Galileo Galilei (GG): the space mission and the prototype

NASA Astrophysics Data System (ADS)

Nobili, A.

"GALILEO GALILEI (GG)" is a proposal to fly a small satellite in low Earth orbit aiming to test the Equivalence Principle of Galileo, Newton and Einstein to 1 part in 1017 at room temperature. Ground tests carried out with artificial test bodies on rotating torsion balances, and tests with celestial bodies based on Lunar Laser Ranging data, have found no violation to about 1 part in 1013 . Competing space pro jects are SCOPE (also at room temperature) aiming to 1 part in 1015 , and STEP (at very low temperature) aiming to 1 part in 1018 . GG is characterized by fast rotation and by the possibility to perform a full scale test on the ground. This talk will present the main features of the GG design, as compared to STEP and SCOPE, and report the experimental results obtained with the first and the second generation laboratory prototypes (natural frequencies, quality factor, stability, sensitivity). Interested scientists are welcome to visit the GG webpage at http://eotvos.dm.unipi.it/nobili.

Restoration of the covariant gauge α in the initial field of gravity in de Sitter spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheong, Lee Yen; Yan, Chew Xiao

2014-03-05

The gravitational field generated by a mass term and the initial surface through covariant retarded Green's function for linearized gravity in de Sitter spacetime was studied recently [4, 5] with the covariant gauges set to β = 2/3 and α = 5/3. In this paper we extend the work to restore the gauge parameter α in the field coming from the initial data using the method of shifting the parameter. The α terms in the initial field cancels exactly with the one coming from the source term. Consequently, the correct field configuration, with two equal mass points moving in itsmore » geodesic, one located at the North pole and another one located at the South pole, is reproduced in the whole manifold of de Sitter spacetime.« less

Galileo's eye: a new vision of the senses in the work of Galileo Galilei.

PubMed

Piccolino, Marco; Wade, Nicholas J

2008-01-01

Reflections on the senses, and particularly on vision, permeate the writings of Galileo Galilei, one of the main protagonists of the scientific revolution. This aspect of his work has received scant attention by historians, in spite of its importance for his achievements in astronomy, and also for the significance in the innovative scientific methodology he fostered. Galileo's vision pursued a different path from the main stream of the then contemporary studies in the field; these were concerned with the dioptrics and anatomy of the eye, as elaborated mainly by Johannes Kepler and Christoph Scheiner. Galileo was more concerned with the phenomenology rather than with the mechanisms of the visual process. His general interest in the senses was psychological and philosophical; it reflected the fallacies and limits of the senses and the ways in which scientific knowledge of the world could be gathered from potentially deceptive appearances. Galileo's innovative conception of the relation between the senses and external reality contrasted with the classical tradition dominated by Aristotle; it paved the way for the modern understanding of sensory processing, culminating two centuries later in Johannes Müller's elaboration of the doctrine of specific nerve energies and in Helmholtz's general theory of perception.

Double gauge invariance and covariantly-constant vector fields in Weyl geometry

NASA Astrophysics Data System (ADS)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

2014-08-01

The wave equation and equations of covariantly-constant vector fields (CCVF) in spaces with Weyl nonmetricity turn out to possess, in addition to the canonical conformal-gauge, a gauge invariance of another type. On a Minkowski metric background, the CCVF system alone allows us to pin down the Weyl 4-metricity vector, identified herein with the electromagnetic potential. The fundamental solution is given by the ordinary Lienard-Wiechert field, in particular, by the Coulomb distribution for a charge at rest. Unlike the latter, however, the magnitude of charge is necessarily unity, "elementary", and charges of opposite signs correspond to retarded and advanced potentials respectively, thus establishing a direct connection between the particle/antiparticle asymmetry and the "arrow of time".

On the regularity of the covariance matrix of a discretized scalar field on the sphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bilbao-Ahedo, J.D.; Barreiro, R.B.; Herranz, D.

2017-02-01

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizationsmore » that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.« less

Nonrelativistic fluids on scale covariant Newton-Cartan backgrounds

NASA Astrophysics Data System (ADS)

Mitra, Arpita

2017-12-01

The nonrelativistic covariant framework for fields is extended to investigate fields and fluids on scale covariant curved backgrounds. The scale covariant Newton-Cartan background is constructed using the localization of space-time symmetries of nonrelativistic fields in flat space. Following this, we provide a Weyl covariant formalism which can be used to study scale invariant fluids. By considering ideal fluids as an example, we describe its thermodynamic and hydrodynamic properties and explicitly demonstrate that it satisfies the local second law of thermodynamics. As a further application, we consider the low energy description of Hall fluids. Specifically, we find that the gauge fields for scale transformations lead to corrections of the Wen-Zee and Berry phase terms contained in the effective action.

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

NASA Astrophysics Data System (ADS)

Klees, R.; Slobbe, D. C.; Farahani, H. H.

2018-03-01

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao's unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters.

Frame covariant nonminimal multifield inflation

NASA Astrophysics Data System (ADS)

Karamitsos, Sotirios; Pilaftsis, Apostolos

2018-02-01

We introduce a frame-covariant formalism for inflation of scalar-curvature theories by adopting a differential geometric approach which treats the scalar fields as coordinates living on a field-space manifold. This ensures that our description of inflation is both conformally and reparameterization covariant. Our formulation gives rise to extensions of the usual Hubble and potential slow-roll parameters to generalized fully frame-covariant forms, which allow us to provide manifestly frame-invariant predictions for cosmological observables, such as the tensor-to-scalar ratio r, the spectral indices nR and nT, their runnings αR and αT, the non-Gaussianity parameter fNL, and the isocurvature fraction βiso. We examine the role of the field space curvature in the generation and transfer of isocurvature modes, and we investigate the effect of boundary conditions for the scalar fields at the end of inflation on the observable inflationary quantities. We explore the stability of the trajectories with respect to the boundary conditions by using a suitable sensitivity parameter. To illustrate our approach, we first analyze a simple minimal two-field scenario before studying a more realistic nonminimal model inspired by Higgs inflation. We find that isocurvature effects are greatly enhanced in the latter scenario and must be taken into account for certain values in the parameter space such that the model is properly normalized to the observed scalar power spectrum PR. Finally, we outline how our frame-covariant approach may be extended beyond the tree-level approximation through the Vilkovisky-De Witt formalism, which we generalize to take into account conformal transformations, thereby leading to a fully frame-invariant effective action at the one-loop level.

Time-odd mean fields in covariant density functional theory: Rotating systems

NASA Astrophysics Data System (ADS)

Afanasjev, A. V.; Abusara, H.

2010-09-01

Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.

Covariance hypotheses for LANDSAT data

NASA Technical Reports Server (NTRS)

Decell, H. P.; Peters, C.

1983-01-01

Two covariance hypotheses are considered for LANDSAT data acquired by sampling fields, one an autoregressive covariance structure and the other the hypothesis of exchangeability. A minimum entropy approximation of the first structure by the second is derived and shown to have desirable properties for incorporation into a mixture density estimation procedure. Results of a rough test of the exchangeability hypothesis are presented.

On covariant Poisson brackets in classical field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Forger, Michael; Salles, Mário O.; Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN

2015-10-15

How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket,more » applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.« less

Field-scale and Regional Variability in Evapotranspiration over Crops in California using Eddy Covariance and Surface Renewal

NASA Astrophysics Data System (ADS)

Kent, E. R.; Clay, J. M.; Leinfelder-Miles, M.; Lambert, J. J.; Little, C.; Monteiro, R. O. C.; Monteiro, P. F. C.; Shapiro, K.; Rice, S.; Snyder, R. L.; Daniele, Z.; Paw U, K. T.

2016-12-01

Evapotranspiration (ET) estimated using a single crop coefficient and a grass reference largely ignores variability due to heterogeneity in microclimate, soils, and crop management. We employ a relatively low cost energy balance residual method using surface renewal and eddy covariance measurements to continuously estimate half-hourly and daily ET across more than 15 fields and orchards spanning four crops and two regions of California. In the Sacramento-San Joaquin River Delta, measurements were taken in corn, pasture, and alfalfa fields, with 4-5 stations in each crop type spread across the region. In the Southern San Joaquin Valley, measurements were taken in three different pistachio orchards, with one orchard having six stations instrumented to examine salinity-induced heterogeneity. We analyze field-scale and regional variability in ET and measured surface energy balance components. Cross comparisons between the eddy covariance and the surface renewal measurements confirm the robustness of the surface renewal method. A hybrid approach in which remotely sensed net radiation is combined with in situ measurements of sensible heat flux is also investigated. This work will provide ground-truth data for satellite and aerial-based ET estimates and will inform water management at the field and regional scales.

Galaxy-galaxy lensing estimators and their covariance properties

NASA Astrophysics Data System (ADS)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uroš; Slosar, Anže; Vazquez Gonzalez, Jose

2017-11-01

We study the covariance properties of real space correlation function estimators - primarily galaxy-shear correlations, or galaxy-galaxy lensing - using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens density field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.

Locally covariant quantum field theory and the problem of formulating the same physics in all space-times.

PubMed

Fewster, Christopher J

2015-08-06

The framework of locally covariant quantum field theory is discussed, motivated in part using 'ignorance principles'. It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be expressed via natural isomorphisms between the corresponding functors. The inhomogeneous scalar field is used to illustrate the ideas. It is argued that there are two reasonable definitions of the local physical content associated with a locally covariant theory; when these coincide, the theory is said to be dynamically local. The status of the dynamical locality condition is reviewed, as are its applications in relation to (i) the foundational question of what it means for a theory to represent the same physics in different space-times and (ii) a no-go result on the existence of natural states. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Covariant diagrams for one-loop matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zhengkang

Here, we present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We also show how such derivation canmore » be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.« less

Covariant diagrams for one-loop matching

DOE PAGES

Zhang, Zhengkang

2017-05-30

Here, we present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We also show how such derivation canmore » be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.« less

Heritability, covariation and natural selection on 24 traits of common evening primrose (Oenothera biennis) from a field experiment.

PubMed

Johnson, M T J; Agrawal, A A; Maron, J L; Salminen, J-P

2009-06-01

This study explored genetic variation and co-variation in multiple functional plant traits. Our goal was to characterize selection, heritabilities and genetic correlations among different types of traits to gain insight into the evolutionary ecology of plant populations and their interactions with insect herbivores. In a field experiment, we detected significant heritable variation for each of 24 traits of Oenothera biennis and extensive genetic covariance among traits. Traits with diverse functions formed several distinct groups that exhibited positive genetic covariation with each other. Genetic variation in life-history traits and secondary chemistry together explained a large proportion of variation in herbivory (r(2) = 0.73). At the same time, selection acted on lifetime biomass, life-history traits and two secondary compounds of O. biennis, explaining over 95% of the variation in relative fitness among genotypes. The combination of genetic covariances and directional selection acting on multiple traits suggests that adaptive evolution of particular traits is constrained, and that correlated evolution of groups of traits will occur, which is expected to drive the evolution of increased herbivore susceptibility. As a whole, our study indicates that an examination of genetic variation and covariation among many different types of traits can provide greater insight into the evolutionary ecology of plant populations and plant-herbivore interactions.

Galaxy–galaxy lensing estimators and their covariance properties

DOE PAGES

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros; ...

2017-07-21

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Galaxy–galaxy lensing estimators and their covariance properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

NASA Astrophysics Data System (ADS)

Sharma, N. K.; Singh, J. K.

2014-12-01

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble's parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ϕ and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.

Performance of internal covariance estimators for cosmic shear correlation functions

DOE PAGES

Friedrich, O.; Seitz, S.; Eifler, T. F.; ...

2015-12-31

Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic shear two-point statistics. We demonstrate how to use log-normal simulations of the convergence field and the corresponding shear field to carry out realistic tests of internal covariance estimators and find that most estimators such as jackknife or sub-sample covariance can reach a satisfactory compromise between bias and variance of the estimated covariance. In a forecast for the complete, 5-year DES survey we show that internally estimated covariance matrices can provide a large fraction of the true uncertainties on cosmological parameters in a 2D cosmic shear analysis. The volume inside contours of constant likelihood in themore » $$\\Omega_m$$-$$\\sigma_8$$ plane as measured with internally estimated covariance matrices is on average $$\\gtrsim 85\\%$$ of the volume derived from the true covariance matrix. The uncertainty on the parameter combination $$\\Sigma_8 \\sim \\sigma_8 \\Omega_m^{0.5}$$ derived from internally estimated covariances is $$\\sim 90\\%$$ of the true uncertainty.« less

A comparison of methods for determining field evapotranspiration: photosynthesis system, sap flow, and eddy covariance

NASA Astrophysics Data System (ADS)

Zhang, Z.; Tian, F.; Hu, H.; Yang, P.

2014-03-01

A multi-scale, multi-technique study was conducted to measure evapotranspiration and its components in a cotton field under mulched drip irrigation conditions in northwestern China. Three measurement techniques at different scales were used: a photosynthesis system (leaf scale), sap flow (plant scale), and eddy covariance (field scale). The experiment was conducted from July to September 2012. To upscale the evapotranspiration from the leaf to plant scale, an approach that incorporated the canopy structure and the relationships between sunlit and shaded leaves was proposed. To upscale the evapotranspiration from the plant to field scale, an approach based on the transpiration per unit leaf area was adopted and modified to incorporate the temporal variability in the relationship between leaf areas and stem diameter. At the plant scale, the estimate of the transpiration based on the photosynthesis system with upscaling was slightly higher (18%) than that obtained by sap flow. At the field scale, the estimates of transpiration derived from sap flow with upscaling and eddy covariance showed reasonable consistency during the cotton's open-boll growth stage, during which soil evaporation can be neglected. The results indicate that the proposed upscaling approaches are reasonable and valid. Based on the measurements and upscaling approaches, evapotranspiration components were analyzed for a cotton field under mulched drip irrigation. During the two analyzed sub-periods in July and August, evapotranspiration rates were 3.94 and 4.53 m day-1, respectively. The fraction of transpiration to evapotranspiration reached 87.1% before drip irrigation and 82.3% after irrigation. The high fraction of transpiration over evapotranspiration was principally due to the mulched film above the drip pipe, low soil water content in the inter-film zone, well-closed canopy, and high water requirement of the crop.

A comparison of methods for determining field evapotranspiration: photosynthesis system, sap flow, and eddy covariance

NASA Astrophysics Data System (ADS)

Zhang, Z.; Tian, F.; Hu, H. C.; Hu, H. P.

2013-11-01

A multi-scale, multi-technique study was conducted to measure evapotranspiration and its components in a cotton field under mulched drip irrigation conditions in northwestern China. Three measurement techniques at different scales were used: photosynthesis system (leaf scale), sap flow (plant scale), and eddy covariance (field scale). The experiment was conducted from July to September 2012. To upscale the evapotranspiration from the leaf to the plant scale, an approach that incorporated the canopy structure and the relationships between sunlit and shaded leaves was proposed. To upscale the evapotranspiration from the plant to the field scale, an approach based on the transpiration per unit leaf area was adopted and modified to incorporate the temporal variability in the relationships between leaf area and stem diameter. At the plant scale, the estimate of the transpiration based on the photosynthesis system with upscaling was slightly higher (18%) than that obtained by sap flow. At the field scale, the estimates of transpiration derived from sap flow with upscaling and eddy covariance shown reasonable consistency during the cotton open boll growth stage when soil evaporation can be neglected. The results indicate that the upscaling approaches are reasonable and valid. Based on the measurements and upscaling approaches, evapotranspiration components were analyzed under mulched drip irrigation. During the two analysis sub-periods in July and August, evapotranspiration rates were 3.94 and 4.53 mm day-1, respectively. The fraction of transpiration to evapotranspiration reached 87.1% before drip irrigation and 82.3% after irrigation. The high fraction of transpiration over evapotranspiration was principally due to the mulched film above drip pipe, low soil water content in the inter-film zone, well-closed canopy, and high water requirement of the crop.

Covariance and the hierarchy of frame bundles

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1987-01-01

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite Lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and for G-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.

Inadequacy of internal covariance estimation for super-sample covariance

NASA Astrophysics Data System (ADS)

Lacasa, Fabien; Kunz, Martin

2017-08-01

We give an analytical interpretation of how subsample-based internal covariance estimators lead to biased estimates of the covariance, due to underestimating the super-sample covariance (SSC). This includes the jackknife and bootstrap methods as estimators for the full survey area, and subsampling as an estimator of the covariance of subsamples. The limitations of the jackknife covariance have been previously presented in the literature because it is effectively a rescaling of the covariance of the subsample area. However we point out that subsampling is also biased, but for a different reason: the subsamples are not independent, and the corresponding lack of power results in SSC underprediction. We develop the formalism in the case of cluster counts that allows the bias of each covariance estimator to be exactly predicted. We find significant effects for a small-scale area or when a low number of subsamples is used, with auto-redshift biases ranging from 0.4% to 15% for subsampling and from 5% to 75% for jackknife covariance estimates. The cross-redshift covariance is even more affected; biases range from 8% to 25% for subsampling and from 50% to 90% for jackknife. Owing to the redshift evolution of the probe, the covariances cannot be debiased by a simple rescaling factor, and an exact debiasing has the same requirements as the full SSC prediction. These results thus disfavour the use of internal covariance estimators on data itself or a single simulation, leaving analytical prediction and simulations suites as possible SSC predictors.

Accurate interatomic force fields via machine learning with covariant kernels

NASA Astrophysics Data System (ADS)

Glielmo, Aldo; Sollich, Peter; De Vita, Alessandro

2017-06-01

We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO (d ) for the relevant dimensionality d . Remarkably, in specific cases the integration can be carried out analytically and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mechanical forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si crystalline systems.

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.

Bispectrum supersample covariance

NASA Astrophysics Data System (ADS)

Chan, Kwan Chuen; Moradinezhad Dizgah, Azadeh; Noreña, Jorge

2018-02-01

Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross-covariance between the power spectrum and the bispectrum. The supersample covariances due to the long-wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and sub-box setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small-scale covariance—which can be computed using a periodic box—is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small-scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross-covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.

Using Analysis of Covariance (ANCOVA) with Fallible Covariates

ERIC Educational Resources Information Center

Culpepper, Steven Andrew; Aguinis, Herman

2011-01-01

Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…

Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

NASA Astrophysics Data System (ADS)

Lee, Taejin

2017-12-01

We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.

Galilei's astronomical discoveries using the telescope and their evaluation found in a writing-calendar from 1611

NASA Astrophysics Data System (ADS)

Herbst, K.-D.

2009-06-01

Yearly calendars were a mass-produced article in early modern times and had an enormous importance in everyday life. Besides a first part, the Calendarium with the monthly tables, they contain a second part, the astrological Prognosticum. At first, the two parts were sold separately. In the second half of the 17th century, the parts were designed as a unity and sold together. The calendars in quart format contain texts which are so interesting that historical research should give them more consideration. Such a text is found, e.g., in the second part of the calendar for 1611, written by Paul Nagel, astronomer and rector of the school in Torgau. Nagel informs about Galilei's discoveries with the telescope. The (Latin) text was written in August 1610. This text is presented and put into perspective in the scientific debates of the time about the telescope as a new invention with consequences to philosophy.

Pairing field methods to improve inference in wildlife surveys while accommodating detection covariance

USGS Publications Warehouse

Clare, John; McKinney, Shawn T.; DePue, John E.; Loftin, Cynthia S.

2017-01-01

It is common to use multiple field sampling methods when implementing wildlife surveys to compare method efficacy or cost efficiency, integrate distinct pieces of information provided by separate methods, or evaluate method-specific biases and misclassification error. Existing models that combine information from multiple field methods or sampling devices permit rigorous comparison of method-specific detection parameters, enable estimation of additional parameters such as false-positive detection probability, and improve occurrence or abundance estimates, but with the assumption that the separate sampling methods produce detections independently of one another. This assumption is tenuous if methods are paired or deployed in close proximity simultaneously, a common practice that reduces the additional effort required to implement multiple methods and reduces the risk that differences between method-specific detection parameters are confounded by other environmental factors. We develop occupancy and spatial capture–recapture models that permit covariance between the detections produced by different methods, use simulation to compare estimator performance of the new models to models assuming independence, and provide an empirical application based on American marten (Martes americana) surveys using paired remote cameras, hair catches, and snow tracking. Simulation results indicate existing models that assume that methods independently detect organisms produce biased parameter estimates and substantially understate estimate uncertainty when this assumption is violated, while our reformulated models are robust to either methodological independence or covariance. Empirical results suggested that remote cameras and snow tracking had comparable probability of detecting present martens, but that snow tracking also produced false-positive marten detections that could potentially substantially bias distribution estimates if not corrected for. Remote cameras detected marten

Pairing field methods to improve inference in wildlife surveys while accommodating detection covariance.

PubMed

Clare, John; McKinney, Shawn T; DePue, John E; Loftin, Cynthia S

2017-10-01

It is common to use multiple field sampling methods when implementing wildlife surveys to compare method efficacy or cost efficiency, integrate distinct pieces of information provided by separate methods, or evaluate method-specific biases and misclassification error. Existing models that combine information from multiple field methods or sampling devices permit rigorous comparison of method-specific detection parameters, enable estimation of additional parameters such as false-positive detection probability, and improve occurrence or abundance estimates, but with the assumption that the separate sampling methods produce detections independently of one another. This assumption is tenuous if methods are paired or deployed in close proximity simultaneously, a common practice that reduces the additional effort required to implement multiple methods and reduces the risk that differences between method-specific detection parameters are confounded by other environmental factors. We develop occupancy and spatial capture-recapture models that permit covariance between the detections produced by different methods, use simulation to compare estimator performance of the new models to models assuming independence, and provide an empirical application based on American marten (Martes americana) surveys using paired remote cameras, hair catches, and snow tracking. Simulation results indicate existing models that assume that methods independently detect organisms produce biased parameter estimates and substantially understate estimate uncertainty when this assumption is violated, while our reformulated models are robust to either methodological independence or covariance. Empirical results suggested that remote cameras and snow tracking had comparable probability of detecting present martens, but that snow tracking also produced false-positive marten detections that could potentially substantially bias distribution estimates if not corrected for. Remote cameras detected marten

Form of the manifestly covariant Lagrangian

NASA Astrophysics Data System (ADS)

Johns, Oliver Davis

1985-10-01

The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

Strangeness S =-1 hyperon-nucleon scattering in covariant chiral effective field theory

NASA Astrophysics Data System (ADS)

Li, Kai-Wen; Ren, Xiu-Lei; Geng, Li-Sheng; Long, Bingwei

2016-07-01

Motivated by the successes of covariant baryon chiral perturbation theory in one-baryon systems and in heavy-light systems, we study relevance of relativistic effects in hyperon-nucleon interactions with strangeness S =-1 . In this exploratory work, we follow the covariant framework developed by Epelbaum and Gegelia to calculate the Y N scattering amplitude at leading order. By fitting the five low-energy constants to the experimental data, we find that the cutoff dependence is mitigated, compared with the heavy-baryon approach. Nevertheless, the description of the experimental data remains quantitatively similar at leading order.

A geometric rationale for invariance, covariance and constitutive relations

NASA Astrophysics Data System (ADS)

Romano, Giovanni; Barretta, Raffaele; Diaco, Marina

2018-01-01

There are, in each branch of science, statements which, expressed in ambiguous or even incorrect but seemingly friendly manner, were repeated for a long time and eventually became diffusely accepted. Objectivity of physical fields and of their time rates and frame indifference of constitutive relations are among such notions. A geometric reflection on the description of frame changes as spacetime automorphisms, on induced push-pull transformations and on proper physico-mathematical definitions of material, spatial and spacetime tensor fields and of their time-derivatives along the motion, is here carried out with the aim of pointing out essential notions and of unveiling false claims. Theoretical and computational aspects of nonlinear continuum mechanics, and especially those pertaining to constitutive relations, involving material fields and their time rates, gain decisive conceptual and operative improvement from a proper geometric treatment. Outcomes of the geometric analysis are frame covariance of spacetime velocity, material stretching and material spin. A univocal and frame-covariant tool for evaluation of time rates of material fields is provided by the Lie derivative along the motion. The postulate of frame covariance of material fields is assessed to be a natural physical requirement which cannot interfere with the formulation of constitutive laws, with claims of the contrary stemming from an improper imposition of equality in place of equivalence.

Explicitly covariant dispersion relations and self-induced transparency

NASA Astrophysics Data System (ADS)

Mahajan, S. M.; Asenjo, Felipe A.

2017-02-01

Explicitly covariant dispersion relations for a variety of plasma waves in unmagnetized and magnetized plasmas are derived in a systematic manner from a fully covariant plasma formulation. One needs to invoke relatively little known invariant combinations constructed from the ambient electromagnetic fields and the wave vector to accomplish the program. The implication of this work applied to the self-induced transparency effect is discussed. Some problems arising from the inconsistent use of relativity are pointed out.

A fully covariant mean-field dynamo closure for numerical 3 + 1 resistive GRMHD

NASA Astrophysics Data System (ADS)

Bucciantini, N.; Del Zanna, L.

2013-01-01

The powerful high-energy phenomena typically encountered in astrophysics invariably involve physical engines, like neutron stars and black hole accretion discs, characterized by a combination of highly magnetized plasmas, strong gravitational fields and relativistic motions. In recent years, numerical schemes for general relativistic magnetohydrodynamics (GRMHD) have been developed to model the multidimensional dynamics of such systems, including the possibility of evolving space-time. Such schemes have been also extended beyond the ideal limit including the effects of resistivity, in an attempt to model dissipative physical processes acting on small scales (subgrid effects) over the global dynamics. Along the same lines, the magnetic field could be amplified by the presence of turbulent dynamo processes, as often invoked to explain the high values of magnetization required in accretion discs and neutron stars. Here we present, for the first time, a further extension to include the possibility of a mean-field dynamo action within the framework of numerical 3 + 1 (resistive) GRMHD. A fully covariant dynamo closure is proposed, in analogy with the classical theory, assuming a simple α-effect in the comoving frame. Its implementation into a finite-difference scheme for GRMHD in dynamical space-times (the x-echo code by Bucciantini & Del Zanna) is described, and a set of numerical test is presented and compared with analytical solutions wherever possible.

Are your covariates under control? How normalization can re-introduce covariate effects.

PubMed

Pain, Oliver; Dudbridge, Frank; Ronald, Angelica

2018-04-30

Many statistical tests rely on the assumption that the residuals of a model are normally distributed. Rank-based inverse normal transformation (INT) of the dependent variable is one of the most popular approaches to satisfy the normality assumption. When covariates are included in the analysis, a common approach is to first adjust for the covariates and then normalize the residuals. This study investigated the effect of regressing covariates against the dependent variable and then applying rank-based INT to the residuals. The correlation between the dependent variable and covariates at each stage of processing was assessed. An alternative approach was tested in which rank-based INT was applied to the dependent variable before regressing covariates. Analyses based on both simulated and real data examples demonstrated that applying rank-based INT to the dependent variable residuals after regressing out covariates re-introduces a linear correlation between the dependent variable and covariates, increasing type-I errors and reducing power. On the other hand, when rank-based INT was applied prior to controlling for covariate effects, residuals were normally distributed and linearly uncorrelated with covariates. This latter approach is therefore recommended in situations were normality of the dependent variable is required.

Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2011-04-01

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of Stäckel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

Covariant relativistic hydrodynamics of multispecies plasma and generalized Ohm's law

NASA Astrophysics Data System (ADS)

Gedalin, Michael

1996-04-01

Fully covariant hydrodynamical equations for a multispecies relativistic plasma in an external electromagnetic field are derived. The derived multifluid description takes into account binary Coulomb collisions, annihilation, and interaction with the photon background in terms of the invariant collision cross sections. A generalized Ohm's law is derived in a manifestly covariant form. Particular attention is devoted to the relativistic electron-positron plasma.

The energy balance experiment EBEX-2000. Part II: Intercomparison of eddy-covariance sensors and post-field data processing methods

NASA Astrophysics Data System (ADS)

Mauder, Matthias; Oncley, Steven P.; Vogt, Roland; Weidinger, Tamas; Ribeiro, Luis; Bernhofer, Christian; Foken, Thomas; Kohsiek, Wim; de Bruin, Henk A. R.; Liu, Heping

2007-04-01

The eddy-covariance method is the primary way of measuring turbulent fluxes directly. Many investigators have found that these flux measurements often do not satisfy a fundamental criterion—closure of the surface energy balance. This study investigates to what extent the eddy-covariance measurement technology can be made responsible for this deficiency, in particular the effects of instrumentation or of the post-field data processing. Therefore, current eddy-covariance sensors and several post-field data processing methods were compared. The differences in methodology resulted in deviations of 10% for the sensible heat flux and of 15% for the latent heat flux for an averaging time of 30 min. These disparities were mostly due to different sensor separation corrections and a linear detrending of the data. The impact of different instrumentation on the resulting heat flux estimates was significantly higher. Large deviations from the reference system of up to 50% were found for some sensor combinations. However, very good measurement quality was found for a CSAT3 sonic together with a KH20 krypton hygrometer and also for a UW sonic together with a KH20. If these systems are well calibrated and maintained, an accuracy of better than 5% can be achieved for 30-min values of sensible and latent heat flux measurements. The results from the sonic anemometers Gill Solent-HS, ATI-K, Metek USA-1, and R.M. Young 81000 showed more or less larger deviations from the reference system. The LI-COR LI-7500 open-path H2O/CO2 gas analyser in the test was one of the first serial numbers of this sensor type and had technical problems regarding direct solar radiation sensitivity and signal delay. These problems are known by the manufacturer and improvements of the sensor have since been made.

N2O fluxes over a corn field from an open-path, laser-based eddy covariance system and static chambers

NASA Astrophysics Data System (ADS)

Tao, L.; Pan, D.; Gelfand, I.; Abraha, M.; Moyer, R.; Poe, A.; Sun, K.; Robertson, P.; Zondlo, M. A.

2015-12-01

Nitrous oxide (N2O) is important greenhouse and ozone-depleting gase. Although many efforts have been paid to N2O emissions, the spatial and temporal variability of N2O emissions still subject to large uncertainty. Application of the eddy covariance method for N2O emissions research would allow continuous ecosystem level flux measurements. The caveat, however, is need for high precision and high frequency measurements in field. In this study, an open-path, quantum cascade-laser-based eddy covariance N2O sensor has been deployed nearly continuously since May 2015 over a corn field at the W.K. Kellogg Biological Station site in SW Michigan. The field precision of the N2O sensor was assessed to be 0.1 ppbv at 10 Hz, and the total consumption was ~ 40 W, allowing the system to be powered solely by solar panels. The stability of the sensor under different temperature and humidity was tested within an environmental chamber. Spectroscopic experiments and cospectra analyses were carried out to study specific corrections associated with the sensor for eddy covariance techniques, including the line broadening effect due to water vapor and high frequency flux attenuation owning to sample path averaging. Ogive analyses indicated that the high-frequency N2O flux loss due to various damping effects was comparable to those of the CO2 flux. The detection limit of flux was estimated to be 0.3 ng N s-1 m-2 with a flux averaging interval of 30 minutes. The results from the EC system were also compared with ground measurements by standard static chambers (SC). Overall, more than 150 individual chamber measurements were taken within the footprint of the EC system. We found good correlation between the EC and SC methods given the spatiotemporal differences between the two techniques (R2 = 0.75). Both methods detected increased emissions during afternoon as compared to morning and night hours. Differences between EC and SC were also studied by investigating spatial variability with a

A class of covariate-dependent spatiotemporal covariance functions

PubMed Central

Reich, Brian J; Eidsvik, Jo; Guindani, Michele; Nail, Amy J; Schmidt, Alexandra M.

2014-01-01

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model non-stationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. In this work, we provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and discuss methods to assess its dependence on local covariate information by means of a simulation study and the analysis of data observed at ozone-monitoring stations in the Southeast United States. PMID:24772199

Covariant balance laws in continua with microstructure

NASA Astrophysics Data System (ADS)

Yavari, Arash; Marsden, Jerrold E.

2009-02-01

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas. We model a structured continuum as a triplet of Riemannian manifolds: a material manifold, the ambient space manifold of material particles and a director field manifold. The Green-Naghdi-Rivlin theorem and its extensions for structured continua are critically reviewed. We show that when the ambient space is Euclidean and when the microstructure manifold is the tangent space of the ambient space manifold, postulating a single balance of energy law and its invariance under time-dependent isometries of the ambient space, one obtains conservation of mass, balances of linear and angular momenta but not a separate balance of linear momentum. We develop a covariant elasticity theory for structured continua by postulating that energy balance is invariant under time-dependent spatial diffeomorphisms of the ambient space, which in this case is the product of two Riemannian manifolds. We then introduce two types of constrained continua in which microstructure manifold is linked to the reference and ambient space manifolds. In the case when at every material point, the microstructure manifold is the tangent space of the ambient space manifold at the image of the material point, we show that the assumption of covariance leads to balances of linear and angular momenta with contributions from both forces and micro-forces along with two Doyle-Ericksen formulas. We show that generalized covariance leads to two balances of linear momentum and a single coupled balance of angular momentum. Using this theory, we covariantly obtain the balance laws for two specific examples, namely elastic

Robust covariance estimation of galaxy-galaxy weak lensing: validation and limitation of jackknife covariance

NASA Astrophysics Data System (ADS)

Shirasaki, Masato; Takada, Masahiro; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma

2017-09-01

We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogues. Using the mock catalogue to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the 'jackknife' (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of the true covariance up to separations comparable with the size of JK subregion. The scatter in JK covariances is found to be ∼10 per cent after we subtract the lensing measurement around random points. However, the JK method tends to underestimate the covariance at the larger separations, more increasingly for a survey with a higher number density of source galaxies. We apply our method to the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS catalogues nicely reproduce the signals and the JK covariance measured from the real data. We then argue that the use of the accurate covariance, compared to the JK covariance, allows us to use the lensing signals at large scales beyond a size of the JK subregion, which contains cleaner cosmological information in the linear regime.

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.

PubMed

Brier, Matthew R; Mitra, Anish; McCarthy, John E; Ances, Beau M; Snyder, Abraham Z

2015-11-01

Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity. Copyright © 2015 Elsevier Inc. All rights reserved.

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization

PubMed Central

Brier, Matthew R.; Mitra, Anish; McCarthy, John E.; Ances, Beau M.; Snyder, Abraham Z.

2015-01-01

Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity. PMID:26208872

Covariate-free and Covariate-dependent Reliability.

PubMed

Bentler, Peter M

2016-12-01

Classical test theory reliability coefficients are said to be population specific. Reliability generalization, a meta-analysis method, is the main procedure for evaluating the stability of reliability coefficients across populations. A new approach is developed to evaluate the degree of invariance of reliability coefficients to population characteristics. Factor or common variance of a reliability measure is partitioned into parts that are, and are not, influenced by control variables, resulting in a partition of reliability into a covariate-dependent and a covariate-free part. The approach can be implemented in a single sample and can be applied to a variety of reliability coefficients.

Higher Order First Integrals of Motion in a Gauge Covariant Hamiltonian Framework

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out.

Earth Observing System Covariance Realism

NASA Technical Reports Server (NTRS)

Zaidi, Waqar H.; Hejduk, Matthew D.

2016-01-01

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Using indirect covariance spectra to identify artifact responses in unsymmetrical indirect covariance calculated spectra.

PubMed

Martin, Gary E; Hilton, Bruce D; Blinov, Kirill A; Williams, Antony J

2008-02-01

Several groups of authors have reported studies in the areas of indirect and unsymmetrical indirect covariance NMR processing methods. Efforts have recently focused on the use of unsymmetrical indirect covariance processing methods to combine various discrete two-dimensional NMR spectra to afford the equivalent of the much less sensitive hyphenated 2D NMR experiments, for example indirect covariance (icv)-heteronuclear single quantum coherence (HSQC)-COSY and icv-HSQC-nuclear Overhauser effect spectroscopy (NOESY). Alternatively, unsymmetrical indirect covariance processing methods can be used to combine multiple heteronuclear 2D spectra to afford icv-13C-15N HSQC-HMBC correlation spectra. We now report the use of responses contained in indirect covariance processed HSQC spectra as a means for the identification of artifacts in both indirect covariance and unsymmetrical indirect covariance processed 2D NMR spectra. Copyright (c) 2007 John Wiley & Sons, Ltd.

Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field

NASA Astrophysics Data System (ADS)

Marseguerra, M.; Zoia, A.

2007-04-01

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous transport has been successfully analysed within the Continuous Time Random Walk (CTRW) model. In this paper, within a Monte Carlo approach to CTRW, we focus on the particle transport through two regions characterized by different physical properties, in presence of an external driving action constituted by an additional advective field, modelled within both the Galilei invariant and Galilei variant schemes. Particular attention is paid to the interplay between the distributions of space and time across the discontinuity. The resident concentration and the flux of the particles are finally evaluated and it is shown that at the interface between the two regions the flux is continuous as required by mass conservation, while the concentration may reveal a neat discontinuity. This result could open the route to the Monte Carlo investigation of the effectiveness of a physical discontinuity acting as a filter on particle concentration.

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

NASA Astrophysics Data System (ADS)

Cremaschini, Claudio; Tessarotto, Massimo

2017-05-01

A challenging issue in General Relativity concerns the determination of the manifestly covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor \\widehat{g}(r)≡ { \\widehat{g}_{μ ν }(r)} solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields x≡ { g,π } obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations. It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

The Performance Analysis Based on SAR Sample Covariance Matrix

PubMed Central

Erten, Esra

2012-01-01

Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR) context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given. PMID:22736976

Scale-covariant theory of gravitation and astrophysical applications

NASA Technical Reports Server (NTRS)

Canuto, V.; Adams, P. J.; Hsieh, S.-H.; Tsiang, E.

1977-01-01

A scale-covariant theory of gravitation is presented which is characterized by a set of equations that are complete only after a choice of the scale function is made. Special attention is given to gauge conditions and units which allow gravitational phenomena to be described in atomic units. The generalized gravitational-field equations are derived by performing a direct scale transformation, by extending Riemannian geometry to Weyl geometry through the introduction of the notion of cotensors, and from a variation principle. Modified conservation laws are provided, a set of dynamical equations is obtained, and astrophysical consequences are considered. The theory is applied to examine certain homogeneous cosmological solutions, perihelion shifts, light deflections, secular variations of planetary orbital elements, stellar structure equations for a star in quasi-static equilibrium, and the past thermal history of earth. The possible relation of the scale-covariant theory to gauge field theories and their predictions of cosmological constants is discussed.

Beamforming using subspace estimation from a diagonally averaged sample covariance.

PubMed

Quijano, Jorge E; Zurk, Lisa M

2017-08-01

The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.

Covariance mapping techniques

NASA Astrophysics Data System (ADS)

Frasinski, Leszek J.

2016-08-01

Recent technological advances in the generation of intense femtosecond pulses have made covariance mapping an attractive analytical technique. The laser pulses available are so intense that often thousands of ionisation and Coulomb explosion events will occur within each pulse. To understand the physics of these processes the photoelectrons and photoions need to be correlated, and covariance mapping is well suited for operating at the high counting rates of these laser sources. Partial covariance is particularly useful in experiments with x-ray free electron lasers, because it is capable of suppressing pulse fluctuation effects. A variety of covariance mapping methods is described: simple, partial (single- and multi-parameter), sliced, contingent and multi-dimensional. The relationship to coincidence techniques is discussed. Covariance mapping has been used in many areas of science and technology: inner-shell excitation and Auger decay, multiphoton and multielectron ionisation, time-of-flight and angle-resolved spectrometry, infrared spectroscopy, nuclear magnetic resonance imaging, stimulated Raman scattering, directional gamma ray sensing, welding diagnostics and brain connectivity studies (connectomics). This review gives practical advice for implementing the technique and interpreting the results, including its limitations and instrumental constraints. It also summarises recent theoretical studies, highlights unsolved problems and outlines a personal view on the most promising research directions.

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

NASA Technical Reports Server (NTRS)

Borovikov, Anna; Rienecker, Michele M.; Keppenne, Christian; Johnson, Gregory C.

2004-01-01

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the

Problems with small area surveys: lensing covariance of supernova distance measurements.

PubMed

Cooray, Asantha; Huterer, Dragan; Holz, Daniel E

2006-01-20

While luminosity distances from type Ia supernovae (SNe) are a powerful probe of cosmology, the accuracy with which these distances can be measured is limited by cosmic magnification due to gravitational lensing by the intervening large-scale structure. Spatial clustering of foreground mass leads to correlated errors in SNe distances. By including the full covariance matrix of SNe, we show that future wide-field surveys will remain largely unaffected by lensing correlations. However, "pencil beam" surveys, and those with narrow (but possibly long) fields of view, can be strongly affected. For a survey with 30 arcmin mean separation between SNe, lensing covariance leads to a approximately 45% increase in the expected errors in dark energy parameters.

Dynamical response of the Galileo Galilei on the ground rotor to test the equivalence principle: Theory, simulation, and experiment. II. The rejection of common mode forces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Comandi, G.L.; Toncelli, R.; Chiofalo, M.L.

'Galileo Galilei on the ground' (GGG) is a fast rotating differential accelerometer designed to test the equivalence principle (EP). Its sensitivity to differential effects, such as the effect of an EP violation, depends crucially on the capability of the accelerometer to reject all effects acting in common mode. By applying the theoretical and simulation methods reported in Part I of this work, and tested therein against experimental data, we predict the occurrence of an enhanced common mode rejection of the GGG accelerometer. We demonstrate that the best rejection of common mode disturbances can be tuned in a controlled way bymore » varying the spin frequency of the GGG rotor.« less

Comparing Multiple Evapotranspiration-calculating Methods, Including Eddy Covariance and Surface Renewal, Using Empirical Measurements from Alfalfa Fields in the Sacramento-San Joaquin River Delta

NASA Astrophysics Data System (ADS)

Clay, J.; Kent, E. R.; Leinfelder-Miles, M.; Lambert, J. J.; Little, C.; Paw U, K. T.; Snyder, R. L.

2016-12-01

Eddy covariance and surface renewal measurements were used to estimate evapotranspiration (ET) over a variety of crop fields in the Sacramento-San Joaquin River Delta during the 2016 growing season. However, comparing and evaluating multiple measurement systems and methods for determining ET was focused upon at a single alfalfa site. The eddy covariance systems included two systems for direct measurement of latent heat flux: one using a separate sonic anemometer and an open path infrared gas analyzer and another using a combined system (Campbell Scientific IRGASON). For these methods, eddy covariance was used with measurements from the Campbell Scientific CSAT3, the LI-COR 7500a, the Campbell Scientific IRGASON, and an additional R.M. Young sonic anemometer. In addition to those direct measures, the surface renewal approach included several energy balance residual methods in which net radiation, ground heat flux, and sensible heat flux (H) were measured. H was measured using several systems and different methods, including using multiple fast-response thermocouple measurements and using the temperatures measured by the sonic anemometers. The energy available for ET was then calculated as the residual of the surface energy balance equation. Differences in ET values were analyzed between the eddy covariance and surface renewal methods, using the IRGASON-derived values of ET as the standard for accuracy.

Dual formulation of covariant nonlinear duality-symmetric action of kappa-symmetric D3-brane

NASA Astrophysics Data System (ADS)

Vanichchapongjaroen, Pichet

2018-02-01

We study the construction of covariant nonlinear duality-symmetric actions in dual formulation. Essentially, the construction is the PST-covariantisation and nonlinearisation of Zwanziger action. The covariantisation made use of three auxiliary scalar fields. Apart from these, the construction proceed in a similar way to that of the standard formulation. For example, the theories can be extended to include interactions with external fields, and that the theories possess two local PST symmetries. We then explicitly demonstrate the construction of covariant nonlinear duality-symmetric actions in dual formulation of DBI theory, and D3-brane. For each of these theories, the twisted selfduality condition obtained from duality-symmetric actions are explicitly shown to match with the duality relation between field strength and its dual from the one-potential actions. Their on-shell actions between the duality-symmetric and the one-potential versions are also shown to match. We also explicitly prove kappa-symmetry of the covariant nonlinear duality-symmetric D3-brane action in dual formulation.

Covariant formulation of scalar-torsion gravity

NASA Astrophysics Data System (ADS)

Hohmann, Manuel; Järv, Laur; Ualikhanova, Ulbossyn

2018-05-01

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, f (T ,ϕ ) , thus encompassing the cases of f (T ) gravity and a nonminimally coupled scalar field as subclasses. The action is manifestly Lorentz invariant when besides the tetrad one allows for a flat but nontrivial spin connection. We derive the field equations and demonstrate how the antisymmetric part of the tetrad equations is automatically satisfied when the spin connection equation holds. The spin connection equation is a vital part of the covariant formulation, since it determines the spin connection associated with a given tetrad. We discuss how the spin connection equation can be solved in general and provide the cosmological and spherically symmetric examples. Finally, we generalize the theory to an arbitrary number of scalar fields.

FLUXPART: An FOSS solution for Eddy covariance flux partitioning

USDA-ARS?s Scientific Manuscript database

We report on efforts to develop a FOSS solution for a particular geoscience application. Eddy covariance (EC) instruments are routinely used to measure field-scale evapotranspiration and CO2 fluxes. For many applications, it is desirable to partition the measured evapotranspiration flux into its c...

Covariance Bell inequalities

NASA Astrophysics Data System (ADS)

Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolas

2017-12-01

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Covariance Manipulation for Conjunction Assessment

NASA Technical Reports Server (NTRS)

Hejduk, M. D.

