Equidistant Time Points Research Articles

Alignment of time-resolved data from high throughput experiments.

To better understand the dynamics of the underlying processes in cells, it is necessary to take measurements over a time course. Modern high-throughput technologies are often used for this purpose to measure the behavior of cell products like metabolites, peptides, proteins, [Formula: see text]RNA or mRNA at different points in time. Compared to classical time series, the number of time points is usually very limited and the measurements are taken at irregular time intervals. The main reasons for this are the costs of the experiments and the fact that the dynamic behavior usually shows a strong reaction and fast changes shortly after a stimulus and then slowly converges to a certain stable state. Another reason might simply be missing values. It is common to repeat the experiments and to have replicates in order to carry out a more reliable analysis. The ideal assumptions that the initial stimulus really started exactly at the same time for all replicates and that the replicates are perfectly synchronized are seldom satisfied. Therefore, there is a need to first adjust or align the time-resolved data before further analysis is carried out. Dynamic time warping (DTW) is considered as one of the common alignment techniques for time series data with equidistant time points. In this paper, we modified the DTW algorithm so that it can align sequences with measurements at different, non-equidistant time points with large gaps in between. This type of data is usually known as time-resolved data characterized by irregular time intervals between measurements as well as non-identical time points for different replicates. This new algorithm can be easily used to align time-resolved data from high-throughput experiments and to come across existing problems such as time scarcity and existing noise in the measurements. We propose a modified method of DTW to adapt requirements imposed by time-resolved data by use of monotone cubic interpolation splines. Our presented approach provides a nonlinear alignment of two sequences that neither need to have equi-distant time points nor measurements at identical time points. The proposed method is evaluated with artificial as well as real data. The software is available as an R package tra (Time-Resolved data Alignment) which is freely available at: http://public.ostfalia.de/klawonn/tra.zip .

A comparative study of Mandarin compound vowels produced by prelingually deafened children with cochlear implants and normal hearing peers

The present study examined the dynamic features of compound vowels in native Mandarin-speaking children with cochlear implants (CIs). Fourteen prelingually deafened children with CIs (aged 2.9−8.3 years) and 14 age-matched, normal-hearing (NH) children produced monosyllables containing six Mandarin vowels (/aɪ/, /aʊ/, /uo/, /iɛ/, /iaʊ/, /ioʊ/). The frequency values of the first two formants were measured at nine equidistant time points (10-20-30-40-50-60-70-80-90%) over the course of vowel duration. All formant frequency values were normalized and then used to calculate vowel trajectory length, vowel section length, overall spectral rate of change, and vowel section rate of change. The results revealed that the CI children produced significantly longer durations for all six compound vowels. They clearly showed positional deviation from the NH children on vowels /aɪ/, /uo/ and /iɛ/. The CI children’s ability to produce formant movement for the compound vowels varied considerably. Some CI children produced ...

Estimation of a time-dependent density

The problem of estimating a time-dependent density at each time point t∈[0,1] is considered, where independent samples of the density at equidistant time points in [0,1] are given. Here all the samples have the same sample size. It is assumed that the distribution corresponding to the density of time t depends smoothly on t. The error of the estimate is measured by the L1-error. Results concerning consistency and rate of convergence of a local average of kernel density estimates of the density at the discrete time points are presented. The finite sample size performance of the estimate is illustrated by applying it to simulated data.

Persistence of Stability for Equilibria of Map Iterations in Banach Spaces Under Small Random Perturbations

This paper addresses the long–term behaviour –in a suitable probabilistic sense– of map iteration in subsets of Banach spaces that are randomly perturbed. The law of the latter change in state is allowed to depend on state. We provide quite general conditions under which a stable fixed point of the deterministic map iteration induces an asymptotically stable ergodic measure of the Markov chain defined by the perturbed system, which is regarded as ‘persistence of stability’. The support of this invariant measure is characterized. The applicability of the framework is illustrated for deterministic dynamical systems that are subject to random interventions at fixed equidistant time points. In particular, we consider systems motivated by population dynamics: a model in ordinary differential equations, a model derived from a reaction–diffusion system and a class of delay equations.

