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.