心肌细胞团搏动整数倍节律的非线性动力学机制

利用心肌细胞耦合模型研究心肌整数倍节律的动力学机理。确定性模型仿真揭示了心肌细胞团同步搏动加周期分岔的节律变化规律;随机模型仿真发现在加周期分岔序列中分岔点附近会出现整数倍节律,其中,0-1整数倍节律产生于从静息到周期1的Hopf分岔点附近,1-2整数倍节律产生于周期1和周期2极限环间的加周期分岔点附近;对系统相空间轨道的分析进一步揭示出整数倍节律是由系统运动在相邻的两个轨道之间随机跃迁形成的。上述分析结果不仅阐明了心肌整数倍节律的机理,并且揭示了各种整数倍节律与加周期分岔序列中相邻节律的内在联系,为重新认识心律变化的规律开辟了新的途径。     

A Comparative Study of Scores for Correspondence Analysis with Ordered Categories

Ordered categorical data can be analysed using correspondence analysis with the ordered categories taken into consideration. Such an analysis was proposed by Beh (1997) and uses orthogonal polynomials which require the input of a scoring scheme to reflect the ordered structure of the categories. This method of correspondence analysis visualises the relationship between the categories, in terms of the location, dispersion and higher order components. The impact of the scoring method on the orthogonal polynomials, and hence upon the correspondence plot and other output of the analysis should therefore be considered. This paper aims at identifying this impact by considering four scoring schemes: integer valued (natural) scores, midrank scores, Nishisato scores and singular vectors from the classical correspondence analysis of the data. It is shown that while the latter two maximise the location component, generally there is little difference when comparing them with the output of the former two scoring schemes. A simple comparative study of profile co-ordinates using different scoring schemes is also discussed.     

On modeling the design of cellular manufacturing systems

A new optimization model is discussed for the design of cellular manufacturing systems. It is based on an integer programming formulation that updates some other models by eliminating redundant machine assignment and cost coefficients dependent on cell configuration. To reduce computational burdens, a simplified integer programming model and a decomposition algorithm are proposed. Several computer solutions were performed to evaluate the performance of the new model. The computational results are discussed.     

Location of zeros of Wiener and distance polynomials

The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated. Also, we examine the quality of such bounds by considering four graph classes and interpret the results.     

Analytical morphometry of seminiferous tubules in maturation arrest: Fourier analysis of the internal contours of tubules

Shape of seminiferous tubuli in maturation arrest, is investigated by harmonic Fourier analysis and upper degree polynomials as attempt to find morphometric parameters useful in morphological diagnosis. Inner luminal contour is considered as a closed curve in a reference system and scattered in a series of points whose coordinates are automatically calculated. Then a software named S.A.M. (Shape Analytical Morphometry) is utilized to find the Kth-order equation and calculate the best-fit curve. Moreover an ellypse is drawn with the same barycenter and axes of original curve. These three curves (real curve, best-fit curve and ellypse) are considered as periodic functions and submitted to Fourier analysis to evaluate the coefficients of the series and the spectrum of harmonics. Among 20 contributors, the subsets of greatest amplitude are selected for comparison and classification in terms of fundamental shape and its perturbations.     

Fixed-point bifurcation analysis in biological models using interval polynomials theory

The paper proposes a systematic method for fixed-point bifurcation analysis in circadian cells and similar biological models using interval polynomials theory. The stages for performing fixed-point bifurcation analysis in such biological systems comprise (i) the computation of fixed points as functions of the bifurcation parameter and (ii) the evaluation of the type of stability for each fixed point through the computation of the eigenvalues of the Jacobian matrix that is associated with the system’s nonlinear dynamics model. Stage (ii) requires the computation of the roots of the characteristic polynomial of the Jacobian matrix. This problem is nontrivial since the coefficients of the characteristic polynomial are functions of the bifurcation parameter and the latter varies within intervals. To obtain a clear view about the values of the roots of the characteristic polynomial and about the stability features they provide to the system, the use of interval polynomials theory and particularly of Kharitonov’s stability theorem is proposed. In this approach, the study of the stability of a characteristic polynomial with coefficients that vary in intervals is equivalent to the study of the stability of four polynomials with crisp coefficients computed from the boundaries of the aforementioned intervals. The efficiency of the proposed approach for the analysis of fixed-point bifurcations in nonlinear models of biological neurons is tested through numerical and simulation experiments.     

