Principal Curves Research Articles

Principal Graph and Structure Learning Based on Reversed Graph Embedding.

Many scientific datasets are of high dimension, and the analysis usually requires retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are mathematically formulated by curves, which is quite restrictive for real applications. A few methods can overcome the above problem, but they either require complicated human-made rules for a specific task with lack of adaption flexibility to different tasks, or cannot obtain explicit structures of data. To address these issues, we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding. As showcases, models that can learn a spanning tree or a weighted undirected `1 graph are proposed, and a new learning algorithm is developed that learns a set of principal points and a graph structure from data, simultaneously. The new algorithm is simple with guaranteed convergence. We then extend the proposed framework to deal with large-scale data. Experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly.

Behavioral Patterns of Common Bottlenose Dolphins (Tursiops truncatus truncatus) Within the Galveston—Port Bolivar Ferry Lane

The objective of this study is to assess Tursiops truncatus truncatus (Common Bottlenose Dolphin) group behavior as a function of spatial, temporal, and vessel proximity variables within the Galveston—Port Bolivar ferry lane, in lower Galveston Bay, TX. This area is subjected to vessel traffic entering the Houston, Texas City, and Galveston ship channels and at risk for environmental accidents. We used the Galveston—Port Bolivar ferries as a platform of opportunity to observe group behavior within the ferry lane. We conducted 1412 hours of observation between 1 June and 30 November 2013 and then utilized canonical correspondence analysis to evaluate behavioral state as a function of spatial, temporal, and vessel-proximity variables. Principal response curve (PRC) analysis showed significant variation in behavioral states over time in the Bolivar and Galveston zones as compared to the passage zone. Chi-square goodness-of-fit tests showed significant deviations from expected behavior observation across zone and time block. These findings demonstrate finescale behavioral variability in an area of high anthropogenic activity.

Improved nutrient status affects soil microbial biomass, respiration, and functional diversity in a Lei bamboo plantation under intensive management

Intensive management, such as fertilization and organic mulching, is applied frequently in Lei bamboo (Phyllostachys praecox) plantations to achieve higher production in subtropical China. However, responses as well as key impact factors of soil microbial properties under such management remain uncertain. We analyzed the relationships between nutrient changes and microbial properties and assessed the main factors determining microbial biomass, activity, and functional diversity in soils under intensive management in a Lei bamboo plantation. Soil samples of treatments of no fertilization (control), chemical fertilization (CF), and chemical and organic fertilization combined with organic mulching (CFOM + M) were taken before mulching. The soil organic carbon (SOC), dissolved organic carbon, and total and available nitrogen (N), phosphorus (P), and potassium (K) were measured. Microbial biomass carbon (MBC), basal respiration, and mineralization were also analyzed. Community level of physiological profile (CLPP) of microorganisms was analyzed by BIOLOG method to estimate the functional diversity and carbon (C) source utilization patterns of microbes. Principal component analysis (PCA), principal response curve (PRC), correlation analysis, regression analysis, and redundancy analysis (RDA) were performed to clarify changes in variables and determine the factors influencing microbial properties. SOC and total and available N, P, and K increased as follows: CFOM + M > CF > control. However, C/P and N/P ratios showed an opposite trend. MBC and respiration were not affected, but microbial quotient and metabolic quotient declined under intensive management. McIntosh diversity index was much higher in CFOM + M. The PCA showed that microorganisms in CFOM + M had a stronger ability to use most C sources. Weaker utilization of serine indicated an alleviation of nutrient deficiency in CFOM + M. PRC of CLPP showed a significant treatment effect and that utilization of serine sensitively responded to nutrient status over the whole incubation time. RDA showed that total and available N, total K, and C/P were the main factors influencing utilization of C sources by microbial communities. Fertilization combined with organic mulching increased soil nutrients, microbial biomass, and respiration in a Lei bamboo plantation. Abundant nutrients also increased C source use efficiency of microorganisms under intensive management. Changes of N and K and C/P might have led to a shift in microorganisms toward a different life strategy and determined the change in C source utilization patterns of microbial communities.

