Censored linear regression in the presence or absence of auxiliary survival information

There has been a rising interest in better exploiting auxiliary summary information from large databases in the analysis of smaller-scale studies that collect more comprehensive patient-level information. The purpose of this paper is twofold: first, we propose a novel approach to synthesize information from both the aggregate summary statistics and the individual-level data in censored linear regression. We show that the auxiliary information amounts to a system of nonsmooth estimating equations and thus can be combined with the conventional weighted log-rank estimating equations by using the generalized method of moments (GMM) approach. The proposed methodology can be further extended to account for the potential inconsistency in information from different sources. Second, in the absence of auxiliary information, we propose to improve estimation efficiency by combining the overidentified weighted log-rank estimating equations with different weight functions via the GMM framework. To deal with the nonsmooth GMM-type objective functions, we develop an asymptotics-guided algorithm for parameter and variance estimation. We establish the asymptotic normality of the proposed GMM-type estimators. Simulation studies show that the proposed estimators can yield substantial efficiency gain over the conventional weighted log-rank estimators. The proposed methods are applied to a pancreatic cancer study for illustration.     

Self-organizing maps: stationary states,metastability and convergence rate

We investigate the effect of various types of neighborhood function on the convergence rates and the presence or absence of metastable stationary states of Kohonen's self-organizing feature map algorithm in one dimension. We demonstrate that the time necessary to form a topographic representation of the unit interval [0, 1] may vary over several orders of magnitude depending on the range and also the shape of the neighborhood function, by which the weight changes of the neurons in the neighborhood of the winning neuron are scaled. We will prove that for neighborhood functions which are convex on an interval given by the length of the Kohonen chain there exist no metastable states. For all other neighborhood functions, metastable states are present and may trap the algorithm during the learning process. For the widely-used Gaussian function there exists a threshold for the width above which metastable states cannot exist. Due to the presence or absence of metastable states, convergence time is very sensitive to slight changes in the shape of the neighborhood function. Fastest convergence is achieved using neighborhood functions which are "convex" over a large range around the winner neuron and yet have large differences in value at neighboring neurons.     

Evaluation of a particle swarm algorithm for biomechanical optimization

Optimization is frequently employed in biomechanics research to solve system identification problems, predict human movement, or estimate muscle or other internal forces that cannot be measured directly. Unfortunately, biomechanical optimization problems often possess multiple local minima, making it difficult to find the best solution. Furthermore, convergence in gradient-based algorithms can be affected by scaling to account for design variables with different length scales or units. In this study we evaluate a recently-developed version of the particle swarm optimization (PSO) algorithm to address these problems. The algorithm's global search capabilities were investigated using a suite of difficult analytical test problems, while its scale-independent nature was proven mathematically and verified using a biomechanical test problem. For comparison, all test problems were also solved with three off-the-shelf optimization algorithms--a global genetic algorithm (GA) and multistart gradient-based sequential quadratic programming (SQP) and quasi-Newton (BFGS) algorithms. For the analytical test problems, only the PSO algorithm was successful on the majority of the problems. When compared to previously published results for the same problems, PSO was more robust than a global simulated annealing algorithm but less robust than a different, more complex genetic algorithm. For the biomechanical test problem, only the PSO algorithm was insensitive to design variable scaling, with the GA algorithm being mildly sensitive and the SQP and BFGS algorithms being highly sensitive. The proposed PSO algorithm provides a new off-the-shelf global optimization option for difficult biomechanical problems, especially those utilizing design variables with different length scales or units.     

Uniform step-by-step observer for aerobic bioreactor based on super-twisting algorithm

This paper describes a fixed-time convergent step-by-step high order sliding mode observer for a certain type of aerobic bioreactor system. The observer was developed using a hierarchical structure based on a modified super-twisting algorithm. The modification included nonlinear gains of the output error that were used to prove uniform convergence of the estimation error. An energetic function similar to a Lyapunov one was used for proving the convergence between the observer and the bioreactor variables. A nonsmooth analysis was proposed to prove the fixed-time convergence of the observer states to the bioreactor variables. The observer was tested to solve the state estimation problem of an aerobic bioreactor described by the time evolution of biomass, substrate and dissolved oxygen. This last variable was used as the output information because it is feasible to measure it online by regular sensors. Numerical simulations showed the superior behavior of this observer compared to the one having linear output error injection terms (high-gain type) and one having an output injection obtaining first-order sliding mode structure. A set of numerical simulations was developed to demonstrate how the proposed observer served to estimate real information obtained from a real aerobic process with substrate inhibition.     

