Minimum Segment Length Research Articles

Ms.FPOP: A Fast Exact Segmentation Algorithm with a Multiscale Penalty

Given a time series in R n with a piecewise constant mean and independent noises, we propose an exact dynamic programming algorithm for minimizing a least-squares criterion with a multiscale penalty, favoring well-spread changepoints. This penalty was proposed by Verzelen et al. and achieves optimal rates for changepoint detection and changepoint localization in a non-asymptotic scenario. Our proposed algorithm, Multiscale Functional Pruning Optimal Partitioning (Ms.FPOP), extends functional pruning ideas presented in Rigaill and Maidstone et al. to multiscale penalties. For large signals ( n ≥ 10 5 ) with sparse changepoints, Ms.FPOP is shown empirically to be quasi-linear and faster than the Pruned Exact Linear Time (PELT) method of Killick et al. applied to the multiscale penalty of Verzelen et al. which exhibits quadratic slowdown in these cases. We propose an efficient implementation of Ms.FPOP coded in C++ interfaced with R that can segment profiles of up to n = 10 6 in a matter of seconds. Our algorithm works for slightly more general multiscale penalties. In particular, it allows a minimum segment length to be imposed. Using simple simulations we then show that where profiles are sufficiently large ( n ≥ 10 4 ), Ms.FPOP using the multiscale penalty of Verzelen et al. is typically more powerful than optimizing a least-squares criterion with the BIC penalty of Yao, a criterion that was shown by Fearnhead and Rigaill to perfom well across a wide range of scenarios. Supplementary materials for this article are available online.

On optimal segmentation and parameter tuning for multiple change-point detection and inference

Change-point analysis is the task of finding abrupt (and significant) changes in the underlying model of a signal or time series. Change-point detection methods typically involve specifying the maximum number of segments to search for and the minimum segment length. However, there is no objective way to pre-specify these two parameters, and it mostly depends upon the particular application. Within this framework, a recursive optimization algorithm is developed that is capable of exploring and fine tuning these two input parameters, and optimally segmenting a time series. This multiple change-point detection technique therefore addresses a wide class of real-life contexts and problems where the identification of optimal level shifts in a time series is the main goal. Extensive simulation results are presented and a real-life example is given to illustrate the implementation of the developed scheme in practice and to unfold its capabilities. Concluding remarks and suggestions for future research are also provided.

Reinforcing Hurst Exponent with Oscillation Detection for Control Performance Analysis: An Industrial Application

Control performance assessment is one of the most important components of control assets monitoring. In the past decades, many different data-based approaches have been presented to assess control performance. Due to the high number of control loops for production industries, the methods requiring less parameters and less priori information became popular in industrial use. Detrended Fluctuation Analysis (DFA) is one of these methods, requiring only closed loop data and a pair of segment length to estimate Hurst exponent based control performance. However, the selection of segment lengths plays an important role in estimation, especially for oscillating control loops. In this paper, we have proposed an additional step (i.e. a step zero) to DFA to estimate control performance. This step uses an autocorrelation based and robust oscillation detection and characterization method to identify the oscillation period. Then, the calculated period is used to select the minimum segment length which leads more robust and precise estimation of control performance based on DFA. The proposed method has been applied and tested on several industrial control loops. The comparisons of the results between two approaches are given.

Effect of segment length, sampling frequency, and imaging modality on the estimation of measures of brain meta-state activation: an MEG/EEG study.

The main objective of this study was to examine the influence that recording length, sampling frequency, and imaging modality have on the estimation and characterization of spontaneous brain meta-states during rest. To this end, a recently developed method of meta-state extraction and characterization was applied to a subset of 16 healthy elderly subjects from two independent electroencephalographic and magnetoencephalographic (EEG/MEG) databases. The recordings were segmented into the first 5, 10, 15, 20, 25, 30, 60 and 90-s of artifact-free activity and meta-states were extracted. Temporal activation sequence (TAS) complexity, which characterizes the complexity of the metastateactivation sequences during rest, was calculated. Then, its stability as a function of segment length, sampling frequency, and imaging modality was assessed. The results showed that, in general, the minimum segment length needed to fully characterize resting-state meta-state activation complexity ranged from 15 to 25 seconds. Moreover, it was found that the sampling frequency has a slight influence on the complexity measure, and that results were similar across EEG and MEG. The findings indicate that the proposed methodology can be applied to both EEG and MEG recordings and displays stable behavior with relatively short segments. However, methodological choices, such as sampling frequency, should be carefully considered.

