The use of time-series analysis to forecast bont tick (Amblyomma hebraeum) infestations in Zimbabwe

Studying the dynamics of tick infestations on cattle is an essential step in developing optimal strategies for tick control. Successful strategic tick control requires accurate predictions of when tick infestations will reach predetermined threshold levels. In the case ofAmblyomma hebraeum, earlier work has shown that there is no consistent pattern of seasonal activity. This means that a statistical model for predictingA. hebraeum infestations cannot reliably use climatic factors as the only independent variables. An alternative method is to apply time-series, or auto-regressive moving-average (ARMA), analysis which uses only the past population patterns to predict future trends. This technique was applied to a data set consisting of 108 weekly tick counts ofA. hebraeum (adult males, standard females, flat females and standard nymphs), conducted at an experimental station in southeastern Zimbabwe. The ability of the ARMA models to fit and predict actual tick infestations was judged using two sets of criteria. The first set focused on the goodness-of-fit, and used the adjustedR ² values,Q statistic and the Akaike Information Criteria. The second set of criteria measured the forecasting accuracy of an estimated equation, and consisted of regressing a 9-period forecast against an actual out-of-sample data set not used in the estimation process. The root mean square error of the forecast was also considered when comparing several models for the same data set. Using these criteria, the models estimated using the ARMA technique were judged to both fit and forecast with sufficient accuracy to warrant their use in strategic tick control. Although the success of using ARMA to forecastA. hebraeum is partly due to the non-seasonal behaviour of the species, the results presented here suggest that it is worthwhile exploring the use of ARMA techniques to model the dynamics of other tick species. Where independent variables exert considerable influence on the dynamics of a tick species, these variables can be incorporated into an ARMA-style model.     

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.     

Comparative autoregressive moving average analysis of kinetochore microtubule dynamics in yeast

To elucidate the regulation of kinetochore microtubules (kMTs) by kinetochore proteins in Saccharomyces cerevisiae, we need tools to characterize and compare stochastic kMT dynamics. Here we show that autoregressive moving average (ARMA) models, combined with a statistical framework for testing the significance of differences between ARMA model parameters, provide a sensitive method for identifying the subtle changes in kMT dynamics associated with kinetochore protein mutations. Applying ARMA analysis to G1 kMT dynamics, we found that 1), kMT dynamics in the kinetochore protein mutants okp1-5 and kip3Delta are different from those in wild-type, demonstrating the regulation of kMTs by kinetochore proteins; 2), the kinase Ipl1p regulates kMT dynamics also in G1; and 3), the mutant dam1-1 exhibits three different phenotypes, indicating the central role of Dam1p in maintaining the attachment of kMTs and regulating their dynamics. We also confirmed that kMT dynamics vary with temperature, and are most likely differentially regulated at 37 degrees C. Therefore, when elucidating the role of a protein in kMT regulation using a temperature-sensitive mutant, dynamics in the mutant at its nonpermissive temperature must be compared to those in wild-type at the same temperature, not to those in the mutant at its permissive temperature.     

Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ_alt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ_alt≤−1. For different BCLs, control values of λ_alt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ_alt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ_alt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.     

Single evoked potential reconstruction by means of wavelet transform

We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach — the wavelet representation of the signal. Wavelets were introduced by Grossman and Morlet in 1984. The method is based on the multiresolution signal decomposition. Wavelets are already used for speech recognition, geophysics investigations and fractal analysis. This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal. We would like to introduce wavelet formalism for the first time to brain signal analysis. One of the most important problems in this field is the analysis of evoked potentials. This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used. This method is based on several assumptions. Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent. These assumptions have been challenged e.g. the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis. In view of the works of Sayers et al. (1974) and Baar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases. Several attempts to overcome the limitation of the averaging method have been made. Heintze and Künkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments. This was possible under two condiitons: high signal to noise ratio and clear separation of the EEG and EP spectra. These assumptions are not easy to fulfill, though. Cerutti et al. (1987) modeled background EEG activity by means of an AR process and event related brain activity by ARMA. In this way they were able to find a filter extracting single EP. Nevertheless, their method was not quite free of assumptions, since they since they used averaged EP to define their ARMA filter. In the following we shall briefly describe the method of the multiresolution decomposition and we will apply it to the analysis and reconstruction of single evoked potentials.     

