Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions

It is of interest in some applications to determine whether there is a relationship between a hazard rate function (or a cumulative incidence function) and a mark variable which is only observed at uncensored failure times. We develop nonparametric tests for this problem when the mark variable is continuous. Tests are developed for the null hypothesis that the mark-specific hazard rate is independent of the mark versus ordered and two-sided alternatives expressed in terms of mark-specific hazard functions and mark-specific cumulative incidence functions. The test statistics are based on functionals of a bivariate test process equal to a weighted average of differences between a Nelson--Aalen-type estimator of the mark-specific cumulative hazard function and a nonparametric estimator of this function under the null hypothesis. The weight function in the test process can be chosen so that the test statistics are asymptotically distribution-free.Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. Specifically, the tests are used to assess if the instantaneous or absolute risk of treatment failure depends on the amount of accumulation of drug resistance mutations in a subject's HIV virus. This assessment helps guide development of anti-HIV therapies that surmount the problem of drug resistance.

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

The utility of preoperative six-minute-walk distance in lung transplantation

RATIONALE The use of 6-minute-walk distance (6MWD) as an indicator of exercise capacity to predict postoperative survival in lung transplantation has not previously been well studied. OBJECTIVES To evaluate the association between 6MWD and postoperative survival following lung transplantation. METHODS Adult, first time, lung-only transplantations per the United Network for Organ Sharing database from May 2005 to December 2011 were analyzed. Kaplan-Meier methods and Cox proportional hazards modeling were used to determine the association between preoperative 6MWD and post-transplant survival after adjusting for potential confounders. A receiver operating characteristic curve was used to determine the 6MWD value that provided maximal separation in 1-year mortality. A subanalysis was performed to assess the association between 6MWD and post-transplant survival by disease category. MEASUREMENTS AND MAIN RESULTS A total of 9,526 patients were included for analysis. The median 6MWD was 787 ft (25th-75th percentiles = 450-1,082 ft). Increasing 6MWD was associated with significantly lower overall hazard of death (P < 0.001). Continuous increase in walk distance through 1,200-1,400 ft conferred an incremental survival advantage. Although 6MWD strongly correlated with survival, the impact of a single dichotomous value to predict outcomes was limited. All disease categories demonstrated significantly longer survival with increasing 6MWD (P ≤ 0.009) except pulmonary vascular disease (P = 0.74); however, the low volume in this category (n = 312; 3.3%) may limit the ability to detect an association. CONCLUSIONS 6MWD is significantly associated with post-transplant survival and is best incorporated into transplant evaluations on a continuous basis given limited ability of a single, dichotomous value to predict outcomes.

The utility of N5 for gene therapy of human cancer

Cancer is a result of defects in the coordination of cell proliferation and programmed cell death. The extent of cell death is physiologically controlled by the activation of a programmed suicide pathway that results in a morphologically recognizable form of death termed apoptosis. Inducing apoptosis in tumor cells by gene therapy provides a potentially effective means to treat human cancers. The p84N5 is a novel nuclear death domain containing protein that has been shown to bind an amino terminal domain of retinoblastoma tumor suppressor gene product (pRb). Expression of N5 can induce apoptosis that is dependent upon its intact death domain and is inhibited by pRb. In many human cancer cells the functions of pRb are either lost through gene mutation or inactivated by different mechanisms. N5 based gene therapy may induce cell death preferentially in tumor cells relative to normal cells. We have demonstrated that N5 gene therapy is less toxic to normal cells than to tumor cells. To test the possibility that N5 could be used in gene therapy of cancer, we have generated a recombinant adenovirus engineered to express N5 and test the effects of viral infection on growth and tumorigenicity of human cancer cells. Adenovirus N5 infection significantly reduced the proliferation and tumorigenicity of breast, ovarian, and osteosarcoma tumor cell lines. Reduced proliferation and tumorigenicity were mediated by an induction of apoptosis as indicated by DNA fragmentation in infected cells. We also test the potential utility of N5 for gene therapy of pancreatic carcinoma that typically respond poorly to conventional treatment. Adenoviral mediated N5 gene transfer inhibits the growth of pancreatic cancer cell lines in vitro. N5 gene transfer also reduces the growth and metastasis of human pancreatic adenocarcinoma in subcutaneous and orthotopic mouse model. Interestingly, the pancreatic adenocarcinoma cells are more sensitive to N5 than they are to p53, suggesting that N5 gene therapy may be effective in tumors resistant to p53. We also test the possibilities of the use of N5 and p53 together on the inhibition of pancreatic cancer cell growth in vitro and vivo. Simultaneous use of N5 and RbΔCDK has been found to exert a greater extent on the inhibition of pancreatic cancer cell growth in vitro and in vivo. ^

MLL, a mammalian trithorax-group gene, functions as a transcriptional maintenance factor in morphogenesis

Determinative events in vertebrate embryogenesis appear to require the continuous expression of spatial regulators such as the clustered homeobox genes. The mechanisms that govern long-term patterns of gene expression are not well understood. In Drosophila, active and silent states of developmentally regulated loci are maintained by trithorax and Polycomb group. We have examined the developmental role of a mammalian homolog of trx and putative oncogene, Mll. Knockout mice reveal that Mll is required for maintenance of gene expression early in embryogenesis. Downstream targets of Mll including Hoxa7 are activated appropriately in the absence of Mll but require Mll for sustaining their expression. The Mll−/− phenotype manifests later in development and is characterized by branchial arch dysplasia and aberrant segmental boundaries of spinal ganglia and somites. Thus, Mll represents an essential mechanism of transcriptional maintenance in mammalian development, which functions in multiple morphogenetic processes.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.

