Fitting of one ARMA model to multiple trials increases the time resolution of instantaneous coherence

This study presents a least mean squares (LMS) algorithm for the ensemble modeling of a multivariate ARMA process. Generally, an LMS algorithm makes possible the tracking of parameters for nonstationary time series. Our estimation incorporates multiple process observations that improve the accuracy of the parameter estimation. As a consequence, the estimation sequences come close to the true model parameters with a fast adaptation speed. This advantage also holds true of spectral quantities (e.g., the momentary coherence), which are derived from the model parameters. Thus the extension of the ARMA fitting from one to multiple trajectories allows the investigation of nonstationary biological signals with an increased time resolution. The applicability of the algorithm is demonstrated for event-related EEG coherence analysis of the Sternberg task. The changing interaction between posterior association cortex and anterior brain area was shown for verbal and nonverbal stimuli by means of the time-variant theta coherence.     

Scaling vs. nonscaling methods of assessing autonomic tone in streptozotocin-induced diabetic rats

We studied heart rate variability in rats by power scaling spectral analysis (PSSA), autoregressive modeling (AR), and detrended fluctuation analysis (DFA), assessed stability by coefficient of variation between consecutive 6-h epochs, and then compared cross-correlation among techniques. These same parameters were checked from baseline conditions through acute and chronic disease states (streptozotocin-induced diabetes) followed by therapeutic intervention (insulin). Cross-correlation between methods over the entire time period was r = 0.94 (DFA and PSSA), r = 0.81 (DFA and AR), and r = 0.77 (AR and PSSA). Under baseline conditions the scaling parameter measured by DFA and PSSA and the high-frequency (HF) component measured by AR fluctuated around an average value, but these fluctuations were different for the three methods. After diabetes induction, a strong correlation was found between the HF power and the short-term scaling parameter. Despite their differences in methodology, DFA and PSSA assess changes in parasympathetic tone as detected by autoregressive modeling.     

Methods for studying recombination on chromosomes that undergo nondisjunction

A lod score method is provided for mapping genes relative to the centromere using family data from autosomal trisomies. Such gene-centromere mapping can be performed whenever two or more members of a meiotic tetrad can be recovered. The critical mapping parameter is not the recombination value theta or the map distance omega, but the probability of nonreduction in a heterozygous host, the probability of heterozygosity (nonreduction) is 1-gamma/2 for a meiosis I error and gamma for a meiosis II error. Under various assumptions regarding chiasma interference, gamma can be related to theta and omega. We provide specific methods for estimating gamma and theta from trisomy data using maximum likelihood, so that recombination may be studied on chromosomes that underwent nondisjunction.     

Maximum likelihood estimation of the heterogeneity of substitution rate among nucleotide sites

This paper presents a maximum likelihood approach to estimating the variation of substitution rate among nucleotide sites. We assume that the rate varies among sites according to an invariant+gamma distribution, which has two parameters: the gamma parameter alpha and the proportion of invariable sites theta. Theoretical treatments on three, four, and five sequences have been conducted, and computer program have been developed. It is shown that rho = (1 + theta alpha)/(1 + alpha) is a good measure for the rate heterogeneity among sites. Extensive simulations show that (1) if the proportion of invariable sites is negligible, i.e., theta = 0, the gamma parameter alpha can be satisfactorily estimated, even with three sequences; (2) if the proportion of invariable sites is not negligible, the heterogeneity rho can still be suitably estimated with four or more sequences; and (3) the distances estimated by the proposed method are almost unbiased and are robust against violation of the assumption of the invariant + gamma distribution.      

Comparison of crystal structures of human androgen receptor ligand-binding domain complexed with various agonists reveals molecular determinants responsible for binding affinity

Androgens exert their effects by binding to the highly specific androgen receptor (AR). In addition to natural potent androgens, AR binds a variety of synthetic agonist or antagonist molecules with different affinities. To identify molecular determinants responsible for this selectivity, we have determined the crystal structure of the human androgen receptor ligand-binding domain (hARLBD) in complex with two natural androgens, testosterone (Testo) and dihydrotestosterone (DHT), and with an androgenic steroid used in sport doping, tetrahydrogestrinone (THG), at 1.64, 1.90, and 1.75 A resolution, respectively. Comparison of these structures first highlights the flexibility of several residues buried in the ligand-binding pocket that can accommodate a variety of ligand structures. As expected, the ligand structure itself (dimension, presence, and position of unsaturated bonds that influence the geometry of the steroidal nucleus or the electronic properties of the neighboring atoms, etc.) determines the number of interactions it can make with the hARLBD. Indeed, THG--which possesses the highest affinity--establishes more van der Waals contacts with the receptor than the other steroids, whereas the geometry of the atoms forming electrostatic interactions at both extremities of the steroid nucleus seems mainly responsible for the higher affinity measured experimentally for DHT over Testo. Moreover, estimation of the ligand-receptor interaction energy through modeling confirms that even minor modifications in ligand structure have a great impact on the strength of these interactions. Our crystallographic data combined with those obtained by modeling will be helpful in the design of novel molecules with stronger affinity for the AR.     