Reducing soil fertility to enable ecological restoration: A new method to test the efficacy of Full-Inversion Tillage

Ecological restoration of high-quality, semi-natural communities of conservation value on ex-arable soils with raised fertility has been a major problem in northern Europe. One suggested way of tackling this problem is to use Full-Inversion Tillage (FIT) where the fertile top-soil is moved below infertile sub-surface layers. This should provide infertile conditions at least in the short- to medium-term for the establishment of communities that require these conditions. Here, we pioneer a rigorous test of the efficacy of this approach. Our new method, using Principal Response Curves (PRCs), overcomes the difficulty in testing for change in soil physico-chemical properties down soil profiles with the inherent problem of autocorrelations between soil layers. Principal Response Curves (PRCs) is a multivariate technique, usually used to test for effects of treatment effects through time on a community matrix. We propose an extension of their use for the multivariate analysis of properties down a soil-depth profile. We tested the effects of FIT in two contrasting soils, before and after treatment. In a clay loam soil, FIT was effective in reducing the soil fertility in the surface 12cm. Indeed the soil available P concentration, a key variable, was more than halved in the surface layers, and was below the lowest literature target threshold for the establishment of semi-natural grassland. In contrast, in the sandy soil, soil properties increased throughout the profile after FIT, primarily because of the pre-treatment nutrient distribution within the soil. Before FIT treatment, the maximum concentrations of most measured variables were at mid-depth and FIT redistributed these to the surface and bottom layers. Our results demonstrate the potential for FIT in ecological restoration, but indicate that its efficacy depends on soil type and the site history. We recommend that in future a pre-treatment assessment of soil properties with depth is undertaken before FIT is implemented, and that afterwards our PRC approach can be used to test efficacy immediately after treatment, and has the potential for measuring soil resilience to perturbation through time.

Principal curve-based monitoring chart for anomaly detection of non-linear process signals

This study proposes a monitoring chart for anomaly detection of non-linear process signals generated by semiconductor manufacturing processes. In these manufacturing processes, fault detection and classification (FDC) and statistical process control (SPC) have been established as fundamental techniques to improve production efficiency and yield. Non-linear process signals are collected through automatic sensing during each operation cycle of a manufacturing process. As these cyclic signals non-linearly vary on the process state, the usage of the prevalent SPC chart is limited. Therefore, we propose a more efficient monitoring chart considering non-linear and time-variant characteristics. Using the principal curve, a non-linear smoothing algorithm, we construct a time-variant centerline that represents the standard pattern of the process. Then, control limits are calculated with time-variant variances over the course of the process. To evaluate performance, the proposed method was applied to industrial data for chemical vapor deposition (CVD), a semiconductor manufacturing process. We employed the misdetection ratio of signals to evaluate the performance. The proposed method demonstrated superior performance compared to other existing methods.

Assessing Potential Impact of Bt Eggplants on Non-Target Arthropods in the Philippines.

Studies on potential adverse effects of genetically engineered crops are part of an environmental risk assessment that is required prior to the commercial release of these crops. Of particular concern are non-target organisms (NTOs) that provide important ecosystem services. Here, we report on studies conducted in the Philippines over three cropping seasons with Bt eggplants expressing Cry1Ac for control of the eggplant fruit and shoot borer (EFSB), Leucinodes orbonalis, to examine potential effects on field abundance, community composition, structure and biodiversity of NTO’s, particularly non-target arthropod (NTA) communities. We document that many arthropod taxa are associated with Bt eggplants and their non-Bt comparators and that the number of taxa and their densities varied within season and across trials. However, we found few significant differences in seasonal mean densities of arthropod taxa between Bt and non-Bt eggplants. As expected, a lower abundance of lepidopteran pests was detected in Bt eggplants. Higher abundance of a few non-target herbivores was detected in non-Bt eggplants as were a few non-target beneficials that might control them. Principal Response Curve (PRC) analyses showed no statistically significant impact of Bt eggplants on overall arthropod communities through time in any season. Furthermore, we found no significant adverse impacts of Bt eggplants on species abundance, diversity and community dynamics, particularly for beneficial NTAs. These results support our previous studies documenting that Bt eggplants can effectively and selectively control the main pest of eggplant in Asia, the EFSB. The present study adds that it can do so without adverse effects on NTAs. Thus, Bt eggplants can be a foundational component for controlling EFSB in an Integrated Pest Management (IPM) program and dramatically reduce dependence on conventional insecticides.

