NASA Astrophysics Data System (ADS)
Awaluddin, Moehammad; Yuwono, Bambang Darmo; Puspita, Yolanda Adya
2016-05-01
Continuous Global Positioning System (GPS) observations showed significant crustal displacements as a result of the 2010 Mentawai earthquake. The Least Square Inversion method of Mentawai earthquake slip distribution from SuGAR observations yielded in an optimum value of slip distribution by giving a weight of smoothing constraint and a weight of slip value constraint = 0 at the edge of the earthquake rupture area. A maximum coseismic slip of the inversion calculation was 1.997 m and concentrated around stations PRKB (Pagai Island). In addition, the values of dip-slip direction tend to be more dominant. The seismic moment calculated from the slip distribution was 6.89 × 10E+20 Nm, which is equivalent to a magnitude of 7.8.
If Coulomb's law were not inverse square: The charge distribution inside a solid conducting sphere
NASA Astrophysics Data System (ADS)
Spencer, Ross L.
1990-04-01
The distribution of charge between concentric conducting shells has been at the heart of the most sensitive tests of the exponent in Coulomb's law since the days of Henry Cavendish. But it appears that no one has ever answered the question of how an excess of charge would distribute itself throughout the interior of a solid conductor if Coulomb's law were other than inverse square. Spherically symmetric solutions to this problem have been found under the assumption that the potential of a point charge varies either as e-kr/r or as 1/rn.
Wang, Ji-Hua; Huang, Wen-Jiang; Lao, Cai-Lian; Zhang, Lu-Da; Luo, Chang-Bing; Wang, Tao; Liu, Liang-Yun; Song, Xiao-Yu; Ma, Zhi-Hong
2007-07-01
With the widespread application of remote sensing (RS) in agriculture, monitoring and prediction of crop nutrition condition attracts attention of many scientists. Foliar nitrogen content (N) is one of the most important nutrients for plant growth, and vertical leaf N gradient is an important indicator of crop nutrition situation. Investigations have been made on N vertical distribution to describe the growth status of winter wheat. Results indicate that from the canopy top to the ground surface, N shows an obvious gradient decreasing trend. The objective of this study was to discuss the inversion method of N vertical distribution with canopy reflected spectrum by the partial least squares regression (PLS) method. PLS was selected for the inversion of upper, middle and lower layers of N. To improve the accuracy of prediction, the N in the upper layer as well as in the middle and bottom layers should be taken into consideration when crop nutrition condition is appraised by RS data. The established models by the observed data in year 2001-2002 were validated by the data in year 2003-2004. The inversion precision and error were acceptable. It provided a theoretic basis for widely and non-damaged variable rate nitrogen application of winter wheat by canopy reflected spectrum.
On the Magic Square and Inverse
ERIC Educational Resources Information Center
Elzaidi, S. M.
2005-01-01
In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose…
Inverse-Square Orbits: A Geometric Approach.
ERIC Educational Resources Information Center
Rainwater, James C.; Weinstock, Robert
1979-01-01
Presents a derivation of Kepler's first law of planetary motion from Newtonian principles. Analogus derivations of the hyperbolic and parabolic orbits of nonreturning comets and the hyperbolic orbit for a particle in a repulsive inverse-square field are also presented. (HM)
Optical inverse-square displacement sensor
Howe, Robert D.; Kychakoff, George
1989-01-01
This invention comprises an optical displacement sensor that uses the inverse-square attenuation of light reflected from a diffused surface to calculate the distance from the sensor to the reflecting surface. Light emerging from an optical fiber or the like is directed onto the surface whose distance is to be measured. The intensity I of reflected light is angle dependent, but within a sufficiently small solid angle it falls off as the inverse square of the distance from the surface. At least a pair of optical detectors are mounted to detect the reflected light within the small solid angle, their ends being at different distances R and R+.DELTA.R from the surface. The distance R can then be found in terms of the ratio of the intensity measurements and the separation length as ##EQU1##
Optical inverse-square displacement sensor
Howe, R.D.; Kychakoff, G.
1989-09-12
This invention comprises an optical displacement sensor that uses the inverse-square attenuation of light reflected from a diffused surface to calculate the distance from the sensor to the reflecting surface. Light emerging from an optical fiber or the like is directed onto the surface whose distance is to be measured. The intensity I of reflected light is angle dependent, but within a sufficiently small solid angle it falls off as the inverse square of the distance from the surface. At least a pair of optical detectors are mounted to detect the reflected light within the small solid angle, their ends being at different distances R and R + [Delta]R from the surface. The distance R can then be found in terms of the ratio of the intensity measurements and the separation length as given in an equation. 10 figs.
Testing Newton's Gravitational Inverse-Square Law
NASA Astrophysics Data System (ADS)
Hagedorn, Charles
2015-04-01
Newton's inverse-square law of gravitation is the oldest standing mathematical description of a fundamental interaction. Experimental tests of gravity's distance-dependence define a frontier between our understanding of gravity and many proposed forms of new physics. These experiments constrain the size of possible extra dimensions, bound attempted resolution of the cosmological-constant problem, search for self-interacting chameleons, make direct measurements at the dark-energy length-scale, and more. As gravity is ~1040 times weaker than electromagnetism, gravity remains hidden by experimental backgrounds at distances smaller than the diameter of a fine human hair. This talk will survey the past, present, and near-future of the experimental field, with substantial emphasis on precision sub-millimeter laboratory experiments.
Tests of the Gravitational Inverse-Square Law
NASA Astrophysics Data System (ADS)
Adelberger, E. G.; Heckel, B. R.; Nelson, A. E.
2003-12-01
We review recent experimental tests of the gravitational inverse-square law and the wide variety of theoretical considerations that suggest the law may break down in experimentally accessible regions.
The Confirmation of the Inverse Square Law Using Diffraction Gratings
ERIC Educational Resources Information Center
Papacosta, Pangratios; Linscheid, Nathan
2014-01-01
Understanding the inverse square law, how for example the intensity of light or sound varies with distance, presents conceptual and mathematical challenges. Students know intuitively that intensity decreases with distance. A light source appears dimmer and sound gets fainter as the distance from the source increases. The difficulty is in…
The Inverse-Square Law with Data Loggers
ERIC Educational Resources Information Center
Bates, Alan
2013-01-01
The inverse-square law for the intensity of light received at a distance from a light source has been verified using various experimental techniques. Typical measurements involve a manual variation of the distance between a light source and a light sensor, usually by sliding the sensor or source along a bench, measuring the source-sensor distance…
Solving the Inverse-Square Problem with Complex Variables
ERIC Educational Resources Information Center
Gauthier, N.
2005-01-01
The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…
From Moon-Fall to Motions under Inverse Square Laws
ERIC Educational Resources Information Center
Foong, S. K.
2008-01-01
The motion of two bodies, along a straight line, under the inverse square law of gravity is considered in detail, progressing from simpler cases to more complex ones: (1) one body fixed and one free; (2) both bodies free and identical mass; (3) both bodies free and different masses; and (4) the inclusion of electrostatic forces for both bodies'…
Robust inverse kinematics using damped least squares with dynamic weighting
NASA Technical Reports Server (NTRS)
Schinstock, D. E.; Faddis, T. N.; Greenway, R. B.
1994-01-01
This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.
Sub-Millimeter Tests of the Newtonian Inverse Square Law
Adelberger, Eric
2005-11-09
It is remarkable that small-scale experiments can address important open issues in fundamental science such as: 'why is gravity so weak compared to the other interactions?' and 'why is the cosmological constant so small compared to the predictions of quantum mechanics?' String theory ideas (new scalar particles and extra dimensions) and other notions hint that Newton's Inverse-Square Law could break down at distances less than 1 mm. I will review some motivations for testing the Inverse-Square Law, and discuss recent mechanical experiments with torsion balances, small-scillators, micro-cantilevers, and ultra-cold neutrons. Our torsion-balance experiments have probed for gravitational-strength interactions with length scales down to 70 micrometers, which is approximately the diameter of a human hair.
Short-range inverse-square law experiment in space
NASA Technical Reports Server (NTRS)
Strayer, D.; Paik, H. J.; Moody, M. V.
2002-01-01
The objective of ISLES (Inverse-Square Law Experiment in Space) is to perform a null test ofNewton's law on the ISS with a resolution of one part in lo5 at ranges from 100 pm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory prediction with R z 5 pm.
Short-range inverse-square law experiment in space
NASA Technical Reports Server (NTRS)
Paik, H. J.; Moody, M. V.
2002-01-01
Newton's inverse-square law is a cornerstone of General Relativity. Its validity has been demonstrated to better than one part in thousand in ranges greater than 1 cm. The range below 1 mm has been left largely unexplored, due to the difficulties associated with designing sensitive short-range experiments. However, the theoretical rationale for testing Newton's law at ranges below 1 mm has become very strong recently.
Inverse-square law violation and reactor antineutrino anomaly
NASA Astrophysics Data System (ADS)
Naumov, D. V.; Naumov, V. A.; Shkirmanov, D. S.
2017-01-01
We discuss a possibility that the so-called reactor antineutrino anomaly can be, at least in part, explained by applying a quantum field-theoretical approach to neutrino oscillations, which in particular predicts a small deviation from the classical inverse-square law at short but macroscopic distances between the neutrino source and detector. An extensive statistical analysis of the reactor data is performed to examine this speculation.
Short-range inverse-square law experiment in space
NASA Astrophysics Data System (ADS)
Paik, H.; Moody, M.; Strayer, D.
Newton's inverse-square law is a cornerstone of General Relativity. Its validity has been demonstrated to better than one part in 103 in ranges1 cm; however, experimental challenges have left ranges1 mm largely unexplored. The theoretical rationale for testing Newton's law at short ranges has become compelling. The "strong CP problem," in the Standard Model of particle physics has led to the prediction of a new particle, called the "axion," which mediates a short-range mass- mass interaction, as well as a force between intrinsic spin and mass. The axion is also a candidate for cold dark matter. A second imp etus for testing the law at the short ranges comes from string theories where a radius of compactification, R1 μm has recently been suggested. This would imply a violation of the inverse-square law at a level of one part in 104 at a 100 μm distance. The objective our proposed Inverse-Square Law Experiment in Space (ISLES) is to perform a null test of Newton's law on ISS with a resolution of one part in 10 5 at distances ranging from 100 μm to 1 mm. Thus ISLES will be sensitive enough to detect axions with the strongest allowed coupling and test the string-theory prediction with R300 nm. This represents a dramatic improvement over existing limits. The experiment will be cooled in LTMPF, which permits superconducting magnetic levitation of the test masses in the micro-g environment. Low magnetic damping, combined with a low-noise SQUID, leads to extremely low intrinsic noise in the detector. To minimize Newtonian errors, ISLES employs a near null source, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a distance of 100 μm and are configured as a superconducting differential accelerometer. As the source position is driven sinusoidally, a violation of the inverse-square law would appear at the second harmonic as a differential acceleration signal. Direct vibration
Testing the gravitational inverse-square law at centimeter scales
NASA Astrophysics Data System (ADS)
Bonicalzi, Ricco
Many attempts to unify gravity with the Standard Model entail a gravitational inverse-square-law violation (ISLV) at some low level. This dissertation reports on the initial phase of a torsion-pendulum null experiment searching for such a violation in the interaction between two macroscopic bodies with a characteristic separation of 12 cm. Central to the experimental design is the special configuration of the mass distributions of both the pendulum and source mass to provide high-sensitivity to the horizontal gradient of the Laplacian of the interaction potential (a signature of ISLV), while strongly suppressing coupling through Newtonian gravity. Specifically, this design ensures that gravitational systematic effects arise only at second order in the fabrication errors of the pendulum and source mass. A key aspect of this work is the choice of the second-harmonic amplitude of pendulum oscillation as the torque observable, instead of the traditional oscillation frequency. This relatively recent torsion-pendulum method is markedly less sensitive to changes in torsion-fiber temperature and enables the ambient-temperature instrumentation of the initial phase to achieve necessary noise performance without heroic efforts to stabilize temperature. As details of the second-harmonic method have not yet been published, the presentation here dwells on a number of subtleties involved in analyzing the data. Experimental results are reported assuming a Yukawa-type interaction anomaly, where a is the strength of the Yukawa term relative to Newtonian gravity. A preliminary set of 34 data runs, each around a day in duration, produced a value of alpha = (-6.3 +/- 7.5) x 10-5. In the absence of significant systematic effects, even this interim result would have placed tighter bounds on ISLV than previously appearing in the literature. Unfortunately, an accelerated Department of Energy deadline for demolition of our Hanford laboratory facility compelled a shift of focus to the
Classical and quantum dynamics in an inverse square potential
Guillaumín-España, Elisa; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2014-10-15
The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence of bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.
Linking Inverse Square Law with Quantum Mechanical Probabilities
NASA Astrophysics Data System (ADS)
Goradia, Shantilal
2008-03-01
(2007 by S Goradia) I modify the Newtonian inverse square law with a postulate that the probability of interaction between two elementary particles varies inversely as the statistical number of Planck lengths separating them. For two nucleons a million Planck lengths apart, the probability of an interaction is a trillionth (almost never), seemingly contradicting gravity. Likewise, statistical expression of the size of the universe implicitly addresses the issue of dark energy by linking fine-structure constant α = 1/137 with the cosmological constant λ = 1/R^2 (abstract submitted 11/11/07 for APS APR2008 meeting). Since light travels one Planck length per Planck time, the radius R of the spherical shape of the universe is 10^60 Planck lengths, linking the cosmological constant λ = 1/10^120 (see equation 14 in Einstein's 1917 paper) with α by the relationship 1/α ln(1/ λ). Intuitive answers to the questions raised suggest that the elementary particles interact via Planck scale mouths ^(1), with higher probabilities at smaller distances. This intuition may be supported by genetics, explaining issues such DNA -- nucleosome interaction ^(2) (3). [1] http://www.arxiv.org/pdf/physics/0210040 [v. 3] [2] www.gravityresearchinstitute.org [3] Segal E. et al, A genomic code for nucleosome positioning. Nature 442, pp. 772-778, 2006.
Gravitational Microlensing in Modified Gravity Theories - Inverse-Square Theorem
NASA Astrophysics Data System (ADS)
Asada, H.
2011-02-01
Microlensing studies are usually based on the lens equation that is valid only to the first order in the gravitational constant G and lens mass M. We consider corrections to the conventional lens equation in terms of differentiable functions, so that they can express not only the second-order effects of GM in general relativity but also modified gravity theories. As a generalization of Ebina et al. (Prog. Theor. Phys. 104 (2000), 1317), we show that, provided that the spacetime is static, spherically symmetric and asymptotically flat, the total amplification by microlensing remains unchanged at the linear order of the correction to the deflection angle, if and only if the correction takes a particular form as the inverse square of the impact parameter, whereas the magnification factor for each image is corrected. It is concluded that the light curve shape by microlensing is inevitably changed and will thus allow us to probe modified gravity, unless a modificati on to the deflection angle takes the particular form. No systematic deviation in microlensing observations has been reported. For instance, therefore, the Yukawa-type correction is constrained as the characteristic length > 10^{14} m.
Superconducting gravity gradiometer and a test of inverse square law
NASA Technical Reports Server (NTRS)
Moody, M. V.; Paik, Ho Jung
1989-01-01
The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth.
On the pole of non-square transfer function matrix Moore-Penrose pseudo-inverses
NASA Astrophysics Data System (ADS)
Zhang, Wei; Ou, Linlin; He, Xing; Zhang, Weidong
2015-10-01
An essential step in many controller design approaches is computing the inverse of the plant. For a square plant, its inverse is stable if the plant is minimum phase (MP). Nevertheless, this conclusion does not hold for a non-square plant. In this paper, the pole feature of the Moore-Penrose pseudo-inverse of a non-square transfer function matrix is analysed. Instead of complicated advanced mathematical tools, only basic results of polynomial theory and the Binet-Cauchy theorem are used in the analysing procedure. The condition for testing the stability of the Moore-Penrose pseudo-inverse of an MP non-square transfer function matrix is given. This condition implies that the Moore-Penrose pseudo-inverse of a non-square transfer function matrix cannot be directly used as the optimal controller. Numerical examples are provided to illustrate the correctness of the condition.
Inequality constraint in least-square inversion of geophysical data
Kim, Hee Joon; Song, Yoonho; Lee, Ki Ha
1998-06-01
This paper presents a simple, generalized parameter constraint using a priori information to obtain a stable inverse of geophysical data. In the constraint the a priori information can be expressed by two limits: lower and upper bounds. This is a kind of inequality constraint, which is usually employed in linear programming. In this paper, we have derived this parameter constraint as a generalized version of positiveness constraint of parameter, which is routinely used in the inversion of electrical and EM data. However, the two bounds are not restricted to positive values. The width of two bounds reflects the reliability of ground information, which is obtained through well logging and surface geology survey. The effectiveness and convenience of this inequality constraint is demonstrated through the smoothness-constrained inversion of synthetic magnetotelluric data.
Development of a superconducting gravity gradiometer for a test of the inverse square law
Mapoles, E.R.
1981-01-01
The inverse square law of gravitation is known to agree with astronomical data to very high accuracy, but recent theoretical and experimental work indicate that the inverse square law may be violated at distances less than 100 km. Such a violation would signal the existence of a new force. In order to check the inverse square law we are preparing to search for a non-newtonian force in a cylindrical shell. The cyclindrical shell has the property that the newtonian effects nearly cancel, so that we are doing a nearly null experiment. We have developed a superconducting gradiometer to measure the gravitational force gradients at the center of this cylindrical shell. By measuring both the vertical and horizontal gradients we can eliminate effects due to imperfections in the cylinder. This thesis describes the instrument and its performance as well as calculations of the sensitivity of the inverse square law test.
Most-Perfect Pandiagonal Magic Squares and Their Moore-Penrose Inverse
ERIC Educational Resources Information Center
Trenkler, Dietrich; Trenkler, Gotz
2004-01-01
In this note 4 x 4 most-perfect pandiagonal magic squares are considered in which rows, columns and the two main, along with the broken, diagonals add up to the same sum. It is shown that the Moore-Penrose inverse of these squares has the same magic property.
The incomplete inverse and its applications to the linear least squares problem
NASA Technical Reports Server (NTRS)
Morduch, G. E.
1977-01-01
A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.
Efficient lookup table using a linear function of inverse distance squared.
Jung, Jaewoon; Mori, Takaharu; Sugita, Yuji
2013-10-30
The major bottleneck in molecular dynamics (MD) simulations of biomolecules exist in the calculation of pairwise nonbonded interactions like Lennard-Jones and long-range electrostatic interactions. Particle-mesh Ewald (PME) method is able to evaluate long-range electrostatic interactions accurately and quickly during MD simulation. However, the evaluation of energy and gradient includes time-consuming inverse square roots and complementary error functions. To avoid such time-consuming operations while keeping accuracy, we propose a new lookup table for short-range interaction in PME by defining energy and gradient as a linear function of inverse distance squared. In our lookup table approach, densities of table points are inversely proportional to squared pair distances, enabling accurate evaluation of energy and gradient at small pair distances. Regardless of the inverse operation here, the new lookup table scheme allows fast pairwise nonbonded calculations owing to efficient usage of cache memory.
High Accuracy Optical Inverse Square Law Experiment Using Inexpensive Light to Frequency Converters
ERIC Educational Resources Information Center
Wanser, Keith H.; Mahrley, Steve; Tanner, Joshua
2012-01-01
In this paper we report on the use of two different light to frequency converters, four different light sources, three of which are novel and inexpensive, and a hand held digital multimeter with a frequency counter, suitable for making accurate and rapid determination of the optical inverse square law exponent of -2 to better than [plus or…
Analysis of Temperature Distributions in Nighttime Inversions
NASA Astrophysics Data System (ADS)
Telyak, Oksana; Krasouski, Aliaksandr; Svetashev, Alexander; Turishev, Leonid; Barodka, Siarhei
2015-04-01
Adequate prediction of temperature inversion in the atmospheric boundary layer is one of prerequisites for successful forecasting of meteorological parameters and severe weather events. Examples include surface air temperature and precipitation forecasting as well as prediction of fog, frosts and smog with hazardous levels of atmospheric pollution. At the same time, reliable forecasting of temperature inversions remains an unsolved problem. For prediction of nighttime inversions over some specific territory, it is important to study characteristic features of local circulation cells formation and to properly take local factors into account to develop custom modeling techniques for operational use. The present study aims to investigate and analyze vertical temperature distributions in tropospheric inversions (isotherms) over the territory of Belarus. We study several specific cases of formation, evolution and decay of deep nighttime temperature inversions in Belarus by means of mesoscale numerical simulations with WRF model, considering basic mechanisms of isothermal and inverse temperature layers formation in the troposphere and impact of these layers on local circulation cells. Our primary goal is to assess the feasibility of advance prediction of inversions formation with WRF. Modeling results reveal that all cases under consideration have characteristic features of radiative inversions (e.g., their formation times, development phases, inversion intensities, etc). Regions of "blocking" layers formation are extensive and often spread over the entire territory of Belarus. Inversions decay starts from the lowermost (near surface) layer (altitudes of 5 to 50 m). In all cases, one can observe formation of temperature gradients that substantially differ from the basic inversion gradient, i.e. the layer splits into smaller layers, each having a different temperature stratification (isothermal, adiabatic, etc). As opposed to various empirical techniques as well as
Particle-Physics Implications of a Recent Test of the Gravitational Inverse-Square Law
Adelberger, E. G.; Heckel, B. R.; Hoedl, S.; Hoyle, C. D.; Kapner, D. J.; Upadhye, A.
2007-03-30
We use data from our recent search for violations of the gravitational inverse-square law to constrain dilaton, radion, and chameleon exchange forces as well as arbitrary vector or scalar Yukawa interactions. We test the interpretation of the PVLAS Collaboration effect and a conjectured ''fat-graviton'' scenario and constrain the {gamma}{sub 5} couplings of pseuodscalar bosons and arbitrary power-law interactions.
A novel study on Kepler’s law and inverse square law of gravitation
NASA Astrophysics Data System (ADS)
Zhang, Bingzhan; Zhen, Shengchao; Zhao, Han; Huang, Kang; Deng, Bin; Chen, Ye-Hwa
2015-05-01
The Udwadia-Kalaba equation is a simple, aesthetic, and thought-provoking description of the world at a very fundamental level. It is about the way systems move. In this paper, we creatively apply the Udwadia-Kalaba approach to study heavenly bodies’ movements (especially on Kepler’s law and the inverse square law of gravitation). In an alternative way, we show that a heavenly body’s motion orbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular momentum. Furthermore, by applying the Udwadia-Kalaba approach, we use the constraint of motion orbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint (or energy conservation constraint) and easily verify that any heavenly body’s motion complies with the inverse square law of gravitation. That is, we study Kepler’s law and Newton’s inverse square law in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move and also makes the celestial mechanician more clear about the analytical mechanics (the Udwadia-Kalaba approach). Furthermore, for the students of dynamics and celestial physics, a different unique perspective is provided for them to study. At the end, we present the detailed process of applying the Udwadia-Kalaba approach to two imaginary cases to show its simplicity and efficiency.
Extended inverse Lindley distribution: properties and application.
Alkarni, Said Hofan
2015-01-01
In this paper, we introduce an extension of the inverse Lindley distribution, which offers more flexibility in modeling upside-down bathtub lifetime data. Some statistical properties of the proposed distribution are explicitly derived. These include density and hazard rate functions with their behavior, moments, moment generating function, skewness, kurtosis measures, and quantile function. Maximum likelihood estimation of the parameters and their estimated asymptotic distribution and confidence intervals are derived. Rényi entropy as a measure of the uncertainty in the model is derived. The application of the model to a real data set i.e., the flood levels for the Susquehanna river at Harrisburg, Pennsylvania, over 20 four-year periods from 1890 to 1969 is compared to the fit attained by some other well-known existing distributions.
Flores-Ruiz, Hugo M; Naumis, Gerardo G
2012-04-01
In the energy landscape picture, the dynamics of glasses and crystals is usually decomposed into two separate contributions: interbasin and intrabasin dynamics. The intrabasin dynamics depends partially on the quadratic displacement distribution on a given metabasin. Here we show that such a distribution can be approximated by a Gamma function, with a mean that depends linearly on the temperature and on the inverse second moment of the density of vibrational states. The width of the distribution also depends on this last quantity, and thus the contribution of the boson peak in glasses is evident on the tail of the distribution function. It causes the distribution of the mean-square displacement to decay slower in glasses than in crystals. When a statistical analysis is performed under many energy basins, we obtain a Gaussian in which the width is regulated by the mean inverse second moment of the density of states. Simulations performed in binary glasses are in agreement with such a result.
Sensitivity analysis of distributed volcanic source inversion
NASA Astrophysics Data System (ADS)
Cannavo', Flavio; Camacho, Antonio G.; González, Pablo J.; Puglisi, Giuseppe; Fernández, José
2016-04-01
A recently proposed algorithm (Camacho et al., 2011) claims to rapidly estimate magmatic sources from surface geodetic data without any a priori assumption about source geometry. The algorithm takes the advantages of fast calculation from the analytical models and adds the capability to model free-shape distributed sources. Assuming homogenous elastic conditions, the approach can determine general geometrical configurations of pressured and/or density source and/or sliding structures corresponding to prescribed values of anomalous density, pressure and slip. These source bodies are described as aggregation of elemental point sources for pressure, density and slip, and they fit the whole data (keeping some 3D regularity conditions). Although some examples and applications have been already presented to demonstrate the ability of the algorithm in reconstructing a magma pressure source (e.g. Camacho et al., 2011,Cannavò et al., 2015), a systematic analysis of sensitivity and reliability of the algorithm is still lacking. In this explorative work we present results from a large statistical test designed to evaluate the advantages and limitations of the methodology by assessing its sensitivity to the free and constrained parameters involved in inversions. In particular, besides the source parameters, we focused on the ground deformation network topology, and noise in measurements. The proposed analysis can be used for a better interpretation of the algorithm results in real-case applications. Camacho, A. G., González, P. J., Fernández, J. & Berrino, G. (2011) Simultaneous inversion of surface deformation and gravity changes by means of extended bodies with a free geometry: Application to deforming calderas. J. Geophys. Res. 116. Cannavò F., Camacho A.G., González P.J., Mattia M., Puglisi G., Fernández J. (2015) Real Time Tracking of Magmatic Intrusions by means of Ground Deformation Modeling during Volcanic Crises, Scientific Reports, 5 (10970) doi:10.1038/srep
Rapid Inversion of Angular Deflection Data for Certain Axisymmetric Refractive Index Distributions
NASA Technical Reports Server (NTRS)
Rubinstein, R.; Greenberg, P. S.
1994-01-01
Certain functions useful for representing axisymmetric refractive-index distributions are shown to have exact solutions for Abel transformation of the resulting angular deflection data. An advantage of this procedure over direct numerical Abel inversion is that least-squares curve fitting is a smoothing process that reduces the noise sensitivity of the computation
Null Test of the Gravitational Inverse Square Law with a Superconducting Gravity Gradiometer.
NASA Astrophysics Data System (ADS)
Chan, Hinghung Anthony
The goal of this research was to develop a cryogenic gravitational null detector and to carry out a prototype test of the inverse square law with the new instrument on a laboratory scale of 1 - 10 m. The Laplacian of the Newtonian gravitational potential (DEL)('2)(phi), is source independent and is a null quantity in vacuum. It has, therefore, been proposed to perform a null test of the inverse square law by using a three-axis gravity gradiometer as a null detector. We have analyzed such a null experiment in detail using gravity sources of various kinds. Errors in the null detector such as misalignment between two differencing component accelerometers, orthogonality errors among three gradiometer axes, and a finite baseline effect have been analyzed. Various orientations and configurations of the detector and the source are suggested to suppress these errors. The single-axis portion of a three-axis superconducting gravity gradiometer has been completed in the course of this research. The theory of the superconducting gravity gradiometer has been generalized and put into a Lagrangian formulation. A condition for frequency-independent common mode balance is derived and verified in the experiment. This balance combined with a multi-stage vibration isolation scheme has enabled a stable operation of the gradiometer for prolonged periods. In a preliminary test, the gradiometer has exhibited a noise level of 1 - 2 E Hz('- 1/2) below 1 Hz, limited by seismic noise, where 1 E (TBOND) 10(' -9) m s('-2) m('-1). To perform a test of the inverse square law, the single-axis gradiometer is mounted with its axis tilted from the vertial by an angle tan('-1(' ))SQRT.(2. The device is then turned incrementally by 120(DEGREES) around the vertical to carry the gradiometer from one axis to the other two axes of an orthogonal coordinate system. A lead pendulum weighing 1,600 kg forms a periodic monopole source of gravity. The gradiometer outputs are individually time-averaged over 2
NASA Astrophysics Data System (ADS)
Alkharji, Mohammed N.
Most fracture characterization methods provide a general description of the fracture parameters as part of the reservoirs parameters; the fracture interaction and geometry within the reservoir is given less attention. T-Matrix and Linear Slip effective medium fracture models are implemented to invert the elastic tensor for the parameters and geometries of the fractures within the reservoir. The fracture inverse problem has an ill-posed, overdetermined, underconstrained rank-deficit system of equations. Least-squares inverse methods are used to solve the problem. A good starting initial model for the parameters is a key factor in the reliability of the inversion. Most methods assume that the starting parameters are close to the solution to avoid inaccurate local minimum solutions. The prior knowledge of the fracture parameters and their geometry is not available. We develop a hybrid, enumerative and Gauss-Newton, method that estimates the fracture parameters and geometry from the elastic tensor with no prior knowledge of the initial parameter values. The fracture parameters are separated into two groups. The first group contains the fracture parameters with no prior information, and the second group contains the parameters with known prior information. Different models are generated from the first group parameters by sampling the solution space over a predefined range of possible solutions for each parameter. Each model generated by the first group is fixed and used as a starting model to invert for the second group of parameters using the Gauss-Newton method. The least-squares residual between the observed elastic tensor and the estimated elastic tensor is calculated for each model. The model parameters that yield the least-squares residual corresponds to the correct fracture reservoir parameters and geometry. Two synthetic examples of fractured reservoirs with oil and gas saturations were inverted with no prior information about the fracture properties. The
NASA Astrophysics Data System (ADS)
Jardani, A.; Revil, A.; Akoa, F.; Schmutz, M.; Florsch, N.; Dupont, J. P.
2006-10-01
We propose a least squares inversion algorithm to determine the spatially variable depth of the water table in shallow unconfined aquifers using self-potential signals measured on the ground surface. Traditionally, the water table is determined only at few locations using piezometers. Our approach relates its shape with the distribution of the self-potential signals according to a Fredholm equation of the first kind. The latter is discretized to obtain a linear matrix formulation of the forward problem. This new formulation is very general and can account for the resistivity distribution of the vadose zone. It is used to setup the inverse problem using the approach of Tarantola (1987) for a test site located in Normandy (France) where 225 self-potential measurements were performed over an area of 15,400 m2. Ground water flows through the loess overlying a low permeability clay-with-flint weathered chalk, at a depth between 1 to 7 meters, into sinkholes in chalk bedrock. The method determines the water table with a precision of 0.4 m.
