Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co

Use of hydrophilic and hydrophobic polymers for the development of controlled release tizanidine matrix tablets

The aim of the present study was to develop tizanidine controlled release matrix. Formulations were designed using central composite method with the help of design expert version 7.0 software. Avicel pH 101 in the range of 14-50% was used as a filler, while HPMC K4M and K100M in the range of 25-55%, Ethylcellulose 10 ST and 10FP in the range of 15 - 45% and Kollidon SR in the range of 25-60% were used as controlled release agents in designing different formulations. Various physical parameters including powder flow for blends and weight variation, thickness, hardness, friability, disintegration time and in-vitro release were tested for tablets. Assay of tablets were also performed as specified in USP 35 NF 32. Physical parameters of both powder blend and compressed tablets such as compressibility index, angle of repose, weight variation, thickness, hardness, friability, disintegration time and assay were evaluated and found to be satisfactory for formulations K4M2, K4M3, K4M9, K100M2, K100M3, K100M9, E10FP2, E10FP9, KSR2, KSR3 & KSR9. In vitro dissolution study was conducted in 900 ml of 0.1N HCl, phosphate buffer pH 4.5 and 6.8 medium using USP Apparatus II. In vitro release profiles indicated that formulations prepared with Ethocel 10 standard were unable to control the release of drug while formulations K4M2, K100M9, E10FP2 & KSR2 having polymer content ranging from 40-55% showed a controlled drug release pattern in the above mentioned medium. Zero-order drug release kinetics was observed for formulations K4M2, K100M9, E10FP2 & KSR2. Similarity test (f2) results for K4M2, E10FP2 & KSR2 were found to be comparable with reference formulation K100M9. Response Surface plots were also prepared for evaluating the effect of independent variable on the responses. Stability study was performed as per ICH guidelines and the calculated shelf life was 24-30 months for formulation K4M2, K100M9 and E10FP2

The PLATO mission

PLATO (PLAnetary Transits and Oscillations of stars) is ESA’s M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2R ) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5%, 10%, 10% for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO‘s target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile towards the end of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases

Variational method in relativistic quantum field theory without cutoff

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the 3 requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.Comment: v2 - major update on the algorithm v1 - 4 pages - see same posting for a longer companion paper "Relativistic continuous matrix product states for quantum fields without cutoff" containing more derivations, context, and explanation

Characterization of Linaria KNOX genes suggests a role in petal-spur development

Spurs are tubular outgrowths of perianth organs that have evolved iteratively among angiosperms. They typically contain nectar and often strongly influence pollinator specificity, potentially mediating reproductive isolation. The identification of Antirrhinum majus mutants with ectopic petal spurs suggested that petal-spur development is dependent on the expression of KNOTTED 1-like homeobox (KNOX) genes, which are better known for their role in maintaining the shoot apical meristem. Here, we tested the role of KNOX genes in petal-spur development by isolating orthologs of the A. majus KNOX genes Hirzina (AmHirz) and Invaginata (AmIna) from Linaria vulgaris, a related species that differs from A. majus in possessing long, narrow petal spurs. We name these genes LvHirz and LvIna, respectively. Using quantitative reverse-transcription PCR, we show that LvHirz is expressed at high levels in the developing petals and demonstrate that the expression of petal-associated KNOX genes is sufficient to induce sac-like outgrowths on petals in a heterologous host. We propose a model in which KNOX gene expression during early petal-spur development promotes and maintains further morphogenetic potential of the petal, as previously described for KNOX gene function in compound leaf development. These data indicate that petal spurs could have evolved by changes in regulatory gene expression that cause rapid and potentially saltational phenotypic modifications. Given the morphological similarity of spur ontogeny in distantly related taxa, changes in KNOX gene expression patterns could be a shared feature of spur development in angiosperms. Mathew S. Box, Steven Dodsworth, Paula J. Rudall, Richard M. Bateman, Beverley J. Glove