Combining a segmentation procedure and the BaRatin stationary model to estimate nonstationary rating curves and the associated uncertainties

Streamflow time series data are fundamental to hydrological science and water management applications, which are commonly derived from stage-discharge rating curves. The rating curves are usually nonstationary due to temporal characteristics of stream channel and human activities such as indiscriminate dig of sediment. This implies the need for an efficient method to estimate nonstationary rating curves from an adequate dataset. This study employed a shifting method to estimate the nonstationary rating curves and the associated uncertainties. The method includes two steps: a coupled algorithm PELT&CROPS was first performed to divide the gauging samples into homogeneous families by detecting the multiple change points in a time series of a residual indicator. Then, the rating curves were calibrated with the BaRatin stationary model using these homogeneous gaugings within each stationary period. The method was applied at Shijiao Hydrological Station in China. We found that: (1) Set the lower and upper limit of parameter CROPS (changepoints for a range of penalties) to 0 and Inf respectively, the whole range of segmentation can be calculated. (2) Parameter Minseglen (minimum segment length) is of great significance to the segmentation result. More changepoints will be detected as the value of Minseglen decreasing. An appropriate Minseglen value should be assigned to find the optimal segmentation. (3) The stage-discharge relationship in the low flow part is more sensitive to the variation of river topography. Ten segmentations are needed to produce an accurate discharge for low flow prediction, while two segmentations for calibration can produce an accurate discharge for high flow prediction. (4) Information redundancy exists in the vast amount of gaugings. The BaRatin model can reduce the use of calibration data by employing stage-discharge function with a precise exponent from the hydraulic knowledge at a hydrological station.

Identifying stationary phases in multivariate time series for highlighting behavioural modes and home range settlements.

Recent advances in biologging open promising perspectives in the study of animal movements at numerous scales. It is now possible to record time series of animal locations and ancillary data (e.g. activity level derived from on-board accelerometers) over extended areas and long durations with a high spatial and temporal resolution. Such time series are often piecewise stationary, as the animal may alternate between different stationary phases (i.e. characterized by a specific mean and variance of some key parameter for limited periods). Identifying when these phases start and end is a critical first step to understand the dynamics of the underlying movement processes. We introduce a new segmentation-clustering method we called segclust2d (available as a r package at cran.r-project.org/package=segclust2d). It can segment bivariate (or more generally multivariate) time series and possibly cluster the various segments obtained, corresponding to different phases assumed to be stationary. This method is easy to use, as it only requires specifying a minimum segment length (to prevent over-segmentation), based on biological rather than statistical considerations. This method can be applied to bivariate piecewise time series of any nature. We focus here on two types of time series related to animal movement, corresponding to (a) at large scale, series of bivariate coordinates of relocations, to highlight temporary home ranges, and (b) at smaller scale, bivariate series derived from relocations data, such as speed and turning angle, to highlight different behavioural modes such as transit, feeding and resting. Using computer simulations, we show that segclust2d can rival and even outperform previous, more complex methods, which were specifically developed to highlight changes of movement modes or home range shifts (based on hidden Markov and Ornstein-Uhlenbeck modelling), which, contrary to our method, usually require the user to provide relevant initial guesses to be efficient. Furthermore, we demonstrate it on actual examples involving a zebra's small-scale movements and an elephant's large-scale movements, to illustrate how various movement modes and home range shifts, respectively, can be identified.

Short Segment Statewide Screening of Midblock Crashes in South Carolina

The AASHTO Highway Safety Manual (HSM) presents a variety of methods for quantitatively estimating crash frequency or severity at a variety of locations. The HSM predictive methods require the roadway network to be divided into homogeneous segments and intersections, or sites populated with a series of attributes. It recommends a minimum segment length of 0.1 mi. This research focuses on segment lengths of less than 0.1 mi for statewide screening of midblock crash locations to identify site specific locations with high crash incidence. The paper makes an argument that many midblock crashes can be concentrated along a very short segment because of an undesirable characteristic of a specific site. The use of longer segments may “hide” the severity of a single location if the rest of the segment has few or no additional crashes. In actuality, this research does not divide sections of roads into short segments. Instead, a short-window approach is used. The underlying road network is used to create a layer of segment polygons using GIS buffering. Crash data are then overlaid and aggregated to the segment polygons for further analysis. The paper makes a case for the use of short fixed segments to do statewide screening and how accurately geocoded crash data is key to its use. A comparison is made with a sliding-window approach (Network Kernel Density). The benefit of using fixed segments is that they are much less complex than using the sliding-window approach. Because the segmentation can be the same from year to year, direct comparisons can be made over time while spatial integrity is maintained.