Response variable selection in principal response curves using permutation testing

Principal response curves analysis (PRC) is widely applied to experimental multivariate longitudinal data for the study of time-dependent treatment effects on the multiple outcomes or response variables (RVs). Often, not all of the RVs included in such a study are affected by the treatment and RV-selection can be used to identify those RVs and so give a better estimate of the principal response. We propose four backward selection approaches, based on permutation testing, that differ in whether coefficient size is used or not in ranking the RVs. These methods are expected to give a more robust result than the use of a straightforward cut-off value for coefficient size. Performance of all methods is demonstrated in a simulation study using realistic data. The permutation testing approach that uses information on coefficient size of RVs speeds up the algorithm without affecting its performance. This most successful permutation testing approach removes roughly 95 % of the RVs that are unaffected by the treatment irrespective of the characteristics of the data set and, in the simulations, correctly identifies up to 97 % of RVs affected by the treatment.

First-principles prediction of the softening of the silicon shock Hugoniot curve

Shock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas-Fermi-based theories lack shell structure. The Kohn-Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining these first-principles EOS results, the principal shock Hugoniot curve of silicon for pressures varying from 1 Mbar to above 10 Gbar was derived. We find that silicon is 20% or more softer than what was predicted by widely-used EOS models. Existing high-pressure experimental data (P = 1 - 2 Mbar) seem to indicate this softening behavior of Si, which calls for future strong-shock experiments (P > 10 Mbar) to benchmark our results.

Quantum molecular dynamics simulations of equation of state of warm dense ethane

The equation of state of warm dense ethane is obtained using quantum molecular dynamics simulations based on finite-temperature density functional theory for densities from 0.1 g/cm3 to 3.1 g/cm3 and temperatures from 0.1 eV to 5.17 eV. The calculated pressure and internal energy are fitted with cubic polynomials in terms of density and temperature. Specific density-temperature-pressure tracks such as the principal and double shock Hugoniot curves along with release isentropes are predicted which are fundamental for the analysis and interpretation of high-pressure experiments. The principal and double shock Hugoniot curves are in agreement with the experimental data from the Sandia Z-Machine [Magyar et al., Phys. Rev. B 91, 134109 (2015)].

MCR-ALS and NIRS applied on the evaluation of the Lepidium meyenii antioxidant activity

The Peruvian Maca (Lepidium Meyenii Walp) is a food which is widely consumed around the Peruvian Andes and has been used in Brazil thanks to medicinal properties attributed by popular culture. Due to lack of information on this cultivar, it was proposed a study to evaluate the effect of adding Peruvian Maca in transgenic soybean oil. For this purpose, the spectra of soybean oil samples with and without addition of Maca after heating at different temperatures were measured at Visible and Near Infrared regions. The results were evaluated by chemometric methods of Principal Component Analysis (PCA) and Multivariate Curve Resolution with Alternating Least Squares (MCR-ALS). The results suggest that Maca inhibits the appearance of oxidation products, which is evidenced when comparing the results obtained for the heated oil with and without addition of Maca.

A rapid marker ordering approach for high-density genetic linkage maps in experimental autotetraploid populations using multidimensional scaling.

The paper proposes and validates a robust method for rapid construction of high-density linkage maps suitable for autotetraploid species. Modern genotyping techniques are producing increasingly high numbers of genetic markers that can be scored in experimental populations of plants and animals. Ordering these markers to form a reliable linkage map is computationally challenging. There is a wide literature on this topic, but most has focussed on populations derived from diploid, homozygous parents. The challenge of ordering markers in an autotetraploid population has received little attention, and there is currently no method that runs sufficiently rapidly to investigate the effects of omitting problematic markers on map order in larger datasets. Here, we have explored the use of multidimensional scaling (MDS) to order markers from a cross between autotetraploid parents, using simulated data with 74-152 markers on a linkage group and also experimental data from a potato population. We compared different functions of the recombination fraction and LOD score to form the MDS stress function and found that an LOD2 weighting generally performed well, including when missing values and genotyping errors are present. We conclude that an initial analysis using unconstrained MDS gives a rapid method to detect and remove problematic markers, and that a subsequent analysis using either constrained MDS or principal curve analysis gives reliable marker orders. The latter approach is also particularly rapid, taking less than 10s on a set of 258 markers compared to 6days for the JoinMap software. This MDS approach could also be applied to experimental populations of diploid species.