On Stability of Distance Measures for Event Sequences Induced by Level-Crossing Sampling

While Shannon's paradigm of sampling is based on equidistant points in time, triggered by a clock, level-crossing sampling schemes are based on the evaluation of the input signal's amplitude. Three types of level-crossing concepts are considered: a) absolute level-crossings, b) absolute level-crossings with hysteretic quantization, that ignores repeated crossings, and c) thresholding changes. The latter is also referred to as send-on-delta. Such event-driven sampling principles are encountered in asynchronous event-based data acquisition of wireless sensor networks in order to reduce the amount of data transfer and energy consumption, in event-based imaging in order to realize high-dynamic range image acquisition or in biology in terms of neuronal spike trains. The paper addresses the similarity between the event sequences which encode the quantized signals resulting from such event-based sampling concepts. It is shown that such event-driven sampling principles induce instability effects when using dissimilarity measures which are state-of-the-art in this context. As an alternative metric, Hermann Weyl's discrepancy norm is introduced, by which such instability effects can be avoided.

Bayesian design for dichotomous repeated measurements with autocorrelation

In medicine and health sciences, binary outcomes are often measured repeatedly to study their change over time. A problem for such studies is that designs with an optimal efficiency for some parameter values may not be efficient for other values. To handle this problem, we propose Bayesian designs which formally account for the uncertainty in the parameter values for a mixed logistic model which allows quadratic changes over time. Bayesian D-optimal allocations of time points are computed for different priors, costs, covariance structures and values of the autocorrelation. Our results show that the optimal number of time points increases with the subject-to-measurement cost ratio, and that neither the optimal number of time points nor the optimal allocations of time points appear to depend strongly on the prior, the covariance structure or on the size of the autocorrelation. It also appears that for subject-to-measurement cost ratios up to five, four equidistant time points, and for larger cost ratios, five or six equidistant time points are highly efficient. Our results are compared with the actual design of a respiratory infection study in Indonesia and it is shown that, selection of a Bayesian optimal design will increase efficiency, especially for small cost ratios.

Bayesian [formula omitted]-optimal designs for the two parameter logistic mixed effects model

Bayesian optimal designs for binary longitudinal responses analyzed with mixed logistic regression describing a linear time effect are considered. In order to find the optimal number and allocations of time points, for different priors, cost constraints and covariance structures of the random effects, a scalar function of the approximate information matrix based on the first order penalized quasi likelihood (PQL1) is optimized. To overcome the problem of dependence of Bayesian designs on the choice of prior distributions, maximin Bayesian D-optimal designs are proposed. The results show that the optimal number of time points depends on the subject-to-measurement cost ratio and increases with the cost ratio. Furthermore, maximin Bayesian D-optimal designs are highly efficient and robust under changes in priors. Locally D-optimal designs are also investigated and maximin locally D-optimal designs are found to have much lower minimum relative efficiency and fewer time points than maximin Bayesian D-optimal designs. When comparing the efficiencies of designs with equidistant time points with the Bayesian D-optimal designs, it was found that three or four equidistant time points are advisable for small cost ratios and five or six equidistant time points for large cost ratios.

The associations between TV viewing, food intake, and BMI. A prospective analysis of data from the Longitudinal Study of Australian Children

ObjectiveDespite cross-sectional evidence of a link between TV viewing and BMI in early childhood, there has been limited longitudinal exploration of this relationship. The aim of the present study was to explore the potential bi-directionality of the relationship between TV viewing and child BMI. A secondary aim was to evaluate whether this relationship is mediated by dietary intake. Study designParents of 9064 children (4724 recruited at birth, 4340 recruited at age 4) from the Longitudinal Study of Australian Children (LSAC) completed measures of their child’s dietary intake and TV viewing habits at three equidistant time points, separated by 2years. Objective measures of height and weight were also obtained at each time point to calculate BMI. Cross-lagged panel analyses were conducted to evaluate potential bi-directional associations between TV viewing and child BMI, and to evaluate mediation effects of dietary intake for this relationship. ResultsOur longitudinal findings suggest that the relationship between TV viewing and BMI is bi-directional: Individuals who watch TV are more likely to gain weight, and individuals who are heavier are also more likely to watch TV. Interestingly, dietary intake mediated the BMI-TV viewing relationship for the older children, but not for the birth cohort. ConclusionsPresent findings suggest that sedentary behaviours, particularly when coupled with unhealthy dietary habits, constitute a significant risk factor for excessive weight gain in early childhood. Interventions targeted at helping parents to develop healthy TV viewing and eating habits in their young children are clearly warranted.

Repeat estradiol exposure differentially regulates protein expression patterns for estrogen receptor and E-cadherin in older mouse ovarian surface epithelium: Implications for replacement and adjuvant hormone therapies?

