Curve Alignment Research Articles

Time-synchronized clustering of gene expression trajectories

Current clustering methods are routinely applied to gene expression time course data to find genes with similar activation patterns and ultimately to understand the dynamics of biological processes. As the dynamic unfolding of a biological process often involves the activation of genes at different rates, successful clustering in this context requires dealing with varying time and shape patterns simultaneously. This motivates the combination of a novel pairwise warping with a suitable clustering method to discover expression shape clusters. We develop a novel clustering method that combines an initial pairwise curve alignment to adjust for time variation within likely clusters. The cluster-specific time synchronization method shows excellent performance over standard clustering methods in terms of cluster quality measures in simulations and for yeast and human fibroblast data sets. In the yeast example, the discovered clusters have high concordance with the known biological processes.

A Polynomial-Based Linear Mapping Strategy for Feedforward Compensation of Hysteresis in Piezoelectric Actuators

A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis response of piezoelectric actuators. These properties, namely, targeting turning points, curve alignment, and wiping-out effect, are applied in a linear mapping strategy to develop a mathematical framework for modeling the hysteresis phenomenon. More specifically, the locations of turning points are detected and recorded for the prediction of future hysteresis trajectory. An internal trajectory is assumed to follow a multiple-segmented path via a continuous connection of several curves passing through every two consequent turning points. These curves adopt their shapes via a linear mapping strategy from the reference hysteresis curves with polynomial configurations. Experimental implementation of the proposed method demonstrates slight improvement over the widely used Prandtl–Ishlinskii hysteresis operator. However, to maintain the level of precision during the operation, a sufficient number of memory units must be included to record the turning points. Otherwise, in the event of memory saturation, two memory-allocation modes, namely, “open” and “closed” strategies, can be implemented. It is shown that the closed memory-allocation strategy demonstrates better performance by keeping the most important target points. The proposed modeling framework is adopted in an inverse model-based control scheme for feedforward compensation of hysteresis nonlinearity. The controller is experimentally implemented on a three-dimensional nanopositioning stage for surface topography tracking, a problem typically encountered in scanning probe microscopy applications.

Curve alignment by moments

A significant problem with most functional data analyses is that of misaligned curves. Without adjustment, even an analysis as simple as estimation of the mean will fail. One common method to synchronize a set of curves involves equating “landmarks” such as peaks or troughs. The landmarks method can work well but will fail if marker events can not be identified or are missing from some curves. An alternative approach, the “continuous monotone registration” method, works by transforming the curves so that they are as close as possible to a target function. This method can also perform well but is highly dependent on identifying an accurate target function. We develop an alignment method based on equating the “moments” of a given set of curves. These moments are intended to capture the locations of important features which may represent local behavior, such as maximums and minimums, or more global characteristics, such as the slope of the curve averaged over time. Our method works by equating the moments of the curves while also shrinking toward a common shape. This allows us to capture the advantages of both the landmark and continuous monotone registration approaches. The method is illustrated on several data sets and a simulation study is performed.

Modification of Kolmogorov-Smirnov Test for DNA Content Data Analysis Through Distribution Alignment

The Kolmogorov-Smirnov (K-S) test is a statistical method often used for comparing two distributions. In high-throughput screening (HTS) studies, such distributions usually arise from the phenotype of independent cell populations. However, the K-S test has been criticized for being overly sensitive in applications, and it often detects a statistically significant difference that is not biologically meaningful. One major reason is that there is a common phenomenon in HTS studies that systematic drifting exists among the distributions due to reasons such as instrument variation, plate edge effect, accidental difference in sample handling, etc. In particular, in high-content cellular imaging experiments, the location shift could be dramatic since some compounds themselves are fluorescent. This oversensitivity of the K-S test is particularly overpowered in cellular assays where the sample sizes are very big (usually several thousands). In this paper, a modified K-S test is proposed to deal with the nonspecific location-shift problem in HTS studies. Specifically, we propose that the distributions are "normalized" by density curve alignment before the K-S test is conducted. In applications to simulation data and real experimental data, the results show that the proposed method has improved specificity.

