Principal Component Analysis Modes Research Articles

Assessment of conservative force models from GRACE accelerometers and precise orbit determination

The accuracy of the conservative force-models is not clear and the new space accelerometers provide a unique opportunity for their validation. In this paper, the conservative-force model deficiencies are investigated via Principal Component Analysis (PCA) using 4 years of GRACE measurements (2006–2009). The deficiencies are assessed by comparing the accelerometer readouts with the differences between the conservative force-model and the precise orbit accelerations. Within this scheme, the spatiotemporal data analysis is synthesized in a time-series of grids whose latitudinal and longitudinal variations are respectively influenced by the half orbital period and the equatorial orbit shift. With maximum amplitude of 50 nm/s2, the mean map shows a positive overestimation in Canada and Brazil and negative in Greenland. Explaining the 74% of the variability, the two first pairs of PCA modes show un-modeled patterns with amplitudes maxima of 80 nm/s2 and 50 nm/s2. Their periodic behavior and wave-length of degree-6 and degree-11s spherical harmonics strongly suggest an additional modeling and improvement. As for the long-term variations, our results show a latitudinal variation of 15 nm/s2 maximum amplitude correlated with the day-night periods. Performing a combined analysis of ascending and descending orbits, a trend of 3 nm/s2yr in the Indian Ocean is also observed. Our new approach for orbital force-models validation can be considered crucial for the current state-of-the-art of precise orbit determination (POD) and Time–Varying Gravity (TVG) modeling.

PCA analysis of the nighttime anomaly in far-from-geomagnetic pole regions from VTEC GNSS data

Abstract The Weddell Sea Anomaly (WSA) is defined when the nighttime plasma density is greater than the daytime density in the area near the Weddell Sea, more specifically in the region limited by 50° S–70° S in latitude and 225° E–315° E in longitude. A similar ionospheric anomaly is also observed near the Okhotsk Sea in the northern hemisphere, and such a feature was named as Okhotsk Sea Anomaly (OSA). The objective of this work is to infer possible physical causes of the WSA and OSA phenomena. To that end, we applied the principal component analysis (PCA) technique to the vertical total electron content (VTEC) from global International GNSS Service (IGS) in order to analyze the temporal and spatial variations of the ionosphere during noon and night in far-from-magnetic pole regions, during a 3-year period at high (2000–2002) and low (2006–2008) solar activity conditions. The first mode of PCA applied on VTEC scattering represents on average the 93 % of the total VTEC variability. Thus, the PCA expansions up to mode 1 resulted enough to show WSA and OSA during summer solstices in both solar activity conditions, as well as WSA during spring equinox during low solar activity. Besides, the analysis of the temporal variations of these first modes should provide the interpretation of a probable physical explanation to the observed anomalies. We conclude that the main contributors to the anomalies should be a combination of the same physical mechanisms that explain annual variation and semiannual anomaly in that regions located far from the magnetic poles.

Characterizing implications of two-dimensional space–time orientations for principal component analysis of geographic time series

This article introduces four new modes of principal component analysis (PCA) to investigate space–time variability in an image time series. Using the concept of tensors, an image time series can be understood as a space–time cube and can be analysed using six different orientations by grouping the basic elements (voxels) of the cube across different dimensions. Voxels grouped across columns or rows of the cube to produce vectors result in profiles. Voxels grouped across different planes to produce matrices result in slices. The traditional S-mode and T-mode PCA are thus the profile modes and slice modes across time and across space, respectively. This research introduces two profile-mode orientations across longitude and latitude and two slice-mode orientations across longitude–time and latitude–time. The research shows that a more complete understanding of the spatio-temporal variability in the data set can be achieved by investigating these different orientation modes, as individual modes have the capability of capturing variability in a particular dimension of a spatio-temporal data set. A case study was carried out using weekly anomalies of the AVISO (Archiving, Validation and Interpretation of Satellite Oceanographic data) sea surface height product filtered for tropical instability waves (TIWs) for a three-year time period from 1997 to 1999 in the tropical Pacific region. The results show that PCA with longitude as the dimension of variability and latitude–time as the dimension of variability were able to capture the TIW and barotropic Rossby wave propagation across the equatorial Pacific. The other two orientation modes were able to detect dominant latitudinal locations for TIW.