Limited-Memory Fast Gradient Descent Method for Graph Regularized Nonnegative Matrix Factorization

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix to the product of two lower-rank nonnegative factor matrices, i.e., and () and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton''s method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.     

On second order sensitivity for stage-based population projection matrix models

In this paper we present a simple method for identifying life-history perturbations in population projection matrices that yield an accelerating population growth rate. Accelerating growth means that the dependence of the growth rate on the perturbation is convex. Convexity, when the second sensitivity of the growth rate is positive, is calculated using a new formula derived from the transfer function of the perturbed system. This formula is used to explore the relationship between stasis and growth probabilities from stage-structured population projection matrices.     

Efficient computation of Hessian-based enhancement filters for tubular structures in 3D images

This work presents guidelines for a computationally efficient implementation of multiscale image filters based on eigenanalysis of the Hessian matrix, for the enhancement of tubular structures. Our focus is the application to 3D medical images of blood vessels. The method uses matrix trace, determinant and sign to discard voxels unlikely to belong to vessels, prior to the calculation of the Hessian eigenvalues. As example of time savings, we provide results obtained in four computed tomography datasets (300 × 300 × 300 voxels) containing coronary and pulmonary arteries. The test based on the Hessian trace avoided the computation of the eigenvalues in half of the voxels on average, while the test combining the Hessian determinant and sign eliminated up to 10% additional voxels. The actual time savings depend on the algorithm used to compute the eigenvalues for the remaining voxels. With a very fast algorithm using a closed-form solution, the computational time was reduced from 20.5 to 12.5 seconds per scale, but the time gained thanks to the more complex of the two tests was negligible. However, this fast algorithm is prone to numerical instabilities. Accurate computation of the eigenvalues requires the use of iterative or hybrid algorithms. In this case, both tests produce time savings and the computational time can be reduced by several minutes per scale.     

Improving metabolic flux estimation via evolutionary optimization for convex solution space

MOTIVATION: Flux estimation by using (13) C-labeling pattern information of metabolites is currently the only method that can give accurate, detailed quantification of all intracellular fluxes in the central metabolism of a microorganism. In essence, it corresponds to a constrained optimization problem which minimizes a weighted distance between measured and simulated results. Characteristics, such as existence of multiple local minima, non-linear and non-differentiable make this problem a special difficulty. RESULTS: In the present work, we propose an evolutionary-based global optimization algorithm taking advantage of the convex feature of the problem's solution space. Based on the characteristics of convex spaces, specialized initial population and evolutionary operators are designed to solve (13)C-based metabolic flux estimation problem robustly and efficiently. The algorithm was applied to estimate the central metabolic fluxes in Escherichia coli and compared with conventional optimization technique. Experimental results illustrated that our algorithm is capable of achieving fast convergence to good near-optima and maintaining the robust nature of evolutionary algorithms at the same time. AVAILABILITY: Available from the authors upon request.     

A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.     

Sequential search and the influence of male quality on female mating decisions

 The patterns of phenotypic association between mated males and females depend on the decision rules that individuals employ during search for a mate. We generalize the sequential search rule and examine how the shape of the function that relates a male character to the benefit of a mating decision influences the threshold value of the male trait that induces females to terminate search. If the fitness function is linear the optimal threshold value of a male character increases with the slope of the function. The phenotypic threshold criterion declines, all else being equal, if the fitness function is made more concave (or less convex) by an increase of the risk of the function. The expression of the trait in females has no effect on the optimal threshold value of a male character if the fitness function is linear and phenotypic values combine additively to influence the benefit of a mating decision; the phenotypic threshold criterion is ubiquitous among females. A convex fitness function induces females with high trait values to adopt a relatively high phenotypic threshold criterion, whereas a concave fitness function induces such females to adopt a low threshold value for the male trait. Thus, linear, convex and concave fitness functions effect random, assortative and disassortative combinations of phenotypes among mated individuals, respectively. Changes of female search behavior induced by changes of the distribution of a male character similarly depend on the shape of the fitness function. A variance-preserving increase of male trait values produces a relatively small increase of the threshold criterion for the male character if the fitness function is concave, relative to conditions in which the fitness function is either linear or convex. Our results suggest that a sequential search rule can in principle induce the kinds of mating patterns observed in nature and that the phenotypic association between mated individuals is likely to depend on how a male character translates into fitness, the distribution of the trait among males and attributes of searching females. Received: 20 September 1997 / Revised version: 13 August 1998     