Testing differences in relative growth rate: A method avoiding curve fitting and pairing

A method is discussed to test differences in relative growth rates. This method is based on an analysis of variance, with In-transformed plant weight as dependent variable. A significant Group × Time interaction indicates differences in relative growth rates between groups. The advantages over the "classical" and "functional" growth analyses are: (1) No pairing procedure is required. (2) More than two groups may be evaluated in one analysis. (3) No decision is required about the polynomial used to fit the data. (4) By partitioning the interaction effect using orthogonal polynomials insight is gained into the nature of differences in relative growth rate. (5) By concentrating attention on the lower order terms of the polynomials, the influence of extraneous variation on conclusions may be minimized.     

A hybrid method for peptide identification using integer linear optimization, local database search, and quadrupole time-of-flight or OrbiTrap tandem mass spectrometry

A novel hybrid methodology for the automated identification of peptides via de novo integer linear optimization, local database search, and tandem mass spectrometry is presented in this article. A modified version of the de novo identification algorithm PILOT, is utilized to construct accurate de novo peptide sequences. A modified version of the local database search tool FASTA is used to query these de novo predictions against the nonredundant protein database to resolve any low-confidence amino acids in the candidate sequences. The computational burden associated with performing several alignments is alleviated with the use of distributive computing. Extensive computational studies are presented for this new hybrid methodology, as well as comparisons with MASCOT for a set of 38 quadrupole time-of-flight (QTOF) and 380 OrbiTrap tandem mass spectra. The results for our proposed hybrid method for the OrbiTrap spectra are also compared with a modified version of PepNovo, which was trained for use on high-precision tandem mass spectra, and the tag-based method InsPecT. The de novo sequences of PILOT and PepNovo are also searched against the nonredundant protein database using CIDentify to compare with the alignments achieved by our modifications of FASTA. The comparative studies demonstrate the excellent peptide identification accuracy gained from combining the strengths of our de novo method, which is based on integer linear optimization, and database driven search methods.     

Analysis of kinetic data for irreversible enzyme inhibition.

Many organophosphorus compounds are irreversible inhibitors of acetylcholinesterase. The methods used in the literature to determine the inhibition kinetic constants usually involve either manual determination of the slope at various points along the inhibition progress curve or fitting polynomials to the curve. The present study investigates the use of non-linear-regression analysis to determine the various parameters. A method is suggested that yields accurate values for the inhibition constants under a range of circumstances.     

Oxygen consumption and osmoregulatory capacity in Neomysis integer reduce competition for resources among mysid shrimp in a temperate estuary

Results of field surveys and laboratory measurements of oxygen consumption and body fluid osmolality at different salinities in the mysids Neomysis integer, Mesopodopsis slabberi, and Rhopalophthalmus mediterraneus from the Guadalquivir estuary (southwest Spain) were used to test the hypothesis that osmotic stress (oxygen consumption vs. isosmotic points) was lowest at salinities that field distributions suggest are optimal. The three species showed overlapping spatial distributions within the estuary but clear segregation along the salinity gradient: N. integer, M. slabberi, and R. mediterraneus displayed maximal densities at lower, intermediate, and higher salinities, respectively. Adults of N. integer were extremely efficient hyperregulators (isosmotic point 30 per thousand) over the full salinity range tested (3 per thousand-32 per thousand), and their oxygen consumption rates were independent of salinity; adults of M. slabberi were strong hyper- and hyporegulators at salinities between 7 per thousand and 29 per thousand (isosmotic point, 21 per thousand) and showed higher oxygen consumptions at the lowest salinity (6 per thousand); adults of R. mediterraneus hyperregulated at salinities between 19 per thousand and seawater (isosmotic point, 36 per thousand), with the lowest oxygen consumption at salinity around their isosmotic point (35 per thousand). Thus, the osmoregulation capabilities of M. slabberi and R. mediterraneus seem to determine the salinity ranges in which most of their adults live, but this is not so for adults of N. integer. Moreover, maximal field densities of M. slabberi (males and females) and R. mediterraneus (males) occur at the same salinities as the lowest oxygen consumption. In contrast, field distribution of N. integer was clearly biased toward the lower end of the salinity ranges within which it osmoregulated. We hypothesize that the greater euryhalinity of N. integer makes it possible for this species to avoid competition with R. mediterraneus by inhabiting the more stressful oligohaline zone.     