Dynamics of βB2-Crystallin Motion Based on Principal Component Analysis and Normal Mode Analysis

The primary function of lens is to focus images perfectly on the retina. Lens crystallins however are flexible nanomachines that frequently accomplish their biological function by collective atomic motions in and/or out the lens. Although genetic and biochemical data on the βB2-crystallin protein are available from several sources, the correlation between conformational changes and dynamic behavior at the atomic level remains to be understood. The βB2-crystallin dimer has studied through a combination of molecular dynamics simulations, principal component analysis (PCA) and normal mode analyses. The changes in interface buried surface shows the mutual orientation of individual domains in βB2-crystallin dimer. The dominant PCA modes for concerted motions of the protein atoms were monitored in a lower-dimensions subspace. Three types of movements found in βB2-crystallin dimer, which are a twist propeller motion, a scissors type hinge motion, and a shear motion between the domains. Both the RMSF and the normal-mode dynamics showed that N-terminal β-sheet is the most correlated segments.

Modes and emergent time scales of embayed beach dynamics

AbstractIn this study, we use a simple numerical model (the Coastline Evolution Model) to explore alongshore transport‐driven shoreline dynamics within generalized embayed beaches (neglecting cross‐shore effects). Using principal component analysis (PCA), we identify two primary orthogonal modes of shoreline behavior that describe shoreline variation about its unchanging mean position: the rotation mode, which has been previously identified and describes changes in the mean shoreline orientation, and a newly identified breathing mode, which represents changes in shoreline curvature. Wavelet analysis of the PCA mode time series reveals characteristic time scales of these modes (typically years to decades) that emerge within even a statistically constant white‐noise wave climate (without changes in external forcing), suggesting that these time scales can arise from internal system dynamics. The time scales of both modes increase linearly with shoreface depth, suggesting that the embayed beach sediment transport dynamics exhibit a diffusive scaling.

Environmental Risk Assessment Based on High-Resolution Spatial Maps of Potentially Toxic Elements Sampled on Stream Sediments of Santiago, Cape Verde

Geochemical mapping is the base knowledge to identify the regions of the planet with critical contents of potentially toxic elements from either natural or anthropogenic sources. Sediments, soils and waters are the vehicles which link the inorganic environment to life through the supply of essential macro and micro nutrients. The chemical composition of surface geological materials may cause metabolic changes which may favor the occurrence of endemic diseases in humans. In order to better understand the relationships between environmental geochemistry and public health, we present environmental risk maps of some harmful elements (As, Cd, Co, Cr, Cu, Hg, Mn, Ni, Pb, V, and Zn) in the stream sediments of Santiago, Cape Verde, identifying the potentially harmful areas in this island. The Estimated Background Values (EBV) of Cd, Co, Cr, Ni and V were found to be above the Canadian guidelines for any type of use of stream sediments and also above the target values of the Dutch and United States guidelines. The Probably Effect Concentrations (PEC), above which harmful effects are likely in sediment dwelling organisms, were found for Cr and Ni. Some associations between the geological formations of the island and the composition of stream sediments were identified and confirmed by descriptive statistics and by Principal Component Analysis (PCA). The EBV spatial distribution of the metals and the results of PCA allowed us to establish relationships between the EBV maps and the geological formations. The first two PCA modes indicate that heavy metals in Santiago stream sediments are mainly originated from weathering of underlying bedrocks. The first metal association (Co, V, Cr, and Mn; first PCA mode) consists of elements enriched in basic rocks and compatible elements. The second association of variables (Zn and Cd as opposed to Ni; second PCA mode) appears to be strongly controlled by the composition of alkaline volcanic rocks and pyroclastic rocks. So, the second PCA mode is also considered as a natural lithogenic mode. The third association (Cu and Pb; third PCA mode) consists of elements of anthropogenic origin.

Regionalization of Precipitation Regimes in Iran Using Principal Component Analysis and Hierarchical Clustering Analysis

Daily gridded precipitation data, between years 1951 and 2007, obtained from APHRODITE database, were analyzed to regionalize precipitation regimes in Iran country. The S–mode of principal component analysis (PCA) was applied on seasonal correlation matrix with eight derived variables. Based on eigenvalues over one, three factors were extracted between the components and varimax rotation was used to enhance interpretability of retained PCA scores. Then, hierarchical clustering analysis (HCA) was applied to group the homogeneous precipitation regimes. According to the HCA, nine distinct and homogenous regions were recognized. Then, the Kolmogorov–Smirnov test on seasonal percentage of precipitation distribution in these regions was used to identify the independent regimes which have been spatially mapped by using GIS. This study showed that the APHRODITE dataset potentially could be used for regionalization of precipitation regimes in Iran. According to the results, use of this dataset in order to group precipitation regimes is recommended for arid and semi–arid regions of mid–latitudes, especially in the Middle East countries.