Null Test of Newtonian Inverse-Square-Law at Short Range: Current Status and Developments
NASA Astrophysics Data System (ADS)
Guan, S.; Tu, L.; Luo, J.; Shao, C.; Liu, L.
Motivated by a variety of novel theories that predict new effects,we will test Newtonian inverse-square law (ISL) at several sub-millimeter separations using a torsion pendulum in its horizontal direction. We had tested ISL at separations ranging down to 176μ m, previous result stated that no new effects were observed. [L. C. Tu, S. G. Guan, J. Luo, C. G. Shao and L. X. Liu, Phys. Rev. Lett. 98 (2007), 201101.] On the basis of before, an improved ISL experiment (IISL) has been proposed, detecting distance will close up to 120μm and prospective result will set a constraint on Yukawa interactions with | α | ≥ 1 at 95% confidence for λ < 33 μ m, which will improve previous short-range constraints by one order at least.
Falling of a quantum particle in an inverse square attractive potential
NASA Astrophysics Data System (ADS)
Vasyuta, Vasyl M.; Tkachuk, Volodymyr M.
2016-12-01
Evolution of a quantum particle in an inverse square potential is studied by analysis of the equation of motion for
Finding a Minimally Informative Dirichlet Prior Distribution Using Least Squares
Dana Kelly; Corwin Atwood
2011-03-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straight-forward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in closed form, and so an approximate beta distribution is used in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial aleatory model for common-cause failure, must be estimated from data that is often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Bielajew, Alex F; Tessier, Frédéric; El Gamal, Islam
2015-12-01
The Nuclear Enterprises (Model 2575) 600 cc ionisation chamber is examined to discover the cause of its anomalous behaviour in inverse-square stability measurements. Measurements and Monte Carlo calculations are employed to isolate the cause of the discrepancy. It is found that most of the effect is due to the long photon attenuation pathlengths in the long side wall of the instrument. A phenomenological procedure, based on measurements, is proposed to correct for the anomaly. The procedure results in inverse-square stability to within 0.5 % over a range of 1-7 m.
NASA Astrophysics Data System (ADS)
Bui, The Anh; D'Ancona, Piero; Duong, Xuan Thinh; Li, Ji; Ly, Fu Ken
2017-02-01
Let La be a Schrödinger operator with inverse square potential a | x|-2 on Rd, d ≥ 3. The main aim of this paper is to prove weighted estimates for fractional powers of La. The proof is based on weighted Hardy inequalities and weighted inequalities for square functions associated to La. As an application, we obtain smoothing estimates regarding the propagator e itLa.
Using a photo-resistor to verify irradiance inverse square and Malus' laws
NASA Astrophysics Data System (ADS)
Tavares, A. Dias; Sosman, L. P.; da Fonseca, R. J. M.; da Mota, L. A. C. P.; Muramatsu, M.
2008-04-01
In this article we present two single teaching experiments both related to light intensity measurements. These simple experiments can be conducted in order to train and teach other concepts and capabilities far exceeding those most obviously involved. The main problem presented to the students is that concerning the light detector. Our experiment uses an inexpensive, find to easy and trustable one, a photo-resistor. The student has to use some well suited method in order to calibrate the photo-resistor for intensities. We explore two methods to achieve this calibration, one very simple and with inexpensive materials and other with more expensive equipment. Afterwards, students proceed studying the behavior of the intensity of a point source with distance in order to verify the inverse square law, as well as the behavior of light intensity with the angle between the transmission axis of two linear polarizers, in order to verify the Malus' Law. Both experiments explore data treatment and graphics in order to choose the best method for the analysis. We present procedures and results obtained with these simple experiments.
A conditionally exactly solvable generalization of the inverse square root potential
NASA Astrophysics Data System (ADS)
Ishkhanyan, A. M.
2016-11-01
We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum.
Cunefare, Kenneth A; Biesel, Van B; Tran, John; Rye, Ryan; Graf, Aaron; Holdhusen, Mark; Albanese, Anne-Marie
2003-02-01
Qualification of anechoic chambers is intended to demonstrate that the chamber supports the intended free-field environment within some permissible tolerance bounds. Key qualification issues include the method used to obtain traverse data, the analysis method for the data, and the use of pure tone or broadband noise as the chamber excitation signal. This paper evaluates the relative merits of continuous versus discrete traverses, of fixed versus optimal reference analysis of the traverse data, and of the use of pure tone versus broadband signals. The current practice of using widely space discrete sampling along a traverse is shown to inadequately sample the complexity of the sound field extant with pure tone traverses, but is suitable for broadband traverses. Continuous traverses, with spatial resolution on the order of 15% of the wavelength at the frequency of interest, are shown to be necessary to fully resolve the spatial complexity of pure tone qualifications. The use of an optimal reference method for computing the deviations from inverse square law is shown to significantly improve the apparent performance of the chamber for pure tone qualifications. Finally, the use of broadband noise as the test signal, as compared to pure tone traverses over the same span, is demonstrated to be a marginal indicator of chamber performance.
ERIC Educational Resources Information Center
Whyntie, T.; Parker, B.
2013-01-01
The Timepix hybrid silicon pixel detector has been used to investigate the inverse square law of radiation from a point source as a demonstration of the CERN [at] school detector kit capabilities. The experiment described uses a Timepix detector to detect the gamma rays emitted by an [superscript 241]Am radioactive source at a number of different…
NASA Astrophysics Data System (ADS)
Choi, S.; Kim, C.; Kim, H. R.; Park, C.; Park, H. Y.
2015-12-01
We performed the marine magnetic and the bathymetry survey in the Lau basin for finding the submarine hydrothermal deposits in October 2009. We acquired magnetic and bathymetry datasets by using Overhouser Proton Magnetometer SeaSPY(Marine Magnetics Co.) and Multi-Beam Echo Sounder EM120(Kongsberg Co.). We conducted the data processing to obtain detailed seabed topography, magnetic anomaly and reduction to the pole(RTP). The Lau basin is one of the youngest back-arc basins in the Southwest Pacific. This region was a lot of hydrothermal activities and hydrothermal deposits. In particular, Tofua Arc(TA) in the Lau basin consists of various and complex stratovolcanos(from Massoth et al., 2007).), We calculated the magnetic susceptibility distribution of the TA19-1 seamount(longitude:176°23.5'W, latitude: 22°42.5'W)area using the RTP data by 3-D magnetic inversion from Jung's previous study(2013). Based on 2D 'compact gravity inversion' by Last & Kubik(1983), we expend it to the 3D algorithm using iterative reweighted least squares method with some weight matrices. The used weight matrices are two types: 1) the minimum gradient support(MGS) that controls the spatial distribution of the solution from Porniaguine and Zhdanov(1999); 2) the depth weight that are used according to the shape of subsurface structures. From the modeling, we derived the appropriate scale factor for the use of depth weight and setting magnetic susceptibility. Furthermore, we have to enter a very small error value to control the computation of the singular point of the inversion model that was able to be easily calculated for modeling. In addition, we applied separately weighted value for the correct shape and depth of the magnetic source. We selected the best results model by change to converge of RMS. Compared between the final modeled result and RTP values in this study, they are generally similar to the each other. But the input values and the modeled values have slightly little difference
Null test of the gravitational inverse square law with a superconducting gravity gradiometer
Chan, H.A.
1982-01-01
The single-axis portion of a three-axis superconducting gravity gradiometer has been completed in the course of this research. The theory of the superconducting gravity gradiometer has been generalized and put into a Lagrangian formulation. A condition for frequency-independent common mode balance combined with a multi-stage vibration isolation scheme has enabled a stable operation of the gradiometer for prolonged periods. In a preliminary test, the gradiometer has exhibited a noise level of 1-2 E Hz/sup -//sup 1/2/ below 1 Hz, limited by seismic noise, where 1 E = 10/sup -9/ m s/sup -2/ m/sup -1/. To perform a test of the inverse square law, the single-axis gradiometer is mounted with its axis tilted from the vertial by an angle tan/sup -1/ ..sqrt..2. The device is then turned incrementally by 120/sup 0/ around the vertical to carry the gradiometer from one axis to the other two axes of an orthogonal coordinate system. A lead pendulum weighing 1600 kg forms a periodic monopole source of gravity. The gradiometer outputs are individually time-averaged over 2000 s for each orientation of the gradients, and then are summed together. With somewhat crude metrology thus far, a preliminary test gives limits -0.012less than or equal to..cap alpha..less than or equal to0.036 for the coupling ..cap alpha.. of the nonNewtonian amplitude at the force rance ..mu../sup -1/ of 1 m, when the force law is written as phi(r) = -GM/r(1 + ..cap alpha..e/sup -//sup ..mu..r/). A few metrological corrections were made to account for errors induced in turning the single-axis detector into the three orientations.
2010-01-01
Micropolar fluids Dipolar fluids a b s t r a c t The exact inverses of a class of Laplace transforms involving doubly-nested square roots and two branch...mechanics, for a micropolar fluid is determined. Published by Elsevier Ltd. 1. Introduction and problem formulation Using the Laplace transform, we...to the case of micropolar fluids, the theory of which was formulated by Eringen (1966). In doing so, we also extend the re- sults of Jordan et al
Fair and Square Computation of Inverse "Z"-Transforms of Rational Functions
ERIC Educational Resources Information Center
Moreira, M. V.; Basilio, J. C.
2012-01-01
All methods presented in textbooks for computing inverse "Z"-transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence "x"("k") whose "Z"-transform is "X"("z"); 2) computation using the inversion integral…
Inverse Beta: Inverse cumulative density function (CDF) of a Beta distribution
NASA Astrophysics Data System (ADS)
Kipping, David
2014-03-01
The Beta Inverse code solves the inverse cumulative density function (CDF) of a Beta distribution, allowing one to sample from the Beta prior directly. The Beta distribution is well suited as a prior for the distribution of the orbital eccentricities of extrasolar planets; imposing a Beta prior on orbital eccentricity is valuable for any type of observation of an exoplanet where eccentricity can affect the model parameters (e.g. transits, radial velocities, microlensing, direct imaging). The Beta prior is an excellent description of the current, empirically determined distribution of orbital eccentricities and thus employing it naturally incorporates an observer’s prior experience of what types of orbits are probable or improbable. The default parameters in the code are currently set to the Beta distribution which best describes the entire population of exoplanets with well-constrained orbits.
Prestack AVA inversion of exact Zoeppritz equations based on modified Trivariate Cauchy distribution
NASA Astrophysics Data System (ADS)
Zhou, Lin; Li, Jingye; Chen, Xiaohong; Liu, Xingye; Chen, Li
2017-03-01
Obtaining interlayer weak reflection information that helps identify properties and accurate density information from complex and elusive reservoirs is particularly important for reservoir characterization and detection. However, conventional prestack amplitude variation with incidence angle inversion method is strongly influenced by the accuracy of the approximate Zoeppritz equations, which suppresses weak reflections coming from the commonly used prior distribution. In this paper, we address these problems by using exact Zoeppritz equations. First, the objective function of the inverse problem was constructed and the modified Cauchy distribution was introduced as the prior information by utilizing Bayes' theorem. In the complicated objective function, the forward operators are the sophisticated and nonlinear Zoeppritz equations with respect to estimate parameters. We then combined the idea of generalized linear inversion with iterative reweighed least-squares algorithm in order to solve the problem. Generalized linear inversion was used to solve the objective function, from which a nonlinear solution of the model parameters' perturbations can be calculated. The iterative reweighed least-squares algorithm was applied to solve the nonlinear expression in an attempt to obtain an updated iterative formula of the model parameters. Therefore the prestack amplitude variation with incidence angle inversion was able to be performed in order to better characterize a reservoir. Both synthetic and field data examples show that the new method can not only directly inverse P-wave velocity, S-wave velocity and density, but also provides accurate estimation results, particularly for density. The introduction of the modified Trivariate Cauchy prior constraints effectively estimated and inverted elastic parameters of weak reflections. Both examples demonstrated the feasibility and effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
de Foy, B.; Cui, Y. Y.; Schauer, J. J.; Janssen, M.; Turner, J. R.; Wiedinmyer, C.
2015-03-01
Emission inventories of elemental carbon (EC) and organic carbon (OC) contain large uncertainties both in their spatial and temporal distributions for different source types. An inverse model was used to evaluate EC and OC emissions based on 1 year of hourly measurements from the St. Louis-Midwest supersite. The input to the model consisted of continuous measurements of EC and OC obtained for 2002 using two semicontinuous analyzers. High resolution meteorological simulations were performed for the entire time period using the Weather Research and Forecasting Model (WRF). These were used to simulate hourly back trajectories at the measurement site using a Lagrangian model (FLEXPART-WRF). In combination, an Eulerian model (CAMx: The Comprehensive Air Quality Model with Extensions ) was used to simulate the impacts at the measurement site using known emissions inventories for point and area sources from the Lake Michigan Directors Consortium (LADCO) as well as for open burning from the Fire Inventory from NCAR (FINN). By considering only passive transport of pollutants, the Bayesian inversion simplifies to a single least squares inversion. The inverse model combines forward Eulerian simulations with backward Lagrangian simulations to yield estimates of emissions from sources in current inventories as well as from emissions that might be missing in the inventories. The CAMx impacts were disaggregated into separate time chunks in order to determine improved diurnal, weekday and monthly temporal patterns of emissions. Because EC is a primary species, the inverse model estimates can be interpreted directly as emissions. In contrast, OC is both a primary and a secondary species. As the inverse model does not differentiate between direct emissions and formation in the plume of those direct emissions, the estimates need to be interpreted as contributions to measured concentrations. Emissions of EC and OC in the St. Louis region from on-road, non-road, marine
Lo, Yen-Li; Pan, Wen-Harn; Hsu, Wan-Lun; Chien, Yin-Chu; Chen, Jen-Yang; Hsu, Mow-Ming; Lou, Pei-Jen; Chen, I-How; Hildesheim, Allan; Chen, Chien-Jen
2016-01-01
Evidence on the association between dietary component, dietary pattern and nasopharyngeal carcinoma (NPC) is scarce. A major challenge is the high degree of correlation among dietary constituents. We aimed to identify dietary pattern associated with NPC and to illustrate the dose-response relationship between the identified dietary pattern scores and the risk of NPC. Taking advantage of a matched NPC case–control study, data from a total of 319 incident cases and 319 matched controls were analyzed. Dietary pattern was derived employing partial least square discriminant analysis (PLS-DA) performed on energy-adjusted food frequencies derived from a 66-item food-frequency questionnaire. Odds ratios (ORs) and 95% confidence intervals (CIs) were estimated with multiple conditional logistic regression models, linking pattern scores and NPC risk. A high score of the PLS-DA derived pattern was characterized by high intakes of fruits, milk, fresh fish, vegetables, tea, and eggs ordered by loading values. We observed that one unit increase in the scores was associated with a significantly lower risk of NPC (ORadj = 0.73, 95% CI = 0.60–0.88) after controlling for potential confounders. Similar results were observed among Epstein-Barr virus seropositive subjects. An NPC protective diet is indicated with more phytonutrient-rich plant foods (fruits, vegetables), milk, other protein-rich foods (in particular fresh fish and eggs), and tea. This information may be used to design potential dietary regimen for NPC prevention. PMID:27249558
Inversion of generalized relaxation time distributions with optimized damping parameter
NASA Astrophysics Data System (ADS)
Florsch, Nicolas; Revil, André; Camerlynck, Christian
2014-10-01
Retrieving the Relaxation Time Distribution (RDT), the Grains Size Distribution (GSD) or the Pore Size Distribution (PSD) from low-frequency impedance spectra is a major goal in geophysics. The “Generalized RTD” generalizes parametric models like Cole-Cole and many others, but remains tricky to invert since this inverse problem is ill-posed. We propose to use generalized relaxation basis function (for instance by decomposing the spectra on basis of generalized Cole-Cole relaxation elements instead of the classical Debye basis) and to use the L-curve approach to optimize the damping parameter required to get smooth and realistic inverse solutions. We apply our algorithm to three examples, one synthetic and two real data sets, and the program includes the possibility of converting the RTD into GSD or PSD by choosing the value of the constant connecting the relaxation time to the characteristic polarization size of interest. A high frequencies (typically above 1 kHz), a dielectric term in taken into account in the model. The code is provided as an open Matlab source as a supplementary file associated with this paper.
A least squares fusion rule in multiple sensors distributed detection systems
NASA Astrophysics Data System (ADS)
Aziz, A. M.
In this paper, a new least square data fusion rule in multiple sensor distributed detection system is proposed. In the proposed approach, the central processor combines the sensors hard decisions through least squares criterion to make the global hard decision of the central processor. In contrast to the optimum Neyman-Pearson fusion, where the distributed detection system is optimized at the fusion center level or at the sensors level, but not simultaneously, the proposed approach achieves global optimization at both the fusion center and at the distributed sensors levels. This is done without knowing the error probabilities of each individual distributed sensor. Thus the proposed least squares fusion rule does not rely on any stability of the noise environment and of the sensors false alarm and detection probabilities. Therefore, the proposed least squares fusion rule is robust and achieves better global performance. Furthermore, the proposed method can easily be applied to any number of sensors and any type of distributed observations. The performance of the proposed least squares fusion rule is evaluated and compared to the optimum Neyman-Pearson fusion rule. The results show that the performance of the proposed least squares fusion rule outperforms the performance of the Neyman-Pearson fusion rule.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.
2006-01-01
The isotopic distribution in mass spectroscopy is described for identifying pure compounds, being able to distinguish molecular fragments by masses. Punnett squares are familiar, easy to compute, and often graphical which makes helpful to students and the relative distribution of isotopic combination is easily generated for even isotopic…
Grate, J W; Patrash, S J; Kaganovet, S N; Abraham, M H; Wise, B M; Gallagher, N B
2001-11-01
In previous work, it was shown that, in principle, vapor descriptors could be derived from the responses of an array of polymer-coated acoustic wave devices. This new chemometric classification approach was based on polymer/vapor interactions following the well-established linear solvation energy relationships (LSERs) and the surface acoustic wave (SAW) transducers being mass sensitive. Mathematical derivations were included and were supported by simulations. In this work, an experimental data set of polymer-coated SAW vapor sensors is investigated. The data set includes 20 diverse polymers tested against 18 diverse organic vapors. It is shown that interfacial adsorption can influence the response behavior of sensors with nonpolar polymers in response to hydrogen-bonding vapors; however, in general, most sensor responses are related to vapor interactions with the polymers. It is also shown that polymer-coated SAW sensor responses can be empirically modeled with LSERs, deriving an LSER for each individual sensor based on its responses to the 18 vapors. Inverse least-squares methods are used to develop models that correlate and predict vapor descriptors from sensor array responses. Successful correlations can be developed by multiple linear regression (MLR), principal components regression (PCR), and partial least-squares (PLS) regression. MLR yields the best fits to the training data, however cross-validation shows that prediction of vapor descriptors for vapors not in the training set is significantly more successful using PCR or PLS. In addition, the optimal dimension of the PCR and PLS models supports the dimensionality of the LSER formulation and SAW response models.
NASA Astrophysics Data System (ADS)
Arkani-Hamed, Nima; Cheng, Hsin-Chia; Luty, Markus; Thaler, Jesse
2005-07-01
We study the universal low-energy dynamics associated with the spontaneous breaking of Lorentz invariance down to spatial rotations. The effective lagrangian for the associated Goldstone field can be uniquely determined by the non-linear realization of a broken time diffeomorphism symmetry, up to some overall mass scales. It has previously been shown that this symmetry breaking pattern gives rise to a Higgs phase of gravity, in which gravity is modified in the infrared. In this paper, we study the effects of direct couplings between the Goldstone boson and standard model fermions, which necessarily accompany Lorentz-violating terms in the theory. The leading interaction is the coupling to the axial vector current, which reduces to spin in the non-relativistic limit. A spin moving relative to the ``ether" rest frame will emit Goldstone Cerenkov radiation. The Goldstone also induces a long-range inverse-square law force between spin sources with a striking angular dependence, reflecting the underlying Goldstone shockwaves and providing a smoking gun for this theory. We discuss the regime of validity of the effective theory describing these phenomena, and the possibility of probing Lorentz violations through Goldstone boson signals in a way that is complementary to direct tests in some regions of parameter space.
ERIC Educational Resources Information Center
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
In this article, we consider the least-squares approach for estimating parameters of a spatial variogram and establish consistency and asymptotic normality of these estimators under general conditions. Large-sample distributions are also established under a sp...
NASA Technical Reports Server (NTRS)
Devasia, Santosh; Bayo, Eduardo
1993-01-01
This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. A new inverse dynamics scheme for computing the nominal lumped and distributed inputs for tracking a prescribed trajectory is given.
NASA Astrophysics Data System (ADS)
Devasia, Santosh; Bayo, Eduardo
1993-02-01
This paper addresses the problem of inverse dynamics for articulated flexible structures with both lumped and distributed actuators. This problem arises, for example, in the combined vibration minimization and trajectory control of space robots and structures. A new inverse dynamics scheme for computing the nominal lumped and distributed inputs for tracking a prescribed trajectory is given.
A variational Bayesian approach for inverse problems with skew-t error distributions
NASA Astrophysics Data System (ADS)
Guha, Nilabja; Wu, Xiaoqing; Efendiev, Yalchin; Jin, Bangti; Mallick, Bani K.
2015-11-01
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.
The origin, global distribution, and functional impact of the human 8p23 inversion polymorphism.
Salm, Maximilian P A; Horswell, Stuart D; Hutchison, Claire E; Speedy, Helen E; Yang, Xia; Liang, Liming; Schadt, Eric E; Cookson, William O; Wierzbicki, Anthony S; Naoumova, Rossi P; Shoulders, Carol C
2012-06-01
Genomic inversions are an increasingly recognized source of genetic variation. However, a lack of reliable high-throughput genotyping assays for these structures has precluded a full understanding of an inversion's phylogenetic, phenotypic, and population genetic properties. We characterize these properties for one of the largest polymorphic inversions in man (the ∼4.5-Mb 8p23.1 inversion), a structure that encompasses numerous signals of natural selection and disease association. We developed and validated a flexible bioinformatics tool that utilizes SNP data to enable accurate, high-throughput genotyping of the 8p23.1 inversion. This tool was applied retrospectively to diverse genome-wide data sets, revealing significant population stratification that largely follows a clinal "serial founder effect" distribution model. Phylogenetic analyses establish the inversion's ancestral origin within the Homo lineage, indicating that 8p23.1 inversion has occurred independently in the Pan lineage. The human inversion breakpoint was localized to an inverted pair of human endogenous retrovirus elements within the large, flanking low-copy repeats; experimental validation of this breakpoint confirmed these elements as the likely intermediary substrates that sponsored inversion formation. In five data sets, mRNA levels of disease-associated genes were robustly associated with inversion genotype. Moreover, a haplotype associated with systemic lupus erythematosus was restricted to the derived inversion state. We conclude that the 8p23.1 inversion is an evolutionarily dynamic structure that can now be accommodated into the understanding of human genetic and phenotypic diversity.
Muralisankar, S; Manivannan, A; Balasubramaniam, P
2015-09-01
The aim of this manuscript is to investigate the mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks with time-delays. The time-delays are assumed to be interval time-varying and randomly occurring. Based on the new Lyapunov-Krasovskii functional and stochastic analysis approach, a novel sufficient condition is obtained in the form of linear matrix inequality such that the delayed stochastic neural networks are globally robustly asymptotically stable in the mean-square sense for all admissible uncertainties. Finally, the derived theoretical results are validated through numerical examples in which maximum allowable upper bounds are calculated for different lower bounds of time-delay.
NASA Technical Reports Server (NTRS)
Rummel, R.; Sjoeberg, L.; Rapp, R. H.
1978-01-01
A numerical method for the determination of gravity anomalies from geoid heights is described using the inverse Stokes formula. This discrete form of the inverse Stokes formula applies a numerical integration over the azimuth and an integration over a cubic interpolatory spline function which approximates the step function obtained from the numerical integration. The main disadvantage of the procedure is the lack of a reliable error measure. The method was applied on geoid heights derived from GEOS-3 altimeter measurements in the calibration area of the GEOS-3 satellite.
Distributed weighted least-squares estimation with fast convergence for large-scale systems.
Marelli, Damián Edgardo; Fu, Minyue
2015-01-01
In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.
Agrawal, Rajeev; Karmeshu
2007-02-01
Ultrasonic tissue characterization through composite probability distributions such as Nakagami-lognormal, Nakagami-gamma, Nakagami-inverse Gaussian has been found to be useful. Such a probabilistic description also depicts heavy tails which arise from multiple scattering in tissue besides local and global variations in scattering cross-sections. A new composite probability distribution, viz. Nakagami-generalized inverse Gaussian distribution (NGIGD) with four parameters is proposed which under different limiting conditions results in approximating the known distributions. A salient aspect of the new distribution is that the probability density function (pdf) of NGIGD variate is available in closed form and is analytically tractable.
Bietenholz, Wolfgang Chryssomalakos, Chryssomalis Salgado, Marcelo
2015-10-15
We comment on a fatal flaw in the analysis contained in the work of Martínez-y-Romero et al., [J. Math. Phys. 54, 053509 (2013)], which concerns the motion of a point particle in an inverse square potential, and show that most conclusions reached there are wrong. In particular, the manifestly senseless claim that, in the attractive potential case, no bounded orbits exist for negative energies, is traced to a sign error. Several more mistakes, both in the classical and the quantum cases, are pointed out.
NASA Astrophysics Data System (ADS)
Bietenholz, Wolfgang; Chryssomalakos, Chryssomalis; Salgado, Marcelo
2015-10-01
We comment on a fatal flaw in the analysis contained in the work of Martínez-y-Romero et al., [J. Math. Phys. 54, 053509 (2013)], which concerns the motion of a point particle in an inverse square potential, and show that most conclusions reached there are wrong. In particular, the manifestly senseless claim that, in the attractive potential case, no bounded orbits exist for negative energies, is traced to a sign error. Several more mistakes, both in the classical and the quantum cases, are pointed out.
Hartzell, S.; Mendoza, C.
1991-01-01
An iterative least-squares technique is used to simultaneously invert the strong-motion records and teleseismic P waveforms for the 1978 Tabas, Iran, earthquake to deduce the rupture history. The effects of using different data sets and different parametrizations of the problem (linear versus nonlinear) are considered. A consensus of all the inversion runs indicates a complex, multiple source for the Tabas earthquake, with four main source regions over a fault length of 90 km and an average rupture velocity of 2.5 km/sec. -from Authors
ERIC Educational Resources Information Center
Sichel, H. S.
1992-01-01
Discusses the use of the generalized inverse Gaussian-Poisson (GIGP) distribution in bibliometric studies. The main types of size-frequency distributions are described, bibliometric distributions in logarithms are examined; parameter estimation is discussed; and goodness-of-fit tests are considered. Examples of applications are included. (17…
NASA Astrophysics Data System (ADS)
Zhu, Liang; Hu, Penghao; Yang, Wenguo; Dang, Xueming; Zhang, Lisong
2016-01-01
The reasonable permanent magnetic field distribution has an important influence on improving the measuring accuracy in intelligent ball joint. In view of the defects on the ring permanent magnet in the previous experiment scheme, a new method on Square Pane Permanent Magnet (SPPM) is put forward. It possesses distinct advantages on orientation identification and model simplification. This paper proposes an optimized theory model of the magnetic field distribution of SPPM and gives the magnetic field theoretical expressions. The experiments have shown that the experimental data basically agreed with the theory value which is less than 4.3% error in full scale. This result verified the correctness of the analytic work and paves the way for improving the measurement accuracy in intelligent ball joint.
NASA Astrophysics Data System (ADS)
Schuster, David M.
1993-04-01
An inverse method has been developed to compute the structural stiffness properties of wings given a specified wing loading and aeroelastic twist distribution. The method directly solves for the bending and torsional stiffness distribution of the wing using a modal representation of these properties. An aeroelastic design problem involving the use of a computational aerodynamics method to optimize the aeroelastic twist distribution of a tighter wing operating at maneuver flight conditions is used to demonstrate the application of the method. This exercise verifies the ability of the inverse scheme to accurately compute the structural stiffness distribution required to generate a specific aeroelastic twist under a specified aeroelastic load.
NASA Astrophysics Data System (ADS)
Ma, Ji-Qiang; Geng, Jian-Hua
2013-12-01
Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fluids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.
Spin Axis Distribution of the Hungaria Asteroids via Lightcurve Inversion
NASA Astrophysics Data System (ADS)
Warner, Brian D.; Harris, Alan W.; Stephens, Robert D.; Coley, Daniel
2014-11-01
Since 2005, we have conducted a dedicated campaign to obtain dense lightcurves of members of the Hungaria asteroid population. As a result, the number of Hungarias in the asteroid lightcurve database (LCDB; Warner et al., 2009; Icarus 202, 134-146) with a statistically valid rotation rate rose from less than 50 to almost 300. The particular value of the Hungarias is that they are smallest and closest-to-sun main belt objects that can be studied with modest-sized telescopes. As such, they are more likely subject to YORP-altered spin states. We have previously verified highly-evolved rotation rates (Warner et al., 2009; Icarus 204, 172-182). This study takes the next step of tracing the evolution of spin orientations. We combined the dense lightcurves from our campaign with so-called “sparse data” from the NEA surveys to model the spin axis orientation using lightcurve inversion methods (see works by Kaasalainen, Torppa, Durech, and Hanus). Because high-dispersion sparse data are of little use for low amplitude objects, we limited the Hungarias to be modeled to those with a maximum amplitude of A ≥ 0.15 mag, an LCDB reliability code of U ≥ 2, the period in the LCDB summary was unambiguous, and the asteroid did not show signs of tumbling (non-principal axis rotation). The result as of mid-August 2014 was a list of 231 Hungaria candidates for modeling. Using a bank of five independent desktop computers and customized software, we first determined the likely sidereal period of the asteroid. That period was then used for a spin axis (pole) search involving 315 discrete longitude-latitude pairs. We report on the results of our searches, including weighting solutions when a unique solution was not found (often the case in lightcurve inversion), and how the results compare to similar studies using a more general asteroid population. BDW and AWH acknowledge funding from NASA NNX13AP56G and NSF grant AST-1210099. RDS acknowledges NASA grant NNX13AP56G and the
Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing
2015-07-01
In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.
NASA Astrophysics Data System (ADS)
Nakata, Ryoko; Kuwatani, Tatsu; Okada, Masato; Hori, Takane
2016-02-01
In geodetic data inversion, insufficient observational data and smoothness constraints for model parameters make it difficult to clearly resolve small-scale heterogeneous structures with discontinuous boundaries. We therefore developed a novel regularization scheme for the inversion problem that uses discontinuity, sparsity, and smoothness constraints. In order to assess its usefulness and applicability, the proposed method was applied to synthetic displacements calculated by a ring-shaped and sharply varying afterslip distribution on a plate interface. The afterslip was obtained from reasonable numerical simulation of earthquake generation cycle with a rate- and state- dependent friction law and realistic three-dimensional plate geometry. The obtained afterslip distribution was heterogeneous, and the discontinuous boundary was sharper than that obtained by using smoothness constraint only. The same inversion test was conducted with a smoothly varying circular slip distribution with large slips inside the ring-shaped distribution. The method accurately reproduces the smooth distribution of the slip area as well as the ring-shaped distribution. Therefore, the method could be applied to any slip distribution, with both discontinuous and continuous boundaries. Adopting this method for measured data will make it possible to obtain detailed heterogeneous distributions of physical structures on fault planes. The proposed method is therefore applicable to various geophysical inversion problems that exhibit discontinuous heterogeneity.
