Error matrices in gas-electron diffraction: II. Influence of weight matrix

In the era of big data, data may come from multiple sources, known as multi-view data. Multi-view clustering aims at generating better clusters by exploiting complementary and consistent information from multiple views rather than relying on the individual view. Due to inevitable system errors caused by data-captured sensors or others, the data in each view may be erroneous. Various types of errors behave differently and inconsistently in each view. More precisely, error could exhibit as noise and corruptions in reality. Unfortunately, none of the existing multi-view clustering approaches handle all of these error types. Consequently, their clustering performance is dramatically degraded. In this paper, we propose a novel Markov chain method for Error-Robust Multi-View Clustering (EMVC). By decomposing each view into a shared transition probability matrix and error matrix and imposing structured sparsity-inducing norms on error matrices, we characterize and handle typical types of errors explicitly. To solve the challenging optimization problem, we propose a new efficient algorithm based on Augmented Lagrangian Multipliers and prove its convergence rigorously. Experimental results on various synthetic and real-world datasets show the superiority of the proposed EMVC method over the baseline methods and its robustness against different types of errors.

The confusion matrix is the standard way to report on the thematic accuracy of geographic information data. Two widely adopted indices for thematic accuracy controls upon error matrix are the overall accuracy and the Kappa coefficient. Provided that a multinomial sampling, this work proposes a new method for testing the homogeneity of two independent thematic classifications which is based on whole error matrices. Specifically, a test function is proposed that uses as a test statistic the discrete Hellinger distance, which null distribution is approximated by bootstrapping. The performance of this approximation is evaluated by simulation, which confirms that it behaves properly, especially for small and moderate sample sizes. Finally an example of application is included.

Forest regeneration assessment is an important forest management goal that requires accurate data about site- specific forest type and stand density. In this study, a methodology was developed to convert regression model output to maps of predicted softwood and hardwood per- cent cover at the scale of a Landsat ETMpixel. These maps provide forest type and percent cover at higher spatial scale (0.09 ha) than traditional GIS forest stand databases employ (e.g., 2 to 4 ha minimum mapping units). A modi- fied accuracy assessment was performed between the Landsat regression derived maps and GIS type maps to evaluate their relative agreement. Two variations of the traditional error matrix were examined. The first was a plus-one matrix, where values next to the diagonal were included in the agreement calculations. The second varia- tion, considered most appropriate for this study, included the use of where the off-diagonal values were weighted for a better approximation of the GIS forest map- ping criteria and forest type composition of the northern New England forest. The fuzzy logic error matrix indicated strong agreement between the regression derived and GIS forest type maps with an overall agreement ranging from 76 percent to 79 percent. Producer's agreement from the fuzzy-logic error matrices ranged from 89 percent to 97 percent for softwood classes and 72 percent to 77 percent for hardwood. User's agreement for softwood ranged from 71 percent to 82 percent and 80 percent to 87 percent for hardwood. These results suggest that the Landsat-derived maps can provide objective and reliable site-specific forest type and percent cover information that is not dependent on subjective photo interpretation methods. These maps will be evaluated in future studies to demonstrate practical forest regeneration management applications.

The linear errors of Mueller matrix measurements are formulated for misalignment, depolarization, and incorrect retardation of the polarimetric components. The measured errors of a Mueller matrix depend not only on the imperfections of the measuring system but also on the Mueller matrix itself. The error matrices for different polarimetric systems are derived and also evaluated for the straight-through case. The error matrix for a polarizer-sample-analyzer system is much simpler than those for more complicated systems. The general error matrix is applied to null ellipsometry, and the obtained errors in ellipsometric parameters psi and delta are identical to the errors specifically derived for null ellipsometry with depolarization.

Error matrices in gas-electron diffraction: I. Effects of systematic errors in intensities