Simulating Large-Scale Conformational Changes of Proteins by Accelerating Collective Motions Obtained from Principal Component Analysis

Enhanced sampling methods remain of continuing interest over the past decades because they are able to explore conformational space of proteins much more extensively than conventional molecular dynamics (MD) simulations. In this paper, we report a new sampling method that utilizes a few collective modes obtained from principal component analysis (PCA) to guide the MD simulations. Two multidomain proteins, bacteriophage T4 lysozyme and human vinculin, are studied to test the method. By updating the PCA modes with a proper frequency, our method can sample large-amplitude conformational changes of the proteins much more efficiently than standard MD. Since those PCA modes are calculated from structural ensembles generated by all-atom simulations, the method may overcome an inherent limitation called "tip effect" that would possibly appear in those sampling techniques based on coarse-grained elastic network models. The algorithm proposed here is potentially very useful in developing tools for flexible fitting of protein structures integrating cryo-electron microscope or small-angle X-ray scattering data.

SU‐E‐T‐271: Quantitative Analysis of Correlations Between Patient Geometry and Dosimetric Variation for Prostate Cancer Cases Using PCA and Step‐Wise Regression

Purpose:To study the potential correlations between patient geometry information and corresponding plan dosimetric variation in terms of planning target volumes (PTVs) coverage and organs‐at‐risk (OARs) dose sparing for prostate cancer cases.Methods:We extracted dosimetric and geometrical data from twenty‐three clinically acceptable prostate treatment plans. Dosimetric data extracted from each patient was PTV dose‐volume historgram (DVH), and dose‐wall‐volume histograms (DWHs) for the bladder and rectum. Geometrical data extracted was the PTV volume, OAR volumes, and COP (closeness of OAR to PTV). COP is the weighted sum of the overlapping wall histogram (OWH). OWH is proposed to describe the complex spatial relationship between PTV and a hollow organ. Principal component analysis (PCA) was performed on the (inverted and downsampled) DVH and DWH data from all the patients. We then fit the patient geometry features to first 3 PCA scores using a step‐wise regression analysis. The fitting results in a mapping from plan geometry information to dosimetric features.Results:First 3 PCA modes were found corresponded to clinically relevant features, indicating a tradeoff between homogenous coverage of the PTV and higher OAR dose, higher average dose to the OARs and PTV, and bladder and rectum dose tradeoffs along the first, second and third principal component respectively. Step‐wise regression results show baldder surface volume and OAR COP more relevant to the 1st PCA modes score rather than other features with p‐value of 0.58 for bladder volume, 0.26 for bladder COP, 0.98 for rectum COP, and less than 0.025 for other features after t‐test.Conclusion:Quantitative correlations were established between patient geometry and corresponding plan dosimetric variation in terms of PTV coverage, trade‐offs between PTV coverage and OAR dose sparing and trade‐offs between different OAR dose sparing. Thus a new patient dosimetric variation tendency can be predicted and act as guidance for setting up planning goals.

Computation of mean and variance of the radiotherapy dose for PCA-modeled random shape and position variations of the target

Radiotherapy dose delivery in the tumor and surrounding healthy tissues is affected by movements and deformations of the corresponding organs between fractions. The random variations may be characterized by non-rigid, anisotropic principal component analysis (PCA) modes. In this article new dynamic dose deposition matrices, based on established PCA modes, are introduced as a tool to evaluate the mean and the variance of the dose at each target point resulting from any given set of fluence profiles. The method is tested for a simple cubic geometry and for a prostate case. The movements spread out the distributions of the mean dose and cause the variance of the dose to be highest near the edges of the beams. The non-rigidity and anisotropy of the movements are reflected in both quantities. The dynamic dose deposition matrices facilitate the inclusion of the mean and the variance of the dose in the existing fluence-profile optimizer for radiotherapy planning, to ensure robust plans with respect to the movements.