Merging microarray cell synchronization experiments through curve alignment

The validity of periodic cell cycle regulation studies in plants is seriously compromised by the relatively poor quality of cell synchrony that is achieved for plant suspension cultures in comparison to yeast and mammals. The present state-of-the-art plant synchronization techniques cannot offer a complete cell cycle coverage and moreover a considerable loss of cell synchrony may occur toward the end of the sampling. One possible solution is to consider combining multiple datasets, produced by different synchronization techniques and thus covering different phases of the cell cycle, in order to arrive at a better cell cycle coverage. We propose a method that enables pasting expression profiles from different plant cell synchronization experiments and results in an expression curve that spans more than one cell cycle. The optimal pasting overlap is determined via a dynamic time warping alignment. Consequently, the different expression time series are merged together by aggregating the corresponding expression values lying within the overlap area. We demonstrate that the periodic analysis of the merged expression profiles produces more reliable p-values for periodicity. Subsequent Gene Ontology analysis of the results confirms that merging synchronization experiments is a more robust strategy for the selection of potentially periodic genes. Additional validation of the proposed algorithm on yeast data is also presented. Results, benchmark sets and scripts are freely available at our website: http://www.psb.ugent.be/cbd/publications.php

Preferences for Headlight Swivel Angles at Curves on Rural Two-Lane Highways

Drivers' preferences for headlight swivel angles were investigated as a function of curve alignment and assessment point before the curve section. In a field experiment using a test vehicle at the test track of the Denso Abashiri Test Center in Hokkaido, Japan, 33 young drivers were surveyed on their headlight swivel-angle preference at three assessment points before each curve. The subjects stopped at each assessment point and selected the preferred low-beam swivel angle from the swivel angles presented. Curve alignment and assessment point were found to have a marked effect on preferred swivel angle. A multiple regression model was developed for estimating optimal swivel angles. It was found that headlight swivel should be predictive toward assisting the driver's judgment of curve sharpness before the curve section. In the near future, headlight swivel systems incorporating a dynamic algorithm should be able to predict the road geometry before arrival at the curve, with the aid of commercial car navigation systems.

Landmark-Based Registration of Curves via the Continuous Wavelet Transform

This article is concerned with the problem of the alignment of multiple sets of curves. We analyze two real examples arising from the biomedical area for which we need to test whether there are any statistically significant differences between two subsets of subjects. To synchronize a set of curves, we propose a new nonparametric landmark-based registration method based on the alignment of the structural intensity of the zero-crossings of a wavelet transform. The structural intensity is a recently proposed multiscale technique that highlights the main features of a signal observed with noise. We conduct a simulation study to compare our landmark-based registration approach with some existing methods for curve alignment. For the two real examples, we compare the registered curves with FANOVA techniques, and a detailed analysis of the warping functions is provided.

Underlying memory-dominant nature of hysteresis in piezoelectric materials

Although the existence of nonlocal memories in hysteresis behavior of piezoelectric materials has been demonstrated, their detailed and thorough properties have yet to be revealed. Along this line, we disclose and demonstrate the underlying memory-dominant nature of hysteresis, and characterize its important properties that must be considered for the accurate prediction of hysteresis trajectory in piezoelectric materials. More specifically, the concept of recording the turning points, targeting the previously recorded turning points, curve alignment, and wiping-out effects at these points are introduced as the basic intellectual properties of hysteresis nonlinearity. A constitutive memory-based mathematical modeling framework is then developed and trained for the precise prediction of a hysteresis path for arbitrarily assigned input profiles. Utilizing a piezoelectric-driven actuator, it is experimentally demonstrated that if the number of memory units is sufficiently selected, model response in the prediction of a hysteresis track is significantly improved.

Time ordering of gene coexpression

Temporal microarray gene expression profiles allow characterization of gene function through time dynamics of gene coexpression within the same genetic pathway. In this paper, we define and estimate a global time shift characteristic for each gene via least squares, inferred from pairwise curve alignments. These time shift characteristics of individual genes reflect a time ordering that is derived from ob- served temporal gene expression profiles. Once these time shift characteristics are obtained for each gene, they can be entered into further analyses, such as clustering. We illustrate the proposed methodology using Drosophila embryonic development and yeast cell-cycle gene expression profiles, as well as simulations. Feasibility is demonstrated through the successful recovery of time ordering. Estimated time shifts for Drosophila maternal and zygotic genes provide excellent discrimination between these two categories and confirm known genetic pathways through the time order of gene expression. The application to yeast cell-cycle data establishes a natural time order of genes that is in line with cell-cycle phases. The method does not require periodicity of gene expression profiles. Asymptotic justifications are also provided.

