Fitting models for the joint action of two drugs using SAS(R)

Combinations of drugs are increasingly being used for a wide variety of diseases and conditions. A pre-clinical study may allow the investigation of the response at a large number of dose combinations. In determining the response to a drug combination, interest may lie in seeking evidence of synergism, in which the joint action is greater than the actions of the individual drugs, or of antagonism, in which it is less. Two well-known response surface models representing no interaction are Loewe additivity and Bliss independence, and Loewe or Bliss synergism or antagonism is defined relative to these. We illustrate an approach to fitting these models for the case in which the marginal single drug dose-response relationships are represented by four-parameter logistic curves with common upper and lower limits, and where the response variable is normally distributed with a common variance about the dose-response curve. When the dose-response curves are not parallel, the relative potency of the two drugs varies according to the magnitude of the desired effect and the models for Loewe additivity and synergism/antagonism cannot be explicitly expressed. We present an iterative approach to fitting these models without the assumption of parallel dose-response curves. A goodness-of-fit test based on residuals is also described. Implementation using the SAS NLIN procedure is illustrated using data from a pre-clinical study. Copyright © 2007 John Wiley & Sons, Ltd.

The Prony fitting method for digital deconvolution problem

The Prony fitting theory is applied in this paper to solve the deconvolution problem. There are two cases in deconvolution in which unstable solution is easy to appear. They are: (1)the frequency band of known kernel is more narraw than that of the unknown kernel; (2) there exists noise. These two cases are studied thoroughly and the effectiveness of Prony fitting method is showed. Finally, this method is simulated in computer. The simulation results are compared with those obtained by using FFT method directly.

Re-fitting Etton: space, time and material culture within a causewayed enclosure in Cambridgeshire

This paper considers the dynamics of deposition around and across the causewayed enclosure at Etton, Cambridgeshire. As a result of detailed re-analysis (particularly refitting) of the pottery and flint assemblages from the site, it proved possible to shed new light both on the temporality of occupation and the character of deposition there. Certain aspects of our work challenge previous interpretations of the site, and of causewayed enclosures in general; but, just as importantly, others confirm materially what has previously been suggested. The quantities of material deposited at Etton reveal that the enclosure was occupied only very intermittently and certainly less regularly than other contemporary sites in the region. The spatial distribution of material suggests that the enclosure ditch lay open for the entirety of the monument's life, but that acts of deposition generally focused on a specific part of the monument at any one time. As well as enhancing our knowledge of one particular causewayed enclosure, it is hoped that this paper – in combination with our earlier analysis of the pit site at Kilverstone – makes clear the potential that detailed material analysis has to offer in relation to our understanding of the temporality of occupation on prehistoric sites in general.

A Generic Deformable Model for Vehicle Recognition

This paper reports the development of a highly parameterised 3-D model able to adopt the shapes of a wide variety of different classes of vehicles (cars, vans, buses, etc), and its subsequent specialisation to a generic car class which accounts for most commonly encountered types of car (includng saloon, hatchback and estate cars). An interactive tool has been developed to obtain sample data for vehicles from video images. A PCA description of the manually sampled data provides a deformable model in which a single instance is described as a 6 parameter vector. Both the pose and the structure of a car can be recovered by fitting the PCA model to an image. The recovered description is sufficiently accurate to discriminate between vehicle sub-classes.

A Filter for Visual Tracking Based on a Stochastic Model for Driver Behaviour

A driver controls a car by turning the steering wheel or by pressing on the accelerator or the brake. These actions are modelled by Gaussian processes, leading to a stochastic model for the motion of the car. The stochastic model is the basis of a new filter for tracking and predicting the motion of the car, using measurements obtained by fitting a rigid 3D model to a monocular sequence of video images. Experiments show that the filter easily outperforms traditional filters.

Hierarchical modeling of entangled polymers

We demonstrate that it is possible to link multi-chain molecular dynamics simulations with the tube model using a single chain slip-links model as a bridge. This hierarchical approach allows significant speed up of simulations, permitting us to span the time scales relevant for a comparison with the tube theory. Fitting the mean-square displacement of individual monomers in molecular dynamics simulations with the slip-spring model, we show that it is possible to predict the stress relaxation. Then, we analyze the stress relaxation from slip-spring simulations in the framework of the tube theory. In the absence of constraint release, we establish that the relaxation modulus can be decomposed as the sum of contributions from fast and longitudinal Rouse modes, and tube survival. Finally, we discuss some open questions regarding possible future directions that could be profitable in rendering the tube model quantitative, even for mildly entangled polymers