Aim To examine patterns in anuran species richness along an elevation gradient and identify factors that govern anuran species richness on a tropical elevational gradient.Location Sampling for anurans was carried out in Kalakad Mundanthurai Tiger Reserve (KMTR) in the southern Western Ghats, India.Methods Night‐time sampling for anuran species richness was carried out from 20 November 2004 to 20 April 2005, during the north‐east monsoon and dry seasons, using transects (50 × 2 m) and visual encounter surveys along the streams. The entire gradient was classified into thirteen 100‐m elevation zones. Sampling at the alpha (single drainage basin) level was carried out in the Chinnapul River drainage basin (40–1260 m a.s.l.) and at the gamma (landscape) level in four drainage basins. Additionally, published records were used to arrive at an empirical species richness (S) for the entire landscape. Mid‐Domain Null software was used to test for the possible influence of geometric constraints on anuran species at both the alpha and gamma levels. The influence of area under each elevation zone on empirical S was tested. The pattern in anuran species richness along the elevational gradient was investigated using: (1) species boundaries in each elevation zone and their habitat correlates, (2) abiotic factors as predictor variables, (3) mean snout vent lengths of anurans, and (4) correlation between the matrices of distance in the elevation zones based on microhabitat parameters and species composition. Cluster analysis on species presence–absence in the elevation zones was used to categorize the entire gradient into high, middle and low elevations. In these three elevation categories, pattern in composition of species was examined for endemism in Western Ghats–Sri Lanka biodiversity hotspot, uniqueness to an elevation zone, adaptations of adults and modes of breeding.Results Species richness at the alpha level increased linearly with elevation, while at the gamma level there were three peaks. Maximum species richness was observed at the highest elevation (1200 m) at both the alpha and the gamma levels. The observed patterns differed significantly from mid‐domain null predictions. The multi‐modal pattern in species richness was a consequence of overlapping species range boundaries. Soil temperature was the best single measure in explaining the majority of variation in species richness at the alpha level (r2 = 0.846, P < 0.01). However, soil moisture was the best predictor when both the alpha and the gamma sites were pooled (r2 = 0.774, P < 0.01). Anuran body size decreased with an increase in elevation. The highest proportions of endemic and unique species were found at high elevations (> 700 m). The proportion of arboreal anurans increased from low to high elevation. Anurans exhibiting direct development were predominantly found at high elevations.Main conclusions Geometric constraints did not influence anuran species richness along the elevational gradient. Overlapping range boundaries influenced species richness at the gamma level. Abiotic factors such as soil temperature and moisture influenced anuran species richness in the mountain range. The ‘Massenerhebung effect’ could be responsible for range restriction and endemism of anurans, differences in guilds and mode of reproduction. These findings highlight the importance of cloud forests for endemic anurans.

The molecular structure of the trans isomer of metal-free phthalocyanine (H2Pc) is determined using the gas electron diffraction (GED) method and high-level quantum chemical calculations. B3LYP calculations employing the basis sets 6-31G**, 6-311++G**, and cc-pVTZ give two tautomeric isomers for the inner H atoms, a trans isomer having D2h symmetry and a cis isomer having C2v symmetry. The trans isomer is calculated to be 41.6 (B3LYP/6-311++G**, zero-point corrected) and 37.3 kJ/mol (B3LYP/cc-pVTZ, not zero-point corrected) more stable than the cis isomer. However, Hartree-Fock (HF) calculations using different basis sets predict that cis is preferred and that trans does not exist as a stable form of the molecule. The equilibrium composition in the gas phase at 471 degrees C (the temperature of the GED experiment) calculated at the B3LYP/6-311++G** level is 99.8% trans and 0.2% cis. This is in very good agreement with the GED data, which indicate that the mole fraction of the cis isomer is close to zero. The transition states for two mechanisms of the NH tautomerization have been characterized. A concerted mechanism where the two H atoms move simultaneously yields a transition state of D2h symmetry and an energy barrier of 95.8 kJ/mol. A two-step mechanism where a trans isomer is converted to a cis isomer, which is converted into another trans isomer, proceeds via two transition states of C(s) symmetry and an energy barrier of 64.2 kJ/mol according to the B3LYP/6-311++G** calculation. The molecular geometry determined from GED is in very good agreement with the geometry obtained from the quantum chemical calculations. Vibrational frequencies, IR, and Raman intensities have been calculated using B3LYP/6-311++G**. These calculations indicate that the molecule is rather flexible with six vibrational frequencies in the range of 20-84 cm(-1) for the trans isomer. The cis isomer might be detected by infrared matrix spectroscopy since the N-H stretching frequencies are very different for the two isomers.