2016-01-01

The manipulation of space object covariances to try to provide additional or improved information to conjunction risk assessment is not an uncommon practice. Types of manipulation include fabricating a covariance when it is missing or unreliable to force the probability of collision (Pc) to a maximum value ('PcMax'), scaling a covariance to try to improve its realism or see the effect of covariance volatility on the calculated Pc, and constructing the equivalent of an epoch covariance at a convenient future point in the event ('covariance forecasting'). In bringing these methods to bear for Conjunction Assessment (CA) operations, however, some do not remain fully consistent with best practices for conducting risk management, some seem to be of relatively low utility, and some require additional information before they can contribute fully to risk analysis. This study describes some basic principles of modern risk management (following the Kaplan construct) and then examines the PcMax and covariance forecasting paradigms for alignment with these principles; it then further examines the expected utility of these methods in the modern CA framework. Both paradigms are found to be not without utility, but only in situations that are somewhat carefully circumscribed.

Bayes linear covariance matrix adjustment

NASA Astrophysics Data System (ADS)

Wilkinson, Darren J.

1995-12-01

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be amenable to a similar approach. Diagnostics for matrix adjustments are also discussed.

Covariance of fluid-turbulence theory.

PubMed

Ariki, Taketo

2015-05-01

Covariance of physical quantities in fluid-turbulence theory and their governing equations under generalized coordinate transformation is discussed. It is shown that the velocity fluctuation and its governing law have a covariance under far wider group of coordinate transformation than that of conventional Euclidean invariance, and, as a natural consequence, various correlations and their governing laws are shown to be formulated in covariant manners under this wider transformation group. In addition, it is also shown that the covariance of the Reynolds stress is tightly connected to the objectivity of the mean flow.

Monitoring ecosystem reclamation recovery using optical remote sensing: Comparison with field measurements and eddy covariance.

PubMed

Chasmer, L; Baker, T; Carey, S K; Straker, J; Strilesky, S; Petrone, R

2018-06-12

Time series remote sensing vegetation indices derived from SPOT 5 data are compared with vegetation structure and eddy covariance flux data at 15 dry to wet reclamation and reference sites within the Oil Sands region of Alberta, Canada. This comprehensive analysis examines the linkages between indicators of ecosystem function and change trajectories observed both at the plot level and within pixels. Using SPOT imagery, we find that higher spatial resolution datasets (e.g. 10 m) improves the relationship between vegetation indices and structural measurements compared with interpolated (lower resolution) pixels. The simple ratio (SR) vegetation index performs best when compared with stem density-based indicators (R 2  = 0.65; p < 0.00), while the normalised difference vegetation index (NDVI) and soil adjusted vegetation index (SAVI) are most comparable to foliage indicators (leaf area index (LAI) and canopy cover (R 2  = 0.52-0.78; p > 0.02). Fluxes (net ecosystem production (NEP) and gross ecosystem production (GEP)) are most related to NDVI and SAVI when these are interpolated to larger 20 m × 20 m pixels (R 2  = 0.44-0.50; p < 0.00). As expected, decreased sensitivity of NDVI is problematic for sites with LAI > 3 m 2  m -2 , making this index more appropriate for newly regenerating reclamation areas. For sites with LAI < 3 m 2  m -2 , trajectories of vegetation change can be mapped over time and are within 2.7% and 3.3% of annual measured LAI changes observed at most sites. This study demonstrates the utility of remote sensing in combination with field and eddy covariance data for monitoring and scaling of reclaimed and reference site productivity within and beyond the Oil Sands Region of western Canada. Copyright © 2018 Elsevier B.V. All rights reserved.

A fully covariant information-theoretic ultraviolet cutoff for scalar fields in expanding Friedmann Robertson Walker spacetimes

NASA Astrophysics Data System (ADS)

Kempf, A.; Chatwin-Davies, A.; Martin, R. T. W.

2013-02-01

While a natural ultraviolet cutoff, presumably at the Planck length, is widely assumed to exist in nature, it is nontrivial to implement a minimum length scale covariantly. This is because the presence of a fixed minimum length needs to be reconciled with the ability of Lorentz transformations to contract lengths. In this paper, we implement a fully covariant Planck scale cutoff by cutting off the spectrum of the d'Alembertian. In this scenario, consistent with Lorentz contractions, wavelengths that are arbitrarily smaller than the Planck length continue to exist. However, the dynamics of modes of wavelengths that are significantly smaller than the Planck length possess a very small bandwidth. This has the effect of freezing the dynamics of such modes. While both wavelengths and bandwidths are frame dependent, Lorentz contraction and time dilation conspire to make the freezing of modes of trans-Planckian wavelengths covariant. In particular, we show that this ultraviolet cutoff can be implemented covariantly also in curved spacetimes. We focus on Friedmann Robertson Walker spacetimes and their much-discussed trans-Planckian question: The physical wavelength of each comoving mode was smaller than the Planck scale at sufficiently early times. What was the mode's dynamics then? Here, we show that in the presence of the covariant UV cutoff, the dynamical bandwidth of a comoving mode is essentially zero up until its physical wavelength starts exceeding the Planck length. In particular, we show that under general assumptions, the number of dynamical degrees of freedom of each comoving mode all the way up to some arbitrary finite time is actually finite. Our results also open the way to calculating the impact of this natural UV cutoff on inflationary predictions for the cosmic microwave background.

One-loop matching and running with covariant derivative expansion

NASA Astrophysics Data System (ADS)

Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi

2018-01-01

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these "mixed" one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of "integrating out" heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.

Covariant Uniform Acceleration

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Scarr, Tzvi

2013-04-01

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation , where F is the 3D force and p = m0γv is the 3D relativistic momentum. The standard 4D equation is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We introduce the 4D velocity, an adaptation of Horwitz and Piron s notion of "off-shell." We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and

The SAMI Galaxy Survey: cubism and covariance, putting round pegs into square holes

NASA Astrophysics Data System (ADS)

Sharp, R.; Allen, J. T.; Fogarty, L. M. R.; Croom, S. M.; Cortese, L.; Green, A. W.; Nielsen, J.; Richards, S. N.; Scott, N.; Taylor, E. N.; Barnes, L. A.; Bauer, A. E.; Birchall, M.; Bland-Hawthorn, J.; Bloom, J. V.; Brough, S.; Bryant, J. J.; Cecil, G. N.; Colless, M.; Couch, W. J.; Drinkwater, M. J.; Driver, S.; Foster, C.; Goodwin, M.; Gunawardhana, M. L. P.; Ho, I.-T.; Hampton, E. J.; Hopkins, A. M.; Jones, H.; Konstantopoulos, I. S.; Lawrence, J. S.; Leslie, S. K.; Lewis, G. F.; Liske, J.; López-Sánchez, Á. R.; Lorente, N. P. F.; McElroy, R.; Medling, A. M.; Mahajan, S.; Mould, J.; Parker, Q.; Pracy, M. B.; Obreschkow, D.; Owers, M. S.; Schaefer, A. L.; Sweet, S. M.; Thomas, A. D.; Tonini, C.; Walcher, C. J.

2015-01-01

We present a methodology for the regularization and combination of sparse sampled and irregularly gridded observations from fibre-optic multiobject integral field spectroscopy. The approach minimizes interpolation and retains image resolution on combining subpixel dithered data. We discuss the methodology in the context of the Sydney-AAO multiobject integral field spectrograph (SAMI) Galaxy Survey underway at the Anglo-Australian Telescope. The SAMI instrument uses 13 fibre bundles to perform high-multiplex integral field spectroscopy across a 1° diameter field of view. The SAMI Galaxy Survey is targeting ˜3000 galaxies drawn from the full range of galaxy environments. We demonstrate the subcritical sampling of the seeing and incomplete fill factor for the integral field bundles results in only a 10 per cent degradation in the final image resolution recovered. We also implement a new methodology for tracking covariance between elements of the resulting data cubes which retains 90 per cent of the covariance information while incurring only a modest increase in the survey data volume.

Covariance Manipulation for Conjunction Assessment

NASA Technical Reports Server (NTRS)

Hejduk, M. D.

2016-01-01

Use of probability of collision (Pc) has brought sophistication to CA. Made possible by JSpOC precision catalogue because provides covariance. Has essentially replaced miss distance as basic CA parameter. Embrace of Pc has elevated methods to 'manipulate' covariance to enable/improve CA calculations. Two such methods to be examined here; compensation for absent or unreliable covariances through 'Maximum Pc' calculation constructs, projection (not propagation) of epoch covariances forward in time to try to enable better risk assessments. Two questions to be answered about each; situations to which such approaches are properly applicable, amount of utility that such methods offer.

Eddy Covariance Measurements Over a Maize Field: The Contribution of Minor Flux Terms to the Energy Balance Gap

NASA Astrophysics Data System (ADS)

Smidt, J.; Ingwersen, J.; Streck, T.

2015-12-01

The lack of energy balance closure is a long-standing problem in eddy covariance (EC) measurements. The energy balance equation is defined as Rn - G = H + λE, where Rn is net radiation, G is the ground heat flux, H is the sensible heat flux and λE is the latent heat flux. In most cases of energy imbalance, either Rn is overestimated or the ground heat and turbulent fluxes are underestimated. Multiple studies have shown that calculations, incorrect instrument installation/calibration and measurement errors alone do not entirely account for this imbalance. Rather, research is now focused on previously neglected sources of heat storage in the soil, biomass and air beneath the EC station. This project examined the potential of five "minor flux terms" - soil heat storage, biomass heat storage, energy consumption by photosynthesis, air heat storage and atmospheric moisture change, to further close the energy balance gap. Eddy covariance measurements were conducted at a maize (Zea mays) field in southwest Germany during summer 2014. Soil heat storage was measured for six weeks at 11 sites around the field footprint. Biomass and air heat storage were measured for six subsequent weeks at seven sites around the field footprint. Energy consumption by photosynthesis was calculated using the CO2 flux data. Evapotranspiration was calculated using the water balance method and then compared to the flux data processed with three post-closure methods: the sensible heat flux, the latent heat flux and the Bowen ratio post-closure methods. An energy balance closure of 66% was achieved by the EC station measurements over the entire investigation period. During the soil heat flux campaign, EC station closure was 74.1%, and the field footprint soil heat storage contributed 3.3% additional closure. During the second minor flux term measurement period, closure with the EC station data was 91%. Biomass heat storage resulted in 1.1% additional closure, the photosynthesis flux closed the gap

Complete super-sample lensing covariance in the response approach

NASA Astrophysics Data System (ADS)

Barreira, Alexandre; Krause, Elisabeth; Schmidt, Fabian

2018-06-01

We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure formation, which is necessary for lensing applications. We derive the lensing SSC formulae for two cases: one under the Limber and flat-sky approximations, and a more general one that goes beyond the Limber approximation in the super-survey mode and is valid for curved sky applications. Quantitatively, we find that for sky fractions fsky ≈ 0.3 and a single source redshift at zS=1, the use of the flat-sky and Limber approximation underestimates the total SSC contribution by ≈ 10%. The contribution from super-survey tidal fields to the lensing SSC, which has not been included in cosmological analyses so far, is shown to represent about 5% of the total lensing covariance on multipoles l1,l2 gtrsim 300. The SSC is the dominant off-diagonal contribution to the total lensing covariance, making it appropriate to include these tidal terms and beyond flat-sky/Limber corrections in cosmic shear analyses.

Evaluating four gap-filling methods for eddy covariance measurements of evapotranspiration over hilly crop fields

NASA Astrophysics Data System (ADS)

Boudhina, Nissaf; Zitouna-Chebbi, Rim; Mekki, Insaf; Jacob, Frédéric; Ben Mechlia, Nétij; Masmoudi, Moncef; Prévot, Laurent

2018-06-01

Estimating evapotranspiration in hilly watersheds is paramount for managing water resources, especially in semiarid/subhumid regions. The eddy covariance (EC) technique allows continuous measurements of latent heat flux (LE). However, time series of EC measurements often experience large portions of missing data because of instrumental malfunctions or quality filtering. Existing gap-filling methods are questionable over hilly crop fields because of changes in airflow inclination and subsequent aerodynamic properties. We evaluated the performances of different gap-filling methods before and after tailoring to conditions of hilly crop fields. The tailoring consisted of splitting the LE time series beforehand on the basis of upslope and downslope winds. The experiment was setup within an agricultural hilly watershed in northeastern Tunisia. EC measurements were collected throughout the growth cycle of three wheat crops, two of them located in adjacent fields on opposite hillslopes, and the third one located in a flat field. We considered four gap-filling methods: the REddyProc method, the linear regression between LE and net radiation (Rn), the multi-linear regression of LE against the other energy fluxes, and the use of evaporative fraction (EF). Regardless of the method, the splitting of the LE time series did not impact the gap-filling rate, and it might improve the accuracies on LE retrievals in some cases. Regardless of the method, the obtained accuracies on LE estimates after gap filling were close to instrumental accuracies, and they were comparable to those reported in previous studies over flat and mountainous terrains. Overall, REddyProc was the most appropriate method, for both gap-filling rate and retrieval accuracy. Thus, it seems possible to conduct gap filling for LE time series collected over hilly crop fields, provided the LE time series are split beforehand on the basis of upslope-downslope winds. Future works should address consecutive vegetation

Coincidence and covariance data acquisition in photoelectron and -ion spectroscopy. II. Analysis and applications

NASA Astrophysics Data System (ADS)

Mikosch, Jochen; Patchkovskii, Serguei

2013-10-01

We use an analytical theory of noisy Poisson processes, developed in the preceding companion publication, to compare coincidence and covariance measurement approaches in photoelectron and -ion spectroscopy. For non-unit detection efficiencies, coincidence data acquisition (DAQ) suffers from false coincidences. The rate of false coincidences grows quadratically with the rate of elementary ionization events. To minimize false coincidences for rare event outcomes, very low event rates may hence be required. Coincidence measurements exhibit high tolerance to noise introduced by unstable experimental conditions. Covariance DAQ on the other hand is free of systematic errors as long as stable experimental conditions are maintained. In the presence of noise, all channels in a covariance measurement become correlated. Under favourable conditions, covariance DAQ may allow orders of magnitude reduction in measurement times. Finally, we use experimental data for strong-field ionization of 1,3-butadiene to illustrate how fluctuations in experimental conditions can contaminate a covariance measurement, and how such contamination can be detected.

On the role of covariance information for GRACE K-band observations in the Celestial Mechanics Approach

NASA Astrophysics Data System (ADS)

Bentel, Katrin; Meyer, Ulrich; Arnold, Daniel; Jean, Yoomin; Jäggi, Adrian

2017-04-01

The Astronomical Institute at the University of Bern (AIUB) derives static and time-variable gravity fields by means of the Celestial Mechanics Approach (CMA) from GRACE (level 1B) data. This approach makes use of the close link between orbit and gravity field determination. GPS-derived kinematic GRACE orbit positions, inter-satellite K-band observations, which are the core observations of GRACE, and accelerometer data are combined to rigorously estimate orbit and spherical harmonic gravity field coefficients in one adjustment step. Pseudo-stochastic orbit parameters are set up to absorb unmodeled noise. The K-band range measurements in along-track direction lead to a much higher correlation of the observations in this direction compared to the other directions and thus, to north-south stripes in the unconstrained gravity field solutions, so-called correlated errors. By using a full covariance matrix for the K-band observations the correlation can be taken into account. One possibility is to derive correlation information from post-processing K-band residuals. This is then used in a second iteration step to derive an improved gravity field solution. We study the effects of pre-defined covariance matrices and residual-derived covariance matrices on the final gravity field product with the CMA.

Using Covariance Matrix for Change Detection of Polarimetric SAR Data

NASA Astrophysics Data System (ADS)

Esmaeilzade, M.; Jahani, F.; Amini, J.

2017-09-01

Nowadays change detection is an important role in civil and military fields. The Synthetic Aperture Radar (SAR) images due to its independent of atmospheric conditions and cloud cover, have attracted much attention in the change detection applications. When the SAR data are used, one of the appropriate ways to display the backscattered signal is using covariance matrix that follows the Wishart distribution. Based on this distribution a statistical test for equality of two complex variance-covariance matrices can be used. In this study, two full polarization data in band L from UAVSAR are used for change detection in agricultural fields and urban areas in the region of United States which the first image belong to 2014 and the second one is from 2017. To investigate the effect of polarization on the rate of change, full polarization data and dual polarization data were used and the results were compared. According to the results, full polarization shows more changes than dual polarization.

Covariance Partition Priors: A Bayesian Approach to Simultaneous Covariance Estimation for Longitudinal Data.

PubMed

Gaskins, J T; Daniels, M J

2016-01-02

The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consists of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow borrowing of strength across potentially similar groups to improve estimation. To that end, we introduce a covariance partition prior which proposes a partition of the groups at each measurement time. Groups in the same set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as a Markov chain to encourage similar structure at nearby measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero. We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study. This article includes Supplementary Material available online.

One-loop matching and running with covariant derivative expansion

DOE PAGES

Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi

2018-01-24

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-knownmore » matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.« less

One-loop matching and running with covariant derivative expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henning, Brian; Lu, Xiaochuan; Murayama, Hitoshi

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-knownmore » matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.« less

Eddy Covariance Method: Overview of General Guidelines and Conventional Workflow

NASA Astrophysics Data System (ADS)

Burba, G. G.; Anderson, D. J.; Amen, J. L.

2007-12-01

Atmospheric flux measurements are widely used to estimate water, heat, carbon dioxide and trace gas exchange between the ecosystem and the atmosphere. The Eddy Covariance method is one of the most direct, defensible ways to measure and calculate turbulent fluxes within the atmospheric boundary layer. However, the method is mathematically complex, and requires significant care to set up and process data. These reasons may be why the method is currently used predominantly by micrometeorologists. Modern instruments and software can potentially expand the use of this method beyond micrometeorology and prove valuable for plant physiology, hydrology, biology, ecology, entomology, and other non-micrometeorological areas of research. The main challenge of the method for a non-expert is the complexity of system design, implementation, and processing of the large volume of data. In the past several years, efforts of the flux networks (e.g., FluxNet, Ameriflux, CarboEurope, Fluxnet-Canada, Asiaflux, etc.) have led to noticeable progress in unification of the terminology and general standardization of processing steps. The methodology itself, however, is difficult to unify, because various experimental sites and different purposes of studies dictate different treatments, and site-, measurement- and purpose-specific approaches. Here we present an overview of theory and typical workflow of the Eddy Covariance method in a format specifically designed to (i) familiarize a non-expert with general principles, requirements, applications, and processing steps of the conventional Eddy Covariance technique, (ii) to assist in further understanding the method through more advanced references such as textbooks, network guidelines and journal papers, (iii) to help technicians, students and new researchers in the field deployment of the Eddy Covariance method, and (iv) to assist in its use beyond micrometeorology. The overview is based, to a large degree, on the frequently asked questions

Mean-Lagrangian formalism and covariance of fluid turbulence.

PubMed

Ariki, Taketo

2017-05-01

Mean-field-based Lagrangian framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of an extended covariance group.

Comparison of Sensible Heat Flux from Eddy Covariance and Scintillometer over different land surface conditions

NASA Astrophysics Data System (ADS)

Zeweldi, D. A.; Gebremichael, M.; Summis, T.; Wang, J.; Miller, D.

2008-12-01

The large source of uncertainty in satellite-based evapotranspiration algorithm results from the estimation of sensible heat flux H. Traditionally eddy covariance sensors, and recently large-aperture scintillometers, have been used as ground truth to evaluate satellite-based H estimates. The two methods rely on different physical measurement principles, and represent different foot print sizes. In New Mexico, we conducted a field campaign during summer 2008 to compare H estimates obtained from the eddy covariance and scintillometer methods. During this field campaign, we installed sonic anemometers; one propeller eddy covariance (OPEC) equipped with net radiometer and soil heat flux sensors; large aperture scintillometer (LAS); and weather station consisting of wind speed, direction and radiation sensors over three different experimental areas consisting of different roughness conditions (desert, irrigated area and lake). Our results show the similarities and differences in H estimates obtained from these various methods over the different land surface conditions. Further, our results show that the H estimates obtained from the LAS agree with those obtained from the eddy covariance method when high frequency thermocouple temperature, instead of the typical weather station temperature measurements, is used in the LAS analysis.

Dynamical response of the Galileo Galilei on the ground rotor to test the equivalence principle: Theory, simulation, and experiment. I. The normal modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Comandi, G.L.; Chiofalo, M.L.; Toncelli, R.

Recent theoretical work suggests that violation of the equivalence principle might be revealed in a measurement of the fractional differential acceleration {eta} between two test bodies-of different compositions, falling in the gravitational field of a source mass--if the measurement is made to the level of {eta}{approx_equal}10{sup -13} or better. This being within the reach of ground based experiments gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in a low orbit around the Earth is likely to provide a much better accuracy. We report onmore » the progress made with the 'Galileo Galilei on the ground' (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following articles (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rotation-in particular, its normal modes (Part I) and rejection of common mode effects (Part II)-can be predicted by means of a simple but effective model that embodies all the relevant physics. Analytical solutions are obtained under special limits, which provide the theoretical understanding. A simulation environment is set up, obtaining a quantitative agreement with the available experimental data on the frequencies of the normal modes and on the whirling behavior. This is a needed and reliable tool for controlling and separating perturbative effects from the expected signal, as well as for planning the optimization of the apparatus.« less

Covariant effective action for a Galilean invariant quantum Hall system

NASA Astrophysics Data System (ADS)

Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.

2016-09-01

We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son's improvement terms to arbitrary order in m.

Covariant effective action for a Galilean invariant quantum Hall system

DOE PAGES

Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.

2016-09-16

Here, we construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of curved Galilean spacetimes, including torsion and a gravitational field, allowing us to study charge, energy, stress and mass currents within a unified framework. A shift symmetry specific to single constituent theories constraints the effective action to couple to an effective background gauge field and spin connection that is solved for by a self-consistent equation, providing a manifestly covariant extension of Hoyos and Son’s improvement terms to arbitrarymore » order in m.« less

Covariance descriptor fusion for target detection

NASA Astrophysics Data System (ADS)

Cukur, Huseyin; Binol, Hamidullah; Bal, Abdullah; Yavuz, Fatih

2016-05-01

Target detection is one of the most important topics for military or civilian applications. In order to address such detection tasks, hyperspectral imaging sensors provide useful images data containing both spatial and spectral information. Target detection has various challenging scenarios for hyperspectral images. To overcome these challenges, covariance descriptor presents many advantages. Detection capability of the conventional covariance descriptor technique can be improved by fusion methods. In this paper, hyperspectral bands are clustered according to inter-bands correlation. Target detection is then realized by fusion of covariance descriptor results based on the band clusters. The proposed combination technique is denoted Covariance Descriptor Fusion (CDF). The efficiency of the CDF is evaluated by applying to hyperspectral imagery to detect man-made objects. The obtained results show that the CDF presents better performance than the conventional covariance descriptor.

Generalized Linear Covariance Analysis

NASA Technical Reports Server (NTRS)

Carpenter, James R.; Markley, F. Landis

2014-01-01

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Adjoints and Low-rank Covariance Representation

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.

2000-01-01

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Gauge covariance of the fermion Schwinger–Dyson equation in QED

DOE PAGES

Jia, Shaoyang; Pennington, Michael R.

2017-03-27

Any practical application of the Schwinger–Dyson equations to the study of n-point Green's functions in a strong coupling field theory requires truncations. In the case of QED, the gauge covariance, governed by the Landau–Khalatnikov–Fradkin transformations (LKFT), provides a unique constraint on such truncation. Here, by using a spectral representation for the massive fermion propagator in QED, we are able to show that the constraints imposed by the LKFT are linear operations on the spectral densities. We formally define these group operations and show with a couple of examples how in practice they provide a straightforward way to test the gaugemore » covariance of any viable truncation of the Schwinger–Dyson equation for the fermion 2-point function.« less

Quantum corrections for the cubic Galileon in the covariant language

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saltas, Ippocratis D.; Vitagliano, Vincenzo, E-mail: isaltas@fc.ul.pt, E-mail: vincenzo.vitagliano@ist.utl.pt

We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which' relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach inmore » this context is discussed, while all calculations are explicitly presented.« less

Computation of transform domain covariance matrices

NASA Technical Reports Server (NTRS)

Fino, B. J.; Algazi, V. R.

1975-01-01

It is often of interest in applications to compute the covariance matrix of a random process transformed by a fast unitary transform. Here, the recursive definition of fast unitary transforms is used to derive recursive relations for the covariance matrices of the transformed process. These relations lead to fast methods of computation of covariance matrices and to substantial reductions of the number of arithmetic operations required.

Relative-Error-Covariance Algorithms

NASA Technical Reports Server (NTRS)

Bierman, Gerald J.; Wolff, Peter J.

1991-01-01

Two algorithms compute error covariance of difference between optimal estimates, based on data acquired during overlapping or disjoint intervals, of state of discrete linear system. Provides quantitative measure of mutual consistency or inconsistency of estimates of states. Relative-error-covariance concept applied, to determine degree of correlation between trajectories calculated from two overlapping sets of measurements and construct real-time test of consistency of state estimates based upon recently acquired data.

Covariate analysis of bivariate survival data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bennett, L.E.

1992-01-01

The methods developed are used to analyze the effects of covariates on bivariate survival data when censoring and ties are present. The proposed method provides models for bivariate survival data that include differential covariate effects and censored observations. The proposed models are based on an extension of the univariate Buckley-James estimators which replace censored data points by their expected values, conditional on the censoring time and the covariates. For the bivariate situation, it is necessary to determine the expectation of the failure times for one component conditional on the failure or censoring time of the other component. Two different methodsmore » have been developed to estimate these expectations. In the semiparametric approach these expectations are determined from a modification of Burke's estimate of the bivariate empirical survival function. In the parametric approach censored data points are also replaced by their conditional expected values where the expected values are determined from a specified parametric distribution. The model estimation will be based on the revised data set, comprised of uncensored components and expected values for the censored components. The variance-covariance matrix for the estimated covariate parameters has also been derived for both the semiparametric and parametric methods. Data from the Demographic and Health Survey was analyzed by these methods. The two outcome variables are post-partum amenorrhea and breastfeeding; education and parity were used as the covariates. Both the covariate parameter estimates and the variance-covariance estimates for the semiparametric and parametric models will be compared. In addition, a multivariate test statistic was used in the semiparametric model to examine contrasts. The significance of the statistic was determined from a bootstrap distribution of the test statistic.« less

Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings

NASA Astrophysics Data System (ADS)

Wells, James D.; Zhang, Zhengkang

2018-05-01

Dismissing traditional naturalness concerns while embracing the Higgs boson mass measurement and unification motivates careful analysis of trans-TeV supersymmetric theories. We take an effective field theory (EFT) approach, matching the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model (SM) EFT by integrating out heavy superpartners, and evolving MSSM and SMEFT parameters according to renormalization group equations in each regime. Our matching calculation is facilitated by the recent covariant diagrams formulation of functional matching techniques, with the full one-loop SUSY threshold corrections encoded in just 30 diagrams. Requiring consistent matching onto the SMEFT with its parameters (those in the Higgs potential in particular) measured at low energies, and in addition requiring unification of bottom and tau Yukawa couplings at the scale of gauge coupling unification, we detail the solution space of superpartner masses from the TeV scale to well above. We also provide detailed views of parameter space where Higgs coupling measurements have probing capability at future colliders beyond the reach of direct superpartner searches at the LHC.

Lorentz covariance of loop quantum gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rovelli, Carlo; Speziale, Simone

2011-05-15

The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the projected spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleulermore » formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are precisely in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.« less

Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.

PubMed

Yoneoka, Daisuke; Henmi, Masayuki

2017-06-01

Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Defining habitat covariates in camera-trap based occupancy studies

PubMed Central

Niedballa, Jürgen; Sollmann, Rahel; Mohamed, Azlan bin; Bender, Johannes; Wilting, Andreas

2015-01-01

In species-habitat association studies, both the type and spatial scale of habitat covariates need to match the ecology of the focal species. We assessed the potential of high-resolution satellite imagery for generating habitat covariates using camera-trapping data from Sabah, Malaysian Borneo, within an occupancy framework. We tested the predictive power of covariates generated from satellite imagery at different resolutions and extents (focal patch sizes, 10–500 m around sample points) on estimates of occupancy patterns of six small to medium sized mammal species/species groups. High-resolution land cover information had considerably more model support for small, patchily distributed habitat features, whereas it had no advantage for large, homogeneous habitat features. A comparison of different focal patch sizes including remote sensing data and an in-situ measure showed that patches with a 50-m radius had most support for the target species. Thus, high-resolution satellite imagery proved to be particularly useful in heterogeneous landscapes, and can be used as a surrogate for certain in-situ measures, reducing field effort in logistically challenging environments. Additionally, remote sensed data provide more flexibility in defining appropriate spatial scales, which we show to impact estimates of wildlife-habitat associations. PMID:26596779

Exploitation of Geometric Occlusion and Covariance Spectroscopy in a Gamma Sensor Array

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukhopadhyay, Sanjoy; Maurer, Richard; Wolff, Ronald

2013-09-01

The National Security Technologies, LLC, Remote Sensing Laboratory has recently used an array of six small-footprint (1-inch diameter by 3-inch long) cylindrical crystals of thallium-doped sodium iodide scintillators to obtain angular information from discrete gamma ray–emitting point sources. Obtaining angular information in a near-field measurement for a field-deployed gamma sensor is a requirement for radiological emergency work. Three of the sensors sit at the vertices of a 2-inch isosceles triangle, while the other three sit on the circumference of a 3-inch-radius circle centered in this triangle. This configuration exploits occlusion of sensors, correlation from Compton scattering within a detector array,more » and covariance spectroscopy, a spectral coincidence technique. Careful placement and orientation of individual detectors with reference to other detectors in an array can provide improved angular resolution for determining the source position by occlusion mechanism. By evaluating the values of, and the uncertainties in, the photopeak areas, efficiencies, branching ratio, peak area correction factors, and the correlations between these quantities, one can determine the precise activity of a particular radioisotope from a mixture of radioisotopes that have overlapping photopeaks that are ordinarily hard to deconvolve. The spectral coincidence technique, often known as covariance spectroscopy, examines the correlations and fluctuations in data that contain valuable information about radiation sources, transport media, and detection systems. Covariance spectroscopy enhances radionuclide identification techniques, provides directional information, and makes weaker gamma-ray emission—normally undetectable by common spectroscopic analysis—detectable. A series of experimental results using the concept of covariance spectroscopy are presented.« less

Levy Matrices and Financial Covariances

NASA Astrophysics Data System (ADS)

Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail

2003-10-01

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Structural Analysis of Covariance and Correlation Matrices.

ERIC Educational Resources Information Center

Joreskog, Karl G.

1978-01-01

A general approach to analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.…

N2O eddy covariance fluxes: From field measurements to flux calculation

NASA Astrophysics Data System (ADS)

Lognoul, Margaux; Debacq, Alain; Heinesch, Bernard; Aubinet, Marc

2017-04-01

From March to October 2016, we performed eddy covariance measurements in a sugar beet crop at the Lonzée Terrestrial Observatory (LTO, candidate ICOS site) in Belgium. N2O and H2O atmospheric concentrations were measured at 10 Hz using a quantum-cascade laser spectrometer (Aerodyne Research, Inc.) and combined to wind speed 3D components measured with a sonic anemometer (Gill HS-50). Flux computation was carried out using the EddyPro Software (LI-COR) with a focus on adaptations needed for tracers like N2O. Data filtering and quality control were performed according to Vickers and Mahrt (1997) and Mauder and Foken (2004). The flags were adapted to N2O time series. In this presentation, different computation steps will be presented. More specifically: 1) Considering that a large proportion of N2O fluxes are small (within ± 0.5 nmol m-2 s-1), the classical stationarity test might lead to excessive data filtering and in such case, some searchers have chosen to use the running mean (RM) as a detrend method over block averaging (BA) and to filter data otherwise. For our dataset, BA mean fluxes combined to the stationarity test did not significantly differ from RM fluxes when the averaging window was 300s or larger, but were significantly larger otherwise, suggesting that significant eddies occurred at the 5-min timescale and that they were not accounted for with a shorter averaging window. 2) The determination of time-lag in the case of N2O fluxes can become tricky for two reasons : (1) the signal amplitude can differ from one time period to the next, making it difficult to use the method of covariance maximization and (2) an additional clock drift can appear if the spectrometer is not logging on the same computer than the anemometer. In our case, the N2O signal was strong enough to solve both problems and to perform time-lag compensation according to the covariance maximization, with a default value equal to the mode of the lag distribution. The automatic time

Dangers in Using Analysis of Covariance Procedures.

ERIC Educational Resources Information Center

Campbell, Kathleen T.

Problems associated with the use of analysis of covariance (ANCOVA) as a statistical control technique are explained. Three problems relate to the use of "OVA" methods (analysis of variance, analysis of covariance, multivariate analysis of variance, and multivariate analysis of covariance) in general. These are: (1) the wasting of information when…

The enigma of Galileo's eyesight: some novel observations on Galileo Galilei's vision and his progression to blindness.

PubMed

Watson, Peter G

2009-01-01

Galileo Galilei became blind. Before this happened he revealed that his left eye had always had less than perfect vision. A study of his written works, his handwriting, and the originals of the portraits undertaken during his lifetime indicate that this probably was the case. These portraits suggest that his left eye tended to lose fixation and that, at the age of 60, he suffered from a mucocoele of the right frontal sinus; but these conditions would not have caused blindness. Considering the systemic diseases from which he suffered over his lifetime, he could possibly have had a long standing uveitis with secondary pupillary block glaucoma, common in those with the group of conditions classified as sero-negative arthropathies. Posterior scleritis with secondary glaucoma is less likely. If either of these were the cause, then the disease was probably triggered by a well-documented, severe acute illness as a young adult, the inflammation being localized to the eye as a result of severe recurrent conjunctival infections in his youth. The intermittent nature of the visual loss, the normal appearance of the cornea and pupils in his portraits, the absence of any evidence of inflammatory joint disease, the presence of halos, and the severe nature of the pain-combined with the high level of visual acuity in between attacks and its persistence until the last few weeks of vision means that angle-closure glaucoma must also be considered. These suggestions might be confirmed or refuted by studying his remains. Application has been made for this to be done.

Covariant harmonic oscillators: 1973 revisited

NASA Technical Reports Server (NTRS)

Noz, M. E.

1993-01-01

Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

Smooth individual level covariates adjustment in disease mapping.

PubMed

Huque, Md Hamidul; Anderson, Craig; Walton, Richard; Woolford, Samuel; Ryan, Louise

2018-05-01

Spatial models for disease mapping should ideally account for covariates measured both at individual and area levels. The newly available "indiCAR" model fits the popular conditional autoregresssive (CAR) model by accommodating both individual and group level covariates while adjusting for spatial correlation in the disease rates. This algorithm has been shown to be effective but assumes log-linear associations between individual level covariates and outcome. In many studies, the relationship between individual level covariates and the outcome may be non-log-linear, and methods to track such nonlinearity between individual level covariate and outcome in spatial regression modeling are not well developed. In this paper, we propose a new algorithm, smooth-indiCAR, to fit an extension to the popular conditional autoregresssive model that can accommodate both linear and nonlinear individual level covariate effects while adjusting for group level covariates and spatial correlation in the disease rates. In this formulation, the effect of a continuous individual level covariate is accommodated via penalized splines. We describe a two-step estimation procedure to obtain reliable estimates of individual and group level covariate effects where both individual and group level covariate effects are estimated separately. This distributed computing framework enhances its application in the Big Data domain with a large number of individual/group level covariates. We evaluate the performance of smooth-indiCAR through simulation. Our results indicate that the smooth-indiCAR method provides reliable estimates of all regression and random effect parameters. We illustrate our proposed methodology with an analysis of data on neutropenia admissions in New South Wales (NSW), Australia. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Dispersion curve estimation via a spatial covariance method with ultrasonic wavefield imaging.

PubMed

Chong, See Yenn; Todd, Michael D

2018-05-01

Numerous Lamb wave dispersion curve estimation methods have been developed to support damage detection and localization strategies in non-destructive evaluation/structural health monitoring (NDE/SHM) applications. In this paper, the covariance matrix is used to extract features from an ultrasonic wavefield imaging (UWI) scan in order to estimate the phase and group velocities of S0 and A0 modes. A laser ultrasonic interrogation method based on a Q-switched laser scanning system was used to interrogate full-field ultrasonic signals in a 2-mm aluminum plate at five different frequencies. These full-field ultrasonic signals were processed in three-dimensional space-time domain. Then, the time-dependent covariance matrices of the UWI were obtained based on the vector variables in Cartesian and polar coordinate spaces for all time samples. A spatial covariance map was constructed to show spatial correlations within the full wavefield. It was observed that the variances may be used as a feature for S0 and A0 mode properties. The phase velocity and the group velocity were found using a variance map and an enveloped variance map, respectively, at five different frequencies. This facilitated the estimation of Lamb wave dispersion curves. The estimated dispersion curves of the S0 and A0 modes showed good agreement with the theoretical dispersion curves. Copyright © 2018 Elsevier B.V. All rights reserved.

Coherent Doppler lidar signal covariance including wind shear and wind turbulence

NASA Technical Reports Server (NTRS)

Frehlich, R. G.

1993-01-01

The performance of coherent Doppler lidar is determined by the statistics of the coherent Doppler signal. The derivation and calculation of the covariance of the Doppler lidar signal is presented for random atmospheric wind fields with wind shear. The random component is described by a Kolmogorov turbulence spectrum. The signal parameters are clarified for a general coherent Doppler lidar system. There are two distinct physical regimes: one where the transmitted pulse determines the signal statistics and the other where the wind field dominates the signal statistics. The Doppler shift of the signal is identified in terms of the wind field and system parameters.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory, using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis publications is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

UDU/T/ covariance factorization for Kalman filtering

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1980-01-01

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

A comparison of methods for determining the cotton field evapotranspiration and its components under mulched drip irrigation conditions: photosynthesis system, sap flow, and eddy covariance

NASA Astrophysics Data System (ADS)

Zhang, Z.; Tian, F.; Hu, H.

2013-12-01

A multi-scale, multi-technique study was conducted to measure evapotranspiration and its components in a cotton field under mulched drip irrigation conditions in northwestern China. Three measurement techniques at different scales were used: photosynthesis system (leaf scale), sap flow (plant scale), and eddy covariance (field scale). The experiment was conducted from July to September 2012. For upscaling the evapotranspiration from the leaf to the plant scale, an approach that incorporated the canopy structure and the relationships between sunlit and shaded leaves was proposed. For upscaling the evapotranspiration from the plant to the field scale, an approach based on the transpiration per unit leaf area was adopted and modified to incorporate the temporal variability in the relationships between the leaf area and the stem diameter. At the plant scale, the estimate of the transpiration based on the photosynthesis system with upscaling is slightly higher (18%) than that obtained by sap flow. At the field scale, the estimate of the transpiration obtained by upscaling the estimate based on sap flow measurements is also systematically higher (10%) compared to that obtained through eddy covariance during the cotton open boll growth stage when soil evaporation can be neglected. Nevertheless, the results derived from these three distinct methods show reasonable consistency at the field scale, which indicates that the upscaling approaches are reasonable and valid. Based on the measurements and the upscaling approaches, the evapotranspiration components were analyzed under mulched drip irrigation. During the cotton flower and bolling stages in July and August, the evapotranspiration are 3.94 and 4.53 mm day-1, respectively. The proportion of transpiration to evapotranspiration reaches 87.1% before drip irrigation and 82.3% after irrigation. The high water use efficiency is principally due to the mulched film above the drip pipe, the low soil water content in the inter

Low-dimensional Representation of Error Covariance

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.; Todling, Ricardo; Marchesin, Dan

2000-01-01

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

On the covariant gauge {alpha} of the linearized gravity in de Sitter spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheong, Lee Yen

2012-09-26

In previous work, we studied the linearized gravity with covariant gauge {beta}= 2/3 and {alpha}= 5/3. It was found that the sum of the source and initial contributions reproduces the correct field configuration over the whole de Sitter spacetime. In this paper, we extend this work to generalizing the linearized gravitational field in an arbitrary value of the gauge parameter {alpha} but the gauge parameter {beta} remains the same.

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Cross-population myelination covariance of human cerebral cortex.

PubMed

Ma, Zhiwei; Zhang, Nanyin

2017-09-01

Cross-population covariance of brain morphometric quantities provides a measure of interareal connectivity, as it is believed to be determined by the coordinated neurodevelopment of connected brain regions. Although useful, structural covariance analysis predominantly employed bulky morphological measures with mixed compartments, whereas studies of the structural covariance of any specific subdivisions such as myelin are rare. Characterizing myelination covariance is of interest, as it will reveal connectivity patterns determined by coordinated development of myeloarchitecture between brain regions. Using myelin content MRI maps from the Human Connectome Project, here we showed that the cortical myelination covariance was highly reproducible, and exhibited a brain organization similar to that previously revealed by other connectivity measures. Additionally, the myelination covariance network shared common topological features of human brain networks such as small-worldness. Furthermore, we found that the correlation between myelination covariance and resting-state functional connectivity (RSFC) was uniform within each resting-state network (RSN), but could considerably vary across RSNs. Interestingly, this myelination covariance-RSFC correlation was appreciably stronger in sensory and motor networks than cognitive and polymodal association networks, possibly due to their different circuitry structures. This study has established a new brain connectivity measure specifically related to axons, and this measure can be valuable to investigating coordinated myeloarchitecture development. Hum Brain Mapp 38:4730-4743, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A Global Covariance Descriptor for Nuclear Atypia Scoring in Breast Histopathology Images.

PubMed

Khan, Adnan Mujahid; Sirinukunwattana, Korsuk; Rajpoot, Nasir

2015-09-01

Nuclear atypia scoring is a diagnostic measure commonly used to assess tumor grade of various cancers, including breast cancer. It provides a quantitative measure of deviation in visual appearance of cell nuclei from those in normal epithelial cells. In this paper, we present a novel image-level descriptor for nuclear atypia scoring in breast cancer histopathology images. The method is based on the region covariance descriptor that has recently become a popular method in various computer vision applications. The descriptor in its original form is not suitable for classification of histopathology images as cancerous histopathology images tend to possess diversely heterogeneous regions in a single field of view. Our proposed image-level descriptor, which we term as the geodesic mean of region covariance descriptors, possesses all the attractive properties of covariance descriptors lending itself to tractable geodesic-distance-based k-nearest neighbor classification using efficient kernels. The experimental results suggest that the proposed image descriptor yields high classification accuracy compared to a variety of widely used image-level descriptors.

Covariate Imbalance and Precision in Measuring Treatment Effects

ERIC Educational Resources Information Center

Liu, Xiaofeng Steven

2011-01-01

Covariate adjustment can increase the precision of estimates by removing unexplained variance from the error in randomized experiments, although chance covariate imbalance tends to counteract the improvement in precision. The author develops an easy measure to examine chance covariate imbalance in randomization by standardizing the average…

Dimension from covariance matrices.

PubMed

Carroll, T L; Byers, J M

2017-02-01

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

Condition Number Regularized Covariance Estimation.

PubMed

Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala

2013-06-01

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the "large p small n " setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required.

New challenges and opportunities in the eddy-covariance methodology for long-term monitoring networks

NASA Astrophysics Data System (ADS)

Papale, Dario; Fratini, Gerardo

2013-04-01

Eddy-covariance is the most direct and most commonly applied methodology for measuring exchange fluxes of mass and energy between ecosystems and the atmosphere. In recent years, the number of environmental monitoring stations deploying eddy-covariance systems increased dramatically at the global level, exceeding 500 sites worldwide and covering most climatic and ecological regions. Several long-term environmental research infrastructures such as ICOS, NEON and AmeriFlux selected the eddy-covariance as a method to monitor GHG fluxes and are currently collaboratively working towards defining common measurements standards, data processing approaches, QA/QC procedures and uncertainty estimation strategies, to the aim of increasing defensibility of resulting fluxes and intra and inter-comparability of flux databases. In the meanwhile, the eddy-covariance research community keeps identifying technical and methodological flaws that, in some cases, can introduce - and can have introduced to date - significant biases in measured fluxes or increase their uncertainty. Among those, we identify three issues of presumably greater concern, namely: (1) strong underestimation of water vapour fluxes in closed-path systems, and its dependency on relative humidity; (2) flux biases induced by erroneous measurement of absolute gas concentrations; (3) and systematic errors due to underestimation of vertical wind variance in non-orthogonal anemometers. If not properly addressed, these issues can reduce the quality and reliability of the method, especially as a standard methodology in long-term monitoring networks. In this work, we review the status of the art regarding such problems, and propose new evidences based on field experiments as well as numerical simulations. Our analyses confirm the potential relevance of these issues but also hint at possible coping approaches, to minimize problems during setup design, data collection and post-field flux correction. Corrections are under

Parametric Covariance Model for Horizon-Based Optical Navigation

NASA Technical Reports Server (NTRS)

Hikes, Jacob; Liounis, Andrew J.; Christian, John A.

2016-01-01

This Note presents an entirely parametric version of the covariance for horizon-based optical navigation measurements. The covariance can be written as a function of only the spacecraft position, two sensor design parameters, the illumination direction, the size of the observed planet, the size of the lit arc to be used, and the total number of observed horizon points. As a result, one may now more clearly understand the sensitivity of horizon-based optical navigation performance as a function of these key design parameters, which is insight that was obscured in previous (and nonparametric) versions of the covariance. Finally, the new parametric covariance is shown to agree with both the nonparametric analytic covariance and results from a Monte Carlo analysis.

Covariant theory of gravitation in the framework of special relativity

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Brentan, H. B.