Mapping quantitative trait loci for longitudinal traits in line crosses

Quantitative traits whose phenotypic values change over time are called longitudinal traits. Genetic analyses of longitudinal traits can be conducted using any of the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the trait under the repeated measurements framework, (2) treating the phenotypes measured from different time points as different traits and analyzing the traits jointly on the basis of the theory of multivariate analysis, and (3) fitting a growth curve to the phenotypic values across time points and analyzing the fitted parameters of the growth trajectory under the theory of multivariate analysis. The third approach has been used in QTL mapping for longitudinal traits by fitting the data to a logistic growth trajectory. This approach applies only to the particular S-shaped growth process. In practice, a longitudinal trait may show a trajectory of any shape. We demonstrate that one can describe a longitudinal trait with orthogonal polynomials, which are sufficiently general for fitting any shaped curve. We develop a mixed-model methodology for QTL mapping of longitudinal traits and a maximum-likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to search for the maximum-likelihood estimates of parameters. The method is verified with simulated data and demonstrated with experimental data from a pseudobackcross family of Populus (poplar) trees.     

Optimal nonsingular control of fed-batch fermentation

Presented is a new simple method for multidimensional optimization of fed-batch fermentations based on the use of the orthogonal collocation technique. Considered is the problem of determination of optimal programs for fermentor temperature, substrate concentration in feed, feeding profile, and process duration. By reformulation of the state and control variables is obtained a nonsingular form of the optimization problem which has considerable advantage over the singular case since a complicated procedure for determination of switching times for feeding is avoided. The approximation of the state variables by Lagrange polynomials enables simple incorporation of split boundary conditions in the approximation, and the use of orthogonal collocations provides stability for integration of state and costate variables. The interpolation points are selected to obtain highest accuracy for approximation of the objective functional by the Radau-Lobatto formula. The control variables are determined by optimization of the Hamiltonian at the collocation points with the DFP method. Constraints are imposed on state and control variables.The method is applied for a homogeneous model of fermentation with volume, substrate, biomass, and product concentrations as the state variables. Computer study shows considerable simplicity of the method, its high accuracy for low order of approximation, and efficient convergence.     

A mathematical programming approach for gene selection and tissue classification

MOTIVATION: Extracting useful information from expression levels of thousands of genes generated with microarray technology needs a variety of analytical techniques. Mathematical programming approaches for classification analysis outperform parametric methods when the data depart from assumptions underlying these methods. Therefore, a mathematical programming approach is developed for gene selection and tissue classification using gene expression profiles. RESULTS: A new mixed integer programming model is formulated for this purpose. The mixed integer programming model simultaneously selects genes and constructs a classification model to classify two groups of tissue samples as accurately as possible. Very encouraging results were obtained with two data sets from the literature as examples. These results show that the mathematical programming approach can rival or outperform traditional classification methods.     

Artocarpus (Moraceae)-gall midge pollination mutualism mediated by a male-flower parasitic fungus

A previously undescribed pollination system involving a monoecious tree species, Artocarpus integer (Moraceae), pollinator gall midges, and fungi is reported from a mixed dipterocarp forest in Sarawak, Borneo. The fungus Choanephora sp. (Choanephoraceae, Mucorales, Zygomycetes) infects male inflorescences of A. integer, and gall midges (Contarinia spp., Cecidomyiinae, Diptera) feed on the fungal mycelia and oviposit on the inflorescence. Their larvae also feed on the mycelia and pupate in the inflorescence. The gall midges are also attracted by female inflorescences lacking mycelia, probably due to a floral fragrance similar to that of male inflorescences. Because of the sticky pollen, dominance of Contarinia spp. in flower visitors, and pollen load observed on Contarinia spp. collected on both male and female inflorescences, Artocarpus integer is thought to be pollinated by the gall midges. Although several pathogenic fungi have been reported to have interactions with pollinators, this is the first report on a pollination mutualism in which a fungus plays an indispensable role. The pollination system described here suggests that we should be more aware of the roles fungi can play in pollinations.     