A Multi-objective Evolutionary Algorithm of Principal Curve Model Based on Clustering Analysis

A Multi-objective Evolutionary Algorithm of Principal Curve Model Based on Clustering Analysis

Principal Response Curves analysis of polyphenol variation in resistant and susceptible cotton after infection by a root-knot nematode (RKN)

The root-knot nematode (RKN), Meloidogyne incognita, attacks cotton root system. This study aimed to compare the induction of phenolic compounds over time in two cotton genotypes, resistant (TX-25) and susceptible (FM966), by RKN. Chemical profiles of cotton roots were obtained by HPLC, NMR, and colorimetric methods at four different time intervals. The Principal Response Curves analysis, a time-dependent, multivariate method, showed consistent variability over time in the profile of phenolic compounds between treatments for both genotypes. The variables that most contributed to the divergence between damaged and undamaged cotton roots were dimethoxylated and non-methoxylated gossypols, total flavonoids, and total phenols.

Online sequential prediction of bearings imbalanced fault diagnosis by extreme learning machine

Diagnosis of bearings generally plays an important role in fault diagnosis of mechanical system, and machine learning has been a promising tool in this field. In many real applications of bearings fault diagnosis, the data tend to be online imbalanced, which means, the number of fault data is much less than the normal data while they are all collected in online sequential way. Suffering from this problem, many traditional diagnosis methods will get low accuracy of fault data which acts as the minority class in the collected bearing data. To address this problem, an online sequential prediction method for imbalanced fault diagnosis problem is proposed based on extreme learning machine. This method introduces the principal curve and granulation division to simulate the flow distribution and overall distribution characteristics of fault data, respectively. Then a confident over-sampling and under-sampling process is proposed to establish the initial offline diagnosis model. In online stage, the obtained granules and principal curves are rebuilt on the bearing data which are arrived in sequence, and after the over-sampling and under-sampling process, the balanced sample set is formed to update the diagnosis model dynamically. A theoretical analysis is provided and proves that, even existing information loss, the proposed method has lower bound of the model reliability. Simulation experiments are conducted on IMS bearing data and CWRU bearing data. The comparative results demonstrate that the proposed method can improve the fault diagnosis accuracy with better effectiveness and robustness than other algorithms.

Holocene dynamics of vegetation change in southern and southeastern Brazil is consistent with climate forcing

At mid to high northern latitudes postglacial vegetation change has often occurred synchronously over large regions triggered mainly by abrupt climate change. Based on 19 pollen diagrams from southern and southeastern Brazil we explore if similar synchronicities in vegetation change were also characteristic for the vegetation dynamics in low latitudes. We used sequence splitting to detect past vegetation change in the pollen diagrams and computed principal curves and rates of change to visually evaluate the changes in composition and dynamics. The results show that vegetation change occurred mostly during the second half of the Holocene with distinct episodes of change. The character of vegetation change is generally consistent with shifts to wetter conditions and agrees with inferred shifts of the South American Monsoon. Speleothems as well as the titanium record from the Cariaco Basin indicate several episodes of rapid shifts in the precipitation regime, which are within the dating uncertainty of the here detected periods of vegetation change (8900, 5900, 2800, 1200 and 550 cal yrs BP). Our results indicate that low latitude vegetation composition follows precession forcing of the hydrology, while change is often triggered and synchronized by rapid climate change much like in high and mid latitudes. Pollen diagrams document changes in the abundance of individual taxa and changes in the amount of woodland cover, while small compositional changes indicate a regional stability of vegetation types during the Holocene.

Addressing potential local adaptation in species distribution models: implications for conservation under climate change.

Species distribution models (SDMs) have been criticized for involving assumptions that ignore or categorize many ecologically relevant factors such as dispersal ability and biotic interactions. Another potential source of model error is the assumption that species are ecologically uniform in their climatic tolerances across their range. Typically, SDMs treat a species as a single entity, although populations of many species differ due to local adaptation or other genetic differentiation. Not taking local adaptation into account may lead to incorrect range prediction and therefore misplaced conservation efforts. A constraint is that we often do not know the degree to which populations are locally adapted. Lacking experimental evidence, we still can evaluate niche differentiation within a species' range to promote better conservation decisions. We explore possible conservation implications of making type I or type II errors in this context. For each of two species, we construct three separate Max-Ent models, one considering the species as a single population and two of disjunct populations. Principal component analyses and response curves indicate different climate characteristics in the current environments of the populations. Model projections into future climates indicate minimal overlap between areas predicted to be climatically suitable by the whole species vs. population-based models. We present a workflow for addressing uncertainty surrounding local adaptation in SDM application and illustrate the value of conducting population-based models to compare with whole-species models. These comparisons might result in more cautious management actions when alternative range outcomes are considered.