2018-04-01

In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a magnetic-like force must be present whenever two or more bodies are in motion. The exact expression for this gravitomagnetic force is then derived purely from special relativity and the consequences of such a covariant theory are developed. For instance, we show that the gravitomagnetic fields satisfy a system of differential equations similar to the Maxwell equations of electrodynamics. This implies that the gravitational waves spread out with the speed of light in a flat spacetime, which is in agreement with the recent results concerning the gravitational waves detection. We also propose that the vector potential can be associated with the interaction momentum in the same way as the scalar potential is usually associated with the interaction energy. Other topics are also discussed, for example, the transformation laws for the fields, the energy and momentum stored in the gravitomagnetic fields, the invariance of the gravitational mass and so on. We remark that is not our intention here to propose an alternative theory of gravitation but, rather, only a first approximation for the gravitational phenomena, so that it can be applied whenever the gravitational force can be regarded as an ordinary effective force field and special relativity can be used with safety. To make this point clear we present briefly a comparison between our approach and that based on the (linearized) Einstein's theory. Finally, we remark that although we have assumed nothing from the electromagnetic theory, we found that gravity and electricity share many properties in common -these similarities, in fact, are just a requirement of special relativity that must apply to any physically acceptable force field.

Static Vented Chamber and Eddy Covariance Methane Flux Comparisons in Mid-South US Rice

NASA Astrophysics Data System (ADS)

Reba, M. L.; Fong, B.; Adviento-Borbe, A.; Runkle, B.; Suvocarev, K.; Rival, I.

2017-12-01

Rice cultivation contributes higher amounts of GHG emissions (CO2 and CH4) due to flooded field conditions. A comparison between eddy covariance and static vented flux chamber measurement techniques is presented. Rice GHG emissions originating from plot level chambers may not accurately describe the aggregate effects of all the soil and micrometeorological variations across a production field. Eddy covariance (EC) is a direct, integrated field measurement of field scale trace gases. Flux measurements were collected in NE Arkansas production size rice fields (16 ha, 40 ac) during the 2015 and 2016 production seasons (June-August) in continuous flood (CF) irrigation. The study objectives included quantifying the difference between chamber and EC measurements, and categorizing flux behavior to growth stage and field history. EC daily average emissions correlated with chamber measurements (R2=0.27-0.54) more than average from 09:00-12:00 which encompassed chamber measurement times (R2=0.23-0.32). Maximum methane emissions occurred in the late afternoon from 14:00-18:00 which corresponded with maximum soil heat flux and air temperature. The total emissions from the study fields ranged from 27-117 kg CH4-C ha-1 season-1. The emission profile was lower in 2015, most likely due to higher rainfall and cooler temperatures during the growing season compared to 2016. These findings improve our understanding of GHG emissions at the field scale under typical production practices and validity of chamber and EC flux measurement techniques.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Rigorous covariance propagation of geoid errors to geodetic MDT estimates

NASA Astrophysics Data System (ADS)

Pail, R.; Albertella, A.; Fecher, T.; Savcenko, R.

2012-04-01

The mean dynamic topography (MDT) is defined as the difference between the mean sea surface (MSS) derived from satellite altimetry, averaged over several years, and the static geoid. Assuming geostrophic conditions, from the MDT the ocean surface velocities as important component of global ocean circulation can be derived from it. Due to the availability of GOCE gravity field models, for the very first time MDT can now be derived solely from satellite observations (altimetry and gravity) down to spatial length-scales of 100 km and even below. Global gravity field models, parameterized in terms of spherical harmonic coefficients, are complemented by the full variance-covariance matrix (VCM). Therefore, for the geoid component a realistic statistical error estimate is available, while the error description of the altimetric component is still an open issue and is, if at all, attacked empirically. In this study we make the attempt to perform, based on the full gravity VCM, rigorous error propagation to derived geostrophic surface velocities, thus also considering all correlations. For the definition of the static geoid we use the third release of the time-wise GOCE model, as well as the satellite-only combination model GOCO03S. In detail, we will investigate the velocity errors resulting from the geoid component in dependence of the harmonic degree, and the impact of using/no using covariances on the MDT errors and its correlations. When deriving an MDT, it is spectrally filtered to a certain maximum degree, which is usually driven by the signal content of the geoid model, by applying isotropic or non-isotropic filters. Since this filtering is acting also on the geoid component, the consistent integration of this filter process into the covariance propagation shall be performed, and its impact shall be quantified. The study will be performed for MDT estimates in specific test areas of particular oceanographic interest.

Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates

PubMed Central

Gill, Mandev S.; Lemey, Philippe; Bennett, Shannon N.; Biek, Roman; Suchard, Marc A.

2016-01-01

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman’s coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late

Controlling Surface Plasmons Through Covariant Transformation of the Spin-Dependent Geometric Phase Between Curved Metamaterials

NASA Astrophysics Data System (ADS)

Zhong, Fan; Li, Jensen; Liu, Hui; Zhu, Shining

2018-06-01

General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different frames. In this Letter, we use one-dimensional curved metamaterials to mimic accelerating particles in curved space-times. The different curved shapes of structures are used to mimic different accelerating frames. The different geometric phases along the structure are used to mimic different movements in the frame. Using the covariant principle of general relativity, we can obtain equivalent nanostructures based on space-time transformations, such as the Lorentz transformation and conformal transformation. In this way, many covariant structures can be found that produce the same surface plasmon fields when excited by spin photons. A new kind of accelerating beam, the Rindler beam, is obtained based on the Rindler metric in gravity. Very large effective indices can be obtained in such systems based on geometric-phase gradient. This general covariant design method can be extended to many other optical media.

Short-time windowed covariance: A metric for identifying non-stationary, event-related covariant cortical sites

PubMed Central

Blakely, Timothy; Ojemann, Jeffrey G.; Rao, Rajesh P.N.

2014-01-01

Background Electrocorticography (ECoG) signals can provide high spatio-temporal resolution and high signal to noise ratio recordings of local neural activity from the surface of the brain. Previous studies have shown that broad-band, spatially focal, high-frequency increases in ECoG signals are highly correlated with movement and other cognitive tasks and can be volitionally modulated. However, significant additional information may be present in inter-electrode interactions, but adding additional higher order inter-electrode interactions can be impractical from a computational aspect, if not impossible. New method In this paper we present a new method of calculating high frequency interactions between electrodes called Short-Time Windowed Covariance (STWC) that builds on mathematical techniques currently used in neural signal analysis, along with an implementation that accelerates the algorithm by orders of magnitude by leveraging commodity, off-the-shelf graphics processing unit (GPU) hardware. Results Using the hardware-accelerated implementation of STWC, we identify many types of event-related inter-electrode interactions from human ECoG recordings on global and local scales that have not been identified by previous methods. Unique temporal patterns are observed for digit flexion in both low- (10 mm spacing) and high-resolution (3 mm spacing) electrode arrays. Comparison with existing methods Covariance is a commonly used metric for identifying correlated signals, but the standard covariance calculations do not allow for temporally varying covariance. In contrast STWC allows and identifies event-driven changes in covariance without identifying spurious noise correlations. Conclusions: STWC can be used to identify event-related neural interactions whose high computational load is well suited to GPU capabilities. PMID:24211499

Automated model selection in covariance estimation and spatial whitening of MEG and EEG signals.

PubMed

Engemann, Denis A; Gramfort, Alexandre

2015-03-01

Magnetoencephalography and electroencephalography (M/EEG) measure non-invasively the weak electromagnetic fields induced by post-synaptic neural currents. The estimation of the spatial covariance of the signals recorded on M/EEG sensors is a building block of modern data analysis pipelines. Such covariance estimates are used in brain-computer interfaces (BCI) systems, in nearly all source localization methods for spatial whitening as well as for data covariance estimation in beamformers. The rationale for such models is that the signals can be modeled by a zero mean Gaussian distribution. While maximizing the Gaussian likelihood seems natural, it leads to a covariance estimate known as empirical covariance (EC). It turns out that the EC is a poor estimate of the true covariance when the number of samples is small. To address this issue the estimation needs to be regularized. The most common approach downweights off-diagonal coefficients, while more advanced regularization methods are based on shrinkage techniques or generative models with low rank assumptions: probabilistic PCA (PPCA) and factor analysis (FA). Using cross-validation all of these models can be tuned and compared based on Gaussian likelihood computed on unseen data. We investigated these models on simulations, one electroencephalography (EEG) dataset as well as magnetoencephalography (MEG) datasets from the most common MEG systems. First, our results demonstrate that different models can be the best, depending on the number of samples, heterogeneity of sensor types and noise properties. Second, we show that the models tuned by cross-validation are superior to models with hand-selected regularization. Hence, we propose an automated solution to the often overlooked problem of covariance estimation of M/EEG signals. The relevance of the procedure is demonstrated here for spatial whitening and source localization of MEG signals. Copyright © 2015 Elsevier Inc. All rights reserved.

Covariance analyses of satellite-derived mesoscale wind fields

NASA Technical Reports Server (NTRS)

Maddox, R. A.; Vonder Haar, T. H.

1979-01-01

Statistical structure functions have been computed independently for nine satellite-derived mesoscale wind fields that were obtained on two different days. Small cumulus clouds were tracked at 5 min intervals, but since these clouds occurred primarily in the warm sectors of midlatitude cyclones the results cannot be considered representative of the circulations within cyclones in general. The field structure varied considerably with time and was especially affected if mesoscale features were observed. The wind fields on the 2 days studied were highly anisotropic with large gradients in structure occurring approximately normal to the mean flow. Structure function calculations for the combined set of satellite winds were used to estimate random error present in the fields. It is concluded for these data that the random error in vector winds derived from cumulus cloud tracking using high-frequency satellite data is less than 1.75 m/s. Spatial correlation functions were also computed for the nine data sets. Normalized correlation functions were considerably different for u and v components and decreased rapidly as data point separation increased for both components. The correlation functions for transverse and longitudinal components decreased less rapidly as data point separation increased.

Metabolic rate covaries with fitness and the pace of the life history in the field

PubMed Central

Pettersen, Amanda K.; White, Craig R.; Marshall, Dustin J.

2016-01-01

Metabolic rate reflects the ‘pace of life’ in every organism. Metabolic rate is related to an organism's capacity for essential maintenance, growth and reproduction—all of which interact to affect fitness. Although thousands of measurements of metabolic rate have been made, the microevolutionary forces that shape metabolic rate remain poorly resolved. The relationship between metabolic rate and components of fitness are often inconsistent, possibly because these fitness components incompletely map to actual fitness and often negatively covary with each other. Here we measure metabolic rate across ontogeny and monitor its effects on actual fitness (lifetime reproductive output) for a marine bryozoan in the field. We also measure key components of fitness throughout the entire life history including growth rate, longevity and age at the onset of reproduction. We found that correlational selection favours individuals with higher metabolic rates in one stage and lower metabolic rates in the other—individuals with similar metabolic rates in each developmental stage displayed the lowest fitness. Furthermore, individuals with the lowest metabolic rates lived for longer and reproduced more, but they also grew more slowly and took longer to reproduce initially. That metabolic rate is related to the pace of the life history in nature has long been suggested by macroevolutionary patterns but this study reveals the microevolutionary processes that probably generated these patterns. PMID:27226476

Students’ Covariational Reasoning in Solving Integrals’ Problems

NASA Astrophysics Data System (ADS)

Harini, N. V.; Fuad, Y.; Ekawati, R.

2018-01-01

Covariational reasoning plays an important role to indicate quantities vary in learning calculus. This study investigates students’ covariational reasoning during their studies concerning two covarying quantities in integral problem. Six undergraduate students were chosen to solve problems that involved interpreting and representing how quantities change in tandem. Interviews were conducted to reveal the students’ reasoning while solving covariational problems. The result emphasizes that undergraduate students were able to construct the relation of dependent variables that changes in tandem with the independent variable. However, students faced difficulty in forming images of continuously changing rates and could not accurately apply the concept of integrals. These findings suggest that learning calculus should be increased emphasis on coordinating images of two quantities changing in tandem about instantaneously rate of change and to promote conceptual knowledge in integral techniques.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1977-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1975-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Condition Number Regularized Covariance Estimation*

PubMed Central

Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala

2012-01-01

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the “large p small n” setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required. PMID:23730197

Background Error Covariance Estimation Using Information from a Single Model Trajectory with Application to Ocean Data Assimilation

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele; Kovach, Robin M.; Vernieres, Guillaume

2014-01-01

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory.SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Integrated approach to estimate the ocean's time variable dynamic topography including its covariance matrix

NASA Astrophysics Data System (ADS)

Müller, Silvia; Brockmann, Jan Martin; Schuh, Wolf-Dieter

2015-04-01

The ocean's dynamic topography as the difference between the sea surface and the geoid reflects many characteristics of the general ocean circulation. Consequently, it provides valuable information for evaluating or tuning ocean circulation models. The sea surface is directly observed by satellite radar altimetry while the geoid cannot be observed directly. The satellite-based gravity field determination requires different measurement principles (satellite-to-satellite tracking (e.g. GRACE), satellite-gravity-gradiometry (GOCE)). In addition, hydrographic measurements (salinity, temperature and pressure; near-surface velocities) provide information on the dynamic topography. The observation types have different representations and spatial as well as temporal resolutions. Therefore, the determination of the dynamic topography is not straightforward. Furthermore, the integration of the dynamic topography into ocean circulation models requires not only the dynamic topography itself but also its inverse covariance matrix on the ocean model grid. We developed a rigorous combination method in which the dynamic topography is parameterized in space as well as in time. The altimetric sea surface heights are expressed as a sum of geoid heights represented in terms of spherical harmonics and the dynamic topography parameterized by a finite element method which can be directly related to the particular ocean model grid. Besides the difficult task of combining altimetry data with a gravity field model, a major aspect is the consistent combination of satellite data and in-situ observations. The particular characteristics and the signal content of the different observations must be adequately considered requiring the introduction of auxiliary parameters. Within our model the individual observation groups are combined in terms of normal equations considering their full covariance information; i.e. a rigorous variance/covariance propagation from the original measurements to the

Earth Observation System Flight Dynamics System Covariance Realism

NASA Technical Reports Server (NTRS)

Zaidi, Waqar H.; Tracewell, David

2016-01-01

This presentation applies a covariance realism technique to the National Aeronautics and Space Administration (NASA) Earth Observation System (EOS) Aqua and Aura spacecraft based on inferential statistics. The technique consists of three parts: collection calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics.

Threshold regression to accommodate a censored covariate.

PubMed

Qian, Jing; Chiou, Sy Han; Maye, Jacqueline E; Atem, Folefac; Johnson, Keith A; Betensky, Rebecca A

2018-06-22

In several common study designs, regression modeling is complicated by the presence of censored covariates. Examples of such covariates include maternal age of onset of dementia that may be right censored in an Alzheimer's amyloid imaging study of healthy subjects, metabolite measurements that are subject to limit of detection censoring in a case-control study of cardiovascular disease, and progressive biomarkers whose baseline values are of interest, but are measured post-baseline in longitudinal neuropsychological studies of Alzheimer's disease. We propose threshold regression approaches for linear regression models with a covariate that is subject to random censoring. Threshold regression methods allow for immediate testing of the significance of the effect of a censored covariate. In addition, they provide for unbiased estimation of the regression coefficient of the censored covariate. We derive the asymptotic properties of the resulting estimators under mild regularity conditions. Simulations demonstrate that the proposed estimators have good finite-sample performance, and often offer improved efficiency over existing methods. We also derive a principled method for selection of the threshold. We illustrate the approach in application to an Alzheimer's disease study that investigated brain amyloid levels in older individuals, as measured through positron emission tomography scans, as a function of maternal age of dementia onset, with adjustment for other covariates. We have developed an R package, censCov, for implementation of our method, available at CRAN. © 2018, The International Biometric Society.

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

Covariance NMR Processing and Analysis for Protein Assignment.

PubMed

Harden, Bradley J; Frueh, Dominique P

2018-01-01

During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.

Modeling uncertainty of evapotranspiration measurements from multiple eddy covariance towers over a crop canopy

USDA-ARS?s Scientific Manuscript database

All measurements have random error associated with them. With fluxes in an eddy covariance system, measurement error can been modelled in several ways, often involving a statistical description of turbulence at its core. Using a field experiment with four towers, we generated four replicates of meas...

Covariant kaon dynamics and kaon flow in heavy ion collisions

NASA Astrophysics Data System (ADS)

Zheng, Yu-Ming; Fuchs, C.; Faessler, Amand; Shekhter, K.; Yan, Yu-Peng; Kobdaj, Chinorat

2004-03-01

The influence of the chiral mean field on the K+ transverse flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasiparticle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the in-medium kaon dynamics and strongly counterbalances the influence of the vector potential on the K+ in-plane flow. The FOPI data can be reasonably described using in-medium kaon potentials based on effective chiral models. The information on the in-medium K+ potential extracted from kaon flow is consistent with the knowledge from other sources.

Covariance Matrix Estimation for Massive MIMO

NASA Astrophysics Data System (ADS)

Upadhya, Karthik; Vorobyov, Sergiy A.

2018-04-01

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

Empirical Likelihood in Nonignorable Covariate-Missing Data Problems.

PubMed

Xie, Yanmei; Zhang, Biao

2017-04-20

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719-30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and

AFCI-2.0 Library of Neutron Cross Section Covariances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herman, M.; Herman,M.; Oblozinsky,P.

2011-06-26

Neutron cross section covariance library has been under development by BNL-LANL collaborative effort over the last three years. The primary purpose of the library is to provide covariances for the Advanced Fuel Cycle Initiative (AFCI) data adjustment project, which is focusing on the needs of fast advanced burner reactors. The covariances refer to central values given in the 2006 release of the U.S. neutron evaluated library ENDF/B-VII. The preliminary version (AFCI-2.0beta) has been completed in October 2010 and made available to the users for comments. In the final 2.0 release, covariances for a few materials were updated, in particular newmore » LANL evaluations for {sup 238,240}Pu and {sup 241}Am were adopted. BNL was responsible for covariances for structural materials and fission products, management of the library and coordination of the work, while LANL was in charge of covariances for light nuclei and for actinides.« less

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Alterations in Anatomical Covariance in the Prematurely Born

PubMed Central

Scheinost, Dustin; Kwon, Soo Hyun; Lacadie, Cheryl; Vohr, Betty R.; Schneider, Karen C.; Papademetris, Xenophon; Constable, R. Todd; Ment, Laura R.

2017-01-01

Abstract Preterm (PT) birth results in long-term alterations in functional and structural connectivity, but the related changes in anatomical covariance are just beginning to be explored. To test the hypothesis that PT birth alters patterns of anatomical covariance, we investigated brain volumes of 25 PTs and 22 terms at young adulthood using magnetic resonance imaging. Using regional volumetrics, seed-based analyses, and whole brain graphs, we show that PT birth is associated with reduced volume in bilateral temporal and inferior frontal lobes, left caudate, left fusiform, and posterior cingulate for prematurely born subjects at young adulthood. Seed-based analyses demonstrate altered patterns of anatomical covariance for PTs compared with terms. PTs exhibit reduced covariance with R Brodmann area (BA) 47, Broca's area, and L BA 21, Wernicke's area, and white matter volume in the left prefrontal lobe, but increased covariance with R BA 47 and left cerebellum. Graph theory analyses demonstrate that measures of network complexity are significantly less robust in PTs compared with term controls. Volumes in regions showing group differences are significantly correlated with phonological awareness, the fundamental basis for reading acquisition, for the PTs. These data suggest both long-lasting and clinically significant alterations in the covariance in the PTs at young adulthood. PMID:26494796

Measuring continuous baseline covariate imbalances in clinical trial data

PubMed Central

Ciolino, Jody D.; Martin, Renee’ H.; Zhao, Wenle; Hill, Michael D.; Jauch, Edward C.; Palesch, Yuko Y.

2014-01-01

This paper presents and compares several methods of measuring continuous baseline covariate imbalance in clinical trial data. Simulations illustrate that though the t-test is an inappropriate method of assessing continuous baseline covariate imbalance, the test statistic itself is a robust measure in capturing imbalance in continuous covariate distributions. Guidelines to assess effects of imbalance on bias, type I error rate, and power for hypothesis test for treatment effect on continuous outcomes are presented, and the benefit of covariate-adjusted analysis (ANCOVA) is also illustrated. PMID:21865270

Field intercomparison of four methane gas analyzers suitable for eddy covariance flux measurements

NASA Astrophysics Data System (ADS)

Peltola, O.; Mammarella, I.; Haapanala, S.; Burba, G.; Vesala, T.

2013-06-01

Performances of four methane gas analyzers suitable for eddy covariance measurements are assessed. The assessment and comparison was performed by analyzing eddy covariance data obtained during summer 2010 (1 April to 26 October) at a pristine fen, Siikaneva, Southern Finland. High methane fluxes with pronounced seasonality have been measured at this fen. The four participating methane gas analyzers are commercially available closed-path units TGA-100A (Campbell Scientific Inc., USA), RMT-200 (Los Gatos Research, USA), G1301-f (Picarro Inc., USA) and an early prototype open-path unit Prototype-7700 (LI-COR Biosciences, USA). The RMT-200 functioned most reliably throughout the measurement campaign, during low and high flux periods. Methane fluxes from RMT-200 and G1301-f had the smallest random errors and the fluxes agree remarkably well throughout the measurement campaign. Cospectra and power spectra calculated from RMT-200 and G1301-f data agree well with corresponding temperature spectra during a high flux period. None of the gas analyzers showed statistically significant diurnal variation for methane flux. Prototype-7700 functioned only for a short period of time, over one month, in the beginning of the measurement campaign during low flux period, and thus, its overall accuracy and season-long performance were not assessed. The open-path gas analyzer is a practical choice for measurement sites in remote locations due to its low power demand, whereas for G1301-f methane measurements interference from water vapor is straightforward to correct since the instrument measures both gases simultaneously. In any case, if only the performance in this intercomparison is considered, RMT-200 performed the best and is the recommended choice if a new fast response methane gas analyzer is needed.

First integrals of motion in a gauge covariant framework, Killing-Maxwell system and quantum anomalies

NASA Astrophysics Data System (ADS)

Visinescu, M.

2012-10-01

Hidden symmetries in a covariant Hamiltonian framework are investigated. The special role of the Stackel-Killing and Killing-Yano tensors is pointed out. The covariant phase-space is extended to include external gauge fields and scalar potentials. We investigate the possibility for a higher-order symmetry to survive when the electromagnetic interactions are taken into account. Aconcrete realization of this possibility is given by the Killing-Maxwell system. The classical conserved quantities do not generally transfer to the quantized systems producing quantum gravitational anomalies. As a rule the conformal extension of the Killing vectors and tensors does not produce symmetry operators for the Klein-Gordon operator.

Empirical State Error Covariance Matrix for Batch Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joe

2015-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. This empirical error covariance matrix may be calculated as a side computation for each unique batch solution. Results based on the proposed technique will be presented for a simple, two observer and measurement error only problem.

Hidden Covariation Detection Produces Faster, Not Slower, Social Judgments

ERIC Educational Resources Information Center

Barker, Lynne A.; Andrade, Jackie

2006-01-01

In P. Lewicki's (1986b) demonstration of hidden covariation detection (HCD), responses of participants were slower to faces that corresponded with a covariation encountered previously than to faces with novel covariations. This slowing contrasts with the typical finding that priming leads to faster responding and suggests that HCD is a unique type…

Double field theory at order α'

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Zwiebach, Barton

2014-11-01

We investigate α' corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled α'-geometry" gives α'-deformed gauge transformations arising in the Green-Schwarz anomaly cancellation mechanism but does not apply to bosonic strings. These require a different deformation of the duality-covariantized Courant bracket which governs the gauge structure. This is revealed by examining the α' corrections in the gauge algebra of closed string field theory. We construct a four-derivative cubic double field theory action invariant under the deformed gauge transformations, giving a first glimpse of the gauge principle underlying bosonic string α' corrections. The usual metric and b-field are related to the duality covariant fields by non-covariant field redefinitions.

Bayes Factor Covariance Testing in Item Response Models.

PubMed

Fox, Jean-Paul; Mulder, Joris; Sinharay, Sandip

2017-12-01

Two marginal one-parameter item response theory models are introduced, by integrating out the latent variable or random item parameter. It is shown that both marginal response models are multivariate (probit) models with a compound symmetry covariance structure. Several common hypotheses concerning the underlying covariance structure are evaluated using (fractional) Bayes factor tests. The support for a unidimensional factor (i.e., assumption of local independence) and differential item functioning are evaluated by testing the covariance components. The posterior distribution of common covariance components is obtained in closed form by transforming latent responses with an orthogonal (Helmert) matrix. This posterior distribution is defined as a shifted-inverse-gamma, thereby introducing a default prior and a balanced prior distribution. Based on that, an MCMC algorithm is described to estimate all model parameters and to compute (fractional) Bayes factor tests. Simulation studies are used to show that the (fractional) Bayes factor tests have good properties for testing the underlying covariance structure of binary response data. The method is illustrated with two real data studies.

Alterations in Anatomical Covariance in the Prematurely Born.

PubMed

Scheinost, Dustin; Kwon, Soo Hyun; Lacadie, Cheryl; Vohr, Betty R; Schneider, Karen C; Papademetris, Xenophon; Constable, R Todd; Ment, Laura R

2017-01-01

Preterm (PT) birth results in long-term alterations in functional and structural connectivity, but the related changes in anatomical covariance are just beginning to be explored. To test the hypothesis that PT birth alters patterns of anatomical covariance, we investigated brain volumes of 25 PTs and 22 terms at young adulthood using magnetic resonance imaging. Using regional volumetrics, seed-based analyses, and whole brain graphs, we show that PT birth is associated with reduced volume in bilateral temporal and inferior frontal lobes, left caudate, left fusiform, and posterior cingulate for prematurely born subjects at young adulthood. Seed-based analyses demonstrate altered patterns of anatomical covariance for PTs compared with terms. PTs exhibit reduced covariance with R Brodmann area (BA) 47, Broca's area, and L BA 21, Wernicke's area, and white matter volume in the left prefrontal lobe, but increased covariance with R BA 47 and left cerebellum. Graph theory analyses demonstrate that measures of network complexity are significantly less robust in PTs compared with term controls. Volumes in regions showing group differences are significantly correlated with phonological awareness, the fundamental basis for reading acquisition, for the PTs. These data suggest both long-lasting and clinically significant alterations in the covariance in the PTs at young adulthood. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Massive data compression for parameter-dependent covariance matrices

NASA Astrophysics Data System (ADS)

Heavens, Alan F.; Sellentin, Elena; de Mijolla, Damien; Vianello, Alvise

2017-12-01

We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated data sets which are required to estimate the covariance matrix required for the analysis of Gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next generation of weak lensing surveys, such as proposed for Euclid and Large Synoptic Survey Telescope, for which the number of summary data (such as band power or shear correlation estimates) is very large, ∼104, due to the large number of tomographic redshift bins which the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an Monte Carlo Markov Chain analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ∼106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible.

Hawking radiation, covariant boundary conditions, and vacuum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Rabin; Kulkarni, Shailesh

2009-04-15

The basic characteristics of the covariant chiral current and the covariant chiral energy-momentum tensor are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Non-perturbative background field calculations

NASA Astrophysics Data System (ADS)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Modeling spatiotemporal covariance for magnetoencephalography or electroencephalography source analysis.

PubMed

Plis, Sergey M; George, J S; Jun, S C; Paré-Blagoev, J; Ranken, D M; Wood, C C; Schmidt, D M

2007-01-01

We propose a new model to approximate spatiotemporal noise covariance for use in neural electromagnetic source analysis, which better captures temporal variability in background activity. As with other existing formalisms, our model employs a Kronecker product of matrices representing temporal and spatial covariance. In our model, spatial components are allowed to have differing temporal covariances. Variability is represented as a series of Kronecker products of spatial component covariances and corresponding temporal covariances. Unlike previous attempts to model covariance through a sum of Kronecker products, our model is designed to have a computationally manageable inverse. Despite increased descriptive power, inversion of the model is fast, making it useful in source analysis. We have explored two versions of the model. One is estimated based on the assumption that spatial components of background noise have uncorrelated time courses. Another version, which gives closer approximation, is based on the assumption that time courses are statistically independent. The accuracy of the structural approximation is compared to an existing model, based on a single Kronecker product, using both Frobenius norm of the difference between spatiotemporal sample covariance and a model, and scatter plots. Performance of ours and previous models is compared in source analysis of a large number of single dipole problems with simulated time courses and with background from authentic magnetoencephalography data.

IIB supergravity and the E 6(6) covariant vector-tensor hierarchy

DOE PAGES

Ciceri, Franz; de Wit, Bernard; Varela, Oscar

2015-04-20

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional ‘dual graviton’. The invariant E 6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions formore » the USp(8) covariant fermion fields. Implications are further discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.« less

Space-Time Modelling of Groundwater Level Using Spartan Covariance Function

NASA Astrophysics Data System (ADS)

Varouchakis, Emmanouil; Hristopulos, Dionissios

2014-05-01

Geostatistical models often need to handle variables that change in space and in time, such as the groundwater level of aquifers. A major advantage of space-time observations is that a higher number of data supports parameter estimation and prediction. In a statistical context, space-time data can be considered as realizations of random fields that are spatially extended and evolve in time. The combination of spatial and temporal measurements in sparsely monitored watersheds can provide very useful information by incorporating spatiotemporal correlations. Spatiotemporal interpolation is usually performed by applying the standard Kriging algorithms extended in a space-time framework. Spatiotemoral covariance functions for groundwater level modelling, however, have not been widely developed. We present a new non-separable theoretical spatiotemporal variogram function which is based on the Spartan covariance family and evaluate its performance in spatiotemporal Kriging (STRK) interpolation. The original spatial expression (Hristopulos and Elogne 2007) that has been successfully used for the spatial interpolation of groundwater level (Varouchakis and Hristopulos 2013) is modified by defining the following space-time normalized distance h = °h2r-+-α h2τ, hr=r- ξr, hτ=τ- ξτ; where r is the spatial lag vector, τ the temporal lag vector, ξr is the correlation length in position space (r) and ξτ in time (τ), h the normalized space-time lag vector, h = |h| is its Euclidean norm of the normalized space-time lag and α the coefficient that determines the relative weight of the time lag. The space-time experimental semivariogram is determined from the biannual (wet and dry period) time series of groundwater level residuals (obtained from the original series after trend removal) between the years 1981 and 2003 at ten sampling stations located in the Mires hydrological basin in the island of Crete (Greece). After the hydrological year 2002-2003 there is a significant

Continuous Covariate Imbalance and Conditional Power for Clinical Trial Interim Analyses

PubMed Central

Ciolino, Jody D.; Martin, Renee' H.; Zhao, Wenle; Jauch, Edward C.; Hill, Michael D.; Palesch, Yuko Y.

2014-01-01

Oftentimes valid statistical analyses for clinical trials involve adjustment for known influential covariates, regardless of imbalance observed in these covariates at baseline across treatment groups. Thus, it must be the case that valid interim analyses also properly adjust for these covariates. There are situations, however, in which covariate adjustment is not possible, not planned, or simply carries less merit as it makes inferences less generalizable and less intuitive. In this case, covariate imbalance between treatment groups can have a substantial effect on both interim and final primary outcome analyses. This paper illustrates the effect of influential continuous baseline covariate imbalance on unadjusted conditional power (CP), and thus, on trial decisions based on futility stopping bounds. The robustness of the relationship is illustrated for normal, skewed, and bimodal continuous baseline covariates that are related to a normally distributed primary outcome. Results suggest that unadjusted CP calculations in the presence of influential covariate imbalance require careful interpretation and evaluation. PMID:24607294

Remediating Non-Positive Definite State Covariances for Collision Probability Estimation

NASA Technical Reports Server (NTRS)

Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.

2017-01-01

The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.

COUSCOus: improved protein contact prediction using an empirical Bayes covariance estimator.

PubMed

Rawi, Reda; Mall, Raghvendra; Kunji, Khalid; El Anbari, Mohammed; Aupetit, Michael; Ullah, Ehsan; Bensmail, Halima

2016-12-15

The post-genomic era with its wealth of sequences gave rise to a broad range of protein residue-residue contact detecting methods. Although various coevolution methods such as PSICOV, DCA and plmDCA provide correct contact predictions, they do not completely overlap. Hence, new approaches and improvements of existing methods are needed to motivate further development and progress in the field. We present a new contact detecting method, COUSCOus, by combining the best shrinkage approach, the empirical Bayes covariance estimator and GLasso. Using the original PSICOV benchmark dataset, COUSCOus achieves mean accuracies of 0.74, 0.62 and 0.55 for the top L/10 predicted long, medium and short range contacts, respectively. In addition, COUSCOus attains mean areas under the precision-recall curves of 0.25, 0.29 and 0.30 for long, medium and short contacts and outperforms PSICOV. We also observed that COUSCOus outperforms PSICOV w.r.t. Matthew's correlation coefficient criterion on full list of residue contacts. Furthermore, COUSCOus achieves on average 10% more gain in prediction accuracy compared to PSICOV on an independent test set composed of CASP11 protein targets. Finally, we showed that when using a simple random forest meta-classifier, by combining contact detecting techniques and sequence derived features, PSICOV predictions should be replaced by the more accurate COUSCOus predictions. We conclude that the consideration of superior covariance shrinkage approaches will boost several research fields that apply the GLasso procedure, amongst the presented one of residue-residue contact prediction as well as fields such as gene network reconstruction.

Eddy covariance measurements of carbon dioxide and water fluxes in Mid-South US cotton

USDA-ARS?s Scientific Manuscript database

An eddy covariance (EC) system was used to quantify carbon dioxide (CO2) and water (H2O) fluxes as net ecosystem exchange (NEE) and crop evapotranspiration (ET), respectively, in a production-sized cotton field in Northeastern Arkansas in 2016 and 2017 growing seasons. Average ET was 0.13±0.01 in d-...

Data Sharing and Scientific Impact in Eddy Covariance Research

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bond-Lamberty, B.

Do the benefits of data sharing outweigh its perceived costs? This is a critical question, and one with the potential to change culture and behavior. Dai et al. (2018) examine how data sharing is related to scientific impact in the field of eddy covariance (EC), and find that data sharers are disproportionately high-impact researchers, and vice versa; they also note strong regional differences in EC data sharing norms. The current policies and restrictions of EC journals and repositories are highly uneven. Incentivizing data sharing and enhancing computational reproducibility are critical next steps for EC, ecology, and science more broadly.

DISSCO: direct imputation of summary statistics allowing covariates

PubMed Central

Xu, Zheng; Duan, Qing; Yan, Song; Chen, Wei; Li, Mingyao; Lange, Ethan; Li, Yun

2015-01-01

Background: Imputation of individual level genotypes at untyped markers using an external reference panel of genotyped or sequenced individuals has become standard practice in genetic association studies. Direct imputation of summary statistics can also be valuable, for example in meta-analyses where individual level genotype data are not available. Two methods (DIST and ImpG-Summary/LD), that assume a multivariate Gaussian distribution for the association summary statistics, have been proposed for imputing association summary statistics. However, both methods assume that the correlations between association summary statistics are the same as the correlations between the corresponding genotypes. This assumption can be violated in the presence of confounding covariates. Methods: We analytically show that in the absence of covariates, correlation among association summary statistics is indeed the same as that among the corresponding genotypes, thus serving as a theoretical justification for the recently proposed methods. We continue to prove that in the presence of covariates, correlation among association summary statistics becomes the partial correlation of the corresponding genotypes controlling for covariates. We therefore develop direct imputation of summary statistics allowing covariates (DISSCO). Results: We consider two real-life scenarios where the correlation and partial correlation likely make practical difference: (i) association studies in admixed populations; (ii) association studies in presence of other confounding covariate(s). Application of DISSCO to real datasets under both scenarios shows at least comparable, if not better, performance compared with existing correlation-based methods, particularly for lower frequency variants. For example, DISSCO can reduce the absolute deviation from the truth by 3.9–15.2% for variants with minor allele frequency <5%. Availability and implementation: http://www.unc.edu/∼yunmli/DISSCO. Contact: yunli

DISSCO: direct imputation of summary statistics allowing covariates.

PubMed

Xu, Zheng; Duan, Qing; Yan, Song; Chen, Wei; Li, Mingyao; Lange, Ethan; Li, Yun

2015-08-01

Imputation of individual level genotypes at untyped markers using an external reference panel of genotyped or sequenced individuals has become standard practice in genetic association studies. Direct imputation of summary statistics can also be valuable, for example in meta-analyses where individual level genotype data are not available. Two methods (DIST and ImpG-Summary/LD), that assume a multivariate Gaussian distribution for the association summary statistics, have been proposed for imputing association summary statistics. However, both methods assume that the correlations between association summary statistics are the same as the correlations between the corresponding genotypes. This assumption can be violated in the presence of confounding covariates. We analytically show that in the absence of covariates, correlation among association summary statistics is indeed the same as that among the corresponding genotypes, thus serving as a theoretical justification for the recently proposed methods. We continue to prove that in the presence of covariates, correlation among association summary statistics becomes the partial correlation of the corresponding genotypes controlling for covariates. We therefore develop direct imputation of summary statistics allowing covariates (DISSCO). We consider two real-life scenarios where the correlation and partial correlation likely make practical difference: (i) association studies in admixed populations; (ii) association studies in presence of other confounding covariate(s). Application of DISSCO to real datasets under both scenarios shows at least comparable, if not better, performance compared with existing correlation-based methods, particularly for lower frequency variants. For example, DISSCO can reduce the absolute deviation from the truth by 3.9-15.2% for variants with minor allele frequency <5%. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Real-time probabilistic covariance tracking with efficient model update.

PubMed

Wu, Yi; Cheng, Jian; Wang, Jinqiao; Lu, Hanqing; Wang, Jun; Ling, Haibin; Blasch, Erik; Bai, Li

2012-05-01

The recently proposed covariance region descriptor has been proven robust and versatile for a modest computational cost. The covariance matrix enables efficient fusion of different types of features, where the spatial and statistical properties, as well as their correlation, are characterized. The similarity between two covariance descriptors is measured on Riemannian manifolds. Based on the same metric but with a probabilistic framework, we propose a novel tracking approach on Riemannian manifolds with a novel incremental covariance tensor learning (ICTL). To address the appearance variations, ICTL incrementally learns a low-dimensional covariance tensor representation and efficiently adapts online to appearance changes of the target with only O(1) computational complexity, resulting in a real-time performance. The covariance-based representation and the ICTL are then combined with the particle filter framework to allow better handling of background clutter, as well as the temporary occlusions. We test the proposed probabilistic ICTL tracker on numerous benchmark sequences involving different types of challenges including occlusions and variations in illumination, scale, and pose. The proposed approach demonstrates excellent real-time performance, both qualitatively and quantitatively, in comparison with several previously proposed trackers.

A three domain covariance framework for EEG/MEG data.

PubMed

Roś, Beata P; Bijma, Fetsje; de Gunst, Mathisca C M; de Munck, Jan C

2015-10-01

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG-fMRI experiments in which the correlation between EEG and fMRI signals is investigated. We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets. Copyright © 2015 Elsevier Inc. All rights reserved.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

Multiple feature fusion via covariance matrix for visual tracking

NASA Astrophysics Data System (ADS)

Jin, Zefenfen; Hou, Zhiqiang; Yu, Wangsheng; Wang, Xin; Sun, Hui

2018-04-01

Aiming at the problem of complicated dynamic scenes in visual target tracking, a multi-feature fusion tracking algorithm based on covariance matrix is proposed to improve the robustness of the tracking algorithm. In the frame-work of quantum genetic algorithm, this paper uses the region covariance descriptor to fuse the color, edge and texture features. It also uses a fast covariance intersection algorithm to update the model. The low dimension of region covariance descriptor, the fast convergence speed and strong global optimization ability of quantum genetic algorithm, and the fast computation of fast covariance intersection algorithm are used to improve the computational efficiency of fusion, matching, and updating process, so that the algorithm achieves a fast and effective multi-feature fusion tracking. The experiments prove that the proposed algorithm can not only achieve fast and robust tracking but also effectively handle interference of occlusion, rotation, deformation, motion blur and so on.

Covariance Matrix Evaluations for Independent Mass Fission Yields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terranova, N., E-mail: nicholas.terranova@unibo.it; Serot, O.; Archier, P.

2015-01-15

Recent needs for more accurate fission product yields include covariance information to allow improved uncertainty estimations of the parameters used by design codes. The aim of this work is to investigate the possibility to generate more reliable and complete uncertainty information on independent mass fission yields. Mass yields covariances are estimated through a convolution between the multi-Gaussian empirical model based on Brosa's fission modes, which describe the pre-neutron mass yields, and the average prompt neutron multiplicity curve. The covariance generation task has been approached using the Bayesian generalized least squared method through the CONRAD code. Preliminary results on mass yieldsmore » variance-covariance matrix will be presented and discussed from physical grounds in the case of {sup 235}U(n{sub th}, f) and {sup 239}Pu(n{sub th}, f) reactions.« less

True covariance simulation of the EUVE update filter

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Harman, R. R.

1989-01-01

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Chamber and eddy covariance comparisons of alternate wetting and drying and continuous flood irrigation in mid-South rice

NASA Astrophysics Data System (ADS)

Reba, M. L.; Fong, B.; Adviento-Borbe, A.; Runkle, B.

2016-12-01

The subtropical humid mid-south region produces nearly 75% of US rice. Rice cultivation contributes higher amounts of GHG emissions (CO2, CH4, and N2O) due to flooded field conditions. Accurate measurements of gas fluxes are important to regional and global climate models. A comparison between eddy covariance and static vented flux chamber measurement techniques is presented. These measurements were collected in two NE Arkansas commercial rice fields in 2015 and 2016 production seasons under two irrigation treatments: Alternate Wetting and Drying (AWD) and continuous flood (CF) irrigation. AWD can reduce GHG emissions and water use compared to CF by introducing aerobic conditions that reduce methanogen activity and drained conditions decrease water loss due to seepage or evapotranspiration. N2O was measured only with vented chambers, while CO2 and CH4 were measured with both techniques. In the vented flux chamber technique, headspace gas sampling occurred at least once a week every 20 minutes for one hour of chamber closure. Gas Chromatograph equipped with ECD and FID were used to analyze gas concentrations. Eddy covariance used high frequency measurements wind and concentration measurements to determine fluxes. Chamber measurements were found to be more sensitive during seedling and early vegetative growth while eddy covariance was more sensitive after canopy closure during mid-vegetative to reproductive growth. Unlike eddy covariance which measured net CO2 exchange, flux chamber method measured only CO2 ecosystem respiration because flux measurements occurred using an opaque chamber material.

Structure and covariance of cloud and rain water in marine stratocumulus

NASA Astrophysics Data System (ADS)

Witte, Mikael; Morrison, Hugh; Gettelman, Andrew

2017-04-01

Many state of the art cloud microphysics parameterizations in large-scale models use assumed probability density functions (pdfs) to represent subgrid scale variability of relevant resolved scale variables such as vertical velocity and cloud liquid water content (LWC). Integration over the assumed pdfs of small scale variability results in physically consistent prediction of nonlinear microphysical process rates and obviates the need to apply arbitrary tuning parameters to the calculated rates. In such parameterizations, the covariance of cloud and rain LWC is an important quantity for parameterizing the accretion process by which rain drops grow via collection of cloud droplets. This covariance has been diagnosed by other workers from a variety of observational and model datasets (Boutle et al., 2013; Larson and Griffin, 2013; Lebsock et al., 2013), but there is poor agreement in findings across the studies. Two key assumptions that may explain some of the discrepancies among past studies are 1) LWC (both cloud and rain) distributions are statistically stationary and 2) spatial structure may be neglected. Given the highly intermittent nature of precipitation and the fact that cloud LWC has been found to be poorly represented by stationary pdfs (e.g. Marshak et al., 1997), neither of the aforementioned assumptions are valid. Therefore covariance must be evaluated as a function of spatial scale without the assumption of stationary statistics (i.e. variability cannot be expressed as a fractional standard deviation, which necessitates well-defined first and second moments of the LWC distribution). The present study presents multifractal analyses of both rain and cloud LWC using aircraft data from the VOCALS-REx field campaign to illustrate the importance of spatial structure in microphysical parameterizations and extends the results of Boutle et al. (2013) to provide a parameterization of rain-cloud water covariance as a function of spatial scale without the

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Perturbative approach to covariance matrix of the matter power spectrum

NASA Astrophysics Data System (ADS)

Mohammed, Irshad; Seljak, Uroš; Vlah, Zvonimir

2017-04-01

We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (supersample variance) and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10 per cent level up to k ˜ 1 h Mpc-1. We show that all the connected components are dominated by the large-scale modes (k < 0.1 h Mpc-1), regardless of the value of the wave vectors k, k΄ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher k, it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.

Cox model with interval-censored covariate in cohort studies.

PubMed

Ahn, Soohyun; Lim, Johan; Paik, Myunghee Cho; Sacco, Ralph L; Elkind, Mitchell S

2018-05-18

In cohort studies the outcome is often time to a particular event, and subjects are followed at regular intervals. Periodic visits may also monitor a secondary irreversible event influencing the event of primary interest, and a significant proportion of subjects develop the secondary event over the period of follow-up. The status of the secondary event serves as a time-varying covariate, but is recorded only at the times of the scheduled visits, generating incomplete time-varying covariates. While information on a typical time-varying covariate is missing for entire follow-up period except the visiting times, the status of the secondary event are unavailable only between visits where the status has changed, thus interval-censored. One may view interval-censored covariate of the secondary event status as missing time-varying covariates, yet missingness is partial since partial information is provided throughout the follow-up period. Current practice of using the latest observed status produces biased estimators, and the existing missing covariate techniques cannot accommodate the special feature of missingness due to interval censoring. To handle interval-censored covariates in the Cox proportional hazards model, we propose an available-data estimator, a doubly robust-type estimator as well as the maximum likelihood estimator via EM algorithm and present their asymptotic properties. We also present practical approaches that are valid. We demonstrate the proposed methods using our motivating example from the Northern Manhattan Study. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Large-Scale Covariability Between Aerosol and Precipitation Over the 7-SEAS Region: Observations and Simulations

NASA Technical Reports Server (NTRS)

Huang, Jingfeng; Hsu, N. Christina; Tsay, Si-Chee; Zhang, Chidong; Jeong, Myeong Jae; Gautam, Ritesh; Bettenhausen, Corey; Sayer, Andrew M.; Hansell, Richard A.; Liu, Xiaohong;

Interspecific analysis of covariance structure in the masticatory apparatus of galagos.