Ekkad, S.V.; Huang, Y.; Han, J.C.
1996-12-31
Modern gas turbine blades have internal serpentine passage for providing effective cooling. Rib turbulators are added periodically on the cooling passage surface to enhance heat transfer. Some of the cooling air is ejected out through bleed (or film) holes for external blade film cooling. The presence of periodic rib turbulators and bleed holes creates strong axial and spanwise variations in the heat transfer distributions on the passage surface. Detailed heat transfer coefficient distributions are presented in this study for a two-pass square channel with a 180{degree} turn. One wall of the channel has periodically placed bleed holes. Four different configurations of 90{degree} parallel, 60{degree} parallel, 60{degree} V ribs, and 60{degree} inverted V ribs are studied in conjunction with the effect of bleed holes on the same wall. The surface is coated with a thin layer of thermochromic liquid crystals and a transient test is run to obtain the detailed heat transfer distributions. The 60{degree} parallel, 60{degree} V, and 60{degree} inverted ribbed channels produce similar levels of heat transfer enhancement in the first pass. However, the 60{degree} inverted V ribbed channel produces higher enhancement in the second pass. Regional averaged heat transfer results indicate that a test surface with bleed holes provides similar heat transfer enhancement as that for a test surface without bleed holes although 20--25% of the inlet mass flow exits through the bleed holes.
Distributed weighted least-squares estimation with fast convergence for large-scale systems☆
Marelli, Damián Edgardo; Fu, Minyue
2015-01-01
In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976
Developing a Near Real-time System for Earthquake Slip Distribution Inversion
NASA Astrophysics Data System (ADS)
Zhao, Li; Hsieh, Ming-Che; Luo, Yan; Ji, Chen
2016-04-01
Advances in observational and computational seismology in the past two decades have enabled completely automatic and real-time determinations of the focal mechanisms of earthquake point sources. However, seismic radiations from moderate and large earthquakes often exhibit strong finite-source directivity effect, which is critically important for accurate ground motion estimations and earthquake damage assessments. Therefore, an effective procedure to determine earthquake rupture processes in near real-time is in high demand for hazard mitigation and risk assessment purposes. In this study, we develop an efficient waveform inversion approach for the purpose of solving for finite-fault models in 3D structure. Full slip distribution inversions are carried out based on the identified fault planes in the point-source solutions. To ensure efficiency in calculating 3D synthetics during slip distribution inversions, a database of strain Green tensors (SGT) is established for 3D structural model with realistic surface topography. The SGT database enables rapid calculations of accurate synthetic seismograms for waveform inversion on a regular desktop or even a laptop PC. We demonstrate our source inversion approach using two moderate earthquakes (Mw~6.0) in Taiwan and in mainland China. Our results show that 3D velocity model provides better waveform fitting with more spatially concentrated slip distributions. Our source inversion technique based on the SGT database is effective for semi-automatic, near real-time determinations of finite-source solutions for seismic hazard mitigation purposes.
Distributed RF Tomography for Tunnel Detection: Suitable Inversion Schemes
2009-01-01
generating a scattered wave- field . The distributed receivers collect samples of the scattered instantaneous electric field , and estimate the complex...valued electric field phasor at their locations. Subsequently, this information is relayed to the overlying base station. To ease the detection process...incoming wave- field . For a given sampling time, the used spectrum is virtually restricted to a single frequency component, thus ensuring ultra
ERIC Educational Resources Information Center
Yuan, Ke-Hai
2008-01-01
In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…
Chen, Shanshan; Wang, Hongzhi; Yang, Peiqiang; Zhang, Xuelong
2014-06-01
It is difficult to reflect the properties of samples from the signal directly collected by the low field nuclear magnetic resonance (NMR) analyzer. People must obtain the relationship between the relaxation time and the original signal amplitude of every relaxation component by inversion algorithm. Consequently, the technology of T2 spectrum inversion is crucial to the application of NMR data. This study optimized the regularization factor selection method and presented the regularization algorithm for inversion of low field NMR relaxation distribution, which is based on the regularization theory of ill-posed inverse problem. The results of numerical simulation experiments by Matlab7.0 showed that this method could effectively analyze and process the NMR relaxation data.
Inverse problem for shape control of flexible space reflectors using distributed solar pressure
NASA Astrophysics Data System (ADS)
Borggräfe, A.; Heiligers, J.; Ceriotti, M.; McInnes, C. R.
2014-07-01
This paper investigates controlled elastic deflection of thin circular space reflectors using an inverse problem approach to non-linear thin membrane theory. When changing the surface reflectivity across the membrane, the distributed loads due to ambient solar radiation pressure can be manipulated optically, thus controlling the surface shape without using mechanical or piezo-electric systems. The surface reflectivity can in principle be modulated using uniformly distributed thin-film electro-chromic coatings. We present an analytic solution to the inverse problem of finding the necessary reflectivity distribution that creates a specific membrane deflection, for example that of a parabolic reflector. Importantly, the reflectivity distribution across the surface is found to be independent of membrane size, thickness and solar distance, enabling engineering of the reflectivity distribution directly during the manufacture of the membrane.
Study of ultrasonic echo envelope based on Nakagami-inverse Gaussian distribution.
Karmeshu; Agrawal, Rajeev
2006-03-01
A new probability density function (pdf) to describe the envelope of the backscattered echoes from tissues is proposed. The combined effect of multiple scattering and randomness arising from local and global variations in scattering cross-section is captured through Nakagami-inverse Gaussian distribution (NIGD). The proposed distribution has the advantage that it has a closed form unlike the realistic Nakagami-lognormal distribution (NLD). The degree of closeness, as measured in terms of Kullback-Leibler (KL) distance between two probability distributions is computed. It is shown that NIGD much more closely approximates NLD compared to Nakagami-gamma distribution (NGD) used to model such problems.
NASA Technical Reports Server (NTRS)
Rutledge, Charles K.
1988-01-01
The validity of applying chi-square based confidence intervals to far-field acoustic flyover spectral estimates was investigated. Simulated data, using a Kendall series and experimental acoustic data from the NASA/McDonnell Douglas 500E acoustics test, were analyzed. Statistical significance tests to determine the equality of distributions of the simulated and experimental data relative to theoretical chi-square distributions were performed. Bias and uncertainty errors associated with the spectral estimates were easily identified from the data sets. A model relating the uncertainty and bias errors to the estimates resulted, which aided in determining the appropriateness of the chi-square distribution based confidence intervals. Such confidence intervals were appropriate for nontonally associated frequencies of the experimental data but were inappropriate for tonally associated estimate distributions. The appropriateness at the tonally associated frequencies was indicated by the presence of bias error and noncomformity of the distributions to the theoretical chi-square distribution. A technique for determining appropriate confidence intervals at the tonally associated frequencies was suggested.
Grechin, S G; Nikolaev, P P; Sharandin, E A
2014-10-31
The functional possibilities of diode-side-pumped laser heads of solid-state lasers for forming inverse population distributions of different types are analysed. The invariants determining the relationship between the laser head parameters upon scaling are found. The results of comparative experimental studies are presented. (lasers)
Goffinet, Bernard; Wickett, Norman J.; Werner, Olaf; Ros, Rosa Maria; Shaw, A. Jonathan; Cox, Cymon J.
2007-01-01
Background and Aims The recent assembly of the complete sequence of the plastid genome of the model taxon Physcomitrella patens (Funariaceae, Bryophyta) revealed that a 71-kb fragment, encompassing much of the large single copy region, is inverted. This inversion of 57% of the genome is the largest rearrangement detected in the plastid genomes of plants to date. Although initially considered diagnostic of Physcomitrella patens, the inversion was recently shown to characterize the plastid genome of two species from related genera within Funariaceae, but was lacking in another member of Funariidae. The phylogenetic significance of the inversion has remained ambiguous. Methods Exemplars of all families included in Funariidae were surveyed. DNA sequences spanning the inversion break ends were amplified, using primers that anneal to genes on either side of the putative end points of the inversion. Primer combinations were designed to yield a product for either the inverted or the non-inverted architecture. Key Results The survey reveals that exemplars of eight genera of Funariaceae, the sole species of Disceliaceae and three generic representatives of Encalyptales all share the 71-kb inversion in the large single copy of the plastid genome. By contrast, the plastid genome of Gigaspermaceae (Funariales) is characterized by a gene order congruent with that described for other mosses, liverworts and hornworts, and hence it does not possess this inversion. Conclusions The phylogenetic distribution of the inversion in the gene order supports a hypothesis only weakly supported by inferences from sequence data whereby Funariales are paraphyletic, with Funariaceae and Disceliaceae sharing a common ancestor with Encalyptales, and Gigaspermaceae sister to this combined clade. To reflect these relationships, Gigaspermaceae are excluded from Funariales and accommodated in their own order, Gigaspermales order nov., within Funariideae. PMID:17337480
On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field
NASA Technical Reports Server (NTRS)
Chao, Benjamin F.
2004-01-01
The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.
Universal inverse power-law distribution for temperature and rainfall in the UK region
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2014-06-01
Meteorological parameters, such as temperature, rainfall, pressure, etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. A general systems theory model predicts universal inverse power-law form incorporating the golden mean for the fractal fluctuations. The model predicted distribution was compared with observed distribution of fractal fluctuations of all size scales (small, large and extreme values) in the historic month-wise temperature (maximum and minimum) and total rainfall for the four stations Oxford, Armagh, Durham and Stornoway in the UK region, for data periods ranging from 92 years to 160 years. For each parameter, the two cumulative probability distributions, namely cmax and cmin starting from respectively maximum and minimum data value were used. The results of the study show that (i) temperature distributions (maximum and minimum) follow model predicted distribution except for Stornowy, minimum temperature cmin. (ii) Rainfall distribution for cmin follow model predicted distribution for all the four stations. (iii) Rainfall distribution for cmax follows model predicted distribution for the two stations Armagh and Stornoway. The present study suggests that fractal fluctuations result from the superimposition of eddy continuum fluctuations.
NASA Astrophysics Data System (ADS)
Benedetto, A.; Magazù, S.; Migliardo, F.; Mondelli, C.; Gonzalez, M. A.
2012-02-01
In the present contribution, a procedure for molecular motion characterization based on the evaluation of the Mean Square Displacement (MSD), through the Self-Distribution Function (SDF), is presented. It is shown how MSD, which represents an important observable for the characterization of dynamical properties, can be decomposed into different partial contributions associated to system dynamical processes within a specific spatial scale. It is also shown how the SDF procedure allows us to evaluate both total MSD and partial MSDs through total and partial SDFs. As a result, total MSD is the weighed sum of partial MSDs in which the weights are obtained by the fitting procedure of measured Elastic Incoherent Neutron Scattering (EINS) intensity. We apply SDF procedure to data collected,by IN13, IN10 and IN4 spectrometers (Institute Laue Langevin), on aqueous mixtures of two homologous disaccharides (sucrose and trehalose) and on dry and hydrated (H2O and D2O) lysozyme with and without disaccharides. It emerges that the hydrogen bond imposed network of the water-trehalose mixture appears to be stronger with respect to that of the water-sucrose mixture. This result can justify the higher bioprotectant effectiveness of trehalose. Furthermore, it emerges that partial MSDs of sucrose and trehalose are equivalent in the low Q domain (0÷1.7) Å-1 whereas they are different in the high Q domain (1.7÷4) Å-1. This suggests that the higher structure sensitivity of sucrose should be related to the small spatial observation windows. Moreover, the role of the instrumental resolution in EINS is considered. The nature of the dynamical transition is highlighted and it is shown that it occurs when the system relaxation time becomes shorter than the instrumental energy time. Finally, the bioprotectants effect on protein dynamics and the amplitude of vibrations in lysozyme are presented.
Vugrinovich, R.G.
1981-01-01
A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm and is given by the median of the set of n(n - 1)/2 slope estimators, which may be calculated by inserting pairs of points (Xi, Yi)and (Xj, Yj)into the slope formula Si = (Yi - Yj)/(Xi - Xj), 1 ??? i k (median {|Ri - Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques. ?? 1981 Plenum Publishing Corporation.
Beno, J.H. )
1991-01-01
In this paper vector potential is solved as a three dimensional, boundary value problem for a conductor geometry consisting of square-bore railgun rails and a stationary armature. Conductors are infinitely conducting and perfect contact is assumed between rails and the armature. From the vector potential solution, surface current distribution is inferred.
Wang, Jing; Guan, Huaiqun; Solberg, Timothy
2011-07-15
Purpose: A statistical projection restoration algorithm based on the penalized weighted least-squares (PWLS) criterion can substantially improve the image quality of low-dose CBCT images. The performance of PWLS is largely dependent on the choice of the penalty parameter. Previously, the penalty parameter was chosen empirically by trial and error. In this work, the authors developed an inverse technique to calculate the penalty parameter in PWLS for noise suppression of low-dose CBCT in image guided radiotherapy (IGRT). Methods: In IGRT, a daily CBCT is acquired for the same patient during a treatment course. In this work, the authors acquired the CBCT with a high-mAs protocol for the first session and then a lower mAs protocol for the subsequent sessions. The high-mAs projections served as the goal (ideal) toward, which the low-mAs projections were to be smoothed by minimizing the PWLS objective function. The penalty parameter was determined through an inverse calculation of the derivative of the objective function incorporating both the high and low-mAs projections. Then the parameter obtained can be used for PWLS to smooth the noise in low-dose projections. CBCT projections for a CatPhan 600 and an anthropomorphic head phantom, as well as for a brain patient, were used to evaluate the performance of the proposed technique. Results: The penalty parameter in PWLS was obtained for each CBCT projection using the proposed strategy. The noise in the low-dose CBCT images reconstructed from the smoothed projections was greatly suppressed. Image quality in PWLS-processed low-dose CBCT was comparable to its corresponding high-dose CBCT. Conclusions: A technique was proposed to estimate the penalty parameter for PWLS algorithm. It provides an objective and efficient way to obtain the penalty parameter for image restoration algorithms that require predefined smoothing parameters.
Inverse Analysis of Heat Conduction in Hollow Cylinders with Asymmetric Source Distributions
NASA Astrophysics Data System (ADS)
Lambrakos, Samuel G.; Michopoulos, John G.; Jones, Harry N.; Boyer, Craig N.
2008-10-01
This paper presents an application of inverse analysis for determining both the temperature field histories and corresponding heat source distributions in hollow cylinders. The primary goal, however, is the development of an inversion infrastructure in a manner that allows taking advantage of all aspects related to its utility, including sensitivity analysis. The conditions generating heat sources are those resulting from intense pulsed-current electrical contact experiments. Under these conditions intense heat currents are generated due to the Joule conversion of the electric conduction currents. Asymmetry of the heat source is induced from the localized melting due to arc-enhanced electric conduction. Experimentally acquired temperature histories and melting domain boundary data are utilized to setup an inverse model of the heat conduction problem. This permits the construction of an estimate not only of the temperature field histories throughout the computational domain but also of an evaluation of the effective thermal diffusivity of the material involved.
Difficulty Factors, Distribution Effects, and the Least Squares Simplex Data Matrix Solution
ERIC Educational Resources Information Center
Ten Berge, Jos M. F.
1972-01-01
In the present article it is argued that the Least Squares Simplex Data Matrix Solution does not deal adequately with difficulty factors inasmuch as the theoretical foundation is insufficient. (Author/CB)
NASA Astrophysics Data System (ADS)
Hori, T.; Nakata, R.; Kuwatani, T.; Okada, M.
2014-12-01
A Trial for Improvement in Reproducibility of Spatial Distribution of Afterslip in Geodetic Data InversionAfterslips of plate boundary earthquakes in subduction zones sometimes show doughnut-shaped slip distribution. For example, little afterslip occurred in the coseismic slip area of the 2003 Tokachi-oki earthquake of magnitude (M) 8.0 while large slip occurred in its surrounding area (ex. Miyazaki et al., 2004). However, it is difficult to resolve such heterogeneous distribution for M7 class earthquakes especially in offshore region. We demonstrated the reproducibility of spatial distribution of afterslip following a M7 class earthquake through numerical experiments to estimate slip distribution on the plate interface beneath the Hyuga-nada offshore region, southwest Japan (Nakata et al., 2013). We calculated synthetic displacement data from the result of numerical simulation conducted for the afterslip following a M 6.8 earthquake, for existing global navigation satellite system stations on land and planned ocean floor pressure gauge network stations. The spatial distribution of fault slip is estimated using a Kalman filter-based inversion. The slip distribution estimated by using ocean floor stations demonstrates that the heterogeneity of plate coupling, which roughly corresponds to the coseismic area of the M 6.8 earthquake with a radius of 10 km. The estimated slip amount in the coseismic area is nearly half of the peak one around it, although no slip is the true answer. This discrepancy is caused by the smoothness constraint in the inversion. To improve the reproducibility of the slip distribution, it is necessary to introduce different type of constraints. Based on a Bayesian approach, we introduce an evaluation function that can treat both discontinuity and smoothness in slip distribution.
A new stochastic algorithm for inversion of dust aerosol size distribution
NASA Astrophysics Data System (ADS)
Wang, Li; Li, Feng; Yang, Ma-ying
2015-08-01
Dust aerosol size distribution is an important source of information about atmospheric aerosols, and it can be determined from multiwavelength extinction measurements. This paper describes a stochastic inverse technique based on artificial bee colony (ABC) algorithm to invert the dust aerosol size distribution by light extinction method. The direct problems for the size distribution of water drop and dust particle, which are the main elements of atmospheric aerosols, are solved by the Mie theory and the Lambert-Beer Law in multispectral region. And then, the parameters of three widely used functions, i.e. the log normal distribution (L-N), the Junge distribution (J-J), and the normal distribution (N-N), which can provide the most useful representation of aerosol size distributions, are inversed by the ABC algorithm in the dependent model. Numerical results show that the ABC algorithm can be successfully applied to recover the aerosol size distribution with high feasibility and reliability even in the presence of random noise.
Nested Global Inversion for the Carbon Flux Distribution in Canada and USA from 1994 to 2003
NASA Astrophysics Data System (ADS)
Chen, J. M.; Deng, F.; Ishizawa, M.; Ju, W.; Mo, G.; Chan, D.; Higuchi, K.; Maksyutov, S.
2007-12-01
Based on TransCom inverse modeling for 22 global regions, we developed a nested global inversion system for estimating carbon fluxes of 30 regions in North America (2 of the 22 regions are divided into 30). Irregular boundaries of these 30 regions are delineated based on ecosystem types and provincial/state borders. Synthesis Bayesian inversion is conducted in monthly steps using CO2 concentration measurements at 88 coastal and continental stations of the globe for the 1994-2003 period (NOAA GlobalView database). Responses of these stations to carbon fluxes from the 50 regions are simulated using the transport model of National Institute for Environmental Studies of Japan and reanalysis wind fields of the National Centers for Environmental Prediction (NCEP). Terrestrial carbon flux fields modeled using BEPS and Biome-BGC driven by NCEP reanalysis meteorological data are used as two different a priori to constrain the inversion. The inversion (top- down) results are compared with remote sensing-based ecosystem modeling (bottom-up) results in Canada's forests and wetlands. There is a broad consistency in the spatial pattern of the carbon source and sink distributions obtained using these two independent methods. Both sets of results also indicate that Canada's forests and wetlands are carbon sinks in 1994-2003, but the top-down method produces consistently larger sinks than the bottom-up results. Reasons for this discrepancy may lie in both methods, and several issues are identified for further investigation.
NASA Astrophysics Data System (ADS)
Glen, R. A.; Hancock, P. L.; Whittaker, A.
Several models of basin inversion described in the literature are tested in a study of Triassic and Early Jurassic strata exposed along the southern margin of the Bristol Channel Basin in Somerset, England that has been exhumed by <3 km. Two key features of the superbly exposed normal faults are that they formed at several times during basin evolution—not during Triassic to Early Jurassic growth, but during Late Jurassic rifting, and during and after inversion; and that >95% of them are still in net extension, despite widespread kinematic evidence for reverse reactivation. When coupled with the general absence of thin-skinned thrusts and the widespread occurrence of regional contractional folds, it appears that none of three main inversion models—the fault-reactivation model, the thin-skinned model and the buttress model—are by themselves applicable. We erect a new model of basin inversion, the distributed deformation model, which consists of three stages of basin inversion. Stage one involved early partial reactivation of large-displacement steep normal faults. Stage two was dominated by folding, wherein fault blocks underwent oblique (non-coaxial) shortening by map scale folding, accompanied by formation of outer arc normal faults, minor cleavage and neoformed thrusts. Stage three involved reverse reactivation of outer arc normal faults and activation of oblique and strike-slip faults that partitioned deformation into compartments.
NASA Astrophysics Data System (ADS)
Völl, Annika; Stollenwerk, Jochen; Loosen, Peter
2016-03-01
Laser beam intensity distribution profiles for material processing techniques are most of the time restricted to be either of Gaussian or tophat shape. This often leads to different kind of problems especially at the edges of the laser-heated tracks, examples are energy losses or unnecessary overlaps. Thus, machining quality and process efficiency could be much improved by using application specific intensity profiles to generate optimal temperature distributions in the processed material. In this work, we present a numerical method to derive a specific intensity profile for a given temperature distribution. As this problem belongs to the set of inverse heat conduction problems, which are ill-posed, special regularization algorithms are needed. The only method to solve this inverse problem in reasonable time is the conjugate gradient method which we extend to the given problem of laser material processing applications. This method is an iterative approach where in each step the actual temperature distribution is calculated by using the finite element method. In general, the proposed method is applicable for materials with constant or temperature dependent coefficients, for static and dynamic distributions as well as for plane or complex geometries. However, restricting ourselves to plane geometries, intensity distributions that create tophat- or stepped temperature distributions on the plane surface of the processed material are derived and will be presented. In future work, we intend to verify these results using freeform optics as well as singly addressable V(E)CSEL arrays.
The application of inverse methods to spatially-distributed acoustic sources
NASA Astrophysics Data System (ADS)
Holland, K. R.; Nelson, P. A.
2013-10-01
Acoustic inverse methods, based on the output of an array of microphones, can be readily applied to the characterisation of acoustic sources that can be adequately modelled as a number of discrete monopoles. However, there are many situations, particularly in the fields of vibroacoustics and aeroacoustics, where the sources are distributed continuously in space over a finite area (or volume). This paper is concerned with the practical problem of applying inverse methods to such distributed source regions via the process of spatial sampling. The problem is first tackled using computer simulations of the errors associated with the application of spatial sampling to a wide range of source distributions. It is found that the spatial sampling criterion for minimising the errors in the radiated far-field reconstructed from the discretised source distributions is strongly dependent on acoustic wavelength but is only weakly dependent on the details of the source field itself. The results of the computer simulations are verified experimentally through the application of the inverse method to the sound field radiated by a ducted fan. The un-baffled fan source with the associated flow field is modelled as a set of equivalent monopole sources positioned on the baffled duct exit along with a matrix of complimentary non-flow Green functions. Successful application of the spatial sampling criterion involves careful frequency-dependent selection of source spacing, and results in the accurate reconstruction of the radiated sound field. Discussions of the conditioning of the Green function matrix which is inverted are included and it is shown that the spatial sampling criterion may be relaxed if conditioning techniques, such as regularisation, are applied to this matrix prior to inversion.
Graphical tests for the assumption of gamma and inverse Gaussian frailty distributions.
Economou, P; Caroni, C
2005-12-01
The common choices of frailty distribution in lifetime data models include the Gamma and Inverse Gaussian distributions. We present diagnostic plots for these distributions when frailty operates in a proportional hazards framework. Firstly, we present plots based on the form of the unconditional survival function when the baseline hazard is assumed to be Weibull. Secondly, we base a plot on a closure property that applies for any baseline hazard, namely, that the frailty distribution among survivors at time t has the same form as the original distribution, with the same shape parameter but different scale parameter. We estimate the shape parameter at different values of t and examine whether it is constant, that is, whether plotted values form a straight line parallel to the time axis. We provide simulation results assuming Weibull baseline hazard and an example to illustrate the methods.
The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics.
Eltoft, Torbjørn
2005-11-01
In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral chi2-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.
Distribution of gap junctions and square array junctions in the mammalian lens.
Costello, M J; McIntosh, T J; Robertson, J D
1989-05-01
The morphology of membrane specializations of the cortex and nucleus of bovine lenses has been analyzed for both isolated membrane fractions and intact tissue fragments. Fractions of fiber cell membranes isolated from the outer cortex and the inner nucleus of lenses have been compared using x-ray diffraction, electron microscopy, SDS polyacrylamide gels and Western blots. Each fraction has distinctive structural characteristics. In x-ray experiments, the cortical fraction gives no sharp equatorial reflections (from the plane of the membrane), whereas the nuclear fraction gives sharp equatorial reflections which index on a square lattice of 6.6 nm. In thin-section electron micrographs, the cortical fraction is composed primarily of closed vesicles and flat membrane sheets, some of which contain pentalamellar structures similar in appearance to the 16-18 nm thick gap junctions found in other tissues. The nuclear fraction contains mostly undulating membrane pairs which often show 11-14 nm pentalamellar profiles and occasionally thicker junctions. In freeze-fracture images the cortical membranes display irregular clusters of intramembrane particles which resemble gap junctions, whereas the nuclear membranes contain numerous large square arrays with a 6.6 nm repeat and few irregular clusters or individual intramembrane particles. Images of fragments of intact lenses used in the membrane isolations give similar results; in the cortex the area covered by gap junctions is over 50 times the area covered by square lattices, whereas nuclear fiber cell membranes contain large square arrays. Thus, cortical and nuclear fiber cell membranes have quite different morphologies. In particular, the size of the square arrays of protein increases as the fiber cells mature. SDS polyacrylamide gels from cortical and nuclear fractions are similar in that they both contain MP26 as the major band. However, Western blot analysis shows increasing quantities of lower molecular weight, 25 kD and
NASA Astrophysics Data System (ADS)
Kusznir, N. J.; Alvey, A.; Roberts, A. M.
2013-12-01
Mapping crustal thickness, continental lithosphere thinning and oceanic lithosphere distribution represents a substantial challenge for the Polar Regions. Using gravity anomaly inversion, we have produced the first comprehensive maps of crustal thickness and oceanic lithosphere distribution for the Arctic. The Arctic region formed as a series of small distinct ocean basins leading to a complex distribution of oceanic crust, thinned continental crust, possible micro-continents and rifted continental margins. Mapping of continental lithosphere thinning factor and crustal thickness from gravity inversion provide predictions of ocean-continent transition structure and magmatic type and continent ocean boundary location independent of magnetic isochrons. Restoration of crustal thickness and continent-ocean boundary location from gravity inversion may be used to test plate tectonic reconstructions. Using crustal thickness and continental lithosphere thinning factor maps with superimposed shaded-relief free-air gravity anomaly, we improve the determination of pre-breakup rifted margin conjugacy and sea-floor spreading trajectory within the Arctic basins. By restoring crustal thickness & continental lithosphere thinning maps of the Eurasia Basin & NE Atlantic to their initial post-breakup configuration we show the geometry and segmentation of the rifted continental margins at their time of breakup, together with the location of highly-stretched failed breakup basins and rifted micro-continents. Our gravity inversion predicts thin crust and high continental lithosphere thinning factors in the Makarov, Podvodnikov, Nautilus and Canada Basins consistent with these basins being underlain by oceanic or highly thinned continental crust. Larger crustal thicknesses, in the range 20 - 30 km, are predicted for the Lomonosov, Alpha and Mendeleev Ridges. Moho depths predicted compare well with seismic estimates. Predicted very thin continental or oceanic crust under the North Chuchki
NASA Astrophysics Data System (ADS)
Kato, Takeyoshi; Sugimoto, Hiroyuki; Suzuoki, Yasuo
We established a procedure for estimating regional electricity demand and regional potential capacity of distributed generators (DGs) by using a grid square statistics data set. A photovoltaic power system (PV system) for residential use and a co-generation system (CGS) for both residential and commercial use were taken into account. As an example, the result regarding Aichi prefecture was presented in this paper. The statistical data of the number of households by family-type and the number of employees by business category for about 4000 grid-square with 1km × 1km area was used to estimate the floor space or the electricity demand distribution. The rooftop area available for installing PV systems was also estimated with the grid-square statistics data set. Considering the relation between a capacity of existing CGS and a scale-index of building where CGS is installed, the potential capacity of CGS was estimated for three business categories, i.e. hotel, hospital, store. In some regions, the potential capacity of PV systems was estimated to be about 10,000kW/km2, which corresponds to the density of the existing area with intensive installation of PV systems. Finally, we discussed the ratio of regional potential capacity of DGs to regional maximum electricity demand for deducing the appropriate capacity of DGs in the model of future electricity distribution system.
NASA Astrophysics Data System (ADS)
Erickson, Ben; Petrasch, Jörg
2012-06-01
Radiative flux measurements at the focal plane of solar concentrators are typically performed using digital cameras in conjunction with Lambertian targets. To accurately predict flux distributions on arbitrary receiver geometries directional information about the radiation is required. Currently, the directional characteristics of solar concentrating systems are predicted via ray tracing simulations. No direct experimental technique to determine intensities of concentrating solar systems is available. In the current paper, multiple parallel flux measurements at varying distances from the focal plane together with a linear inverse method and Tikhonov regularization are used to identify the directional and spatial intensity distribution at the solution plane. The directional binning feature of an in-house Monte Carlo ray tracing program is used to provide a reference solution. The method has been successfully applied to two-dimensional concentrators, namely parabolic troughs and elliptical troughs using forward Monte Carlo ray tracing simulations that provide the flux maps as well as consistent, associated intensity distribution for validation. In the two-dimensional case, intensity distributions obtained from the inverse method approach the Monte Carlo forward solution. In contrast, the method has not been successful for three dimensional and circular symmetric concentrator geometries.
3D Self-Potential Inversion for Monitoring DNAPL Contaminant Distributions
NASA Astrophysics Data System (ADS)
Minsley, B. J.; Sogade, J.; Vichabian, Y.; Morgan, F. D.