Ternary Organic Solar Cells with Minimum Voltage Losses

A new strategy for designing ternary solar cells is reported in this paper. A low‐bandgap polymer named PTB7‐Th and a high‐bandgap polymer named PBDTTS‐FTAZ sharing the same bulk ionization potential and interface positive integer charge transfer energy while featuring complementary absorption spectra are selected. They are used to fabricate efficient ternary solar cells, where the hole can be transported freely between the two donor polymers and collected by the electrode as in one broadband low bandgap polymer. Furthermore, the fullerene acceptor is chosen so that the energy of the positive integer charge transfer state of the two donor polymers is equal to the energy of negative integer charge transfer state of the fullerene, enabling enhanced dissociation of all polymer donor and fullerene acceptor excitons and suppressed bimolecular and trap assistant recombination. The two donor polymers feature good miscibility and energy transfer from high‐bandgap polymer of PBDTTS‐FTAZ to low‐bandgap polymer of PTB7‐Th, which contribute to enhanced performance of the ternary solar cell.     

Fitting parametrized polynomials with scattered surface data.

Currently used joint-surface models require the measurements to be structured according to a grid. With the currently available tracking devices a large quantity of unstructured surface points can be measured in a relatively short time. In this paper a method is presented to fit polynomial functions to three-dimensional unstructured data points. To test the method spherical, cylindrical, parabolic, hyperbolic, exponential, logarithmic, and sellar surfaces with different undulations were used. The resulting polynomials were compared with the original shapes. The results show that even complex joint surfaces can be modelled with polynomial functions. In addition, the influence of noise and the number of data points was also analyzed. From a surface (diam: 20 mm) which is measured with a precision of 0.2 mm a model can be constructed with a precision of 0.02 mm.     

Design of Nature Reserve System for Red-Crowned Crane in China

A system of nature reserves is a necessary component of an integrated conservation strategy. The basic problem in the design of a nature reserve system is to select the smallest number of sites from a region for some conservation objectives. There are 33 nature reserves intended for the conservation of Red-Crowned Crane (Grus japonensis), totalling 3.1 million ha. Other habitats of Red-Crowned Crane are facing severe problems due to economic development and other human activities. GIS, iterative methods and the integer programming approach were employed to design the nature reserve system for Red-Crowned Crane, with conservation goals to protect 70 and 60% areas of highly and moderately suitable wetlands, respectively. The results indicated the need to designate six new nature reserves in Wulagai marsh, Duluhe River, Tumen River, Rizhao, Gaoyou Lake and Hongze Lake, and showed a protection zone in Songnen Plain (between Heilongjiang Province and Jilin Province) and three clusters of nature reserves in Sanjing Plain, which, will be used as reference for the designation of new nature reserves, or enlargement and adjustment of existing nature reserves. The iterative method and integer programming approaches were feasible for design of nature reserve system.     

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Reducing the Time Requirement of k-Means Algorithm

Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in d-dimensional space R^d and an integer k. The problem is to determine a set of k points in R^d, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARI_HA). We found that when k is close to d, the quality is good (ARI_HA>0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARI_HA>0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data.     

Maximum likelihood Jukes-Cantor triplets: analytic solutions

Maximum likelihood (ML) is a popular method for inferring a phylogenetic tree of the evolutionary relationship of a set of taxa, from observed homologous aligned genetic sequences of the taxa. Generally, the computation of the ML tree is based on numerical methods, which in a few cases, are known to converge to a local maximum on a tree, which is suboptimal. The extent of this problem is unknown, one approach is to attempt to derive algebraic equations for the likelihood equation and find the maximum points analytically. This approach has so far only been successful in the very simplest cases, of three or four taxa under the Neyman model of evolution of two-state characters. In this paper we extend this approach, for the first time, to four-state characters, the Jukes-Cantor model under a molecular clock, on a tree T on three taxa, a rooted triple. We employ spectral methods (Hadamard conjugation) to express the likelihood function parameterized by the path-length spectrum. Taking partial derivatives, we derive a set of polynomial equations whose simultaneous solution contains all critical points of the likelihood function. Using tools of algebraic geometry (the resultant of two polynomials) in the computer algebra packages (Maple), we are able to find all turning points analytically. We then employ this method on real sequence data and obtain realistic results on the primate-rodents divergence time.