Multi-prediction based scheduling for hybrid workloads in the cloud data center

Cloud computing can leverage over-provisioned resources that are wasted in traditional data centers hosting production applications by consolidating tasks with lower QoS and SLA requirements. However, the dramatic fluctuation of workloads with lower QoS and SLA requirements may impact the performance of production applications. Frequent task eviction, killing and rescheduling operations also waste CPU cycles and create overhead. This paper aims to schedule hybrid workloads in the cloud data center to reduce task failures and increase resource utilization. The multi-prediction model, including the ARMA model and the feedback based online AR model, is used to predict the current and the future resource availability. Decision to accept or reject a new task is based on the available resources and task properties. Evaluations show that the scheduler can reduce the host overload and failed tasks by nearly 70%, and increase effective resource utilization by more than 65%. The task delay performance degradation is also acceptable.     

Maturity Dispersion,Stock Auto-Correlation,and Management Strategy in Exploited Populations

Fishery management policies need to be based on historical summaries of stock status which are well correlated with the size of the group of individuals who will be affected by any harvest. This paper is motivated by the problem of managing stocks of Atlantic salmon, which can be accurately monitored during the riverine stages of their life-history, but which spend a lengthy period at sea before returning to spawn. We begin by formulating a minimal stochastic model of stock-recruitment driven population dynamics, which linearises to a standard ARMA form. We investigate the relation between maturity dispersion and the auto-covariance of stock fluctuations driven by process noise in the recruitment process and/or random variability in survival from recruitment to spawning. We demonstrate that significant reductions in fluctuation intensity and/or increases in long-run average yield can be achieved by controlling harvesting in response to the value of a historical summary focussed on lags at which the uncontrolled population dynamics produce strong correlations. We apply our minimal model to two well-characterised Atlantic salmon populations, and find poor agreement between predicted and observed stock fluctuation ACF. Re-examination of the ancilliary data available for one of our two exemplary systems leads us to propose an extended model which also linearises to ARMA form, and which predicts a fluctuation ACF more closely in agreement with that observed, and could thus form a satisfactory vehicle for policy discussion.     

Using genetic variation and environmental risk factor data to identify individuals at high risk for age-related macular degeneration

A major goal of personalized medicine is to pre-symptomatically identify individuals at high risk for disease using knowledge of each individual's particular genetic profile and constellation of environmental risk factors. With the identification of several well-replicated risk factors for age-related macular degeneration (AMD), the leading cause of legal blindness in older adults, this previously unreachable goal is beginning to seem less elusive. However, recently developed algorithms have either been much less accurate than expected, given the strong effects of the identified risk factors, or have not been applied to independent datasets, leaving unknown how well they would perform in the population at large. We sought to increase accuracy by using novel modeling strategies, including multifactor dimensionality reduction (MDR) and grammatical evolution of neural networks (GENN), in addition to the traditional logistic regression approach. Furthermore, we rigorously designed and tested our models in three distinct datasets: a Vanderbilt-Miami (VM) clinic-based case-control dataset, a VM family dataset, and the population-based Age-related Maculopathy Ancillary (ARMA) Study cohort. Using a consensus approach to combine the results from logistic regression and GENN models, our algorithm was successful in differentiating between high- and low-risk groups (sensitivity 77.0%, specificity 74.1%). In the ARMA cohort, the positive and negative predictive values were 63.3% and 70.7%, respectively. We expect that future efforts to refine this algorithm by increasing the sample size available for model building, including novel susceptibility factors as they are discovered, and by calibrating the model for diverse populations will improve accuracy.     

Time series analysis of hybrid neurophysiological data and application of mutual information

Multivariate time series data of which some components are continuous time series and the rest are point processes are called hybrid data. Such data sets routinely arise while working with neuroscience data, EEG and spike trains would perhaps be the most obvious example. In this paper, we discuss the modeling of a hybrid time series, with the continuous component being the physiological tremors in the distal phalanx of the middle finger, and motor unit firings in the middle finger portion of the extensor digitorum communis (EDC) muscle. We employ a model for the two components based on Auto-regressive Moving Average (ARMA) type models. Another major issue to arise in the modeling of such data is to assess the goodness of fit. We suggest a visual procedure based on mutual information towards assessing the dependence pattern of hybrid data. The goodness of fit is also verified by standard model fitting diagnostic techniques for univariate data.     