2005-05-01
Self-potential (SP) data are collected over an area known to be contaminated with Dense Non-Aqueous Phase Liquids (DNAPLs) at the Savannah River Site in South Carolina. The field experiment consists of approximately 100 SP measurements on a surface grid and in four boreholes, and is repeated after one year. DNAPLs are known to undergo redox reactions during their degradation in the environment, which is often biologically mediated. Self-potential geophysics is employed in this study because of its sensitivity to the in-situ biochemical processes that degrade the contaminants. These reactions provide an electrochemical source that is manifested as an SP signature at the measurement locations remote from the contaminated areas. 3D inversion of the SP data is therefore needed to spatially locate the distribution of sources, which is related to contaminant presence. The inversion incorporates the 3D resistivity structure collected at the same site, and is better constrained in depth by using borehole data and regularization. Ground truth information taken after the first field experiment provides concentration data with depth for several DNAPL species in five boreholes. There is a good correlation between the ground truth data and SP source inversion, though this comparison is limited by several factors: the difference in resolution of the ground truth and inverted data, and the dependence of the redox processes on other constituents that were not measured during the ground truthing, such as oxygen content or microbial presence. Inversion of the second year's dataset provides information on the changes in the contaminant distribution, either due to natural degradation or ongoing remediation.
Arctic and N Atlantic Crustal Thickness and Oceanic Lithosphere Distribution from Gravity Inversion
NASA Astrophysics Data System (ADS)
Kusznir, Nick; Alvey, Andy
2014-05-01
The ocean basins of the Arctic and N. Atlantic formed during the Mesozoic and Cenozoic as a series of distinct ocean basins, both small and large, leading to a complex distribution of oceanic crust, thinned continental crust and rifted continental margins. The plate tectonic framework of this region was demonstrated by the pioneering work of Peter Ziegler in AAPG Memoir 43 " Evolution of the Arctic-North Atlantic and the Western Tethys" published in 1988. The spatial evolution of Arctic Ocean and N Atlantic ocean basin geometry and bathymetry are critical not only for hydrocarbon exploration but also for understanding regional palaeo-oceanography and ocean gateway connectivity, and its influence on global climate. Mapping crustal thickness and oceanic lithosphere distribution represents a substantial challenge for the Polar Regions. Using gravity anomaly inversion we have produced comprehensive maps of crustal thickness and oceanic lithosphere distribution for the Arctic and N Atlantic region, We determine Moho depth, crustal basement thickness, continental lithosphere thinning and ocean-continent transition location using a 3D spectral domain gravity inversion method, which incorporates a lithosphere thermal gravity anomaly correction (Chappell & Kusznir 2008). Gravity anomaly and bathymetry data used in the gravity inversion are from the NGA (U) Arctic Gravity Project and IBCAO respectively; sediment thickness is from a new regional compilation. The resulting maps of crustal thickness and continental lithosphere thinning factor are used to determine continent-ocean boundary location and the distribution of oceanic lithosphere. Crustal cross-sections using Moho depth from the gravity inversion allow continent-ocean transition structure to be determined and magmatic type (magma poor, "normal" or magma rich). Our gravity inversion predicts thin crust and high continental lithosphere thinning factors in the Eurasia, Canada, Makarov, Podvodnikov and Baffin Basins
NASA Astrophysics Data System (ADS)
Novotny, O.; Plicka, V.; Zahradnik, J.
The space-time dependence of slip on a fault was modelled for the strong Athens earthquake of 7 September 1999, Mw=5.9. Seismograms from regional broadband seismic stations JAN, KZN, APE, RDO (National Observatory of Athens) and SER (Charles University and Patras University) were used in the modelling. The epicentral distances ranged between about 150 and 380 km. The problem was solved in the frequency domain using an approach similar to that of Cotton and Campillo (1995). The fault plane orientation, given by strike=123°, dip=55° and rake=-84° (USGS), was in a good agreement with aftershock distribution (Tselentis and Zahradnik, 2000) . Therefore, we kept these values fixed during the inversion. The fault plane (16 x 13 km) was subdivided into 144 subfaults, and each subfault was approximated by a point source. Green function spectra for the point sources were computed by discrete wave-number method. A revised model of the crustal structure was employed in these computations (Novotny et al., 2000). Three unknown parameters, namely the final slip, rupture time and rise time, were sought for each subfault. To determine the unknown parameters, two different inversion procedures were applied, in particular a generalised method of conjugate gradients and a modification of the single parameter variation. Synthetic experiments were performed to study the stability of the inversion with respect to the individual subfault parameters. The slip distributions obtained for the Athens earthquake data are compared with other solutions, especially with the recent solution of Baumont et al., who used empirical Green functions.
Pore Size Distributions Inferred from Modified Inversion Percolation Modeling of Drainage Curves
NASA Astrophysics Data System (ADS)
Dralus, D. E.; Wang, H. F.; Strand, T. E.; Glass, R. J.; Detwiler, R. L.
2005-12-01
Experiments have been conducted of drainage in sand packs. At equilibrium, the interface between the fluids forms a saturation transition fringe where the saturation decreases monotonically with height. This behavior was observed in a 1-inch thick pack of 20-30 sand contained front and back within two thin, 12-inch-by-24-inch glass plates. The translucent chamber was illuminated from behind by a bank of fluorescent bulbs. Acquired data were in the form of images captured by a CCD camera with resolution on the grain scale. The measured intensity of the transmitted light was used to calculate the average saturation at each point in the chamber. This study used a modified invasion percolation (MIP) model to simulate the drainage experiments to evaluate the relationship between the saturation-versus-height curve at equilibrium and the pore size distribution associated with the granular medium. The simplest interpretation of a drainage curve is in terms of a distribution of capillary tubes whose radii reproduce the the observed distribution of rise heights. However, this apparent radius distribution obtained from direct inversion of the saturation profile did not yield the assumed radius distribution. Further investigation demonstrated that the equilibrium height distribution is controlled primarily by the Bond number (ratio of gravity to capillary forces) with some influence from the width of the pore radius distribution. The width of the equilibrium fringe is quantified in terms of the ratio of Bond number to the standard deviation of the pore throat distribution. The normalized saturation-vs-height curves exhibit a power-law scaling behavior consistent with both Brooks-Corey and Van Genuchten type curves. Fundamental tenets of percolation theory were used to quantify the relationship between the apparent and actual radius distributions as a function of the mean coordination number and of the ratio of Bond number to standard deviation, which was supported by both MIP
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Li, Weixuan; Lin, Guang
2015-08-01
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.
Mendoza, C.; Hartzell, S.H.
1988-01-01
We have inverted the teleseismic P waveforms recorded by stations of the Global Digital Seismograph Network for the 8 July 1986 North Palm Springs, California, the 28 October 1983 Borah Peak, Idaho, and the 19 September 1985 Michoacan, Mexico, earthquakes to recover the distribution of slip on each of the faults using a point-by-point inversion method with smoothing and positivity constraints. Results of the inversion indicate that the Global digital Seismograph Network data are useful for deriving fault dislocation models for moderate to large events. However, a wide range of frequencies is necessary to infer the distribution of slip on the earthquake fault. Although the long-period waveforms define the size (dimensions and seismic moment) of the earthquake, data at shorter period provide additional constraints on the variation of slip on the fault. Dislocation models obtained for all three earthquakes are consistent with a heterogeneous rupture process where failure is controlled largely by the size and location of high-strength asperity regions. -from Authors
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Li, Weixuan; Lin, Guang
2015-03-21
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.
An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions
Li, Weixuan; Lin, Guang
2015-03-21
Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less
Budic, Lara; Didenko, Gregor; Dormann, Carsten F
2016-01-01
In species distribution analyses, environmental predictors and distribution data for large spatial extents are often available in long-lat format, such as degree raster grids. Long-lat projections suffer from unequal cell sizes, as a degree of longitude decreases in length from approximately 110 km at the equator to 0 km at the poles. Here we investigate whether long-lat and equal-area projections yield similar model parameter estimates, or result in a consistent bias. We analyzed the environmental effects on the distribution of 12 ungulate species with a northern distribution, as models for these species should display the strongest effect of projectional distortion. Additionally we choose four species with entirely continental distributions to investigate the effect of incomplete cell coverage at the coast. We expected that including model weights proportional to the actual cell area should compensate for the observed bias in model coefficients, and similarly that using land coverage of a cell should decrease bias in species with coastal distribution. As anticipated, model coefficients were different between long-lat and equal-area projections. Having progressively smaller and a higher number of cells with increasing latitude influenced the importance of parameters in models, increased the sample size for the northernmost parts of species ranges, and reduced the subcell variability of those areas. However, this bias could be largely removed by weighting long-lat cells by the area they cover, and marginally by correcting for land coverage. Overall we found little effect of using long-lat rather than equal-area projections in our analysis. The fitted relationship between environmental parameters and occurrence probability differed only very little between the two projection types. We still recommend using equal-area projections to avoid possible bias. More importantly, our results suggest that the cell area and the proportion of a cell covered by land should be
Technology Transfer Automated Retrieval System (TEKTRAN)
The beard testing method for measuring cotton fiber length is based on the fibrogram theory. However, in the instrumental implementations, the engineering complexity alters the original fiber length distribution observed by the instrument. This causes challenges in obtaining the entire original le...
NASA Astrophysics Data System (ADS)
Franssens, Ghislain; de Maziére, Martine; Fonteyn, Dominique
2000-08-01
A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz s model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.
Franssens, G; De Maziére, M; Fonteyn, D
2000-08-20
A new derivation is presented for the analytical inversion of aerosol spectral extinction data to size distributions. It is based on the complex analytic extension of the anomalous diffraction approximation (ADA). We derive inverse formulas that are applicable to homogeneous nonabsorbing and absorbing spherical particles. Our method simplifies, generalizes, and unifies a number of results obtained previously in the literature. In particular, we clarify the connection between the ADA transform and the Fourier and Laplace transforms. Also, the effect of the particle refractive-index dispersion on the inversion is examined. It is shown that, when Lorentz's model is used for this dispersion, the continuous ADA inverse transform is mathematically well posed, whereas with a constant refractive index it is ill posed. Further, a condition is given, in terms of Lorentz parameters, for which the continuous inverse operator does not amplify the error.
Simplified Solution of the Inverse Problem for Instantaneous Cometary Dust Size Distribution
NASA Astrophysics Data System (ADS)
Kocifaj, M.; Klačka, J.; Kundracek, F.; Videen, G.
Available optical measurements indicate that the modal radius rm of a cometary dust population is in the submicron range and that the dust refractive index m changes slightly in the visible region of the spectrum. A realistic instantaneous particle size distribution f(r) may be determined by processing the measured intensity of continuum at several wavelengths. The solution of the inverse problem for particle size distribution is based on rigorous Mie theory. Additionally, an application of the Rayleigh-Gans approximation enables to construct an accelerated solution scheme since the total intensity of the scattered radiation can then be expressed in an analytical form. However, the range of validity of the approximation is strongly limited to very small submicron-sized particles. The numerical simulations of light scattering by Mie cometary dust particles are performed for two model size distributions - power function f(r) µ r-n and modified gamma function f(r) µ ra e-br, which are commonly used to represent real dust populations. It is shown that the cometary dust size distribution may easily be reproduced analysing the spectral behaviour of measured intensity of the scattered radiation IJ(l). The more rapid increasing of continuum with the wavelength of incident radiation the larger particles are contained in cometary dusty environment.
Layer 1 VPN services in distributed next-generation SONET/SDH networks with inverse multiplexing
NASA Astrophysics Data System (ADS)
Ghani, N.; Muthalaly, M. V.; Benhaddou, D.; Alanqar, W.
2006-05-01
Advances in next-generation SONET/SDH along with GMPLS control architectures have enabled many new service provisioning capabilities. In particular, a key services paradigm is the emergent Layer 1 virtual private network (L1 VPN) framework, which allows multiple clients to utilize a common physical infrastructure and provision their own 'virtualized' circuit-switched networks. This precludes expensive infrastructure builds and increases resource utilization for carriers. Along these lines, a novel L1 VPN services resource management scheme for next-generation SONET/SDH networks is proposed that fully leverages advanced virtual concatenation and inverse multiplexing features. Additionally, both centralized and distributed GMPLS-based implementations are also tabled to support the proposed L1 VPN services model. Detailed performance analysis results are presented along with avenues for future research.
Lee, Chien-Wei; Hwu, Jenn-Gwo
2013-10-15
We derive a statistical physics model of two-dimensional electron gas (2DEG) and propose an accurate approximation method for calculating the quantum-mechanical effects of metal-oxide-semiconductor (MOS) structure in accumulation and strong inversion regions. We use an exponential surface potential approximation in solving the quantization energy levels and derive the function of density of states in 2D to 3D transition region by applying uncertainty principle and Schrödinger equation in k-space. The simulation results show that our approximation method and theory of density of states solve the two major problems of previous researches: the non-negligible error caused by the linear potential approximation and the inconsistency of density of states and carrier distribution in 2D to 3D transition region.
Hirao, S; Hayashi, R; Moriizumi, J; Yamazawa, H; Tohjima, Y; Mukai, H
2015-11-01
In this study, the (222)Rn flux density distribution at surface was estimated in East Asia with the Bayesian synthesis inversion using measurement data and a long-range atmospheric (222)Rn transport model. Surface atmospheric (222)Rn concentrations measured at Hateruma Island in January 2008 were used. The estimated (222)Rn flux densities were generally higher than the prior ones. The area-weighted mean (222)Rn flux density for East Asia in January 2008 was estimated to be 44.0 mBq m(-2) s(-1). The use of the estimated (222)Rn flux density improved the discrepancy of the model-calculated concentrations with the measurements at Hateruma Island.
Inverse modeling of InSAR and ground leveling data for 3D volumetric strain distribution
NASA Astrophysics Data System (ADS)
Gallardo, L. A.; Glowacka, E.; Sarychikhina, O.
2015-12-01
Wide availability of modern Interferometric Synthetic aperture Radar (InSAR) data have made possible the extensive observation of differential surface displacements and are becoming an efficient tool for the detailed monitoring of terrain subsidence associated to reservoir dynamics, volcanic deformation and active tectonism. Unfortunately, this increasing popularity has not been matched by the availability of automated codes to estimate underground deformation, since many of them still rely on trial-error subsurface model building strategies. We posit that an efficient algorithm for the volumetric modeling of differential surface displacements should match the availability of current leveling and InSAR data and have developed an algorithm for the joint inversion of ground leveling and dInSAR data in 3D. We assume the ground displacements are originated by a stress free-volume strain distribution in a homogeneous elastic media and determined the displacement field associated to an ensemble of rectangular prisms. This formulation is then used to develop a 3D conjugate gradient inversion code that searches for the three-dimensional distribution of the volumetric strains that predict InSAR and leveling surface displacements simultaneously. The algorithm is regularized applying discontinuos first and zero order Thikonov constraints. For efficiency, the resulting computational code takes advantage of the resulting convolution integral associated to the deformation field and some basic tools for multithreading parallelization. We extensively test our algorithm on leveling and InSAR test and field data of the Northwest of Mexico and compare to some feasible geological scenarios of underground deformation.
Paramonov, L.E.
1994-12-01
Scattering of electromagnetic radiation from the elementary volume containing particles of an arbitrary shape with an arbitrary square integrable orientation distribution function is considered. Based on the T-matrix approach and the quantum theory of angular momentum, an analytical method is suggested for estimating the Mueller matrix elements and the Stokes vector of radiation scattered from an ensemble of particles in the case of an arbituary number of incident radiation sources. The constructive existence theorem is proved for the expansion of the scattering matrix elements as a power series in Wigner functions in the elementary volume having a rotational symmetry relative to the direction of the incident radiation propagation. Corollaries of the results obtained are considered. 24 refs.
ERIC Educational Resources Information Center
Leung, Issic Kui Chiu; Ding, Lin; Leung, Allen Yuk Lun; Wong, Ngai Ying
2016-01-01
This study is part of a larger study investigating the subject matter knowledge and pedagogical content knowledge of Hong Kong prospective mathematics teachers, the relationship between the knowledge of algebraic operation and its inverse, and their teaching competency. In this paper, we address the subject matter knowledge and pedagogical content…
Pan, Feifei; Peters-lidard, Christa D.; King, Anthony Wayne
2010-11-01
Soil particle size distribution (PSD) (i.e., clay, silt, sand, and rock contents) information is one of critical factors for understanding water cycle since it affects almost all of water cycle processes, e.g., drainage, runoff, soil moisture, evaporation, and evapotranspiration. With information about soil PSD, we can estimate almost all soil hydraulic properties (e.g., saturated soil moisture, field capacity, wilting point, residual soil moisture, saturated hydraulic conductivity, pore-size distribution index, and bubbling capillary pressure) based on published empirical relationships. Therefore, a regional or global soil PSD database is essential for studying water cycle regionally or globally. At the present stage, three soil geographic databases are commonly used, i.e., the Soil Survey Geographic database, the State Soil Geographic database, and the National Soil Geographic database. Those soil data are map unit based and associated with great uncertainty. Ground soil surveys are a way to reduce this uncertainty. However, ground surveys are time consuming and labor intensive. In this study, an inverse method for estimating mean and standard deviation of soil PSD from observed soil moisture is proposed and applied to Throughfall Displacement Experiment sites in Walker Branch Watershed in eastern Tennessee. This method is based on the relationship between spatial mean and standard deviation of soil moisture. The results indicate that the suggested method is feasible and has potential for retrieving soil PSD information globally from remotely sensed soil moisture data.
NASA Astrophysics Data System (ADS)
Baer, P.; Mastrandrea, M.
2006-12-01
Simple probabilistic models which attempt to estimate likely transient temperature change from specified CO2 emissions scenarios must make assumptions about at least six uncertain aspects of the causal chain between emissions and temperature: current radiative forcing (including but not limited to aerosols), current land use emissions, carbon sinks, future non-CO2 forcing, ocean heat uptake, and climate sensitivity. Of these, multiple PDFs (probability density functions) have been published for the climate sensitivity, a couple for current forcing and ocean heat uptake, one for future non-CO2 forcing, and none for current land use emissions or carbon cycle uncertainty (which are interdependent). Different assumptions about these parameters, as well as different model structures, will lead to different estimates of likely temperature increase from the same emissions pathway. Thus policymakers will be faced with a range of temperature probability distributions for the same emissions scenarios, each described by a central tendency and spread. Because our conventional understanding of uncertainty and probability requires that a probabilistically defined variable of interest have only a single mean (or median, or modal) value and a well-defined spread, this "multidimensional" uncertainty defies straightforward utilization in policymaking. We suggest that there are no simple solutions to the questions raised. Crucially, we must dispel the notion that there is a "true" probability probabilities of this type are necessarily subjective, and reasonable people may disagree. Indeed, we suggest that what is at stake is precisely the question, what is it reasonable to believe, and to act as if we believe? As a preliminary suggestion, we demonstrate how the output of a simple probabilistic climate model might be evaluated regarding the reasonableness of the outputs it calculates with different input PDFs. We suggest further that where there is insufficient evidence to clearly
Xia, J.; Miller, R.D.; Xu, Y.
2008-01-01
Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (>2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data. ?? Birkhaueser 2008.
NASA Technical Reports Server (NTRS)
Wu, Xiaoping; Argus, Donald F.; Heflin, Michael B.; Ivins, Erik R.; Webb, Frank H.
2002-01-01
Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher-degree (n greater than or equal 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center-of-figure approximation in the inverse formulation could cause 10- 15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher-degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80 - 95% for two load scenarios.
NASA Astrophysics Data System (ADS)
Elsaghir, Ahmed; Shannon, Steve
2008-10-01
Electron energy distribution function (EEDF) extraction from Langmuir probe data is an ill-posed problem due to the integral relationship between electron current and EEDF with respect to probe voltage. Curve fitting solutions to extract this EEDF assume a specific type of distribution. Point by point extraction of the second derivative relationship uses a small fraction of the integrated data to extract the EEDF. Recently EEDF extraction techniques have been evaluated using regularized solutions to the integral problem.ootnotetextGuti'errez-Tapia and Flores-Llamas, Phys. Plasmas 11 5102 (2004) These techniques do not assume any mathematical representation of the EEDF and solve the integral problem for any function that best represents the EEDF. In this paper the electron current for arbitrary functions is derived assuming that the electron density is a sum of step functions representing such a function. This technique for EEDF extraction is validated by adding noise to numerically generated data and using a regularized least squares method to calculate the original function by solving for the individual step function contribution to the total electron current. The methodology, reconstruction, and comparison to current best-known methods will be presented.
NASA Astrophysics Data System (ADS)
Shi, Yan-Ling; Hu, Zu-Zhi; Huang, Wen-Hui; Wei, Qiang; Zhang, Sheng; Meng, Cui-Xian; Ji, Lian-Sheng
2016-09-01
The coal-bearing strata of the deep Upper Paleozoic in the GS Sag have high hydrocarbon potential. Because of the absence of seismic data, we use electromagnetic (MT) and gravity data jointly to delineate the distribution of deep targets based on well logging and geological data. First, a preliminary geological model is established by using three-dimensional (3D) MT inversion results. Second, using the formation density and gravity anomalies, the preliminary geological model is modified by interactive inversion of the gravity data. Then, we conduct MT-constrained inversion based on the modified model to obtain an optimal geological model until the deviations at all stations are minimized. Finally, the geological model and a seismic profile in the middle of the sag is analysed. We determine that the deep reflections of the seismic profile correspond to the Upper Paleozoic that reaches thickness up to 800 m. The processing of field data suggests that the joint MT-gravity modeling and constrained inversion can reduce the multiple solutions for single geophysical data and thus improve the recognition of deep formations. The MT-constrained inversion is consistent with the geological features in the seismic section. This suggests that the joint MT and gravity modeling and constrained inversion can be used to delineate deep targets in similar basins.
Zhou, C.; Liu, L.; Lane, J.W.
2001-01-01
A nonlinear tomographic inversion method that uses first-arrival travel-time and amplitude-spectra information from cross-hole radar measurements was developed to simultaneously reconstruct electromagnetic velocity and attenuation distribution in earth materials. Inversion methods were developed to analyze single cross-hole tomography surveys and differential tomography surveys. Assuming the earth behaves as a linear system, the inversion methods do not require estimation of source radiation pattern, receiver coupling, or geometrical spreading. The data analysis and tomographic inversion algorithm were applied to synthetic test data and to cross-hole radar field data provided by the US Geological Survey (USGS). The cross-hole radar field data were acquired at the USGS fractured-rock field research site at Mirror Lake near Thornton, New Hampshire, before and after injection of a saline tracer, to monitor the transport of electrically conductive fluids in the image plane. Results from the synthetic data test demonstrate the algorithm computational efficiency and indicate that the method robustly can reconstruct electromagnetic (EM) wave velocity and attenuation distribution in earth materials. The field test results outline zones of velocity and attenuation anomalies consistent with the finding of previous investigators; however, the tomograms appear to be quite smooth. Further work is needed to effectively find the optimal smoothness criterion in applying the Tikhonov regularization in the nonlinear inversion algorithms for cross-hole radar tomography. ?? 2001 Elsevier Science B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Selvam, A. M.
2017-01-01
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference
NASA Technical Reports Server (NTRS)
Zhang, Y. C.; Zhang, J. Z. H.; Kouri, D. J.; Haug, K.; Schwenke, D. W.
1988-01-01
Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.
Piskozub, J.
1994-12-31
The multifrequency lidar inverse problem discussed consists of calculating the size distribution of sol particles from backscattered lidar data. Sea-water (marine) aerosol is particularly well suited for this kind of study as its scattering characteristics can be accurately represented by Mie theory as its particles are almost spherical and their complex index of refraction is well known. Here, a solution of the inverse problem concerning finding aerosol size distribution for a multifrequency lidar system working on a small number of wavelengths is proposed. The solution involves a best-fit method of finding parameters in a pre-set formula of particle size distribution. A comparison of results calculated with the algorithm from experimental lidar profiles with PMS data collected in Baltic Sea coastal zone is given.
NASA Astrophysics Data System (ADS)
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
NASA Astrophysics Data System (ADS)
li, L.; Huang, Z.
2013-12-01
It has been shown that the characteristics of a tsunami wave including wave heights recorded by DARTs in deep sea, waveforms recorded by tide gauges, and runup heights are useful to constrain some earthquake source parameters. In this study, we investigate the slip distribution of the 2010 Mentawai earthquake, a tsunami earthquake that occurred seaward of the southern Mentawai islands of Sumatra, and produced a locally devastating tsunami, with runup commonly in excess of 6 m. As a unique tsunami earthquake case, there is a significant discrepancy between the observed small GPS displacement and the very large tsunami runup (maximum value > 16 m), which cannot be explained by the conventional GPS or seismic inversion model. The goal of this work is to compare the slip distributions of this earthquake inferred from the available waveforms recorded by nearby tide gauges or from the tsunami height and runup data collected in a field survey, using two inversion models. One is based on Green's fuctions technique. The other is based on adjoint method which is an application of optimal control theory. The inversion by Green's functions requires a linear link between data and unknown variables. The adjoint method has the advantage of being able to use either linear or non-linear forward propagation models that can account for non-linear advection and run-up effects. The limitations of these two methods are discussed.
NASA Astrophysics Data System (ADS)
Li, Liang; Chen, Zhiqiang; Xu, Ronglan; Huang, Ya
2011-12-01
The plasma density distribution of plasmasphere in the geomagnetic equatorial plane can help us study the magnetosphere like plasmasphere, ionosphere and their kinetics. In this paper, we introduce a new inversion method, GE-ART, to calculate the plasma density distribution in the geomagnetic equatorial plane from the Extreme Ultraviolet (EUV) data of IMAGE satellite under the assumption that the plasma density is constant along each geomagnetic field line. The new GE-ART algorithm was derived from the traditional Algebraic Reconstruction Techniques (ART) in Computed Tomography (CT) which was different from the several existing methods. In this new method, each value of the EUV image data was back-projected evenly to the geomagnetic field lines intersected by this EUV sight. A 3-D inversion matrix was produced by the contributions of all the voxels contained in the plasmasphere covered by the EUV sensor. That is, we considered that each value of the EUV image data was relative to the plasma densities of all the voxels passed through by the corresponding EUV radiation, which is the biggest difference to all the existing inversion methods. Finally, the GE-ART algorithm was evaluated by the real EUV data from the IMAGE satellite.
NASA Astrophysics Data System (ADS)
Kusznir, N. J.; Tymms, V.
2009-04-01
Satellite gravity anomaly inversion incorporating a lithosphere thermal gravity anomaly correction has been used to determine Moho depth, crustal thickness and lithosphere thinning factor for the NW Indian Ocean and to map ocean-continent transition location (OCT) and micro-continent distribution. Input data is satellite gravity (Sandwell & Smith 1997) and digital bathymetry (Gebco 2003). Crustal thicknesses predicted by gravity inversion under the Seychelles and Mascarenes are in excess of 30 km and form a single micro-continent extending southwards towards Mauritius. Thick crust (> 25 km) offshore SW India is predicted to extend oceanwards under the Lacadive and Maldive Islands and southwards under the Chagos Archipelago. Superposition of illuminated satellite gravity data onto crustal thickness maps from gravity inversion clearly shows pre-separation conjugacy of the thick crust underlying the Chagos and Mascarene Islands. Maps of crustal thickness from gravity inversion show a pronounced discontinuity in crustal thickness between Mauritius-Reunion and the Mascarene Basin which is of Late Cretaceous age and pre-dates recent plume volcanism. Gravity inversion to determine Moho depth and crustal thickness variation is carried out in the 3D spectral domain and incorporates a lithosphere thermal gravity anomaly correction for both oceanic and continental margin lithosphere (Chappell & Kusznir 2008). Failure to incorporate a lithosphere thermal gravity anomaly correction gives a substantial over-estimate of crustal thickness predicted by gravity inversion. The lithosphere thermal model used to predict the lithosphere thermal gravity anomaly correction may be conditioned using magnetic isochron data to provide the age of oceanic lithosphere (Mueller et al. 1997). The resulting crustal thickness determination and the location of the OCT are sensitive to errors in the magnetic isochron data. An alternative method of inverting satellite gravity to give crustal thickness
Chen, J. M.; Fung, J. W.; Mo, G.; Deng, F.; West, Tristram O.
2015-01-01
In order to improve quantification of the spatial distribution of carbon sinks and sources in the conterminous USA, we conduct a nested global atmospheric inversion with consideration of the spatial information of crop production and consumption. Spatially distributed 5 county-level cropland net primary productivity, harvested biomass, soil carbon change, and human and livestock consumption data over the conterminous USA are used for this purpose. Time-dependent Bayesian synthesis inversions are conducted based on CO₂ observations at 210 stations to infer CO₂ fluxes globally at monthly time steps with a nested focus on 30 regions in North America. Prior land surface carbon 10 fluxes are first generated using a biospheric model, and the inversions are constrained using prior fluxes with and without adjustments for crop production and consumption over the 2002–2007 period. After these adjustments, the inverted regional carbon sink in the US Midwest increases from 0.25 ± 0.03 Pg C yr⁻¹ to 0.42 ± 0.13 Pg C yr⁻¹, whereas the large sink in the US Southeast forest region is weakened from 0.41±0.12 Pg C yr⁻¹ 15 to 0.29 ±0.12 Pg C yr⁻¹. These adjustments also reduce the inverted sink in the West region from 0.066 ± 0.04 Pg C yr⁻¹ to 0.040 ± 0.02 Pg C yr⁻1 because of high crop consumption and respiration by humans and livestock. The general pattern of sink increase in crop production areas and sink decreases (or source increases) in crop consumption areas highlights the importance of considering the lateral carbon transfer in crop 20 products in atmospheric inverse modeling, which provides an atmospheric perspective of the overall carbon balance of a region.
NASA Astrophysics Data System (ADS)
He, Zhenzong; Qi, Hong; Wang, Yuqing; Ruan, Liming
2014-10-01
Four improved Ant Colony Optimization (ACO) algorithms, i.e. the probability density function based ACO (PDF-ACO) algorithm, the Region ACO (RACO) algorithm, Stochastic ACO (SACO) algorithm and Homogeneous ACO (HACO) algorithm, are employed to estimate the particle size distribution (PSD) of the spheroidal particles. The direct problems are solved by the extended Anomalous Diffraction Approximation (ADA) and the Lambert-Beer law. Three commonly used monomodal distribution functions i.e. the Rosin-Rammer (R-R) distribution function, the normal (N-N) distribution function, and the logarithmic normal (L-N) distribution function are estimated under dependent model. The influence of random measurement errors on the inverse results is also investigated. All the results reveal that the PDF-ACO algorithm is more accurate than the other three ACO algorithms and can be used as an effective technique to investigate the PSD of the spheroidal particles. Furthermore, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution functions to retrieve the PSD of spheroidal particles using PDF-ACO algorithm. The investigation shows a reasonable agreement between the original distribution function and the general distribution function when only considering the variety of the length of the rotational semi-axis.