Intra-observer Reproducibility and Interobserver Reliability of the Radiographic Parameters in the Spinal Deformity Study Groupʼs AIS Radiographic Measurement Manual

Retrospective cross-sectional assessment of the reproducibility and reliability of radiographic parameters. To measure the intra-examiner and interexaminer reproducibility and reliability of salient radiographic features. The management and treatment of adolescent idiopathic scoliosis (AIS) depends on accurate and reproducible radiographic measurements of the deformity. Ten sets of radiographs were randomly selected from a sample of patients with AIS, with initial curves between 20 degrees and 45 degrees. Fourteen measures of the deformity were measured from posteroanterior and lateral radiographs by 2 examiners, and were repeated 5 times at intervals of 3-5 days. Intra-examiner and interexaminer differences were examined. The parameters include measures of curve size, spinal imbalance, sagittal kyphosis and alignment, maximum apical vertebral rotation, T1 tilt, spondylolysis/spondylolisthesis, and skeletal age. Intra-examiner reproducibility was generally excellent for parameters measured from the posteroanterior radiographs but only fair to good for parameters from the lateral radiographs, in which some landmarks were not clearly visible. Of the 13 parameters observed, 7 had excellent interobserver reliability. The measurements from the lateral radiograph were less reproducible and reliable and, thus, may not add value to the assessment of AIS. Taking additional measures encourages a systematic and comprehensive assessment of spinal radiographs.

Theoretical Model of Shield Behavior During Excavation. I: Theory

Closed-type shield tunneling methods were developed together with computer-aided automatic control systems. However, automatic control systems are based on empirical relationships and do not have a precise theoretical background. In this paper, a model of the theoretical dynamic load acting on the shield during excavation is developed, taking into account shield tunnel engineering practices; i.e., the excavated area, the tail clearance, the rotation direction of the cutter face, sliding of the shield, ground loosening at the shield crown, and the dynamic equilibrium condition. To evaluate the validity of the model qualitatively, the simulation of shield behavior and the sensitivity analysis of the model parameters on the shield behavior are carried out in both straight and curve alignments for both sandy and clayey ground. The results for the shield behavior are examined, comparing them with the empirical and the theoretical one, and it is confirmed that the proposed model represents the shield behavior reasonably well.

Retrofitting to Correct Uplift of Curved Girder Bridge Through: Field Testing and Analysis

The Ramp C bridge at the New York State Thruway interchange with I-287 and New York State Route 17 in Rockland County near the New Jersey state line is a continuous four-span bridge with a reverse horizontal curve alignment. It consists of five steel girders with radial abutments and skewed pier supports (61 degrees). During construction immediately after the girders were erected and the counterweights were poured, at low temperatures, an unanticipated girder uplift occurred at one corner of an end span. Physical testing and analysis were undertaken to investigate this occurrence and to estimate the uplift forces. The data were used to design a tie-down system to correct the uplift problem and thus avoid delays in opening the bridge to traffic.

Automated Calculation of Sight Distance from Horizontal Geometry

This paper describes a method for automatic calculation of sight distance, subject only to constraints of horizontal geometry, along an arbitrary alignment of tangent sections, circular curves, and spiral transition curves. A parametric representation is used to describe the alignment and its tangent and normal vectors at all points. From this information, other parametric forms are derived that describe the curve along the center of the traveled lane and the lateral obstruction curve. Finally, an automatic method to determine sight distance is described, which is analogous to the manual “graphical method” often employed in practice. An example alignment is considered for demonstration purposes. The method is accurate, efficient, and consistent with manual calculations. It might be used for situations where detailed information about possible sight distance obstructions is not available, such as planning, preliminary design, or to support passing behavior modules of microscopic simulation models.