BackgroundEstrogen replacement therapy increases risk for ovarian epithelial cancer, a cancer of mainly older women, yet the response of older ovarian surface epithelium (OSE) to repeat estrogen exposure overtime has not been studied. We have previously reported significant reductions in estrogen receptor (ER) protein expression, particularly the ERβ1 isoform, in older mouse OSE following a single depot estradiol injection. The current study examined OSE from older mice following a single, and repeat estradiol injection, given 14days apart over 28days. MethodsCohorts of mice were sacrificed 48hours following each estradiol injection, and at three other equidistant time points. Serum and ovarian tissue estradiol concentration was correlated to immunohistochemical and morphometric parameters used to identify evidence of OSE hyperplasia and hypertrophy. Using immunohistochemistry, E-cadherin expression was investigated in OSE 48hours following both estradiol injections, while ERα and ERβ1 expression was examined in OSE following repeat estradiol exposure only. ResultsFirst exposure to exogenous estradiol resulted in OSE hypertrophy and hyperplasia, and high levels of E-cadherin expression. In contrast, repeat estradiol exposure resulted in no OSE hyperplasia or hypertrophy, low levels of E-cadherin expression, high ERα and reduced ERβ1 protein expression in OSE, and low stromal ERα expression. Blood and ovarian tissue estradiol levels following repeat estradiol injection were half those recorded after a first dose equivalent injection, but remained significantly elevated above controls. ConclusionRepeat estradiol exposure leads to accumulation of estradiol in ovarian tissue, differentially regulating protein expression patterns for E-cadherin in OSE and ER in OSE and stroma.

Dynamic CT technique for assessment of wrist joint instabilities

To develop a 4D [three-dimensional (3D) + time] CT technique to capture high spatial and temporal resolution images of wrist joint motion so that dynamic joint instabilities can be detected before the development of static joint instability and onset of osteoarthritis (OA). A cadaveric wrist was mounted onto a custom motion simulator and scanned with a dual source CT scanner during radial-ulnar deviation. A dynamic 4D CT technique was utilized to reconstruct images at 20 equidistant time points from one motion cycle. 3D images of carpal bones were generated using volume rendering techniques (VRT) at each of the 20 time points and then 4D movies were generated to depict the dynamic joint motion. The same cadaveric wrist was also scanned after cutting all portions of the scapholunate interosseus ligament to simulate scapholunate joint instability. Image quality were assessed on an ordinal scale (1-4, 4 being excellent) by three experienced orthopedic surgeons (specialized in hand surgery) by scoring 2D axial images. Dynamic instability was evaluated by the same surgeons by comparing the two 4D movies of joint motion. Finally, dose reduction was investigated using the cadaveric wrist by scanning at different dose levels to determine the lowest radiation dose that did not substantially alter diagnostic image quality. The mean image quality scores for dynamic and static CT images were 3.7 and 4.0, respectively. The carpal bones, distal radius and ulna, and joint spaces were clearly delineated in the 3D VRT images, without motion blurring or banding artifacts, at all time points during the motion cycle. Appropriate viewing angles could be interactively selected to view any articulating structure using different 3D processing techniques. The motion of each carpal bone and the relative motion among the carpal bones were easily observed in the 4D movies. Joint instability was correctly and easily detected in the scan performed after the ligament was cut by observing the relative motion between the scaphoid and lunate bones. Diagnostic capability was not sacrificed with a volume CT dose index (CTDI(vol)) as low as 18 mGy for the whole scan, with estimated skin dose of approximately 33 mGy, which is much lower than the threshold for transient skin erythema (2000 mGy). The proposed dynamic 4D CT imaging technique generated high spatial and high temporal resolution images without requiring periodic joint motion. Preliminary results from this cadaveric study demonstrate the feasibility of detecting joint instability using this technique.

An acoustical study of American English diphthongs.

English diphthongs are usually produced with more than one vocal tract shape. This study attempts to collect acoustical data of English diphthongs published by Hillenbrand et al. (1995) online and to examine acoustic features of the diphthongs for phoneticians and English teachers. 63 American males and females were chosen after excluding those subjects with different target vowels or ambiguous formant tracks. The author used PRAAT to obtain the acoustical data systematically at 11 equidistant timepoints over the diphthongal segment. Results show that the formant trajectories of the diphthongs produced by the American males and females appeared quite similar. When the female formant values were uniformly normalized to those of the males, almost a perfect collapse occurred. Second, the diphthongal movements on the vowel space appeared not linear due to the coarticulatory gesture for the following consonant. Third, the average duration of the diphthongs produced by the females was 1.156 times longer than that of the males while the pitch ratio between the two groups turned out to be 1.746 with a similar contour over measurement points. The author concludes that English diphthongs produced by various groups can be compared systematically when the acoustical values are obtained at proportional timepoints.