On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations

We initiate in this paper the study of the geometry of the cross-cap in Minkowski 3-space $\mathbb{R}^3_1$. We distinguish between three types of cross caps according to their tangential line being spacelike, timelike or lightlike. For each of these types, the principal plane which is generated by the tangential line and the limiting tangent direction to the curve of self-intersection of the cross-cap plays a key role. We obtain special parametrisations for the three types of cross-caps and consider their affine properties. The pseudo-metric on the cross-cap changes signature along a curve and the singularities of this curve depend on the type of the cross-cap. We also study the binary differential equations of the lightlike curves and of the principal curves in the parameters space and obtain their topological models as well as the configurations of their solution curves.

Meander reconnection method determines restoration success for macroinvertebrate communities in a German lowland river

Re‐meandering of degraded rivers is a frequently implemented measure in river restoration. A simple solution is reconnection of old meanders; however, its success likely depends on the reconnection method. We conducted a field study to analyze the benefits of a fully reconnected (fully opened meander, blocked main channel) and a partially reconnected meander (opened downstream, pipe bypass from main channel upstream, still open main channel) for macroinvertebrate communities in a German lowland river. Immediately upon reconnection of the two meanders, habitat diversity, and macroinvertebrates were recorded for three years with sampling in spring and in summer each year. The results of a principal response curve analysis show that the macroinvertebrate community in the fully reconnected meander reflected main channel reference conditions after 1.5 years. The macroinvertebrate community composition was not improved relative to in‐stream reference conditions within the partially reconnected meander, which could be attributed to the almost complete lack of flow changes that resulted in missing improvements of substrate diversity. Our results show that the meander reconnection method must sufficiently affect the basic hydromorphological requirements to achieve reference macroinvertebrate community composition. Measures including hydromorphological conditions are therefore recommended for employment in environmental management.

Ground beetle assemblages across a habitat gradient in a stream watershed during 16 years of observation.

Most studies on riverine ground beetle assemblages last 1-2 years, and studies on carabids from lowland stream ecosystems are rare. In 1999, a 16-year study was launched to gain insight into the structure and diversity of carabid assemblages in a cross-section of four habitats located beside a 5 m wide stream: Meadow (wet meadow), Clumps (meadow scattered with birch and willow clumps farther from the river), Birch (birch stand), and Pine (pine stand located the farthest from the stream). The total number of 14, 216 individuals representing 118 carabid species were collected. Eleven functional carabid groups have been analysed. Principal response curve analysis showed significant differences existing during the whole study period among carabid assemblages from the four habitats. Generalised Linear Mixed Models analysis revealed a dependence of Chao2 estimator performance on temperature and ground water level, whereas life traits of carabids depended solely on the latter factor, affecting species composition (i.e., proportions of autumn and spring breeders, large and small zoophages, hemizoophages, forest, generalists and open area species, wingless species, hygrophilous, mesophilous and xerophilous species). The lower the ground water level, the higher was the proportion of late-successional species. Both Chao2 value and the proportion of late-successional species were growing with the increasing distance from the stream, peaking in the Pine habitat. Early-successional fauna dominated in streamside assemblages. IndVal analysis identified 1-9 characteristic species for each habitat type, mostly non-recurrent during the study period. Thus, species composition of riverine carabid assemblages should be studied for longer periods than 1-2 years to avoid accidental observations.

Smoothing Three-Dimensional Manifold Data, with Application to Tectonic Fault Detection

Three-dimensional manifold data arise in many contexts of geoscience, such as laser scanning, drilling surveys and seismic catalogs. They provide point measurements of complex surfaces, which cannot be fitted by common statistical techniques, like kriging interpolation and principal curves. This paper focuses on iterative methods of manifold smoothing based on local averaging and principal components; it shows their relationships and provides some methodological developments. In particular, it develops a kernel spline estimator and a data-driven method for selecting its smoothing coefficients. It also shows the ability of this approach to select the number of nearest neighbors and the optimal number of iterations in blurring-type smoothers. Extensive numerical applications to simulated and seismic data compare the performance of the discussed methods and check the efficacy of the proposed solutions.