Principal component analysis identifies major muscles recruited during elite vertical jump

The vertical jump is an essential skill used in a volleyball match but the information on the principal muscles used is incomplete. The present study aimed to identify the major muscles used in vertical jump by employing the principal component analysis (PCA) and the analysis of area under the curve (AUC). Ten elite female volleyball players (NV) and 10 female sedentary controls (SC) participated in this study. Each subject performed 2 jumping styles: squat jump and vertical stop jump. Electrical activities from thirteen muscles in the arm, trunk, and leg were recorded with electromyography (EMG). EMG data were processed using PCA and AUC methods, and the major muscles were identified by the first mode of PCA and the highest AUC. Our results showed that the PCA method was more sensitive than the AUC method for classifying the group differences in major muscles during jumping. Distinct activation of the erector spinae may explain the better performance in the NV compared to the SC, who preferentially used other trunk muscles in jumping. Our observation indicates that the PCA method is an appropriate analytical tool to differentiate the major muscles used in jumping between elite athletes and sedentary controls. This finding provides important information for designing training programmes especially for vertical jumps in sports.

Semiautomatic bladder segmentation on CBCT using a population-based model for multiple-plan ART of bladder cancer

The aim of this study is to develop a novel semiautomatic bladder segmentation approach for selecting the appropriate plan from the library of plans for a multiple-plan adaptive radiotherapy (ART) procedure. A population-based statistical bladder model was first built from a training data set (95 bladder contours from 8 patients). This model was then used as constraint to segment the bladder in an independent validation data set (233 CBCT scans from the remaining 22 patients). All 3D bladder contours were converted into parametric surface representations using spherical harmonic expansion. Principal component analysis (PCA) was applied in the spherical harmonic-based shape parameter space to calculate the major variation of bladder shapes. The number of dominating PCA modes was chosen such that 95% of the total shape variation of the training data set was described. The automatic segmentation started from the bladder contour of the planning CT of each patient, which was modified by changing the weight of each PCA mode. As a result, the segmentation contour was deformed consistently with the training set to best fit the bladder boundary in the localization CBCT image. A cost function was defined to measure the goodness of fit of the segmentation on the localization CBCT image. The segmentation was obtained by minimizing this cost function using a simplex optimizer. After automatic segmentation, a fast manual correction method was provided to correct those bladders (parts) that were poorly segmented. Volume- and distance-based metrics and the accuracy of plan selection from multiple plans were evaluated to quantify the performance of the automatic and semiautomatic segmentation methods. For the training data set, only seven PCA modes were needed to represent 95% of the bladder shape variation. The mean CI overlap and residual error (SD) of automatic bladder segmentation over all of the validation data were 70.5% and 0.39 cm, respectively. The agreement of plan selection between automatic bladder segmentation and manual delineation was 56.7%. The automatic segmentation and visual assessment took on average 7.8 and 9.7 s, respectively. In 53.4% of the cases, manual correction was performed after automatic segmentation. The manual correction improved the mean CI overlap, mean residual error and plan selection agreement to 77.7%, 0.30 cm and 80.7%, respectively. Manual correction required on average 8.4 markers and took on average 35.5 s. The statistical shape-based segmentation approach allows automatic segmentation of the bladder on CBCT with moderate accuracy. Limited user intervention can quickly and reliably improve the bladder contours. This segmentation method is suitable to select the appropriate plan for multiple-plan ART of bladder cancer.

A statistical analysis of Gulf Stream variability from 18+ years of altimetry data