Formula omitted] transience, and its applications to overload detection

When controlling communication networks, it is of crucial importance to have procedures that are capable of checking whether there are unanticipated load changes. In this paper we develop techniques for detecting such load changes, in a setting in which each connection consumes roughly the same amount of bandwidth (with VoIP as a leading example). For the situation of exponential holding times an explicit analysis can be performed in a large-deviations regime, leading to approximations of the test statistic of interest (and, in addition, to results for the transient of the M/ M/ ∞ queue, which are of independent interest). Since this procedure is applicable to exponential holding times only, and is rather numerically involved, we develop an approximate procedure for general holding times. In this procedure we record the number of trunks occupied at equidistant points in time Δ , 2 Δ , … , where Δ is chosen sufficiently large to safely assume that the samples are independent; this procedure is backed by results on the transient of the M / G / ∞ queue, thus complementing earlier results on relaxation times. The validity of the testing procedures is demonstrated through an extensive set of numerical experiments.

Regional Dialect Variation in the Vowel Systems of Typically Developing Children

To investigate regional dialect variation in the vowel systems of typically developing 8- to 12-year-old children. Thirteen vowels in isolated h_d words were produced by 94 children and 93 adults (males and females). All participants spoke American English and were born and raised in 1 of 3 distinct dialect regions in the United States: western North Carolina (Southern dialect), central Ohio (Midland dialect), and southeastern Wisconsin (Northern Midwestern dialect). Acoustic analysis included formant frequencies (F1 and F2) measured at 5 equidistant time points in a vowel and formant movement (trajectory length). Children's productions showed many dialect-specific features comparable to those in adult speakers, both in terms of vowel dispersion patterns and formant movement. Different features were also found, including systemic vowel changes, significant monophthongization of selected vowels, and greater formant movement in diphthongs. The acoustic results provide evidence for regional distinctiveness in children's vowel systems. Children acquire not only the systemic relations among vowels but also their dialect-specific patterns of formant dynamics. Directing attention to the regional variation in the production of American English vowels, this work may prove helpful in better understanding and interpreting the development of vowel categories and vowel systems in children.

Some statistical properties of differencing schemes for baseline correction of sedimentation velocity data

For the detailed analysis of sedimentation velocity data, the consideration of radial-dependent baseline offsets is indispensable. Two main approaches are data differencing (“delta-c” approach) and explicit inclusion of baseline parameters in the model (“direct boundary model” of the raw data). The current work aims to clarify the relationships between the two approaches. To this end, a simple model problem is examined. We show that the explicit consideration of the baseline in the model is equivalent to a differencing scheme where the average value is subtracted from all data points. Pairwise differencing in the delta-c approach always results in higher parameter uncertainty. For equidistant time points, the increase is smallest when the reference points are taken at intervals of 1/3 or 2/3 of the total number of time points. If the difference data are misinterpreted to be statistically independent samples, errors in the calculation of the parameter uncertainties can occur. Contrary to claims in the literature, we observe that there is no distinction in the approaches regarding their “model dependence”; both approaches arise from the integral or differential form of the same model, and both approaches can and should provide explicit estimates of the baseline values in the original data space for optimal discrimination between macromolecular sedimentation models.

Estimation for the discretely observed telegraph process

The telegraph process {X(t), t>0}, is supposed to be observed at n+1 equidistant time points t_i=i Delta_n,i=0,1,... , n. The unknown value of lambda, the underlying rate of the Poisson process, is a parameter to be estimated. The asymptotic framework considered is the following: Delta_n -> 0, n Delta_n = T -> infty as n -> infty. We show that previously proposed moment type estimators are consistent and asymptotically normal but not efficient. We study further an approximated moment type estimator which is still not efficient but comes in explicit form. For this estimator the additional assumption n Delta_n^3 -> 0 is required in order to obtain asymptotic normality. Finally, we propose a new estimator which is consistent, asymptotically normal and asymptotically efficient under no additional hypotheses.