A new two-breath technique for extracting the cerebrovascular response to arterial carbon dioxide

Cerebrovascular autoregulation is evaluated from spontaneous fluctuations in mean flow velocity (MFV) by transcranial Doppler ultrasound of the middle cerebral artery (MCA) with respect to changes in arterial blood pressure (BP(MCA)), but the effects of spontaneous fluctuations in arterial Pco(2) on MFV have been largely ignored. Autoregressive moving average analysis (ARMA), a closed-loop system identification technique, was applied to data from nine healthy subjects during spontaneous breathing, during inspiration of 10% CO(2) for two breaths once per minute for 4 min, and during sustained breathing of 7% CO(2). Cerebrovascular resistance index (CVRi) was calculated (CVRi = BP(MCA)/MFV). Reliable estimates of gain for BP(MCA) --> MFV were obtained for spontaneous breathing and the two-breath method. In contrast, reliable gain estimates for Pco(2) --> MFV or Pco(2) --> CVRi were achieved only under the two-breath method. Pco(2) --> MFV gain was smaller with the two-breath method than during sustained 7% CO(2) (P < 0.05). BP(MCA) was elevated by 7% CO(2) but not by the two-breath method. The closed-loop model provides insight into interactions between BP(MCA) and Pco(2) on cerebrovascular control, but reliable solutions for Pco(2) effects with ARMA analysis require perturbation by the two-breath method.     

Nonlinear Mixed-Effects (NLME) Diameter Growth Models for Individual China-Fir (Cunninghamia lanceolata) Trees in Southeast China

An individual-tree diameter growth model was developed for Cunninghamia lanceolata in Fujian province, southeast China. Data were obtained from 72 plantation-grown China-fir trees in 24 single-species plots. Ordinary non-linear least squares regression was used to choose the best base model from among 5 theoretical growth equations; selection criteria were the smallest absolute mean residual and root mean square error and the largest adjusted coefficient of determination. To account for autocorrelation in the repeated-measures data, we developed one-level and nested two-level nonlinear mixed-effects (NLME) models, constructed on the selected base model; the NLME models incorporated random effects of the tree and plot. The best random-effects combinations for the NLME models were identified by Akaike''s information criterion, Bayesian information criterion and −2 logarithm likelihood. Heteroscedasticity was reduced with two residual variance functions, a power function and an exponential function. The autocorrelation was addressed with three residual autocorrelation structures: a first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)] and a compound symmetry structure (CS). The one-level (tree) NLME model performed best. Independent validation data were used to test the performance of the models and to demonstrate the advantage of calibrating the NLME models.     

Impaired cerebrovascular autoregulation and reduced CO₂ reactivity after long duration spaceflight

Long duration habitation on the International Space Station (ISS) is associated with chronic elevations in arterial blood pressure in the brain compared with normal upright posture on Earth and elevated inspired CO(2). Although results from short-duration spaceflights suggested possibly improved cerebrovascular autoregulation, animal models provided evidence of structural and functional changes in cerebral vessels that might negatively impact autoregulation with longer periods in microgravity. Seven astronauts (1 woman) spent 147 ± 49 days on ISS. Preflight testing (30-60 days before launch) was compared with postflight testing on landing day (n = 4) or the morning 1 (n = 2) or 2 days (n = 1) after return to Earth. Arterial blood pressure at the level of the middle cerebral artery (BP(MCA)) and expired CO(2) were monitored along with transcranial Doppler ultrasound assessment of middle cerebral artery (MCA) blood flow velocity (CBFV). Cerebrovascular resistance index was calculated as (CVRi = BP(MCA)/CBFV). Cerebrovascular autoregulation and CO(2) reactivity were assessed in a supine position from an autoregressive moving average (ARMA) model of data obtained during a test where two breaths of 10% CO(2) were given four times during a 5-min period. CBFV and Doppler pulsatility index were reduced during -20 mmHg lower body negative pressure, with no differences pre- to postflight. The postflight indicator of dynamic autoregulation from the ARMA model revealed reduced gain for the CVRi response to BP(MCA) (P = 0.017). The postflight responses to CO(2) were reduced for CBFV (P = 0.056) and CVRi (P = 0.047). These results indicate that long duration missions on the ISS impaired dynamic cerebrovascular autoregulation and reduced cerebrovascular CO(2) reactivity.     