PubMed

Vinyard, Christopher J

2007-01-01

The primate masticatory apparatus (MA) is a functionally integrated set of features, each of which performs important functions in biting, ingestive, and chewing behaviors. A comparison of morphological covariance structure among species for these MA features will help us to further understand the evolutionary history of this region. In this exploratory analysis, the covariance structure of the MA is compared across seven galago species to investigate 1) whether there are differences in covariance structure in this region, and 2) if so, how has this covariation changed with respect to size, MA form, diet, and/or phylogeny? Ten measurements of the MA functionally related to bite force production and load resistance were obtained from 218 adults of seven galago species. Correlation matrices were generated for these 10 dimensions and compared among species via matrix correlations and Mantel tests. Subsequently, pairwise covariance disparity in the MA was estimated as a measure of difference in covariance structure between species. Covariance disparity estimates were correlated with pairwise distances related to differences in body size, MA size and shape, genetic distance (based on cytochrome-b sequences) and percentage of dietary foods to determine whether one or more of these factors is linked to differences in covariance structure. Galagos differ in MA covariance structure. Body size appears to be a major factor correlated with differences in covariance structure among galagos. The largest galago species, Otolemur crassicaudatus, exhibits large differences in body mass and covariance structure relative to other galagos, and thus plays a primary role in creating this association. MA size and shape do not correlate with covariance structure when body mass is held constant. Diet also shows no association. Genetic distance is significantly negatively correlated with covariance disparity when body mass is held constant, but this correlation appears to be a function of

Position Error Covariance Matrix Validation and Correction

NASA Technical Reports Server (NTRS)

Frisbee, Joe, Jr.

2016-01-01

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona

NASA Technical Reports Server (NTRS)

Titov, V. S.

2007-01-01

The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coordinates. At least two overlapping regular systems of coordinates for each of the boundaries are necessary in this case to avoid spherical-pole-like singularities in the coordinates of the footpoints. This implies that the basic characteristic of magnetic connectivity-the squashing degree or factor Q of elemental flux tubes, according to Titov and coworkers-must be rewritten in covariant form. Such a covariant expression of Q is derived in this work. The derived expression is very flexible and highly efficient for describing the global magnetic connectivity in the solar corona. In addition, a general expression for a new characteristic Q1, which defines a squashing of the flux tubes in the directions perpendicular to the field lines, is determined. This new quantity makes it possible to filter out the quasi-separatrix layers whose large values of Q are caused by a projection effect at the field lines nearly touching the photosphere. Thus, the value Q1 provides a much more precise description of the volumetric properties of the magnetic field structure. The difference between Q and Q1 is illustrated by comparing their distributions for two configurations, one of which is the Titov-Demoulin model of a twisted magnetic field.

Tonic and phasic co-variation of peripheral arousal indices in infants

PubMed Central

Wass, S.V.; de Barbaro, K.; Clackson, K.

2015-01-01

Tonic and phasic differences in peripheral autonomic nervous system (ANS) indicators strongly predict differences in attention and emotion regulation in developmental populations. However, virtually all previous research has been based on individual ANS measures, which poses a variety of conceptual and methodlogical challenges to comparing results across studies. Here we recorded heart rate, electrodermal activity (EDA), pupil size, head movement velocity and peripheral accelerometry concurrently while a cohort of 37 typical 12-month-old infants completed a mixed assessment battery lasting approximately 20 min per participant. We analysed covariation of these autonomic indices in three ways: first, tonic (baseline) arousal; second, co-variation in spontaneous (phasic) changes during testing; third, phasic co-variation relative to an external stimulus event. We found that heart rate, head velocity and peripheral accelerometry showed strong positive co-variation across all three analyses. EDA showed no co-variation in tonic activity levels but did show phasic positive co-variation with other measures, that appeared limited to sections of high but not low general arousal. Tonic pupil size showed significant positive covariation, but phasic pupil changes were inconsistent. We conclude that: (i) there is high covariation between autonomic indices in infants, but that EDA may only be sensitive at extreme arousal levels, (ii) that tonic pupil size covaries with other indices, but does not show predicted patterns of phasic change and (iii) that motor activity appears to be a good proxy measure of ANS activity. The strongest patterns of covariation were observed using epoch durations of 40 s per epoch, although significant covariation between indices was also observed using shorter epochs (1 and 5 s). PMID:26316360

The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure.

PubMed

Davies, Christopher E; Glonek, Gary Fv; Giles, Lynne C

2017-08-01

One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost.

Perturbative approach to covariance matrix of the matter power spectrum

DOE PAGES

Mohammed, Irshad; Seljak, Uros; Vlah, Zvonimir

2016-12-14

Here, we evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (beat coupling or super-sample variance), and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10\\% level up tomore » $$k \\sim 1 h {\\rm Mpc^{-1}}$$. We also show that all the connected components are dominated by the large-scale modes ($$k<0.1 h {\\rm Mpc^{-1}}$$), regardless of the value of the wavevectors $$k,\\, k'$$ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher $k$ it is dominated by a single eigenmode. Furthermore, the full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.« less

Covariant Derivatives and the Renormalization Group Equation

NASA Astrophysics Data System (ADS)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Covariance Function for Nearshore Wave Assimilation Systems

DTIC Science & Technology

2018-01-30

covariance can be modeled by a parameterized Gaussian function, for nearshore wave assimilation applications, the covariance function depends primarily on...case of missing values at the compiled time series, the gaps were filled by weighted interpolation. The weights depend on the number of the...averaging, in order to create the continuous time series, filters out the dependency on the instantaneous meteorological and oceanographic conditions

Pu239 Cross-Section Variations Based on Experimental Uncertainties and Covariances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sigeti, David Edward; Williams, Brian J.; Parsons, D. Kent

2016-10-18

Algorithms and software have been developed for producing variations in plutonium-239 neutron cross sections based on experimental uncertainties and covariances. The varied cross-section sets may be produced as random samples from the multi-variate normal distribution defined by an experimental mean vector and covariance matrix, or they may be produced as Latin-Hypercube/Orthogonal-Array samples (based on the same means and covariances) for use in parametrized studies. The variations obey two classes of constraints that are obligatory for cross-section sets and which put related constraints on the mean vector and covariance matrix that detemine the sampling. Because the experimental means and covariances domore » not obey some of these constraints to sufficient precision, imposing the constraints requires modifying the experimental mean vector and covariance matrix. Modification is done with an algorithm based on linear algebra that minimizes changes to the means and covariances while insuring that the operations that impose the different constraints do not conflict with each other.« less

Spectral analysis of large-eddy advection in ET from eddy covariance towers and a large weighting lysimeter

USDA-ARS?s Scientific Manuscript database

Evapotranspiration was continuously measured by an array of eddy covariance systems and large weighting lysimeter in a cotton field in Bushland, Texas. The advective divergence from both horizontal and vertical directions were measured through profile measurements above canopy. All storage terms wer...

Eliciting Systematic Rule Use in Covariation Judgment [the Early Years].

ERIC Educational Resources Information Center

Shaklee, Harriet; Paszek, Donald

Related research suggests that children may show some simple understanding of event covariations by the early elementary school years. The present experiments use a rule analysis methodology to investigate covariation judgments of children in this age range. In Experiment 1, children in second, third and fourth grade judged covariations on 12…

Robust infrared targets tracking with covariance matrix representation

NASA Astrophysics Data System (ADS)

Cheng, Jian

2009-07-01

Robust infrared target tracking is an important and challenging research topic in many military and security applications, such as infrared imaging guidance, infrared reconnaissance, scene surveillance, etc. To effectively tackle the nonlinear and non-Gaussian state estimation problems, particle filtering is introduced to construct the theory framework of infrared target tracking. Under this framework, the observation probabilistic model is one of main factors for infrared targets tracking performance. In order to improve the tracking performance, covariance matrices are introduced to represent infrared targets with the multi-features. The observation probabilistic model can be constructed by computing the distance between the reference target's and the target samples' covariance matrix. Because the covariance matrix provides a natural tool for integrating multiple features, and is scale and illumination independent, target representation with covariance matrices can hold strong discriminating ability and robustness. Two experimental results demonstrate the proposed method is effective and robust for different infrared target tracking, such as the sensor ego-motion scene, and the sea-clutter scene.

Un-reduction in field theory.

PubMed

Arnaudon, Alexis; López, Marco Castrillón; Holm, Darryl D

2018-01-01

The un-reduction procedure introduced previously in the context of classical mechanics is extended to covariant field theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter). Other possibilities are also explored: nonlinear [Formula: see text]-models and the hyperbolic flows of curves.

Signs of depth-luminance covariance in 3-D cluttered scenes.

PubMed

Scaccia, Milena; Langer, Michael S

2018-03-01

In three-dimensional (3-D) cluttered scenes such as foliage, deeper surfaces often are more shadowed and hence darker, and so depth and luminance often have negative covariance. We examined whether the sign of depth-luminance covariance plays a role in depth perception in 3-D clutter. We compared scenes rendered with negative and positive depth-luminance covariance where positive covariance means that deeper surfaces are brighter and negative covariance means deeper surfaces are darker. For each scene, the sign of the depth-luminance covariance was given by occlusion cues. We tested whether subjects could use this sign information to judge the depth order of two target surfaces embedded in 3-D clutter. The clutter consisted of distractor surfaces that were randomly distributed in a 3-D volume. We tested three independent variables: the sign of the depth-luminance covariance, the colors of the targets and distractors, and the background luminance. An analysis of variance showed two main effects: Subjects performed better when the deeper surfaces were darker and when the color of the target surfaces was the same as the color of the distractors. There was also a strong interaction: Subjects performed better under a negative depth-luminance covariance condition when targets and distractors had different colors than when they had the same color. Our results are consistent with a "dark means deep" rule, but the use of this rule depends on the similarity between the color of the targets and color of the 3-D clutter.

Killing vector fields in three dimensions: a method to solve massive gravity field equations

NASA Astrophysics Data System (ADS)

Gürses, Metin

2010-10-01

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Empirical Performance of Covariates in Education Observational Studies

ERIC Educational Resources Information Center

Wong, Vivian C.; Valentine, Jeffrey C.; Miller-Bains, Kate

2017-01-01

This article summarizes results from 12 empirical evaluations of observational methods in education contexts. We look at the performance of three common covariate-types in observational studies where the outcome is a standardized reading or math test. They are: pretest measures, local geographic matching, and rich covariate sets with a strong…

The mass-zero spin-two field and gravitational theory.

NASA Technical Reports Server (NTRS)

Coulter, C. A.

1972-01-01

Demonstration that the conventional theory of the mass-zero spin-two field with sources introduces extraneous nonspin-two field components in source regions and fails to be covariant under the full or restricted conformal group. A modified theory is given, expressed in terms of the physical components of mass-zero spin-two field rather than in terms of 'potentials,' which has no extraneous components inside or outside sources, and which is covariant under the full conformal group. For a proper choice of source term, this modified theory has the correct Newtonian limit and automatically implies that a symmetric second-rank source tensor has zero divergence. It is shown that possibly a generally covariant form of the spin-two theory derived here can be constructed to agree with general relativity in all currently accessible experimental situations.

Conditional Covariance Theory and Detect for Polytomous Items

ERIC Educational Resources Information Center

Zhang, Jinming

2007-01-01

This paper extends the theory of conditional covariances to polytomous items. It has been proven that under some mild conditions, commonly assumed in the analysis of response data, the conditional covariance of two items, dichotomously or polytomously scored, given an appropriately chosen composite is positive if, and only if, the two items…

A covariant approach to entropic dynamics

NASA Astrophysics Data System (ADS)

Ipek, Selman; Abedi, Mohammad; Caticha, Ariel

2017-06-01

Entropic Dynamics (ED) is a framework for constructing dynamical theories of inference using the tools of inductive reasoning. A central feature of the ED framework is the special focus placed on time. In [2] a global entropic time was used to derive a quantum theory of relativistic scalar fields. This theory, however, suffered from a lack of explicit or manifest Lorentz symmetry. In this paper we explore an alternative formulation in which the relativistic aspects of the theory are manifest. The approach we pursue here is inspired by the methods of Dirac, Kuchař, and Teitelboim in their development of covariant Hamiltonian approaches. The key ingredient here is the adoption of a local notion of entropic time, which allows compatibility with an arbitrary notion of simultaneity. However, in order to ensure that the evolution does not depend on the particular sequence of hypersurfaces, we must impose a set of constraints that guarantee a consistent evolution.

Phenotypic covariance at species' borders.

PubMed

Caley, M Julian; Cripps, Edward; Game, Edward T

2013-05-28

Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species' borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes. Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species. Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species' borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future.

Eddy covariance measurement of isoprene fluxes

NASA Astrophysics Data System (ADS)

Guenther, Alex B.; Hills, Alan J.

1998-06-01

A system has been developed to directly measure isoprene flux above a forest canopy by eddy covariance using the combination of a fast response, real-time isoprene sensor and sonic anemometer. This system is suitable for making nearly unattended, long-term, and continuous measurements of isoprene fluxes. Isoprene detection is based on chemiluminescence between isoprene and reactant ozone, which produces green light at 500 nm. The sensor has a noise level (1σ) of 450 pptv for a 1-s integration which is dominated by random high-frequency noise that does not significantly degrade eddy covariance flux measurements. Interference from the flux of other compounds is primarily due to the emission of monoterpenes, propene, ethene, and methyl butenol and the deposition of methacrolein and methyl vinyl ketone. The average total interference for North American landscapes in midday summer is estimated to be about 5% for emissions and -3% for deposition fluxes. In only a few North American landscapes, where isoprene emissions are very low and methyl butenol emissions are high, are interferences predicted to be significant. The system was field tested on a tower above a mixed deciduous forest canopy (Duke Forest, North Carolina, U.S.A.) dominated by oak trees, which are strong isoprene emitters. Isoprene fluxes were estimated for 307 half-hour sampling periods over 10 days. Daytime fluxes ranging from 1 to 14 mg C m-2 h-1 were strongly correlated with light and temperature. The daytime mean flux of 6 mg C m-2 h-1 is similar to previous estimates determined by relaxed eddy accumulation by Geron et al [1997] at this site. Nighttime fluxes were near zero (0.01±0.03 mg C m-2 h-1).

A consistent covariant quantization of the Brink-Schwarz superparticle

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

We perform the covariant quantization of the ten-dimensional Brink-Schwarz superparticle by reducing it to a system whose constraints are all first class, covariant and have only two levels of reducibility. Research supported by the Rothschild Fellowship.

Estimation for the Linear Model With Uncertain Covariance Matrices

NASA Astrophysics Data System (ADS)

Zachariah, Dave; Shariati, Nafiseh; Bengtsson, Mats; Jansson, Magnus; Chatterjee, Saikat

2014-03-01

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

Quantification of Covariance in Tropical Cyclone Activity across Teleconnected Basins

NASA Astrophysics Data System (ADS)

Tolwinski-Ward, S. E.; Wang, D.

2015-12-01

Rigorous statistical quantification of natural hazard covariance across regions has important implications for risk management, and is also of fundamental scientific interest. We present a multivariate Bayesian Poisson regression model for inferring the covariance in tropical cyclone (TC) counts across multiple ocean basins and across Saffir-Simpson intensity categories. Such covariability results from the influence of large-scale modes of climate variability on local environments that can alternately suppress or enhance TC genesis and intensification, and our model also simultaneously quantifies the covariance of TC counts with various climatic modes in order to deduce the source of inter-basin TC covariability. The model explicitly treats the time-dependent uncertainty in observed maximum sustained wind data, and hence the nominal intensity category of each TC. Differences in annual TC counts as measured by different agencies are also formally addressed. The probabilistic output of the model can be probed for probabilistic answers to such questions as: - Does the relationship between different categories of TCs differ statistically by basin? - Which climatic predictors have significant relationships with TC activity in each basin? - Are the relationships between counts in different basins conditionally independent given the climatic predictors, or are there other factors at play affecting inter-basin covariability? - How can a portfolio of insured property be optimized across space to minimize risk? Although we present results of our model applied to TCs, the framework is generalizable to covariance estimation between multivariate counts of natural hazards across regions and/or across peril types.

Using machine learning to assess covariate balance in matching studies.

PubMed

Linden, Ariel; Yarnold, Paul R

2016-12-01

In order to assess the effectiveness of matching approaches in observational studies, investigators typically present summary statistics for each observed pre-intervention covariate, with the objective of showing that matching reduces the difference in means (or proportions) between groups to as close to zero as possible. In this paper, we introduce a new approach to distinguish between study groups based on their distributions of the covariates using a machine-learning algorithm called optimal discriminant analysis (ODA). Assessing covariate balance using ODA as compared with the conventional method has several key advantages: the ability to ascertain how individuals self-select based on optimal (maximum-accuracy) cut-points on the covariates; the application to any variable metric and number of groups; its insensitivity to skewed data or outliers; and the use of accuracy measures that can be widely applied to all analyses. Moreover, ODA accepts analytic weights, thereby extending the assessment of covariate balance to any study design where weights are used for covariate adjustment. By comparing the two approaches using empirical data, we are able to demonstrate that using measures of classification accuracy as balance diagnostics produces highly consistent results to those obtained via the conventional approach (in our matched-pairs example, ODA revealed a weak statistically significant relationship not detected by the conventional approach). Thus, investigators should consider ODA as a robust complement, or perhaps alternative, to the conventional approach for assessing covariate balance in matching studies. © 2016 John Wiley & Sons, Ltd.

Cox regression analysis with missing covariates via nonparametric multiple imputation.

PubMed

Hsu, Chiu-Hsieh; Yu, Mandi

2018-01-01

We consider the situation of estimating Cox regression in which some covariates are subject to missing, and there exists additional information (including observed event time, censoring indicator and fully observed covariates) which may be predictive of the missing covariates. We propose to use two working regression models: one for predicting the missing covariates and the other for predicting the missing probabilities. For each missing covariate observation, these two working models are used to define a nearest neighbor imputing set. This set is then used to non-parametrically impute covariate values for the missing observation. Upon the completion of imputation, Cox regression is performed on the multiply imputed datasets to estimate the regression coefficients. In a simulation study, we compare the nonparametric multiple imputation approach with the augmented inverse probability weighted (AIPW) method, which directly incorporates the two working models into estimation of Cox regression, and the predictive mean matching imputation (PMM) method. We show that all approaches can reduce bias due to non-ignorable missing mechanism. The proposed nonparametric imputation method is robust to mis-specification of either one of the two working models and robust to mis-specification of the link function of the two working models. In contrast, the PMM method is sensitive to misspecification of the covariates included in imputation. The AIPW method is sensitive to the selection probability. We apply the approaches to a breast cancer dataset from Surveillance, Epidemiology and End Results (SEER) Program.

Covariance and correlation estimation in electron-density maps.

PubMed

Altomare, Angela; Cuocci, Corrado; Giacovazzo, Carmelo; Moliterni, Anna; Rizzi, Rosanna

2012-03-01

Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution.

Effect of correlation on covariate selection in linear and nonlinear mixed effect models.

PubMed

Bonate, Peter L

2017-01-01

The effect of correlation among covariates on covariate selection was examined with linear and nonlinear mixed effect models. Demographic covariates were extracted from the National Health and Nutrition Examination Survey III database. Concentration-time profiles were Monte Carlo simulated where only one covariate affected apparent oral clearance (CL/F). A series of univariate covariate population pharmacokinetic models was fit to the data and compared with the reduced model without covariate. The "best" covariate was identified using either the likelihood ratio test statistic or AIC. Weight and body surface area (calculated using Gehan and George equation, 1970) were highly correlated (r = 0.98). Body surface area was often selected as a better covariate than weight, sometimes as high as 1 in 5 times, when weight was the covariate used in the data generating mechanism. In a second simulation, parent drug concentration and three metabolites were simulated from a thorough QT study and used as covariates in a series of univariate linear mixed effects models of ddQTc interval prolongation. The covariate with the largest significant LRT statistic was deemed the "best" predictor. When the metabolite was formation-rate limited and only parent concentrations affected ddQTc intervals the metabolite was chosen as a better predictor as often as 1 in 5 times depending on the slope of the relationship between parent concentrations and ddQTc intervals. A correlated covariate can be chosen as being a better predictor than another covariate in a linear or nonlinear population analysis by sheer correlation These results explain why for the same drug different covariates may be identified in different analyses. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties

PubMed Central

Chi, Eric C.; Lange, Kenneth

2014-01-01

Estimation of a covariance matrix or its inverse plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. The current paper introduces a novel prior to ensure a well-conditioned maximum a posteriori (MAP) covariance estimate. The prior shrinks the sample covariance estimator towards a stable target and leads to a MAP estimator that is consistent and asymptotically efficient. Thus, the MAP estimator gracefully transitions towards the sample covariance matrix as the number of samples grows relative to the number of covariates. The utility of the MAP estimator is demonstrated in two standard applications – discriminant analysis and EM clustering – in this sampling regime. PMID:25143662

Covariance specification and estimation to improve top-down Green House Gas emission estimates

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Whetstone, J. R.

2015-12-01

The National Institute of Standards and Technology (NIST) operates the North-East Corridor (NEC) project and the Indianapolis Flux Experiment (INFLUX) in order to develop measurement methods to quantify sources of Greenhouse Gas (GHG) emissions as well as their uncertainties in urban domains using a top down inversion method. Top down inversion updates prior knowledge using observations in a Bayesian way. One primary consideration in a Bayesian inversion framework is the covariance structure of (1) the emission prior residuals and (2) the observation residuals (i.e. the difference between observations and model predicted observations). These covariance matrices are respectively referred to as the prior covariance matrix and the model-data mismatch covariance matrix. It is known that the choice of these covariances can have large effect on estimates. The main objective of this work is to determine the impact of different covariance models on inversion estimates and their associated uncertainties in urban domains. We use a pseudo-data Bayesian inversion framework using footprints (i.e. sensitivities of tower measurements of GHGs to surface emissions) and emission priors (based on Hestia project to quantify fossil-fuel emissions) to estimate posterior emissions using different covariance schemes. The posterior emission estimates and uncertainties are compared to the hypothetical truth. We find that, if we correctly specify spatial variability and spatio-temporal variability in prior and model-data mismatch covariances respectively, then we can compute more accurate posterior estimates. We discuss few covariance models to introduce space-time interacting mismatches along with estimation of the involved parameters. We then compare several candidate prior spatial covariance models from the Matern covariance class and estimate their parameters with specified mismatches. We find that best-fitted prior covariances are not always best in recovering the truth. To achieve

Predicting the risk of toxic blooms of golden alga from cell abundance and environmental covariates

USGS Publications Warehouse

Patino, Reynaldo; VanLandeghem, Matthew M.; Denny, Shawn

2016-01-01

Golden alga (Prymnesium parvum) is a toxic haptophyte that has caused considerable ecological damage to marine and inland aquatic ecosystems worldwide. Studies focused primarily on laboratory cultures have indicated that toxicity is poorly correlated with the abundance of golden alga cells. This relationship, however, has not been rigorously evaluated in the field where environmental conditions are much different. The ability to predict toxicity using readily measured environmental variables and golden alga abundance would allow managers rapid assessments of ichthyotoxicity potential without laboratory bioassay confirmation, which requires additional resources to accomplish. To assess the potential utility of these relationships, several a priori models relating lethal levels of golden alga ichthyotoxicity to golden alga abundance and environmental covariates were constructed. Model parameters were estimated using archived data from four river basins in Texas and New Mexico (Colorado, Brazos, Red, Pecos). Model predictive ability was quantified using cross-validation, sensitivity, and specificity, and the relative ranking of environmental covariate models was determined by Akaike Information Criterion values and Akaike weights. Overall, abundance was a generally good predictor of ichthyotoxicity as cross validation of golden alga abundance-only models ranged from ∼ 80% to ∼ 90% (leave-one-out cross-validation). Environmental covariates improved predictions, especially the ability to predict lethally toxic events (i.e., increased sensitivity), and top-ranked environmental covariate models differed among the four basins. These associations may be useful for monitoring as well as understanding the abiotic factors that influence toxicity during blooms.

Parametric number covariance in quantum chaotic spectra.

PubMed

Vinayak; Kumar, Sandeep; Pandey, Akhilesh

2016-03-01

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

Covariant approach of perturbations in Lovelock type brane gravity

NASA Astrophysics Data System (ADS)

Bagatella-Flores, Norma; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

2016-12-01

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field Φ . Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for Φ possessing a tachyonic mass. This shows that, to some extent, these types of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

Cortisol Covariation Within Parents of Young Children: Moderation by Relationship Aggression

PubMed Central

Saxbe, Darby E.; Adam, Emma K.; Dunkel Schetter, Christine; Guardino, Christine M.; Simon, Clarissa; McKinney, Chelsea O.; Shalowitz, Madeleine U.; Shriver, Eunice Kennedy

2015-01-01

Covariation in diurnal cortisol has been observed in several studies of cohabiting couples. In two such studies (Liu et al, 2013, Saxbe & Repetti, 2010), relationship distress was associated with stronger within-couple correlations, suggesting that couples’ physiological linkage with each other may indicate problematic dyadic functioning. Although intimate partner aggression has been associated with dysregulation in women’s diurnal cortisol, it has not yet been tested as a moderator of within-couple covariation. This study reports on a diverse sample of 122 parents who sampled salivary cortisol on matched days for two years following the birth of an infant. Partners showed strong positive cortisol covariation. In couples with higher levels of partner-perpetrated aggression reported by women at one year postpartum, both women and men had a flatter diurnal decrease in cortisol and stronger correlations with partners’ cortisol sampled at the same timepoints. In other words, relationship aggression was linked both with indices of suboptimal cortisol rhythms in both members of the couples and with stronger within-couple covariation coefficients. These results persisted when relationship satisfaction and demographic covariates were included in the model. During some of the sampling days, some women were pregnant with a subsequent child, but pregnancy did not significantly moderate cortisol levels or within-couple covariation. The findings suggest that couples experiencing relationship aggression have both suboptimal neuroendocrine profiles and stronger covariation. Cortisol covariation is an understudied phenomenon with potential implications for couples’ relationship functioning and physical health. PMID:26298691

Marginalized zero-inflated Poisson models with missing covariates.

PubMed

Benecha, Habtamu K; Preisser, John S; Divaris, Kimon; Herring, Amy H; Das, Kalyan

2018-05-11

Unlike zero-inflated Poisson regression, marginalized zero-inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school-based fluoride mouthrinse program. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

An Empirical State Error Covariance Matrix Orbit Determination Example

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance

Optimal estimation of spatially variable recharge and transmissivity fields under steady-state groundwater flow. Part 1. Theory

NASA Astrophysics Data System (ADS)

Graham, Wendy D.; Tankersley, Claude D.

1994-05-01

Stochastic methods are used to analyze two-dimensional steady groundwater flow subject to spatially variable recharge and transmissivity. Approximate partial differential equations are developed for the covariances and cross-covariances between the random head, transmissivity and recharge fields. Closed-form solutions of these equations are obtained using Fourier transform techniques. The resulting covariances and cross-covariances can be incorporated into a Bayesian conditioning procedure which provides optimal estimates of the recharge, transmissivity and head fields given available measurements of any or all of these random fields. Results show that head measurements contain valuable information for estimating the random recharge field. However, when recharge is treated as a spatially variable random field, the value of head measurements for estimating the transmissivity field can be reduced considerably. In a companion paper, the method is applied to a case study of the Upper Floridan Aquifer in NE Florida.

Galaxy two-point covariance matrix estimation for next generation surveys

NASA Astrophysics Data System (ADS)

Howlett, Cullan; Percival, Will J.

2017-12-01

We perform a detailed analysis of the covariance matrix of the spherically averaged galaxy power spectrum and present a new, practical method for estimating this within an arbitrary survey without the need for running mock galaxy simulations that cover the full survey volume. The method uses theoretical arguments to modify the covariance matrix measured from a set of small-volume cubic galaxy simulations, which are computationally cheap to produce compared to larger simulations and match the measured small-scale galaxy clustering more accurately than is possible using theoretical modelling. We include prescriptions to analytically account for the window function of the survey, which convolves the measured covariance matrix in a non-trivial way. We also present a new method to include the effects of super-sample covariance and modes outside the small simulation volume which requires no additional simulations and still allows us to scale the covariance matrix. As validation, we compare the covariance matrix estimated using our new method to that from a brute-force calculation using 500 simulations originally created for analysis of the Sloan Digital Sky Survey Main Galaxy Sample. We find excellent agreement on all scales of interest for large-scale structure analysis, including those dominated by the effects of the survey window, and on scales where theoretical models of the clustering normally break down, but the new method produces a covariance matrix with significantly better signal-to-noise ratio. Although only formally correct in real space, we also discuss how our method can be extended to incorporate the effects of redshift space distortions.

On the discrepancy between eddy covariance and lysimetry-based surface flux measurements under strongly advective conditions

NASA Astrophysics Data System (ADS)

Alfieri, Joseph G.; Kustas, William P.; Prueger, John H.; Hipps, Lawrence E.; Evett, Steven R.; Basara, Jeffrey B.; Neale, Christopher M. U.; French, Andrew N.; Colaizzi, Paul; Agam, Nurit; Cosh, Michael H.; Chavez, José L.; Howell, Terry A.

2012-12-01

Discrepancies can arise among surface flux measurements collected using disparate techniques due to differences in both the instrumentation and theoretical underpinnings of the different measurement methods. Using data collected primarily within a pair of irrigated cotton fields as a part of the 2008 Bushland Evapotranspiration and Remote Sensing Experiment (BEAREX08), flux measurements collected with two commonly-used methods, eddy covariance (EC) and lysimetry (LY), were compared and substantial differences were found. Daytime mean differences in the flux measurements from the two techniques could be in excess of 200 W m-2 under strongly advective conditions. Three causes for this disparity were found: (i) the failure of the eddy covariance systems to fully balance the surface energy budget, (ii) flux divergence due to the local advection of warm, dry air over the irrigated cotton fields, and (iii) the failure of lysimeters to accurately represent the surface properties of the cotton fields as a whole. Regardless of the underlying cause, the discrepancy among the flux measurements underscores the difficulty in collecting these measurements under strongly advective conditions. It also raises awareness of the uncertainty associated with in situ micrometeorological measurements and the need for caution when using such data for model validation or as observational evidence to definitively support or refute scientific hypotheses.

Data Fusion of Gridded Snow Products Enhanced with Terrain Covariates and a Simple Snow Model

NASA Astrophysics Data System (ADS)

Snauffer, A. M.; Hsieh, W. W.; Cannon, A. J.

2017-12-01

Hydrologic planning requires accurate estimates of regional snow water equivalent (SWE), particularly areas with hydrologic regimes dominated by spring melt. While numerous gridded data products provide such estimates, accurate representations are particularly challenging under conditions of mountainous terrain, heavy forest cover and large snow accumulations, contexts which in many ways define the province of British Columbia (BC), Canada. One promising avenue of improving SWE estimates is a data fusion approach which combines field observations with gridded SWE products and relevant covariates. A base artificial neural network (ANN) was constructed using three of the best performing gridded SWE products over BC (ERA-Interim/Land, MERRA and GLDAS-2) and simple location and time covariates. This base ANN was then enhanced to include terrain covariates (slope, aspect and Terrain Roughness Index, TRI) as well as a simple 1-layer energy balance snow model driven by gridded bias-corrected ANUSPLIN temperature and precipitation values. The ANN enhanced with all aforementioned covariates performed better than the base ANN, but most of the skill improvement was attributable to the snow model with very little contribution from the terrain covariates. The enhanced ANN improved station mean absolute error (MAE) by an average of 53% relative to the composing gridded products over the province. Interannual peak SWE correlation coefficient was found to be 0.78, an improvement of 0.05 to 0.18 over the composing products. This nonlinear approach outperformed a comparable multiple linear regression (MLR) model by 22% in MAE and 0.04 in interannual correlation. The enhanced ANN has also been shown to estimate better than the Variable Infiltration Capacity (VIC) hydrologic model calibrated and run for four BC watersheds, improving MAE by 22% and correlation by 0.05. The performance improvements of the enhanced ANN are statistically significant at the 5% level across the province and

Altered Cerebral Blood Flow Covariance Network in Schizophrenia.

PubMed

Liu, Feng; Zhuo, Chuanjun; Yu, Chunshui

2016-01-01

Many studies have shown abnormal cerebral blood flow (CBF) in schizophrenia; however, it remains unclear how topological properties of CBF network are altered in this disorder. Here, arterial spin labeling (ASL) MRI was employed to measure resting-state CBF in 96 schizophrenia patients and 91 healthy controls. CBF covariance network of each group was constructed by calculating across-subject CBF covariance between 90 brain regions. Graph theory was used to compare intergroup differences in global and nodal topological measures of the network. Both schizophrenia patients and healthy controls had small-world topology in CBF covariance networks, implying an optimal balance between functional segregation and integration. Compared with healthy controls, schizophrenia patients showed reduced small-worldness, normalized clustering coefficient and local efficiency of the network, suggesting a shift toward randomized network topology in schizophrenia. Furthermore, schizophrenia patients exhibited altered nodal centrality in the perceptual-, affective-, language-, and spatial-related regions, indicating functional disturbance of these systems in schizophrenia. This study demonstrated for the first time that schizophrenia patients have disrupted topological properties in CBF covariance network, which provides a new perspective (efficiency of blood flow distribution between brain regions) for understanding neural mechanisms of schizophrenia.

Phenotypic covariance at species’ borders

PubMed Central

2013-01-01

Background Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species’ borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes. Results Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species. Conclusions Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species’ borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future. PMID:23714580

Covariant n/sup 2/-plet mass formulas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, A.

Using a generalized internal symmetry group analogous to the Lorentz group, we have constructed a covariant n/sup 2/-plet mass operator. This operator is built as a scalar matrix in the (n;n*) representation, and its SU(n) breaking parameters are identified as intrinsic boost ones. Its basic properties are: covariance, Hermiticity, positivity, charge conjugation, quark contents, and a self-consistent n/sup 2/-1, 1 mixing. The GMO and the Okubo formulas are obtained by considering two different limits of the same generalized mass formula.

Covariance Based Pre-Filters and Screening Criteria for Conjunction Analysis

NASA Astrophysics Data System (ADS)

George, E., Chan, K.

2012-09-01

Several relationships are developed relating object size, initial covariance and range at closest approach to probability of collision. These relationships address the following questions: - Given the objects' initial covariance and combined hard body size, what is the maximum possible value of the probability of collision (Pc)? - Given the objects' initial covariance, what is the maximum combined hard body radius for which the probability of collision does not exceed the tolerance limit? - Given the objects' initial covariance and the combined hard body radius, what is the minimum miss distance for which the probability of collision does not exceed the tolerance limit? - Given the objects' initial covariance and the miss distance, what is the maximum combined hard body radius for which the probability of collision does not exceed the tolerance limit? The first relationship above allows the elimination of object pairs from conjunction analysis (CA) on the basis of the initial covariance and hard-body sizes of the objects. The application of this pre-filter to present day catalogs with estimated covariance results in the elimination of approximately 35% of object pairs as unable to ever conjunct with a probability of collision exceeding 1x10-6. Because Pc is directly proportional to object size and inversely proportional to covariance size, this pre-filter will have a significantly larger impact on future catalogs, which are expected to contain a much larger fraction of small debris tracked only by a limited subset of available sensors. This relationship also provides a mathematically rigorous basis for eliminating objects from analysis entirely based on element set age or quality - a practice commonly done by rough rules of thumb today. Further, these relations can be used to determine the required geometric screening radius for all objects. This analysis reveals the screening volumes for small objects are much larger than needed, while the screening volumes for

Dynamic Tasking of Networked Sensors Using Covariance Information

DTIC Science & Technology

2010-09-01

has been created under an effort called TASMAN (Tasking Autonomous Sensors in a Multiple Application Network). One of the first studies utilizing this...environment was focused on a novel resource management approach, namely covariance-based tasking. Under this scheme, the state error covariance of...resident space objects (RSO), sensor characteristics, and sensor- target geometry were used to determine the effectiveness of future observations in

Cortisol covariation within parents of young children: Moderation by relationship aggression.

PubMed

Saxbe, Darby E; Adam, Emma K; Schetter, Christine Dunkel; Guardino, Christine M; Simon, Clarissa; McKinney, Chelsea O; Shalowitz, Madeleine U

2015-12-01

Covariation in diurnal cortisol has been observed in several studies of cohabiting couples. In two such studies (Liu et al., 2013; Saxbe and Repetti, 2010), relationship distress was associated with stronger within-couple correlations, suggesting that couples' physiological linkage with each other may indicate problematic dyadic functioning. Although intimate partner aggression has been associated with dysregulation in women's diurnal cortisol, it has not yet been tested as a moderator of within-couple covariation. This study reports on a diverse sample of 122 parents who sampled salivary cortisol on matched days for two years following the birth of an infant. Partners showed strong positive cortisol covariation. In couples with higher levels of partner-perpetrated aggression reported by women at one year postpartum, both women and men had a flatter diurnal decrease in cortisol and stronger correlations with partners' cortisol sampled at the same timepoints. In other words, relationship aggression was linked both with indices of suboptimal cortisol rhythms in both members of the couples and with stronger within-couple covariation coefficients. These results persisted when relationship satisfaction and demographic covariates were included in the model. During some of the sampling days, some women were pregnant with a subsequent child, but pregnancy did not significantly moderate cortisol levels or within-couple covariation. The findings suggest that couples experiencing relationship aggression have both suboptimal neuroendocrine profiles and stronger covariation. Cortisol covariation is an understudied phenomenon with potential implications for couples' relationship functioning and physical health. Copyright © 2015 Elsevier Ltd. All rights reserved.

How large are the consequences of covariate imbalance in cluster randomized trials: a simulation study with a continuous outcome and a binary covariate at the cluster level.

PubMed

Moerbeek, Mirjam; van Schie, Sander

2016-07-11

The number of clusters in a cluster randomized trial is often low. It is therefore likely random assignment of clusters to treatment conditions results in covariate imbalance. There are no studies that quantify the consequences of covariate imbalance in cluster randomized trials on parameter and standard error bias and on power to detect treatment effects. The consequences of covariance imbalance in unadjusted and adjusted linear mixed models are investigated by means of a simulation study. The factors in this study are the degree of imbalance, the covariate effect size, the cluster size and the intraclass correlation coefficient. The covariate is binary and measured at the cluster level; the outcome is continuous and measured at the individual level. The results show covariate imbalance results in negligible parameter bias and small standard error bias in adjusted linear mixed models. Ignoring the possibility of covariate imbalance while calculating the sample size at the cluster level may result in a loss in power of at most 25 % in the adjusted linear mixed model. The results are more severe for the unadjusted linear mixed model: parameter biases up to 100 % and standard error biases up to 200 % may be observed. Power levels based on the unadjusted linear mixed model are often too low. The consequences are most severe for large clusters and/or small intraclass correlation coefficients since then the required number of clusters to achieve a desired power level is smallest. The possibility of covariate imbalance should be taken into account while calculating the sample size of a cluster randomized trial. Otherwise more sophisticated methods to randomize clusters to treatments should be used, such as stratification or balance algorithms. All relevant covariates should be carefully identified, be actually measured and included in the statistical model to avoid severe levels of parameter and standard error bias and insufficient power levels.

Bayesian semiparametric estimation of covariate-dependent ROC curves

PubMed Central

Rodríguez, Abel; Martínez, Julissa C.

2014-01-01

Receiver operating characteristic (ROC) curves are widely used to measure the discriminating power of medical tests and other classification procedures. In many practical applications, the performance of these procedures can depend on covariates such as age, naturally leading to a collection of curves associated with different covariate levels. This paper develops a Bayesian heteroscedastic semiparametric regression model and applies it to the estimation of covariate-dependent ROC curves. More specifically, our approach uses Gaussian process priors to model the conditional mean and conditional variance of the biomarker of interest for each of the populations under study. The model is illustrated through an application to the evaluation of prostate-specific antigen for the diagnosis of prostate cancer, which contrasts the performance of our model against alternative models. PMID:24174579

Hawking radiation and covariant anomalies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Rabin; Kulkarni, Shailesh

2008-01-15

Generalizing the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.

An Empirical State Error Covariance Matrix for Batch State Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the

Noise covariance incorporated MEG-MUSIC algorithm: a method for multiple-dipole estimation tolerant of the influence of background brain activity.

PubMed

Sekihara, K; Poeppel, D; Marantz, A; Koizumi, H; Miyashita, Y

1997-09-01

This paper proposes a method of localizing multiple current dipoles from spatio-temporal biomagnetic data. The method is based on the multiple signal classification (MUSIC) algorithm and is tolerant of the influence of background brain activity. In this method, the noise covariance matrix is estimated using a portion of the data that contains noise, but does not contain any signal information. Then, a modified noise subspace projector is formed using the generalized eigenvectors of the noise and measured-data covariance matrices. The MUSIC localizer is calculated using this noise subspace projector and the noise covariance matrix. The results from a computer simulation have verified the effectiveness of the method. The method was then applied to source estimation for auditory-evoked fields elicited by syllable speech sounds. The results strongly suggest the method's effectiveness in removing the influence of background activity.

Structural and Maturational Covariance in Early Childhood Brain Development.

PubMed

Geng, Xiujuan; Li, Gang; Lu, Zhaohua; Gao, Wei; Wang, Li; Shen, Dinggang; Zhu, Hongtu; Gilmore, John H

2017-03-01

Brain structural covariance networks (SCNs) composed of regions with correlated variation are altered in neuropsychiatric disease and change with age. Little is known about the development of SCNs in early childhood, a period of rapid cortical growth. We investigated the development of structural and maturational covariance networks, including default, dorsal attention, primary visual and sensorimotor networks in a longitudinal population of 118 children after birth to 2 years old and compared them with intrinsic functional connectivity networks. We found that structural covariance of all networks exhibit strong correlations mostly limited to their seed regions. By Age 2, default and dorsal attention structural networks are much less distributed compared with their functional maps. The maturational covariance maps, however, revealed significant couplings in rates of change between distributed regions, which partially recapitulate their functional networks. The structural and maturational covariance of the primary visual and sensorimotor networks shows similar patterns to the corresponding functional networks. Results indicate that functional networks are in place prior to structural networks, that correlated structural patterns in adult may arise in part from coordinated cortical maturation, and that regional co-activation in functional networks may guide and refine the maturation of SCNs over childhood development. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.

PubMed

Lee, Keunbaik; Baek, Changryong; Daniels, Michael J

2017-11-01

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

Combined chamber-tower approach: Using eddy covariance measurements to cross-validate carbon fluxes modeled from manual chamber campaigns

NASA Astrophysics Data System (ADS)

Brümmer, C.; Moffat, A. M.; Huth, V.; Augustin, J.; Herbst, M.; Kutsch, W. L.

2016-12-01

Manual carbon dioxide flux measurements with closed chambers at scheduled campaigns are a versatile method to study management effects at small scales in multiple-plot experiments. The eddy covariance technique has the advantage of quasi-continuous measurements but requires large homogeneous areas of a few hectares. To evaluate the uncertainties associated with interpolating from individual campaigns to the whole vegetation period, we installed both techniques at an agricultural site in Northern Germany. The presented comparison covers two cropping seasons, winter oilseed rape in 2012/13 and winter wheat in 2013/14. Modeling half-hourly carbon fluxes from campaigns is commonly performed based on non-linear regressions for the light response and respiration. The daily averages of net CO2 modeled from chamber data deviated from eddy covariance measurements in the range of ± 5 g C m-2 day-1. To understand the observed differences and to disentangle the effects, we performed four additional setups (expert versus default settings of the non-linear regressions based algorithm, purely empirical modeling with artificial neural networks versus non-linear regressions, cross-validating using eddy covariance measurements as campaign fluxes, weekly versus monthly scheduling of campaigns) to model the half-hourly carbon fluxes for the whole vegetation period. The good agreement of the seasonal course of net CO2 at plot and field scale for our agricultural site demonstrates that both techniques are robust and yield consistent results at seasonal time scale even for a managed ecosystem with high temporal dynamics in the fluxes. This allows combining the respective advantages of factorial experiments at plot scale with dense time series data at field scale. Furthermore, the information from the quasi-continuous eddy covariance measurements can be used to derive vegetation proxies to support the interpolation of carbon fluxes in-between the manual chamber campaigns.

Covariant electrodynamics in linear media: Optical metric

NASA Astrophysics Data System (ADS)

Thompson, Robert T.

2018-03-01

While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance—form invariance under general coordinate transformations, including between accelerating frames—that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framework for electrodynamics in general dielectric media residing in curved background space-times. In particular, I derive a relation for the spatial medium parameters measured by an arbitrary timelike observer. In terms of those medium parameters I derive an explicit expression for the pseudo-Finslerian optical metric of birefringent media and show how it reduces to a pseudo-Riemannian optical metric for nonbirefringent media. This formulation provides a basis for a unified approach to ray and congruence tracing through media in curved space-times that may smoothly vary among positively refracting, negatively refracting, and vacuum.

