Extensions of system signatures to dependent lifetimes: Explicit expressions and interpretations

The concept of system signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. We consider its extension to the continuous dependent case and give an explicit expression for this extension as a difference of weighted means of the structure function values. We then derive a formula for the computation of the coefficients of these weighted means in the special case of independent continuous lifetimes. Finally, we interpret this extended concept of signature through a natural least squares approximation problem

Component importance measures for complex repairable system

In recent years, the system signature has been recognized as an important tool to quantify the reliability of systems consist of independent and identically distributed (iid) or exchangeable components with respect the random failure times. System signature separates the system structure from the component probabilistic failure distribution. However, when it is adopted to solve a complex system with more than one component type, it requires the computation of the probabilities of all possible different ordering statistics of each component failure lifetime distributions, which is often an intractable procedure

Nonparametric predictive inference for system failure time based on bounds for the signature

System signatures provide a powerful framework for reliability assessment for systems consisting of exchangeable components. The use of signatures in nonparametric predictive inference has been presented and leads to lower and upper survival functions for the system failure time, given failure times of tested components. However, deriving the system signature is computationally complex. This article presents how limited information about the signature can be used to derive bounds on such lower and upper survival functions and related inferences. If such bounds are sufficiently decisive they also indicate that more detailed computation of the system signature is not required

Symmetric approximations of pseudo-Boolean functions with applications to influence indexes

We introduce an index for measuring the influence of the k-th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear combinations of order statistic functions. We give explicit expressions for both the index and the approximation and discuss some properties of the index. Finally, we show that this index subsumes the concept of system signature in engineering reliability and that of cardinality index in decision making

Elucidating the genotype-phenotype map by automatic enumeration and analysis of the phenotypic repertoire.

BackgroundThe gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process.MethodsThe strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters.ResultsOur strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed.ConclusionsStarting with a system's relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy

Desk study on the control of weeds in organic arable and horticultural production systems OF0152

The Ministry is seeking to encourage an expansion of organic farming with a research programme to provide information of benefit to organic farmers and to policy makers. The lack of a reliable and effective weed control system that does not rely on herbicides, has been highlighted as the major problem in limiting the growth of organic farming in the UK. Studies have been made that are aimed specifically at developing organic weed control techniques. There has also been work on non-chemical methods for dealing with weeds in conventional systems. Research in weed biology, population dynamics, and competition modelling from conventional systems also provide valuable information for improving weed control strategies. In addition, research into novel and improved methods of plant husbandry, plant breeding, and the application of new technology in guidance systems etc., can also make a contribution to providing better weed control in organic and conventional systems. However, because of the diverse nature of the research it is not easy to assess the current state of the art for weed control in organic farming systems. The main objective of the present project was to identify and collate the relevant R&D that has been carried out and published on weed control in organic arable and horticultural production systems. The study was also intended to define the current state of the art in non chemical weed control, allowing recommendations to be made for future research work

Cultural methods for controlling docks in organically farmed grassland (extension 1998-99) (OFT0115T)

Docks are considered to be one of the main weed problems of grassland. The absence of an effective non-chemical control may be a deterrent to organic-conversion for farmers accustomed to using herbicides for dock control. This work addresses this problem in the context of MAFF policy to encourage more farmers to adopt organic farming, and to encourage a reduction in the use of herbicides in farming generally. The project was based around hypotheses that physical techniques and management strategies can affect the relative competitiveness of docks within the grass-based sward, and that by exploiting this relative competitiveness the problem can be reduced or contained within acceptable limits. During the initial phase of the project (01/05/95 to 31/03/98) we investigated these hypotheses through a series of four linked experimental objectives. The results obtained during that period (i.e. the 1996 and 1997 seasons) were reported to MAFF in a CSG13 in 1998. In the case of two of these experiments in particular, it was apparent that the observation and recording periods were too short to draw meaningful conclusions, and that the value of the overall project would be improved by an additional recording period. This CSG13 updates the previous one and reports primarily on the results from these two experiments obtained during 1998-99 (the 1998 growing season). The outcomes of these two approaches (Objectives 2 and 3 on the original CSG7) are summarized below. Objective 2: Trials were carried out to determine the effects of using a mechanical soil aerator in spring, and its timing, on the subsequent development of docks in existing dock-infested areas of silage fields (action through stimulation of grass growth in spring through improved soil physical conditions, and/or potentially deleterious effect on docks by severing their rooting systems). The findings of this experiment during 1996 and 1997 were encouraging but showed the need for evaluations over a longer period than two years. The experiment was conducted in a situation where docks were increasing and dock ramet density increased on all treatments. The greatest increase occurred on the non-aerated control. The most significant effect resulted from the aeration treatment made in April (compared with June or April-plus-June). In the third year, 1998, there were no significant differences between the control and the three aeration treatments. Our overall conclusion from the three years of results with this technique on just one site is that it is a technique which offers some control of dock, but refining of the management guidelines and evaluation on a field scale on different soils are required. Objective 3: Micro-plot trials using transplanted, spaced dock plants (to provide uniform density in swards) were used to investigate the effects of a wide range of options for controlling dock plants by cutting. Treatments included cutting at different intervals and to different residual sward heights. Assessments of results from 1996 had shown that the proportion of dock in the total herbage DM was lowest in treatments which were defoliated at regular 4-5 week intervals, and highest under less frequently defoliated regimes which simulated silage and hay regimes. These assessments were repeated in 1997 and the differences widened. However, total herbage DM yield was also higher on the ‘hay’ and ‘silage’ treatments, though differences were proportionately less than for the dock component. The micro-plot trial recorded in 1998 had been established from dock plug plants transplanted in 1996 and recorded in 1997. This method proved to be an effective one for establishment of experimental dock infestations of uniform density needed for investigations of this type, and one that would be practicable if required on a larger scale. The more frequently cut treatments had the lowest proportion of dock in the total herbage harvested, though this was in Year 2 only. This was a very similar result to that from the similar trial that had been recorded during 1996 and 1997. It seems likely that the effects resulting from cutting frequency may be cumulative, and at least two years of the frequent cutting may be required before dock plant size and vigor is reduced. The duration of these trials has not been long enough to determine whether long-term frequent cutting can eventually result in the elimination of dock plants. The effect of cutting height, which had no significant effects in either year of the experiment recorded in 1996 and 1997, was a significant factor affecting docks in the second year of this experiment. The low cutting height was favourable to docks. It seems likely that docks either respond to the lower cutting height by morphological adaptation, or that the lower sward height reduces the relative competitiveness of the other sward components. The results obtained from this suite of experiments (including the objectives completed before 1 April 1998) indicate that physical methods have a role in containing dock problems to an acceptable level, particularly in ensuring that flowering and seed dispersal does not occur. If resources were to be available for future work our recommendations would include the following: (1) The use of the soil mechanical treatment has been encouraging though further on-farm field-scale evaluations and refinement of management guidelines are needed before this can be recommended for general use by farmers. (2) As frequency of defoliation appears to be a factor affecting growth of docks and their total contribution to the sward, there is a need to establish whether docks can be eliminated, rather than being kept at a manageable level of infestation, and the management factors and timescale associated with this need to be determined. (3) The effects of increased seed rate and cover crop on limiting the development of seedling docks at establishment (shown in sward box studies in the 1996-97 phase of this research contract) needs to be evaluated at the field scale and on different soil types