Protein sequence and structure relationship ARMA spectral analysis: application to membrane proteins.

If it is assumed that the primary sequence determines the three-dimensional folded structure of a protein, then the regular folding patterns, such as alpha-helix, beta-sheet, and other ordered patterns in the three-dimensional structure must correspond to the periodic distribution of the physical properties of the amino acids along the primary sequence. An AutoRegressive Moving Average (ARMA) model method of spectral analysis is applied to analyze protein sequences represented by the hydrophobicity of their amino acids. The results for several membrane proteins of known structures indicate that the periodic distribution of hydrophobicity of the primary sequence is closely related to the regular folding patterns in a protein's three-dimensional structure. We also applied the method to the transmembrane regions of acetylcholine receptor alpha subunit and Shaker potassium channel for which no atomic resolution structure is available. This work is an extension of our analysis of globular proteins by a similar method.     

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.
     

Weak population regulation in ecological time series

How strongly natural populations are regulated has a long history of debate in ecology. Here, we discuss concepts of population regulation appropriate for stochastic population dynamics. We then analyse two large collections of data sets with autoregressive-moving average (ARMA) models, using model selection techniques to find best-fitting models. We estimated two metrics of population regulation: the characteristic return rate of populations to stationarity and the variability of the stationary distribution (the long-term distribution of population abundance). Empirically, longer time series were more likely to show weakly regulated population dynamics. For data sets of length ≥ 20, more than 35% had characteristic return times > 6 years, and more than 29% had stationary distributions whose coefficients of variation were more than two times greater than would be the case if they were maximally regulated. These results suggest that many natural populations are weakly regulated.
Ecology Letters (2010) 13: 21–31     

Analytical Model for Estimating Terrestrial Cosmic Ray Fluxes Nearly Anytime and Anywhere in the World: Extension of PARMA/EXPACS

By extending our previously established model, here we present a new model called “PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 3.0,” which can instantaneously estimate terrestrial cosmic ray fluxes of neutrons, protons, ions with charge up to 28 (Ni), muons, electrons, positrons, and photons nearly anytime and anywhere in the Earth’s atmosphere. The model comprises numerous analytical functions with parameters whose numerical values were fitted to reproduce the results of the extensive air shower (EAS) simulation performed by Particle and Heavy Ion Transport code System (PHITS). The accuracy of the EAS simulation was well verified using various experimental data, while that of PARMA3.0 was confirmed by the high R ² values of the fit. The models to be used for estimating radiation doses due to cosmic ray exposure, cosmic ray induced ionization rates, and count rates of neutron monitors were validated by investigating their capability to reproduce those quantities measured under various conditions. PARMA3.0 is available freely and is easy to use, as implemented in an open-access software program EXcel-based Program for Calculating Atmospheric Cosmic ray Spectrum (EXPACS). Because of these features, the new version of PARMA/EXPACS can be an important tool in various research fields such as geosciences, cosmic ray physics, and radiation research.     

Linear Mixed-Effects Models to Describe Individual Tree Crown Width for China-Fir in Fujian Province,Southeast China

A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike’s information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R ²). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.     

Universal Optimality of Nearest Neighbour Balanced Block Designs using Second Order Correlated Models

Block designs for observations correlated in one dimension are investigated. Santharam and Ponnusamy (1995) investigated the universal optimality of Nearest Neighbour balanced block designs (NNBD) using first order correlated models (AR(1), MA(1) and ARMA(1,1)). In this article we have investigated the universal optimality of NNBD using second order correlated models (ar(2), and MA (2)).