physics. The networks have degree distributions that can be approximated by a power-law with a cut-off. The assortativity of the isolated networks has also been investigated and the results indicate distinct patterns for each subject. We estimated the betweenness centrality of each node considering the full Wikipedia network, which contains the nodes of the four subjects and the edges between them. In addition, the average shortest path length between the subjects revealed a close relationship between the subjects of Biology and Physics, and also between Medicine and Physics. Our results indicate that the analysis of the full Wikipedia network cannot predict the behavior of the isolated categories since their properties can be very different from those observed in the full network. (C) 2011 Elsevier Ltd. All rights reserved.