Displacement of Zn through acidic light-textured soils

In order to gain understanding of the movement of pollutant metals in soil. the chemical mechanisms involved in the transport of zinc were studied. The displacement of zinc through mixtures of sand and cation exchange resin was measured to validate the methods used for soil. With cation exchange capacities of 2.5 and 5.0 cmol(c) kg(-1). 5.6 and 8.4 pore volumes of 10 mM CaCl2, respectively, were required to displace a pulse of ZnCl2. A simple Burns-type model (Wineglass) using an adsorption coefficient (K-d) determined by fitting a straight line relationship to an adsorption isotherm gave a good fit to the data (K-d=0.73 and 1.29 ml g(-1), respectively). Surface and subsurface samples of an acidic sandy loam (organic matter 4.7 and 1.0%. cation exchange capacity (CEC) 11.8 and 6.1 cmol(c) kg(-1) respectively) were leached with 10 mM calcium chloride. nitrate and perchlorate. With chloride. the zinc pulse was displaced after 25 and 5 pore volumes, respectively. The Kd values were 6.1 and 2.0 ml g(-1). but are based on linear relationships fitted to isotherms which are both curved and show hysteresis. Thus. a simple model has limited value although it does give a general indication of rate of displacement. Leaching with chloride and perchlorate gave similar displacement and Kd values, but slower movement occurred with nitrate in both soil samples (35 and 7 pore volumes, respectively) which reflected higher Kd values when the isotherms were measured using this anion (7.7 and 2.8 ml g(-1) respectively). Although pH values were a little hi-her with nitrate in the leachates, the differences were insufficient to suggest that this increased the CEC enough to cause the delay. No increases in pH occurred with nitrate in the isotherm experiments. Geochem was used to calculate the proportions of Zn complexed with the three anions and with fulvic acid determined from measurements of dissolved organic matter. In all cases, more than 91% of the Zn was present as Zn2+ and there were only minor differences between the anions. Thus, there is an unexplained factor associated with the greater adsorption of Zn in the presence of nitrate. Because as little as five pore volumes of solution displaced Zn through the subsurface soil, contamination of ground waters may be a hazard where Zn is entering a light-textured soil, particularly where soil salinity is increased. Reductions in organic matter content due to cultivation will increase the hazard. (C) 2004 Elsevier B.V. All rights reserved.

Wiggle-match dating of tree-ring sequences

Given the non-monotonic form of the radiocarbon calibration curve, the precision of single C-14 dates on the calendar timescale will always be limited. One way around this limitation is through comparison of time-series, which should exhibit the same irregular patterning as the calibration curve. This approach can be employed most directly in the case of wood samples with many years growth present (but not able to be dated by dendrochronology), where the tree-ring series of unknown date can be compared against the similarly constructed C-14 calibration curve built from known-age wood. This process of curve-fitting has come to be called "wiggle-matching." In this paper, we look at the requirements for getting good precision by this method: sequence length, sampling frequency, and measurement precision. We also look at 3 case studies: one a piece of wood which has been independently dendrochronologically dated, and two others of unknown age relating to archaeological activity at Silchester, UK (Roman) and Miletos, Anatolia (relating to the volcanic eruption at Thera).

Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.

A GIS-based empirical model for vegetation prediction in Lefka Ori, Crete

The aim of the study was to establish and verify a predictive vegetation model for plant community distribution in the alti-Mediterranean zone of the Lefka Ori massif, western Crete. Based on previous work three variables were identified as significant determinants of plant community distribution, namely altitude, slope angle and geomorphic landform. The response of four community types against these variables was tested using classification trees analysis in order to model community type occurrence. V-fold cross-validation plots were used to determine the length of the best fitting tree. The final 9node tree selected, classified correctly 92.5% of the samples. The results were used to provide decision rules for the construction of a spatial model for each community type. The model was implemented within a Geographical Information System (GIS) to predict the distribution of each community type in the study site. The evaluation of the model in the field using an error matrix gave an overall accuracy of 71%. The user's accuracy was higher for the Crepis-Cirsium (100%) and Telephium-Herniaria community type (66.7%) and relatively lower for the Peucedanum-Alyssum and Dianthus-Lomelosia community types (63.2% and 62.5%, respectively). Misclassification and field validation points to the need for improved geomorphological mapping and suggests the presence of transitional communities between existing community types.

Modelling seasonally varying data: A case study for sudden infant death syndrome (SIDS)

Many time series are measured monthly, either as averages or totals, and such data often exhibit seasonal variability-the values of the series are consistently larger for some months of the year than for others. A typical series of this type is the number of deaths each month attributed to SIDS (Sudden Infant Death Syndrome). Seasonality can be modelled in a number of ways. This paper describes and discusses various methods for modelling seasonality in SIDS data, though much of the discussion is relevant to other seasonally varying data. There are two main approaches, either fitting a circular probability distribution to the data, or using regression-based techniques to model the mean seasonal behaviour. Both are discussed in this paper.