Modeling the alignment of fundamental frequency contours

Segmental factors can cause large temporal changes in local fundamental frequency (F0) movements associated with accented syllables (‘‘accent curves’’), but these changes are often not phonologically or perceptually significant. Yet, other factors can cause temporal changes that are smaller but nevertheless significant. A model is proposed according to which accent curves are (phonologically, perceptually) equivalent when they are generated from a common accent curve template using a common set of alignment rules. These alignment rules specify where the points making up the template are to be placed on the time axis, based on the durations of the segments in the syllable sequence with which the accent curve is associated. This model is shown to provide a detailed and accurate account of alignment of accent curves over a wide range of segmental configurations. The model is embedded in a superpositional framework, in which accent curves, segmental perturbation curves, and phrase curves are combined to account for complicated surface F0 contours. Height of accent curves is determined via a multiplicative model from factors related to prominence and position in the phrase.

A fuzzy algorithm for curve and surface alignment

We describe a fuzzy algorithm for the alignment of curves and surfaces which avoids the matching operation. To align a pair of shapes, each feature point selected in the first shape is associated to all the points in the second. A confidence degree is computed for each of these matches. The unknown parameters (pose variables and confidence degrees) are obtained by the minimization of a fuzzy energy, similar to the one proposed by Dunn and Bezdek in the context of fuzzy clustering. Closed form expressions are derived for the estimates of the unknown parameters. The performance of the proposed algorithm is illustrated by experimental results.

Alignment of curves by dynamic time warping

When studying some process or development in different subjects or units--be it biological, chemical or physical--we usually see a typical pattern, common to all curves. Yet there is variation both in amplitude and dynamics between curves. Following some ideas of structural analysis introduced by Kneip and Gasser, we study a method--dynamic time warping with a proper cost function--for estimating the shift or warping function from one curve to another to align the two functions. For some models this method can identify the true shift functions if the data are noise free. Noisy data are smoothed by a nonparametric function estimate such as a kernel estimate. It is shown that the proposed estimator is asymptotically normal and converges to the true shift function as the sample size per subject goes to infinity. Some simulation results are presented to illustrate the performance of this method.

A stochastic representation of cursive Chinese characters for on-line recognition

In this paper, a stochastic representation of on-line Chinese characters of cursive style is proposed. A character in this representation is modeled by a sequence of concatenated stochastic curves, termed stochastic cubic Bézier curves (SCBC), with random noises. Furthermore, we also propose a curve alignment procedure to consistently match an input character with a stochastic reference one. Some classification experiments were performed. The stochastic approach is hardly sensitive to the characters with linked and degraded strokes; meanwhile, its recognition rate is higher than 95% even for deformed confusing characters.

Alignment of planar curves

Often points on a planar curve are recorded by taking two or more overlapping views of the curve. One then wishes to align the data so that the common part of the curve in the two views matches. The alignment can be done easily by a human, but it can be a tedious process. In this paper a new method is developed for performing the alignment automatically by computer.

Transaortic Valve Gradient Determined by a Dual Lumen Pressure Monitoring Catheter

Simultaneous recordings of left ventricular (LV) and central aortic pressures (AO) provide the greatest accuracy for determination of the transaortic pressure difference. We describe a very simple technique for simultaneous measurement of LV and AO pressures using a new, dual lumen pressure monitoring catheter. Using this device, we compared simultaneous LV and AO as well as LV and femoral artery (FA) pressures before and after aortic valvuloplasty in seven consecutive patients. The difference between the mean aortic gradient or aortic valve area determined by the LV‐AO and LV‐FA measurement techniques was not statistically significant. Our initial experience with the double lumen pigtail catheter indicates that this device facilitates direct measurement of the LV‐AO pressure gradient and eliminates the need for two arterial punctures, a transseplal approach or alignment of LV and FA pressure curves.

Zielke instrumentation.

Zielke modified Dwyer's anterior spinal instrumentation to produce the Ventral Derotational Spondylodesis (VDS) System. The primary indication for VDS instrumentation is the treatment of progressive, single, major lumbar or thoracolumbar curves in idiopathic scoliosis. The surgical technique, including selection of appropriate curvatures and levels of instrumentation, is described. A group of 25 consecutive patients undergoing VDS instrumentation for lumbar or thoracolumbar curvatures was reviewed. The average correction of the major curve was 76%. The minor curvature was corrected with an average of 47%. A significant complication was a 20% incidence of pseudarthrosis and rod breakage. The implications of these problems are discussed. Zielke instrumentation is a powerful technique for the correction of selected curves. The system provides greater correction of the major curve, improved frontal and sagittal alignment, and preservation of distal motion segments.