Altimetry data that bracket the core of the Gulf Stream (GS) between 32–39°N and 68–72°W are analyzed from a combined data set spanning the duration of the Topex, Jason-1, and Jason-2 missions. Absolute sea surface height, SSH, referenced to a geoid model and sea surface height anomaly, SSHA, referenced to a global mean sea surface model are calculated using pass 50 data from Topex cycle-002 (04-October-1992) through Jason-2 cycle-098 (02-Mar-2011). Five different indices of GS variability: (i) ΔSSH—the change in absolute height across the GS; (ii) ΔSSHA—the change in sea surface height anomaly across the GS; (iii) a barotropic velocity index; (iv) a baroclinic transport index; and (v) the position of the GS, are estimated from the 18+ year time series via seasonal time series, power spectral density functions, auto-covariance functions, and a principal component analysis (PCA). The average annual distribution of all the variables except velocity index increases from a spring/summer minimum to a fall maximum, then decreases during the winter to minimum values in spring and early summer. The average signal in barotropic velocity index reaches a maximum in summer, whereas the maximum baroclinic transport occurs in the fall. The seasonal signal in GS position is better approximated by a seasonal sinusoid than the dynamical variables, with minimum (southerly) positions in spring and maximum (northerly) positions in the fall. Variations in height difference across the current are in phase with changes in the width of the current, leading to smaller seasonal variations in the velocity which are out of phase with the other variables. None of the seasonal time series except GS position resemble a pure sinusoid; they more closely resemble the signal of a nonlinear oscillator.The three dominant periods for ΔSSH are 15–21 months, 7 months, and 4 years, with an integral time scale of 32 days. The dominant periods for ΔSSHA are 9 months, 21 months, and 5–6 months, with an integral time scale of 38 days. The spectral and PCA analyses of both ΔSSH and ΔSSHA are “pink”, indicating an energetic broad-band spectra. The dominant PCA modes explain less than 30% of the variability, indicative of highly nonlinear processes. The dominant periods for the barotropic velocity index are 9 months, 21 months, and 5 months, with an integral time scale of 14 days. The dominant periods for the baroclinic transport index are 11 months, 2–3 months, and monthly, with an integral time scale of 24 days. The dominant PCA modes of the velocity and transport indices explain 52% and 48% of the variability of their respective time series. The dominant periods for GS position are 9, 11, 13 months, and 1.5–6 years, with an integral time scale of 35 days. The first GS position PCA mode explains 50% of position variability. All of the time series of GS variability and the correlation between the North Atlantic Oscillation and GS position exhibit non-stationary behavior.

Automatic bladder segmentation on CBCT for multiple plan ART of bladder cancer using a patient-specific bladder model

In multiple plan adaptive radiotherapy (ART) strategies of bladder cancer, a library of plans corresponding to different bladder volumes is created based on images acquired in early treatment sessions. Subsequently, the plan for the smallest PTV safely covering the bladder on cone-beam CT (CBCT) is selected as the plan of the day. The aim of this study is to develop an automatic bladder segmentation approach suitable for CBCT scans and test its ability to select the appropriate plan from the library of plans for such an ART procedure. Twenty-three bladder cancer patients with a planning CT and on average 11.6 CBCT scans were included in our study. For each patient, all CBCT scans were matched to the planning CT on bony anatomy. Bladder contours were manually delineated for each planning CT (for model building) and CBCT (for model building and validation). The automatic segmentation method consisted of two steps. A patient-specific bladder deformation model was built from the training data set of each patient (the planning CT and the first five CBCT scans). Then, the model was applied to automatically segment bladders in the validation data of the same patient (the remaining CBCT scans). Principal component analysis (PCA) was applied to the training data to model patient-specific bladder deformation patterns. The number of PCA modes for each patient was chosen such that the bladder shapes in the training set could be represented by such number of PCA modes with less than 0.1 cm mean residual error. The automatic segmentation started from the bladder shape of a reference CBCT, which was adjusted by changing the weight of each PCA mode. As a result, the segmentation contour was deformed consistently with the training set to fit the bladder in the validation image. A cost function was defined by the absolute difference between the directional gradient field of reference CBCT sampled on the corresponding bladder contour and the directional gradient field of validation CBCT sampled on the segmentation contour candidate. The cost function measured the goodness of fit of the segmentation on the validation image and was minimized using a simplex optimizer. For each validation CBCT image, the segmentations were done five times using a different reference CBCT. The one with the lowest cost function was selected as the final bladder segmentation. Volume- and distance-based metrics and the accuracy of plan selection were evaluated to quantify the performance. Two to four PCA modes were needed to represent the bladder shape variation with less than 0.1 cm average residual error for the training data of each patient. The automatically segmented bladders had a 78.5% mean conformity index with the manual delineations. The mean SD of the local residual error over all patients was 0.24 cm. The agreement of plan selection between automatic and manual bladder segmentations was 77.5%. PCA is an efficient method to describe patient-specific bladder deformation. The statistical-shape-based segmentation approach is robust to handle the relatively poor CBCT image quality and allows for fast and reliable automatic segmentation of the bladder on CBCT for selecting the appropriate plan from a library of plans.