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
ERIC Educational Resources Information Center
Hubbard, Guy
2003-01-01
Discusses the role of the square in art and explains that students can study modern art. Includes background information and artwork by four artists: (1) Richard Anuszkiewicz; (2) Victor Vasarely; (3) Frank Stella; and (4) Bridget Riley. (CMK)
NASA Astrophysics Data System (ADS)
Fakhreddine, Sarah; Lee, Jonghyun; Kitanidis, Peter K.; Fendorf, Scott; Rolle, Massimo
2016-02-01
The spatial distribution of reactive minerals in the subsurface is often a primary factor controlling the fate and transport of contaminants in groundwater systems. However, direct measurement and estimation of heterogeneously distributed minerals are often costly and difficult to obtain. While previous studies have shown the utility of using hydrologic measurements combined with inverse modeling techniques for tomography of physical properties including hydraulic conductivity, these methods have seldom been used to image reactive geochemical heterogeneities. In this study, we focus on As-bearing reactive minerals as aquifer contaminants. We use synthetic applications to demonstrate the ability of inverse modeling techniques combined with mechanistic reactive transport models to image reactive mineral lenses in the subsurface and quantify estimation error using indirect, commonly measured groundwater parameters. Specifically, we simulate the mobilization of arsenic via kinetic oxidative dissolution of As-bearing pyrite due to dissolved oxygen in the ambient groundwater, which is an important mechanism for arsenic release in groundwater both under natural conditions and engineering applications such as managed aquifer recharge and recovery operations. The modeling investigation is carried out at various scales and considers different flow-through domains including (i) a 1D lab-scale column (80 cm), (ii) a 2D lab-scale setup (60 cm × 30 cm) and (iii) a 2D field-scale domain (20 m × 4 m). In these setups, synthetic dissolved oxygen data and forward reactive transport simulations are used to image the spatial distribution of As-bearing pyrite using the Principal Component Geostatistical Approach (PCGA) for inverse modeling.
Identified particle distributions in pp and Au+Au collisions at square root of (sNN)=200 GeV.
Adams, J; Adler, C; Aggarwal, M M; Ahammed, Z; Amonett, J; Anderson, B D; Anderson, M; Arkhipkin, D; Averichev, G S; Badyal, S K; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellwied, R; Berger, J; Bezverkhny, B I; Bhardwaj, S; Bhaskar, P; Bhati, A K; Bichsel, H; Billmeier, A; Bland, L C; Blyth, C O; Bonner, B E; Botje, M; Boucham, A; Brandin, A; Bravar, A; Cadman, R V; Cai, X Z; Caines, H; Calderón de la Barca Sánchez, M; Carroll, J; Castillo, J; Castro, M; Cebra, D; Chaloupka, P; Chattopadhyay, S; Chen, H F; Chen, Y; Chernenko, S P; Cherney, M; Chikanian, A; Choi, B; Christie, W; Coffin, J P; Cormier, T M; Cramer, J G; Crawford, H J; Das, D; Das, S; Derevschikov, A A; Didenko, L; Dietel, T; Dong, X; Draper, J E; Du, F; Dubey, A K; Dunin, V B; Dunlop, J C; Dutta Majumdar, M R; Eckardt, V; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Estienne, M; Fachini, P; Faine, V; Faivre, J; Fatemi, R; Filimonov, K; Filip, P; Finch, E; Fisyak, Y; Flierl, D; Foley, K J; Fu, J; Gagliardi, C A; Ganti, M S; Gutierrez, T D; Gagunashvili, N; Gans, J; Gaudichet, L; Germain, M; Geurts, F; Ghazikhanian, V; Ghosh, P; Gonzalez, J E; Grachov, O; Grigoriev, V; Gronstal, S; Grosnick, D; Guedon, M; Guertin, S M; Gupta, A; Gushin, E; Hallman, T J; Hardtke, D; Harris, J W; Heinz, M; Henry, T W; Heppelmann, S; Herston, T; Hippolyte, B; Hirsch, A; Hjort, E; Hoffmann, G W; Horsley, M; Huang, H Z; Huang, S L; Humanic, T J; Igo, G; Ishihara, A; Jacobs, P; Jacobs, W W; Janik, M; Johnson, I; Jones, P G; Judd, E G; Kabana, S; Kaneta, M; Kaplan, M; Keane, D; Kiryluk, J; Kisiel, A; Klay, J; Klein, S R; Klyachko, A; Koetke, D D; Kollegger, T; Konstantinov, A S; Kopytine, M; Kotchenda, L; Kovalenko, A D; Kramer, M; Kravtsov, P; Krueger, K; Kuhn, C; Kulikov, A I; Kumar, A; Kunde, G J; Kunz, C L; Kutuev, R Kh; Kuznetsov, A A; Lamont, M A C; Landgraf, J M; Lange, S; Lansdell, C P; Lasiuk, B; Laue, F; Lauret, J; Lebedev, A; Lednický, R; Leontiev, V M; LeVine, M J; Li, C; Li, Q; Lindenbaum, S J; Lisa, M A; Liu, F; Liu, L; Liu, Z; Liu, Q J; Ljubicic, T; Llope, W J; Long, H; Longacre, R S; Lopez-Noriega, M; Love, W A; Ludlam, T; Lynn, D; Ma, J; Ma, Y G; Magestro, D; Mahajan, S; Mangotra, L K; Mahapatra, D P; Majka, R; Manweiler, R; Margetis, S; Markert, C; Martin, L; Marx, J; Matis, H S; Matulenko, Yu A; McShane, T S; Meissner, F; Melnick, Yu; Meschanin, A; Messer, M; Miller, M L; Milosevich, Z; Minaev, N G; Mironov, C; Mishra, D; Mitchell, J; Mohanty, B; Molnar, L; Moore, C F; Mora-Corral, M J; Morozov, V; de Moura, M M; Munhoz, M G; Nandi, B K; Nayak, S K; Nayak, T K; Nelson, J M; Nevski, P; Nikitin, V A; Nogach, L V; Norman, B; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Paic, G; Pandey, S U; Pal, S K; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Perevoztchikov, V; Peryt, W; Petrov, V A; Phatak, S C; Picha, R; Planinic, M; Pluta, J; Porile, N; Porter, J; Poskanzer, A M; Potekhin, M; Potrebenikova, E; Potukuchi, B V K S; Prindle, D; Pruneau, C; Putschke, J; Rai, G; Rakness, G; Raniwala, R; Raniwala, S; Ravel, O; Ray, R L; Razin, S V; Reichhold, D; Reid, J G; Renault, G; Retiere, F; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevski, O V; Romero, J L; Rose, A; Roy, C; Ruan, L J; Sahoo, R; Sakrejda, I; Salur, S; Sandweiss, J; Savin, I; Schambach, J; Scharenberg, R P; Schmitz, N; Schroeder, L S; Schweda, K; Seger, J; Seliverstov, D; Seyboth, P; Shahaliev, E; Shao, M; Sharma, M; Shestermanov, K E; Shimanskii, S S; Singaraju, R N; Simon, F; Skoro, G; Smirnov, N; Snellings, R; Sood, G; Sorensen, P; Sowinski, J; Spinka, H M; Srivastava, B; Stanislaus, S; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Struck, C; Suaide, A A P; Sugarbaker, E; Suire, C; Sumbera, M; Surrow, B; Symons, T J M; de Toledo, A Szanto; Szarwas, P; Tai, A; Takahashi, J; Tang, A H; Thein, D; Thomas, J H; Tikhomirov, V; Tokarev, M; Tonjes, M B; Trainor, T A; Trentalange, S; Tribble, R E; Trivedi, M D; Trofimov, V; Tsai, O; Ullrich, T; Underwood, D G; Van Buren, G; VanderMolen, A M; Vasiliev, A N; Vasiliev, M; Vigdor, S E; Viyogi, Y P; Voloshin, S A; Waggoner, W; Wang, F; Wang, G; Wang, X L; Wang, Z M; Ward, H; Watson, J W; Wells, R; Westfall, G D; Whitten, C; Wieman, H; Willson, R; Wissink, S W; Witt, R; Wood, J; Wu, J; Xu, N; Xu, Z; Xu, Z Z; Yakutin, A E; Yamamoto, E; Yang, J; Yepes, P; Yurevich, V I; Zanevski, Y V; Zborovský, I; Zhang, H; Zhang, H Y; Zhang, W M; Zhang, Z P; Zołnierczuk, P A; Zoulkarneev, R; Zoulkarneeva, J; Zubarev, A N
2004-03-19
Transverse mass and rapidity distributions for charged pions, charged kaons, protons, and antiprotons are reported for square root of [sNN]=200 GeV pp and Au+Au collisions at Relativistic Heary Ion Collider (RHIC). Chemical and kinetic equilibrium model fits to our data reveal strong radial flow and long duration from chemical to kinetic freeze-out in central Au+Au collisions. The chemical freeze-out temperature appears to be independent of initial conditions at RHIC energies.
A Three-Parameter Inversion of the Drop Size Distribution Using NASA/TRMM Microwave Link Data
NASA Technical Reports Server (NTRS)
Rincon, Rafael F.; Lang, Roger H.; Meneghini, Robert
2003-01-01
Attenuation measurements at 25 and 38 GHz performed with the NASA/TRMM Microwave Link provide information about the drop size distribution (DSD) along the propagation path. Additional path-average measurements along the Link path, such as a third attenuation measurement or the rain rate from well-calibrated raingauges, can provide further DSD information. This paper explores an inversion procedure for determining simultaneously three parameters of a gamma DSD by using three measurements. Also, some preliminary results obtained using Link data are presented.
Chen, J. M.; Fung, J. W.; Mo, G.; ...
2015-01-19
In order to improve quantification of the spatial distribution of carbon sinks and sources in the conterminous US, we conduct a nested global atmospheric inversion with detailed spatial information on crop production and consumption. County-level cropland net primary productivity, harvested biomass, soil carbon change, and human and livestock consumption data over the conterminous US are used for this purpose. Time-dependent Bayesian synthesis inversions are conducted based on CO₂ observations at 210 stations to infer CO₂ fluxes globally at monthly time steps with a nested focus on 30 regions in North America. Prior land surface carbon fluxes are first generated usingmore » a biospheric model, and the inversions are constrained using prior fluxes with and without adjustments for crop production and consumption over the 2002–2007 period. After these adjustments, the inverted regional carbon sink in the US Midwest increases from 0.25 ± 0.03 to 0.42 ± 0.13 Pg C yr⁻¹, whereas the large sink in the US southeast forest region is weakened from 0.41 ± 0.12 to 0.29 ± 0.12 Pg C yr⁻¹. These adjustments also reduce the inverted sink in the west region from 0.066 ± 0.04 to 0.040 ± 0.02 Pg C yr⁻¹ because of high crop consumption and respiration by humans and livestock. The general pattern of sink increases in crop production areas and sink decreases (or source increases) in crop consumption areas highlights the importance of considering the lateral carbon transfer in crop products in atmospheric inverse modeling, which provides a reliable atmospheric perspective of the overall carbon balance at the continental scale but is unreliable for separating fluxes from different ecosystems.« less
Chen, J. M.; Fung, J. W.; Mo, G.; Deng, F.; West, T. O.
2015-01-19
In order to improve quantification of the spatial distribution of carbon sinks and sources in the conterminous US, we conduct a nested global atmospheric inversion with detailed spatial information on crop production and consumption. County-level cropland net primary productivity, harvested biomass, soil carbon change, and human and livestock consumption data over the conterminous US are used for this purpose. Time-dependent Bayesian synthesis inversions are conducted based on CO₂ observations at 210 stations to infer CO₂ fluxes globally at monthly time steps with a nested focus on 30 regions in North America. Prior land surface carbon fluxes are first generated using a biospheric model, and the inversions are constrained using prior fluxes with and without adjustments for crop production and consumption over the 2002–2007 period. After these adjustments, the inverted regional carbon sink in the US Midwest increases from 0.25 ± 0.03 to 0.42 ± 0.13 Pg C yr⁻¹, whereas the large sink in the US southeast forest region is weakened from 0.41 ± 0.12 to 0.29 ± 0.12 Pg C yr⁻¹. These adjustments also reduce the inverted sink in the west region from 0.066 ± 0.04 to 0.040 ± 0.02 Pg C yr⁻¹ because of high crop consumption and respiration by humans and livestock. The general pattern of sink increases in crop production areas and sink decreases (or source increases) in crop consumption areas highlights the importance of considering the lateral carbon transfer in crop products in atmospheric inverse modeling, which provides a reliable atmospheric perspective of the overall carbon balance at the continental scale but is unreliable for separating fluxes from different ecosystems.
NASA Astrophysics Data System (ADS)
Liu, Qing; Zhan, Yong-hong; Yang, Di; Zeng, Chang-e.
2014-11-01
In this paper, we try to find a model that can apply to predict the polarization characteristics of the targets on the ground correctly. In the first place, we give an introduction to several kinds of existing models which are divided into three categories: Empirical models are precise but occupy too much source of computer; Physical-based models can predict the phenomenon of reflection exactly but hardly get the final results; Semi-empirical models have both advantages mentioned above and avoid their disadvantages effectively. Then we make an analysis of the Priest-Germer (PG) pBRDF model, one of semi-empirical models, which is suitable for our study. The methods of parameters inversing and testing are proposed based on this model and the test system from which we can get enough data to verify the accuracy of the model is designed independently. At last, we make a simulation of the whole process of the parameters inversing based on PG pBRDF model. From the analysis of the simulation curves, we briefly know the direction we go in the following work to make an amendment.
Edwards, A W F
2012-03-01
The origin and development of Punnett's Square for the enumeration and display of genotypes arising in a cross in Mendelian genetics is described. Due to R. C. Punnett, the idea evolved through the work of the 'Cambridge geneticists', including Punnett's colleagues William Bateson, E. R. Saunders and R. H. Lock, soon after the rediscovery of Mendel's paper in 1900. These geneticists were thoroughly familiar with Mendel's paper, which itself contained a similar square diagram. A previously-unpublished three-factor diagram by Sir Francis Galton existing in the Bateson correspondence in Cambridge University Library is then described. Finally the connection between Punnett's Square and Venn Diagrams is emphasized, and it is pointed out that Punnett, Lock and John Venn overlapped as Fellows of Gonville and Caius College, Cambridge. Copious illustrations are given.
NASA Astrophysics Data System (ADS)
Mara, Thierry A.; Fajraoui, Noura; Younes, Anis; Delay, Frederick
2015-02-01
We introduce the concept of maximal conditional posterior distribution (MCPD) to assess the uncertainty of model parameters in a Bayesian framework. Although, Markov Chains Monte Carlo (MCMC) methods are particularly suited for this task, they become challenging with highly parameterized nonlinear models. The MCPD represents the conditional probability distribution function of a given parameter knowing that the other parameters maximize the conditional posterior density function. Unlike MCMC which accepts or rejects solutions sampled in the parameter space, MCPD is calculated through several optimization processes. Model inversion using MCPD algorithm is particularly useful for highly parameterized problems because calculations are independent. Consequently, they can be evaluated simultaneously with a multi-core computer. In the present work, the MCPD approach is applied to invert a 2D stochastic groundwater flow problem where the log-transmissivity field of the medium is inferred from scarce and noisy data. For this purpose, the stochastic field is expanded onto a set of orthogonal functions using a Karhunen-Loève (KL) transformation. Though the prior guess on the stochastic structure (covariance) of the transmissivity field is erroneous, the MCPD inference of the KL coefficients is able to extract relevant inverse solutions.
Spin-axis distribution of the Hungaria asteroids via lightcurve inversion
NASA Astrophysics Data System (ADS)
Warner, B.; Harris, A.; Stephens, R.; Coley, D.
2014-07-01
Since 2005, we have conducted a dedicated campaign to obtain dense lightcurves of members of the Hungaria asteroid population. As a result, the number of Hungarias in the asteroid lightcurve database (LCDB; Warner et al. [1]) with a statistically valid rotation rate rose from less than 50 to almost 300. The particular value of the Hungarias is that they are smallest and closest-to-sun main belt objects that can be studied with modest-sized telescopes. As such, they are more likely subject to YORP-altered spin states. We have previously verified highly-evolved rotation rates within the Hungarias (Warner et al. [2]). This study takes the next step of tracing the evolution of spin orientations. We combined the dense lightcurves from our campaign with so-called "sparse data" from the NEA surveys to model the spin axis orientation using lightcurve inversion methods (see works by Kaasalainen, Torppa, Durech, and Hanus). Because high-dispersion sparse data are of little use for low amplitude objects, we limited the Hungarias to be modeled to those with a maximum amplitude of A >= 0.15 mag, an LCDB reliability code of U >= 2, the period in the LCDB summary was unambiguous, and the asteroid did not show signs of tumbling (non-principal axis rotation). The result as of early February 2014 was a list of 227 of Hungaria candidates for modeling. Using a bank of five independent desktop computers and customized software, we first determined the likely sidereal period of the asteroid. That period was then used for spin axis (pole) search involving 315 discrete longitude-latitude pairs. The result of one such search is shown in the figure. We report on the results of our searches, including weighting solutions when a unique solution was not found (often the case in lightcurve inversion), and how the results compare to similar studies using a more general asteroid population.
NASA Astrophysics Data System (ADS)
Convers, Jaime; Custodio, Susana
2016-04-01
Rapid assessment of seismological parameters pertinent to the nucleation and rupture of earthquakes are now routinely calculated by local and regional seismic networks. With the increasing number of stations, fast data transmission, and advanced computer power, we can now go beyond accurate magnitude and epicentral locations, to rapid estimations of other higher-order earthquake parameters such as seismic moment tensor. Although an increased number of stations can minimize azimuthal gaps, it also increases computation time, and potentially introduces poor quality data that often leads to a lower the stability of automated inversions. In this presentation, we focus on moment tensor calculations for earthquakes occurring offshore the southwestern Iberian peninsula. The available regional seismic data in this region has a significant azimuthal gap that results from the geographical setting. In this case, increasing the number of data from stations spanning a small area (and at a small azimuthal angle) increases the calculation time without necessarily improving the accuracy of the inversion. Additionally, limited regional data coverage makes it imperative to exclude poor-quality data, as their negative effect on moment tensor inversions is often significant. In our work, we analyze methods to minimize the effects of large azimuthal gaps in a regional station coverage, of potential bias by uneven station distribution, and of poor data quality in moment tensor inversions obtained for earthquakes offshore the southwestern Iberian peninsula. We calculate moment tensors using the KIWI tools, and we implement different configurations of station-weighing, and cross-correlation of neighboring stations, with the aim of automatically estimating and selecting high-quality data, improving the accuracy of results, and reducing the computation time of moment tensor inversions. As the available recent intermediate-size events offshore the Iberian peninsula is limited due to the long
NASA Astrophysics Data System (ADS)
Agata, R.; Ichimura, T.; Hirahara, K.; Hori, T.; Hyodo, M.; Hori, M.
2013-12-01
Many studies have focused on geodetic inversion analysis method of coseismic slip distribution with combination of observation data of coseismic crustal deformation on the ground and simplified crustal models such like analytical solution in elastic half-space (Okada, 1985). On the other hand, displacements on the seafloor or near trench axes due to actual earthquakes has been observed by seafloor observatories (e.g. the 2011 Tohoku-oki Earthquake (Tohoku Earthquake) (Sato et. al. 2011) (Kido et. al. 2011)). Also, some studies on tsunamis due to the Tohoku Earthquake indicate that large fault slips near the trench axis may have occurred. Those facts suggest that crustal models considering complex geometry and heterogeneity of the material property near the trench axis should be used for geodetic inversion analysis. Therefore, our group has developed a mesh generation method for finite element models of the Japanese Islands of higher fidelity and a fast crustal deformation analysis method for the models. Degree-of-freedom of the models generated by this method is about 150 million. In this research, the method is extended for inversion analyses of coseismic slip distribution. Since inversion analyses need computation of hundreds of slip response functions due to a unit fault slip assigned for respective divided cells on the fault, parallel computing environment is used. Plural crustal deformation analyses are simultaneously run in a Message Passing Interface (MPI) job. In the job, dynamic load balancing is implemented so that a better parallel efficiency is obtained. Submitting the necessary number of serial job of our previous method is also possible, but the proposed method needs less computation time, places less stress on file systems, and allows simpler job management. A method for considering the fault slip right near the trench axis is also developed. As the displacement distribution of unit fault slip for computing response function, 3rd order B
Adler, C; Ahammed, Z; Allgower, C; Amonett, J; Anderson, B D; Anderson, M; Averichev, G S; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellwied, R; Berger, J; Bichsel, H; Bland, L C; Blyth, C O; Bonner, B E; Bossingham, R; Boucham, A; Brandin, A; Caines, H; Calderón De La Barca Sánchez, M; Cardenas, A; Carroll, J; Castillo, J; Castro, M; Cebra, D; Chattopadhyay, S; Chen, M L; Chen, Y; Chernenko, S P; Cherney, M; Chikanian, A; Choi, B; Christie, W; Coffin, J P; Conin, L; Cormier, T M; Cramer, J G; Crawford, H J; DeMello, M; Deng, W S; Derevschikov, A A; Didenko, L; Draper, J E; Dunin, V B; Dunlop, J C; Eckardt, V; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Fachini, P; Finch, E; Fisyak, Y; Flierl, D; Foley, K J; Fu, J; Gagunashvili, N; Gans, J; Gaudichet, L; Germain, M; Geurts, F; Ghazikhanian, V; Grabski, J; Grachov, O; Greiner, D; Grigoriev, V; Guedon, M; Gushin, E; Hallman, T J; Hardtke, D; Harris, J W; Heffner, M; Heppelmann, S; Herston, T; Hippolyte, B; Hirsch, A; Hjort, E; Hoffmann, G W; Horsley, M; Huang, H Z; Humanic, T J; Hümmler, H; Igo, G; Ishihara, A; Ivanshin, Y I; Jacobs, P; Jacobs, W W; Janik, M; Johnson, I; Jones, P G; Judd, E; Kaneta, M; Kaplan, M; Keane, D; Kisiel, A; Klay, J; Klein, S R; Klyachko, A; Konstantinov, A S; Kotchenda, L; Kovalenko, A D; Kramer, M; Kravtsov, P; Krueger, K; Kuhn, C; Kulikov, A I; Kunde, G J; Kunz, C L; Kutuev, R K; Kuznetsov, A A; Lakehal-Ayat, L; Lamas-Valverde, J; Lamont, M A; Landgraf, J M; Lange, S; Lansdell, C P; Lasiuk, B; Laue, F; Lebedev, A; LeCompte, T; Lednický, R; Leontiev, V M; Leszczynski, P; LeVine, M J; Li, Q; Li, Q; Lindenbaum, S J; Lisa, M A; Ljubicic, T; Llope, W J; LoCurto, G; Long, H; Longacre, R S; Lopez-Noriega, M; Love, W A; Lynn, D; Majka, R; Maliszewski, A; Margetis, S; Martin, L; Marx, J; Matis, H S; Matulenko, Y A; McShane, T S; Meissner, F; Melnick, Y; Meschanin, A; Messer, M; Miller, M L; Milosevich, Z; Minaev, N G; Mitchell, J; Moiseenko, V A; Moltz, D; Moore, C F; Morozov, V; de Moura, M M; Munhoz, M G; Mutchler, G S; Nelson, J M; Nevski, P; Nikitin, V A; Nogach, L V; Norman, B; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Paic, G; Pandey, S U; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Perevoztchikov, V; Peryt, W; Petrov, V A; Pinganaud, W; Platner, E; Pluta, J; Porile, N; Porter, J; Poskanzer, A M; Potrebenikova, E; Prindle, D; Pruneau, C; Radomski, S; Rai, G; Ravel, O; Ray, R L; Razin, S V; Reichhold, D; Reid, J G; Retiere, F; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevski, O V; Romero, J L; Roy, C; Russ, D; Rykov, V; Sakrejda, I; Sandweiss, J; Saulys, A C; Savin, I; Schambach, J; Scharenberg, R P; Schweda, K; Schmitz, N; Schroeder, L S; Schüttauf, A; Seger, J; Seliverstov, D; Seyboth, P; Shahaliev, E; Shestermanov, K E; Shimanskii, S S; Shvetcov, V S; Skoro, G; Smirnov, N; Snellings, R; Sowinski, J; Spinka, H M; Srivastava, B; Stephenson, E J; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Stroebele, H; Struck, C; Suaide, A A; Sugarbaker, E; Suire, C; Sumbera, M; Symons, T J; Szanto De Toledo, A; Szarwas, P; Takahashi, J; Tang, A H; Thomas, J H; Tikhomirov, V; Trainor, T A; Trentalange, S; Tokarev, M; Tonjes, M B; Trofimov, V; Tsai, O; Turner, K; Ullrich, T; Underwood, D G; Van Buren, G; VanderMolen, A M; Vanyashin, A; Vasilevski, I M; Vasiliev, A N; Vigdor, S E; Voloshin, S A; Wang, F; Ward, H; Watson, J W; Wells, R; Wenaus, T; Westfall, G D; Whitten, C; Wieman, H; Willson, R; Wissink, S W; Witt, R; Xu, N; Xu, Z; Yakutin, A E; Yamamoto, E; Yang, J; Yepes, P; Yokosawa, A; Yurevich, V I; Zanevski, Y V; Zborovský, I; Zhang, W M; Zoulkarneev, R; Zubarev, A N
2001-09-10
The minimum-bias multiplicity distribution and the transverse momentum and pseudorapidity distributions for central collisions have been measured for negative hadrons ( h(-)) in Au+Au interactions at square root of ([s(NN)]) = 130 GeV. The multiplicity density at midrapidity for the 5% most central interactions is dN(h(-))/d(eta)/(eta = 0) = 280+/-1(stat)+/-20(syst), an increase per participant of 38% relative to pp collisions at the same energy. The mean transverse momentum is 0.508+/-0.012 GeV/c and is larger than in central Pb+Pb collisions at lower energies. The scaling of the h(-) yield per participant is a strong function of p( perpendicular). The pseudorapidity distribution is almost constant within /eta/<1.
Boudjema, A.; Tremolieres, P.
1988-01-01
Fieldwork and subsurface studies (350 bore holes and more than 100 seismic profiles) show the structural evolution of the Triassic Saharian basin. This evolution is controlled by the successive motions of ancient faults of the Paleozoic basement during the different compressional and distensional tectonic phases. These movements led to some tectonic inversions. Depending on the strike of the faults, the present results correspond to normal throw or reverse throw at the level of hydrocarbon reservoirs. These tectonic phases clearly result from relative motions between African, American, and European lithospheric plates. The Triassic basin, a mobile zone between two rigid shields, constitutes a very good indication of the successive motions. The distribution and the nature of hydrocarbon fields are clearly related to the proximity of the faults, the post-tectonic erosion of a part of the source rocks, the burial and maturation of the organic matter, and the age of structural traps.
Electromagnetic Response Inversion for a 3D Distribution of Conductivity/Dielect
Newman, Gregory
2001-10-24
NLCGCS inverts electromagnetic responses for a 3D distribution of electrical conductivity and dielectric permittivity within the earth for geophysical applications using single processor computers. The software comes bundled with a graphical user interface to aid in model construction and analysis and viewing of earth images. The solution employs both dipole and finite size source configurations for harmonic oscillatory sources. A new nonlinear preconditioner is included in the solution to speed up solution convergence.
NASA Astrophysics Data System (ADS)
He, Zhenzong; Qi, Hong; Yao, Yuchen; Ruan, Liming
2014-12-01
The Ant Colony Optimization algorithm based on the probability density function (PDF-ACO) is applied to estimate the bimodal aerosol particle size distribution (PSD). The direct problem is solved by the modified Anomalous Diffraction Approximation (ADA, as an approximation for optically large and soft spheres, i.e., χ≫1 and |m-1|≪1) and the Beer-Lambert law. First, a popular bimodal aerosol PSD and three other bimodal PSDs are retrieved in the dependent model by the multi-wavelength extinction technique. All the results reveal that the PDF-ACO algorithm can be used as an effective technique to investigate the bimodal PSD. Then, the Johnson's SB (J-SB) function and the modified beta (M-β) function are employed as the general distribution function to retrieve the bimodal PSDs under the independent model. Finally, the J-SB and M-β functions are applied to recover actual measurement aerosol PSDs over Beijing and Shanghai obtained from the aerosol robotic network (AERONET). The numerical simulation and experimental results demonstrate that these two general functions, especially the J-SB function, can be used as a versatile distribution function to retrieve the bimodal aerosol PSD when no priori information about the PSD is available.
NASA Astrophysics Data System (ADS)
Long, Andrew J.; Putnam, Larry D.
2009-10-01
SummaryConvolution modeling is useful for investigating the temporal distribution of groundwater age based on environmental tracers. The framework of a quasi-transient convolution model that is applicable to two-domain flow in karst aquifers is presented. The model was designed to provide an acceptable level of statistical confidence in parameter estimates when only chlorofluorocarbon (CFC) and tritium ( 3H) data are available. We show how inverse modeling and uncertainty assessment can be used to constrain model parameterization to a level warranted by available data while allowing major aspects of the flow system to be examined. As an example, the model was applied to water from a pumped well open to the Madison aquifer in central USA with input functions of CFC-11, CFC-12, CFC-113, and 3H, and was calibrated to several samples collected during a 16-year period. A bimodal age distribution was modeled to represent quick and slow flow less than 50 years old. The effects of pumping and hydraulic head on the relative volumetric fractions of these domains were found to be influential factors for transient flow. Quick flow and slow flow were estimated to be distributed mainly within the age ranges of 0-2 and 26-41 years, respectively. The fraction of long-term flow (>50 years) was estimated but was not dateable. The different tracers had different degrees of influence on parameter estimation and uncertainty assessments, where 3H was the most critical, and CFC-113 was least influential.
Long, A.J.; Putnam, L.D.
2009-01-01
Convolution modeling is useful for investigating the temporal distribution of groundwater age based on environmental tracers. The framework of a quasi-transient convolution model that is applicable to two-domain flow in karst aquifers is presented. The model was designed to provide an acceptable level of statistical confidence in parameter estimates when only chlorofluorocarbon (CFC) and tritium (3H) data are available. We show how inverse modeling and uncertainty assessment can be used to constrain model parameterization to a level warranted by available data while allowing major aspects of the flow system to be examined. As an example, the model was applied to water from a pumped well open to the Madison aquifer in central USA with input functions of CFC-11, CFC-12, CFC-113, and 3H, and was calibrated to several samples collected during a 16-year period. A bimodal age distribution was modeled to represent quick and slow flow less than 50 years old. The effects of pumping and hydraulic head on the relative volumetric fractions of these domains were found to be influential factors for transient flow. Quick flow and slow flow were estimated to be distributed mainly within the age ranges of 0-2 and 26-41 years, respectively. The fraction of long-term flow (>50 years) was estimated but was not dateable. The different tracers had different degrees of influence on parameter estimation and uncertainty assessments, where 3H was the most critical, and CFC-113 was least influential.
Anisotropic electron-distribution function in inverse-bremsstrahlung-heated plasmas.