Optimal Designs for Empirical Bayes Estimators of Individual Linear and Quadratic Growth Curves in Linear Mixed Models

Many studies on optimal designs for linear mixed model analysis of repeated measures data have focussed on estimating the fixed effects. The present study investigates the optimal number of time points and subjects in case random effects have to be estimated. Linear mixed models with a linear or quadratic trend across equidistant time points are studied. Given a particular cost function, we examine which designs minimise the expected average squared prediction error. Robustness of the optimal design, important when one does not know the underlying model, is also treated.

Optimal designs for clinical trials with second-order polynomial treatment effects

The effect of adding intermediate measures on the efficiency of treatment effect estimation is considered for a second-order polynomial treatment effect, equidistant time-points, different covariance structures and two optimality criteria, assuming either a fixed sample size or a fixed budget. The benefit of adding intermediate measures (at the expense of subjects) depends strongly on the assumed covariance structure and is hardly affected by the two used optimality criteria (Ds or c). For a fixed sample size, the increase in efficiency by adding intermediate measures is large for a compound symmetric structure and small for a first-order auto-regressive structure. For a first-order auto-regressive structure with measurement error, the results depend on the covariance parameter values. For a fixed budget and linear cost function, the design with only three measures per subject is often highly efficient. If the structure resembles compound symmetry and the cost per subject is eight or more times larger than the cost per repeated measure, however, more than three measures are required to obtain highly efficient treatment effect estimators. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. Given a design with three repeated measures and a second-order polynomial treatment effect, equidistant time-points are either optimal (Ds-) or highly efficient (c-optimality criterion). The results are illustrated by a practical example.

ON LIKELIHOOD ESTIMATION FOR DISCRETELY OBSERVED MARKOV JUMP PROCESSES

SummaryThe parameter estimation problem for a Markov jump process sampled at equidistant time points is considered here. Unlike the diffusion case where a closed form of the likelihood function is usually unavailable, here an explicit expansion of the likelihood function of the sampled chain is provided. Under suitable ergodicity conditions on the jump process, the consistency and the asymptotic normality of the likelihood estimator are established as the observation period tends to infinity. Simulation experiments are conducted to demonstrate the computational facility of the method.

Endovascular Aneurysm Repair Alters Renal Artery Movement: A Preliminary Evaluation Using Dynamic CTA

To observe the natural renal artery motion during cardiac cycles in patients with abdominal aortic aneurysm (AAA) and how the implantation of stent-grafts may distort this movement. Data on 29 renal arteries from 15 male patients (mean age 72.6 years, range 66-83) treated with Talent or Excluder stent-grafts were acquired using an electrocardiographically (ECG)-gated dynamic 64-slice CT scanner. ECG-triggered retrospective reconstructions were made at 8 equidistant time points over the R-R cardiac cycle. The gated datasets were reconstructed perpendicular to the center flow lumen of each renal artery at 1.2 and 2.4 cm from the renal ostium. Center of mass displacement was determined per cardiac cycle for pre- and post-EVAR renal arteries and compared. Normal renal artery motion in AAA patients was impressive, with up to 3-mm movement both near and distant from the aorta (mean 2.0+/-0.6 mm, range 1.1-3.0). EVAR inhibited proximal renal motion, resulting in a 31% decrease in maximal movement (mean 1.4+/-0.7 mm, range 0.7-2.0; p < or = 0.05). Distal renal artery motion was unaffected by EVAR, with motion similar to the pre-EVAR state. ECG-gated dynamic CTA is feasible on a 64-slice scanner with a standard radiation dose and can detect potentially serious consequences of EVAR. EVAR alters renal artery motion by limiting proximal motion while leaving distal motion unaffected.

Parametric Estimation for the Standard and Geometric Telegraph Process Observed at Discrete Times

The telegraph process X(t), t>0, (Goldstein, 1951) and the geometric telegraph process S(t) = s_0 *exp((mu - 0.5*sigma^2)*t + sigma * X(t)) with mu a known constant and sigma>0 a parameter are supposed to be observed at N+1 equidistant time points ti=i*DeltaN,i=0,1,..., N. For both models lambda, the underlying rate of the Poisson process, is a parameter to be estimated. In the geometric case, also sigma>0 has to be estimated. We propose different estimators of the parameters and we investigate their performance under the high frequency asymptotics, i.e. DeltaN -> 0, $N*DeltaN = T, T finite, as N -> infinity, with T>0 fixed. The process X(t) in non markovian, non stationary and not ergodic thus we use approximation arguments to derive estimators. Given the complexity of the equations involved only estimators on the first model can be studied analytically. Therefore, we run an extensive Monte Carlo analysis to study the performance of the proposed estimators also for small sample size N.