Decadal amplitude modulation of two types of ENSO and its relationship with the mean state

In this study, we classified two types of El Nino–Southern Oscillation (ENSO) events within the decadal ENSO amplitude modulation cycle using a long-term coupled general circulation model simulation. We defined two climate states—strong and weak ENSO amplitude periods—and separated the characteristics of ENSO that occurred in both periods. There are two major features in the characteristics of ENSO: the first is the asymmetric spatial structure between El Nino and La Nina events; the second is that the El Nino–La Nina asymmetry is reversed during strong and weak ENSO amplitude periods. El Nino events during strong (weak) ENSO amplitude periods resemble the Eastern Pacific (Central Pacific) El Nino in terms of the spatial distribution of sea surface temperature anomalies (SSTA) and physical characteristics based on heat budget analysis. The spatial pattern of the thermocline depth anomaly for strong (weak) El Nino is identical to that for weak (strong) La Nina, but for an opposite sign and slightly different amplitude. The accumulated residuals of these asymmetric anomalies dominated by an east–west contrast structure could feed into the tropical Pacific mean state. Moreover, the residual pattern associated with El Nino–La Nina asymmetry resembles the first principal component analysis (PCA) mode of tropical Pacific decadal variability, indicating that the accumulated residuals could generate the change in climate state. Thus, the intensified ENSO amplitude yields the warm residuals due to strong El Nino and weak La Nina over the eastern tropical Pacific. This linear relationship between ENSO and the mean state is strong during the mature phases of decadal oscillation, but it is weak during the transition phases. Furthermore, the second PCA mode of tropical Pacific decadal variability plays an important role in changing the phase of the first mode. Consequently, the feedback between ENSO and the mean state is positive feedback to amplify the first PCA mode, whereas the second PCA mode is a negative feedback to lead the phase change of the first PCA mode due to their lead-lag relationship. These features could be regarded as evidence that the decadal change in properties of ENSO could be generated by the nonlinear interaction between ENSO and the mean state on a decadal-to-interdecadal time scale.

Principal Component Analysis of Observed and Modeled Diurnal Rainfall in the Maritime Continent

Principal component analysis (PCA) is able to diagnose the diurnal rain cycle in the Maritime Continent into two modes that explain most of the diurnal variability in the region. The first mode results from the differential variation in potential instability forced by surface heat flux, insolation, and longwave radiative cooling on land and sea. The second mode is associated with intrinsic mesoscale dynamics of convective systems and its interactions with gravity waves, density currents, and local circulations in coastal regions or mountainous terrain. The spatial phase relation between the two modes determines whether a diurnal signal is propagating or stationary. Thus, validating model simulations of diurnal rainfall using PCA provides insights on the representation of dynamics and physics. In this paper, the main modes of diurnal rain variability in the Maritime Continent from satellite observations are studied and are compared with those from Weather Research and Forecasting (WRF) model simulations. Hovmoeller analyses of the reconstructed rainfall from the first two PCA modes clarify the impact of coastlines and mountains as sources of propagating signals. Wave cavities are identified in the Straits of Malacca, Malay Peninsula, and north Sumatra where stationary signals are produced. WRF reproduces the first two modes but each with a phase lead of about 1–2 h or longer, depending on the satellite rainfall product used for comparison. The basic diurnal forcing in the model seems to be too strong and the model responds too strongly to small islands and small-scale topography. The phase speed of propagating signals over open sea is correctly modeled but that over land is too slow.

A Fast Influence Coefficient Method for Aerodynamically Mistuned Disks Aeroelasticity Analysis

The blade geometric variations are usually ignored in the prediction of bladed disk aerodynamic damping values. This situation is the result of the high computational cost associated with the full-annulus unsteady flow CFD models required to account for these blade geometric differences. This paper presents an approach that can account for these geometric differences with high fidelity and at a reasonable one-time cost. The approach is based on the use of the influence-coefficient (IC) method together with a set of sensitivity coefficients defined for the blade geometry changing effects. The sensitivity coefficients make use of a set of principal component analysis (PCA) modes that describe the measured blade geometry variation. Once the sensitivity coefficients are determined, they are used to construct the IC matrices and to predict the aerodynamic damping values associated with the geometrically mistuned disk. The currently proposed method is unique in two aspects. The first is to follow the observed physics while making assumptions in the linearization process to reduce the number of required sensitivity coefficients. The second is to construct the multiblade CFD model, with blades of different geometries, in a unique way to reduce the data generation costs. Two IC approximation formulas were developed. If NP denotes the number of PCA modes used to describe the blade geometric variation, one formula reduces the number of required multiblade unsteady CFD models from (NP +1) [3] to (NP +1) [2], the other reduces the number of CFD models from (NP +1) [2] to NP +1. Results obtained from these two formulas are compared and validated.