The molecular structures of phthalocyaninatozinc (HPc-Zn) and hexadecafluorophthalocyaninatozinc (FPc- Zn) are determined using the gas electron diffraction (GED) method and high-level density functional theory (DFT) quantum chemical calculations. Calculations at the B3LYP/6-311++G** level indicate that the equilibrium structures of HPc-Zn and FPc-Zn have D4h symmetry and yield structural parameters in good agreement with those obtained by GED at 480 and 523 degrees C respectively. The calculated force fields indicate that both molecules are flexible. Normal coordinate calculations on HPc-Zn yield five vibrational frequencies (one degenerate) in the range 22-100 cm(-1), and ten vibrational frequencies ranging from 13 to 100 cm(-1) (three degenerate) for FPc-Zn. The high-level force field calculations confirm most of the previous vibrational assignments, and some new ones are suggested. The out-of-plane vibration of the Zn atom in HPc-Zn was studied in detail optimizing models in which the distance from the Zn atom to the two symmetry equivalent diagonally opposed N atoms (h) was fixed. The calculations indicate that the vibrationally activated vertically displacement of the Zn atom is accompanied by distortion of the ligand from D4h to C2v symmetry. The average height, h, at the temperature of the GED experiment was calculated to be 14.5 pm. Small structural changes indicate that a full F substitution on the benzo-subunits do not significantly alter the geometry, however there are indications that the benzo-subunits may shrink slightly with perfluorination.

Gas-phase structure and conformation of diethyl ketone studied by molecular orbital constrained electron diffraction

Gas-phase structure and conformation of diethyl ketone studied by molecular orbital constrained electron diffraction

An evaluation has been made of some of the errors introduced into the electron diffraction of gases by failure of the sample to be localized, and by secondary and higher order scattering. The degree to which poor nozzle design may contribute to these factors was investigated experimentally by measurements of the pressure in the camera and absorption measurements of the main electron beam when a small volume of gas was allowed to expand into the camera; and theoretically for the cumulative effects of higher order scattering on the final picture. This evidence was complemented by density measurements on photographic plates taken under similar conditions. The effect of using liquid air cooled surfaces around the nozzle was tested. Of the nozzles tested, better ``image to background'' ratios were obtained with the ``hydrodynamic'' and ``comparison'' nozzles than with the ``conventional'' nozzle, but the gas must be admitted slowly enough so that less than about 10 percent of the main beam is appreciably scattered. The ``image to background'' ratios were always higher using adequate cooling on the condensing surfaces surrounding the nozzle. In the case of pressure and electron beam absorption measurements short exposures were advantageous, where secondary scattering was not directly considered, and high camera pumping speeds were always advantageous. On the basis of these results some general design suggestions for electron diffraction cameras, and requirements for good efficiency in nozzles can be made. A nozzle design is proposed which would reduce materially the errors normally encountered in electron diffraction work.

The molecular structure of isothiazole from electron diffraction and ab initio calculations

Download options Please wait... Supplementary files Tables of calculated and experimental (GED) root-mean-square amplitudes of vibration and figures showing experimental and calculated modified molecular intensity curves for i-Pr 2Zn, t-Bu 2Zn, neo-Pe 2Zn and (Me 3SiCH 2) 2Zn DOC (678K) Article information DOI https://doi.org/10.1039/B306840B Article type Paper Submitted 16 Jun 2003 Accepted 02 Sep 2003 First published 19 Sep 2003 Download Citation Dalton Trans., 2003, 4356-4366 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions The length, strength and polarity of metal–carbon bonds: dialkylzinc compounds studied by density functional theory calculations, gas electron diffraction and photoelectron spectroscopy A. Haaland, J. C. Green, G. S. McGrady, A. J. Downs, E. Gullo, M. J. Lyall, J. Timberlake, A. V. Tutukin, H. V. Volden and K. Østby, Dalton Trans., 2003, 4356 DOI: 10.1039/B306840B To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author Arne Haaland Jennifer C. Green G. Sean McGrady Anthony J. Downs Emanuel Gullo Mark J. Lyall Jessima Timberlake Andrey V. Tutukin Hans Vidar Volden Kari-Anne Østby

The use of a non-diagonal weight matrix for momentum determination with magnetic spectrometers

A control law for a rigid robotic manipulator optimizing quadratic cost functional composed of sliding surface and its derivative for fixed final time and free final state was proposed by Z. Ahmad (1995; 2000). Closed form solutions for such a control law corresponding to constant in time and specific diagonal time-varying weighting matrices are presented. These closed form solutions for the two point boundary value problem greatly reduce computational load and allow for real time implementation. Simulation results for a two degree of freedom manipulator are also provided.