Classification using log Gaussian Cox processes

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.

Estimating Sensor Motion from Wide-Field Optical Flow on a Log-Dipolar Sensor

Log-polar image architectures, motivated by the structure of the human visual field, have long been investigated in computer vision for use in estimating motion parameters from an optical flow vector field. Practical problems with this approach have been: (i) dependence on assumed alignment of the visual and motion axes; (ii) sensitivity to occlusion form moving and stationary objects in the central visual field, where much of the numerical sensitivity is concentrated; and (iii) inaccuracy of the log-polar architecture (which is an approximation to the central 20°) for wide-field biological vision. In the present paper, we show that an algorithm based on generalization of the log-polar architecture; termed the log-dipolar sensor, provides a large improvement in performance relative to the usual log-polar sampling. Specifically, our algorithm: (i) is tolerant of large misalignmnet of the optical and motion axes; (ii) is insensitive to significant occlusion by objects of unknown motion; and (iii) represents a more correct analogy to the wide-field structure of human vision. Using the Helmholtz-Hodge decomposition to estimate the optical flow vector field on a log-dipolar sensor, we demonstrate these advantages, using synthetic optical flow maps as well as natural image sequences.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

La Mancha Triassic and Lower Lias Stratigraphy, a well log interpretation

La estratigrafía del intervalo sedimentario correspondiente al Keuper, Triásico, y al Lías basal ha atraído históricamente mucho menos interés que los sedimentos adyacentes del Muschelkalk y Buntsandstein, y del Lías Inferior y Medio. Se ha confeccionado una correlación de 12 sondeos profundos del área de La Mancha para mostrar la distribución de facies de estas formaciones, así como su ordenación en secuencias sedimentarias. Los datos de pozo muestran la existencia de secuencias evaporíticas complejas y multiepisódicas en la unidad inferior K1, de carácter más salino, y en la unidad superior K4-K5, relativamente más anhidrítica. El episodio clástico correspondiente a las unidades K2-K3 está extendido en toda la zona, con varias áreas preferenciales de acumulación de arenas. La unidad K6, la más alta del Keuper, constituye un excelente nivel guía. La sedimentación continúa en el Lías basal con otra potente unidad evaporítica, la Zona de Anhidrita, que muestra un episodio salino muy signifi cativo en la parte central de la correlación. Es de resaltar la buena correlación que existe entre los afl oramientos y las sondeos para estas formaciones.

Log gf values for astrophysically important transitions Fe II

Aims. In a recent measurement, Meléndez & Barbuy (2009, A&A, 497, 611) report accurate log gf values for 142 important astrophysical lines with wavelengths in the range 4000 Å to 8000 Å. Their results include both solar and laboratory measurements. In this paper, we describe a theoretical study of these lines. Methods. The CIV3 structure codes, combined with our "fine-tuning" extrapolation process, are used to undertake a large-scale CI calculation involving the lowest 262 fine-structure levels belonging to the 3d4s, 3d, 3d4s, 3d4p, and 3d4s4p configurations. Results. We find that many of the 142 transitions are very weak intercombination lines. Other transitions are weak because the dominant configurations in the two levels differ by two orbitals. Conclusions. The comparison between our log gf values and the experimental values generally shows good agreement for most of these transitions, with our theoretical values agreeing slightly more closely with the solar than with the laboratory measurements. A detailed analysis of the small number of transitions for which the agreement between theory and experiment is not as good shows that such disagreements largely arise from severe cancellation due to CI mixing.