Transient prenatal vitamin D deficiency is associated with subtle alterations in learning and memory functions in adult rats

Based on clues from epidemiology, low prenatal vitamin D has been proposed as a candidate risk factor for schizophrenia. Recent animal experiments have demonstrated that transient prenatal vitamin D deficiency is associated with persistent alterations in brain morphology and neurotrophin expression. In order to explore the utility of the vitamin D animal model of schizophrenia, we examined different types of learning and memory in adult rats exposed to transient prenatal vitamin D deficiency. Compared to control animals, the prenatally deplete animals had a significant impairment of latent inhibition, a feature often associated with schizophrenia. In addition, the deplete group was (a) significantly impaired on hole board habituation and (b) significantly better at maintaining previously learnt rules of brightness discrimination in a Y-chamber. In contrast, the prenatally deplete animals showed no impairment on the spatial learning task in the radial maze, nor on two-way active avoidance learning in the shuttle-box. The results indicate that transient prenatal vitamin D depletion in the rat is associated with subtle and discrete alterations in learning and memory. The behavioural phenotype associated with this animal model may provide insights into the neurobiological correlates of the cognitive impairments of schizophrenia. (c) 2005 Elsevier B.V. All rights reserved.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Why people underestimate y when extrapolating in linear functions

E. L. DeLosh, J. R. Busemeyer, and M. A. McDaniel (1997) found that when learning a positive, linear relationship between a continuous predictor (x) and a continuous criterion (y), trainees tend to underestimate y on items that ask the trainee to extrapolate. In 3 experiments, the authors examined the phenomenon and found that the tendency to underestimate y is reliable only in the so-called lower extrapolation region-that is, new values of x that lie between zero and the edge of the training region. Existing models of function learning, such as the extrapolation-association model (DeLosh et al., 1997) and the population of linear experts model (M. L. Kalish, S. Lewandowsky, & J. Kruschke, 2004), cannot account for these results. The authors show that with minor changes, both models can predict the correct pattern of results.

On building a principled framework for evaluating and testing evolutionary algorithms: A continuous landscape generator

In this paper, we address some issue related to evaluating and testing evolutionary algorithms. A landscape generator based on Gaussian functions is proposed for generating a variety of continuous landscapes as fitness functions. Through some initial experiments, we illustrate the usefulness of this landscape generator in testing evolutionary algorithms.

Polymer fractionation by continuous chromatography

A review is given of general chromatographic theory, the factors affecting the performance of chromatographi c columns, and aspects of scale-up of the chromatographic process. The theory of gel permeation chromatography (g. p. c.) is received, and the results of an experimental study to optimize the performance of an analytical g.p.c. system are reported. The design and construction of a novel sequential continuous chromatographic refining unit (SCCR3), for continuous liquid-liquid chromatography applications, is described. Counter-current operation is simulated by sequencing a system of inlet and outlet port functions around a connected series of fixed, 5.1 cm internal diameter x 70 cm long, glass columns. The number of columns may be varied, and, during this research, a series of either twenty or ten columns was used. Operation of the unit for continuous fractionation of a dextran polymer (M. W. - 30,000) by g.p.c. is reported using 200-400 µm diameter porous silica beads (Spherosil XOB07S) as packing, and distilled water for the mobile phase. The effects of feed concentration, feed flow rate, and mobile and stationary phase flow rates have been investigated, by means of both product, and on-column, concentrations and molecular weight distributions. The ability to operate the unit successfully at on-column concentrations as high as 20% w/v dextran has been demonstrated, and removal of both high and low molecular weight ends of a polymer feed distribution, to produce products meeting commercial specifications, has been achieved. Equivalent throughputs have been as high as 2.8 tonnes per annum for ten columns, based on continuous operation for 8000 hours per annum. A concentration dependence of the equilibrium distribution coefficient, KD observed during continuous fractionation studies, is related to evidence in the literature and experimental results obtained on a small-scale batch column. Theoretical treatments of the counter-current chromatographic process are outlined, and a preliminary computer simulation of the SCCR3 unit t is presented.

Vector Combinatorial Problems in a Space of Combinations with Linear Fractional Functions of Criteria

The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linear- fractional functions of criteria on a set of combinations.

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo