Non-monotonic Pattern Research Articles

Solving unconstrained optimization problem with a filter-based nonmonotone pattern search algorithm

This paper proposes a new frame-based pattern search algorithm for unconstrained optimization. The implementation of filter leads the sequence of function values at iterates { x ( k ) } nonmonotonically decreasing and thus motivates us to consider nonmonotone technique. Furthermore, the use of these two techniques can improve the efficiency of general pattern search algorithms. The numerical results show that the new algorithm is practical and efficient.

Towards patterns tree of gene coexpression in eukaryotic species

Cellular pathways behave coordinated regulation activity, and some reported works also have affirmed that genes in the same pathway have similar expression pattern. However, the complexity of biological systems regulation actually causes expression relationships between genes to display multiple patterns, such as linear, non-linear, local, global, linear with time-delayed, non-linear with time-delayed, monotonic and non-monotonic, which should be the explicit representation of cellular inner regulation mechanism in mRNA level. To investigate the relationship between different patterns, our work aims to systematically reveal gene-expression relationship patterns in cellular pathways and to check for the existence of dominating gene-expression pattern. By a large scale analysis of genes expression in three eukaryotic species, Saccharomyces cerevisiae, Caenorhabditis elegans and Human, we constructed gene coexpression patterns tree to systematically and hierarchically illustrate the different patterns and their interrelations. The results show that the linear is the dominating expression pattern in the same pathway. The time-shifted pattern is another important relationship pattern. Many genes from the different pathway also present coexpression patterns. The non-linear, non-monotonic and time-delayed relationship patterns reflect the remote interactions between the genes in cellular processes. Gene coexpression phenomena in the same pathways are diverse in different species. Genes in S.cerevisiae and C.elegans present strong coexpression relationships, especially in C.elegans, coexpression is more universal and stronger due to its special array of genes. However in Human, gene coexpression is not apparent and the human genome involves more complicated functional relationships. In conclusion, different patterns corresponding to different coordinating behaviors coexist. The patterns trees of different species give us comprehensive insight and understanding of genes expression activity in the cellular society.

Earnings Inequality and Skill-Biased Technological Change with Endogenous Choice of Education

This article analyzes the impact of stochastic skill-biased technological change on earnings inequality in a general equilibrium OLG model. Wage dispersion is determined by the heterogeneity of skills by allowing for productivity differences due to education, ability, and age. The model performs well in reproducing stylized facts on the time pattern of the U.S. wage distribution and human capital accumulation. In particular, it shows that slow adjustment of the supply of educated labor can itself explain the nonmonotonic time pattern of the college premium. (JEL: D31, J24, J31)

Testing Monotonicity of Pricing Kernels

The behaviour of market agents has always been extensively covered in the literature. Risk averse behaviour, described by von Neumann and Morgenstern (1944) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over uncertain choice with the same expected value, however lately there has been a lot of discussion about the reliability of this approach. Some authors have shown that there is a reference point where market utility functions are convex. In this paper we have constructed a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotone decreasing EPK corresponds to a concave utility function while non-monotone decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigated the EPK for German DAX data for years 2000, 2002 and 2004 and found the evidence of non-concave utility functions: H0 hypothesis of monotone decreasing pricing kernel was rejected at 5% and 10% significance level in 2002 and at 10% significance level in 2000.

Demodulation of a single interferogram based on continuous wavelet transform and phase derivative

A novel method based on continuous wavelet transform (CWT) and guidance of phase derivative is developed to measure the phase of a single fringe pattern which contains closed fringes. Wrapped phase values are retrieved by ridge extraction algorithms based on CWT which has the capability of better noise reduction and thus increases the resolution of measurement significantly. To further reduce the noise, the scales detected by maximum ridge algorithm are filtered iteratively before retrieval of wrapped phase. The proposed method also identifies any ambiguous point in a non-monotonous fringe pattern by directly tracking an inflexion point from an unwrapped phase map without the use of a carrier. The algorithm developed is validated by computer simulation and experimental results. Based on micro interferometry the experimental results for both static and dynamic deformations of a micro structure demonstrate that the proposed method is an effective tool for the analysis of closed fringe patterns and subsequent deformation measurement. However, the proposed technique is limited to measurement of surface which is relatively smooth compared to the mean wavelength of the light source. In addition, prior knowledge of the sign of surface slope is required in cases where a spatial carrier is not available or adaptable.

Bayesian hierarchical multiresolution hazard model for the study of time-dependent failure patterns in early stage breast cancer

The multiresolution estimator, developed originally in engineering applications as a wavelet-based method for density estimation, has been recently extended and adapted for estimation of hazard functions (Bouman et al. 2005, 2007). Using the multiresolution hazard (MRH) estimator in the Bayesian framework, we are able to incorporate any a priori desired shape and amount of smoothness in the hazard function. The MRH method's main appeal is in its relatively simple estimation and inference procedures, making it possible to obtain simultaneous confidence bands on the hazard function over the entire time span of interest. Moreover, these confidence bands properly reflect the multiple sources of uncertainty, such as multiple centers or heterogeneity in the patient population. Also, rather than the commonly employed approach of estimating covariate effects and the hazard function separately, the Bayesian MRH method estimates all of these parameters jointly, thus resulting in properly adjusted inference about any of the quantities.In this paper, we extend the previously proposed MRH methods (Bouman et al. 2005, 2007) into the hierarchical multiresolution hazard setting (HMRH), to accommodate the case of separate hazard rate functions within each of several strata as well as some common covariate effects across all strata while accounting for within-stratum correlation. We apply this method to examine patterns of tumor recurrence after treatment for early stage breast cancer, using data from two large-scale randomized clinical trials that have substantially influenced breast cancer treatment standards. We implement the proposed model to estimate the recurrence hazard and explore how the shape differs between patients grouped by a key tumor characteristic (estrogen receptor status) and treatment types, after adjusting for other important patient characteristics such as age, tumor size and progesterone level. We also comment on whether the hazards exhibit nonmonotonic patterns consistent with recent hypotheses suggesting multiple hazard change-points at specific time landmarks.

Bias in regression coefficient estimates upon different treatments of systematically missing data

In this simulation study, the bias in regression coefficient estimates was investigated in a four-predictor multiple regression model involving four missing data treatments, namely expectation maximization (EM), mean substitution (MS), pairwise deletion (PD) and regression imputation (RI) methods. This was done under different conditions of percent missing, pattern of systematically missing data and non-normality. Findings indicate no significant difference across the four MDTs in the bias for b2, b3 and b4, the regression coefficients of X 2 , X 3 and X 4 , respectively. Therefore, only the bias in b1, the regression coefficient of the variable with no missing data, is reported. Overall, the bias under monotonic missing pattern was lower than that under non-monotonic missing pattern. For monotonic pattern, the lowest bias was under regression imputation (RI), followed by expectation-maximization method (EM). For this pattern, mean substitution (MS), pairwise deletion (PD) and regression imputation (RI) consistently overestimated the population parameter, regardless of percent missing and level of non-normality. The overestimation consistently increased with percent missing. The findings under non-monotonic pattern indicate that RI had the lowest bias, followed by EM. MS and PW consistently overestimated the population parameter. EM and RI, on the other hand, tended to consistently underestimate the population parameter under non-monotonic pattern. Keywords : Missing data, bias, regression, percent missing, non-normality, missing pattern > East African Journal of Statistics Vol. 1 (2) 2006: pp. 185-197

Bias in regression coefficient estimates upon different treatments of systematically missing data

In this simulation study, the bias in regression coefficient estimates was investigated in a four-predictor multiple regression model involving four missing data treatments, namely expectation maximization (EM), mean substitution (MS), pairwise deletion (PD) and regression imputation (RI) methods. This was done under different conditions of percent missing, pattern of systematically missing data and non-normality. Findings indicate no significant difference across the four MDTs in the bias for b2, b3 and b4, the regression coefficients of X2, X3 and X4, respectively. Therefore, only the bias in b1, the regression coefficient of the variable with no missing data, is reported. Overall, the bias under monotonic missing pattern was lower than that under non-monotonic missing pattern. For monotonic pattern, the lowest bias was under regression imputation (RI), followed by expectation-maximization method (EM). For this pattern, mean substitution (MS), pairwise deletion (PD) and regression imputation (RI) consistently overestimated the population parameter, regardless of percent missing and level of non-normality. The overestimation consistently increased with percent missing. The findings under non-monotonic pattern indicate that RI had the lowest bias, followed by EM. MS and PW consistently overestimated the population parameter. EM and RI, on the other hand, tended to consistently underestimate the population parameter under non-monotonic pattern. Keywords: Missing data, bias, regression, percent missing, non-normality, missing pattern > East African Journal of Statistics Vol. 1 (2) 2006: pp. 185-197

Weighted estimating equations for longitudinal studies with death and non‐monotone missing time‐dependent covariates and outcomes

We propose a marginal modeling approach to estimate the association between a time-dependent covariate and an outcome in longitudinal studies where some study participants die during follow-up and both variables have non-monotone response patterns. The proposed method is an extension of weighted estimating equations that allows the outcome and covariate to have different missing-data patterns. We present methods for both random and non-random missing-data mechanisms. A study of functional recovery in a cohort of elderly female hip-fracture patients motivates the approach.

Binary polymeric blends to microencapsulate nitroflurbiprofen: Physicochemical and in silico studies

Nitroflurbiprofen, NFP, a practically insoluble liquid drug, was microencapsulated in hydrophilic micromatrices made of poly( N-vinylpyrrolidone) (PVP), or polyaminomethacrylate (PAMA), or binary blends of polymers thereof. The PAMA/PVP miscibility was assessed both in the solid state (DSC and ATF-FTIR spectroscopy) and in solution by viscometric measurements. The in vitro NFP release test was carried out in over saturation condition to discriminate the increase of NFP apparent solubility (supersaturation degree, SD). Drug/polymer/polymer/water interactions were studied in silico by molecular dynamic (MD) simulations. PAMA and PVP resulted miscible only in aqueous solution. The release of NFP from microparticles occurred according to a non-monotonic pattern due to the formation of instable supersaturated systems and the drug separation in the dissolution medium. After 5 min, the SD was at least 3. The use of PVP/PAMA micromatrices reduced the instability of the supersaturated solutions. MD simulations evidenced that water molecules play a key role in the PAMA/PVP compatibilization process and in stabilization of NFP supersaturated systems by means of H-bond. The docking analyses here find a novel and successful application to predict the different ability of a drug to interact with polymeric blends in solution.

The Duration of Fixed Exchange Rate Regimes

This paper studies the survival of fixed exchange rate regimes. The probability of an exit from a fixed exchange rate regime depends on the time spent within this regime. In such a context durations models are appropriate, in particular because of the possible non-monotonic pattern of duration dependence. Non-parametric estimates show that the pattern of duration dependence exhibits non-monotonic behaviour and that it differs across types of economies. This behaviour persists when we control for time-varying covariates in a proportional hazard specification. We conclude that how long a regime has lasted will affect the probability that it will end, in a non-monotonic fashion.

Population Size, Change, and Crime in U.S. Cities

The sometimes noted contradiction between cross-sectional and longitudinal relationships concerning city population size and crime rates is reexamined using more complex analytic procedures, controlling for extraneous variables, and allowing for non-monotonic relationships. Instead of a simple cross-sectional relationship between population size and crime rates, the more sophisticated analysis reveals either no association or a quadratic relationship. Similarly, instead of a simple lack of longitudinal relationship or a negative one, the more complicated analysis shows a non-monotonic pattern for three of six offenses. However, we contend that these divergent patterns for cross-sectional relative to longitudinal data are not necessarily indicative of an “anomaly.” Instead, they represent different aspects of a dynamic process in need of more extensive theorizing. Finally, the cross-sectional results showing that city size and crime rates are either not linked or when linked are in a non-monotonic pattern call into question one of the accepted relationships in criminology that have long guided thinking about crime.

ACCUMULATION AND DISTRIBUTION OF URANIUM IN RATS AFTER CHRONIC EXPOSURE BY INGESTION

Data describing the biokinetics of radionuclides after contamination come mainly from experimental acute exposures of laboratory animals and follow-up of incidental exposures of humans. These data were compiled to form reference models that could be used for dose calculation in humans. In case of protracted exposure, the same models are applied, assuming that they are not modified by the duration of exposure. This work aims at testing this hypothesis. It presents new experimental data on retention of uranium after chronic intake, which are compared to values calculated from a biokinetic model that is based on experiments of acute exposure of rats to uranium. Experiments were performed with 56 male Sprague Dawley rats, from which 35 were exposed during their whole adult life to 40 mg L of uranyl nitrate dissolved in mineral water and 21 were kept as controls. Animals were euthanatized at 32, 95, 186, 312, 368, and 570 d after the beginning of contamination. Urine and all tissues were removed, weighted, mineralized, and then analyzed for uranium content by Kinetics Phosphorescence Analysis (KPA) or by ICP-MS. Experimental data showed that uranium accumulated in most organs, following a nonmonotonous pattern. Peaks of activities were observed at 1-3, 10, and 19 mo after the beginning of exposure. Additionally, accumulation was shown to occur in tissues such as teeth and brain that are not usually described as target organs. Comparison with model prediction showed that the accumulation of uranium in target organs after chronic exposure is overestimated by the use of a model designed for acute exposure. These differences indicate that protracted exposure to uranium may induce changes in biokinetic parameters when compared to acute contamination and that calculation of dose resulting from chronic intake of radionuclides may need specific models that are not currently available.

Pseudo-likelihood methods for longitudinal binary data with non-ignorable missing responses and covariates

In this paper we consider longitudinal studies in which the outcome to be measured over time is binary, and the covariates of interest are categorical. In longitudinal studies it is common for the outcomes and any time-varying covariates to be missing due to missed study visits, resulting in non-monotone patterns of missingness. Moreover, the reasons for missed visits may be related to the specific values of the response and/or covariates that should have been obtained, i.e. missingness is non-ignorable. With non-monotone non-ignorable missing response and covariate data, a full likelihood approach is quite complicated, and maximum likelihood estimation can be computationally prohibitive when there are many occasions of follow-up. Furthermore, the full likelihood must be correctly specified to obtain consistent parameter estimates. We propose a pseudo-likelihood method for jointly estimating the covariate effects on the marginal probabilities of the outcomes and the parameters of the missing data mechanism. The pseudo-likelihood requires specification of the marginal distributions of the missingness indicator, outcome, and possibly missing covariates at each occasions, but avoids making assumptions about the joint distribution of the data at two or more occasions. Thus, the proposed method can be considered semi-parametric. The proposed method is an extension of the pseudo-likelihood approach in Troxel et al. to handle binary responses and possibly missing time-varying covariates. The method is illustrated using data from the Six Cities study, a longitudinal study of the health effects of air pollution.

Bayesian methods for early detection of changes in childhood cancer incidence: Trends for acute lymphoblastic leukaemia are consistent with an infectious aetiology

Published data on time trends in the incidence of childhood leukaemia show inconsistent patterns, with some studies showing increases and others showing relatively stable incidence rates. Data on time trends in childhood cancer incidence from the Childhood Cancer Registry of Piedmont, Italy were analysed using two different approaches: standard Poisson regression and a Bayesian regression approach including an autoregressive component. Our focus was on acute lymphoblastic leukaemia (ALL), since this is hypothesised to have an infectious aetiology, but for purposes of comparison we also conducted similar analyses for selected other childhood cancer sites (acute non-lymphoblastic leukaemia (AnLL), central nervous system (CNS) tumours and neuroblastoma (NB)). The two models fitted the data equally well, but led to different interpretations of the time trends. The first produced ever-increasing rates, while the latter produced non-monotonic patterns, particularly for ALL, which showed evidence of a cyclical pattern. The Bayesian analysis produced findings that are consistent with the hypothesis of an infectious aetiology for ALL, but not for AnLL or for solid tumours (CNS and NB). Although sudden changes in time trends should be interpreted with caution, the results of the Bayesian approach are consistent with current knowledge of the natural history of childhood ALL, including a short latency time and the postulated infectious aetiology of the disease.