Effect of Segment length on domain wall pinning in multisegmented Co/Ni nanowires for 3D memory applications

Abstract The interfaces between different materials in multisegmented nanowires act as pinning centers for domain walls, making these nanowires attractive materials for 3D memory devices. Here, the switching events which accompany a domain wall pinning and depinning in two-segmented Co/Ni nanowires with 80 nm in diameter have been simulated for various segment lengths, using the MAGPAR package within the Virtual Micromagnetics environment. Different switching mechanisms of the magnetization were found for nanowires with different segment lengths, contributing to different values of the pinning and depinnning fields. Domain wall pinning is caused by the stray field from the Co segment; therefore, the position of the pinned domain wall depends on the cobalt segment’s length: in case of the smaller segment lengths, the domain wall is pinned at the interface itself, whereas in case of 700 nm segments a 150 nm displacement of the pinned domain wall from the interface is found, consistent with experimental reports. Domain wall pinning is manifested as a plateau in the magnetization curve. In case of nanowires with shorter segments, another plateau is observed that is related to the creation of a magnetic vortex structure. These findings are crucial towards determining the minimum segment length to achieve a higher bit density that displays optimal pinning and depinning fields.

Tapered vs Cylindrical Stem Fixation in a Model of Femoral Bone Deficiency in Revision Total Hip Arthroplasty

Distal fixation achieved with a tapered stem design has demonstrated favorable clinical results in revision total hip arthroplasty in the setting of severe bone defects. However, stem subsidence is common with this stem design. The purpose of this study is to compare the initial fixation stability of a tapered stem design to a fully porous-coated cylindrical stem design in a model of severe femoral bone deficiency. Tapered and cylindrical stems (n= 8) were implanted into a model femur with progressively shorter segments for fixation (9, 6, or 3 cm). The stems were axially loaded, and the force to produce subsidence was recorded. Average loads to produce 150 μm of displacement with a 3-cm segment were higher forthetapered stem (393 N vs 221 N, P < .01). No difference was observed in the 6- or 9-cm models. Average loads to produce failure (>4-mm subsidence) were also higher for tapered stems with a 3-cm segment (1574 N vs 500 N, P < .0001). A regression analysis determined the minimum segment length of 1.5-2.5 cm to obtain stable fixation with a tapered stem design (R(2)= 0.78, P < .001). Tapered stems required higher loads to produce subsidence than cylindrical stems in a revision THA model. Revision tapered stems require a minimum intact segment of 1.5-2.5 cm to obtain adequate initial fixation stability. Revision tapered stems have superior initial fixation stability to cylindrical stems in the setting of severe bone loss.

New polymer syntheses. XCVII. Hyperbranched LC‐polyesters based on β‐(4‐hydroxyphenyl)propionic acid and 4‐hydroxybenzoic acid

Two classes of liquid crystalline hyperbranched copolyesters were prepared by the copolycondensation of silylated 3,5-bis(acetoxy)benzoic acid with mixtures of mesogenic difunctional monomers. The first class of LC-copolyesters was obtained from 1 : 1 mixtures (molar ratio) of silylated β-(4-acetoxyphenyl)propionic acid and silylated 4-acetoxybenzoic acid (poly(HPPA/HBA)). The second class of LC-copolyesters was obtained by additional copolycondensation of silylated 6-acetoxy-2-naphthoic acid. The hyperbranched copolyesters of this ternary system poly(HPPA/HBA/HNA) proved to be less crystalline in contrast to the binary system. In both classes of LC-copolyesters the degree of branching was varied via the feed ratio of 3,5-dihydroxybenzoic acid. A minimum segment length of 6 difunctional monomer units between the branching points is required to establish a nematic phase. However, a greater segment length is needed to obtain a homogeneous LC-phase. The poly(HPPA/HBA) copolyesters were also characterized by melt rheology. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1397–1405, 1998

New polymer syntheses. XCVII. Hyperbranched LC-polyesters based on ?-(4-hydroxyphenyl)propionic acid and 4-hydroxybenzoic acid

