Previous algorithms for constructing regression tree models for longitudinal and multiresponse data have mostly followed the CART approach. Consequently, they inherit the same selection biases and computational difficulties as CART. We propose an alternative, based on the GUIDE approach, that treats each longitudinal data series as a curve and uses chi-squared tests of the residual curve patterns to select a variable to split each node of the tree. Besides being unbiased, the method is applicable to data with fixed and random time points and with missing values in the response or predictor variables. Simulation results comparing its mean squared prediction error with that of MVPART are given, as well as examples comparing it with standard linear mixed effects and generalized estimating equation models. Conditions for asymptotic consistency of regression tree function estimates are also given.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS596 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

An automated method is presented for determining individual leaf positions of the Siemens dual focus multileaf collimator (MLC) using the Siemens BEAMVIEW(PLUS) electronic portal imaging device (EPID). Leaf positions are computed with an error of 0.6 mm at one standard deviation (sigma) using separate computations of pixel dimensions, image distortion, and radiation center. The pixel dimensions are calculated by superimposing the film image of a graticule with the corresponding EPID image. A spatial correction is used to compensate for the optical distortions of the EPID, reducing the mean distortion from 3.5 pixels (uncorrected) per localized x-ray marker to 2 pixels (1 mm) for a rigid rotation and 1 pixel for a third degree polynomial warp. A correction for a nonuniform dosimetric response across the field of view of the EPID images is not necessary due to the sharp intensity gradients across leaf edges. The radiation center, calculated from the average of the geometric centers of a square field at 0 degrees and 180 degrees collimator angles, is independent of graticule placement error. Its measured location on the EPID image was stable to within 1 pixel based on 3 weeks of repeated extensions/retractions of the EPID. The MLC leaf positions determined from the EPID images agreed to within a pixel of the corresponding values measured using film and ionization chamber. Several edge detection algorithms were tested: contour, Sobel, Roberts, Prewitt, Laplace, morphological, and Canny. These agreed with each other to within < or = 1.2 pixels for the in-air EPID images. Using a test pattern, individual MLC leaves were found to be typically within 1 mm of the corresponding record-and-verify values, with a maximum difference of 1.8 mm, and standard deviations of <0.3 mm in the daily reproducibility. This method presents a fast, automatic, and accurate alternative to using film or a light field for the verification and calibration of the MLC.

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The interference model has been widely used and studied in block experiments where the treatment for a particular plot has effects on its neighbor plots. In this paper, we study optimal circular designs for the proportional interference model, in which the neighbor effects of a treatment are proportional to its direct effect. Kiefer's equivalence theorems for estimating both the direct and total treatment effects are developed with respect to the criteria of A, D, E and T. Parallel studies are carried out for the undirectional model, where the neighbor effects do not depend on whether they are from the left or right. Moreover, the connection between optimal designs for the directional and undiretional models is built. Importantly, one can easily develop a computer program for finding optimal designs based on these theorems.1. Introduction. In many agricultural experiments, the treatment assigned to a particular plot could also have effects on its neighbor plots. This is well recognized in literature. See Draper and Guttman (1980), Kempton (1982), Besag and Kempton (1986), Langton (1990), Gill (1993 and Goldringer, Brabant and Kempton (1994), for examples. To adjust the biases caused by these neighbor effects, the interference model is widely adopted. In a block design with n blocks of size k and t treatments, the response, y dij , observed from the jth plot of block i is decomposed into the following items:

In wireless sensor networks (WSNs), provenance records the data source, forwarding, and aggregating information of data packets on their way to the base station. Provenance is critical for assessing the trustworthiness of the received data, diagnosing network failures, detecting early signs of attacks, etc. However, because the provenance size expands rapidly with the increase in packet transmission hops, the provenance schemes developed for use in wired computer networks are not generally applicable to WSNs. Therefore, specific provenance techniques have been developed for WSNs that take into account the constrained resources of sensor nodes. In this paper, we survey such techniques. Special focus in the paper is devoted to a systematic and comprehensive classification of the solutions proposed in the literature. We review each solution by highlighting its pros and cons. Finally, we discuss recent trends in provenance encoding schemes for WSNs.