Volatile fractionation in the early solar system and chondrule/matrix complementarity.

Bulk chondritic meteorites and terrestrial planets show a monotonic depletion in moderately volatile and volatile elements relative to the Sun's photosphere and CI carbonaceous chondrites. Although volatile depletion was the most fundamental chemical process affecting the inner solar nebula, debate continues as to its cause. Carbonaceous chondrites are the most primitive rocks available to us, and fine-grained, volatile-rich matrix is the most primitive component in these rocks. Several volatile depletion models posit a pristine matrix, with uniform CI-like chemistry across the different chondrite groups. To understand the nature of volatile fractionation, we studied minor and trace element abundances in fine-grained matrices of a variety of carbonaceous chondrites. We find that matrix trace element abundances are characteristic for a given chondrite group; they are depleted relative to CI chondrites, but are enriched relative to bulk compositions of their parent meteorites, particularly in volatile siderophile and chalcophile elements. This enrichment produces a highly nonmonotonic trace element pattern that requires a complementary depletion in chondrule compositions to achieve a monotonic bulk. We infer that carbonaceous chondrite matrices are not pristine: they formed from a material reservoir that was already depleted in volatile and moderately volatile elements. Additional thermal processing occurred during chondrule formation, with exchange of volatile siderophile and chalcophile elements between chondrules and matrix. This chemical complementarity shows that these chondritic components formed in the same nebula region.

Agglomeration in a vertically-related oligopoly

This paper examines the location of three vertically-linked firms. In a spatial economy composed of two regions, a monopolist firm supplies an input to two consumer goods firms that compete in quantities. It is concluded that agglomeration is more likely to occur when the ratio between the transport cost of the intermediate good and the transport cost of the final good is higher. If this proportion is low, the likelihood of an agglomeration decreases with transport costs. If the ratio has an intermediate value, a non-monotonic pattern is obtained that is different from Krugman and Venables (1995).

Multiple imputation of missing data with ante-dependence covariance structure

A controlled clinical trial was conducted to investigate the efficacy effect of a chemical compound in the treatment of Premenstrual Dysphoric Disorder (PMDD). The data from the trial showed a non-monotone pattern of missing data and an ante-dependence covariance structure. A new analytical method for imputing the missing data with the ante-dependence covariance is proposed. The PMDD data are analysed by the non-imputation method and two imputation methods: the proposed method and the MCMC method.

Comparative Analysis of Age Dynamics of Average Values of Body Dimensions in Children from Birth to 7 years

Mean values of different body dimensions in different age cohorts of children make it possible to learn a lot about their dynamic changes. Their comparative analysis, as is usually practiced, in fact leads to a simple description of changes in measurement units (mm or cm) at the average level of some body dimension during a shorter or longer period of time. To estimate comparative intensity of the growth process of different body dimensions, the authors use the analogue of Mahalanobis distance, the so-called Kullback divergence (1967), which does not demand stability of dispersion or correlation coefficients of dimensions in compared cohorts of children. Most of the dimensions, excluding skinfolds, demonstrate growth dynamics with gradually reducing increments from birth to 7 years. Body length has the highest integrative increment, leg length about 94% of body length, body mass 77%, and trunk and extremities circumferences 56%. Skinfolds have a non-monotonic pattern of accumulated standardized increments with some increase until 1-2 years of age.

Sensitivity analysis of longitudinal binary data with non-monotone missing values.

This paper highlights the consequences of incomplete observations in the analysis of longitudinal binary data, in particular non-monotone missing data patterns. Sensitivity analysis is advocated and a method is proposed based on a log-linear model. A sensitivity parameter that represents the relationship between the response mechanism and the missing data mechanism is introduced. It is shown that although this parameter is identifiable, its estimation is highly questionable. A far better approach is to consider a range of plausible values and to estimate the parameters of interest conditionally upon each value of the sensitivity parameter. This allows us to assess the sensitivity of study's conclusion to assumptions regarding the missing data mechanism. The method is applied to a randomized clinical trial comparing the efficacy of two treatment regimens in patients with persistent asthma.