Economic impact of Hessian fly (Diptera: Cecidomyiidae) on spring wheat in Oregon and additive yield losses with Fusarium crown rot and lesion nematode

Damage caused by Hessian fly, Mayetiola destructor (Say), was quantified in spring wheat, Triticum aestivum L., trials near Pendleton and Moro, OR, during 2001 and 2002. Five field experiments were established to examine genetic resistance to Fusarium crown rot, Fusarium pseudograminearum (O'Donnell & Aoki), and economic damage by lesion nematode, Pratylenchus neglectus (Rensch, 1924) (Filipjev Schuurmanns & Stekhoven, 1941) and Pratylenchus thornei (Sher & Allen, 1941). Hessian fly became the dominant factor affecting grain yield in four experiments. Genotypes carrying the H3-resistance gene had grain yields 66 and 68% higher than susceptible genotypes in cultivar trials during 2001 and 2002, respectively. Yield reductions were detected when Hessian fly infestation rates exceeded 50% plants during 2001 and 15% plants (8% tillers) during 2002. In two trials during 2001, in-furrow application of aldicarb (Temik) at planting improved yields of four Hessian fly-susceptible cultivars by 72 and 144% (up to 1,959 kg/ha) and yields of one Hessian fly-resistant cultivar by 2 and 3%. Resistant cultivars and aldicarb improved grain quality as much as two market grades during 2001. The value of increased grain production with Hessian fly-resistant cultivars in four field experiments ranged from dollar 112 to dollar 252/ha, excluding price incentives for improved market quality. Yield reduction due to combined damage from Hessian fly and either Fusarium crown rot or lesion nematode was additive. This report seems to be the first quantitative yield loss estimate for Hessian fly in spring wheat in the semiarid environment of the inland Pacific Northwest.     

Microarray missing data imputation based on a set theoretic framework and biological knowledge

Gene expressions measured using microarrays usually suffer from the missing value problem. However, in many data analysis methods, a complete data matrix is required. Although existing missing value imputation algorithms have shown good performance to deal with missing values, they also have their limitations. For example, some algorithms have good performance only when strong local correlation exists in data while some provide the best estimate when data is dominated by global structure. In addition, these algorithms do not take into account any biological constraint in their imputation. In this paper, we propose a set theoretic framework based on projection onto convex sets (POCS) for missing data imputation. POCS allows us to incorporate different types of a priori knowledge about missing values into the estimation process. The main idea of POCS is to formulate every piece of prior knowledge into a corresponding convex set and then use a convergence-guaranteed iterative procedure to obtain a solution in the intersection of all these sets. In this work, we design several convex sets, taking into consideration the biological characteristic of the data: the first set mainly exploit the local correlation structure among genes in microarray data, while the second set captures the global correlation structure among arrays. The third set (actually a series of sets) exploits the biological phenomenon of synchronization loss in microarray experiments. In cyclic systems, synchronization loss is a common phenomenon and we construct a series of sets based on this phenomenon for our POCS imputation algorithm. Experiments show that our algorithm can achieve a significant reduction of error compared to the KNNimpute, SVDimpute and LSimpute methods.     

A scaled line-based kernel density estimator for the retrieval of utilization distributions and home ranges from GPS movement tracks

Utilization distributions (UDs) can be used to describe the intensity with which an animal or human has used a certain geographical location. Within the domain of wildlife ecology, a density distribution model represents one way to describe an animals' home range. Several methods have been developed to derive UDs, and subsequently home ranges. Most of these methods, e.g. kernel density estimation (KDE), and local convex hull methods, have been developed with point-based datasets in mind, and do not utilize additional information that comes with GPS-based tracking data (e.g., temporal information). To employ such additional information we extend the point-based KDE approach to work with sequential GPS-point tracks, the outcome of which is a line-based KDE. We first describe the design criteria for the line-KDE algorithm. Then we introduce the basic modeling approach and its refinement through the introduction of a scaling function. This scaling function modifies the utilization distribution so that a bone-like probability distribution for a single GPS track segment is obtained. Finally we compare the estimated utilization distributions and home ranges for two datasets derived using our line-KDE approach with those obtained using the point-KDE and Brownian Bridge (BB) approaches. Advantages of the line-based KDE by design are (i) a better representation of utilization density near GPS points when compared against the BB approach, and (ii) the ability to model and retain movement corridors when compared against point-KDE.     