Two classes of liquid crystalline hyperbranched copolyesters were prepared by the copolycondensation of silylated 3,5-bis(acetoxy)benzoic acid with mixtures of mesogenic difunctional monomers. The first class of LC-copolyesters was obtained from 1 : 1 mixtures (molar ratio) of silylated β-(4-acetoxyphenyl)propionic acid and silylated 4-acetoxybenzoic acid (poly(HPPA/HBA)). The second class of LC-copolyesters was obtained by additional copolycondensation of silylated 6-acetoxy-2-naphthoic acid. The hyperbranched copolyesters of this ternary system poly(HPPA/HBA/HNA) proved to be less crystalline in contrast to the binary system. In both classes of LC-copolyesters the degree of branching was varied via the feed ratio of 3,5-dihydroxybenzoic acid. A minimum segment length of 6 difunctional monomer units between the branching points is required to establish a nematic phase. However, a greater segment length is needed to obtain a homogeneous LC-phase. The poly(HPPA/HBA) copolyesters were also characterized by melt rheology. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1397–1405, 1998

Separating the ground and airborne laser sampling phases to estimate tropical forest basal area, volume, and biomass

Airborne laser profiling data were used to estimate the basal area, volume, and biomass of primary tropical forests. A procedure was developed and tested to divorce the laser and ground data collection efforts using three distinct data sets acquired in and over the tropical forests of Costa Rica. Fixed-area ground plot data were used to simulate the height characteristics of the tropical forest canopy and to simulate laser measurements of that canopy. On two of the three study sites, the airborne laser estimates of basal area, volume, and biomass grossly misrepresented ground estimates of same. On the third study site, where the widest ground plots were utilized, airborne and ground estimates agreed within 24%. Basal area, volume, and biomass prediction inaccuracies in the first two study areas were tied directly to disagreements between simulated laser estimates and the corresponding airborne measurements of average canopy height, height variability, and canopy density. A number of sampling issues were investigated; the following results were noted in the analyses of the three study areas. 1) Of the four ground segment lengths considered (25 m, 50 m, 75 m, and 100 m), the 25 m segment length introduced a level of variability which may severely degrade prediction accuracy in these Costa Rican primary tropical forests. This effect was more pronounced as plot width decreased. A minimum segment length was on the order of 50 m. 2) The decision to transform or not to transform the dependent variable (e.g., biomass) was by far the most important factor of those considered in this experiment. The natural log transformation of the dependent variable increased prediction error, and error increased dramatically at the shorter segment lengths. The most accurate models were multiple linear models with forced zero intercept and an untransformed dependent variable. 3) General linear models were developed to predict basal area, volume, and biomass using airborne laser height measurements. Useful laser measurements include average canopy height, all pulses (ha), average canopy height, canopy hits (hc) and the coefficients of variation of these terms (ca and cc). Coefficients of determination range from 0.4 to 0.6. Based on this research, airborne laser and ground sampling procedures are proposed for use for reconnaissance level surveys of inaccessible forested regions.

Hydroxyapatite chromatography of short double-helical DNA

Short double-helical segments of T7 DNA, ranging in length from 16 to more than 2000 nucleotide pairs, were specifically cleaved by the restriction endonuclease from Hemophilus aegyptius , endonuclease Z. These segments were separated by gel electrophoresis, and assigned lengths on the basis of their mobility using the known lengths of Hin II + III and H. aegyptius endonuclease III segments of ФX replicative form I as a standard. Shorter segments elute from hydroxyapatite at lower concentrations of sodium or potassium phosphate buffer: the concentration of phosphate buffer causing elution is inversely proportional to the reciprocal of the segment length. On the basis of these plots one may estimate that double-helical segments having more than 17 nucleotide pairs will be retained on hydroxyapatite at 25 °C in 0.14 M potassium buffer. When this expectation is tested by prolonged eluting with 0.14 M potassium phosphate buffer, the minimum segment length that is quantitatively retained was found to be between 28 and 37 nucleotide pairs long. Similar experiments with sodium phosphate buffer at 60 °C indicate segments longer than 43 to 54 will be quantitatively retained on hydroxyapatite in spite of prolonged washing with 0.12 M sodium phosphate buffer. When duplex segments are treated with exonuclease III to produce partly single-chained molecules, it is found that the elution position is that expected for single-chain-free duplex segments of the calculated shorter length. This suggests that the presence of single chains has no effect on binding of duplexes to hydroxyapatite.