Bendib, A; Bendib-Kalache, K; Cros, B; Maynard, G
2016-04-01
The electron-distribution function in homogeneous plasmas heated by a high-frequency laser field is calculated in velocity space from the Vlasov-Landau equation. The kinetic model is valid for moderate laser intensity defined by the relevant parameter α=v_{0}^{2}/v_{t}^{2}<0.5 where v_{0} and v_{t} are the peak velocity of oscillation in the high-frequency electric field and the thermal velocity, respectively. The results obtained constitute an improvement of the results reported in the literature devoted to weak electric field intensities. The electron-distribution function is calculated solving the kinetic equation with the use of the Legendre polynomial expansion within the laser field dipole approximation. It results in an infinite set of equations for the isotropic component f_{0}(v) and the anisotropic components f_{n≥1}(v) that we have solved numerically with appropriate truncation. For the second anisotropy f_{2}(v), we found that its maximum increases from the weak electric field intensity (α<0.01) to a moderate one (α=0.5) by a factor f_{2max}(α=0.5)/f_{2max}(α=0.01)≈48. Applications to the radiation pressure, electromagnetic instabilities, and photoabsorption are also considered.
NASA Technical Reports Server (NTRS)
Fymat, A. L.
1978-01-01
Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968).
Abazov, V M; Abbott, B; Abolins, M; Acharya, B S; Adams, M; Adams, T; Aguilo, E; Ahsan, M; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Ancu, L S; Andeen, T; Anzelc, M S; Aoki, M; Arnoud, Y; Arov, M; Arthaud, M; Askew, A; Asman, B; Atramentov, O; Avila, C; BackusMayes, J; Badaud, F; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, S; Barberis, E; Barfuss, A-F; Bargassa, P; Baringer, P; Barreto, J; Bartlett, J F; Bassler, U; Bauer, D; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Bellavance, A; Benitez, J A; Beri, S B; Bernardi, G; Bernhard, R; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Blazey, G; Blessing, S; Bloom, K; Boehnlein, A; Boline, D; Bolton, T A; Boos, E E; Borissov, G; Bose, T; Brandt, A; Brock, R; Brooijmans, G; Bross, A; Brown, D; Bu, X B; Buchholz, D; Buehler, M; Buescher, V; Bunichev, V; Burdin, S; Burnett, T H; Buszello, C P; Calfayan, P; Calpas, B; Calvet, S; Cammin, J; Carrasco-Lizarraga, M A; Carrera, E; Carvalho, W; Casey, B C K; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chandra, A; Cheu, E; Cho, D K; Choi, S; Choudhary, B; Christoudias, T; Cihangir, S; Claes, D; Clutter, J; Cooke, M; Cooper, W E; Corcoran, M; Couderc, F; Cousinou, M-C; Crépé-Renaudin, S; Cutts, D; Cwiok, M; Das, A; Davies, G; De, K; de Jong, S J; De la Cruz-Burelo, E; DeVaughan, K; Déliot, F; Demarteau, M; Demina, R; Denisov, D; Denisov, S P; Desai, S; Diehl, H T; Diesburg, M; Dominguez, A; Dorland, T; Dubey, A; Dudko, L V; Duflot, L; Duggan, D; Duperrin, A; Dutt, S; Dyshkant, A; Eads, M; Edmunds, D; Ellison, J; Elvira, V D; Enari, Y; Eno, S; Escalier, M; Evans, H; Evdokimov, A; Evdokimov, V N; Facini, G; Ferapontov, A V; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Fortner, M; Fox, H; Fu, S; Fuess, S; Gadfort, T; Galea, C F; Garcia-Bellido, A; Gavrilov, V; Gay, P; Geist, W; Geng, W; Gerber, C E; Gershtein, Y; Gillberg, D; Ginther, G; Gómez, B; Goussiou, A; Grannis, P D; Greder, S; Greenlee, H; Greenwood, Z D; Gregores, E M; Grenier, G; Gris, Ph; Grivaz, J-F; Grohsjean, A; Grünendahl, S; Grünewald, M W; Guo, F; Guo, J; Gutierrez, G; Gutierrez, P; Haas, A; Haefner, P; Hagopian, S; Haley, J; Hall, I; Hall, R E; Han, L; Harder, K; Harel, A; Hauptman, J M; Hays, J; Hebbeker, T; Hedin, D; Hegeman, J G; Heinson, A P; Heintz, U; Hensel, C; Heredia-De la Cruz, I; Herner, K; Hesketh, G; Hildreth, M D; Hirosky, R; Hoang, T; Hobbs, J D; Hoeneisen, B; Hohlfeld, M; Hossain, S; Houben, P; Hu, Y; Hubacek, Z; Huske, N; Hynek, V; Iashvili, I; Illingworth, R; Ito, A S; Jabeen, S; Jaffré, M; Jain, S; Jakobs, K; Jamin, D; Jesik, R; Johns, K; Johnson, C; Johnson, M; Johnston, D; Jonckheere, A; Jonsson, P; Juste, A; Kajfasz, E; Karmanov, D; Kasper, P A; Katsanos, I; Kaushik, V; Kehoe, R; Kermiche, S; Khalatyan, N; Khanov, A; Kharchilava, A; Kharzheev, Y N; Khatidze, D; Kim, T J; Kirby, M H; Kirsch, M; Klima, B; Kohli, J M; Konrath, J-P; Kozelov, A V; Kraus, J; Kuhl, T; Kumar, A; Kupco, A; Kurca, T; Kuzmin, V A; Kvita, J; Lacroix, F; Lam, D; Lammers, S; Landsberg, G; Lebrun, P; Lee, W M; Leflat, A; Lellouch, J; Li, J; Li, L; Li, Q Z; Lietti, S M; Lim, J K; Lincoln, D; Linnemann, J; Lipaev, V V; Lipton, R; Liu, Y; Liu, Z; Lobodenko, A; Lokajicek, M; Love, P; Lubatti, H J; Luna-Garcia, R; Lyon, A L; Maciel, A K A; Mackin, D; Mättig, P; Magaña-Villalba, R; Magerkurth, A; Mal, P K; Malbouisson, H B; Malik, S; Malyshev, V L; Maravin, Y; Martin, B; McCarthy, R; McGivern, C L; Meijer, M M; Melnitchouk, A; Mendoza, L; Menezes, D; Mercadante, P G; Merkin, M; Merritt, K W; Meyer, A; Meyer, J; Mitrevski, J; Mondal, N K; Moore, R W; Moulik, T; Muanza, G S; Mulhearn, M; Mundal, O; Mundim, L; Nagy, E; Naimuddin, M; Narain, M; Neal, H A; Negret, J P; Neustroev, P; Nilsen, H; Nogima, H; Novaes, S F; Nunnemann, T; Obrant, G; Ochando, C; Onoprienko, D; Orduna, J; Oshima, N; Osman, N; Osta, J; Otec, R; Otero y Garzón, G J; Owen, M; Padilla, M; Padley, P; Pangilinan, M; Parashar, N; 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Spurlock, B; Stark, J; Stolin, V; Stoyanova, D A; Strandberg, J; Strang, M A; Strauss, E; Strauss, M; Ströhmer, R; Strom, D; Stutte, L; Sumowidagdo, S; Svoisky, P; Takahashi, M; Tanasijczuk, A; Taylor, W; Tiller, B; Titov, M; Tokmenin, V V; Torchiani, I; Tsybychev, D; Tuchming, B; Tully, C; Tuts, P M; Unalan, R; Uvarov, L; Uvarov, S; Uzunyan, S; van den Berg, P J; Van Kooten, R; van Leeuwen, W M; Varelas, N; Varnes, E W; Vasilyev, I A; Verdier, P; Vertogradov, L S; Verzocchi, M; Vilanova, D; Vint, P; Vokac, P; Voutilainen, M; Wagner, R; Wahl, H D; Wang, M H L S; Warchol, J; Watts, G; Wayne, M; Weber, G; Weber, M; Welty-Rieger, L; Wenger, A; Wetstein, M; White, A; Wicke, D; Williams, M R J; Wilson, G W; Wimpenny, S J; Wobisch, M; Wood, D R; Wyatt, T R; Xie, Y; Xu, C; Yacoob, S; Yamada, R; Yang, W-C; Yasuda, T; Yatsunenko, Y A; Ye, Z; Yin, H; Yip, K; Yoo, H D; Youn, S W; Yu, J; Zeitnitz, C; Zelitch, S; Zhao, T; Zhou, B; Zhu, J; Zielinski, M; Zieminska, D; Zivkovic, L; Zutshi, V; Zverev, E G
2009-11-06
We present the first measurement of dijet angular distributions in pp collisions at square root(s) = 1.96 TeV at the Fermilab Tevatron Collider. The measurement is based on a dataset corresponding to an integrated luminosity of 0.7 fb(-1) collected with the D0 detector. Dijet angular distributions have been measured over a range of dijet masses, from 0.25 TeV to above 1.1 TeV. The data are in good agreement with the predictions of perturbative QCD and are used to constrain new physics models including quark compositeness, large extra dimensions, and TeV(-1) scale extra dimensions. For all models considered, we set the most stringent direct limits to date.
NASA Astrophysics Data System (ADS)
Ruden, E. L.; Amdahl, D. J.; Cooksey, R. H.; Robinson, P. R.; Analla, F. T.; Brown, D. J.; Kostora, M. R.; Camacho, J. F.
2014-10-01
Measurements are presented of the current per unit length as a function of the transverse distance from the center of a water-tamped 80 μm Al foil that narrows to a central width of 15.2 cm as it explodes into warm dense matter by Ohmic heating. Current is delivered by the discharge of a 36 μF capacitor bank charged to 30 kV and discharged to a peak current of 342 kA in 2.0 μs. The distribution is calculated by the linear regularized inversion of signals from an array of B-dot probes distributed along the foil's central half-width. The probes are far enough away from the foil (1 cm) be noninvasive and mechanically undisturbed during the time of interest. These results are compared to 3-D MHD ALEGRA simulations of the geometry driven by an external coupled two-loop lumped circuit model which accurately represents the driver. The goal of the effort is to test, in conjunction with other diagnostics, ab initio models of the equation of state and electrical conductivity of matter under conditions encountered in single-shot pulsed power devices (1 - 10 eV and 0.1 - 1 × solid density). This work was supported by AFOSR LRIR 11RD02COR.
Illuminati, S; Annibaldi, A; Truzzi, C; Scarponi, G
2016-10-15
May sponge spicules represent a "tank" to accumulate heavy metals? In this study we test this hypothesis determining the distribution of Cd, Pb and Cu concentrations between organic and siliceous tissues in Antarctic Demospongia (Sphaerotylus antarcticus, Kirkpatrikia coulmani and Haliclona sp.) and in the Mediterranean species Petrosia ficiformis. Results show that although, in these sponges, spicules represent about 80% of the mass content, the accumulation of pollutant is lower in the spicules than in the corresponding organic fraction. The contribution of tissues to the total sponge content of Cd, Pb and Cu is respectively 99%, 82% and 97% for Antarctic sponges and 96%, 95% and 96% for P. ficiformis, similar in polar and temperate organisms. These results pave the way to a better understanding of the role of marine sponges in uptaking heavy metals and to their possible use as monitor of marine ecosystems, recommend by the Water Framework Directive.
NASA Astrophysics Data System (ADS)
Nishida, Kazuhiro; Namita, Takeshi; Kato, Yuji; Shimizu, Koichi
2015-03-01
We have proposed a new nonlinear inversion technique to estimate the spatial distribution of the absorption coefficient (μa) in the depth direction of a turbid medium by spatially resolved backscattering measurement. With this technique, we can obtain cross-sectional image of μa as deep as the backscattered light traveled even when the transmitted light through the medium cannot be detected. In this technique, the depth distribution of absorption coefficient is determined by iterative calculation using the spatial path-length distribution (SPD) of traveled photons as a function of source-detector distance. In this calculation, the variance of path-length of many photons in each layer is also required. The SPD and the variance of path-length are obtained by Monte Carlo simulation using a known reduced scattering coefficient (μs'). Therefore, we need to know the μs' of the turbid medium beforehand. We have shown in computer simulation that this technique works well when the μs' is the typical values of mammalian body tissue, or 1.0 /mm. In this study, the accuracy of the μa estimation was analyzed and its dependence on the μs' was clarified quantitatively in various situations expected in practice. 10% deviations in μs' resulted in about 30% error in μa estimation, in average. This suggested that the measurement or the appropriate estimation of μs' is required to utilize the proposed technique effectively. Through this analysis, the effectiveness and the limitation of the newly proposed technique were clarified, and the problems to be solved were identified.
NASA Astrophysics Data System (ADS)
Pagnoni, G.; Tinti, S.; Armigliato, A.; Tonini, R.; Gallazzi, S.; Manucci, A.; Zaniboni, F.
2006-12-01
study the run-up heights. In both cases, we divide the earthquake fault in a given number of sub-faults, and then compute the tsunami generated by each sub-fault by means of two different codes: a finite-difference code implementing the linear shallow-water equations for the ocean-wide domain, and a finite-element code solving the non-linear version of the same equations in the local domain. In the case of the altimeter data, the adopted inversion technique is an implementation of the classical generalized linear least-squares theory. A more sophisticated technique, allowing one to determine also different amplification factors along different coastal segments, is employed to invert run-up data. We discuss the slip distributions obtained separately in the two approaches, and compare the results with those retrieved by modeling seismic and geodetic data.
Wave-equation dispersion inversion
NASA Astrophysics Data System (ADS)
Li, Jing; Feng, Zongcai; Schuster, Gerard
2017-03-01
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
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Smoron, A; Strom, D; Varelas, N; Akgun, U; Albayrak, E A; Bilki, B; Cankocak, K; Clarida, W; Duru, F; Lae, C K; McCliment, E; Merlo, J-P; Mestvirishvili, A; Moeller, A; Nachtman, J; Newsom, C R; Norbeck, E; Olson, J; Onel, Y; Ozok, F; Sen, S; Wetzel, J; Yetkin, T; Yi, K; Barnett, B A; Blumenfeld, B; Bonato, A; Eskew, C; Fehling, D; Giurgiu, G; Gritsan, A V; Guo, Z J; Hu, G; Maksimovic, P; Rappoccio, S; Swartz, M; Tran, N V; Whitbeck, A; Baringer, P; Bean, A; Benelli, G; Grachov, O; Murray, M; Radicci, V; Sanders, S; Wood, J S; Zhukova, V; Bandurin, D; Bolton, T; Chakaberia, I; Ivanov, A; Kaadze, K; Maravin, Y; Shrestha, S; Svintradze, I; Wan, Z; Gronberg, J; Lange, D; Wright, D; Baden, D; Boutemeur, M; Eno, S C; Ferencek, D; Hadley, N J; Kellogg, R G; Kirn, M; Mignerey, A; Rossato, K; Rumerio, P; Santanastasio, F; Skuja, A; Temple, J; Tonjes, M B; Tonwar, S C; Twedt, E; Alver, B; Bauer, G; Bendavid, J; Busza, W; Butz, E; Cali, I A; Chan, M; D'Enterria, D; Everaerts, P; Gomez Ceballos, G; Goncharov, M; Hahn, K A; Harris, P; Kim, Y; Klute, M; Lee, Y-J; Li, W; Loizides, C; Luckey, P D; Ma, T; Nahn, S; Paus, C; Roland, C; Roland, G; Rudolph, M; Stephans, G S F; Sumorok, K; Sung, K; Wenger, E A; Wyslouch, B; Xie, S; Yilmaz, Y; Yoon, A S; Zanetti, M; Cole, P; Cooper, S I; Cushman, P; Dahmes, B; De Benedetti, A; Dudero, P R; Franzoni, G; Haupt, J; Klapoetke, K; Kubota, Y; Mans, J; Petyt, D; Rekovic, V; Rusack, R; Sasseville, M; Singovsky, A; Cremaldi, L M; Godang, R; Kroeger, R; Perera, L; Rahmat, R; Sanders, D A; Sonnek, P; Summers, D; Bloom, K; Bose, S; Butt, J; Claes, D R; Dominguez, A; Eads, M; Keller, J; Kelly, T; Kravchenko, I; Lazo-Flores, J; Lundstedt, C; Malbouisson, H; Malik, S; Snow, G R; Baur, U; Iashvili, I; Kharchilava, A; Kumar, A; Smith, K; Strang, M; Zennamo, J; Alverson, G; Barberis, E; Baumgartel, D; Boeriu, O; Reucroft, S; Swain, J; Wood, D; Zhang, J; Anastassov, A; Kubik, A; Ofierzynski, R A; Pozdnyakov, A; Schmitt, M; Stoynev, S; Velasco, M; Won, S; Antonelli, L; Berry, D; Hildreth, M; Jessop, C; Karmgard, D J; Kolb, J; Kolberg, T; Lannon, K; Lynch, S; Marinelli, N; Morse, D M; Ruchti, R; Slaunwhite, J; Valls, N; Warchol, J; Wayne, M; Ziegler, J; Bylsma, B; Durkin, L S; Gu, J; Killewald, P; Ling, T Y; Williams, G; Adam, N; Berry, E; Elmer, P; Gerbaudo, D; Halyo, V; Hunt, A; Jones, J; Laird, E; Lopes Pegna, D; Marlow, D; Medvedeva, T; Mooney, M; Olsen, J; Piroué, P; Stickland, D; Tully, C; Werner, J S; Zuranski, A; Acosta, J G; Huang, X T; Lopez, A; Mendez, H; Oliveros, S; Ramirez Vargas, J E; Zatzerklyaniy, A; Alagoz, E; Barnes, V E; Bolla, G; Borrello, L; Bortoletto, D; Everett, A; Garfinkel, A F; Gecse, Z; Gutay, L; Jones, M; Koybasi, O; Laasanen, A T; Leonardo, N; Liu, C; Maroussov, V; Merkel, P; Miller, D H; Neumeister, N; Potamianos, K; Shipsey, I; Silvers, D; Yoo, H D; Zablocki, J; Zheng, Y; Jindal, P; Parashar, N; Cuplov, V; Ecklund, K M; Geurts, F J M; Liu, J H; Morales, J; Padley, B P; Redjimi, R; Roberts, J; Betchart, B; Bodek, A; Chung, Y S; de Barbaro, P; Demina, R; Flacher, H; Garcia-Bellido, A; Gotra, Y; Han, J; Harel, A; Miner, D C; Orbaker, D; Petrillo, G; Vishnevskiy, D; Zielinski, M; Bhatti, A; Demortier, L; Goulianos, K; Hatakeyama, K; Lungu, G; Mesropian, C; Yan, M; Atramentov, O; Gershtein, Y; Gray, R; Halkiadakis, E; Hidas, D; Hits, D; Lath, A; Rose, K; Schnetzer, S; Somalwar, S; Stone, R; Thomas, S; Cerizza, G; Hollingsworth, M; Spanier, S; Yang, Z C; York, A; Asaadi, J; Eusebi, R; Gilmore, J; Gurrola, A; Kamon, T; Khotilovich, V; Montalvo, R; Nguyen, C N; Pivarski, J; Safonov, A; Sengupta, S; Toback, D; Weinberger, M; Akchurin, N; Bardak, C; Damgov, J; Jeong, C; Kovitanggoon, K; Lee, S W; Mane, P; Roh, Y; Sill, A; Volobouev, I; Wigmans, R; Yazgan, E; Appelt, E; Brownson, E; Engh, D; Florez, C; Gabella, W; Johns, W; Kurt, P; Maguire, C; Melo, A; Sheldon, P; Velkovska, J; Arenton, M W; Balazs, M; Buehler, M; Conetti, S; Cox, B; Hirosky, R; Ledovskoy, A; Neu, C; Yohay, R; Gollapinni, S; Gunthoti, K; Harr, R; Karchin, P E; Mattson, M; Milstène, C; Sakharov, A; Anderson, M; Bachtis, M; Bellinger, J N; Carlsmith, D; Dasu, S; Dutta, S; Efron, J; Gray, L; Grogg, K S; Grothe, M; Hall-Wilton, R; Herndon, M; Klabbers, P; Klukas, J; Lanaro, A; Lazaridis, C; Leonard, J; Lomidze, D; Loveless, R; Mohapatra, A; Polese, G; Reeder, D; Savin, A; Smith, W H; Swanson, J; Weinberg, M
2010-07-09
Charged-hadron transverse-momentum and pseudorapidity distributions in proton-proton collisions at square root of s = 7 TeV are measured with the inner tracking system of the CMS detector at the LHC. The charged-hadron yield is obtained by counting the number of reconstructed hits, hit pairs, and fully reconstructed charged-particle tracks. The combination of the three methods gives a charged-particle multiplicity per unit of pseudorapidity dN(ch)/dη|(|η|<0.5) = 5.78 ± 0.01(stat) ± 0.23(syst) for non-single-diffractive events, higher than predicted by commonly used models. The relative increase in charged-particle multiplicity from square root of s = 0.9 to 7 TeV is [66.1 ± 1.0(stat) ± 4.2(syst)]%. The mean transverse momentum is measured to be 0.545 ± 0.005(stat) ± 0.015(syst) GeV/c. The results are compared with similar measurements at lower energies.
NASA Technical Reports Server (NTRS)
Lemen, J. R.; Mewe, R.; Schrijver, C. J.; Fludra, A.
1989-01-01
EXOSAT soft X-ray spectra of three binary systems of cool stars are analyzed: Capella (G6 III + F9 III), Sigma-squared CrB (F8 V + G1 V), and Procyon (F5 IV-V + DF). The EXOSAT transmission grating spectrometer permits the study of individual spectral lines and line complexes between 10 and 200 A with approximately 3 A resolution. First it is demonstrated that the spectra can be described reasonably well by a two-temperature model corona. Then the assumption that only two temperatures exist in the stellar coronas is relaxed and differential emission measure distributions are derived from the three spectra. The results from the multithermal modeling are consistent with those of the two-temperature models: emission from the coronas of each of the three stars is dominated by plasma in two relative narrow temperature intervals. These intervals are centered on 5 MK and 25 MK in the cases of Capella and Sigma-squared CrB, and 0.6 MK and 3 MK in the case of Procyon. The implications of the results for the structure of stellar coronas are briefly discussed.
A Simple Parameterization of 3 x 3 Magic Squares
ERIC Educational Resources Information Center
Trenkler, Gotz; Schmidt, Karsten; Trenkler, Dietrich
2012-01-01
In this article a new parameterization of magic squares of order three is presented. This parameterization permits an easy computation of their inverses, eigenvalues, eigenvectors and adjoints. Some attention is paid to the Luoshu, one of the oldest magic squares.
NASA Astrophysics Data System (ADS)
Fung, Jonathan Winston
Carbon dioxide is taken up by crops during production and released back to the atmosphere at different geographical locations through respiration of consumed crop commodities. In this study, spatially distributed county-level US cropland net primary productivity, harvested biomass, changes in soil carbon, and human and livestock consumption data were integrated into the prior terrestrial biosphere flux generated by the Boreal Ecosystem Productivity Simulator (BEPS). A global time-dependent Bayesian synthesis inversion with a nested focus on North America was carried out based on CO2 observations at 210 stations. Overall, the inverted annual North American CO2 sink weakened by 6.5% over the period from 2002 to 2007 compared to simulations disregarding US crop statistical data. The US Midwest is found to be the major sink of 0.36±0.13 PgC yr-1 whereas the large sink in the US Southeast forests weakened to 0.16±0.12 PgC yr-1 partly due to local CO2 sources from crop consumption.
Joint inversion for mapping subsurface hydrologicalparameters
Tseng, Hung-Wen; Lee, Ki Ha
2001-03-07
Using electromagnetic (EM) and seismic travel time data and a least-square criteria, a two-dimensional joint inversion algorithm is under development to assess the feasibility of directly mapping subsurface hydrological properties in a crosswell setup. A simplified Archie's law combined with the time average equation relates the magnetic fields and seismic travel time to two hydrological parameters; rock porosity and pore fluid electrical conductivity. For simplicity, the hydrological parameter distributions are assumed to be two-dimensional. Preliminary results show that joint inversion does have better resolving power for the interpretation than using the EM method alone. Various inversion scenarios have been tested, and it has been found that alternately perturbing just one of the two parameters at each iteration gives the best data fit.
NASA Astrophysics Data System (ADS)
Schutz, A.; Vannier, M.; Mary, D.; Ferrari, A.; Millour, F.; Petrov, R.
2014-05-01
Context. In optical interferometry, the visibility squared moduli are generally assumed to follow a Gaussian distribution and to be independent of each other. A quantitative analysis of the relevance of such assumptions is important to help improving the exploitation of existing and upcoming multi-wavelength interferometric instruments. Aims: The aims of this study are to analyse the statistical behaviour of both the absolute and the colour-differential squared visibilities: distribution laws, correlations and cross-correlations between different baselines. Methods: We use observations of stellar calibrators obtained with the AMBER instrument on the Very Large Telescope Interferometer (VLTI) in different instrumental and observing configurations, from which we extract the frame-by-frame transfer function. Statistical hypotheses tests and diagnostics are then systematically applied. We also compute the same analysis after correcting the instantaneous squared visibilities from the piston and jitter chromatic effects, using a low-order fit subtraction. Results: For both absolute and differential squared visibilities and under all instrumental and observing conditions, we find a better fit for the Student distribution than for the Gaussian, log-normal, and Cauchy distributions. We find and analyse clear correlation effects caused by atmospheric perturbations. The differential squared visibilities allow us to keep a larger fraction of data with respect to selected absolute squared visibilities and thus benefit from reduced temporal dispersion, while their distribution is more clearly characterised. Conclusions: The frame selection based on the criterion of a fixed signal-to-noise value might result in either a biased sample of frames or one with severe selection. Instead, we suggest an adaptive frame selection procedure based on the stability of the modes of the observed squared visibility distributions. In addition, taking into account the correlations effects between
NASA Astrophysics Data System (ADS)
Swanson, Charles; Jandovitz, Peter; Bosh, Alexandra; Cohen, Samuel
2016-10-01
The PFRC is an odd-parity Rotating Magnetic Field (RMF) driven Field-Reversed Configuration plasma confinement experiment equipped with Si-PIN and SDD x-ray detectors. It is predicted that the electron energy distribution is non-thermal when the RMF is active. Using a novel inversion technique, we present full electron distribution functions as reconstructed (``spectrally inverted'') from the x-ray Bremsstrahlung emissions. This method regularizes the inverse treating the measurement as a Poisson random variable, as opposed to state-of-the-art methods which assume a Normal random variable. The method maximizes the log-likelihood of the solution, determined from Bayes' Theorem. This work was supported, in part, by DOE Contract Number DE-AC02-09CH11466.
Conover, W.J.; Cox, D.D.; Martz, H.F.
1997-12-01
When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poisson exposure times vary. Nine examples illustrate the application of the methods, using real data from such diverse applications as the loss of feedwater flow rates in nuclear power plants, the probability of failure to run on demand and the failure rates of the high pressure coolant injection systems at US commercial boiling water reactors, the probability of failure to run on demand of emergency diesel generators in US commercial nuclear power plants, the rate of failure of aircraft air conditioners, baseball batting averages, the probability of testing positive for toxoplasmosis, and the probability of tumors in rats. The tests are easily applied in practice by means of corresponding Mathematica{reg_sign} computer programs which are provided.
2010-04-27
Laboratory 2. Seminars of the Department of Mathematics of the University of North Carolina at Charlotte 3. SPIE meeting in San Francisco 4. Henry ... Poincare Institute, Paris, France 5. Workshop on Inverse Problems at Chinese University of Hong Kong (plenary speaker) 6. International Conference on
All Square Chiliagonal Numbers
ERIC Educational Resources Information Center
A?iru, Muniru A.
2016-01-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…
A Bibliometric Distribution Which Really Works.
ERIC Educational Resources Information Center
Sichel, H. S.
1985-01-01
The Generalized Inverse Gaussian-Poisson Distribution is suggested as an all-embracing mathematical model for bibliometric frequency distributions. Twelve examples are given which show that the new model cannot be rejected by virtue of an objective chi-squared test. A mathematical appendix and 20 references are included. (Author/EJS)
Costa, Éderson D'M; Lemes, Nelson H T; O Alves, Márcio; Braga, João P
2014-08-01
In this study it is reported the retrieval of the phonon density of states for solid aluminium from the temperature dependent heat capacity, the inverse heat capacity problem. The singularity in this ill posed problem was removed by the Tikhonov approach with the regularization parameter calculated as the L curve maximum curvature. A sensitivity analysis was also coupled to the numerical inversion. For temperatures ranging from 15 K to 300 K the heat capacity results, calculated from the inverted phonon density of states, yields an average error of about 0.3%, within the experimental errors that ranged from 2% to 3%. The predicted entropy, enthalpy and Gibbs free energy are also within experimental errors.
Weighted conditional least-squares estimation
Booth, J.G.
1987-01-01
A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered.
NASA Technical Reports Server (NTRS)
Fymat, A. L.; Smith, C. B.
1979-01-01
It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.
NASA Astrophysics Data System (ADS)
Chen, Youlin; Niu, Fenglin
2016-02-01
We present shear wave velocity structure beneath China by joint modeling of teleseismic receiver function and Rayleigh wave group velocity dispersion data observed at +1000 permanent broadband seismic stations in the Chinese National Digital Seismic Network (CNDSN). A ray-parameter-based stacking method is employed to minimize artifacts in stacking receiver functions from different sources. The Rayleigh wave dispersion curve is extracted from group velocity tomographic models at all applicable periods. Enhanced preconditions are applied on the linearized iterative inversion to regularize and balance multiple types of data. The velocity profile inversion at each station starts from an initial model derived from sediments, crustal thickness, Vp/Vs ratio and Pn/Sn models. This multistep approach not only reduces uncertainty and nonuniqueness of the velocity inversion but also efficiently fills information gap in each data set. We then generate a 3-D S velocity model by combining and smoothing all the 1-D models. The obtained 3-D model reveals crustal and upper mantle velocity structures that are well correlated with tectonic features of China, for example, our model shows a clear east-west bimodal distribution at 35 km deep, low velocity in the crust beneath central and eastern Tibetan plateau, and sedimentary structure in major cratons and basins. Our model is consistent with existing tomographic models in large scale but provides more structural details in regional and local scales.
Improved regularized solution of the inverse problem in turbidimetric measurements.
Mroczka, Janusz; Szczuczyński, Damian
2010-08-20
We present results of simulation research on the constrained regularized least-squares (RLS) solution of the ill-conditioned inverse problem in turbidimetric measurements. The problem is formulated in terms of the discretized Fredholm integral equation of the first kind. The inverse problem in turbidimetric measurements consists in determining particle size distribution (PSD) function of particulate system on the basis of turbidimetric measurements. The desired PSD should satisfy two constraints: nonnegativity of PSD values and normalization of PSD to unity when integrated over the whole range of particle size. Incorporating the constraints into the RLS method leads to the constrained regularized least-squares (CRLS) method, which is realized by means of an active set algorithm of quadratic programming. Results of simulation research prove that the CRLS method performs considerably better with reconstruction of PSD than the RLS method in terms of better fidelity and smaller uncertainty.
Dirken, J J; Vlaanderen, W
1994-01-01
Inversion of the uterus is a rare complication of childbirth. A primigravida aged 21 and a multigravida aged 32, hospitalized as emergency cases because of inversion of the uterus with major blood loss, were treated with infusion of liquids (to combat shock), repositioning of the uterus under anaesthesia and prevention of reinversion by uterine tonics. Inversion of the uterus should be part of the differential diagnosis in every case of fluxus post partum.