Calculation of hydrodynamic properties of small nucleic acids from their atomic structure

Hydrodynamic properties (translational diffusion, sedimentation coefficients and correlation times) of short B-DNA oligonucleotides are calculated from the atomic-level structure using a bead modeling procedure in which each non-hydrogen atom is represented by a bead. Using available experimental data of hydrodynamic properties for several oligonucleotides, the best fit for the hydrodynamic radius of the atoms is found to be ~2.8 Å. Using this value, the predictions for the properties corresponding to translational motion and end-over-end rotation are accurate to within a few percent error. Analysis of NMR correlation times requires accounting for the internal flexibility of the double helix, and allows an estimation of ~0.85 for the Lipari–Szabo generalized order parameter. Also, the degree of hydration can be determined from hydrodynamics, with a result of ~0.3 g (water)/g (DNA). These numerical results are quite similar to those found for globular proteins. If the hydrodynamic model for the short DNA is simply a cylindrical rod, the predictions for overall translation and rotation are slightly worse, but the NMR correlation times and the degree of hydration, which depend more on the cross-sectional structure, are more severely affected.     

The effects of visual input on postural control mechanisms: an analysis of center-of-pressure trajectories using the auto-regressive model

New measures to characterize center-of-pressure (COP) trajectories during quiet standing were proposed and then utilized to investigate changes in postural control with respect to visual input. Eleven healthy male subjects (aged 20-27 years) were included in this study. An instrumented force platform was used to measure the time-varying displacements of the COP under each subject's feet during quiet standing. The subjects were tested under eyes-open and eyes-closed conditions. The COP time series were separately analyzed for the medio-lateral and antero-posterior directions. The proposed measures were obtained from the parameter estimation of auto-regressive (AR) models. The percentage contributions and geometrical moment of AR coefficients showed statistically significant differences between vision conditions. The present COP displacements under the eyes-open condition showed higher correlation with the past COP displacements at longer lag times, when compared to the eyes-closed condition. In contrast, no significant differences between vision conditions were found for conventional summary statistics, e.g., the total length of the COP path. These results suggest that the AR parameters are useful for the evaluation of postural stability and balance function, even for healthy young individuals. The role of visual input in the postural control system and implications of the findings were discussed.     

基于线性混合模型的红松人工林一级枝条大小预测模拟

基于黑龙江省孟家岗林场60株人工红松955个标准枝数据,采用线性混合效应模型理论和方法,考虑树木效应,利用SAS软件中的MIXED模块拟合红松人工林一级枝条各因子(基径、枝长、着枝角度)的预测模型.结果表明： 通过选择合适的随机参数和方差协方差结构能够提高模型的拟合精度;把相关性结构包括复合对称结构CS、一阶自回归结构AR(1)及一阶自回归与滑动平均结构ARMA(1,1)加入到一级枝条大小最优混合模型中,AR(1)可显著提高枝条基径和角度混合模型的拟合精度,但3种结构均不能提高枝条角度混合模型的精度.为了描述混合模型构建过程中产生的异方差现象,把CF₁和CF₂函数加入到枝条混合模型中,CF₁函数显著提高了枝条角度混合模型的拟合效果,CF₂函数显著提高了枝条基径和长度混合模型拟合效果.模型检验结果表明：对于红松人工林一级枝条大小预测模型,混合效应模型的估计精度比传统回归模型估计精度明显提高.
     