Earth Observing System Covariance Realism Updates

NASA Technical Reports Server (NTRS)

Ojeda Romero, Juan A.; Miguel, Fred

2017-01-01

This presentation will be given at the International Earth Science Constellation Mission Operations Working Group meetings June 13-15, 2017 to discuss the Earth Observing System Covariance Realism updates.

A Class of Population Covariance Matrices in the Bootstrap Approach to Covariance Structure Analysis

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro; Yanagihara, Hirokazu

2007-01-01

Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given…

Background Error Covariance Estimation using Information from a Single Model Trajectory with Application to Ocean Data Assimilation into the GEOS-5 Coupled Model

NASA Technical Reports Server (NTRS)

Keppenne, Christian L.; Rienecker, Michele M.; Kovach, Robin M.; Vernieres, Guillaume; Koster, Randal D. (Editor)

2014-01-01

An attractive property of ensemble data assimilation methods is that they provide flow dependent background error covariance estimates which can be used to update fields of observed variables as well as fields of unobserved model variables. Two methods to estimate background error covariances are introduced which share the above property with ensemble data assimilation methods but do not involve the integration of multiple model trajectories. Instead, all the necessary covariance information is obtained from a single model integration. The Space Adaptive Forecast error Estimation (SAFE) algorithm estimates error covariances from the spatial distribution of model variables within a single state vector. The Flow Adaptive error Statistics from a Time series (FAST) method constructs an ensemble sampled from a moving window along a model trajectory. SAFE and FAST are applied to the assimilation of Argo temperature profiles into version 4.1 of the Modular Ocean Model (MOM4.1) coupled to the GEOS-5 atmospheric model and to the CICE sea ice model. The results are validated against unassimilated Argo salinity data. They show that SAFE and FAST are competitive with the ensemble optimal interpolation (EnOI) used by the Global Modeling and Assimilation Office (GMAO) to produce its ocean analysis. Because of their reduced cost, SAFE and FAST hold promise for high-resolution data assimilation applications.

Autism-specific covariation in perceptual performances: "g" or "p" factor?

PubMed

Meilleur, Andrée-Anne S; Berthiaume, Claude; Bertone, Armando; Mottron, Laurent

2014-01-01

Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination) and mid-level (e.g., pattern matching) tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals. We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ) and Raven Progressive Matrices (RPM). We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence. In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism. Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or "g" factor). Instead, this residual covariation is accounted for by a common perceptual process (or "p" factor), which may drive perceptual abilities differently in autistic and

Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem*

PubMed Central

Katsevich, E.; Katsevich, A.; Singer, A.

2015-01-01

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise. PMID:25699132

Shrinkage Estimation of Varying Covariate Effects Based On Quantile Regression

PubMed Central

Peng, Limin; Xu, Jinfeng; Kutner, Nancy

2013-01-01

Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed quantile regression model, is to retain variables that have effects on all quantiles of interest as well as those that influence only part of quantiles considered. Current work on l1-penalized quantile regression either does not concern varying covariate effects or may not produce consistent variable selection in the presence of covariates with partial effects, a practical scenario of interest. In this work, we propose a shrinkage approach by adopting a novel uniform adaptive LASSO penalty. The new approach enjoys easy implementation without requiring smoothing. Moreover, it can consistently identify the true model (uniformly across quantiles) and achieve the oracle estimation efficiency. We further extend the proposed shrinkage method to the case where responses are subject to random right censoring. Numerical studies confirm the theoretical results and support the utility of our proposals. PMID:25332515

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials

PubMed Central

Diaz-Ordaz, Karla; Bartlett, Jonathan W

2016-01-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group. PMID:27177885

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials.

PubMed

Hossain, Anower; Diaz-Ordaz, Karla; Bartlett, Jonathan W

2017-06-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group.

Triangular covariance factorizations for. Ph.D. Thesis. - Calif. Univ.

NASA Technical Reports Server (NTRS)

Thornton, C. L.

1976-01-01

An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.

Video based object representation and classification using multiple covariance matrices.

PubMed

Zhang, Yurong; Liu, Quan

2017-01-01

Video based object recognition and classification has been widely studied in computer vision and image processing area. One main issue of this task is to develop an effective representation for video. This problem can generally be formulated as image set representation. In this paper, we present a new method called Multiple Covariance Discriminative Learning (MCDL) for image set representation and classification problem. The core idea of MCDL is to represent an image set using multiple covariance matrices with each covariance matrix representing one cluster of images. Firstly, we use the Nonnegative Matrix Factorization (NMF) method to do image clustering within each image set, and then adopt Covariance Discriminative Learning on each cluster (subset) of images. At last, we adopt KLDA and nearest neighborhood classification method for image set classification. Promising experimental results on several datasets show the effectiveness of our MCDL method.

The utility of covariance of combining ability in plant breeding.

PubMed

Arunachalam, V

1976-11-01

The definition of covariances of half- and full sibs, and hence that of variances of general and specific combining ability with regard to a quantitative character, is extended to take into account the respective covariances between a pair of characters. The interpretation of the dispersion and correlation matrices of general and specific combining ability is discussed by considering a set of single, three- and four-way crosses, made using diallel and line × tester mating systems in Pennisetum typhoides. The general implications of the concept of covariance of combining ability in plant breeding are discussed.

Bayesian Analysis of Structural Equation Models with Nonlinear Covariates and Latent Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…

To Covary or Not to Covary, That is the Question

NASA Astrophysics Data System (ADS)

Oehlert, A. M.; Swart, P. K.

2016-12-01

The meaning of covariation between the δ13C values of carbonate carbon and that of organic material is classically interpreted as reflecting original variations in the δ13C values of the dissolved inorganic carbon in the depositional environment. However, recently it has been shown by the examination of a core from Great Bahama Bank (Clino) that during exposure not only do the rocks become altered acquiring a negative δ13C value, but at the same time terrestrial vegetation adds organic carbon to the system masking the original marine values. These processes yield a strong positive covariation between δ13Corg and δ13Ccar values even though the signals are clearly not original and unrelated to the marine δ13C values. Examining the correlation between the organic and inorganic system in a stratigraphic sense at Clino and in a second more proximally located core (Unda) using a windowed correlation coefficient technique reveals that the correlation is even more complex. Changes in slope and the magnitude of the correlation are associated with exposure surfaces, facies changes, dolomitized bodies, and non-depositional surfaces. Finally other isotopic systems such as the δ13C value of specific organic compounds as well as δ15N values of bulk and individual compounds can provide additional information. In the case of δ15N values, decreases reflect a changes in the influence of terrestrial organic material and an increase contribution of organic material from the platform surface where the main source of nitrogen is derived from the activities of cyanobacteria.

A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix.

PubMed

Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun

2017-09-21

The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

PubMed Central

LIU, Han; WANG, Lie; ZHAO, Tuo

2014-01-01

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online. PMID:25620866

Competing risks models and time-dependent covariates

PubMed Central

Barnett, Adrian; Graves, Nick

2008-01-01

New statistical models for analysing survival data in an intensive care unit context have recently been developed. Two models that offer significant advantages over standard survival analyses are competing risks models and multistate models. Wolkewitz and colleagues used a competing risks model to examine survival times for nosocomial pneumonia and mortality. Their model was able to incorporate time-dependent covariates and so examine how risk factors that changed with time affected the chances of infection or death. We briefly explain how an alternative modelling technique (using logistic regression) can more fully exploit time-dependent covariates for this type of data. PMID:18423067

Evaluation of digital soil mapping approaches with large sets of environmental covariates

NASA Astrophysics Data System (ADS)

Nussbaum, Madlene; Spiess, Kay; Baltensweiler, Andri; Grob, Urs; Keller, Armin; Greiner, Lucie; Schaepman, Michael E.; Papritz, Andreas

2018-01-01

The spatial assessment of soil functions requires maps of basic soil properties. Unfortunately, these are either missing for many regions or are not available at the desired spatial resolution or down to the required soil depth. The field-based generation of large soil datasets and conventional soil maps remains costly. Meanwhile, legacy soil data and comprehensive sets of spatial environmental data are available for many regions. Digital soil mapping (DSM) approaches relating soil data (responses) to environmental data (covariates) face the challenge of building statistical models from large sets of covariates originating, for example, from airborne imaging spectroscopy or multi-scale terrain analysis. We evaluated six approaches for DSM in three study regions in Switzerland (Berne, Greifensee, ZH forest) by mapping the effective soil depth available to plants (SD), pH, soil organic matter (SOM), effective cation exchange capacity (ECEC), clay, silt, gravel content and fine fraction bulk density for four soil depths (totalling 48 responses). Models were built from 300-500 environmental covariates by selecting linear models through (1) grouped lasso and (2) an ad hoc stepwise procedure for robust external-drift kriging (georob). For (3) geoadditive models we selected penalized smoothing spline terms by component-wise gradient boosting (geoGAM). We further used two tree-based methods: (4) boosted regression trees (BRTs) and (5) random forest (RF). Lastly, we computed (6) weighted model averages (MAs) from the predictions obtained from methods 1-5. Lasso, georob and geoGAM successfully selected strongly reduced sets of covariates (subsets of 3-6 % of all covariates). Differences in predictive performance, tested on independent validation data, were mostly small and did not reveal a single best method for 48 responses. Nevertheless, RF was often the best among methods 1-5 (28 of 48 responses), but was outcompeted by MA for 14 of these 28 responses. RF tended to over

Conformal killing tensors and covariant Hamiltonian dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cariglia, M., E-mail: marco@iceb.ufop.br; Gibbons, G. W., E-mail: G.W.Gibbons@damtp.cam.ac.uk; LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans

2014-12-15

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector formore » planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.« less

Covariant deformed oscillator algebras

NASA Technical Reports Server (NTRS)

Quesne, Christiane

1995-01-01

The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

WAIS-IV subtest covariance structure: conceptual and statistical considerations.

PubMed

Ward, L Charles; Bergman, Maria A; Hebert, Katina R

2012-06-01

D. Wechsler (2008b) reported confirmatory factor analyses (CFAs) with standardization data (ages 16-69 years) for 10 core and 5 supplemental subtests from the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV). Analyses of the 15 subtests supported 4 hypothesized oblique factors (Verbal Comprehension, Working Memory, Perceptual Reasoning, and Processing Speed) but also revealed unexplained covariance between Block Design and Visual Puzzles (Perceptual Reasoning subtests). That covariance was not included in the final models. Instead, a path was added from Working Memory to Figure Weights (Perceptual Reasoning subtest) to improve fit and achieve a desired factor pattern. The present research with the same data (N = 1,800) showed that the path from Working Memory to Figure Weights increases the association between Working Memory and Matrix Reasoning. Specifying both paths improves model fit and largely eliminates unexplained covariance between Block Design and Visual Puzzles but with the undesirable consequence that Figure Weights and Matrix Reasoning are equally determined by Perceptual Reasoning and Working Memory. An alternative 4-factor model was proposed that explained theory-implied covariance between Block Design and Visual Puzzles and between Arithmetic and Figure Weights while maintaining compatibility with WAIS-IV Index structure. The proposed model compared favorably with a 5-factor model based on Cattell-Horn-Carroll theory. The present findings emphasize that covariance model comparisons should involve considerations of conceptual coherence and theoretical adherence in addition to statistical fit. (c) 2012 APA, all rights reserved

Neutron star mass-radius relation with gravitational field shielding by a scalar field

NASA Astrophysics Data System (ADS)

Zhang, Bo-Jun; Zhang, Tian-Xi; Guggilla, Padmaja; Dokhanian, Mostafa

2013-05-01

The currently well-developed models for equations of state (EoSs) have been severely impacted by recent measurements of neutron stars with a small radius and/or large mass. To explain these measurements, the theory of gravitational field shielding by a scalar field is applied. This theory was recently developed in accordance with the five-dimensional (5D) fully covariant Kaluza-Klein (KK) theory that has successfully unified Einstein's general relativity and Maxwell's electromagnetic theory. It is shown that a massive, compact neutron star can generate a strong scalar field, which can significantly shield or reduce its gravitational field, thus making it more massive and more compact. The mass-radius relation developed under this type of modified gravity can be consistent with these recent measurements of neutron stars. In addition, the effect of gravitational field shielding helps explain why the supernova explosions of some very massive stars (e.g., 40 Msolar as measured recently) actually formed neutron stars rather than black holes as expected. The EoS models, ruled out by measurements of small radius and/or large mass neutron stars according to the theory of general relativity, can still work well in terms of the 5D fully covariant KK theory with a scalar field.

Super-sample covariance approximations and partial sky coverage

NASA Astrophysics Data System (ADS)

Lacasa, Fabien; Lima, Marcos; Aguena, Michel

2018-04-01

Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.

Revealing hidden covariation detection: evidence for implicit abstraction at study.

PubMed

Rossnagel, C S

2001-09-01

Four experiments in the brain scans paradigm (P. Lewicki, T. Hill, & I. Sasaki, 1989) investigated hidden covariation detection (HCD). In Experiment 1 HCD was found in an implicit- but not in an explicit-instruction group. In Experiment 2 HCD was impaired by nonholistic perception of stimuli but not by divided attention. In Experiment 3 HCD was eliminated by interspersing stimuli that deviated from the critical covariation. In Experiment 4 a transfer procedure was used. HCD was found with dissimilar test stimuli that preserved the covariation but was almost eliminated with similar stimuli that were neutral as to the covariation. Awareness was assessed both by objective and subjective tests in all experiments. Results suggest that HCD is an effect of implicit rule abstraction and that similarity processing plays only a minor role. HCD might be suppressed by intentional search strategies that induce inappropriate aggregation of stimulus information.

A heteroskedastic error covariance matrix estimator using a first-order conditional autoregressive Markov simulation for deriving asympotical efficient estimates from ecological sampled Anopheles arabiensis aquatic habitat covariates

PubMed Central

Jacob, Benjamin G; Griffith, Daniel A; Muturi, Ephantus J; Caamano, Erick X; Githure, John I; Novak, Robert J

2009-01-01

Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices) in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression). The eigenfunction values from the spatial

Covariation Neglect among Novice Investors

ERIC Educational Resources Information Center

Hedesstrom, Ted Martin; Svedsater, Henrik; Garling, Tommy

2006-01-01

In 4 experiments, undergraduates made hypothetical investment choices. In Experiment 1, participants paid more attention to the volatility of individual assets than to the volatility of aggregated portfolios. The results of Experiment 2 show that most participants diversified even when this increased risk because of covariation between the returns…

Structural Covariance of the Default Network in Healthy and Pathological Aging

PubMed Central

Turner, Gary R.

2013-01-01

Significant progress has been made uncovering functional brain networks, yet little is known about the corresponding structural covariance networks. The default network's functional architecture has been shown to change over the course of healthy and pathological aging. We examined cross-sectional and longitudinal datasets to reveal the structural covariance of the human default network across the adult lifespan and through the progression of Alzheimer's disease (AD). We used a novel approach to identify the structural covariance of the default network and derive individual participant scores that reflect the covariance pattern in each brain image. A seed-based multivariate analysis was conducted on structural images in the cross-sectional OASIS (N = 414) and longitudinal Alzheimer's Disease Neuroimaging Initiative (N = 434) datasets. We reproduced the distributed topology of the default network, based on a posterior cingulate cortex seed, consistent with prior reports of this intrinsic connectivity network. Structural covariance of the default network scores declined in healthy and pathological aging. Decline was greatest in the AD cohort and in those who progressed from mild cognitive impairment to AD. Structural covariance of the default network scores were positively associated with general cognitive status, reduced in APOEε4 carriers versus noncarriers, and associated with CSF biomarkers of AD. These findings identify the structural covariance of the default network and characterize changes to the network's gray matter integrity across the lifespan and through the progression of AD. The findings provide evidence for the large-scale network model of neurodegenerative disease, in which neurodegeneration spreads through intrinsically connected brain networks in a disease specific manner. PMID:24048852

Covariance Applications in Criticality Safety, Light Water Reactor Analysis, and Spent Fuel Characterization

DOE PAGES

Williams, M. L.; Wiarda, D.; Ilas, G.; ...

2014-06-15

Recently, we processed a new covariance data library based on ENDF/B-VII.1 for the SCALE nuclear analysis code system. The multigroup covariance data are discussed here, along with testing and application results for critical benchmark experiments. Moreover, the cross section covariance library, along with covariances for fission product yields and decay data, is used to compute uncertainties in the decay heat produced by a burned reactor fuel assembly.

Methane fluxes above the Hainich forest by True Eddy Accumulation and Eddy Covariance

NASA Astrophysics Data System (ADS)

Siebicke, Lukas; Gentsch, Lydia; Knohl, Alexander

2016-04-01

Understanding the role of forests for the global methane cycle requires quantifying vegetation-atmosphere exchange of methane, however observations of turbulent methane fluxes remain scarce. Here we measured turbulent fluxes of methane (CH4) above a beech-dominated old-growth forest in the Hainich National Park, Germany, and validated three different measurement approaches: True Eddy Accumulation (TEA, closed-path laser spectroscopy), and eddy covariance (EC, open-path and closed-path laser spectroscopy, respectively). The Hainich flux tower is a long-term Fluxnet and ICOS site with turbulent fluxes and ecosystem observations spanning more than 15 years. The current study is likely the first application of True Eddy Accumulation (TEA) for the measurement of turbulent exchange of methane and one of the very few studies comparing open-path and closed-path eddy covariance (EC) setups side-by-side. We observed uptake of methane by the forest during the day (a methane sink with a maximum rate of 0.03 μmol m-2 s-1 at noon) and no or small fluxes of methane from the forest to the atmosphere at night (a methane source of typically less than 0.01 μmol m-2 s-1) based on continuous True Eddy Accumulation measurements in September 2015. First results comparing TEA to EC CO2 fluxes suggest that True Eddy Accumulation is a valid option for turbulent flux quantifications using slow response gas analysers (here CRDS laser spectroscopy, other potential techniques include mass spectroscopy). The TEA system was one order of magnitude more energy efficient compared to closed-path eddy covariance. The open-path eddy covariance setup required the least amount of user interaction but is often constrained by low signal-to-noise ratios obtained when measuring methane fluxes over forests. Closed-path eddy covariance showed good signal-to-noise ratios in the lab, however in the field it required significant amounts of user intervention in addition to a high power consumption. We conclude

Random sampling and validation of covariance matrices of resonance parameters

NASA Astrophysics Data System (ADS)

Plevnik, Lucijan; Zerovnik, Gašper

2017-09-01

Analytically exact methods for random sampling of arbitrary correlated parameters are presented. Emphasis is given on one hand on the possible inconsistencies in the covariance data, concentrating on the positive semi-definiteness and consistent sampling of correlated inherently positive parameters, and on the other hand on optimization of the implementation of the methods itself. The methods have been applied in the program ENDSAM, written in the Fortran language, which from a file from a nuclear data library of a chosen isotope in ENDF-6 format produces an arbitrary number of new files in ENDF-6 format which contain values of random samples of resonance parameters (in accordance with corresponding covariance matrices) in places of original values. The source code for the program ENDSAM is available from the OECD/NEA Data Bank. The program works in the following steps: reads resonance parameters and their covariance data from nuclear data library, checks whether the covariance data is consistent, and produces random samples of resonance parameters. The code has been validated with both realistic and artificial data to show that the produced samples are statistically consistent. Additionally, the code was used to validate covariance data in existing nuclear data libraries. A list of inconsistencies, observed in covariance data of resonance parameters in ENDF-VII.1, JEFF-3.2 and JENDL-4.0 is presented. For now, the work has been limited to resonance parameters, however the methods presented are general and can in principle be extended to sampling and validation of any nuclear data.

Methane Emissions from Permafrost Regions using Low-Power Eddy Covariance Stations

NASA Astrophysics Data System (ADS)

Burba, G.; Sturtevant, C.; Schreiber, P.; Peltola, O.; Zulueta, R.; Mammarella, I.; Haapanala, S.; Rinne, J.; Vesala, T.; McDermitt, D.; Oechel, W.

2012-04-01

Methane is an important greenhouse gas with a warming potential 23 times that of carbon dioxide over a 100-year cycle. The permafrost regions of the world store significant amounts of organic materials under anaerobic conditions, leading to large methane production and accumulation in the upper layers of bedrock, soil and ice. These regions are currently undergoing dramatic change in response to warming trends, and may become a significant potential source of global methane release under a warming climate over the coming decades and centuries. Presently, most measurements of methane fluxes in permafrost regions have been made with static chamber techniques, and very few were done with the eddy covariance approach using closed-path analyzers. Although chambers and closed-path analyzers have advantages, both techniques have significant limitations, especially for permafrost research. Static chamber measurements are discrete in time and space, and particularly difficult to use over polygonal tundra with highly non-uniform micro-topography and active water layer. They also may not capture the dynamics of methane fluxes on varying time scales (hours to annual estimates). In addition, placement of the chamber may disturb the surface integrity causing a significant over-estimation of the measured flux. Closed-path gas analyzers for measuring methane eddy fluxes employ advanced technologies such as TDLS (Tunable Diode Laser Spectroscopy), ICOS (Integrated Cavity Output Spectroscopy), WS-CRDS (wavelength scanned cavity ring-down spectroscopy), but require high flow rates at significantly reduced optical cell pressures to provide adequate response time and sharpen absorption features. Such methods, when used with the eddy covariance technique, require a vacuum pump and a total of 400-1500 Watts of grid power for the pump and analyzer system. The weight of such systems often exceeds 100-200 lbs, restricting practical applicability for remote or portable field studies. As a

The evolution of phenotypic integration: How directional selection reshapes covariation in mice

PubMed Central

Penna, Anna; Melo, Diogo; Bernardi, Sandra; Oyarzabal, Maria Inés; Marroig, Gabriel

2017-01-01

Abstract Variation is the basis for evolution, and understanding how variation can evolve is a central question in biology. In complex phenotypes, covariation plays an even more important role, as genetic associations between traits can bias and alter evolutionary change. Covariation can be shaped by complex interactions between loci, and this genetic architecture can also change during evolution. In this article, we analyzed mouse lines experimentally selected for changes in size to address the question of how multivariate covariation changes under directional selection, as well as to identify the consequences of these changes to evolution. Selected lines showed a clear restructuring of covariation in their cranium and, instead of depleting their size variation, these lines increased their magnitude of integration and the proportion of variation associated with the direction of selection. This result is compatible with recent theoretical works on the evolution of covariation that take the complexities of genetic architecture into account. This result also contradicts the traditional view of the effects of selection on available covariation and suggests a much more complex view of how populations respond to selection. PMID:28685813

Directional selection effects on patterns of phenotypic (co)variation in wild populations

PubMed Central

Patton, J. L.; Hubbe, A.; Marroig, G.

2016-01-01

Phenotypic (co)variation is a prerequisite for evolutionary change, and understanding how (co)variation evolves is of crucial importance to the biological sciences. Theoretical models predict that under directional selection, phenotypic (co)variation should evolve in step with the underlying adaptive landscape, increasing the degree of correlation among co-selected traits as well as the amount of genetic variance in the direction of selection. Whether either of these outcomes occurs in natural populations is an open question and thus an important gap in evolutionary theory. Here, we documented changes in the phenotypic (co)variation structure in two separate natural populations in each of two chipmunk species (Tamias alpinus and T. speciosus) undergoing directional selection. In populations where selection was strongest (those of T. alpinus), we observed changes, at least for one population, in phenotypic (co)variation that matched theoretical expectations, namely an increase of both phenotypic integration and (co)variance in the direction of selection and a re-alignment of the major axis of variation with the selection gradient. PMID:27881744

Directional selection effects on patterns of phenotypic (co)variation in wild populations.

PubMed

Assis, A P A; Patton, J L; Hubbe, A; Marroig, G

2016-11-30

Phenotypic (co)variation is a prerequisite for evolutionary change, and understanding how (co)variation evolves is of crucial importance to the biological sciences. Theoretical models predict that under directional selection, phenotypic (co)variation should evolve in step with the underlying adaptive landscape, increasing the degree of correlation among co-selected traits as well as the amount of genetic variance in the direction of selection. Whether either of these outcomes occurs in natural populations is an open question and thus an important gap in evolutionary theory. Here, we documented changes in the phenotypic (co)variation structure in two separate natural populations in each of two chipmunk species (Tamias alpinus and T. speciosus) undergoing directional selection. In populations where selection was strongest (those of T. alpinus), we observed changes, at least for one population, in phenotypic (co)variation that matched theoretical expectations, namely an increase of both phenotypic integration and (co)variance in the direction of selection and a re-alignment of the major axis of variation with the selection gradient. © 2016 The Author(s).

Covariate Balance in Bayesian Propensity Score Approaches for Observational Studies

ERIC Educational Resources Information Center

Chen, Jianshen; Kaplan, David

2015-01-01

Bayesian alternatives to frequentist propensity score approaches have recently been proposed. However, few studies have investigated their covariate balancing properties. This article compares a recently developed two-step Bayesian propensity score approach to the frequentist approach with respect to covariate balance. The effects of different…

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance

PubMed Central

Zheng, Binqi; Yuan, Xiaobing

2018-01-01

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results. PMID:29518960

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance.

PubMed

Zheng, Binqi; Fu, Pengcheng; Li, Baoqing; Yuan, Xiaobing

2018-03-07

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results.

Variance and covariance estimates for weaning weight of Senepol cattle.

PubMed

Wright, D W; Johnson, Z B; Brown, C J; Wildeus, S

1991-10-01

Variance and covariance components were estimated for weaning weight from Senepol field data for use in the reduced animal model for a maternally influenced trait. The 4,634 weaning records were used to evaluate 113 sires and 1,406 dams on the island of St. Croix. Estimates of direct additive genetic variance (sigma 2A), maternal additive genetic variance (sigma 2M), covariance between direct and maternal additive genetic effects (sigma AM), permanent maternal environmental variance (sigma 2PE), and residual variance (sigma 2 epsilon) were calculated by equating variances estimated from a sire-dam model and a sire-maternal grandsire model, with and without the inverse of the numerator relationship matrix (A-1), to their expectations. Estimates were sigma 2A, 139.05 and 138.14 kg2; sigma 2M, 307.04 and 288.90 kg2; sigma AM, -117.57 and -103.76 kg2; sigma 2PE, -258.35 and -243.40 kg2; and sigma 2 epsilon, 588.18 and 577.72 kg2 with and without A-1, respectively. Heritability estimates for direct additive (h2A) were .211 and .210 with and without A-1, respectively. Heritability estimates for maternal additive (h2M) were .47 and .44 with and without A-1, respectively. Correlations between direct and maternal (IAM) effects were -.57 and -.52 with and without A-1, respectively.

Phenotypic Covariation and Morphological Diversification in the Ruminant Skull.

PubMed

Haber, Annat

2016-05-01

Differences among clades in their diversification patterns result from a combination of extrinsic and intrinsic factors. In this study, I examined the role of intrinsic factors in the morphological diversification of ruminants, in general, and in the differences between bovids and cervids, in particular. Using skull morphology, which embodies many of the adaptations that distinguish bovids and cervids, I examined 132 of the 200 extant ruminant species. As a proxy for intrinsic constraints, I quantified different aspects of the phenotypic covariation structure within species and compared them with the among-species divergence patterns, using phylogenetic comparative methods. My results show that for most species, divergence is well aligned with their phenotypic covariance matrix and that those that are better aligned have diverged further away from their ancestor. Bovids have dispersed into a wider range of directions in morphospace than cervids, and their overall disparity is higher. This difference is best explained by the lower eccentricity of bovids' within-species covariance matrices. These results are consistent with the role of intrinsic constraints in determining amount, range, and direction of dispersion and demonstrate that intrinsic constraints can influence macroevolutionary patterns even as the covariance structure evolves.

Covariate Imbalance and Adjustment for Logistic Regression Analysis of Clinical Trial Data

PubMed Central

Ciolino, Jody D.; Martin, Reneé H.; Zhao, Wenle; Jauch, Edward C.; Hill, Michael D.; Palesch, Yuko Y.

2014-01-01

In logistic regression analysis for binary clinical trial data, adjusted treatment effect estimates are often not equivalent to unadjusted estimates in the presence of influential covariates. This paper uses simulation to quantify the benefit of covariate adjustment in logistic regression. However, International Conference on Harmonization guidelines suggest that covariate adjustment be pre-specified. Unplanned adjusted analyses should be considered secondary. Results suggest that that if adjustment is not possible or unplanned in a logistic setting, balance in continuous covariates can alleviate some (but never all) of the shortcomings of unadjusted analyses. The case of log binomial regression is also explored. PMID:24138438

Realistic Covariance Prediction for the Earth Science Constellation

NASA Technical Reports Server (NTRS)

Duncan, Matthew; Long, Anne

2006-01-01

Routine satellite operations for the Earth Science Constellation (ESC) include collision risk assessment between members of the constellation and other orbiting space objects. One component of the risk assessment process is computing the collision probability between two space objects. The collision probability is computed using Monte Carlo techniques as well as by numerically integrating relative state probability density functions. Each algorithm takes as inputs state vector and state vector uncertainty information for both objects. The state vector uncertainty information is expressed in terms of a covariance matrix. The collision probability computation is only as good as the inputs. Therefore, to obtain a collision calculation that is a useful decision-making metric, realistic covariance matrices must be used as inputs to the calculation. This paper describes the process used by the NASA/Goddard Space Flight Center's Earth Science Mission Operations Project to generate realistic covariance predictions for three of the Earth Science Constellation satellites: Aqua, Aura and Terra.

Handling Correlations between Covariates and Random Slopes in Multilevel Models

ERIC Educational Resources Information Center

Bates, Michael David; Castellano, Katherine E.; Rabe-Hesketh, Sophia; Skrondal, Anders

2014-01-01

This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between…

Linear Covariance Analysis For Proximity Operations Around Asteroid 2008 EV5

NASA Technical Reports Server (NTRS)

Wright, Cinnamon A.; Bhatt, Sagar; Woffinden, David; Strube, Matthew; D'Souza, Chris

2015-01-01

The NASA initiative to collect an asteroid, the Asteroid Robotic Redirect Mission (ARRM), is currently investigating the option of retrieving a boulder from an asteroid, demonstrating planetary defense with an enhanced gravity tractor technique, and returning it to a lunar orbit. Techniques for accomplishing this are being investigated by the Satellite Servicing Capabilities Office (SSCO) at NASA GSFC in collaboration with JPL, NASA JSC, LaRC, and Draper Laboratory, Inc. Two critical phases of the mission are the descent to the boulder and the Enhanced Gravity Tractor demonstration. A linear covariance analysis is done for these phases to assess the feasibility of these concepts with the proposed design of the sensor and actuator suite of the Asteroid Redirect Vehicle (ARV). The sensor suite for this analysis includes a wide field of view camera, LiDAR, and an IMU. The proposed asteroid of interest is currently the C-type asteroid 2008 EV5, a carbonaceous chondrite that is of high interest to the scientific community. This paper presents an overview of the linear covariance analysis techniques and simulation tool, provides sensor and actuator models, and addresses the feasibility of descending to the surface of the asteroid within allocated requirements as well as the possibility of maintaining a halo orbit to demonstrate the Enhanced Gravity Tractor technique.

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

The contribution of Giordano Bruno to the principle of relativity

NASA Astrophysics Data System (ADS)

De Angelis, Alessandro; Santo, Catarina Espirito

2015-11-01

The trial and condemnation of Giordano Bruno was mainly based on arguments of a philosophical and theological nature, and therefore different from Galileo Galilei's trial. Such elements contribute to unfairly devalue the scientific contribution of Bruno and do not properly account for his contribution to physics. This paper discusses the contribution that Bruno made to the principle of relativity. This was first discussed by Galileo Galilei in 1632 using the metaphor known today as 'Galileo's ship', but we shall show that this same metaphor and some of the examples in Galileo's book were already contained in a dialogue published by Bruno in 1584. In fact, Bruno largely anticipated the arguments of Galilei on the relativity principle, in particular to support the Copernican view. It is likely that Galilei was aware of Bruno's work, and it is possible that the young Galilei discussed it with Bruno, since they both stayed in Venice for long periods in 1592.

Testing covariates of Type 2 diabetes-cognition associations in older adults: moderating or mediating effects?

PubMed

McFall, G Peggy; Geall, Bonnie P; Fischer, Ashley L; Dolcos, Sanda; Dixon, Roger A

2010-09-01

The general goal of this study was to advance our understanding of Type 2 diabetes (T2D)-cognition relationships in older adults by linking and testing comprehensive sets of potential moderators, potential mediators, and multiple cognitive outcomes. We identified in the literature 13 health-related (but T2D-distal) potential covariates, representing four informal domains (i.e., biological vitality, personal affect, subjective health, lifestyle activities). Cross-sectional data from the Victoria Longitudinal Study (age range = 53-90 years; n = 41 T2D and n = 458 control participants) were used. We first examined whether any of the 13 potential covariates influenced T2D-cognition associations, as measured by a comprehensive neuropsychological battery (15 measures). Next, using standard regression-based moderator and mediator analyses, we systematically tested whether the identified covariates would significantly alter observed T2D-cognition relationships. Six potential covariates were found to be sensitive to T2D associations with performance on seven cognitive measures. Three factors (systolic blood pressure, gait-balance composite, subjective health) were significant mediators. Each mediated multiple cognitive outcomes, especially measures of neurocognitive speed, executive functioning, and episodic memory. Our findings offer a relatively comprehensive perspective of T2D-related cognitive deficits, comorbidities, and modulating influences. The implications for future research reach across several fields of study and application. These include (1) neuropsychological research on neural and biological bases of T2D-related cognitive decline, (2) clinical research on intervention and treatment strategies, and (3) larger-scale longitudinal studies examining the potential multilateral and dynamic relationships among T2D status, related comorbidities, and cognitive outcomes. Copyright 2010 APA, all rights reserved.

PREFACE: IARD 2012: 8th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

NASA Astrophysics Data System (ADS)

Horwitz, L. P.; Land, Martin C.; Gill, Tepper; Lusanna, Luca; Salucci, Paolo

2013-04-01

Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Lindner et al [Physical Review Letters 95 0040401 (2005)] as well as the more recent proposal of Palacios et al [Phys. Rev. Lett. 103 253001 (2009)] and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg [Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)] could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular

Multiple Imputation of a Randomly Censored Covariate Improves Logistic Regression Analysis.

PubMed

Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A

2016-01-01

Randomly censored covariates arise frequently in epidemiologic studies. The most commonly used methods, including complete case and single imputation or substitution, suffer from inefficiency and bias. They make strong parametric assumptions or they consider limit of detection censoring only. We employ multiple imputation, in conjunction with semi-parametric modeling of the censored covariate, to overcome these shortcomings and to facilitate robust estimation. We develop a multiple imputation approach for randomly censored covariates within the framework of a logistic regression model. We use the non-parametric estimate of the covariate distribution or the semiparametric Cox model estimate in the presence of additional covariates in the model. We evaluate this procedure in simulations, and compare its operating characteristics to those from the complete case analysis and a survival regression approach. We apply the procedures to an Alzheimer's study of the association between amyloid positivity and maternal age of onset of dementia. Multiple imputation achieves lower standard errors and higher power than the complete case approach under heavy and moderate censoring and is comparable under light censoring. The survival regression approach achieves the highest power among all procedures, but does not produce interpretable estimates of association. Multiple imputation offers a favorable alternative to complete case analysis and ad hoc substitution methods in the presence of randomly censored covariates within the framework of logistic regression.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Structural Covariance Networks in Children with Autism or ADHD

PubMed Central

Romero-Garcia, R.; Mak, E.; Bullmore, E. T.; Baron-Cohen, S.

2017-01-01

Abstract Background While autism and attention-deficit/hyperactivity disorder (ADHD) are considered distinct conditions from a diagnostic perspective, clinically they share some phenotypic features and have high comorbidity. Regardless, most studies have focused on only one condition, with considerable heterogeneity in their results. Taking a dual-condition approach might help elucidate shared and distinct neural characteristics. Method Graph theory was used to analyse topological properties of structural covariance networks across both conditions and relative to a neurotypical (NT; n = 87) group using data from the ABIDE (autism; n = 62) and ADHD-200 datasets (ADHD; n = 69). Regional cortical thickness was used to construct the structural covariance networks. This was analysed in a theoretical framework examining potential differences in long and short-range connectivity, with a specific focus on relation between central graph measures and cortical thickness. Results We found convergence between autism and ADHD, where both conditions show an overall decrease in CT covariance with increased Euclidean distance between centroids compared with a NT population. The 2 conditions also show divergence. Namely, there is less modular overlap between the 2 conditions than there is between each condition and the NT group. The ADHD group also showed reduced cortical thickness and lower degree in hub regions than the autism group. Lastly, the ADHD group also showed reduced wiring costs compared with the autism groups. Conclusions Our results indicate a need for taking an integrated approach when considering highly comorbid conditions such as autism and ADHD. Furthermore, autism and ADHD both showed alterations in the relation between inter-regional covariance and centroid distance, where both groups show a steeper decline in covariance as a function of distance. The 2 groups also diverge on modular organization, cortical thickness of hub regions and wiring cost of the

Structural Covariance Networks in Children with Autism or ADHD.

PubMed

Bethlehem, R A I; Romero-Garcia, R; Mak, E; Bullmore, E T; Baron-Cohen, S

2017-08-01

While autism and attention-deficit/hyperactivity disorder (ADHD) are considered distinct conditions from a diagnostic perspective, clinically they share some phenotypic features and have high comorbidity. Regardless, most studies have focused on only one condition, with considerable heterogeneity in their results. Taking a dual-condition approach might help elucidate shared and distinct neural characteristics. Graph theory was used to analyse topological properties of structural covariance networks across both conditions and relative to a neurotypical (NT; n = 87) group using data from the ABIDE (autism; n = 62) and ADHD-200 datasets (ADHD; n = 69). Regional cortical thickness was used to construct the structural covariance networks. This was analysed in a theoretical framework examining potential differences in long and short-range connectivity, with a specific focus on relation between central graph measures and cortical thickness. We found convergence between autism and ADHD, where both conditions show an overall decrease in CT covariance with increased Euclidean distance between centroids compared with a NT population. The 2 conditions also show divergence. Namely, there is less modular overlap between the 2 conditions than there is between each condition and the NT group. The ADHD group also showed reduced cortical thickness and lower degree in hub regions than the autism group. Lastly, the ADHD group also showed reduced wiring costs compared with the autism groups. Our results indicate a need for taking an integrated approach when considering highly comorbid conditions such as autism and ADHD. Furthermore, autism and ADHD both showed alterations in the relation between inter-regional covariance and centroid distance, where both groups show a steeper decline in covariance as a function of distance. The 2 groups also diverge on modular organization, cortical thickness of hub regions and wiring cost of the covariance network. Thus, on some network features the

Genome-Wide Networks of Amino Acid Covariances Are Common among Viruses

PubMed Central

Donlin, Maureen J.; Szeto, Brandon; Gohara, David W.; Aurora, Rajeev

2012-01-01

Coordinated variation among positions in amino acid sequence alignments can reveal genetic dependencies at noncontiguous positions, but methods to assess these interactions are incompletely developed. Previously, we found genome-wide networks of covarying residue positions in the hepatitis C virus genome (R. Aurora, M. J. Donlin, N. A. Cannon, and J. E. Tavis, J. Clin. Invest. 119:225–236, 2009). Here, we asked whether such networks are present in a diverse set of viruses and, if so, what they may imply about viral biology. Viral sequences were obtained for 16 viruses in 13 species from 9 families. The entire viral coding potential for each virus was aligned, all possible amino acid covariances were identified using the observed-minus-expected-squared algorithm at a false-discovery rate of ≤1%, and networks of covariances were assessed using standard methods. Covariances that spanned the viral coding potential were common in all viruses. In all cases, the covariances formed a single network that contained essentially all of the covariances. The hepatitis C virus networks had hub-and-spoke topologies, but all other networks had random topologies with an unusually large number of highly connected nodes. These results indicate that genome-wide networks of genetic associations and the coordinated evolution they imply are very common in viral genomes, that the networks rarely have the hub-and-spoke topology that dominates other biological networks, and that network topologies can vary substantially even within a given viral group. Five examples with hepatitis B virus and poliovirus are presented to illustrate how covariance network analysis can lead to inferences about viral biology. PMID:22238298

Alternative Multiple Imputation Inference for Mean and Covariance Structure Modeling

ERIC Educational Resources Information Center

Lee, Taehun; Cai, Li

2012-01-01

Model-based multiple imputation has become an indispensable method in the educational and behavioral sciences. Mean and covariance structure models are often fitted to multiply imputed data sets. However, the presence of multiple random imputations complicates model fit testing, which is an important aspect of mean and covariance structure…

Least-Squares Data Adjustment with Rank-Deficient Data Covariance Matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, J.G.

2011-07-01

A derivation of the linear least-squares adjustment formulae is required that avoids the assumption that the covariance matrix of prior parameters can be inverted. Possible proofs are of several kinds, including: (i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. In this paper, the least-squares adjustment equations are derived in both these ways, while explicitly assuming that the covariance matrix of prior parameters is singular. It will be proved that the solutions are unique and that, contrary to statements that have appeared inmore » the literature, the least-squares adjustment problem is not ill-posed. No modification is required to the adjustment formulae that have been used in the past in the case of a singular covariance matrix for the priors. In conclusion: The linear least-squares adjustment formula that has been used in the past is valid in the case of a singular covariance matrix for the covariance matrix of prior parameters. Furthermore, it provides a unique solution. Statements in the literature, to the effect that the problem is ill-posed are wrong. No regularization of the problem is required. This has been proved in the present paper by two methods, while explicitly assuming that the covariance matrix of prior parameters is singular: i) extension of standard results for the linear regression formulae, and (ii) minimization by differentiation of a quadratic form of the deviations in parameters and responses. No modification is needed to the adjustment formulae that have been used in the past. (author)« less

Covariability of Central America/Mexico winter precipitation and tropical sea surface temperatures

NASA Astrophysics Data System (ADS)

Pan, Yutong; Zeng, Ning; Mariotti, Annarita; Wang, Hui; Kumar, Arun; Sánchez, René Lobato; Jha, Bhaskar

2018-06-01

In this study, the relationships between Central America/Mexico (CAM) winter precipitation and tropical Pacific/Atlantic sea surface temperatures (SSTs) are examined based on 68-year (1948-2015) observations and 59-year (1957-2015) atmospheric model simulations forced by observed SSTs. The covariability of the winter precipitation and SSTs is quantified using the singular value decomposition (SVD) method with observational data. The first SVD mode relates out-of-phase precipitation anomalies in northern Mexico and Central America to the tropical Pacific El Niño/La Niña SST variation. The second mode links a decreasing trend in the precipitation over Central America to the warming of SSTs in the tropical Atlantic, as well as in the tropical western Pacific and the tropical Indian Ocean. The first mode represents 67% of the covariance between the two fields, indicating a strong association between CAM winter precipitation and El Niño/La Niña, whereas the second mode represents 20% of the covariance. The two modes account for 32% of CAM winter precipitation variance, of which, 17% is related to the El Niño/La Niña SST and 15% is related to the SST warming trend. The atmospheric circulation patterns, including 500-hPa height and low-level winds obtained by linear regressions against the SVD SST time series, are dynamically consistent with the precipitation anomaly patterns. The model simulations driven by the observed SSTs suggest that these precipitation anomalies are likely a response to tropical SST forcing. It is also shown that there is significant potential predictability of CAM winter precipitation given tropical SST information.

Analysis of capture-recapture models with individual covariates using data augmentation

USGS Publications Warehouse

Royle, J. Andrew

2009-01-01

I consider the analysis of capture-recapture models with individual covariates that influence detection probability. Bayesian analysis of the joint likelihood is carried out using a flexible data augmentation scheme that facilitates analysis by Markov chain Monte Carlo methods, and a simple and straightforward implementation in freely available software. This approach is applied to a study of meadow voles (Microtus pennsylvanicus) in which auxiliary data on a continuous covariate (body mass) are recorded, and it is thought that detection probability is related to body mass. In a second example, the model is applied to an aerial waterfowl survey in which a double-observer protocol is used. The fundamental unit of observation is the cluster of individual birds, and the size of the cluster (a discrete covariate) is used as a covariate on detection probability.

Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure.

PubMed

Yung, Yiu-Fai; Browne, Michael W; Zhang, Wei

2015-02-01

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple-group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy-to-use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large. © 2014 The British Psychological Society.

A Semiparametric Approach to Simultaneous Covariance Estimation for Bivariate Sparse Longitudinal Data

PubMed Central

Das, Kiranmoy; Daniels, Michael J.