Monitoring daily MLC positional errors using trajectory log files and EPID measurements for IMRT and VMAT deliveries

This work investigated the differences between multileaf collimator (MLC) positioning accuracy determined using either log files or electronic portal imaging devices (EPID) and then assessed the possibility of reducing patient specific quality control (QC) via phantom-less methodologies. In-house software was developed, and validated, to track MLC positional accuracy with the rotational and static gantry picket fence tests using an integrated electronic portal image. This software was used to monitor MLC daily performance over a 1 year period for two Varian TrueBeam linear accelerators, with the results directly compared with MLC positions determined using leaf trajectory log files. This software was validated by introducing known shifts and collimator errors. Skewness of the MLCs was found to be 0.03 ± 0.06° (mean ±1 standard deviation (SD)) and was dependent on whether the collimator was rotated manually or automatically. Trajectory log files, analysed using in-house software, showed average MLC positioning errors with a magnitude of 0.004 ± 0.003 mm (rotational) and 0.004 ± 0.011 mm (static) across two TrueBeam units over 1 year (mean ±1 SD). These ranges, as indicated by the SD, were lower than the related average MLC positioning errors of 0.000 ± 0.025 mm (rotational) and 0.000 ± 0.039 mm (static) that were obtained using the in-house EPID based software. The range of EPID measured MLC positional errors was larger due to the inherent uncertainties of the procedure. Over the duration of the study, multiple MLC positional errors were detected using the EPID based software but these same errors were not detected using the trajectory log files. This work shows the importance of increasing linac specific QC when phantom-less methodologies, such as the use of log files, are used to reduce patient specific QC. Tolerances of 0.25 mm have been created for the MLC positional errors using the EPID-based automated picket fence test. The software allows diagnosis of any specific leaf that needs repair and gives an indication as to the course of action that is required.

Correlation of phantom-based and log file patient-specific QA with complexity scores for VMAT

The motivation for this study was to reduce physics workload relating to patient- specific quality assurance (QA). VMAT plan delivery accuracy was determined from analysis of pre- and on-treatment trajectory log files and phantom-based ionization chamber array measurements. The correlation in this combination of measurements for patient-specific QA was investigated. The relationship between delivery errors and plan complexity was investigated as a potential method to further reduce patient-specific QA workload. Thirty VMAT plans from three treatment sites - prostate only, prostate and pelvic node (PPN), and head and neck (H&N) - were retrospectively analyzed in this work. The 2D fluence delivery reconstructed from pretreatment and on-treatment trajectory log files was compared with the planned fluence using gamma analysis. Pretreatment dose delivery verification was also car- ried out using gamma analysis of ionization chamber array measurements compared with calculated doses. Pearson correlations were used to explore any relationship between trajectory log file (pretreatment and on-treatment) and ionization chamber array gamma results (pretreatment). Plan complexity was assessed using the MU/ arc and the modulation complexity score (MCS), with Pearson correlations used to examine any relationships between complexity metrics and plan delivery accu- racy. Trajectory log files were also used to further explore the accuracy of MLC and gantry positions. Pretreatment 1%/1 mm gamma passing rates for trajectory log file analysis were 99.1% (98.7%-99.2%), 99.3% (99.1%-99.5%), and 98.4% (97.3%-98.8%) (median (IQR)) for prostate, PPN, and H&N, respectively, and were significantly correlated to on-treatment trajectory log file gamma results (R = 0.989, p < 0.001). Pretreatment ionization chamber array (2%/2 mm) gamma results were also significantly correlated with on-treatment trajectory log file gamma results (R = 0.623, p < 0.001). Furthermore, all gamma results displayed a significant correlation with MCS (R > 0.57, p < 0.001), but not with MU/arc. Average MLC position and gantry angle errors were 0.001 ± 0.002 mm and 0.025° ± 0.008° over all treatment sites and were not found to affect delivery accuracy. However, vari- ability in MLC speed was found to be directly related to MLC position accuracy. The accuracy of VMAT plan delivery assessed using pretreatment trajectory log file fluence delivery and ionization chamber array measurements were strongly correlated with on-treatment trajectory log file fluence delivery. The strong corre- lation between trajectory log file and phantom-based gamma results demonstrates potential to reduce our current patient-specific QA. Additionally, insight into MLC and gantry position accuracy through trajectory log file analysis and the strong cor- relation between gamma analysis results and the MCS could also provide further methodologies to both optimize the VMAT planning and QA process.