Nonrandom variability in respiratory cycle parameters of humans during stage 2 sleep

We analyzed breath-to-breath inspiratory time (TI), expiratory time (TE), inspiratory volume (VI), and minute ventilation (Vm) from 11 normal subjects during stage 2 sleep. The analysis consisted of 1) fitting first- and second-order autoregressive models (AR1 and AR2) and 2) obtaining the power spectra of the data by fast-Fourier transform. For the AR2 model, the only coefficients that were statistically different from zero were the average alpha 1 (a1) for TI, VI, and Vm (a1 = 0.19, 0.29, and 0.15, respectively). However, the power spectra of all parameters often exhibited peaks at low frequency (less than 0.2 cycles/breath) and/or at high frequency (greater than 0.2 cycles/breath), indicative of periodic oscillations. After accounting for the corrupting effects of added oscillations on the a1 estimates, we conclude that 1) breath-to-breath fluctuations of VI, and to a lesser extent TI and Vm, exhibit a first-order autoregressive structure such that fluctuations of each breath are positively correlated with those of immediately preceding breaths and 2) the correlated components of variability in TE are mostly due to discrete high- and/or low-frequency oscillations with no underlying autoregressive structure. We propose that the autoregressive structure of VI, TI, and Vm during spontaneous breathing in stage 2 sleep may reflect either a central neural mechanism or the effects of noise in respiratory chemical feedback loops; the presence of low-frequency oscillations, seen more often in Vm, suggests possible instability in the chemical feedback loops. Mechanisms of high-frequency periodicities, seen more often in TE, are unknown.     

Robustness of Generalized Estimating Equation (GEE) Tests of Significance against Misspecification of the Error Structure Model

Generalized linear model analyses of repeated measurements typically rely on simplifying mathematical models of the error covariance structure for testing the significance of differences in patterns of change across time. The robustness of the tests of significance depends, not only on the degree of agreement between the specified mathematical model and the actual population data structure, but also on the precision and robustness of the computational criteria for fitting the specified covariance structure to the data. Generalized estimating equation (GEE) solutions utilizing the robust empirical sandwich estimator for modeling of the error structure were compared with general linear mixed model (GLMM) solutions that utilized the commonly employed restricted maximum likelihood (REML) procedure. Under the conditions considered, the GEE and GLMM procedures were identical in assuming that the data are normally distributed and that the variance‐covariance structure of the data is the one specified by the user. The question addressed in this article concerns relative sensitivity of tests of significance for treatment effects to varying degrees of misspecification of the error covariance structure model when fitted by the alternative procedures. Simulated data that were subjected to monte carlo evaluation of actual Type I error and power of tests of the equal slopes hypothesis conformed to assumptions of ordinary linear model ANOVA for repeated measures except for autoregressive covariance structures and missing data due to dropouts. The actual within‐groups correlation structures of the simulated repeated measurements ranged from AR(1) to compound symmetry in graded steps, whereas the GEE and GLMM formulations restricted the respective error structure models to be either AR(1), compound symmetry (CS), or unstructured (UN). The GEE‐based tests utilizing empirical sandwich estimator criteria were documented to be relatively insensitive to misspecification of the covariance structure models, whereas GLMM tests which relied on restricted maximum likelihood (REML) were highly sensitive to relatively modest misspecification of the error correlation structure even though normality, variance homogeneity, and linearity were not an issue in the simulated data.Goodness‐of‐fit statistics were of little utility in identifying cases in which relatively minor misspecification of the GLMM error structure model resulted in inadequate alpha protection for tests of the equal slopes hypothesis. Both GEE and GLMM formulations that relied on unstructured (UN) error model specification produced nonconservative results regardless of the actual correlation structure of the repeated measurements. A random coefficients model produced robust tests with competitive power across all conditions examined. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

生理信号回归问题的一种解法

一自适应在线过程可通过Kalman滤波表示为时间变多变量的的自回归模型。时变模型的参数的估计能被用以计算线相关的瞬时测量,此方法对生理信号的分析非常有用。本文着重讨论了在呼吸运动,心率波动,血压的分析中的应用。     

TSEE: an elastic embedding method to visualize the dynamic gene expression patterns of time series single-cell RNA sequencing data

Background

Time series single-cell RNA sequencing (scRNA-seq) data are emerging. However, the analysis of time series scRNA-seq data could be compromised by 1) distortion created by assorted sources of data collection and generation across time samples and 2) inheritance of cell-to-cell variations by stochastic dynamic patterns of gene expression. This calls for the development of an algorithm able to visualize time series scRNA-seq data in order to reveal latent structures and uncover dynamic transition processes.

Results

In this study, we propose an algorithm, termed time series elastic embedding (TSEE), by incorporating experimental temporal information into the elastic embedding (EE) method, in order to visualize time series scRNA-seq data. TSEE extends the EE algorithm by penalizing the proximal placement of latent points that correspond to data points otherwise separated by experimental time intervals. TSEE is herein used to visualize time series scRNA-seq datasets of embryonic developmental processed in human and zebrafish. We demonstrate that TSEE outperforms existing methods (e.g. PCA, tSNE and EE) in preserving local and global structures as well as enhancing the temporal resolution of samples. Meanwhile, TSEE reveals the dynamic oscillation patterns of gene expression waves during zebrafish embryogenesis.