2014-01-01

Summary Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium and low) at baseline. PMID:24400941

Eddy Covariance Method for CO2 Emission Measurements: CCS Applications, Principles, Instrumentation and Software

NASA Astrophysics Data System (ADS)

Burba, George; Madsen, Rod; Feese, Kristin

2013-04-01

The Eddy Covariance method is a micrometeorological technique for direct high-speed measurements of the transport of gases, heat, and momentum between the earth's surface and the atmosphere. Gas fluxes, emission and exchange rates are carefully characterized from single-point in-situ measurements using permanent or mobile towers, or moving platforms such as automobiles, helicopters, airplanes, etc. Since the early 1990s, this technique has been widely used by micrometeorologists across the globe for quantifying CO2 emission rates from various natural, urban and agricultural ecosystems [1,2], including areas of agricultural carbon sequestration. Presently, over 600 eddy covariance stations are in operation in over 120 countries. In the last 3-5 years, advancements in instrumentation and software have reached the point when they can be effectively used outside the area of micrometeorology, and can prove valuable for geological carbon capture and sequestration, landfill emission measurements, high-precision agriculture and other non-micrometeorological industrial and regulatory applications. In the field of geological carbon capture and sequestration, the magnitude of CO2 seepage fluxes depends on a variety of factors. Emerging projects utilize eddy covariance measurement to monitor large areas where CO2 may escape from the subsurface, to detect and quantify CO2 leakage, and to assure the efficiency of CO2 geological storage [3,4,5,6,7,8]. Although Eddy Covariance is one of the most direct and defensible ways to measure and calculate turbulent fluxes, the method is mathematically complex, and requires careful setup, execution and data processing tailor-fit to a specific site and a project. With this in mind, step-by-step instructions were created to introduce a novice to the conventional Eddy Covariance technique [9], and to assist in further understanding the method through more advanced references such as graduate-level textbooks, flux networks guidelines, journals

Covariant Structure of Models of Geophysical Fluid Motion

NASA Astrophysics Data System (ADS)

Dubos, Thomas

2018-01-01

Geophysical models approximate classical fluid motion in rotating frames. Even accurate approximations can have profound consequences, such as the loss of inertial frames. If geophysical fluid dynamics are not strictly equivalent to Newtonian hydrodynamics observed in a rotating frame, what kind of dynamics are they? We aim to clarify fundamental similarities and differences between relativistic, Newtonian, and geophysical hydrodynamics, using variational and covariant formulations as tools to shed the necessary light. A space-time variational principle for the motion of a perfect fluid is introduced. The geophysical action is interpreted as a synchronous limit of the relativistic action. The relativistic Levi-Civita connection also has a finite synchronous limit, which provides a connection with which to endow geophysical space-time, generalizing Cartan (1923). A covariant mass-momentum budget is obtained using covariance of the action and metric-preserving properties of the connection. Ultimately, geophysical models are found to differ from the standard compressible Euler model only by a specific choice of a metric-Coriolis-geopotential tensor akin to the relativistic space-time metric. Once this choice is made, the same covariant mass-momentum budget applies to Newtonian and all geophysical hydrodynamics, including those models lacking an inertial frame. Hence, it is argued that this mass-momentum budget provides an appropriate, common fundamental principle of dynamics. The postulate that Euclidean, inertial frames exist can then be regarded as part of the Newtonian theory of gravitation, which some models of geophysical hydrodynamics slightly violate.

Einstein-aether theory with a Maxwell field: General formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, Alexander B., E-mail: Alexander.Balakin@kpfu.ru; Lemos, José P.S., E-mail: joselemos@ist.utl.pt

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shearmore » and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.« less

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

PubMed Central

2011-01-01

Background The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors. Results We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects. Conclusions The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings. PMID:21269481

Relativistic covariance of Ohm's law

NASA Astrophysics Data System (ADS)

Starke, R.; Schober, G. A. H.

2016-04-01

The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor χμ ν relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between χμ ν and the microscopic conductivity tensor σkℓ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.

Covariance expressions for eigenvalue and eigenvector problems

NASA Astrophysics Data System (ADS)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Covariation assessment for neutral and emotional verbal stimuli in paranoid delusions.

PubMed

Díez-Alegría, Cristina; Vázquez, Carmelo; Hernández-Lloreda, María J

2008-11-01

Selective processing of emotion-relevant information is considered a central feature in various types of psychopathology, yet the mechanisms underlying these biases are not well understood. One of the first steps in processing information is to gather data to judge the covariation or association of events. The aim of this study was to explore whether patients with persecutory delusions would show a covariation bias when processing stimuli related to social threat. We assessed estimations of covariation in-patients with current persecutory (CP) beliefs (N=40), patients with past persecutory (PP) beliefs (N=25), and a non-clinical control (NC) group (N=36). Covariation estimations were assessed under three different experimental conditions. The first two conditions focused on neutral behaviours (Condition 1) and psychological traits (Condition 2) for two distant cultural groups, while the third condition included self-relevant material by exposing the participant to either protective social (positive) or threatening social (negative) statements about the participant or a third person. Our results showed that all participants were precise in their covariation estimations. However, when judging covariation for self-relevant sentences related to social statements (Condition 3), all groups showed a significant tendency to associate positive social interaction (protection themed) sentences to the self. Yet, when using sentences related to social-threat, the CP group showed a bias consisting of overestimating the number of self-referent sentences. Our results showed that there was no specific covariation assessment bias related to paranoid beliefs. Both NCs and participants with persecutory beliefs showed a similar pattern of results when processing neutral or social threat-related sentences. The implications for understanding of the role of self-referent information processing biases in delusion formation are discussed.

Generating survival times to simulate Cox proportional hazards models with time-varying covariates.

PubMed

Austin, Peter C

2012-12-20

Simulations and Monte Carlo methods serve an important role in modern statistical research. They allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible. A key element in any statistical simulation is the existence of an appropriate data-generating process: one must be able to simulate data from a specified statistical model. We describe data-generating processes for the Cox proportional hazards model with time-varying covariates when event times follow an exponential, Weibull, or Gompertz distribution. We consider three types of time-varying covariates: first, a dichotomous time-varying covariate that can change at most once from untreated to treated (e.g., organ transplant); second, a continuous time-varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition; third, a dichotomous time-varying covariate with a subject being able to move repeatedly between treatment states (e.g., current compliance or use of a medication). In each setting, we derive closed-form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time-invariant covariates and to a single time-varying covariate. We illustrate the utility of our closed-form expressions for simulating event times by using Monte Carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time-varying covariates. This is compared with the statistical power to detect as statistically significant a binary time-invariant covariate. Copyright © 2012 John Wiley & Sons, Ltd.

Application of copulas to improve covariance estimation for partial least squares.

PubMed

D'Angelo, Gina M; Weissfeld, Lisa A

2013-02-20

Dimension reduction techniques, such as partial least squares, are useful for computing summary measures and examining relationships in complex settings. Partial least squares requires an estimate of the covariance matrix as a first step in the analysis, making this estimate critical to the results. In addition, the covariance matrix also forms the basis for other techniques in multivariate analysis, such as principal component analysis and independent component analysis. This paper has been motivated by an example from an imaging study in Alzheimer's disease where there is complete separation between Alzheimer's and control subjects for one of the imaging modalities. This separation occurs in one block of variables and does not occur with the second block of variables resulting in inaccurate estimates of the covariance. We propose the use of a copula to obtain estimates of the covariance in this setting, where one set of variables comes from a mixture distribution. Simulation studies show that the proposed estimator is an improvement over the standard estimators of covariance. We illustrate the methods from the motivating example from a study in the area of Alzheimer's disease. Copyright © 2012 John Wiley & Sons, Ltd.

Spatial design and strength of spatial signal: Effects on covariance estimation

USGS Publications Warehouse

Irvine, Kathryn M.; Gitelman, Alix I.; Hoeting, Jennifer A.

2007-01-01

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.

A Formalism for Covariant Polarized Radiative Transport by Ray Tracing

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Leung, Po Kin

2012-06-01

We write down a covariant formalism for polarized radiative transfer appropriate for ray tracing through a turbulent plasma. The polarized radiation field is represented by the polarization tensor (coherency matrix) N αβ ≡ langa α k a*β k rang, where ak is a Fourier coefficient for the vector potential. Using Maxwell's equations, the Liouville-Vlasov equation, and the WKB approximation, we show that the transport equation in vacuo is k μ∇μ N αβ = 0. We show that this is equivalent to Broderick & Blandford's formalism based on invariant Stokes parameters and a rotation coefficient, and suggest a modification that may reduce truncation error in some situations. Finally, we write down several alternative approaches to integrating the transfer equation.

Combinatorial invariants and covariants as tools for conical intersections.

PubMed

Ryb, Itai; Baer, Roi

2004-12-01

The combinatorial invariant and covariant are introduced as practical tools for analysis of conical intersections in molecules. The combinatorial invariant is a quantity depending on adiabatic electronic states taken at discrete nuclear configuration points. It is invariant to the phase choice (gauge) of these states. In the limit that the points trace a loop in nuclear configuration space, the value of the invariant approaches the corresponding Berry phase factor. The Berry phase indicates the presence of an odd or even number of conical intersections on surfaces bounded by these loops. Based on the combinatorial invariant, we develop a computationally simple and efficient method for locating conical intersections. The method is robust due to its use of gauge invariant nature. It does not rely on the landscape of intersecting potential energy surfaces nor does it require the computation of nonadiabatic couplings. We generalize the concept to open paths and combinatorial covariants for higher dimensions obtaining a technique for the construction of the gauge-covariant adiabatic-diabatic transformation matrix. This too does not make use of nonadiabatic couplings. The importance of using gauge-covariant expressions is underlined throughout. These techniques can be readily implemented by standard quantum chemistry codes. (c) 2004 American Institute of Physics.

Simultaneous Mean and Covariance Correction Filter for Orbit Estimation.

PubMed

Wang, Xiaoxu; Pan, Quan; Ding, Zhengtao; Ma, Zhengya

2018-05-05

This paper proposes a novel filtering design, from a viewpoint of identification instead of the conventional nonlinear estimation schemes (NESs), to improve the performance of orbit state estimation for a space target. First, a nonlinear perturbation is viewed or modeled as an unknown input (UI) coupled with the orbit state, to avoid the intractable nonlinear perturbation integral (INPI) required by NESs. Then, a simultaneous mean and covariance correction filter (SMCCF), based on a two-stage expectation maximization (EM) framework, is proposed to simply and analytically fit or identify the first two moments (FTM) of the perturbation (viewed as UI), instead of directly computing such the INPI in NESs. Orbit estimation performance is greatly improved by utilizing the fit UI-FTM to simultaneously correct the state estimation and its covariance. Third, depending on whether enough information is mined, SMCCF should outperform existing NESs or the standard identification algorithms (which view the UI as a constant independent of the state and only utilize the identified UI-mean to correct the state estimation, regardless of its covariance), since it further incorporates the useful covariance information in addition to the mean of the UI. Finally, our simulations demonstrate the superior performance of SMCCF via an orbit estimation example.

Factor Covariance Analysis in Subgroups.

ERIC Educational Resources Information Center

Pennell, Roger

The problem considered is that of an investigator sampling two or more correlation matrices and desiring to fit a model where a factor pattern matrix is assumed to be identical across samples and we need to estimate only the factor covariance matrix and the unique variance for each sample. A flexible, least squares solution is worked out and…

Multiple imputation of covariates by fully conditional specification: Accommodating the substantive model

PubMed Central

Seaman, Shaun R; White, Ian R; Carpenter, James R

2015-01-01

Missing covariate data commonly occur in epidemiological and clinical research, and are often dealt with using multiple imputation. Imputation of partially observed covariates is complicated if the substantive model is non-linear (e.g. Cox proportional hazards model), or contains non-linear (e.g. squared) or interaction terms, and standard software implementations of multiple imputation may impute covariates from models that are incompatible with such substantive models. We show how imputation by fully conditional specification, a popular approach for performing multiple imputation, can be modified so that covariates are imputed from models which are compatible with the substantive model. We investigate through simulation the performance of this proposal, and compare it with existing approaches. Simulation results suggest our proposal gives consistent estimates for a range of common substantive models, including models which contain non-linear covariate effects or interactions, provided data are missing at random and the assumed imputation models are correctly specified and mutually compatible. Stata software implementing the approach is freely available. PMID:24525487

A quantile regression model for failure-time data with time-dependent covariates

PubMed Central

Gorfine, Malka; Goldberg, Yair; Ritov, Ya’acov

2017-01-01

Summary Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This article provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992, Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell, N. P., Dietz, K. and Farewell, V. T. (editors), AIDS Epidemiology. Boston: Birkhaäuser, pp. 297–331.). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset. PMID:27485534

Survival analysis with functional covariates for partial follow-up studies.

PubMed

Fang, Hong-Bin; Wu, Tong Tong; Rapoport, Aaron P; Tan, Ming

2016-12-01

Predictive or prognostic analysis plays an increasingly important role in the era of personalized medicine to identify subsets of patients whom the treatment may benefit the most. Although various time-dependent covariate models are available, such models require that covariates be followed in the whole follow-up period. This article studies a new class of functional survival models where the covariates are only monitored in a time interval that is shorter than the whole follow-up period. This paper is motivated by the analysis of a longitudinal study on advanced myeloma patients who received stem cell transplants and T cell infusions after the transplants. The absolute lymphocyte cell counts were collected serially during hospitalization. Those patients are still followed up if they are alive after hospitalization, while their absolute lymphocyte cell counts cannot be measured after that. Another complication is that absolute lymphocyte cell counts are sparsely and irregularly measured. The conventional method using Cox model with time-varying covariates is not applicable because of the different lengths of observation periods. Analysis based on each single observation obviously underutilizes available information and, more seriously, may yield misleading results. This so-called partial follow-up study design represents increasingly common predictive modeling problem where we have serial multiple biomarkers up to a certain time point, which is shorter than the total length of follow-up. We therefore propose a solution to the partial follow-up design. The new method combines functional principal components analysis and survival analysis with selection of those functional covariates. It also has the advantage of handling sparse and irregularly measured longitudinal observations of covariates and measurement errors. Our analysis based on functional principal components reveals that it is the patterns of the trajectories of absolute lymphocyte cell counts, instead of

Natural Covariant Planck Scale Cutoffs and the Cosmic Microwave Background Spectrum.

PubMed

Chatwin-Davies, Aidan; Kempf, Achim; Martin, Robert T W

2017-07-21

We calculate the impact of quantum gravity-motivated ultraviolet cutoffs on inflationary predictions for the cosmic microwave background spectrum. We model the ultraviolet cutoffs fully covariantly to avoid possible artifacts of covariance breaking. Imposing these covariant cutoffs results in the production of small, characteristically k-dependent oscillations in the spectrum. The size of the effect scales linearly with the ratio of the Planck to Hubble lengths during inflation. Consequently, the relative size of the effect could be as large as one part in 10^{5}; i.e., eventual observability may not be ruled out.

Corrected score estimation in the proportional hazards model with misclassified discrete covariates

PubMed Central

Zucker, David M.; Spiegelman, Donna

2013-01-01

SUMMARY We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain ‘localized error’ condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer. PMID:18219700

Inventory Uncertainty Quantification using TENDL Covariance Data in Fispact-II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eastwood, J.W.; Morgan, J.G.; Sublet, J.-Ch., E-mail: jean-christophe.sublet@ccfe.ac.uk

2015-01-15

The new inventory code Fispact-II provides predictions of inventory, radiological quantities and their uncertainties using nuclear data covariance information. Central to the method is a novel fast pathways search algorithm using directed graphs. The pathways output provides (1) an aid to identifying important reactions, (2) fast estimates of uncertainties, (3) reduced models that retain important nuclides and reactions for use in the code's Monte Carlo sensitivity analysis module. Described are the methods that are being implemented for improving uncertainty predictions, quantification and propagation using the covariance data that the recent nuclear data libraries contain. In the TENDL library, above themore » upper energy of the resolved resonance range, a Monte Carlo method in which the covariance data come from uncertainties of the nuclear model calculations is used. The nuclear data files are read directly by FISPACT-II without any further intermediate processing. Variance and covariance data are processed and used by FISPACT-II to compute uncertainties in collapsed cross sections, and these are in turn used to predict uncertainties in inventories and all derived radiological data.« less

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Improving chemical species tomography of turbulent flows using covariance estimation.

PubMed

Grauer, Samuel J; Hadwin, Paul J; Daun, Kyle J

2017-05-01

Chemical species tomography (CST) experiments can be divided into limited-data and full-rank cases. Both require solving ill-posed inverse problems, and thus the measurement data must be supplemented with prior information to carry out reconstructions. The Bayesian framework formalizes the role of additive information, expressed as the mean and covariance of a joint-normal prior probability density function. We present techniques for estimating the spatial covariance of a flow under limited-data and full-rank conditions. Our results show that incorporating a covariance estimate into CST reconstruction via a Bayesian prior increases the accuracy of instantaneous estimates. Improvements are especially dramatic in real-time limited-data CST, which is directly applicable to many industrially relevant experiments.

Covariate Selection for Multilevel Models with Missing Data

PubMed Central

Marino, Miguel; Buxton, Orfeu M.; Li, Yi

2017-01-01

Missing covariate data hampers variable selection in multilevel regression settings. Current variable selection techniques for multiply-imputed data commonly address missingness in the predictors through list-wise deletion and stepwise-selection methods which are problematic. Moreover, most variable selection methods are developed for independent linear regression models and do not accommodate multilevel mixed effects regression models with incomplete covariate data. We develop a novel methodology that is able to perform covariate selection across multiply-imputed data for multilevel random effects models when missing data is present. Specifically, we propose to stack the multiply-imputed data sets from a multiple imputation procedure and to apply a group variable selection procedure through group lasso regularization to assess the overall impact of each predictor on the outcome across the imputed data sets. Simulations confirm the advantageous performance of the proposed method compared with the competing methods. We applied the method to reanalyze the Healthy Directions-Small Business cancer prevention study, which evaluated a behavioral intervention program targeting multiple risk-related behaviors in a working-class, multi-ethnic population. PMID:28239457

a Simpler Solution of the Non-Uniqueness Problem of the Covariant Dirac Theory

NASA Astrophysics Data System (ADS)

Arminjon, Mayeul

2013-05-01

Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory.

The evolution of phenotypic integration: How directional selection reshapes covariation in mice.

PubMed

Penna, Anna; Melo, Diogo; Bernardi, Sandra; Oyarzabal, Maria Inés; Marroig, Gabriel

2017-10-01

Variation is the basis for evolution, and understanding how variation can evolve is a central question in biology. In complex phenotypes, covariation plays an even more important role, as genetic associations between traits can bias and alter evolutionary change. Covariation can be shaped by complex interactions between loci, and this genetic architecture can also change during evolution. In this article, we analyzed mouse lines experimentally selected for changes in size to address the question of how multivariate covariation changes under directional selection, as well as to identify the consequences of these changes to evolution. Selected lines showed a clear restructuring of covariation in their cranium and, instead of depleting their size variation, these lines increased their magnitude of integration and the proportion of variation associated with the direction of selection. This result is compatible with recent theoretical works on the evolution of covariation that take the complexities of genetic architecture into account. This result also contradicts the traditional view of the effects of selection on available covariation and suggests a much more complex view of how populations respond to selection. © 2017 The Author(s). Evolution published by Wiley Periodicals, Inc. on behalf of The Society for the Study of Evolution.

Algal-bacterial co-variation in streams: a cross-stream comparison

Treesearch

Xueqing Gao; Ola A. Olapade; Mark W. Kershner; Laura G. Leff

2004-01-01

Algal-bacterial co-variation has been frequently observed in lentic and marine environments, but the existence of such relationships in lotic ecosystems is not well established. To examine possible co-variation, bacterial number and chlorophyll-a concentration in water and sediments of nine streams from different regions in the USA were examined. In the water, a strong...

Are Low-order Covariance Estimates Useful in Error Analyses?

NASA Astrophysics Data System (ADS)

Baker, D. F.; Schimel, D.

2005-12-01

Atmospheric trace gas inversions, using modeled atmospheric transport to infer surface sources and sinks from measured concentrations, are most commonly done using least-squares techniques that return not only an estimate of the state (the surface fluxes) but also the covariance matrix describing the uncertainty in that estimate. Besides allowing one to place error bars around the estimate, the covariance matrix may be used in simulation studies to learn what uncertainties would be expected from various hypothetical observing strategies. This error analysis capability is routinely used in designing instrumentation, measurement campaigns, and satellite observing strategies. For example, Rayner, et al (2002) examined the ability of satellite-based column-integrated CO2 measurements to constrain monthly-average CO2 fluxes for about 100 emission regions using this approach. Exact solutions for both state vector and covariance matrix become computationally infeasible, however, when the surface fluxes are solved at finer resolution (e.g., daily in time, under 500 km in space). It is precisely at these finer scales, however, that one would hope to be able to estimate fluxes using high-density satellite measurements. Non-exact estimation methods such as variational data assimilation or the ensemble Kalman filter could be used, but they achieve their computational savings by obtaining an only approximate state estimate and a low-order approximation of the true covariance. One would like to be able to use this covariance matrix to do the same sort of error analyses as are done with the full-rank covariance, but is it correct to do so? Here we compare uncertainties and `information content' derived from full-rank covariance matrices obtained from a direct, batch least squares inversion to those from the incomplete-rank covariance matrices given by a variational data assimilation approach solved with a variable metric minimization technique (the Broyden-Fletcher- Goldfarb

The Covariance Adjustment Approaches for Combining Incomparable Cox Regressions Caused by Unbalanced Covariates Adjustment: A Multivariate Meta-Analysis Study.

PubMed

Dehesh, Tania; Zare, Najaf; Ayatollahi, Seyyed Mohammad Taghi

2015-01-01

Univariate meta-analysis (UM) procedure, as a technique that provides a single overall result, has become increasingly popular. Neglecting the existence of other concomitant covariates in the models leads to loss of treatment efficiency. Our aim was proposing four new approximation approaches for the covariance matrix of the coefficients, which is not readily available for the multivariate generalized least square (MGLS) method as a multivariate meta-analysis approach. We evaluated the efficiency of four new approaches including zero correlation (ZC), common correlation (CC), estimated correlation (EC), and multivariate multilevel correlation (MMC) on the estimation bias, mean square error (MSE), and 95% probability coverage of the confidence interval (CI) in the synthesis of Cox proportional hazard models coefficients in a simulation study. Comparing the results of the simulation study on the MSE, bias, and CI of the estimated coefficients indicated that MMC approach was the most accurate procedure compared to EC, CC, and ZC procedures. The precision ranking of the four approaches according to all above settings was MMC ≥ EC ≥ CC ≥ ZC. This study highlights advantages of MGLS meta-analysis on UM approach. The results suggested the use of MMC procedure to overcome the lack of information for having a complete covariance matrix of the coefficients.

Structural covariance networks across the life span, from 6 to 94 years of age.

PubMed

DuPre, Elizabeth; Spreng, R Nathan

2017-10-01

Structural covariance examines covariation of gray matter morphology between brain regions and across individuals. Despite significant interest in the influence of age on structural covariance patterns, no study to date has provided a complete life span perspective-bridging childhood with early, middle, and late adulthood-on the development of structural covariance networks. Here, we investigate the life span trajectories of structural covariance in six canonical neurocognitive networks: default, dorsal attention, frontoparietal control, somatomotor, ventral attention, and visual. By combining data from five open-access data sources, we examine the structural covariance trajectories of these networks from 6 to 94 years of age in a sample of 1,580 participants. Using partial least squares, we show that structural covariance patterns across the life span exhibit two significant, age-dependent trends. The first trend is a stable pattern whose integrity declines over the life span. The second trend is an inverted-U that differentiates young adulthood from other age groups. Hub regions, including posterior cingulate cortex and anterior insula, appear particularly influential in the expression of this second age-dependent trend. Overall, our results suggest that structural covariance provides a reliable definition of neurocognitive networks across the life span and reveal both shared and network-specific trajectories.

Structural covariance networks across the life span, from 6 to 94 years of age

PubMed Central

DuPre, Elizabeth; Spreng, R. Nathan

2017-01-01

Structural covariance examines covariation of gray matter morphology between brain regions and across individuals. Despite significant interest in the influence of age on structural covariance patterns, no study to date has provided a complete life span perspective—bridging childhood with early, middle, and late adulthood—on the development of structural covariance networks. Here, we investigate the life span trajectories of structural covariance in six canonical neurocognitive networks: default, dorsal attention, frontoparietal control, somatomotor, ventral attention, and visual. By combining data from five open-access data sources, we examine the structural covariance trajectories of these networks from 6 to 94 years of age in a sample of 1,580 participants. Using partial least squares, we show that structural covariance patterns across the life span exhibit two significant, age-dependent trends. The first trend is a stable pattern whose integrity declines over the life span. The second trend is an inverted-U that differentiates young adulthood from other age groups. Hub regions, including posterior cingulate cortex and anterior insula, appear particularly influential in the expression of this second age-dependent trend. Overall, our results suggest that structural covariance provides a reliable definition of neurocognitive networks across the life span and reveal both shared and network-specific trajectories. PMID:29855624

Altered structural covariance of the striatum in functional dyspepsia patients.

PubMed

Liu, P; Zeng, F; Yang, F; Wang, J; Liu, X; Wang, Q; Zhou, G; Zhang, D; Zhu, M; Zhao, R; Wang, A; Gong, Q; Liang, F

2014-08-01

Functional dyspepsia (FD) is thought to be involved in dysregulation within the brain-gut axis. Recently, altered striatum activation has been reported in patients with FD. However, the gray matter (GM) volumes in the striatum and structural covariance patterns of this area are rarely explored. The purpose of this study was to examine the GM volumes and structural covariance patterns of the striatum between FD patients and healthy controls (HCs). T1-weighted magnetic resonance images were obtained from 44 FD patients and 39 HCs. Voxel-based morphometry (VBM) analysis was adopted to examine the GM volumes in the two groups. The caudate- or putamen-related regions identified from VBM analysis were then used as seeds to map the whole brain voxel-wise structural covariance patterns. Finally, a correlation analysis was used to investigate the effects of FD symptoms on the striatum. The results showed increased GM volumes in the bilateral putamen and right caudate. Compared with the structural covariance patterns of the HCs, the FD-related differences were mainly located in the amygdala, hippocampus/parahippocampus (HIPP/paraHIPP), thalamus, lingual gyrus, and cerebellum. And significant positive correlations were found between the volumes in the striatum and the FD duration in the patients. These findings provided preliminary evidence for GM changes in the striatum and different structural covariance patterns in patients with FD. The current results might expand our understanding of the pathophysiology of FD. © 2014 John Wiley & Sons Ltd.

Multilevel covariance regression with correlated random effects in the mean and variance structure.

PubMed

Quintero, Adrian; Lesaffre, Emmanuel

2017-09-01

Multivariate regression methods generally assume a constant covariance matrix for the observations. In case a heteroscedastic model is needed, the parametric and nonparametric covariance regression approaches can be restrictive in the literature. We propose a multilevel regression model for the mean and covariance structure, including random intercepts in both components and allowing for correlation between them. The implied conditional covariance function can be different across clusters as a result of the random effect in the variance structure. In addition, allowing for correlation between the random intercepts in the mean and covariance makes the model convenient for skewedly distributed responses. Furthermore, it permits us to analyse directly the relation between the mean response level and the variability in each cluster. Parameter estimation is carried out via Gibbs sampling. We compare the performance of our model to other covariance modelling approaches in a simulation study. Finally, the proposed model is applied to the RN4CAST dataset to identify the variables that impact burnout of nurses in Belgium. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

NASA Technical Reports Server (NTRS)

Menga, G.

1975-01-01

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

NASA Technical Reports Server (NTRS)

Koch, D. W.

1975-01-01

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

Reconstructing signals from noisy data with unknown signal and noise covariance.

PubMed

Oppermann, Niels; Robbers, Georg; Ensslin, Torsten A

2011-10-01

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle of minimum Gibbs free energy, which was previously used to derive a signal reconstruction algorithm handling uncertainties in the signal covariance. We extend this algorithm to simultaneously uncertain noise and signal covariances using the same principles in the derivation. The resulting equations are general enough to be applied in many different contexts. We demonstrate the performance of the algorithm by applying it to specific example situations and compare it to algorithms not allowing for uncertainties in the noise covariance. The results show that the method we suggest performs very well under a variety of circumstances and is indeed qualitatively superior to the other methods in cases where uncertainty in the noise covariance is present.

The Coriolis field

NASA Astrophysics Data System (ADS)

Costa, L. Filipe; Natário, José

2016-05-01

We present a pedagogical discussion of the Coriolis field, emphasizing its not-so-well-understood aspects. We show that this field satisfies the field equations of the so-called Newton-Cartan theory, a generalization of Newtonian gravity that is covariant under changes of arbitrarily rotating and accelerated frames. Examples of solutions of this theory are given, including the Newtonian analogue of the Gödel universe. We discuss how to detect the Coriolis field by its effect on gyroscopes, of which the gyrocompass is an example. Finally, using a similar framework, we discuss the Coriolis field generated by mass currents in general relativity, and its measurement by the gravity probe B and LAGEOS/LARES experiments.

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Exoatmospheric Applications of Obscurants and Smokes.

DTIC Science & Technology

1985-09-01

field equations (.14)-(19) with substra- tum and their Galilei transformation (24)-(28) represent a field theory in terms of absolute or Galilean space r...of Scientific Research (AFOSR) c ntrat-is-concerned with experimental and theoretical investigations on electrically conducting aerosols for...Another method of reducing the decay rate of ferromagnetic aerosols is to spray the ferromagnetic particles with electric charges. The resulting

Agreement between total corneal astigmatism calculated by vector summation and total corneal astigmatism measured by ray tracing using Galilei double Scheimpflug analyzer.

PubMed

Feizi, Sepehr; Delfazayebaher, Siamak; Ownagh, Vahid; Sadeghpour, Fatemeh

To evaluate the agreement between total corneal astigmatism calculated by vector summation of anterior and posterior corneal astigmatism (TCA Vec ) and total corneal astigmatism measured by ray tracing (TCA Ray ). This study enrolled a total of 204 right eyes of 204 normal subjects. The eyes were measured using a Galilei double Scheimpflug analyzer. The measured parameters included simulated keratometric astigmatism using the keratometric index, anterior corneal astigmatism using the corneal refractive index, posterior corneal astigmatism, and TCA Ray . TCA Vec was derived by vector summation of the astigmatism on the anterior and posterior corneal surfaces. The magnitudes and axes of TCA Vec and TCA Ray were compared. The Pearson correlation coefficient and Bland-Altman plots were used to assess the relationship and agreement between TCA Vec and TCA Ray , respectively. The mean TCA Vec and TCA Ray magnitudes were 0.76±0.57D and 1.00±0.78D, respectively (P<0.001). The mean axis orientations were 85.12±30.26° and 89.67±36.76°, respectively (P=0.02). Strong correlations were found between the TCA Vec and TCA Ray magnitudes (r=0.96, P<0.001). Moderate associations were observed between the TCA Vec and TCA Ray axes (r=0.75, P<0.001). Bland-Altman plots produced the 95% limits of agreement for the TCA Vec and TCA Ray magnitudes from -0.33 to 0.82D. The 95% limits of agreement between the TCA Vec and TCA Ray axes was -43.0 to 52.1°. The magnitudes and axes of astigmatisms measured by the vector summation and ray tracing methods cannot be used interchangeably. There was a systematic error between the TCA Vec and TCA Ray magnitudes. Copyright © 2017 Spanish General Council of Optometry. Published by Elsevier España, S.L.U. All rights reserved.

A comparative study of mixture cure models with covariate

NASA Astrophysics Data System (ADS)

Leng, Oh Yit; Khalid, Zarina Mohd

2017-05-01

In survival analysis, the survival time is assumed to follow a non-negative distribution, such as the exponential, Weibull, and log-normal distributions. In some cases, the survival time is influenced by some observed factors. The absence of these observed factors may cause an inaccurate estimation in the survival function. Therefore, a survival model which incorporates the influences of observed factors is more appropriate to be used in such cases. These observed factors are included in the survival model as covariates. Besides that, there are cases where a group of individuals who are cured, that is, not experiencing the event of interest. Ignoring the cure fraction may lead to overestimate in estimating the survival function. Thus, a mixture cure model is more suitable to be employed in modelling survival data with the presence of a cure fraction. In this study, three mixture cure survival models are used to analyse survival data with a covariate and a cure fraction. The first model includes covariate in the parameterization of the susceptible individuals survival function, the second model allows the cure fraction to depend on covariate, and the third model incorporates covariate in both cure fraction and survival function of susceptible individuals. This study aims to compare the performance of these models via a simulation approach. Therefore, in this study, survival data with varying sample sizes and cure fractions are simulated and the survival time is assumed to follow the Weibull distribution. The simulated data are then modelled using the three mixture cure survival models. The results show that the three mixture cure models are more appropriate to be used in modelling survival data with the presence of cure fraction and an observed factor.

Conditional Covariance-Based Nonparametric Multidimensionality Assessment.

ERIC Educational Resources Information Center

Stout, William; And Others

1996-01-01

Three nonparametric procedures that use estimates of covariances of item-pair responses conditioned on examinee trait level for assessing dimensionality of a test are described. The HCA/CCPROX, DIMTEST, and DETECT are applied to a dimensionality study of the Law School Admission Test. (SLD)

Limited plasticity in the phenotypic variance-covariance matrix for male advertisement calls in the black field cricket, Teleogryllus commodus

PubMed Central

Pitchers, W. R.; Brooks, R.; Jennions, M. D.; Tregenza, T.; Dworkin, I.; Hunt, J.

2013-01-01

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders’ equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent work, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance-covariance matrix (P) stability is sparse, and largely focused on morphological traits. Here we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild-caught crickets from each of the populations and then a second subset after rearing crickets under common-garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high- and low-nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit. PMID:23530814

The causes of variation in the presence of genetic covariance between sexual traits and preferences.

PubMed

Fowler-Finn, Kasey D; Rodríguez, Rafael L

2016-05-01

Mating traits and mate preferences often show patterns of tight correspondence across populations and species. These patterns of apparent coevolution may result from a genetic association between traits and preferences (i.e. trait-preference genetic covariance). We review the literature on trait-preference covariance to determine its prevalence and potential biological relevance. Of the 43 studies we identified, a surprising 63% detected covariance. We test multiple hypotheses for factors that may influence the likelihood of detecting this covariance. The main predictor was the presence of genetic variation in mate preferences, which is one of the three main conditions required for the establishment of covariance. In fact, 89% of the nine studies where heritability of preference was high detected covariance. Variables pertaining to the experimental methods and type of traits involved in different studies did not greatly influence the detection of trait-preference covariance. Trait-preference genetic covariance appears to be widespread and therefore represents an important and currently underappreciated factor in the coevolution of traits and preferences. © 2015 Cambridge Philosophical Society.

Constant covariance in local vertical coordinates for near-circular orbits

NASA Technical Reports Server (NTRS)

Shepperd, Stanley W.

1991-01-01

A method is presented for devising a covariance matrix that either remains constant or grows in keeping with the presence of a period error in a rotating local-vertical coordinate system. The solution presented may prove useful in the initialization of simulation covariance matrices for near-circular-orbit problems. Use is made of the Clohessy-Wiltshire equations and the travelling-ellipse formulation.

SMURC: High-Dimension Small-Sample Multivariate Regression With Covariance Estimation.

PubMed

Bayar, Belhassen; Bouaynaya, Nidhal; Shterenberg, Roman

2017-03-01

We consider a high-dimension low sample-size multivariate regression problem that accounts for correlation of the response variables. The system is underdetermined as there are more parameters than samples. We show that the maximum likelihood approach with covariance estimation is senseless because the likelihood diverges. We subsequently propose a normalization of the likelihood function that guarantees convergence. We call this method small-sample multivariate regression with covariance (SMURC) estimation. We derive an optimization problem and its convex approximation to compute SMURC. Simulation results show that the proposed algorithm outperforms the regularized likelihood estimator with known covariance matrix and the sparse conditional Gaussian graphical model. We also apply SMURC to the inference of the wing-muscle gene network of the Drosophila melanogaster (fruit fly).

Visualizing DOM super-spectrum covariance in vanKrevelen space

NASA Astrophysics Data System (ADS)

Fatland, D. R.; Kalawe, J.; Stubbins, A.; Spencer, R. G.; Sleighter, R. L.; Abdulla, H. A.; Dittmar, T.

2011-12-01

We investigate the fate of terrigenous organic matter, DOM exported to the coastal marine environ. Many methods (fluor., FT-ICR-MS, NMR, 13C, lignin, etc) help characterize this DOM. We define a 'super spectrum' as amalgamation of analyses to a data stack and we search for physically significant patterns therein beginning with covariance across 31 samples from six circum-Arctic rivers: The Ob, Kolyma, Mackenzie, Yukon, Lena, and Yenisey sampled five times throughout the year. A vanKrevelen diagram is convenient to view distributions of molecules provided by Fourier Transform Ion Cyclotron Resonance Mass Spectometry (FT-ICR-MS). We augment this distribution space in the vertical dimension, for example to show peak height, molecular mass, principle component weighting or covariance. We use Worldwide Telescope, a virtual globe with strong data support from Microsoft Research to explore covariance results along 3+ dimensions (adding brightness, color and a parameter slide). The results show interesting covariance e.g. between molecules and PARAFAC peaks, a step towards fluorophore and cohort identification in the terrigenous DOM spectrum. Given the geoscience explosion in data volume and data complexity we feel these results should survive beyond the end point of a journal article. We are building a cloud-based Library on the Microsoft Azure platform to support this and subsequent analyses to enable data and methods to carry over and benefit other research groups and objectives.

An Adaptive Low-Cost INS/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation.

PubMed

Li, Zheng; Zhang, Hai; Zhou, Qifan; Che, Huan

2017-09-05

The main objective of the introduced study is to design an adaptive Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) tightly-coupled integration system that can provide more reliable navigation solutions by making full use of an adaptive Kalman filter (AKF) and satellite selection algorithm. To achieve this goal, we develop a novel redundant measurement noise covariance estimation (RMNCE) theorem, which adaptively estimates measurement noise properties by analyzing the difference sequences of system measurements. The proposed RMNCE approach is then applied to design both a modified weighted satellite selection algorithm and a type of adaptive unscented Kalman filter (UKF) to improve the performance of the tightly-coupled integration system. In addition, an adaptive measurement noise covariance expanding algorithm is developed to mitigate outliers when facing heavy multipath and other harsh situations. Both semi-physical simulation and field experiments were conducted to evaluate the performance of the proposed architecture and were compared with state-of-the-art algorithms. The results validate that the RMNCE provides a significant improvement in the measurement noise covariance estimation and the proposed architecture can improve the accuracy and reliability of the INS/GNSS tightly-coupled systems. The proposed architecture can effectively limit positioning errors under conditions of poor GNSS measurement quality and outperforms all the compared schemes.

An Adaptive Low-Cost INS/GNSS Tightly-Coupled Integration Architecture Based on Redundant Measurement Noise Covariance Estimation

PubMed Central

Li, Zheng; Zhang, Hai; Zhou, Qifan; Che, Huan

2017-01-01

The main objective of the introduced study is to design an adaptive Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) tightly-coupled integration system that can provide more reliable navigation solutions by making full use of an adaptive Kalman filter (AKF) and satellite selection algorithm. To achieve this goal, we develop a novel redundant measurement noise covariance estimation (RMNCE) theorem, which adaptively estimates measurement noise properties by analyzing the difference sequences of system measurements. The proposed RMNCE approach is then applied to design both a modified weighted satellite selection algorithm and a type of adaptive unscented Kalman filter (UKF) to improve the performance of the tightly-coupled integration system. In addition, an adaptive measurement noise covariance expanding algorithm is developed to mitigate outliers when facing heavy multipath and other harsh situations. Both semi-physical simulation and field experiments were conducted to evaluate the performance of the proposed architecture and were compared with state-of-the-art algorithms. The results validate that the RMNCE provides a significant improvement in the measurement noise covariance estimation and the proposed architecture can improve the accuracy and reliability of the INS/GNSS tightly-coupled systems. The proposed architecture can effectively limit positioning errors under conditions of poor GNSS measurement quality and outperforms all the compared schemes. PMID:28872629

Evaluation of Approaches to Deal with Low-Frequency Nuisance Covariates in Population Pharmacokinetic Analyses.

PubMed

Lagishetty, Chakradhar V; Duffull, Stephen B

2015-11-01

Clinical studies include occurrences of rare variables, like genotypes, which due to their frequency and strength render their effects difficult to estimate from a dataset. Variables that influence the estimated value of a model-based parameter are termed covariates. It is often difficult to determine if such an effect is significant, since type I error can be inflated when the covariate is rare. Their presence may have either an insubstantial effect on the parameters of interest, hence are ignorable, or conversely they may be influential and therefore non-ignorable. In the case that these covariate effects cannot be estimated due to power and are non-ignorable, then these are considered nuisance, in that they have to be considered but due to type 1 error are of limited interest. This study assesses methods of handling nuisance covariate effects. The specific objectives include (1) calibrating the frequency of a covariate that is associated with type 1 error inflation, (2) calibrating its strength that renders it non-ignorable and (3) evaluating methods for handling these non-ignorable covariates in a nonlinear mixed effects model setting. Type 1 error was determined for the Wald test. Methods considered for handling the nuisance covariate effects were case deletion, Box-Cox transformation and inclusion of a specific fixed effects parameter. Non-ignorable nuisance covariates were found to be effectively handled through addition of a fixed effect parameter.

New symmetries and ghost structure of covariant string theories

NASA Astrophysics Data System (ADS)

Neveu, A.; Nicolai, H.; West, P.

1986-02-01

It is shown that there exists an infinite set of new symmetries of the previously given covariant string formulations. These symmetries have themselves an infinite set of hidden local symmetries and so on. A new physically equivalent further extended string action is given in which the infinite set of symmetries is most easily displayed. A quantization involving gauge fixing and ghosts of the various covariant string actions is given. permanent address: Kings College, Mathematics Department, London WC2R 2LS, UK.

Noncommutative Field Theories and (super)string Field Theories

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Belov, D. M.; Giryavets, A. A.; Koshelev, A. S.; Medvedev, P. B.

2002-11-01

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, "comma" and matrix representations of vertices.

Power and money in cluster randomized trials: when is it worth measuring a covariate?

PubMed

Moerbeek, Mirjam

2006-08-15

The power to detect a treatment effect in cluster randomized trials can be increased by increasing the number of clusters. An alternative is to include covariates into the regression model that relates treatment condition to outcome. In this paper, formulae are derived in order to evaluate both strategies on basis of their costs. It is shown that the strategy that uses covariates is more cost-efficient in detecting a treatment effect when the costs to measure these covariates are small and the correlation between the covariates and outcome is sufficiently large. The minimum required correlation depends on the cluster size, and the costs to recruit a cluster and to measure the covariate, relative to the costs to recruit a person. Measuring a covariate that varies at the person level only is recommended when cluster sizes are small and the costs to recruit and measure a cluster are large. Measuring a cluster level covariate is recommended when cluster sizes are large and the costs to recruit and measure a cluster are small. An illustrative example shows the use of the formulae in a practical setting. Copyright 2006 John Wiley & Sons, Ltd.

(13)C-(15)N correlation via unsymmetrical indirect covariance NMR: application to vinblastine.

PubMed

Martin, Gary E; Hilton, Bruce D; Blinov, Kirill A; Williams, Antony J

2007-12-01

Unsymmetrical indirect covariance processing methods allow the derivation of hyphenated 2D NMR data from the component 2D spectra, potentially circumventing the acquisition of the much lower sensitivity hyphenated 2D NMR experimental data. Calculation of HSQC-COSY and HSQC-NOESY spectra from GHSQC, COSY, and NOESY spectra, respectively, has been reported. The use of unsymmetrical indirect covariance processing has also been applied to the combination of (1)H- (13)C GHSQC and (1)H- (15)N long-range correlation data (GHMBC, IMPEACH, or CIGAR-HMBC). The application of unsymmetrical indirect covariance processing to spectra of vinblastine is now reported, specifically the algorithmic extraction of (13)C- (15)N correlations via the unsymmetrical indirect covariance processing of the combination of (1)H- (13)C GHSQC and long-range (1)H- (15)N GHMBC to produce the equivalent of a (13)C- (15)N HSQC-HMBC correlation spectrum. The elimination of artifact responses with aromatic solvent-induced shifts (ASIS) is shown in addition to a method of forecasting potential artifact responses through the indirect covariance processing of the GHSQC spectrum used in the unsymmetrical indirect covariance processing.

Evaluation of subset matching methods and forms of covariate balance.

PubMed

de Los Angeles Resa, María; Zubizarreta, José R

2016-11-30

This paper conducts a Monte Carlo simulation study to evaluate the performance of multivariate matching methods that select a subset of treatment and control observations. The matching methods studied are the widely used nearest neighbor matching with propensity score calipers and the more recently proposed methods, optimal matching of an optimally chosen subset and optimal cardinality matching. The main findings are: (i) covariate balance, as measured by differences in means, variance ratios, Kolmogorov-Smirnov distances, and cross-match test statistics, is better with cardinality matching because by construction it satisfies balance requirements; (ii) for given levels of covariate balance, the matched samples are larger with cardinality matching than with the other methods; (iii) in terms of covariate distances, optimal subset matching performs best; (iv) treatment effect estimates from cardinality matching have lower root-mean-square errors, provided strong requirements for balance, specifically, fine balance, or strength-k balance, plus close mean balance. In standard practice, a matched sample is considered to be balanced if the absolute differences in means of the covariates across treatment groups are smaller than 0.1 standard deviations. However, the simulation results suggest that stronger forms of balance should be pursued in order to remove systematic biases due to observed covariates when a difference in means treatment effect estimator is used. In particular, if the true outcome model is additive, then marginal distributions should be balanced, and if the true outcome model is additive with interactions, then low-dimensional joints should be balanced. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Metrics for covariate balance in cohort studies of causal effects.

PubMed

Franklin, Jessica M; Rassen, Jeremy A; Ackermann, Diana; Bartels, Dorothee B; Schneeweiss, Sebastian

2014-05-10

Inferring causation from non-randomized studies of exposure requires that exposure groups can be balanced with respect to prognostic factors for the outcome. Although there is broad agreement in the literature that balance should be checked, there is confusion regarding the appropriate metric. We present a simulation study that compares several balance metrics with respect to the strength of their association with bias in estimation of the effect of a binary exposure on a binary, count, or continuous outcome. The simulations utilize matching on the propensity score with successively decreasing calipers to produce datasets with varying covariate balance. We propose the post-matching C-statistic as a balance metric and found that it had consistently strong associations with estimation bias, even when the propensity score model was misspecified, as long as the propensity score was estimated with sufficient study size. This metric, along with the average standardized difference and the general weighted difference, outperformed all other metrics considered in association with bias, including the unstandardized absolute difference, Kolmogorov-Smirnov and Lévy distances, overlapping coefficient, Mahalanobis balance, and L1 metrics. Of the best-performing metrics, the C-statistic and general weighted difference also have the advantage that they automatically evaluate balance on all covariates simultaneously and can easily incorporate balance on interactions among covariates. Therefore, when combined with the usual practice of comparing individual covariate means and standard deviations across exposure groups, these metrics may provide useful summaries of the observed covariate imbalance. Copyright © 2013 John Wiley & Sons, Ltd.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances.