Computational studies on the conformations of some large‐ring cyclodextrins (CDn, n = 20, 21, 22, 23)

Computational studies were carried out on the conformations of large-ring cyclodextrins with degree of polymerization from 20 to 23. Principal component analysis (PCA) was applied for postprocessing of trajectories from conformational search, based on 100.0 ns molecular dynamics simulations. The dominant PCA modes for concerted motions of the macroring atoms were monitored in a lower-dimensions subspace. The first six lowest indexed principal components contribute more than 90% of the total atomic motions in all cases, with about 70% (CD21) to 83% (CD22) contribution coming from the three highest-eigenvalue principal components. Representative average geometries of the cyclodextrin macrorings were also obtained for the whole simulation and for the ten 10.0 ns time intervals of the simulation. We concluded that resemblance exists of the representative conformations of these four cyclodextrins with the circularized three-turn single helical structure proposed for CD21 from small-angle X-ray scattering, as well as with the representative conformations of CD26.

Reduced order constrained optimization (ROCO): Clinical application to lung IMRT

The authors use reduced-order constrained optimization (ROCO) to create clinically acceptable IMRT plans quickly and automatically for advanced lung cancer patients. Their new ROCO implementation works with the treatment planning system and full dose calculation used at Memorial Sloan-Kettering Cancer Center (MSKCC). The authors have implemented mean dose hard constraints, along with the point-dose and dose-volume constraints that the authors used for our previous work on the prostate. ROCO consists of three major steps. First, the space of treatment plans is sampled by solving a series of optimization problems using penalty-based quadratic objective functions. Next, an efficient basis for this space is found via principal component analysis (PCA); this reduces the dimensionality of the problem. Finally, a constrained optimization problem is solved over this basis to find a clinically acceptable IMRT plan. Dimensionality reduction makes constrained optimization computationally efficient. The authors apply ROCO to 12 stage III non-small-cell lung cancer (NSCLC) cases, generating IMRT plans that meet all clinical constraints and are clinically acceptable, and demonstrate that they are competitive with the clinical treatment plans. The authors also test how many samples and PCA modes are necessary to achieve an adequate lung plan, demonstrate the importance of long-range dose calculation for ROCO, and evaluate the performance of nonspecific normal tissue ("rind") constraints in ROCO treatment planning for the lung. Finally, authors show that ROCO can save time for planners, and they estimate that in the clinic, planning using their approach would save a median of 105 min for the patients in the study. New challenges arise when applying ROCO to the lung site, which include the lack of a class solution, a larger treatment site, an increased number of parameters and beamlets, a variable number of beams and beam arrangement, and the customary use of rinds in clinical plans to avoid high-dose areas outside the PTV. In the authors previous work, use of an approximate dose calculation in the hard constraint optimization sometimes meant that clinical constraints were not met when evaluated with the full dose calculation. This difficulty has been removed in the current work by using the full dose calculation in the hard constraint optimization. The authors have demonstrated that ROCO offers a fast and automatic way to create IMRT plans for advanced NSCLC, which extends their previous application of ROCO to prostate cancer IMRT planning.

Conformations of some lower-size large-ring cyclodextrins derived from conformational search with molecular dynamics and principal component analysis

Abstract Computational studies were conducted on the conformations of some lower-size large-ring cyclodextrins, CD n ( n = 11, 12, 13, 15, 16, 17). Principal component analysis (PCA) was applied for post-processing of trajectories from conformational search based on 100.0 ns molecular dynamics (MD) simulations. The dominant PCA modes for concerted motions of the macroring atoms were monitored in a lower-dimensions subspace. The first six lowest indexed principal components contribute more than 90% of the total atomic motions in all cases, with about 70% (CD12) to 90% (CD17) contribution coming from the three highest-eigenvalue principal components. Representative average geometries of the cyclodextrin macrorings were also obtained for the whole simulation and for the ten 10.0 ns time intervals of the simulation. We concluded that the whole set of structures could be sorted into two clearly distinguished groups, separated by the figure-eight conformation of CD14: ( i ) open bent boat-like macrorings (CD11 to CD13), and ( ii ) two winded single helical strands (an anti-parallel double helix with foldbacks at each end), CD15 to CD17, shaped as number eight for the odd-number-residues cases, CD15 and CD17. CD13 and CD14 mark the borderline between lower and higher flexibilities of the lower-size LR-CDs macrorings.