Reynolds, D R; Chapman, J W; Edwards, A S; Smith, A D; Wood, C R; Barlow, J F; Woiwod, I P
2005-06-01
Insects migrating over two sites in southern UK (Malvern in Worcestershire, and Harpenden in Hertfordshire) have been monitored continuously with nutating vertical-looking radars (VLRs) equipped with powerful control and analysis software. These observations make possible, for the first time, a systematic investigation of the vertical distribution of insect aerial density in the atmosphere, over temporal scales ranging from the short (instantaneous vertical profiles updated every 15 min) to the very long (profiles aggregated over whole seasons or even years). In the present paper, an outline is given of some general features of insect stratification as revealed by the radars, followed by a description of occasions during warm nights in the summer months when intense insect layers developed. Some of these nocturnal layers were due to the insects flying preferentially at the top of strong surface temperature inversions, and in other cases, layering was associated with higher-altitude temperature maxima, such as those due to subsidence inversions. The layers were formed from insects of a great variety of sizes, but peaks in the mass distributions pointed to a preponderance of medium-sized noctuid moths on certain occasions.
NASA Astrophysics Data System (ADS)
Huang, Mong-Han; Fielding, Eric J.; Dickinson, Haylee; Sun, Jianbao; Gonzalez-Ortega, J. Alejandro; Freed, Andrew M.; Bürgmann, Roland
2017-01-01
The 4 April 2010 Mw 7.2 El Mayor-Cucapah (EMC) earthquake in Baja, California, and Sonora, Mexico, had primarily right-lateral strike-slip motion and a minor normal-slip component. The surface rupture extended about 120 km in a NW-SE direction, west of the Cerro Prieto fault. Here we use geodetic measurements including near- to far-field GPS, interferometric synthetic aperture radar (InSAR), and subpixel offset measurements of radar and optical images to characterize the fault slip during the EMC event. We use dislocation inversion methods and determine an optimal nine-segment fault geometry, as well as a subfault slip distribution from the geodetic measurements. With systematic perturbation of the fault dip angles, randomly removing one geodetic data constraint, or different data combinations, we are able to explore the robustness of the inferred slip distribution along fault strike and depth. The model fitting residuals imply contributions of early postseismic deformation to the InSAR measurements as well as lateral heterogeneity in the crustal elastic structure between the Peninsular Ranges and the Salton Trough. We also find that with incorporation of near-field geodetic data and finer fault patch size, the shallow slip deficit is reduced in the EMC event by reductions in the level of smoothing. These results show that the outcomes of coseismic inversions can vary greatly depending on model parameterization and methodology.
Constructing inverse probability weights for continuous exposures: a comparison of methods.
Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S
2014-03-01
Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.
NASA Astrophysics Data System (ADS)
Wood, W.; Knapp, C. C.; Knapp, J. H.
2010-12-01
The seafloor mound at the Gulf of Mexico lease block MC (Mississippi Canyon) 118 is a known active seep lying directly above a salt dome. The site lies at 850-900 m water depth - within the methane hydrate stability zone, but there is no obvious BSR or other indicator of large quantities of gas or gas hydrate. Air-gun seismic data acquired with a 4180 cu in source and 7200 m, 288-channel hydrophone array, exhibit several bright, but laterally-limited reflections in the ~500 m sediment column above the salt. The bright spots are largely conformable with the strata, and there is no apparent pull-up or push-down associated with the bright spots, suggesting they are thin. There are also no significant frequency changes below the bright spots. We interpret the bright spots to be caused by gas, gas hydrate, or carbonate, or combinations of the three. The long offsets used to acquire these data allow for the analysis of refracted arrivals that not only provide accurate P-wave velocities, but also provide a background velocity profile for full waveform inversion. Preliminary results from the waveform inversion confirm at least some of the bright spots are free gas, constraining the position of the gas hydrate stability zone, but very thin (sub-wavelength) layers of carbonate and hydrate may also be present. Knowing the exact composition of the material responsible for the bright spots will better constrain the linkage between the salt tectonics (with implied fault activity) and seep activity, as well as the longevity of the hydrate system at MC 118.
NASA Technical Reports Server (NTRS)
Gross, Bernard
1996-01-01
Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.
ERIC Educational Resources Information Center
Watson, Gale A.
2003-01-01
Demonstrates the transformations that are possible to construct a variety of magic squares, including modifications to challenge students from elementary grades through algebra. Presents an example of using magic squares with students who have special needs. (YDS)
Joint inversion of fundamental and higher mode Rayleigh waves
Luo, Y.-H.; Xia, J.-H.; Liu, J.-P.; Liu, Q.-S.
2008-01-01
In this paper, we analyze the characteristics of the phase velocity of fundamental and higher mode Rayleigh waves in a six-layer earth model. The results show that fundamental mode is more sensitive to the shear velocities of shallow layers (< 7 m) and concentrated in a very narrow band (around 18 Hz) while higher modes are more sensitive to the parameters of relatively deeper layers and distributed over a wider frequency band. These properties provide a foundation of using a multi-mode joint inversion to define S-wave velocity. Inversion results of both synthetic data and a real-world example demonstrate that joint inversion with the damped least squares method and the SVD (Singular Value Decomposition) technique to invert Rayleigh waves of fundamental and higher modes can effectively reduce the ambiguity and improve the accuracy of inverted S-wave velocities.
ERIC Educational Resources Information Center
Emanouilidis, Emanuel
2005-01-01
Latin squares have existed for hundreds of years but it wasn't until rather recently that Latin squares were used in other areas such as statistics, graph theory, coding theory and the generation of random numbers as well as in the design and analysis of experiments. This note describes Latin and diagonal Latin squares, a method of constructing…
Das, Shyamal C; Zhou, Qi; Morton, David A V; Larson, Ian; Stewart, Peter J
2011-07-17
The purpose was to employ a new finite dilution approach to determine total surface energy distributions of mechanofused powders by inverse gas chromatography (IGC) to contribute to the understanding of their improved flow properties and to help optimise the magnesium stearate (MgSt) coating. Pharmatose 450M was mechanofused with between 0.1 and 8% (w/w) of MgSt. The non-polar, polar and total surface energies and work of cohesion at infinite dilution and the energy distributions at finite dilution were constructed using IGC. Brunauer-Emmet-Teller (BET) surface area and particle morphology were determined by IGC and scanning electron microscope, respectively. Surface energies determined at finite dilution appeared more consistent with the observed flow behaviour of mechanofused powders than comparative surface energy determination at infinite dilution. Polar and total surface energy distributions together with BET surface area measurements were the lowest when lactose was mechanofused with 1-2% MgSt (w/w). In conclusion, the surface energy distribution profiles measured at finite dilution were argued to be more informative and useful in reporting the surface energy changes during mechanofusion, optimising MgSt concentration in the mechanofusion process, and the flow behaviour of mechanofused powders.
High-Resolution Cortical Dipole Imaging Using Spatial Inverse Filter Based on Filtering Property
2016-01-01
Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter that optimizes filtering property using a sigmoid function. The ability of the proposed method was compared with the traditional inverse techniques, such as Tikhonov regularization, truncated singular value decomposition (TSVD), and truncated total least squares (TTLS), in a computer simulation. The proposed method was applied to human experimental data of visual evoked potentials. As a result, the estimation accuracy was improved and the localized dipole distribution was obtained with less noise. PMID:27688747
Inversion of magnetotelluric data in a sparse model domain
NASA Astrophysics Data System (ADS)
Nittinger, Christian G.; Becken, Michael
2016-08-01
The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least-squares ℓ2 sense and of a model coefficient norm in an ℓ1 sense (ℓ2-ℓ1 minimization). The ℓ1 coefficient norm renders the solution sparse in a suitable representation such as the multiresolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for ℓ2 regularization. The presented numerical algorithm solves the mixed ℓ2-ℓ1 norm minimization problem for the nonlinear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.
Kazakopoulos, Pavlos; Moustakas, Aris L
2008-07-01
We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive nonlinear Schrödinger equation with a Gaussian random pulse as an initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through nonlinear optical fibers.
Adcox, K; Adler, S S; Ajitanand, N N; Akiba, Y; Alexander, J; Aphecetche, L; Arai, Y; Aronson, S H; Averbeck, R; Awes, T C; Barish, K N; Barnes, P D; Barrette, J; Bassalleck, B; Bathe, S; Baublis, V; Bazilevsky, A; Belikov, S; Bellaiche, F G; Belyaev, S T; Bennett, M J; Berdnikov, Y; Botelho, S; Brooks, M L; Brown, D S; Bruner, N; Bucher, D; Buesching, H; Bumazhnov, V; Bunce, G; Burward-Hoy, J; Butsyk, S; Carey, T A; Chand, P; Chang, J; Chang, W C; Chavez, L L; Chernichenko, S; Chi, C Y; Chiba, J; Chiu, M; Choudhury, R K; Christ, T; Chujo, T; Chung, M S; Chung, P; Cianciolo, V; Cole, B A; D'Enterria, D G; David, G; Delagrange, H; Denisov, A; Deshpande, A; Desmond, E J; Dietzsch, O; Dinesh, B V; Drees, A; Durum, A; Dutta, D; Ebisu, K; Efremenko, Y V; El Chenawi, K; En'yo, H; Esumi, S; Ewell, L; Ferdousi, T; Fields, D E; Fokin, S L; Fraenkel, Z; Franz, A; Frawley, A D; Fung, S Y; Garpman, S; Ghosh, T K; Glenn, A; Godoi, A L; Goto, Y; Greene, S V; Grosse Perdekamp, M; Gupta, S K; Guryn, W; Gustafsson, H A; Haggerty, J S; Hamagaki, H; Hansen, A G; Hara, H; Hartouni, E P; Hayano, R; Hayashi, N; He, X; Hemmick, T K; Heuser, J M; Hibino, M; Hill, J C; Ho, D S; Homma, K; Hong, B; Hoover, A; Ichihara, T; Imai, K; Ippolitov, M S; Ishihara, M; Jacak, B V; Jang, W Y; Jia, J; Johnson, B M; Johnson, S C; Joo, K S; Kametani, S; Kang, J H; Kann, M; Kapoor, S S; Kelly, S; Khachaturov, B; Khanzadeev, A; Kikuchi, J; Kim, D J; Kim, H J; Kim, S Y; Kim, Y G; Kinnison, W W; Kistenev, E; Kiyomichi, A; Klein-Boesing, C; Klinksiek, S; Kochenda, L; Kochetkov, D; Kochetkov, V; Koehler, D; Kohama, T; Kozlov, A; Kroon, P J; Kurita, K; Kweon, M J; Kwon, Y; Kyle, G S; Lacey, R; Lajoie, J G; Lauret, J; Lebedev, A; Lee, D M; Leitch, M J; Li, X H; Li, Z; Lim, D J; Liu, M X; Liu, X; Liu, Z; Maguire, C F; Mahon, J; Makdisi, Y I; Manko, V I; Mao, Y; Mark, S K; Markacs, S; Martinez, G; Marx, M D; Masaike, A; Matathias, F; Matsumoto, T; McGaughey, P L; Melnikov, E; Merschmeyer, M; Messer, F; Messer, M; Miake, Y; Miller, T E; Milov, A; Mioduszewski, S; Mischke, R E; Mishra, G C; Mitchell, J T; Mohanty, A K; Morrison, D P; Moss, J M; Mühlbacher, F; Muniruzzaman, M; Murata, J; Nagamiya, S; Nagasaka, Y; Nagle, J L; Nakada, Y; Nandi, B K; Newby, J; Nikkinen, L; Nilsson, P; Nishimura, S; Nyanin, A S; Nystrand, J; O'Brien, E; Ogilvie, C A; Ohnishi, H; Ojha, I D; Ono, M; Onuchin, V; Oskarsson, A; Osterman, L; Otterlund, I; Oyama, K; Paffrath, L; Palounek, A P; Pantuev, V S; Papavassiliou, V; Pate, S F; Peitzmann, T; Petridis, A N; Pinkenburg, C; Pisani, R P; Pitukhin, P; Plasil, F; Pollack, M; Pope, K; Purschke, M L; Ravinovich, I; Read, K F; Reygers, K; Riabov, V; Riabov, Y; Rosati, M; Rose, A A; Ryu, S S; Saito, N; Sakaguchi, A; Sakaguchi, T; Sako, H; Sakuma, T; Samsonov, V; Sangster, T C; Santo, R; Sato, H D; Sato, S; Sawada, S; Schlei, B R; Schutz, Y; Semenov, V; Seto, R; Shea, T K; Shein, I; Shibata, T A; Shigaki, K; Shiina, T; Shin, Y H; Sibiriak, I G; Silvermyr, D; Sim, K S; Simon-Gillo, J; Singh, C P; Singh, V; Sivertz, M; Soldatov, A; Soltz, R A; Sorensen, S; Stankus, P W; Starinsky, N; Steinberg, P; Stenlund, E; Ster, A; Stoll, S P; Sugioka, M; Sugitate, T; Sullivan, J P; Sumi, Y; Sun, Z; Suzuki, M; Takagui, E M; Taketani, A; Tamai, M; Tanaka, K H; Tanaka, Y; Taniguchi, E; Tannenbaum, M J; Thomas, J; Thomas, J H; Thomas, T L; Tian, W; Tojo, J; Torii, H; Towell, R S; Tserruya, I; Tsuruoka, H; Tsvetkov, A A; Tuli, S K; Tydesjö, H; Tyurin, N; Ushiroda, T; van Hecke, H W; Velissaris, C; Velkovska, J; Velkovsky, M; Vinogradov, A A; Volkov, M A; Vorobyov, A; Vznuzdaev, E; Wang, H; Watanabe, Y; White, S N; Witzig, C; Wohn, F K; Woody, C L; Xie, W; Yagi, K; Yokkaichi, S; Young, G R; Yushmanov, I E; Zajc, W A; Zhang, Z; Zhou, S
2001-07-30
The first measurement of energy produced transverse to the beam direction at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory is presented. The midrapidity transverse energy density per participating nucleon rises steadily with the number of participants, closely paralleling the rise in charged-particle density, such that
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices
NASA Astrophysics Data System (ADS)
Piñeros, William D.; Baldea, Michael; Truskett, Thomas M.
2016-08-01
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices.
Piñeros, William D; Baldea, Michael; Truskett, Thomas M
2016-08-07
Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.
NASA Astrophysics Data System (ADS)
Eberts, S.; Bohlke, J. K.
2009-12-01
Estimates of groundwater age distributions at public-supply wells can provide insight into the vulnerability of these wells to contamination. Such estimates can be used to explore past and future water-quality trends and contaminant peak concentrations when combined with information on contaminant input at the water table. Information on groundwater age distributions, however, is not routinely applied to water quality issues at public-supply wells. This may be due, in part, to the difficulty in obtaining such estimates from poorly characterized aquifers with limited environmental tracer data. To this end, we compared distributions of groundwater ages in discharge from public-supply wells estimated from age tracer data (SF6, CFCs, 3H, 3He) using two different inverse modeling approaches: relatively simple lumped parameter models and more complex distributed-parameter numerical flow models with particle tracking. These comparisons were made in four contrasting hydrogeologic settings across the United States: unconsolidated alluvial fan sediments, layered confined unconsolidated sediments, unconsolidated valley-fill sediments, and carbonate rocks. In all instances, multiple age tracer measurements for the public-supply well of interest were available. We compared the following quantities, which were derived from simulated breakthrough curves that were generated using the various estimated age distributions for the selected wells and assuming the same hypothetical contaminant input: time lag to peak concentration, dilution at peak concentration, and contaminant arrival and flush times. Apparent tracer-based ages and mean and median simulated ages also were compared. For each setting, both types of models yielded similar age distributions and concentration trends, when based on similar conceptual models of local hydrogeology and calibrated to the same tracer measurements. Results indicate carefully chosen and calibrated simple lumped parameter age distribution models
Pan, Min-Cheng; Pan, Min-Chun
2010-01-01
A promising method to achieve rapid convergence for image reconstruction is introduced for the continuous-wave near-infrared (NIR) diffuse optical tomography (DOT). Tomographic techniques are usually implemented off line and are time consuming to realize image reconstruction, especially for NIR DOT. Therefore, it is essential to both speed up reconstruction and achieve stable and convergent solutions. We propose an approach using a constraint based on a Lorentzian distributed function incorporated into Tikhonov regularization, thereby rapidly converging a stable solution. It is found in the study that using the proposed method with around five or six iterations leads to a stable solution. The result is compared to the primary method usually converging in approximately 25 iterations. Our algorithm rapidly converges to stable solution in the case of noisy (>20 dB) detected intensities.
Recursive inversion of externally defined linear systems
NASA Technical Reports Server (NTRS)
Bach, Ralph E., Jr.; Baram, Yoram
1988-01-01
The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.
Sequential Geoacoustic Filtering and Geoacoustic Inversion
2014-09-30
1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Sequential Geoacoustic Filtering and Geoacoustic Inversion ...geoacoustic inversion methods, their use in the analysis of shallow water experimental data, and evaluation of geoacoustic model and parameter...uncertainties including the mapping of these uncertainties through to system performance uncertainties. OBJECTIVES Analysis of geoacoustic inversion
Wang, Zhengxin; Marcus, R Kenneth
2014-07-18
Capillary-channeled polymer (C-CP) fibers have been utilized as liquid chromatography stationary phases, primarily for biomacromolecule separations on the analytical and preparative scales. The collinear packing of the eight-channeled C-CP fibers provides for very efficient flow, allowing operation at high linear velocity (u>100mm s(-1)) and low backpressure (<2000psi) in analytical-scale separations. To take advantage of these fluid transport properties, there must not be mass transfer limitations as would be imposed by having an appreciably porous phase, wherein solute diffusion limits the overall mass transport rates. To better understand the physical nano-/micro- structure of C-CP fibers, inverse size exclusion chromatography (iSEC) has been employed to determine the pore size distribution (PSD) within C-CP fibers. A diversity of test species (from metal ions to large proteins) was used as probes under non-retaining conditions to obtain a response curve reflecting the apparent partition coefficient (Kd) versus hydrodynamic radii (rm). A mean pore radius (rp) of 4.2nm with standard deviation (sp) of ±1.1nm was calculated by fitting the Kd versus rm data to model equations with a Gaussian pore size distribution, and a pore radius of 4.0±0.1nm was calculated based on a log-normal distribution. The derived mean pore radius is much smaller than traditional support materials, with the standard deviation showing a relatively uniform pore distribution. van Deemter plots were analyzed to provide practical confirmation of the structural implications. Large molecules (e.g., proteins) that are fully excluded from pores have no significant C-terms in the van Deemter plots whereas small molecules that can access the pore volumes display appreciable C-terms, as expected. Fitting of retention data to the Knox equation suggests that the columns operate with a characteristic particle diameter (dp) of ∼53μm.
NASA Astrophysics Data System (ADS)
Lv, Qian; Su, Tao; Zheng, Jibin; Zhang, Jiancheng
2016-01-01
Inverse synthetic aperture radar (ISAR) can achieve high-resolution two-dimensional images of maneuvering targets. However, due to the indeterminate relative motion between radar and target, ISAR imaging does not provide the three-dimensional (3-D) position information of a target and suffers from great difficulty in target recognition. To tackle this issue, a 3-D interferometric ISAR (InISAR) imaging algorithm based on the joint cross modified Wigner-Ville distribution (MWVD) is presented to form 3-D images of maneuvering targets. First, we form two orthogonal interferometric baselines with three receiving antennas to establish an InISAR imaging system. Second, after the uniform range alignment and phase adjustment, the joint cross MWVD is used for all range cell of each antenna pair to generate the separation of the scatterer as well as preserve the phase that contains position information of the scatterer. At last, the 3-D images of the target can be directly reconstructed from the distribution. Simulation results demonstrate the validity of the proposal.
NASA Astrophysics Data System (ADS)
Ganas, Athanassios; Karastathis, Vassilios; Moshou, Alexandra; Valkaniotis, Sotirios; Mouzakiotis, Evangelos; Papathanassiou, George
2014-03-01
On August 7, 2013 a moderate earthquake (NOA ML = 5.1, NOA Mw = 5.4) occurred in central Kallidromon Mountain, in the Pthiotis region of central Greece. 2270 aftershocks were relocated using a modified 1-D velocity model for this area. The b-value of the aftershock sequence was b = 0.85 for a completeness magnitude of Mc = 1.7. The rate of aftershock decay was determined at p = 0.63. The spatial distribution of the aftershock sequence points towards the reactivation of a N70° ± 10°E striking normal fault at crustal depths between 8 and 13 km. A NNW-SSE cross-section imaged the activation of a steep, south dipping normal fault. A stress inversion analysis of 12 focal mechanisms showed that the minimum horizontal stress is extensional at N173°E. No primary surface ruptures were observed in the field; however, the earthquake caused severe damage in the villages of the Kallidromon area. The imaged fault strike and the orientation of the long-axis of the aftershock sequence distribution are both at a high-angle to the strike of known active faults in this area of central Greece. We interpret the Kallidromon seismic sequence as release of extensional seismic strain on secondary, steep faults inside the Fokida-Viotia crustal block.
The inverse electroencephalography pipeline
NASA Astrophysics Data System (ADS)
Weinstein, David Michael
The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.
NASA Astrophysics Data System (ADS)
van Hout, Rene; Rabencov, Boris; Arca, Javier
2014-11-01
Near neutrally buoyant, polystyrene beads (583 micrometers) were tracked in a square (50 × 50 mm2), closed-loop, turbulent water duct at a bulk flow Reynolds number of 10,602 (friction velocity 0.0208 m/s) using single view, inline digital holographic cinematography (at 1 kHz). The volume of interest (50 × 17.4 × 17.4 mm3) was positioned at the bottom part of the channel. The mean bead diameter normalized by inner wall coordinates was d+ = 14.2, with Stokes numbers of 8.5. In-house developed algorithms, fine-tuned to tracking single and overlapping beads were developed. Bead in-focus positions were determined by maximum intensity gradient method. Results showed that in agreement with literature publications, ascending beads lagged the mean streamwise water velocity while descending ones had similar velocities. Average streamwise bead velocities and number densities collapsed onto wall-normal-streamwise and spanwise-streamwise planes, indicated preferential segregation of ascending and descending beads up to a height of 100 wall units. Spanwise ``lane'' separation distances ranged between 150-200 wall units, larger but of the same order as the spanwise extent of coherent near-wall turbulence structures. Duct corners were nearly devoid of beads likely caused by secondary flows. Israel Science Foundation Grant 915/10 and COST Actions MP0806 and FP1005.
Abelev, B I; Aggarwal, M M; Ahammed, Z; Anderson, B D; Anderson, M; Arkhipkin, D; Averichev, G S; Bai, Y; Balewski, J; Barannikova, O; Barnby, L S; Baudot, J; Bekele, S; Belaga, V V; Bellingeri-Laurikainen, A; Bellwied, R; Benedosso, F; Bhardwaj, S; Bhasin, A; Bhati, A K; Bichsel, H; Bielcik, J; Bielcikova, J; Bland, L C; Blyth, S-L; Bonner, B E; Botje, M; Bouchet, J; Brandin, A V; Bravar, A; Burton, T P; Bystersky, M; Cadman, R V; Cai, X Z; Caines, H; Calderón de la Barca Sánchez, M; Castillo, J; Catu, O; Cebra, D; Chajecki, Z; Chaloupka, P; Chattopadhyay, S; Chen, H F; Chen, J H; Cheng, J; Cherney, M; Chikanian, A; Christie, W; Coffin, J P; Cormier, T M; Cosentino, M R; Cramer, J G; Crawford, H J; Das, D; Das, S; Dash, S; Daugherity, M; de Moura, M M; Dedovich, T G; Dephillips, M; Derevschikov, A A; Didenko, L; Dietel, T; Djawotho, P; Dogra, S M; Dong, W J; Dong, X; Draper, J E; Du, F; Dunin, V B; Dunlop, J C; Dutta Mazumdar, M R; Eckardt, V; Edwards, W R; Efimov, L G; Emelianov, V; Engelage, J; Eppley, G; Erazmus, B; Estienne, M; Fachini, P; Fatemi, R; Fedorisin, J; Filip, P; Finch, E; Fine, V; Fisyak, Y; Fu, J; Gagliardi, C A; Gaillard, L; Ganti, M S; Ghazikhanian, V; Ghosh, P; Gonzalez, J E; Gorbunov, Y G; Gos, H; Grebenyuk, O; Grosnick, D; Guertin, S M; Guimaraes, K S F F; Gupta, N; Gutierrez, T D; Haag, B; Hallman, T J; Hamed, A; Harris, J W; He, W; Heinz, M; Henry, T W; Hepplemann, S; Hippolyte, B; Hirsch, A; Hjort, E; Hoffman, A M; Hoffmann, G W; Horner, M J; Huang, H Z; Huang, S L; Hughes, E W; Humanic, T J; Igo, G; Jacobs, P; Jacobs, W W; Jakl, P; Jia, F; Jiang, H; Jones, P G; Judd, E G; Kabana, S; Kang, K; Kapitan, J; Kaplan, M; Keane, D; Kechechyan, A; Khodyrev, V Yu; Kim, B C; Kiryluk, J; Kisiel, A; Kislov, E M; Klein, S R; Kocoloski, A; Koetke, D D; Kollegger, T; Kopytine, M; Kotchenda, L; Kouchpil, V; Kowalik, K L; Kramer, M; Kravtsov, P; Kravtsov, V I; Krueger, K; Kuhn, C; Kulikov, A I; Kumar, A; Kuznetsov, A A; Lamont, M A C; Landgraf, J M; Lange, S; Lapointe, S; Laue, F; Lauret, J; Lebedev, A; Lednicky, R; Lee, C-H; Lehocka, S; Levine, M J; Li, C; Li, Q; Li, Y; Lin, G; Lin, X; Lindenbaum, S J; Lisa, M A; Liu, F; Liu, H; Liu, J; Liu, L; Liu, Z; Ljubicic, T; Llope, W J; Long, H; Longacre, R S; Love, W A; Lu, Y; Ludlam, T; Lynn, D; Ma, G L; Ma, J G; Ma, Y G; Magestro, D; Mahapatra, D P; Majka, R; Mangotra, L K; Manweiler, R; Margetis, S; Markert, C; Martin, L; Matis, H S; Matulenko, Yu A; McClain, C J; McShane, T S; Melnick, Yu; Meschanin, A; Millane, J; Miller, M L; Minaev, N G; Mioduszewski, S; Mironov, C; Mischke, A; Mishra, D K; Mitchell, J; Mohanty, B; Molnar, L; Moore, C F; Morozov, D A; Munhoz, M G; Nandi, B K; Nattrass, C; Nayak, T K; Nelson, J M; Nepali, N S; Netrakanti, P K; Nogach, L V; Nurushev, S B; Odyniec, G; Ogawa, A; Okorokov, V; Oldenburg, M; Olson, D; Pachr, M; Pal, S K; Panebratsev, Y; Panitkin, S Y; Pavlinov, A I; Pawlak, T; Peitzmann, T; Perevoztchikov, V; Perkins, C; Peryt, W; Phatak, S C; Picha, R; Planinic, M; Pluta, J; Poljak, N; Porile, N; Porter, J; Poskanzer, A M; Potekhin, M; Potrebenikova, E; Potukuchi, B V K S; Prindle, D; Pruneau, C; Putschke, J; Rakness, G; Raniwala, R; Raniwala, S; Ray, R L; Razin, S V; Reinnarth, J; Relyea, D; Ridiger, A; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Rose, A; Roy, C; Ruan, L; Russcher, M J; Sahoo, R; Sakuma, T; Salur, S; Sandweiss, J; Sarsour, M; Sazhin, P S; Schambach, J; Scharenberg, R P; Schmitz, N; Seger, J; Selyuzhenkov, I; Seyboth, P; Shabetai, A; Shahaliev, E; Shao, M; Sharma, M; Shen, W Q; Shimanskiy, S S; Sichtermann, E P; Simon, F; Singaraju, R N; Smirnov, N; Snellings, R; Sood, G; Sorensen, P; Sowinski, J; Speltz, J; Spinka, H M; Srivastava, B; Stadnik, A; Stanislaus, T D S; Stock, R; Stolpovsky, A; Strikhanov, M; Stringfellow, B; Suaide, A A P; Subba, N L; Sugarbaker, E; Sumbera, M; Sun, Z; Surrow, B; Swanger, M; Symons, T J M; Szanto de Toledo, A; Tai, A; Takahashi, J; Tang, A H; Tarnowsky, T; Thein, D; Thomas, J H; Timmins, A R; Timoshenko, S; Tokarev, M; Trainor, T A; Trentalange, S; Tribble, R E; Tsai, O D; Ulery, J; Ullrich, T; Underwood, D G; Van Buren, G; van der Kolk, N; van Leeuwen, M; Vander Molen, A M; Varma, R; Vasilevski, I M; Vasiliev, A N; Vernet, R; Vigdor, S E; Viyogi, Y P; Vokal, S; Voloshin, S A; Waggoner, W T; Wang, F; Wang, G; Wang, J S; Wang, X L; Wang, Y; Watson, J W; Webb, J C; Westfall, G D; Wetzler, A; Whitten, C; Wieman, H; Wissink, S W; Witt, R; Wood, J; Wu, J; Xu, N; Xu, Q H; Xu, Z; Yepes, P; Yoo, I-K; Yurevich, V I; Zhan, W; Zhang, H; Zhang, W M; Zhang, Y; Zhang, Z P; Zhao, Y; Zhong, C; Zoulkarneev, R; Zoulkarneeva, Y; Zubarev, A N; Zuo, J X
2006-10-13
Transverse momentum spectra of pi+/-, p, and p up to 12 GeV/c at midrapidity in centrality selected Au + Au collisions at square root sNN=200 GeV are presented. In central Au + Au collisions, both pi +/- and p(p) show significant suppression with respect to binary scaling at pT approximately >4 GeV/c. Protons and antiprotons are less suppressed than pi+/-, in the range 1.5 approximately < pT approximately < 6 GeV/c. The pi-/pi+ and p/p ratios show at most a weak pT dependence and no significant centrality dependence. The p/pi ratios in central Au + Au collisions approach the values in p + p and d + Au collisions at pT approximately >5 GeV/c. The results at high pT indicate that the partonic sources of pi+/-, p, and p have similar energy loss when traversing the nuclear medium.
ERIC Educational Resources Information Center
Wagon, Stan; Cox, Barry
2009-01-01
A technique discovered in 1939 can be used to build a device that is driven by standard circular motion (as in a drill press) and drills exact square holes. This device is quite different from the classic design by Watts, which uses a Reuleaux triangle and drills a hole that is almost, but not exactly, square. We describe the device in detail,…
ERIC Educational Resources Information Center
Misiurewicz, Michal
2013-01-01
If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?