PubMed

Gil, Manuel

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error.

Fast and accurate estimation of the covariance between pairwise maximum likelihood distances

PubMed Central

2014-01-01

Pairwise evolutionary distances are a model-based summary statistic for a set of molecular sequences. They represent the leaf-to-leaf path lengths of the underlying phylogenetic tree. Estimates of pairwise distances with overlapping paths covary because of shared mutation events. It is desirable to take these covariance structure into account to increase precision in any process that compares or combines distances. This paper introduces a fast estimator for the covariance of two pairwise maximum likelihood distances, estimated under general Markov models. The estimator is based on a conjecture (going back to Nei & Jin, 1989) which links the covariance to path lengths. It is proven here under a simple symmetric substitution model. A simulation shows that the estimator outperforms previously published ones in terms of the mean squared error. PMID:25279263

A generalized spatiotemporal covariance model for stationary background in analysis of MEG data.

PubMed

Plis, S M; Schmidt, D M; Jun, S C; Ranken, D M

2006-01-01

Using a noise covariance model based on a single Kronecker product of spatial and temporal covariance in the spatiotemporal analysis of MEG data was demonstrated to provide improvement in the results over that of the commonly used diagonal noise covariance model. In this paper we present a model that is a generalization of all of the above models. It describes models based on a single Kronecker product of spatial and temporal covariance as well as more complicated multi-pair models together with any intermediate form expressed as a sum of Kronecker products of spatial component matrices of reduced rank and their corresponding temporal covariance matrices. The model provides a framework for controlling the tradeoff between the described complexity of the background and computational demand for the analysis using this model. Ways to estimate the value of the parameter controlling this tradeoff are also discussed.

Solid-state NMR covariance of homonuclear correlation spectra.

PubMed

Hu, Bingwen; Amoureux, Jean-Paul; Trebosc, Julien; Deschamps, Michael; Tricot, Gregory

2008-04-07

Direct covariance NMR spectroscopy, which does not involve a Fourier transformation along the indirect dimension, is demonstrated to obtain homonuclear correlation two-dimensional (2D) spectra in the solid state. In contrast to the usual 2D Fourier transform (2D-FT) NMR, in a 2D covariance (2D-Cov) spectrum the spectral resolution in the indirect dimension is determined by the resolution along the detection dimension, thereby largely reducing the time-consuming indirect sampling requirement. The covariance method does not need any separate phase correction or apodization along the indirect dimension because it uses those applied in the detection dimension. We compare in detail the specifications obtained with 2D-FT and 2D-Cov, for narrow and broad resonances. The efficiency of the covariance data treatment is demonstrated in organic and inorganic samples that are both well crystallized and amorphous, for spin -1/2 nuclei with 13C, 29Si, and 31P through-space or through-bond homonuclear 2D correlation spectra. In all cases, the experimental time has been reduced by at least a factor of 10, without any loss of resolution and signal to noise ratio, with respect to what is necessary with the 2D-FT NMR. According to this method, we have been able to study the silicate network of glasses by 2D NMR within reasonable experimental time despite the very long relaxation time of the 29Si nucleus. The main limitation of the 2D-Cov data treatment is related to the introduction of autocorrelated peaks onto the diagonal, which does not represent any actual connectivity.

White matter tract covariance patterns predict age-declining cognitive abilities.

PubMed

Gazes, Yunglin; Bowman, F DuBois; Razlighi, Qolamreza R; O'Shea, Deirdre; Stern, Yaakov; Habeck, Christian

2016-01-15

Previous studies investigating the relationship of white matter (WM) integrity to cognitive abilities and aging have either focused on a global measure or a few selected WM tracts. Ideally, contribution from all of the WM tracts should be evaluated at the same time. However, the high collinearity among WM tracts precludes systematic examination of WM tracts simultaneously without sacrificing statistical power due to stringent multiple-comparison corrections. Multivariate covariance techniques enable comprehensive simultaneous examination of all WM tracts without being penalized for high collinearity among observations. In this study, Scaled Subprofile Modeling (SSM) was applied to the mean integrity of 18 major WM tracts to extract covariance patterns that optimally predicted four cognitive abilities (perceptual speed, episodic memory, fluid reasoning, and vocabulary) in 346 participants across ages 20 to 79years old. Using expression of the covariance patterns, age-independent effects of white matter integrity on cognition and the indirect effect of WM integrity on age-related differences in cognition were tested separately, but inferences from the indirect analyses were cautiously made given that cross-sectional data set was used in the analysis. A separate covariance pattern was identified that significantly predicted each cognitive ability after controlling for age except for vocabulary, but the age by WM covariance pattern interaction was not significant for any of the three abilities. Furthermore, each of the patterns mediated the effect of age on the respective cognitive ability. A distinct set of WM tracts was most influential in each of the three patterns. The WM covariance pattern accounting for fluid reasoning showed the most number of influential WM tracts whereas the episodic memory pattern showed the least number. Specific patterns of WM tracts make significant contributions to the age-related differences in perceptual speed, episodic memory, and

Working covariance model selection for generalized estimating equations.

PubMed

Carey, Vincent J; Wang, You-Gan

2011-11-20

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

Effects of Nicotine Deprivation on Craving Response Covariation in Smokers

PubMed Central

Sayette, Michael A.; Martin, Christopher S.; Hull, Jay G.; Wertz, Joan M.; Perrott, Michael A.

2009-01-01

Most models of craving propose that when cravings are strong, diverse responses—thought to index an underlying craving state— covary. Previous studies provided weak support for this hypothesis. The authors tested whether nicotine deprivation affects degree of covariation across multiple measures related to craving. Heavy and light smokers (N = 127) were exposed to smoking cues while either nicotine deprived or nondeprived. Measures included urge ratings, affective valence, a behavioral choice task assessing perceived reinforcement value of smoking, and smoking-related judgment tasks. Results indicated higher correlations in the nicotine-deprived than in nondeprived group. The measures principally responsible for this effect loaded onto a single common Craving factor for nicotine-deprived but not nondeprived smokers. These findings suggest that, under certain conditions, measures of craving-related processes covary. PMID:12653419

Using Fit Indexes to Select a Covariance Model for Longitudinal Data

ERIC Educational Resources Information Center

Liu, Siwei; Rovine, Michael J.; Molenaar, Peter C. M.

2012-01-01

This study investigated the performance of fit indexes in selecting a covariance structure for longitudinal data. Data were simulated to follow a compound symmetry, first-order autoregressive, first-order moving average, or random-coefficients covariance structure. We examined the ability of the likelihood ratio test (LRT), root mean square error…

Simulation-Extrapolation for Estimating Means and Causal Effects with Mismeasured Covariates

ERIC Educational Resources Information Center

Lockwood, J. R.; McCaffrey, Daniel F.

2015-01-01

Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with…

Structural covariance of brain region volumes is associated with both structural connectivity and transcriptomic similarity.

PubMed

Yee, Yohan; Fernandes, Darren J; French, Leon; Ellegood, Jacob; Cahill, Lindsay S; Vousden, Dulcie A; Spencer Noakes, Leigh; Scholz, Jan; van Eede, Matthijs C; Nieman, Brian J; Sled, John G; Lerch, Jason P

2018-05-18

An organizational pattern seen in the brain, termed structural covariance, is the statistical association of pairs of brain regions in their anatomical properties. These associations, measured across a population as covariances or correlations usually in cortical thickness or volume, are thought to reflect genetic and environmental underpinnings. Here, we examine the biological basis of structural volume covariance in the mouse brain. We first examined large scale associations between brain region volumes using an atlas-based approach that parcellated the entire mouse brain into 318 regions over which correlations in volume were assessed, for volumes obtained from 153 mouse brain images via high-resolution MRI. We then used a seed-based approach and determined, for 108 different seed regions across the brain and using mouse gene expression and connectivity data from the Allen Institute for Brain Science, the variation in structural covariance data that could be explained by distance to seed, transcriptomic similarity to seed, and connectivity to seed. We found that overall, correlations in structure volumes hierarchically clustered into distinct anatomical systems, similar to findings from other studies and similar to other types of networks in the brain, including structural connectivity and transcriptomic similarity networks. Across seeds, this structural covariance was significantly explained by distance (17% of the variation, up to a maximum of 49% for structural covariance to the visceral area of the cortex), transcriptomic similarity (13% of the variation, up to maximum of 28% for structural covariance to the primary visual area) and connectivity (15% of the variation, up to a maximum of 36% for structural covariance to the intermediate reticular nucleus in the medulla) of covarying structures. Together, distance, connectivity, and transcriptomic similarity explained 37% of structural covariance, up to a maximum of 63% for structural covariance to the

Autism-Specific Covariation in Perceptual Performances: “g” or “p” Factor?

PubMed Central

Meilleur, Andrée-Anne S.; Berthiaume, Claude; Bertone, Armando; Mottron, Laurent

2014-01-01

Background Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination) and mid-level (e.g., pattern matching) tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals. Methods We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ) and Raven Progressive Matrices (RPM). We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence. Results In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism. Conclusions Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or “g” factor). Instead, this residual covariation is accounted for by a common perceptual process (or “p” factor), which may drive

Treatment selection in a randomized clinical trial via covariate-specific treatment effect curves.

PubMed

Ma, Yunbei; Zhou, Xiao-Hua

2017-02-01

For time-to-event data in a randomized clinical trial, we proposed two new methods for selecting an optimal treatment for a patient based on the covariate-specific treatment effect curve, which is used to represent the clinical utility of a predictive biomarker. To select an optimal treatment for a patient with a specific biomarker value, we proposed pointwise confidence intervals for each covariate-specific treatment effect curve and the difference between covariate-specific treatment effect curves of two treatments. Furthermore, to select an optimal treatment for a future biomarker-defined subpopulation of patients, we proposed confidence bands for each covariate-specific treatment effect curve and the difference between each pair of covariate-specific treatment effect curve over a fixed interval of biomarker values. We constructed the confidence bands based on a resampling technique. We also conducted simulation studies to evaluate finite-sample properties of the proposed estimation methods. Finally, we illustrated the application of the proposed method in a real-world data set.

Comparison of bias-corrected covariance estimators for MMRM analysis in longitudinal data with dropouts.

PubMed

Gosho, Masahiko; Hirakawa, Akihiro; Noma, Hisashi; Maruo, Kazushi; Sato, Yasunori

2017-10-01

In longitudinal clinical trials, some subjects will drop out before completing the trial, so their measurements towards the end of the trial are not obtained. Mixed-effects models for repeated measures (MMRM) analysis with "unstructured" (UN) covariance structure are increasingly common as a primary analysis for group comparisons in these trials. Furthermore, model-based covariance estimators have been routinely used for testing the group difference and estimating confidence intervals of the difference in the MMRM analysis using the UN covariance. However, using the MMRM analysis with the UN covariance could lead to convergence problems for numerical optimization, especially in trials with a small-sample size. Although the so-called sandwich covariance estimator is robust to misspecification of the covariance structure, its performance deteriorates in settings with small-sample size. We investigated the performance of the sandwich covariance estimator and covariance estimators adjusted for small-sample bias proposed by Kauermann and Carroll ( J Am Stat Assoc 2001; 96: 1387-1396) and Mancl and DeRouen ( Biometrics 2001; 57: 126-134) fitting simpler covariance structures through a simulation study. In terms of the type 1 error rate and coverage probability of confidence intervals, Mancl and DeRouen's covariance estimator with compound symmetry, first-order autoregressive (AR(1)), heterogeneous AR(1), and antedependence structures performed better than the original sandwich estimator and Kauermann and Carroll's estimator with these structures in the scenarios where the variance increased across visits. The performance based on Mancl and DeRouen's estimator with these structures was nearly equivalent to that based on the Kenward-Roger method for adjusting the standard errors and degrees of freedom with the UN structure. The model-based covariance estimator with the UN structure under unadjustment of the degrees of freedom, which is frequently used in applications

A formal and data-based comparison of measures of motor-equivalent covariation.

PubMed

Verrel, Julius

2011-09-15

Different analysis methods have been developed for assessing motor-equivalent organization of movement variability. In the uncontrolled manifold (UCM) method, the structure of variability is analyzed by comparing goal-equivalent and non-goal-equivalent variability components at the level of elemental variables (e.g., joint angles). In contrast, in the covariation by randomization (CR) approach, motor-equivalent organization is assessed by comparing variability at the task level between empirical and decorrelated surrogate data. UCM effects can be due to both covariation among elemental variables and selective channeling of variability to elemental variables with low task sensitivity ("individual variation"), suggesting a link between the UCM and CR method. However, the precise relationship between the notion of covariation in the two approaches has not been analyzed in detail yet. Analysis of empirical and simulated data from a study on manual pointing shows that in general the two approaches are not equivalent, but the respective covariation measures are highly correlated (ρ > 0.7) for two proposed definitions of covariation in the UCM context. For one-dimensional task spaces, a formal comparison is possible and in fact the two notions of covariation are equivalent. In situations in which individual variation does not contribute to UCM effects, for which necessary and sufficient conditions are derived, this entails the equivalence of the UCM and CR analysis. Implications for the interpretation of UCM effects are discussed. Copyright © 2011 Elsevier B.V. All rights reserved.

Examination of various roles for covariance matrices in the development, evaluation, and application of nuclear data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, D.L.

The last decade has been a period of rapid development in the implementation of covariance-matrix methodology in nuclear data research. This paper offers some perspective on the progress which has been made, on some of the unresolved problems, and on the potential yet to be realized. These discussions address a variety of issues related to the development of nuclear data. Topics examined are: the importance of designing and conducting experiments so that error information is conveniently generated; the procedures for identifying error sources and quantifying their magnitudes and correlations; the combination of errors; the importance of consistent and well-characterized measurementmore » standards; the role of covariances in data parameterization (fitting); the estimation of covariances for values calculated from mathematical models; the identification of abnormalities in covariance matrices and the analysis of their consequences; the problems encountered in representing covariance information in evaluated files; the role of covariances in the weighting of diverse data sets; the comparison of various evaluations; the influence of primary-data covariance in the analysis of covariances for derived quantities (sensitivity); and the role of covariances in the merging of the diverse nuclear data information. 226 refs., 2 tabs.« less

Treatment decisions based on scalar and functional baseline covariates.

PubMed

Ciarleglio, Adam; Petkova, Eva; Ogden, R Todd; Tarpey, Thaddeus

2015-12-01

The amount and complexity of patient-level data being collected in randomized-controlled trials offer both opportunities and challenges for developing personalized rules for assigning treatment for a given disease or ailment. For example, trials examining treatments for major depressive disorder are not only collecting typical baseline data such as age, gender, or scores on various tests, but also data that measure the structure and function of the brain such as images from magnetic resonance imaging (MRI), functional MRI (fMRI), or electroencephalography (EEG). These latter types of data have an inherent structure and may be considered as functional data. We propose an approach that uses baseline covariates, both scalars and functions, to aid in the selection of an optimal treatment. In addition to providing information on which treatment should be selected for a new patient, the estimated regime has the potential to provide insight into the relationship between treatment response and the set of baseline covariates. Our approach can be viewed as an extension of "advantage learning" to include both scalar and functional covariates. We describe our method and how to implement it using existing software. Empirical performance of our method is evaluated with simulated data in a variety of settings and also applied to data arising from a study of patients with major depressive disorder from whom baseline scalar covariates as well as functional data from EEG are available. © 2015, The International Biometric Society.

Eddy Covariance Measurements of the Sea-Spray Aerosol Flu

NASA Astrophysics Data System (ADS)

Brooks, I. M.; Norris, S. J.; Yelland, M. J.; Pascal, R. W.; Prytherch, J.

2015-12-01

Historically, almost all estimates of the sea-spray aerosol source flux have been inferred through various indirect methods. Direct estimates via eddy covariance have been attempted by only a handful of studies, most of which measured only the total number flux, or achieved rather coarse size segregation. Applying eddy covariance to the measurement of sea-spray fluxes is challenging: most instrumentation must be located in a laboratory space requiring long sample lines to an inlet collocated with a sonic anemometer; however, larger particles are easily lost to the walls of the sample line. Marine particle concentrations are generally low, requiring a high sample volume to achieve adequate statistics. The highly hygroscopic nature of sea salt means particles change size rapidly with fluctuations in relative humidity; this introduces an apparent bias in flux measurements if particles are sized at ambient humidity. The Compact Lightweight Aerosol Spectrometer Probe (CLASP) was developed specifically to make high rate measurements of aerosol size distributions for use in eddy covariance measurements, and the instrument and data processing and analysis techniques have been refined over the course of several projects. Here we will review some of the issues and limitations related to making eddy covariance measurements of the sea spray source flux over the open ocean, summarise some key results from the last decade, and present new results from a 3-year long ship-based measurement campaign as part of the WAGES project. Finally we will consider requirements for future progress.

Linear Regression with a Randomly Censored Covariate: Application to an Alzheimer's Study.

PubMed

Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A

2017-01-01

The association between maternal age of onset of dementia and amyloid deposition (measured by in vivo positron emission tomography (PET) imaging) in cognitively normal older offspring is of interest. In a regression model for amyloid, special methods are required due to the random right censoring of the covariate of maternal age of onset of dementia. Prior literature has proposed methods to address the problem of censoring due to assay limit of detection, but not random censoring. We propose imputation methods and a survival regression method that do not require parametric assumptions about the distribution of the censored covariate. Existing imputation methods address missing covariates, but not right censored covariates. In simulation studies, we compare these methods to the simple, but inefficient complete case analysis, and to thresholding approaches. We apply the methods to the Alzheimer's study.

Quasilocal conserved charges in a covariant theory of gravity.

PubMed

Kim, Wontae; Kulkarni, Shailesh; Yi, Sang-Heon

2013-08-23

In any generally covariant theory of gravity, we show the relationship between the linearized asymptotically conserved current and its nonlinear completion through the identically conserved current. Our formulation for conserved charges is based on the Lagrangian description, and so completely covariant. By using this result, we give a prescription to define quasilocal conserved charges in any higher derivative gravity. As applications of our approach, we demonstrate the angular momentum invariance along the radial direction of black holes and reproduce more efficiently the linearized potential on the asymptotic anti-de Sitter space.

Consistent compactification of double field theory on non-geometric flux backgrounds

NASA Astrophysics Data System (ADS)

Hassler, Falk; Lüst, Dieter

2014-05-01

In this paper, we construct non-trivial solutions to the 2 D-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies 2( D - d) internal directions with a twist U M N which is directly connected to the covariant fluxes ABC . It exhibits 2( D - d) linear independent generalized Killing vectors K I J and gives rise to a gauged supergravity in d dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For ( D - d) = 3 we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

Kernel Equating Under the Non-Equivalent Groups With Covariates Design

PubMed Central

Bränberg, Kenny

2015-01-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests. PMID:29881012

The evolutionary stability of cross-sex, cross-trait genetic covariances.

PubMed

Gosden, Thomas P; Chenoweth, Stephen F

2014-06-01

Although knowledge of the selective agents behind the evolution of sexual dimorphism has advanced considerably in recent years, we still lack a clear understanding of the evolutionary durability of cross-sex genetic covariances that often constrain its evolution. We tested the relative stability of cross-sex genetic covariances for a suite of homologous contact pheromones of the fruit fly Drosophila serrata, along a latitudinal gradient where these traits have diverged in mean. Using a Bayesian framework, which allowed us to account for uncertainty in all parameter estimates, we compared divergence in the total amount and orientation of genetic variance across populations, finding divergence in orientation but not total variance. We then statistically compared orientation divergence of within-sex (G) to cross-sex (B) covariance matrices. In line with a previous theoretical prediction, we find that the cross-sex covariance matrix, B, is more variable than either within-sex G matrix. Decomposition of B matrices into their symmetrical and nonsymmetrical components revealed that instability is linked to the degree of asymmetry. We also find that the degree of asymmetry correlates with latitude suggesting a role for spatially varying natural selection in shaping genetic constraints on the evolution of sexual dimorphism. © 2014 The Author(s). Evolution © 2014 The Society for the Study of Evolution.

Kernel Equating Under the Non-Equivalent Groups With Covariates Design.

PubMed

Wiberg, Marie; Bränberg, Kenny

2015-07-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests.

TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION

PubMed Central

Allen, Genevera I.; Tibshirani, Robert

2015-01-01

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so called transposable regularized covariance models allow for maximum likelihood estimation of the mean and non-singular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility. PMID:26877823

TRANSPOSABLE REGULARIZED COVARIANCE MODELS WITH AN APPLICATION TO MISSING DATA IMPUTATION.

PubMed

Allen, Genevera I; Tibshirani, Robert

2010-06-01

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable , meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal , in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so called transposable regularized covariance models allow for maximum likelihood estimation of the mean and non-singular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.

Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models.

PubMed

Garcia, Tanya P; Ma, Yanyuan

2017-10-01

We develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates. We assume the model error and covariate distributions are unspecified, and the measurement error distribution is a general parametric distribution with unknown variance-covariance. We construct root- n consistent, asymptotically normal and locally efficient estimators using the semiparametric efficient score. We do not estimate any unknown distribution or model error heteroskedasticity. Instead, we form the estimator under possibly incorrect working distribution models for the model error, error-prone covariate, or both. Empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error-prone covariates.

Observed Score Linear Equating with Covariates

ERIC Educational Resources Information Center

Branberg, Kenny; Wiberg, Marie

2011-01-01

This paper examined observed score linear equating in two different data collection designs, the equivalent groups design and the nonequivalent groups design, when information from covariates (i.e., background variables correlated with the test scores) was included. The main purpose of the study was to examine the effect (i.e., bias, variance, and…

Meta-analytical synthesis of regression coefficients under different categorization scheme of continuous covariates.

PubMed

Yoneoka, Daisuke; Henmi, Masayuki

2017-11-30

Recently, the number of clinical prediction models sharing the same regression task has increased in the medical literature. However, evidence synthesis methodologies that use the results of these regression models have not been sufficiently studied, particularly in meta-analysis settings where only regression coefficients are available. One of the difficulties lies in the differences between the categorization schemes of continuous covariates across different studies. In general, categorization methods using cutoff values are study specific across available models, even if they focus on the same covariates of interest. Differences in the categorization of covariates could lead to serious bias in the estimated regression coefficients and thus in subsequent syntheses. To tackle this issue, we developed synthesis methods for linear regression models with different categorization schemes of covariates. A 2-step approach to aggregate the regression coefficient estimates is proposed. The first step is to estimate the joint distribution of covariates by introducing a latent sampling distribution, which uses one set of individual participant data to estimate the marginal distribution of covariates with categorization. The second step is to use a nonlinear mixed-effects model with correction terms for the bias due to categorization to estimate the overall regression coefficients. Especially in terms of precision, numerical simulations show that our approach outperforms conventional methods, which only use studies with common covariates or ignore the differences between categorization schemes. The method developed in this study is also applied to a series of WHO epidemiologic studies on white blood cell counts. Copyright © 2017 John Wiley & Sons, Ltd.

Free Quantum Field Theory from Quantum Cellular Automata

NASA Astrophysics Data System (ADS)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro

2015-10-01

After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).

Estimation of Covariance Matrix on Bi-Response Longitudinal Data Analysis with Penalized Spline Regression

NASA Astrophysics Data System (ADS)

Islamiyati, A.; Fatmawati; Chamidah, N.

2018-03-01

The correlation assumption of the longitudinal data with bi-response occurs on the measurement between the subjects of observation and the response. It causes the auto-correlation of error, and this can be overcome by using a covariance matrix. In this article, we estimate the covariance matrix based on the penalized spline regression model. Penalized spline involves knot points and smoothing parameters simultaneously in controlling the smoothness of the curve. Based on our simulation study, the estimated regression model of the weighted penalized spline with covariance matrix gives a smaller error value compared to the error of the model without covariance matrix.

Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

NASA Astrophysics Data System (ADS)

Lee, Taejin

2018-01-01

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

Structural Covariance of the Prefrontal-Amygdala Pathways Associated with Heart Rate Variability.

PubMed

Wei, Luqing; Chen, Hong; Wu, Guo-Rong

2018-01-01

The neurovisceral integration model has shown a key role of the amygdala in neural circuits underlying heart rate variability (HRV) modulation, and suggested that reciprocal connections from amygdala to brain regions centered on the central autonomic network (CAN) are associated with HRV. To provide neuroanatomical evidence for these theoretical perspectives, the current study used covariance analysis of MRI-based gray matter volume (GMV) to map structural covariance network of the amygdala, and then determined whether the interregional structural correlations related to individual differences in HRV. The results showed that covariance patterns of the amygdala encompassed large portions of cortical (e.g., prefrontal, cingulate, and insula) and subcortical (e.g., striatum, hippocampus, and midbrain) regions, lending evidence from structural covariance analysis to the notion that the amygdala was a pivotal node in neural pathways for HRV modulation. Importantly, participants with higher resting HRV showed increased covariance of amygdala to dorsal medial prefrontal cortex and anterior cingulate cortex (dmPFC/dACC) extending into adjacent medial motor regions [i.e., pre-supplementary motor area (pre-SMA)/SMA], demonstrating structural covariance of the prefrontal-amygdala pathways implicated in HRV, and also implying that resting HRV may reflect the function of neural circuits underlying cognitive regulation of emotion as well as facilitation of adaptive behaviors to emotion. Our results, thus, provide anatomical substrates for the neurovisceral integration model that resting HRV may index an integrative neural network which effectively organizes emotional, cognitive, physiological and behavioral responses in the service of goal-directed behavior and adaptability.

Structural Covariance of the Prefrontal-Amygdala Pathways Associated with Heart Rate Variability

PubMed Central

Wei, Luqing; Chen, Hong; Wu, Guo-Rong

2018-01-01

The neurovisceral integration model has shown a key role of the amygdala in neural circuits underlying heart rate variability (HRV) modulation, and suggested that reciprocal connections from amygdala to brain regions centered on the central autonomic network (CAN) are associated with HRV. To provide neuroanatomical evidence for these theoretical perspectives, the current study used covariance analysis of MRI-based gray matter volume (GMV) to map structural covariance network of the amygdala, and then determined whether the interregional structural correlations related to individual differences in HRV. The results showed that covariance patterns of the amygdala encompassed large portions of cortical (e.g., prefrontal, cingulate, and insula) and subcortical (e.g., striatum, hippocampus, and midbrain) regions, lending evidence from structural covariance analysis to the notion that the amygdala was a pivotal node in neural pathways for HRV modulation. Importantly, participants with higher resting HRV showed increased covariance of amygdala to dorsal medial prefrontal cortex and anterior cingulate cortex (dmPFC/dACC) extending into adjacent medial motor regions [i.e., pre-supplementary motor area (pre-SMA)/SMA], demonstrating structural covariance of the prefrontal-amygdala pathways implicated in HRV, and also implying that resting HRV may reflect the function of neural circuits underlying cognitive regulation of emotion as well as facilitation of adaptive behaviors to emotion. Our results, thus, provide anatomical substrates for the neurovisceral integration model that resting HRV may index an integrative neural network which effectively organizes emotional, cognitive, physiological and behavioral responses in the service of goal-directed behavior and adaptability. PMID:29545744

Covariance analysis for evaluating head trackers

NASA Astrophysics Data System (ADS)

Kang, Donghoon

2017-10-01

Existing methods for evaluating the performance of head trackers usually rely on publicly available face databases, which contain facial images and the ground truths of their corresponding head orientations. However, most of the existing publicly available face databases are constructed by assuming that a frontal head orientation can be determined by compelling the person under examination to look straight ahead at the camera on the first video frame. Since nobody can accurately direct one's head toward the camera, this assumption may be unrealistic. Rather than obtaining estimation errors, we present a method for computing the covariance of estimation error rotations to evaluate the reliability of head trackers. As an uncertainty measure of estimators, the Schatten 2-norm of a square root of error covariance (or the algebraic average of relative error angles) can be used. The merit of the proposed method is that it does not disturb the person under examination by asking him to direct his head toward certain directions. Experimental results using real data validate the usefulness of our method.

An alternative covariance estimator to investigate genetic heterogeneity in populations.

PubMed

Heslot, Nicolas; Jannink, Jean-Luc

2015-11-26

For genomic prediction and genome-wide association studies (GWAS) using mixed models, covariance between individuals is estimated using molecular markers. Based on the properties of mixed models, using available molecular data for prediction is optimal if this covariance is known. Under this assumption, adding individuals to the analysis should never be detrimental. However, some empirical studies showed that increasing training population size decreased prediction accuracy. Recently, results from theoretical models indicated that even if marker density is high and the genetic architecture of traits is controlled by many loci with small additive effects, the covariance between individuals, which depends on relationships at causal loci, is not always well estimated by the whole-genome kinship. We propose an alternative covariance estimator named K-kernel, to account for potential genetic heterogeneity between populations that is characterized by a lack of genetic correlation, and to limit the information flow between a priori unknown populations in a trait-specific manner. This is similar to a multi-trait model and parameters are estimated by REML and, in extreme cases, it can allow for an independent genetic architecture between populations. As such, K-kernel is useful to study the problem of the design of training populations. K-kernel was compared to other covariance estimators or kernels to examine its fit to the data, cross-validated accuracy and suitability for GWAS on several datasets. It provides a significantly better fit to the data than the genomic best linear unbiased prediction model and, in some cases it performs better than other kernels such as the Gaussian kernel, as shown by an empirical null distribution. In GWAS simulations, alternative kernels control type I errors as well as or better than the classical whole-genome kinship and increase statistical power. No or small gains were observed in cross-validated prediction accuracy. This alternative

More than maths and mindreading: sex differences in empathizing/systemizing covariance.

PubMed

Valla, Jeffrey M; Ganzel, Barbara L; Yoder, Keith J; Chen, Grace M; Lyman, Laura T; Sidari, Anthony P; Keller, Alex E; Maendel, Jeffrey W; Perlman, Jordan E; Wong, Stephanie K L; Belmonte, Matthew K

2010-08-01

Empathizing-Systemizing theory posits a continuum of cognitive traits extending from autism into normal cognitive variation. Covariance data on empathizing and systemizing traits have alternately suggested inversely dependent, independent, and sex-dependent (one sex dependent, the other independent) structures. A total of 144 normal undergraduates (65 men, 79 women) completed the Reading the Mind in the Eyes, Embedded Figures, and Benton face recognition tests, the Autism Spectrum Quotient, and measures of digit length ratio and field of study; some also completed tests of motion coherence threshold (64) and go/no-go motor inhibition (128). Empathizing and systemizing traits were independent in women, but largely dependent in men. In men, level of systemizing skill required by field of study was directly related to social interactive and mindreading deficits; men's social impairments correlated with prolonged go/no-go response times, and men tended to apply systemizing strategies to solve problems of empathizing or global processing: rapid perceptual disembedding predicted heightened sensitivity to facial emotion. In women, level of systemizing in field was related to male-typical digit ratios and autistic superiorities in detail orientation, but not to autistic social and communicative impairments; and perceptual disembedding was related to social interactive skills but independent of facial emotion and visual motion perception.

Homonuclear long-range correlation spectra from HMBC experiments by covariance processing.

PubMed

Schoefberger, Wolfgang; Smrecki, Vilko; Vikić-Topić, Drazen; Müller, Norbert

2007-07-01

We present a new application of covariance nuclear magnetic resonance processing based on 1H--13C-HMBC experiments which provides an effective way for establishing indirect 1H--1H and 13C--13C nuclear spin connectivity at natural isotope abundance. The method, which identifies correlated spin networks in terms of covariance between one-dimensional traces from a single decoupled HMBC experiment, derives 13C--13C as well as 1H--1H spin connectivity maps from the two-dimensional frequency domain heteronuclear long-range correlation data matrix. The potential and limitations of this novel covariance NMR application are demonstrated on two compounds: eugenyl-beta-D-glucopyranoside and an emodin-derivative. Copyright (c) 2007 John Wiley & Sons, Ltd.

Eddy covariance N2O flux measurements at low flux rates: results from the InGOS campaign in a Danish willow field.

NASA Astrophysics Data System (ADS)

Ibrom, Andreas; Brümmer, Christian; Hensen, Arjan; van Asperen, Hella; Carter, Mette S.; Gasche, Rainer; Famulari, Daniela; Kutsch, Werner; Pilegaard, Kim; Ambus, Per

2014-05-01

Nitrous oxide (N2O) fluxes from soils are characterised by their high spatial and temporal variability. The fluxes depend on the availability of the substrates for nitrification and denitrification and soil physical and chemical conditions that control the metabolic microbial activity. The sporadic nature of the fluxes and their high sensitivity to alterations of the soil climate put very high demands on measurement approaches. Laser spectroscopy enables accurate and fast response detection of atmospheric N2O concentrations and is used for eddy covariance (EC) flux measurements. Alternatively N2O fluxes can be measured with chambers together with high precision analysers. Differences in the measurement approaches and system designs are expected to have a considerable influence on the accuracy of the flux estimation. This study investigates how three different eddy covariance systems perform in a situation of low N2O fluxes from a flat surface. Chamber flux measurements with differing chamber and analyser designs are used for comparison. In April 2013, the EU research infrastructure project InGOS (http://www.ingos-infrastructure.eu/) organised a campaign of N2O flux measurements in a willow plantation close to the Risø Campus of the Technical University of Denmark. The willow field was harvested in February 2013 and received mineral fertiliser equivalent to 120 kg N ha-1 before the campaign started. Three different eddy covariance systems took part in the campaign: two Aerodyne quantum cascade laser (QCL) based systems and one Los Gatos Research off-axis integrated-cavity-output spectroscopy (ICOS) system for N2O and CO. The sonic anemometers were all installed at 2 m height above the bare ground. Gill R3 type sonic anemometers were used with QCL systems and a Gil HS-50 with the ICOS system. The 10 Hz raw data were analysed with group specific softwares and procedures. The local conditions in the exceptionally cold and dry spring 2013 did not lead to large N2O flux

Treating Sample Covariances for Use in Strongly Coupled Atmosphere-Ocean Data Assimilation

NASA Astrophysics Data System (ADS)

Smith, Polly J.; Lawless, Amos S.; Nichols, Nancy K.

2018-01-01

Strongly coupled data assimilation requires cross-domain forecast error covariances; information from ensembles can be used, but limited sampling means that ensemble derived error covariances are routinely rank deficient and/or ill-conditioned and marred by noise. Thus, they require modification before they can be incorporated into a standard assimilation framework. Here we compare methods for improving the rank and conditioning of multivariate sample error covariance matrices for coupled atmosphere-ocean data assimilation. The first method, reconditioning, alters the matrix eigenvalues directly; this preserves the correlation structures but does not remove sampling noise. We show that it is better to recondition the correlation matrix rather than the covariance matrix as this prevents small but dynamically important modes from being lost. The second method, model state-space localization via the Schur product, effectively removes sample noise but can dampen small cross-correlation signals. A combination that exploits the merits of each is found to offer an effective alternative.

A stochastic multiple imputation algorithm for missing covariate data in tree-structured survival analysis.

PubMed

Wallace, Meredith L; Anderson, Stewart J; Mazumdar, Sati

2010-12-20

Missing covariate data present a challenge to tree-structured methodology due to the fact that a single tree model, as opposed to an estimated parameter value, may be desired for use in a clinical setting. To address this problem, we suggest a multiple imputation algorithm that adds draws of stochastic error to a tree-based single imputation method presented by Conversano and Siciliano (Technical Report, University of Naples, 2003). Unlike previously proposed techniques for accommodating missing covariate data in tree-structured analyses, our methodology allows the modeling of complex and nonlinear covariate structures while still resulting in a single tree model. We perform a simulation study to evaluate our stochastic multiple imputation algorithm when covariate data are missing at random and compare it to other currently used methods. Our algorithm is advantageous for identifying the true underlying covariate structure when complex data and larger percentages of missing covariate observations are present. It is competitive with other current methods with respect to prediction accuracy. To illustrate our algorithm, we create a tree-structured survival model for predicting time to treatment response in older, depressed adults. Copyright © 2010 John Wiley & Sons, Ltd.

Complementary nonparametric analysis of covariance for logistic regression in a randomized clinical trial setting.

PubMed

Tangen, C M; Koch, G G

1999-03-01

In the randomized clinical trial setting, controlling for covariates is expected to produce variance reduction for the treatment parameter estimate and to adjust for random imbalances of covariates between the treatment groups. However, for the logistic regression model, variance reduction is not obviously obtained. This can lead to concerns about the assumptions of the logistic model. We introduce a complementary nonparametric method for covariate adjustment. It provides results that are usually compatible with expectations for analysis of covariance. The only assumptions required are based on randomization and sampling arguments. The resulting treatment parameter is a (unconditional) population average log-odds ratio that has been adjusted for random imbalance of covariates. Data from a randomized clinical trial are used to compare results from the traditional maximum likelihood logistic method with those from the nonparametric logistic method. We examine treatment parameter estimates, corresponding standard errors, and significance levels in models with and without covariate adjustment. In addition, we discuss differences between unconditional population average treatment parameters and conditional subpopulation average treatment parameters. Additional features of the nonparametric method, including stratified (multicenter) and multivariate (multivisit) analyses, are illustrated. Extensions of this methodology to the proportional odds model are also made.

Local conditions for the generalized covariant entropy bound

NASA Astrophysics Data System (ADS)

Gao, Sijie; Lemos, José P.

2005-04-01

A set of sufficient conditions for the generalized covariant entropy bound given by Strominger and Thompson is as follows: Suppose that the entropy of matter can be described by an entropy current sa. Let ka be any null vector along L and s≡-kasa. Then the generalized bound can be derived from the following conditions: (i) s'≤2πTabkakb, where s'=ka∇as and Tab is the stress-energy tensor; (ii) on the initial 2-surface B, s(0)≤-1/4θ(0), where θ is the expansion of ka. We prove that condition (ii) alone can be used to divide a spacetime into two regions: The generalized entropy bound holds for all light sheets residing in the region where s<-1/4θ and fails for those in the region where s>-1/4θ. We check the validity of these conditions in FRW flat universe and a scalar field spacetime. Some apparent violations of the entropy bounds in the two spacetimes are discussed. These holographic bounds are important in the formulation of the holographic principle.

Development and Testing of Neutron Cross Section Covariance Data for SCALE 6.2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marshall, William BJ J; Williams, Mark L; Wiarda, Dorothea

2015-01-01

Neutron cross-section covariance data are essential for many sensitivity/uncertainty and uncertainty quantification assessments performed both within the TSUNAMI suite and more broadly throughout the SCALE code system. The release of ENDF/B-VII.1 included a more complete set of neutron cross-section covariance data: these data form the basis for a new cross-section covariance library to be released in SCALE 6.2. A range of testing is conducted to investigate the properties of these covariance data and ensure that the data are reasonable. These tests include examination of the uncertainty in critical experiment benchmark model k eff values due to nuclear data uncertainties, asmore » well as similarity assessments of irradiated pressurized water reactor (PWR) and boiling water reactor (BWR) fuel with suites of critical experiments. The contents of the new covariance library, the testing performed, and the behavior of the new covariance data are described in this paper. The neutron cross-section covariances can be combined with a sensitivity data file generated using the TSUNAMI suite of codes within SCALE to determine the uncertainty in system k eff caused by nuclear data uncertainties. The Verified, Archived Library of Inputs and Data (VALID) maintained at Oak Ridge National Laboratory (ORNL) contains over 400 critical experiment benchmark models, and sensitivity data are generated for each of these models. The nuclear data uncertainty in k eff is generated for each experiment, and the resulting uncertainties are tabulated and compared to the differences in measured and calculated results. The magnitude of the uncertainty for categories of nuclides (such as actinides, fission products, and structural materials) is calculated for irradiated PWR and BWR fuel to quantify the effect of covariance library changes between the SCALE 6.1 and 6.2 libraries. One of the primary applications of sensitivity/uncertainty methods within SCALE is the assessment of similarities

Efficient retrieval of landscape Hessian: Forced optimal covariance adaptive learning

NASA Astrophysics Data System (ADS)

Shir, Ofer M.; Roslund, Jonathan; Whitley, Darrell; Rabitz, Herschel

2014-06-01

Knowledge of the Hessian matrix at the landscape optimum of a controlled physical observable offers valuable information about the system robustness to control noise. The Hessian can also assist in physical landscape characterization, which is of particular interest in quantum system control experiments. The recently developed landscape theoretical analysis motivated the compilation of an automated method to learn the Hessian matrix about the global optimum without derivative measurements from noisy data. The current study introduces the forced optimal covariance adaptive learning (FOCAL) technique for this purpose. FOCAL relies on the covariance matrix adaptation evolution strategy (CMA-ES) that exploits covariance information amongst the control variables by means of principal component analysis. The FOCAL technique is designed to operate with experimental optimization, generally involving continuous high-dimensional search landscapes (≳30) with large Hessian condition numbers (≳104). This paper introduces the theoretical foundations of the inverse relationship between the covariance learned by the evolution strategy and the actual Hessian matrix of the landscape. FOCAL is presented and demonstrated to retrieve the Hessian matrix with high fidelity on both model landscapes and quantum control experiments, which are observed to possess nonseparable, nonquadratic search landscapes. The recovered Hessian forms were corroborated by physical knowledge of the systems. The implications of FOCAL extend beyond the investigated studies to potentially cover other physically motivated multivariate landscapes.

Covariance, correlation matrix, and the multiscale community structure of networks.

PubMed

Shen, Hua-Wei; Cheng, Xue-Qi; Fang, Bin-Xing

2010-07-01

Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this paper, we consider detecting the multiscale community structure of network from the perspective of dimension reduction. According to this perspective, a covariance matrix of network is defined to uncover the multiscale community structure through the translation and rotation transformations. It is proved that the covariance matrix is the unbiased version of the well-known modularity matrix. We then point out that the translation and rotation transformations fail to deal with the heterogeneous network, which is very common in nature and society. To address this problem, a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix. Extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix, identically the modularity matrix, as regards identifying the multiscale community structure of network. This work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure. Through introducing the correlation matrix, we further conclude that the rescaling transformation is crucial to identify the multiscale community structure of network, as well as the translation and rotation transformations.

Generation of intensity covariations of the oxygen green and red lines in the nightglow

NASA Astrophysics Data System (ADS)

Misawa, K.; Takeuchi, I.; Kato, Y.; Aoyama, I.

1984-02-01

The cause of intensity covariations of the oxygen green and red lines is studied. Intensity covariations are compared with the auroral-electrojet-activity index AE, the substorm Pi2, and the magnetogram. It is suggested that intensity covariations or double-intensity maxima of the red line occur in association with intense auroral substorms, and that they are the direct experimental evidences of Testud's theory (1973).

Comparing laser-based open- and closed-path gas analyzers to measure methane fluxes using the eddy covariance method

USGS Publications Warehouse

Detto, Matteo; Verfaillie, Joseph; Anderson, Frank; Xu, Liukang; Baldocchi, Dennis

2011-01-01

Closed- and open-path methane gas analyzers are used in eddy covariance systems to compare three potential methane emitting ecosystems in the Sacramento-San Joaquin Delta (CA, USA): a rice field, a peatland pasture and a restored wetland. The study points out similarities and differences of the systems in field experiments and data processing. The closed-path system, despite a less intrusive placement with the sonic anemometer, required more care and power. In contrast, the open-path system appears more versatile for a remote and unattended experimental site. Overall, the two systems have comparable minimum detectable limits, but synchronization between wind speed and methane data, air density corrections and spectral losses have different impacts on the computed flux covariances. For the closed-path analyzer, air density effects are less important, but the synchronization and spectral losses may represent a problem when fluxes are small or when an undersized pump is used. For the open-path analyzer air density corrections are greater, due to spectroscopy effects and the classic Webb–Pearman–Leuning correction. Comparison between the 30-min fluxes reveals good agreement in terms of magnitudes between open-path and closed-path flux systems. However, the scatter is large, as consequence of the intensive data processing which both systems require.

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

Non-linear matter power spectrum covariance matrix errors and cosmological parameter uncertainties

NASA Astrophysics Data System (ADS)

Blot, L.; Corasaniti, P. S.; Amendola, L.; Kitching, T. D.

2016-06-01

The covariance of the matter power spectrum is a key element of the analysis of galaxy clustering data. Independent realizations of observational measurements can be used to sample the covariance, nevertheless statistical sampling errors will propagate into the cosmological parameter inference potentially limiting the capabilities of the upcoming generation of galaxy surveys. The impact of these errors as function of the number of realizations has been previously evaluated for Gaussian distributed data. However, non-linearities in the late-time clustering of matter cause departures from Gaussian statistics. Here, we address the impact of non-Gaussian errors on the sample covariance and precision matrix errors using a large ensemble of N-body simulations. In the range of modes where finite volume effects are negligible (0.1 ≲ k [h Mpc-1] ≲ 1.2), we find deviations of the variance of the sample covariance with respect to Gaussian predictions above ˜10 per cent at k > 0.3 h Mpc-1. Over the entire range these reduce to about ˜5 per cent for the precision matrix. Finally, we perform a Fisher analysis to estimate the effect of covariance errors on the cosmological parameter constraints. In particular, assuming Euclid-like survey characteristics we find that a number of independent realizations larger than 5000 is necessary to reduce the contribution of sampling errors to the cosmological parameter uncertainties at subpercent level. We also show that restricting the analysis to large scales k ≲ 0.2 h Mpc-1 results in a considerable loss in constraining power, while using the linear covariance to include smaller scales leads to an underestimation of the errors on the cosmological parameters.