Theoretical study of W values in hydrocarbon gases

The recent measurements by D. Srdoc, B. Obeli?, and I. Krajcar Broni? (J. Phys. B, 20, 4473-4484, 1987) and by I. Krajcar Broni?, D. Srdoc, and B. Obeli? (Radiat. Res., 115, 213-222, 1988) revealed nonsmooth, oscillatory variation of the W value for low-energy electrons as a function of the number of carbon atoms in normal alkanes. This behavior is contrary to what has been expected generally and prompted us to undertake the present study. Calculations were carried out using the continuous-slowing-down approximation for the degradation spectrum, the binary-encounter theory for cross sections, and relevant molecular properties, to explain the behavior of the W value. The main contributor to the oscillatory variation is the branching ratio for neutral dissociation to ionization of super-excited states. We also present an interpretation of the trend of the W value in the series C2H2, C2H4, and C2H6.     

Virulence in Hessian fly (Diptera: Cecidomyiidae) field collections from the southeastern United States to 21 resistance genes in wheat

Genetic resistance in wheat, Triticum aestivum L., is the most efficacious method for control of Hessian fly, Mayetiola destructor (Say) (Diptera: Cecidomyiidae). However, because of the appearance of new genotypes (biotypes) in response to deployment of resistance, field collections of Hessian fly need to be evaluated on a regular basis to provide breeders and producers information on the efficacy of resistance (R) genes with respect to the genotype composition of Hessian fly in regional areas. We report here on the efficacy of 21 R genes in wheat to field collections of Hessian fly from the southeastern United States. Results documented that of the 21 R genes evaluated only five would provide effective protection of wheat from Hessian fly in the southeastern United States. These genes were H12, H18, H24, H25, and H26. Although not all of the 33 identified R genes were evaluated in the current study, these results indicate that identified genetic resistance to protect wheat from Hessian attack in the southeastern United States is a limited resource. Historically, R genes for Hessian fly resistance in wheat have been deployed as single gene releases. Although this strategy has been successful in the past, we recommend that in the future deployment of combinations of highly effective previously undeployed genes, such as H24 and H26, be considered. Our study also highlights the need to identify new and effective sources of resistance in wheat to Hessian fly if genetic resistance is to continue as a viable option for protection of wheat in the southeastern United States.     

A pseudolikelihood method for analyzing interval censored data

We introduce a method based on a pseudolikelihood ratio forestimating the distribution function of the survival time ina mixed-case interval censoring model. In a mixed-case model,an individual is observed a random number of times, and at eachtime it is recorded whether an event has happened or not. Oneseeks to estimate the distribution of time to event. We usea Poisson process as the basis of a likelihood function to constructa pseudolikelihood ratio statistic for testing the value ofthe distribution function at a fixed point, and show that thisconverges under the null hypothesis to a known limit distribution,that can be expressed as a functional of different convex minorantsof a two-sided Brownian motion process with parabolic drift.Construction of confidence sets then proceeds by standard inversion.The computation of the confidence sets is simple, requiringthe use of the pool-adjacent-violators algorithm or a standardisotonic regression algorithm. We also illustrate the superiorityof the proposed method over competitors based on resamplingtechniques or on the limit distribution of the maximum pseudolikelihoodestimator, through simulation studies, and illustrate the differentmethods on a dataset involving time to HIV seroconversion ina group of haemophiliacs.     

An MLP training algorithm taking into account known errors on inputs and outputs

A training algorithm is introduced that takes into account a priori known errors on both inputs and outputs in an MLP network. The new cost function introduced for this case is based on a linear approximation of the network function over the input distribution for a given input pattern. Update formulas, in the form of the gradient of the new cost function, is given for a MLP network, together with expressions for the Hessian matrix. This is later used to calculate error bars in a Bayesian framework. The error bars thus derived are discussed in relation to the more commonly used width of the target posterior predictive distribution. It will also be shown that the taking into account of known input uncertainties in the way suggested in this article will have a strong regularizing effect on the solution.