Conclusions

TSEE can efficiently visualize time series scRNA-seq data by diluting the distortions of assorted sources of data variation across time stages and achieve the temporal resolution enhancement by preserving temporal order and structure. TSEE uncovers the subtle dynamic structures of gene expression patterns, facilitating further downstream dynamic modeling and analysis of gene expression processes. The computational framework of TSEE is generalizable by allowing the incorporation of other sources of information.

     

Speed controls the amplitude and timing of the hippocampal gamma rhythm

Cortical and hippocampal gamma oscillations have been implicated in many behavioral tasks. The hippocampus is required for spatial navigation where animals run at varying speeds. Hence we tested the hypothesis that the gamma rhythm could encode the running speed of mice. We found that the amplitude of slow (20-45 Hz) and fast (45-120 Hz) gamma rhythms in the hippocampal local field potential (LFP) increased with running speed. The speed-dependence of gamma amplitude was restricted to a narrow range of theta phases where gamma amplitude was maximal, called the preferred theta phase of gamma. The preferred phase of slow gamma precessed to lower values with increasing running speed. While maximal fast and slow gamma occurred at coincident phases of theta at low speeds, they became progressively more theta-phase separated with increasing speed. These results demonstrate a novel influence of speed on the amplitude and timing of the hippocampal gamma rhythm which could contribute to learning of temporal sequences and navigation.     

Segmentation of EEG during sleep using time-varying autoregressive modeling

Time-varying AR modeling is applied to sleep EEG signal, in order to perform parameter estimation and detect changes in the signal characteristics (segmentation). Several types of basis functions have been analyzed to determine how closely they can approximate parameter changes characteristics of the EEG signal. The TV-AR model was applied to a large number of simulated signal segments, in order to examine the behaviour of the estimation under various conditions such as variations in the EEG parameters and in the location of segment boundaries, and different orders of the basis functions. The set of functions that is the basis for the Discrete Cosine Transform (DCT), and the Walsh functions were found to be the most efficient in the estimation of the model parameters. A segmentation algorithm based on an “Identification function” calculated from the estimated model parameters is suggested.     

Pattern Detection in Intensive Care Monitoring Time Series with Autoregressive Models: Influence of the Model Order

The detection of patterns in monitoring data of vital signs is of great importance for adequate bedside decision support in critical care. Currently used alarm systems, which are based on fixed thresholds and independency assumptions, are not satisfactory in clinical practice. Time series techniques such as AR‐models consider autocorrelations within the series, which can be used for pattern recognition in the data. For practical applications in intensive care the data analysis has to be automated. An important issue is the suitable choice of the model order which is difficult to accomplish online. In a comparative case‐study we analyzed 34564 univariate time series of hemodynamic variables in critically ill patients by autoregressive models of different orders and compared the results of pattern detection. AR(2)‐models seem to be most suitable for the detection of clinically relevant patterns, thus affirming that treating the data as independent leads to false alarms. Moreover, using AR(2)‐models affords only short estimation periods. These findings for pattern detection in intensive care data are of medical importance as they justify a preselection of a model order, easing further automated statistical online analysis.     

Predator migration in response to prey density: What are the consequences?

A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically.     

Analysis of elicited EEG synchronization and desynchronization in emotional activation: temporal and topographic characteristics

Event-related synchronization (ERS) and desynchronization (ERD) in delta, theta1, theta2, alpha1, alpha2, beta1, beta2, beta3, and gamma were measured in 20 healthy right-handed subjects in response to IAPS stimuli with low, moderate, and high arousal reactions. The 62-channel EEG was simultaneously recorded while subjects viewed sequentially presented pictures and subjectively rated them after each presentation. The results show that emotionally loaded stimuli induced higher ERS in the delta, theta1, theta2, beta1, beta3, and gamma bands along with combined ERD and ERS effects in alpha2 band. As to hemispheric asymmetries, the effects of emotional arousal were restricted not only to right parietal (theta1 and theta2 ERS, alpha2 ERD) but also to left frontal (theta2 ERS) regions. In terms of affective chronometry, lower theta was the first to catch the affective salience of incoming stimuli (time window 0-600 ms after the stimulus input). For theta2, alpha2, and gamma bands this process was delayed to 600-1000 ms.