Electromagnetic fields in curved spacetimes

NASA Astrophysics Data System (ADS)

Tsagas, Christos G.

2005-01-01

We consider the evolution of electromagnetic fields in curved spacetimes and calculate the exact wave equations for the associated electric and magnetic components. Our analysis is fully covariant, applies to a general spacetime and isolates all the sources that affect the propagation of these waves. Among others, we explicitly show how the different components of the gravitational field act as driving sources of electromagnetic disturbances. When applied to perturbed Friedmann Robertson Walker cosmologies, our results argue for a superadiabatic-type amplification of large-scale cosmological magnetic fields in Friedmann models with open spatial curvature.

Covariance Recovery from a Square Root Information Matrix for Data Association

DTIC Science & Technology

2009-07-02

association is one of the core problems of simultaneous localization and mapping (SLAM), and it requires knowledge about the uncertainties of the...association is one of the core problems of simultaneous localization and mapping (SLAM), and it requires knowledge about the uncertainties of the...back-substitution as well as efficient access to marginal covariances, which is described next. 2.2. Recovering Marginal Covariances Knowledge of the

Eddy covariance measurements of carbon dioxide, latent and sensible energy fluxes above a meadow on a mountain slope

PubMed Central

Hammerle, Albin; Haslwanter, Alois; Schmitt, Michael; Bahn, Michael; Tappeiner, Ulrike; Cernusca, Alexander; Wohlfahrt, Georg

2014-01-01

Carbon dioxide, latent and sensible energy fluxes were measured by means of the eddy covariance method above a mountain meadow situated on a steep slope in the Stubai Valley/Austria, based on the hypothesis that, due to the low canopy height, measurements can be made in the shallow equilibrium layer where the wind field exhibits characteristics akin to level terrain. In order to test the validity of this hypothesis and to identify effects of complex terrain in the turbulence measurements, data were subjected to a rigorous testing procedure using a series of quality control measures established for surface layer flows. The resulting high-quality data set comprised 36 % of the original observations, the substantial reduction being mainly due to a change in surface roughness and associated fetch limitations in the wind sector dominating during nighttime and transition periods. The validity of the high-quality data set was further assessed by two independent tests: i) a comparison with the net ecosystem carbon dioxide exchange measured by means of ecosystem chambers and ii) the ability of the eddy covariance measurements to close the energy balance. The net ecosystem CO2 exchange measured by the eddy covariance method agreed reasonably with ecosystem chamber measurements. The assessment of the energy balance closure showed that there was no significant difference in the correspondence between the meadow on the slope and another one situated on flat ground at the bottom of the Stubai Valley, available energy being underestimated by 28 and 29 %, respectively. We thus conclude that, appropriate quality control provided, the eddy covariance measurements made above a mountain meadow on a steep slope are of similar quality as compared to flat terrain. PMID:24465032

Covariance versus correlation in capacitated vehicle routing problem-investment fund allocation problem

NASA Astrophysics Data System (ADS)

Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah@Rozita

2017-04-01

Capacitated Vehicle Routing Problem-Investment Fund Allocation Problem (CVRP-IFAP) provides investors with a sequence of assets to allocate their funds into. To minimize total risks of investment in CVRP-IFAP covariance values measure the risks between two assets. Another measure of risks are correlation values between returns. The correlation values can be used to diversify the risk of investment loss in order to optimize expected return against a certain level of risk. This study compares the total risk obtained from CVRP-IFAP when using covariance values and correlation values. Results show that CVRP-IFAP with covariance values provides lesser total risks and a significantly better measure of risk.

Multivariate generalized hidden Markov regression models with random covariates: Physical exercise in an elderly population.

PubMed

Punzo, Antonio; Ingrassia, Salvatore; Maruotti, Antonello

2018-04-22

A time-varying latent variable model is proposed to jointly analyze multivariate mixed-support longitudinal data. The proposal can be viewed as an extension of hidden Markov regression models with fixed covariates (HMRMFCs), which is the state of the art for modelling longitudinal data, with a special focus on the underlying clustering structure. HMRMFCs are inadequate for applications in which a clustering structure can be identified in the distribution of the covariates, as the clustering is independent from the covariates distribution. Here, hidden Markov regression models with random covariates are introduced by explicitly specifying state-specific distributions for the covariates, with the aim of improving the recovering of the clusters in the data with respect to a fixed covariates paradigm. The hidden Markov regression models with random covariates class is defined focusing on the exponential family, in a generalized linear model framework. Model identifiability conditions are sketched, an expectation-maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients, as well as of the hidden path parameters, are evaluated through simulation experiments and compared with those of HMRMFCs. The method is applied to physical activity data. Copyright © 2018 John Wiley & Sons, Ltd.

A trade-off solution between model resolution and covariance in surface-wave inversion

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

2010-01-01

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Guided transect sampling - a new design combining prior information and field surveying

Treesearch

Anna Ringvall; Goran Stahl; Tomas Lamas

2000-01-01

Guided transect sampling is a two-stage sampling design in which prior information is used to guide the field survey in the second stage. In the first stage, broad strips are randomly selected and divided into grid-cells. For each cell a covariate value is estimated from remote sensing data, for example. The covariate is the basis for subsampling of a transect through...

Mapping structural covariance networks of facial emotion recognition in early psychosis: A pilot study.

PubMed

Buchy, Lisa; Barbato, Mariapaola; Makowski, Carolina; Bray, Signe; MacMaster, Frank P; Deighton, Stephanie; Addington, Jean

2017-11-01

People with psychosis show deficits recognizing facial emotions and disrupted activation in the underlying neural circuitry. We evaluated associations between facial emotion recognition and cortical thickness using a correlation-based approach to map structural covariance networks across the brain. Fifteen people with an early psychosis provided magnetic resonance scans and completed the Penn Emotion Recognition and Differentiation tasks. Fifteen historical controls provided magnetic resonance scans. Cortical thickness was computed using CIVET and analyzed with linear models. Seed-based structural covariance analysis was done using the mapping anatomical correlations across the cerebral cortex methodology. To map structural covariance networks involved in facial emotion recognition, the right somatosensory cortex and bilateral fusiform face areas were selected as seeds. Statistics were run in SurfStat. Findings showed increased cortical covariance between the right fusiform face region seed and right orbitofrontal cortex in controls than early psychosis subjects. Facial emotion recognition scores were not significantly associated with thickness in any region. A negative effect of Penn Differentiation scores on cortical covariance was seen between the left fusiform face area seed and right superior parietal lobule in early psychosis subjects. Results suggest that facial emotion recognition ability is related to covariance in a temporal-parietal network in early psychosis. Copyright © 2017 Elsevier B.V. All rights reserved.

Networks of myelin covariance.

PubMed

Melie-Garcia, Lester; Slater, David; Ruef, Anne; Sanabria-Diaz, Gretel; Preisig, Martin; Kherif, Ferath; Draganski, Bogdan; Lutti, Antoine

2018-04-01

Networks of anatomical covariance have been widely used to study connectivity patterns in both normal and pathological brains based on the concurrent changes of morphometric measures (i.e., cortical thickness) between brain structures across subjects (Evans, ). However, the existence of networks of microstructural changes within brain tissue has been largely unexplored so far. In this article, we studied in vivo the concurrent myelination processes among brain anatomical structures that gathered together emerge to form nonrandom networks. We name these "networks of myelin covariance" (Myelin-Nets). The Myelin-Nets were built from quantitative Magnetization Transfer data-an in-vivo magnetic resonance imaging (MRI) marker of myelin content. The synchronicity of the variations in myelin content between anatomical regions was measured by computing the Pearson's correlation coefficient. We were especially interested in elucidating the effect of age on the topological organization of the Myelin-Nets. We therefore selected two age groups: Young-Age (20-31 years old) and Old-Age (60-71 years old) and a pool of participants from 48 to 87 years old for a Myelin-Nets aging trajectory study. We found that the topological organization of the Myelin-Nets is strongly shaped by aging processes. The global myelin correlation strength, between homologous regions and locally in different brain lobes, showed a significant dependence on age. Interestingly, we also showed that the aging process modulates the resilience of the Myelin-Nets to damage of principal network structures. In summary, this work sheds light on the organizational principles driving myelination and myelin degeneration in brain gray matter and how such patterns are modulated by aging. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Differential Age-Related Changes in Structural Covariance Networks of Human Anterior and Posterior Hippocampus.

PubMed

Li, Xinwei; Li, Qiongling; Wang, Xuetong; Li, Deyu; Li, Shuyu

2018-01-01

The hippocampus plays an important role in memory function relying on information interaction between distributed brain areas. The hippocampus can be divided into the anterior and posterior sections with different structure and function along its long axis. The aim of this study is to investigate the effects of normal aging on the structural covariance of the anterior hippocampus (aHPC) and the posterior hippocampus (pHPC). In this study, 240 healthy subjects aged 18-89 years were selected and subdivided into young (18-23 years), middle-aged (30-58 years), and older (61-89 years) groups. The aHPC and pHPC was divided based on the location of uncal apex in the MNI space. Then, the structural covariance networks were constructed by examining their covariance in gray matter volumes with other brain regions. Finally, the influence of age on the structural covariance of these hippocampal sections was explored. We found that the aHPC and pHPC had different structural covariance patterns, but both of them were associated with the medial temporal lobe and insula. Moreover, both increased and decreased covariances were found with the aHPC but only increased covariance was found with the pHPC with age ( p < 0.05, family-wise error corrected). These decreased connections occurred within the default mode network, while the increased connectivity mainly occurred in other memory systems that differ from the hippocampus. This study reveals different age-related influence on the structural networks of the aHPC and pHPC, providing an essential insight into the mechanisms of the hippocampus in normal aging.

Dark matter statistics for large galaxy catalogs: power spectra and covariance matrices

NASA Astrophysics Data System (ADS)

Klypin, Anatoly; Prada, Francisco

2018-06-01

Large-scale surveys of galaxies require accurate theoretical predictions of the dark matter clustering for thousands of mock galaxy catalogs. We demonstrate that this goal can be achieve with the new Parallel Particle-Mesh (PM) N-body code GLAM at a very low computational cost. We run ˜22, 000 simulations with ˜2 billion particles that provide ˜1% accuracy of the dark matter power spectra P(k) for wave-numbers up to k ˜ 1hMpc-1. Using this large data-set we study the power spectrum covariance matrix. In contrast to many previous analytical and numerical results, we find that the covariance matrix normalised to the power spectrum C(k, k΄)/P(k)P(k΄) has a complex structure of non-diagonal components: an upturn at small k, followed by a minimum at k ≈ 0.1 - 0.2 hMpc-1, and a maximum at k ≈ 0.5 - 0.6 hMpc-1. The normalised covariance matrix strongly evolves with redshift: C(k, k΄)∝δα(t)P(k)P(k΄), where δ is the linear growth factor and α ≈ 1 - 1.25, which indicates that the covariance matrix depends on cosmological parameters. We also show that waves longer than 1h-1Gpc have very little impact on the power spectrum and covariance matrix. This significantly reduces the computational costs and complexity of theoretical predictions: relatively small volume ˜(1h-1Gpc)3 simulations capture the necessary properties of dark matter clustering statistics. As our results also indicate, achieving ˜1% errors in the covariance matrix for k < 0.50 hMpc-1 requires a resolution better than ɛ ˜ 0.5h-1Mpc.

Generalized reduced rank latent factor regression for high dimensional tensor fields, and neuroimaging-genetic applications

PubMed Central

Tao, Chenyang; Nichols, Thomas E.; Hua, Xue; Ching, Christopher R.K.; Rolls, Edmund T.; Thompson, Paul M.; Feng, Jianfeng

2017-01-01

We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches. PMID:27666385

Optical Implementation of the Optimal Universal and Phase-Covariant Quantum Cloning Machines

NASA Astrophysics Data System (ADS)

Ye, Liu; Song, Xue-Ke; Yang, Jie; Yang, Qun; Ma, Yang-Cheng

Quantum cloning relates to the security of quantum computation and quantum communication. In this paper, firstly we propose a feasible unified scheme to implement optimal 1 → 2 universal, 1 → 2 asymmetric and symmetric phase-covariant cloning, and 1 → 2 economical phase-covariant quantum cloning machines only via a beam splitter. Then 1 → 3 economical phase-covariant quantum cloning machines also can be realized by adding another beam splitter in context of linear optics. The scheme is based on the interference of two photons on a beam splitter with different splitting ratios for vertical and horizontal polarization components. It is shown that under certain condition, the scheme is feasible by current experimental technology.

Comparison of Repeatability and Agreement between Swept-Source Optical Biometry and Dual-Scheimpflug Topography.

PubMed

Jung, Soyeon; Chin, Hee Seung; Kim, Na Rae; Lee, Kang Won; Jung, Ji Won

2017-01-01

To assess the repeatability and agreement of parameters obtained with two biometers and to compare the predictability. Biometry was performed on 101 eyes with cataract using the IOLMaster 700 and the Galilei G6. Three measurements were obtained per eye with each device, and repeatability was evaluated. The axial length (AL), anterior chamber depth (ACD), keratometry (K), white-to-white (WTW) corneal diameter, central corneal thickness (CCT), and lens thickness (LT) were measured and postoperative predictability was compared. Measurements could not be obtained with the IOLMaster 700 in one eye and in seven eyes with the Galilei G6 due to dense cataract. Both the IOLMaster 700 and Galilei G6 showed good repeatability, although the IOLMaster 700 showed better repeatability than the Galilei G6. There were no statistically significant differences in AL, ACD, steepest K, WTW, and LT ( P > 0.050), although flattest K, mean K, and CCT differed ( P < 0.050). The proportion of eyes with an absolute prediction error within 0.5 D was 85.0% for the IOLMaster 700 and was 80.0% for the Galilei G6 based on the SRK/T formula. Two biometers showed high repeatability and relatively good agreements. The swept-source optical biometer demonstrated better repeatability, penetration, and an overall lower prediction error.

Metagenomic covariation along densely sampled environmental gradients in the Red Sea

PubMed Central

Thompson, Luke R; Williams, Gareth J; Haroon, Mohamed F; Shibl, Ahmed; Larsen, Peter; Shorenstein, Joshua; Knight, Rob; Stingl, Ulrich

2017-01-01

Oceanic microbial diversity covaries with physicochemical parameters. Temperature, for example, explains approximately half of global variation in surface taxonomic abundance. It is unknown, however, whether covariation patterns hold over narrower parameter gradients and spatial scales, and extending to mesopelagic depths. We collected and sequenced 45 epipelagic and mesopelagic microbial metagenomes on a meridional transect through the eastern Red Sea. We asked which environmental parameters explain the most variation in relative abundances of taxonomic groups, gene ortholog groups, and pathways—at a spatial scale of <2000 km, along narrow but well-defined latitudinal and depth-dependent gradients. We also asked how microbes are adapted to gradients and extremes in irradiance, temperature, salinity, and nutrients, examining the responses of individual gene ortholog groups to these parameters. Functional and taxonomic metrics were equally well explained (75–79%) by environmental parameters. However, only functional and not taxonomic covariation patterns were conserved when comparing with an intruding water mass with different physicochemical properties. Temperature explained the most variation in each metric, followed by nitrate, chlorophyll, phosphate, and salinity. That nitrate explained more variation than phosphate suggested nitrogen limitation, consistent with low surface N:P ratios. Covariation of gene ortholog groups with environmental parameters revealed patterns of functional adaptation to the challenging Red Sea environment: high irradiance, temperature, salinity, and low nutrients. Nutrient-acquisition gene ortholog groups were anti-correlated with concentrations of their respective nutrient species, recapturing trends previously observed across much larger distances and environmental gradients. This dataset of metagenomic covariation along densely sampled environmental gradients includes online data exploration supplements, serving as a community

Interacting quantum fields and the chronometric principle

PubMed Central

Segal, I. E.

1976-01-01

A form of interaction in quantum field theory is described that is physically intrinsic rather than superimposed via a postulated nonlinearity on a hypothetical free field. It derives from the extension to general symmetries of the distinction basic for the chronometric cosmology between the physical (driving) and the observed energies, together with general precepts of quantum field theory applicable to nonunitary representations. The resulting interacting field is covariant, causal, involves real particle production, and is devoid of nontrivial ultraviolet divergences. Possible physical applications are discussed. PMID:16592353

ANL Critical Assembly Covariance Matrix Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

McKnight, Richard D.; Grimm, Karl N.

2014-01-15

This report discusses the generation of a covariance matrix for selected critical assemblies that were carried out by Argonne National Laboratory (ANL) using four critical facilities-all of which are now decommissioned. The four different ANL critical facilities are: ZPR-3 located at ANL-West (now Idaho National Laboratory- INL), ZPR-6 and ZPR-9 located at ANL-East (Illinois) and ZPPr located at ANL-West.

Structural whole-brain covariance of the anterior and posterior hippocampus: Associations with age and memory.

PubMed

Nordin, Kristin; Persson, Jonas; Stening, Eva; Herlitz, Agneta; Larsson, Elna-Marie; Söderlund, Hedvig

2018-02-01

The hippocampus (HC) interacts with distributed brain regions to support memory and shows significant volume reductions in aging, but little is known about age effects on hippocampal whole-brain structural covariance. It is also unclear whether the anterior and posterior HC show similar or distinct patterns of whole-brain covariance and to what extent these are related to memory functions organized along the hippocampal longitudinal axis. Using the multivariate approach partial least squares, we assessed structural whole-brain covariance of the HC in addition to regional volume, in young, middle-aged and older adults (n = 221), and assessed associations with episodic and spatial memory. Based on findings of sex differences in both memory and brain aging, we further considered sex as a potential modulating factor of age effects. There were two main covariance patterns: one capturing common anterior and posterior covariance, and one differentiating the two regions by capturing anterior-specific covariance only. These patterns were differentially related to associative memory while unrelated to measures of single-item memory and spatial memory. Although patterns were qualitatively comparable across age groups, participants' expression of both patterns decreased with age, independently of sex. The results suggest that the organization of hippocampal structural whole-brain covariance remains stable across age, but that the integrity of these networks decreases as the brain undergoes age-related alterations. © 2017 Wiley Periodicals, Inc.

Metabolic rate associates with, but does not generate covariation between, behaviours in western stutter-trilling crickets, Gryllus integer.

PubMed

Krams, Indrikis A; Niemelä, Petri T; Trakimas, Giedrius; Krams, Ronalds; Burghardt, Gordon M; Krama, Tatjana; Kuusik, Aare; Mänd, Marika; Rantala, Markus J; Mänd, Raivo; Kekäläinen, Jukka; Sirkka, Ilkka; Luoto, Severi; Kortet, Raine

2017-03-29

The causes and consequences of among-individual variation and covariation in behaviours are of substantial interest to behavioural ecology, but the proximate mechanisms underpinning this (co)variation are still unclear. Previous research suggests metabolic rate as a potential proximate mechanism to explain behavioural covariation. We measured the resting metabolic rate (RMR), boldness and exploration in western stutter-trilling crickets, Gryllus integer , selected differentially for short and fast development over two generations. After applying mixed-effects models to reveal the sign of the covariation, we applied structural equation models to an individual-level covariance matrix to examine whether the RMR generates covariation between the measured behaviours. All traits showed among-individual variation and covariation: RMR and boldness were positively correlated, RMR and exploration were negatively correlated, and boldness and exploration were negatively correlated. However, the RMR was not a causal factor generating covariation between boldness and exploration. Instead, the covariation between all three traits was explained by another, unmeasured mechanism. The selection lines differed from each other in all measured traits and significantly affected the covariance matrix structure between the traits, suggesting that there is a genetic component in the trait integration. Our results emphasize that interpretations made solely from the correlation matrix might be misleading. © 2017 The Author(s).

Metabolic rate associates with, but does not generate covariation between, behaviours in western stutter-trilling crickets, Gryllus integer

PubMed Central

Trakimas, Giedrius; Krams, Ronalds; Burghardt, Gordon M.; Krama, Tatjana; Kuusik, Aare; Mänd, Marika; Rantala, Markus J.; Mänd, Raivo; Sirkka, Ilkka; Luoto, Severi; Kortet, Raine

2017-01-01

The causes and consequences of among-individual variation and covariation in behaviours are of substantial interest to behavioural ecology, but the proximate mechanisms underpinning this (co)variation are still unclear. Previous research suggests metabolic rate as a potential proximate mechanism to explain behavioural covariation. We measured the resting metabolic rate (RMR), boldness and exploration in western stutter-trilling crickets, Gryllus integer, selected differentially for short and fast development over two generations. After applying mixed-effects models to reveal the sign of the covariation, we applied structural equation models to an individual-level covariance matrix to examine whether the RMR generates covariation between the measured behaviours. All traits showed among-individual variation and covariation: RMR and boldness were positively correlated, RMR and exploration were negatively correlated, and boldness and exploration were negatively correlated. However, the RMR was not a causal factor generating covariation between boldness and exploration. Instead, the covariation between all three traits was explained by another, unmeasured mechanism. The selection lines differed from each other in all measured traits and significantly affected the covariance matrix structure between the traits, suggesting that there is a genetic component in the trait integration. Our results emphasize that interpretations made solely from the correlation matrix might be misleading. PMID:28330918

High-quality eddy-covariance CO2 budgets under cold climate conditions

NASA Astrophysics Data System (ADS)

Kittler, Fanny; Eugster, Werner; Foken, Thomas; Heimann, Martin; Kolle, Olaf; Göckede, Mathias

2017-08-01

This study aimed at quantifying potential negative effects of instrument heating to improve eddy-covariance flux data quality in cold environments. Our overarching objective was to minimize heating-related bias in annual CO2 budgets from an Arctic permafrost system. We used continuous eddy-covariance measurements covering three full years within an Arctic permafrost ecosystem with parallel sonic anemometers operation with activated heating and without heating as well as parallel operation of open- and closed-path gas analyzers, the latter serving as a reference. Our results demonstrate that the sonic anemometer heating has a direct effect on temperature measurements while the turbulent wind field is not affected. As a consequence, fluxes of sensible heat are increased by an average 5 W m-2 with activated heating, while no direct effect on other scalar fluxes was observed. However, the biased measurements in sensible heat fluxes can have an indirect effect on the CO2 fluxes in case they are used as input for a density-flux WPL correction of an open-path gas analyzer. Evaluating the self-heating effect of the open-path gas analyzer by comparing CO2 flux measurements between open- and closed-path gas analyzers, we found systematically higher CO2 uptake recorded with the open-path sensor, leading to a cumulative annual offset of 96 gC m-2, which was not only the result of the cold winter season but also due to substantial self-heating effects during summer. With an inclined sensor mounting, only a fraction of the self-heating correction for vertically mounted instruments is required.

The spatiotemporal MEG covariance matrix modeled as a sum of Kronecker products.

PubMed

Bijma, Fetsje; de Munck, Jan C; Heethaar, Rob M

2005-08-15

The single Kronecker product (KP) model for the spatiotemporal covariance of MEG residuals is extended to a sum of Kronecker products. This sum of KP is estimated such that it approximates the spatiotemporal sample covariance best in matrix norm. Contrary to the single KP, this extension allows for describing multiple, independent phenomena in the ongoing background activity. Whereas the single KP model can be interpreted by assuming that background activity is generated by randomly distributed dipoles with certain spatial and temporal characteristics, the sum model can be physiologically interpreted by assuming a composite of such processes. Taking enough terms into account, the spatiotemporal sample covariance matrix can be described exactly by this extended model. In the estimation of the sum of KP model, it appears that the sum of the first 2 KP describes between 67% and 93%. Moreover, these first two terms describe two physiological processes in the background activity: focal, frequency-specific alpha activity, and more widespread non-frequency-specific activity. Furthermore, temporal nonstationarities due to trial-to-trial variations are not clearly visible in the first two terms, and, hence, play only a minor role in the sample covariance matrix in terms of matrix power. Considering the dipole localization, the single KP model appears to describe around 80% of the noise and seems therefore adequate. The emphasis of further improvement of localization accuracy should be on improving the source model rather than the covariance model.

An Empirical State Error Covariance Matrix for the Weighted Least Squares Estimation Method

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the un-certainty in the estimated states. By a reinterpretation of the equations involved in the weighted least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. This proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. Results based on the proposed technique will be presented for a simple, two observer, measurement error only problem.

On analyzing ordinal data when responses and covariates are both missing at random.

PubMed

Rana, Subrata; Roy, Surupa; Das, Kalyan

2016-08-01

In many occasions, particularly in biomedical studies, data are unavailable for some responses and covariates. This leads to biased inference in the analysis when a substantial proportion of responses or a covariate or both are missing. Except a few situations, methods for missing data have earlier been considered either for missing response or for missing covariates, but comparatively little attention has been directed to account for both missing responses and missing covariates, which is partly attributable to complexity in modeling and computation. This seems to be important as the precise impact of substantial missing data depends on the association between two missing data processes as well. The real difficulty arises when the responses are ordinal by nature. We develop a joint model to take into account simultaneously the association between the ordinal response variable and covariates and also that between the missing data indicators. Such a complex model has been analyzed here by using the Markov chain Monte Carlo approach and also by the Monte Carlo relative likelihood approach. Their performance on estimating the model parameters in finite samples have been looked into. We illustrate the application of these two methods using data from an orthodontic study. Analysis of such data provides some interesting information on human habit. © The Author(s) 2013.

Bayesian source term determination with unknown covariance of measurements

NASA Astrophysics Data System (ADS)

Belal, Alkomiet; Tichý, Ondřej; Šmídl, Václav

2017-04-01

Determination of a source term of release of a hazardous material into the atmosphere is a very important task for emergency response. We are concerned with the problem of estimation of the source term in the conventional linear inverse problem, y = Mx, where the relationship between the vector of observations y is described using the source-receptor-sensitivity (SRS) matrix M and the unknown source term x. Since the system is typically ill-conditioned, the problem is recast as an optimization problem minR,B(y - Mx)TR-1(y - Mx) + xTB-1x. The first term minimizes the error of the measurements with covariance matrix R, and the second term is a regularization of the source term. There are different types of regularization arising for different choices of matrices R and B, for example, Tikhonov regularization assumes covariance matrix B as the identity matrix multiplied by scalar parameter. In this contribution, we adopt a Bayesian approach to make inference on the unknown source term x as well as unknown R and B. We assume prior on x to be a Gaussian with zero mean and unknown diagonal covariance matrix B. The covariance matrix of the likelihood R is also unknown. We consider two potential choices of the structure of the matrix R. First is the diagonal matrix and the second is a locally correlated structure using information on topology of the measuring network. Since the inference of the model is intractable, iterative variational Bayes algorithm is used for simultaneous estimation of all model parameters. The practical usefulness of our contribution is demonstrated on an application of the resulting algorithm to real data from the European Tracer Experiment (ETEX). This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

Estimation of covariate-specific time-dependent ROC curves in the presence of missing biomarkers.

PubMed

Li, Shanshan; Ning, Yang

2015-09-01

Covariate-specific time-dependent ROC curves are often used to evaluate the diagnostic accuracy of a biomarker with time-to-event outcomes, when certain covariates have an impact on the test accuracy. In many medical studies, measurements of biomarkers are subject to missingness due to high cost or limitation of technology. This article considers estimation of covariate-specific time-dependent ROC curves in the presence of missing biomarkers. To incorporate the covariate effect, we assume a proportional hazards model for the failure time given the biomarker and the covariates, and a semiparametric location model for the biomarker given the covariates. In the presence of missing biomarkers, we propose a simple weighted estimator for the ROC curves where the weights are inversely proportional to the selection probability. We also propose an augmented weighted estimator which utilizes information from the subjects with missing biomarkers. The augmented weighted estimator enjoys the double-robustness property in the sense that the estimator remains consistent if either the missing data process or the conditional distribution of the missing data given the observed data is correctly specified. We derive the large sample properties of the proposed estimators and evaluate their finite sample performance using numerical studies. The proposed approaches are illustrated using the US Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. © 2015, The International Biometric Society.

Robust Averaging of Covariances for EEG Recordings Classification in Motor Imagery Brain-Computer Interfaces.

PubMed

Uehara, Takashi; Sartori, Matteo; Tanaka, Toshihisa; Fiori, Simone

2017-06-01

The estimation of covariance matrices is of prime importance to analyze the distribution of multivariate signals. In motor imagery-based brain-computer interfaces (MI-BCI), covariance matrices play a central role in the extraction of features from recorded electroencephalograms (EEGs); therefore, correctly estimating covariance is crucial for EEG classification. This letter discusses algorithms to average sample covariance matrices (SCMs) for the selection of the reference matrix in tangent space mapping (TSM)-based MI-BCI. Tangent space mapping is a powerful method of feature extraction and strongly depends on the selection of a reference covariance matrix. In general, the observed signals may include outliers; therefore, taking the geometric mean of SCMs as the reference matrix may not be the best choice. In order to deal with the effects of outliers, robust estimators have to be used. In particular, we discuss and test the use of geometric medians and trimmed averages (defined on the basis of several metrics) as robust estimators. The main idea behind trimmed averages is to eliminate data that exhibit the largest distance from the average covariance calculated on the basis of all available data. The results of the experiments show that while the geometric medians show little differences from conventional methods in terms of classification accuracy in the classification of electroencephalographic recordings, the trimmed averages show significant improvement for all subjects.

Estimation of genetic connectedness diagnostics based on prediction errors without the prediction error variance-covariance matrix.

PubMed

Holmes, John B; Dodds, Ken G; Lee, Michael A

2017-03-02

An important issue in genetic evaluation is the comparability of random effects (breeding values), particularly between pairs of animals in different contemporary groups. This is usually referred to as genetic connectedness. While various measures of connectedness have been proposed in the literature, there is general agreement that the most appropriate measure is some function of the prediction error variance-covariance matrix. However, obtaining the prediction error variance-covariance matrix is computationally demanding for large-scale genetic evaluations. Many alternative statistics have been proposed that avoid the computational cost of obtaining the prediction error variance-covariance matrix, such as counts of genetic links between contemporary groups, gene flow matrices, and functions of the variance-covariance matrix of estimated contemporary group fixed effects. In this paper, we show that a correction to the variance-covariance matrix of estimated contemporary group fixed effects will produce the exact prediction error variance-covariance matrix averaged by contemporary group for univariate models in the presence of single or multiple fixed effects and one random effect. We demonstrate the correction for a series of models and show that approximations to the prediction error matrix based solely on the variance-covariance matrix of estimated contemporary group fixed effects are inappropriate in certain circumstances. Our method allows for the calculation of a connectedness measure based on the prediction error variance-covariance matrix by calculating only the variance-covariance matrix of estimated fixed effects. Since the number of fixed effects in genetic evaluation is usually orders of magnitudes smaller than the number of random effect levels, the computational requirements for our method should be reduced.

Continental-scale temperature covariance in proxy reconstructions and climate models

NASA Astrophysics Data System (ADS)

Hartl-Meier, Claudia; Büntgen, Ulf; Smerdon, Jason; Zorita, Eduardo; Krusic, Paul; Ljungqvist, Fredrik; Schneider, Lea; Esper, Jan

2017-04-01

Inter-continental temperature variability over the past millennium has been reported to be more coherent in climate model simulations than in multi-proxy-based reconstructions, a finding that undermines the representation of spatial variability in either of these approaches. We assess the covariance of summer temperatures among Northern Hemisphere continents by comparing tree-ring based temperature reconstructions with state-of-the-art climate model simulations over the past millennium. We find inter-continental temperature covariance to be larger in tree-ring-only reconstructions compared to those derived from multi-proxy networks, thus enhancing the agreement between proxy- and model-based spatial representations. A detailed comparison of simulated temperatures, however, reveals substantial spread among the models. Over the past millennium, inter-continental temperature correlations are driven by the cooling after major volcanic eruptions in 1257, 1452, 1601, and 1815. The coherence of these synchronizing events appears to be elevated in several climate simulations relative to their own covariance baselines and the proxy reconstructions, suggesting these models overestimate the amplitude of cooling in response to volcanic forcing at large spatial scales.

Small vessel disease is linked to disrupted structural network covariance in Alzheimer's disease.

PubMed

Nestor, Sean M; Mišić, Bratislav; Ramirez, Joel; Zhao, Jiali; Graham, Simon J; Verhoeff, Nicolaas P L G; Stuss, Donald T; Masellis, Mario; Black, Sandra E

2017-07-01

Cerebral small vessel disease (SVD) is thought to contribute to Alzheimer's disease (AD) through abnormalities in white matter networks. Gray matter (GM) hub covariance networks share only partial overlap with white matter connectivity, and their relationship with SVD has not been examined in AD. We developed a multivariate analytical pipeline to elucidate the cortical GM thickness systems that covary with major network hubs and assessed whether SVD and neurodegenerative pathologic markers were associated with attenuated covariance network integrity in mild AD and normal elderly control subjects. SVD burden was associated with reduced posterior cingulate corticocortical GM network integrity and subneocorticocortical hub network integrity in AD. These findings provide evidence that SVD is linked to the selective disruption of cortical hub GM networks in AD brains and point to the need to consider GM hub covariance networks when assessing network disruption in mixed disease. Copyright © 2017 the Alzheimer's Association. Published by Elsevier Inc. All rights reserved.

Evaluation of a lower-powered analyzer and sampling system for eddy-covariance measurements of nitrous oxide fluxes

NASA Astrophysics Data System (ADS)

Brown, Shannon E.; Sargent, Steve; Wagner-Riddle, Claudia

2018-03-01

Nitrous oxide (N2O) fluxes measured using the eddy-covariance method capture the spatial and temporal heterogeneity of N2O emissions. Most closed-path trace-gas analyzers for eddy-covariance measurements have large-volume, multi-pass absorption cells that necessitate high flow rates for ample frequency response, thus requiring high-power sample pumps. Other sampling system components, including rain caps, filters, dryers, and tubing, can also degrade system frequency response. This field trial tested the performance of a closed-path eddy-covariance system for N2O flux measurements with improvements to use less power while maintaining the frequency response. The new system consists of a thermoelectrically cooled tunable diode laser absorption spectrometer configured to measure both N2O and carbon dioxide (CO2). The system features a relatively small, single-pass sample cell (200 mL) that provides good frequency response with a lower-powered pump ( ˜ 250 W). A new filterless intake removes particulates from the sample air stream with no additional mixing volume that could degrade frequency response. A single-tube dryer removes water vapour from the sample to avoid the need for density or spectroscopic corrections, while maintaining frequency response. This eddy-covariance system was collocated with a previous tunable diode laser absorption spectrometer model to compare N2O and CO2 flux measurements for two full growing seasons (May 2015 to October 2016) in a fertilized cornfield in Southern Ontario, Canada. Both spectrometers were placed outdoors at the base of the sampling tower, demonstrating ruggedness for a range of environmental conditions (minimum to maximum daily temperature range: -26.1 to 31.6 °C). The new system rarely required maintenance. An in situ frequency-response test demonstrated that the cutoff frequency of the new system was better than the old system (3.5 Hz compared to 2.30 Hz) and similar to that of a closed-path CO2 eddy-covariance system (4

Evaluation of orbits with incomplete knowledge of the mathematical expectancy and the matrix of covariation of errors

NASA Technical Reports Server (NTRS)

Bakhshiyan, B. T.; Nazirov, R. R.; Elyasberg, P. E.

1980-01-01

The problem of selecting the optimal algorithm of filtration and the optimal composition of the measurements is examined assuming that the precise values of the mathematical expectancy and the matrix of covariation of errors are unknown. It is demonstrated that the optimal algorithm of filtration may be utilized for making some parameters more precise (for example, the parameters of the gravitational fields) after preliminary determination of the elements of the orbit by a simpler method of processing (for example, the method of least squares).

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Do current cosmological observations rule out all covariant Galileons?

NASA Astrophysics Data System (ADS)

Peirone, Simone; Frusciante, Noemi; Hu, Bin; Raveri, Marco; Silvestri, Alessandra

2018-03-01

We revisit the cosmology of covariant Galileon gravity in view of the most recent cosmological data sets, including weak lensing. As a higher derivative theory, covariant Galileon models do not have a Λ CDM limit and predict a very different structure formation pattern compared with the standard Λ CDM scenario. Previous cosmological analyses suggest that this model is marginally disfavored, yet cannot be completely ruled out. In this work we use a more recent and extended combination of data, and we allow for more freedom in the cosmology, by including a massive neutrino sector with three different mass hierarchies. We use the Planck measurements of cosmic microwave background temperature and polarization; baryonic acoustic oscillations measurements by BOSS DR12; local measurements of H0; the joint light-curve analysis supernovae sample; and, for the first time, weak gravitational lensing from the KiDS Collaboration. We find, that in order to provide a reasonable fit, a nonzero neutrino mass is indeed necessary, but we do not report any sizable difference among the three neutrino hierarchies. Finally, the comparison of the Bayesian evidence to the Λ CDM one shows that in all the cases considered, covariant Galileon models are statistically ruled out by cosmological data.

Boundary Conditions for Scalar (Co)Variances over Heterogeneous Surfaces

NASA Astrophysics Data System (ADS)

Machulskaya, Ekaterina; Mironov, Dmitrii

2018-05-01

The problem of boundary conditions for the variances and covariances of scalar quantities (e.g., temperature and humidity) at the underlying surface is considered. If the surface is treated as horizontally homogeneous, Monin-Obukhov similarity suggests the Neumann boundary conditions that set the surface fluxes of scalar variances and covariances to zero. Over heterogeneous surfaces, these boundary conditions are not a viable choice since the spatial variability of various surface and soil characteristics, such as the ground fluxes of heat and moisture and the surface radiation balance, is not accounted for. Boundary conditions are developed that are consistent with the tile approach used to compute scalar (and momentum) fluxes over heterogeneous surfaces. To this end, the third-order transport terms (fluxes of variances) are examined analytically using a triple decomposition of fluctuating velocity and scalars into the grid-box mean, the fluctuation of tile-mean quantity about the grid-box mean, and the sub-tile fluctuation. The effect of the proposed boundary conditions on mixing in an archetypical stably-stratified boundary layer is illustrated with a single-column numerical experiment. The proposed boundary conditions should be applied in atmospheric models that utilize turbulence parametrization schemes with transport equations for scalar variances and covariances including the third-order turbulent transport (diffusion) terms.

Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation.

PubMed

Lam, Clifford; Fan, Jianqing

2009-01-01

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration problems under a unified framework with a general penalty function. We show that the rates of convergence for these problems under the Frobenius norm are of order (s(n) log p(n)/n)(1/2), where s(n) is the number of nonzero elements, p(n) is the size of the covariance matrix and n is the sample size. This explicitly spells out the contribution of high-dimensionality is merely of a logarithmic factor. The conditions on the rate with which the tuning parameter λ(n) goes to 0 have been made explicit and compared under different penalties. As a result, for the L(1)-penalty, to guarantee the sparsistency and optimal rate of convergence, the number of nonzero elements should be small: sn'=O(pn) at most, among O(pn2) parameters, for estimating sparse covariance or correlation matrix, sparse precision or inverse correlation matrix or sparse Cholesky factor, where sn' is the number of the nonzero elements on the off-diagonal entries. On the other hand, using the SCAD or hard-thresholding penalty functions, there is no such a restriction.

Investigating Approaches to Estimating Covariate Effects in Growth Mixture Modeling: A Simulation Study

ERIC Educational Resources Information Center

Li, Ming; Harring, Jeffrey R.

2017-01-01

Researchers continue to be interested in efficient, accurate methods of estimating coefficients of covariates in mixture modeling. Including covariates related to the latent class analysis not only may improve the ability of the mixture model to clearly differentiate between subjects but also makes interpretation of latent group membership more…

The Importance of Covariate Selection in Controlling for Selection Bias in Observational Studies

ERIC Educational Resources Information Center

Steiner, Peter M.; Cook, Thomas D.; Shadish, William R.; Clark, M. H.

2010-01-01

The assumption of strongly ignorable treatment assignment is required for eliminating selection bias in observational studies. To meet this assumption, researchers often rely on a strategy of selecting covariates that they think will control for selection bias. Theory indicates that the most important covariates are those highly correlated with…

Neutron Reference Benchmark Field Specification: ACRR Free-Field Environment (ACRR-FF-CC-32-CL).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vega, Richard Manuel; Parma, Edward J.; Griffin, Patrick J.

2015-07-01

This report was put together to support the International Atomic Energy Agency (IAEA) REAL- 2016 activity to validate the dosimetry community’s ability to use a consistent set of activation data and to derive consistent spectral characterizations. The report captures details of integral measurements taken in the Annular Core Research Reactor (ACRR) central cavity free-field reference neutron benchmark field. The field is described and an “a priori” calculated neutron spectrum is reported, based on MCNP6 calculations, and a subject matter expert (SME) based covariance matrix is given for this “a priori” spectrum. The results of 31 integral dosimetry measurements in themore » neutron field are reported.« less

A pilot study of cognitive insight and structural covariance in first-episode psychosis.

PubMed

Kuang, Corin; Buchy, Lisa; Barbato, Mariapaola; Makowski, Carolina; MacMaster, Frank P; Bray, Signe; Deighton, Stephanie; Addington, Jean

2017-01-01

Cognitive insight is described as a balance between one's self-reflectiveness (recognition and correction of dysfunctional reasoning), and self-certainty (overconfidence). Neuroimaging studies have linked the ventrolateral prefrontal cortex (VLPFC) to cognitive insight in people with psychosis. However, the relationship between cognitive insight and structural connectivity between the VLPFC and other brain areas is unknown. Here, we investigated the modulation of cognitive insight on structural covariance networks involving the VLPFC in a first-episode psychosis sample. Fifteen patients with a first-episode psychosis provided magnetic resonance (MR) scans and completed the Beck Cognitive Insight Scale (BCIS). MR scans were also available for 15 historical controls. Seed-based analysis of structural covariance was conducted using the Mapping Anatomical Correlations Across the Cerebral Cortex (MACACC) methodology, whereby Pearson correlation coefficients were extracted between seed regions in left and right VLPFC and cortical thickness across the brain. Structural covariance maps between groups were compared at each vertex. In first-episode subjects, we evaluated the modulation of BCIS scores on cortical covariance between VLPFC and every other vertex. Findings showed no significant group difference between first-episode psychosis subjects and controls in thickness covariance seeded from left or right VLPFC. However, in first-episode psychosis subjects, a positive association with self-certainty was found in networks seeded from both left and right VLPFC with thickness in medial frontal cortex and right pars triangularis. No significant associations were found for self-reflectiveness. These results suggest that self-certainty, but not self-reflectiveness, positively modulated cortical covariance in a frontal network in patients with a first-episode psychosis. Copyright © 2016 Elsevier B.V. All rights reserved.

Structural covariance of neostriatal and limbic regions in patients with obsessive-compulsive disorder.

PubMed

Subirà, Marta; Cano, Marta; de Wit, Stella J; Alonso, Pino; Cardoner, Narcís; Hoexter, Marcelo Q; Kwon, Jun Soo; Nakamae, Takashi; Lochner, Christine; Sato, João R; Jung, Wi Hoon; Narumoto, Jin; Stein, Dan J; Pujol, Jesus; Mataix-Cols, David; Veltman, Dick J; Menchón, José M; van den Heuvel, Odile A; Soriano-Mas, Carles

2016-03-01

Frontostriatal and frontoamygdalar connectivity alterations in patients with obsessive-compulsive disorder (OCD) have been typically described in functional neuroimaging studies. However, structural covariance, or volumetric correlations across distant brain regions, also provides network-level information. Altered structural covariance has been described in patients with different psychiatric disorders, including OCD, but to our knowledge, alterations within frontostriatal and frontoamygdalar circuits have not been explored. We performed a mega-analysis pooling structural MRI scans from the Obsessive-compulsive Brain Imaging Consortium and assessed whole-brain voxel-wise structural covariance of 4 striatal regions (dorsal and ventral caudate nucleus, and dorsal-caudal and ventral-rostral putamen) and 2 amygdalar nuclei (basolateral and centromedial-superficial). Images were preprocessed with the standard pipeline of voxel-based morphometry studies using Statistical Parametric Mapping software. Our analyses involved 329 patients with OCD and 316 healthy controls. Patients showed increased structural covariance between the left ventral-rostral putamen and the left inferior frontal gyrus/frontal operculum region. This finding had a significant interaction with age; the association held only in the subgroup of older participants. Patients with OCD also showed increased structural covariance between the right centromedial-superficial amygdala and the ventromedial prefrontal cortex. This was a cross-sectional study. Because this is a multisite data set analysis, participant recruitment and image acquisition were performed in different centres. Most patients were taking medication, and treatment protocols differed across centres. Our results provide evidence for structural network-level alterations in patients with OCD involving 2 frontosubcortical circuits of relevance for the disorder and indicate that structural covariance contributes to fully characterizing brain

Field theory of hyperfluid

NASA Astrophysics Data System (ADS)

Ariki, Taketo

2018-02-01

A hyperfluid model is constructed on the basis of its action entirely free from external constraints, regarding the hyperfluid as a self-consistent classical field. Intrinsic hypermomentum is no longer a supplemental variable given by external constraints, but arises purely from the diffeomorphism covariance of dynamical field. The field-theoretic approach allows natural classification of a hyperfluid on the basis of its symmetry group and corresponding homogeneous space; scalar, spinor, vector, and tensor fluids are introduced as simple examples. Apart from phenomenological constraints, the theory predicts the hypermomentum exchange of fluid via field-theoretic interactions of various classes; fluid–fluid interactions, minimal and non-minimal SU(n) -gauge couplings, and coupling with metric-affine gravity are all successfully formulated within the classical regime.

Non-stationary pre-envelope covariances of non-classically damped systems

NASA Astrophysics Data System (ADS)

Muscolino, G.