ERIC Educational Resources Information Center
Adams, Deborah
2006-01-01
This article describes an approach to teaching square dance that is advantageous for both the teacher and students. Lessons in dance become more meaningful to students when the music and vocabulary is consistent with experiences in their own lives. When students create their own squaring to the rap, lessons become more student-centered,…
1982-11-01
l’ajustement d’une fonction mathematique aux valeurs mesuries de la densite optique. L’appendice B traite de l’aspect informatique de l’etude. Ce travail a...selon l’expresslon mathematique 17. Les details relatifs au calcul des coefficients de la meilleure courbe sont donnSs en appen- dlce A. Les fig. 6...expressions mathematiques des meilleures courbes de la densitS optique. Les fonctlons de distribution initiale des poudres avant dissemination de’termine’es
Leavitt, M.A.; Lutz, I.C.
1958-08-01
An amplifier circuit is described for amplifying sigmals having an alternating current component superimposed upon a direct current component, without loss of any segnnent of the alternating current component. The general circuit arrangement includes a vibrator, two square wave amplifiers, and recombination means. The amplifier input is connected to the vibrating element of the vibrator and is thereby alternately applied to the input of each square wave amplifier. The detailed circuitry of the recombination means constitutes the novelty of the annplifier and consists of a separate, dual triode amplifier coupled to the output of each square wave amplifier with a recombination connection from the plate of one amplifier section to a grid of one section of the other amplifier. The recombination circuit has provisions for correcting distortion caused by overlapping of the two square wave voltages from the square wave amplifiers.
ERIC Educational Resources Information Center
Sawilowsky, Shlomo
1985-01-01
The Random Normal Scores Test (RNST) has been suggested as a powerful alternative to the use of the parametric analysis of variance (ANOVA) test when the underlying population is non-normally distributed. The major support for this suggestion rests on asymptotic theory. An empirical analysis of the RNST performed under the F and Chi-square…
NASA Astrophysics Data System (ADS)
Yoshioka, Shoichi; Matsuoka, Yoshiko; Ide, Satoshi
2015-06-01
We estimated spatiotemporal slip distributions from three long-term slow slip events (L-SSEs) that occurred beneath the Bungo Channel at the convergent plate boundary between the subducting oceanic Philippine Sea plate and the continental Amurian plate in southwest Japan between 1997 and 1998, 2002 and 2004 and 2009 and 2011. For this purpose, we employed an inversion method using a Bayesian Information Criterion (ABIC), which included the following three prior constraints: the spatial slip distribution was smooth to some extent, slip directions were mostly oriented in the direction of plate convergence and the temporal change in slip was smooth to some extent. Our results revealed that the three L-SSEs had a common feature: slipped regions expanded southwestward at accelerating slip velocities. We also found that major slipped regions migrated southwestward by approximately 50-100 km yr-1. In contrast, southwestward and northeastward migration of the slipped regions, whose direction differed from event to event, was also identified before or after the periods when the slip velocities were at their greatest. Comparing the obtained spatiotemporal slip distributions of the three L-SSEs with slip-deficit rate distributions obtained in our previous study, we investigated the accumulation process of the slip deficit caused by slip-deficit rate distributions and the release processes of the slip deficit caused by the obtained spatiotemporal slip distributions of the three L-SSEs. At the western plate interface of the Bungo Channel, as the slip-deficit rate was small and the amounts of slips associated with the three L-SSEs were large, most of the accumulated slip deficit was estimated to have been released. In contrast, at the eastern plate interface, as the slip-deficit rate was large and the amounts of slips associated with the three L-SSEs were small, the slip deficit was estimated to have accumulated effectively. These results suggest that the slipped regions of the
NASA Astrophysics Data System (ADS)
Fukahata, Yukitoshi; Hashimoto, Manabu
2016-12-01
At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault, where main ruptures occurred, but also along the Hinagu fault. To estimate the slip distribution on these faults, we extend a method of nonlinear inversion analysis (Fukahata and Wright in Geophys J Int 173:353-364, 2008) to a two-fault system. With the method of Fukahata and Wright (2008), we can simultaneously determine the optimal dip angle of a fault and the slip distribution on it, based on Akaike's Bayesian information criterion by regarding the dip angle as an hyperparameter. By inverting the InSAR data with the developed method, we obtain the dip angles of the Futagawa and Hinagu faults as 61° ± 6° and 74° ± 12°, respectively. The slip on the Futagawa fault is mainly strike slip. The largest slip on it is over 5 m around the center of the model fault (130.9° in longitude) with a significant normal slip component. The slip on the Futagawa fault quickly decreases to zero beyond the intersection with the Hinagu fault. On the other hand, the slip has a local peak just inside Aso caldera, which would be a cause of severe damage in this area. A relatively larger reverse fault slip component on a deeper part around the intersection with Aso caldera suggests that something complicated happened there. The slip on the Hinagu fault is almost a pure strike slip with a peak of about 2.4 m. The developed method is useful in clarifying the slip distribution, when a complicated rupture like the Kumamoto earthquake happens in a remote area.[Figure not available: see fulltext.
ERIC Educational Resources Information Center
Wilson, William Wynne
1976-01-01
This article describes techniques which enable the user of a comparatively simple calculator to perform calculations of cube roots, nth roots, trigonometric, and inverse trigonometric functions, logarithms, and exponentials. (DT)
Shedding Light on the Inverse-Square Law
ERIC Educational Resources Information Center
Uthe, Richard E.
2004-01-01
Many students in introductory science courses at both the secondary and tertiary levels learn science as a miscellaneous collection of facts, concepts, and equations that must be memorized to pass examinations. One way to show students that they actually can "do" science is to have them use an observable event to generate a relationship that can…
The inverse-square law and quantum gravity
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Goldman, T.; Hughes, Richard J.
1989-01-01
A program is described which measures the gravitational acceleration of antiprotons. This idea was approached from a particle physics point of view. That point of view is examined starting with some history of physics over the last 200 years.
Cryogenic Test of the Gravitational Inverse-Square Law
NASA Astrophysics Data System (ADS)
Paik, Ho Jung; Venkateswara, Krishna Y.; Vol Moody, M.; Prieto, Violeta
2010-04-01
In string theories, the law of gravity changes as the distance r is reduced to below the radius of compactification, R. Gravity-only large extra dimensions with R ~ 100 μm could solve the gauge hierarchy problem in grand unification. On the other hand, the observed accelerating expansion of the universe is consistent with a vacuum-energy density 10120 times smaller than the value predicted from the quantum corrections to it. This enormous discrepancy could be eliminated if gravitons were 'fat' with the size of the order of 50 μm. Both of these possibilities would lead to a violation of the 1/r2 law below 100 μm. We are conducting a sub-millimeter test of the 1/r2 law at 4.2 K. To minimize Newtonian errors, the experiment employs a near-null source, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are positioned on the two sides of the source mass at a nominal distance of 260 μm. The test masses are connected to a SQUID to form a superconducting differential accelerometer. As the source is driven sinusoidally, a violation signal should appear at the second harmonic due to symmetry. The detector is rigidly mounted on the housing and the source mass is suspended separately and driven from outside the housing. The source is driven at its resonance frequency. In this paper, we discuss the design, principle, and progress of this experiment.
An optimal constrained linear inverse method for magnetic source imaging
Hughett, P.
1993-09-01
Magnetic source imaging is the reconstruction of the current distribution inside an inaccessible volume from magnetic field measurements made outside the volume. If the unknown current distribution is expressed as a linear combination of elementary current distributions in fixed positions, then the magnetic field measurements are linear in the unknown source amplitudes and both the least square and minimum mean square reconstructions are linear problems. This offers several advantages: The problem is well understood theoretically and there is only a single, global minimum. Efficient and reliable software for numerical linear algebra is readily available. If the sources are localized and statistically uncorrelated, then a map of expected power dissipation is equivalent to the source covariance matrix. Prior geological or physiological knowledge can be used to determine such an expected power map and thus the source covariance matrix. The optimal constrained linear inverse method (OCLIM) derived in this paper uses this prior knowledge to obtain a minimum mean square error estimate of the current distribution. OCLIM can be efficiently computed using the Cholesky decomposition, taking about a second on a workstation-class computer for a problem with 64 sources and 144 detectors. Any source and detector configuration is allowed as long as their positions are fixed a priori. Correlations among source and noise amplitudes are permitted. OCLIM reduces to the optimally weighted pseudoinverse method of Shim and Cho if the source amplitudes are independent and identically distributed and to the minimum-norm least squares estimate in the limit of no measurement noise or no prior knowledge of the source amplitudes. In the general case, OCLIM has better mean square error than either previous method. OCLIM appears well suited to magnetic imaging, since it exploits prior information, provides the minimum reconstruction error, and is inexpensive to compute.
Eckert-Gallup, Aubrey C.; Sallaberry, Cédric J.; Dallman, Ann R.; ...
2016-01-06
Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulations as a part of the standard current practice for designing marine structures to survive extreme sea states. These environmental contours are characterized by combinations of significant wave height (Hs) and either energy period (Te) or peak period (Tp) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first-order reliability method (I-FORM) is a standard design practice for generating environmental contours. This papermore » develops enhanced methodologies for data analysis prior to the application of the I-FORM, including the use of principal component analysis (PCA) to create an uncorrelated representation of the variables under consideration as well as new distribution and parameter fitting techniques. As a result, these modifications better represent the measured data and, therefore, should contribute to the development of more realistic representations of environmental contours of extreme sea states for determining design loads for marine structures.« less
NASA Astrophysics Data System (ADS)
Yanyan, Li; Tao, Su; Jibin, Zheng
2015-01-01
For targets with complex motions, the time-varying Doppler frequency deteriorates inverse synthetic aperture radar (ISAR) images. After range alignment and phase adjustment, azimuth echoes in a range cell can be modeled as multicomponent cubic phase signals (CPSs). The chirp rate and the quadratic chirp rate of the CPS are identified as the causes of the time-varying Doppler frequency; thus, it is necessary to estimate these two parameters correctly to obtain a well-focused ISAR image. The parameter-estimation algorithm based on the modified chirp rate-quadratic chirp rate distribution (M-CRQCRD) is proposed for the CPS and applied to the ISAR imaging of targets with complex motions. The computational cost of M-CRQCRD is low, because it can be implemented by the fast Fourier transform (FFT) and the nonuniform FFT easily. Compared to two representative parameter-estimation algorithms, the M-CRQCRD can acquire a higher antinoise performance due to the introduction of an optimal lag-time. Through simulations and analyses for the synthetic radar data, the effectiveness of the M-CRQCRD and the imaging algorithm based on the M-CRQCRD are verified.
NASA Astrophysics Data System (ADS)
Laminack, William; Gole, James
2015-12-01
A unique MEMS/NEMS approach is presented for the modeling of a detection platform for mixed gas interactions. Mixed gas analytes interact with nanostructured decorating metal oxide island sites supported on a microporous silicon substrate. The Inverse Hard/Soft acid/base (IHSAB) concept is used to assess a diversity of conductometric responses for mixed gas interactions as a function of these nanostructured metal oxides. The analyte conductometric responses are well represented using a combination diffusion/absorption-based model for multi-gas interactions where a newly developed response absorption isotherm, based on the Fermi distribution function is applied. A further coupling of this model with the IHSAB concept describes the considerations in modeling of multi-gas mixed analyte-interface, and analyte-analyte interactions. Taking into account the molecular electronic interaction of both the analytes with each other and an extrinsic semiconductor interface we demonstrate how the presence of one gas can enhance or diminish the reversible interaction of a second gas with the extrinsic semiconductor interface. These concepts demonstrate important considerations in the array-based formats for multi-gas sensing and its applications.
Eckert-Gallup, Aubrey C.; Sallaberry, Cédric J.; Dallman, Ann R.; Neary, Vincent S.
2016-01-06
Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulations as a part of the standard current practice for designing marine structures to survive extreme sea states. These environmental contours are characterized by combinations of significant wave height (H_{s}) and either energy period (T_{e}) or peak period (T_{p}) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first-order reliability method (I-FORM) is a standard design practice for generating environmental contours. This paper develops enhanced methodologies for data analysis prior to the application of the I-FORM, including the use of principal component analysis (PCA) to create an uncorrelated representation of the variables under consideration as well as new distribution and parameter fitting techniques. As a result, these modifications better represent the measured data and, therefore, should contribute to the development of more realistic representations of environmental contours of extreme sea states for determining design loads for marine structures.
ERIC Educational Resources Information Center
Hignite, Karla
2003-01-01
Details the $1 billion in facilities projects being undertaken by Georgia Institute of Technology, including the 8-acre Technology Square, which involve partnerships with its neighbors to accomplish urban revitalization. (EV)
ERIC Educational Resources Information Center
Lindley, Eric; Wheeler, Frederick P.
2001-01-01
Depicts the Learning Square as a model of organizational learning processes with the following elements: multidimensional goals, shared vision, continual learning, and tacit knowledge. A case study illustrates its use in the development of information systems. (Contains 31 references.) (SK)
ERIC Educational Resources Information Center
Parker, Dan
2001-01-01
Presents design features of the Dawson Elementary School (Corpus Chriti, Texas) where an atmosphere of an old town square and the feeling of community have been created. Photos and a floor plan are provided. (GR)
NASA Astrophysics Data System (ADS)
Hesse, M. A.; Stadler, G.
2012-12-01
Remote sensing and geodetic measurements are providing a wealth of new, spatially-distributed, time-series data that promise to improve the characterization of the subsurface and the monitoring of pressure transients due to fluid injection and production. These geodetic measurements have to be integrated with hydrological observations, which requires a fully-coupled hydrogeophysical inversion for the aquifer parameters, based on a geomechanical and hydrological process model. As a first step, we formulate a fully-coupled hydrogeophysical inverse problem to infer the permeability distribution in a quasi-static poroelastic model from a joint inversion of time-series surface deformation and well pressure measurements. The inverse problem is formulated in a Bayesian inference framework, that is, we study the posterior probability density function, which combines prior information on the parameters with information from measurement data. To compute the maximum a posterior (MAP) point of this distribution, the squared norm of the misfit between model prediction and observed surface deformation as well as hydrological data is minimized under the constraint given by the poroelastic equations. The resulting least-squares optimization problem is solved using an inexact Newton method using derivatives computed efficiently through adjoint poroelastic equations. We suggest two benchmarks for the poroelastic inverse problem based on the analytic solutions provided by Mandel (1953) and Segall (1985). Our results show that surface deformation data contains significant additional information about the permeability field in comparison to inversions based on well pressures alone (hydraulic tomography). The fully-coupled joint-inversion of geodetic and hydrological data sets therefore has the potential to improve the characterization of the subsurface and the monitoring of pressure transients. References: Mandel (1953) Consolidation des sols (étude mathématique). Géotechniue 3, 287
NASA Astrophysics Data System (ADS)
Sergienko, Olga
2013-04-01
Since Doug MacAyeal's pioneering studies of the ice-stream basal traction optimizations by control methods, inversions for unknown parameters (e.g., basal traction, accumulation patterns, etc) have become a hallmark of the present-day ice-sheet modeling. The common feature of such inversion exercises is a direct relationship between optimized parameters and observations used in the optimization procedure. For instance, in the standard optimization for basal traction by the control method, ice-stream surface velocities constitute the control data. The optimized basal traction parameters explicitly appear in the momentum equations for the ice-stream velocities (compared to the control data). The inversion for basal traction is carried out by minimization of the cost (or objective, misfit) function that includes the momentum equations facilitated by the Lagrange multipliers. Here, we build upon this idea, and demonstrate how to optimize for parameters indirectly related to observed data using a suite of nested constraints (like Russian dolls) with additional sets of Lagrange multipliers in the cost function. This method opens the opportunity to use data from a variety of sources and types (e.g., velocities, radar layers, surface elevation changes, etc.) in the same optimization process.
ERIC Educational Resources Information Center
Smith, Scott G.
1993-01-01
A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)
NASA Technical Reports Server (NTRS)
1940-01-01
This 1940s photo of the South side of Square in downtown Huntsville, Alabama, looking west, shows a historical bank in the background with cars parked just South of the Courthouse (not shown in photo). (Courtesy of Huntsville/Madison County Public Library)
A new approach for inversion of large random matrices in massive MIMO systems.
Anjum, Muhammad Ali Raza; Ahmed, Muhammad Mansoor
2014-01-01
We report a novel approach for inversion of large random matrices in massive Multiple-Input Multiple Output (MIMO) systems. It is based on the concept of inverse vectors in which an inverse vector is defined for each column of the principal matrix. Such an inverse vector has to satisfy two constraints. Firstly, it has to be in the null-space of all the remaining columns. We call it the null-space problem. Secondly, it has to form a projection of value equal to one in the direction of selected column. We term it as the normalization problem. The process essentially decomposes the inversion problem and distributes it over columns. Each column can be thought of as a node in the network or a particle in a swarm seeking its own solution, the inverse vector, which lightens the computational load on it. Another benefit of this approach is its applicability to all three cases pertaining to a linear system: the fully-determined, the over-determined, and the under-determined case. It eliminates the need of forming the generalized inverse for the last two cases by providing a new way to solve the least squares problem and the Moore and Penrose's pseudoinverse problem. The approach makes no assumption regarding the size, structure or sparsity of the matrix. This makes it fully applicable to much in vogue large random matrices arising in massive MIMO systems. Also, the null-space problem opens the door for a plethora of methods available in literature for null-space computation to enter the realm of matrix inversion. There is even a flexibility of finding an exact or approximate inverse depending on the null-space method employed. We employ the Householder's null-space method for exact solution and present a complete exposition of the new approach. A detailed comparison with well-established matrix inversion methods in literature is also given.
A New Approach for Inversion of Large Random Matrices in Massive MIMO Systems
Anjum, Muhammad Ali Raza; Ahmed, Muhammad Mansoor
2014-01-01
We report a novel approach for inversion of large random matrices in massive Multiple-Input Multiple Output (MIMO) systems. It is based on the concept of inverse vectors in which an inverse vector is defined for each column of the principal matrix. Such an inverse vector has to satisfy two constraints. Firstly, it has to be in the null-space of all the remaining columns. We call it the null-space problem. Secondly, it has to form a projection of value equal to one in the direction of selected column. We term it as the normalization problem. The process essentially decomposes the inversion problem and distributes it over columns. Each column can be thought of as a node in the network or a particle in a swarm seeking its own solution, the inverse vector, which lightens the computational load on it. Another benefit of this approach is its applicability to all three cases pertaining to a linear system: the fully-determined, the over-determined, and the under-determined case. It eliminates the need of forming the generalized inverse for the last two cases by providing a new way to solve the least squares problem and the Moore and Penrose's pseudoinverse problem. The approach makes no assumption regarding the size, structure or sparsity of the matrix. This makes it fully applicable to much in vogue large random matrices arising in massive MIMO systems. Also, the null-space problem opens the door for a plethora of methods available in literature for null-space computation to enter the realm of matrix inversion. There is even a flexibility of finding an exact or approximate inverse depending on the null-space method employed. We employ the Householder's null-space method for exact solution and present a complete exposition of the new approach. A detailed comparison with well-established matrix inversion methods in literature is also given. PMID:24733148
Least-squares RTM with L1 norm regularisation
NASA Astrophysics Data System (ADS)
Wu, Di; Yao, Gang; Cao, Jingjie; Wang, Yanghua
2016-10-01
Reverse time migration (RTM), for imaging complex Earth models, is a reversal procedure of the forward modelling of seismic wavefields, and hence can be formulated as an inverse problem. The least-squares RTM method attempts to minimise the difference between the observed field data and the synthetic data generated by the migration image. It can reduce the artefacts in the images of a conventional RTM which uses an adjoint operator, instead of an inverse operator, for the migration. However, as the least-squares inversion provides an average solution with minimal variation, the resolution of the reflectivity image is compromised. This paper presents the least-squares RTM method with a model constraint defined by an L1-norm of the reflectivity image. For solving the least-squares RTM with L1 norm regularisation, the inversion is reformulated as a ‘basis pursuit de-noise (BPDN)’ problem, and is solved directly using an algorithm called ‘spectral projected gradient for L1 minimisation (SPGL1)’. Three numerical examples demonstrate the effectiveness of the method which can mitigate artefacts and produce clean images with significantly higher resolution than the least-squares RTM without such a constraint.
Inversion Algorithms for Geophysical Problems
1987-12-16
ktdud* Sccumy Oass/Kjoon) Inversion Algorithms for Geophysical Problems (U) 12. PERSONAL AUTHOR(S) Lanzano, Paolo 13 «. TYPE OF REPORT Final 13b...spectral density. 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 13 UNCLASSIFIED/UNLIMITED D SAME AS RPT n OTIC USERS 22a. NAME OF RESPONSIBLE...Research Laboratory ’^^ SSZ ’.Washington. DC 20375-5000 NRLrMemorandum Report-6138 Inversion Algorithms for Geophysical Problems p. LANZANO Space
Fouka, M.; Ouichaoui, S. E-mail: souichaoui@usthb.dz
2011-08-20
We have calculated the inverse Compton (IC) integrated spectral power within the Thomson limit for a monoenergetic isotropic photon field upscattered off highly relativistic electrons assuming an isotropic power-law distribution of the latter, N({gamma}) = C{gamma}{sup -p}, with Lorentz parameter values {gamma}{sub 1} < {gamma} < {gamma}{sub 2}. Our interest was essentially focused on the case of a finite energy range (finite {gamma}{sub 2}) possibly having realistic applications in high-energy astrophysical sites, mainly relativistic shock regions. To this end, we have defined and derived a dimensionless parametric function, F{sub p} (z{sub 1}, {eta}), with variables z{sub 1} = {epsilon}{sub 1}/4{gamma}{sup 2}{sub 1}{epsilon} and {eta} = {gamma}{sub 2}/{gamma}{sub 1}. This result was used to derive the IC-integrated spectral power for an upscattered blackbody (BB) photon field using a dimensionless parametric function, W{sub p} ({xi}, {eta}), with variable {xi} = {epsilon}{sub 1}/4{gamma}{sup 2}{sub 1} kT. Asymptotic forms of this function have been derived for three energy ranges, i.e., {xi} << 1, 1 << {xi} << {eta}{sup 2}, and {xi} >> {eta}{sup 2}. Then, a characteristic value, {eta}{sub c}(p, {epsilon}) with {epsilon} << 1, of parameter {eta} was defined such that the middle range asymptotic form of W{sub p} ({xi}, {eta}) could be valid and good when {eta} {approx}> {eta}{sub c}(p, {epsilon}), by deriving an approximate expression of this particular value for {epsilon} = 10{sup -3}. The resulting spectra featured by a high-energy cutoff in the case of low values of the ratio {eta} can be discussed at least for a population of short gamma-ray bursts (GRBs), those best described by the cutoff power-law model with a low-energy spectral index, {alpha} {approx} 0. Furthermore, it is suggested that for GRB spectra with {alpha} < -1/2 pertaining to the prompt emission phase, the IC is a likely emission mechanism for both monoenergetic and BB photon fields if one
NASA Astrophysics Data System (ADS)
Fouka, M.; Ouichaoui, S.
2011-08-01
We have calculated the inverse Compton (IC) integrated spectral power within the Thomson limit for a monoenergetic isotropic photon field upscattered off highly relativistic electrons assuming an isotropic power-law distribution of the latter, N(γ) = Cγ-p , with Lorentz parameter values γ1 < γ < γ2. Our interest was essentially focused on the case of a finite energy range (finite γ2) possibly having realistic applications in high-energy astrophysical sites, mainly relativistic shock regions. To this end, we have defined and derived a dimensionless parametric function, Fp (z 1, η), with variables z 1 = epsilon1/4γ2 1epsilon and η = γ2/γ1. This result was used to derive the IC-integrated spectral power for an upscattered blackbody (BB) photon field using a dimensionless parametric function, Wp (ξ, η), with variable ξ = epsilon1/4γ2 1 kT. Asymptotic forms of this function have been derived for three energy ranges, i.e., ξ Lt 1, 1 Lt ξ Lt η2, and ξ Gt η2. Then, a characteristic value, η c (p, ɛ) with ɛ Lt 1, of parameter η was defined such that the middle range asymptotic form of Wp (ξ, η) could be valid and good when η >~ η c (p, ɛ), by deriving an approximate expression of this particular value for ɛ = 10-3. The resulting spectra featured by a high-energy cutoff in the case of low values of the ratio η can be discussed at least for a population of short gamma-ray bursts (GRBs), those best described by the cutoff power-law model with a low-energy spectral index, α ≈ 0. Furthermore, it is suggested that for GRB spectra with α < -1/2 pertaining to the prompt emission phase, the IC is a likely emission mechanism for both monoenergetic and BB photon fields if one assumes that the former photon field could exist specifically in the GRB environment. Various suitable astrophysical applications are presented and discussed.
NASA Astrophysics Data System (ADS)
Nath, Saurabh; Mukherjee, Anish; Chatterjee, Souvick; Ganguly, Ranjan; Sen, Swarnendu; Mukhopadhyay, Achintya; Boreyko, Jonathan
2014-11-01
We have observed that capillarity forces may cause floatation in a few non-intuitive configurations. These may be divided into 2 categories: i) floatation of heavier liquid droplets on lighter immiscible ones and ii) fully submerged floatation of lighter liquid droplets in a heavier immiscible medium. We call these counter-intuitive because of the inverse floatation configuration. For case (i) we have identified and studied in detail the several factors affecting the shape and maximum volume of the floating drop. We used water and vegetable oil combinations as test fluids and established the relation between Bond Number and maximum volume contained in a floating drop (in the order of μL). For case (ii), we injected vegetable oil drop-wise into a pool of water. The fully submerged configuration of the drop is not stable and a slight perturbation to the system causes the droplet to burst and float in partially submerged condition. Temporal variation of a characteristic length of the droplet is analyzed using MATLAB image processing. The constraint of small Bond Number establishes the assumption of lubrication regime in the thin gap. A brief theoretical formulation also shows the temporal variation of the gap thickness. Jadavpur University, Jagadis Bose Centre of Excellence, Virginia Tech.
Review of the Generalized Least Squares Method
NASA Astrophysics Data System (ADS)
Menke, William
2014-09-01
The generalized least squares (GLS) method uses both data and prior information to solve for a best-fitting set of model parameters. We review the method and present simplified derivations of its essential formulas. Concepts of resolution and covariance—essential in all of inverse theory—are applicable to GLS, but their meaning, and especially that of resolution, must be carefully interpreted. We introduce derivations that show that the quantity being resolved is the deviation of the solution from the prior model and that the covariance of the model depends on both the uncertainty in the data and the uncertainty in the prior information. On face value, the GLS formulas for resolution and covariance seem to require matrix inverses that may be difficult to calculate for the very large (but often sparse) linear systems encountered in practical inverse problems. We demonstrate how to organize the computations in an efficient manner and present MATLAB code that implements them. Finally, we formulate the well-understood problem of interpolating data with minimum curvature splines as an inverse problem and use it to illustrate the GLS method.
Review of the Generalized Least Squares Method
NASA Astrophysics Data System (ADS)
Menke, William
2015-01-01
The generalized least squares (GLS) method uses both data and prior information to solve for a best-fitting set of model parameters. We review the method and present simplified derivations of its essential formulas. Concepts of resolution and covariance—essential in all of inverse theory—are applicable to GLS, but their meaning, and especially that of resolution, must be carefully interpreted. We introduce derivations that show that the quantity being resolved is the deviation of the solution from the prior model and that the covariance of the model depends on both the uncertainty in the data and the uncertainty in the prior information. On face value, the GLS formulas for resolution and covariance seem to require matrix inverses that may be difficult to calculate for the very large (but often sparse) linear systems encountered in practical inverse problems. We demonstrate how to organize the computations in an efficient manner and present MATLAB code that implements them. Finally, we formulate the well-understood problem of interpolating data with minimum curvature splines as an inverse problem and use it to illustrate the GLS method.
Hybrid least squares multivariate spectral analysis methods
Haaland, David M.
2002-01-01
A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following estimation or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The "hybrid" method herein means a combination of an initial classical least squares analysis calibration step with subsequent analysis by an inverse multivariate analysis method. A "spectral shape" herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The "shape" can be continuous, discontinuous, or even discrete points illustrative of the particular effect.
NASA Astrophysics Data System (ADS)
de Carvalho, R. Egydio; Leonel, Edson D.
2016-12-01
A periodic time perturbation is introduced in the logistic map as an attempt to investigate new scenarios of bifurcations and new mechanisms toward the chaos. With a squared sine perturbation we observe that a point attractor reaches the chaotic attractor without following a cascade of bifurcations. One fixed point of the system presents a new scenario of bifurcations through an infinite sequence of alternating changes of stability. At the bifurcations, the perturbation does not modify the scaling features observed in the convergence toward the stationary state.
Dory, R.A.; Uckan, N.A.; Ard, W.B.; Batchelor, D.B.; Berry, L.A.; Bryan, W.E.; Dandl, R.A.; Guest, G.E.; Haste, G.R.; Hastings, D.E.
1986-10-01
The ELMO Bumpy Square (EBS) concept consists of four straight magnetic mirror arrays linked by four high-field corner coils. Extensive calculations show that this configuration offers major improvements over the ELMO Bumpy Torus (EBT) in particle confinement, heating, transport, ring production, and stability. The components of the EBT device at Oak Ridge National Laboratory can be reconfigured into a square arrangement having straight sides composed of EBT coils, with new microwave cavities and high-field corners designed and built for this application. The elimination of neoclassical convection, identified as the dominant mechanism for the limited confinement in EBT, will give the EBS device substantially improved confinement and the flexibility to explore the concepts that produce this improvement. The primary goals of the EBS program are twofold: first, to improve the physics of confinement in toroidal systems by developing the concepts of plasma stabilization using the effects of energetic electrons and confinement optimization using magnetic field shaping and electrostatic potential control to limit particle drift, and second, to develop bumpy toroid devices as attractive candidates for fusion reactors. This report presents a brief review of the physics analyses that support the EBS concept, discussions of the design and expected performance of the EBS device, a description of the EBS experimental program, and a review of the reactor potential of bumpy toroid configurations. Detailed information is presented in the appendices.
Latin square three dimensional gage master
Jones, Lynn L.
1982-01-01
A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.
NASA Astrophysics Data System (ADS)
Andrade, Miguel Ángel Gutiérrez; García, Eric Alfredo Rincón
The design of electoral zones is a complex problem in which democracy of the electoral processes is promoted by some constraints such as population balance, contiguity and compactness. In fact, the computational complexity of zone design problems has been shown to be NP-Hard. This paper propose the use of a new measure of compactness, which uses a mesh formed with square cells to measure the quality of the electoral zones. Finally, a practical real case was chosen, which topographical settings causes some traditional measures of compactness to give very poor quality results, and was designed an algorithm based on simulated annealing that realizes a search in the space of feasible solutions. The results show that the new measure favors the creation of zones with straight forms and avoids twisted or dispersed figures, without an important effect to the population balance, which are considered zones of high quality.
Bayesian least squares deconvolution
NASA Astrophysics Data System (ADS)
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Generalized conjugate gradient squared
Fokkema, D.R.; Sleijpen, G.L.G.
1994-12-31
In order to solve non-symmetric linear systems of equations, the Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient method. This is what you may expect, since CGS uses the square of the BiCG polynomial. However, CGS may suffer from its erratic convergence behavior. The method may diverge or the approximate solution may be inaccurate. BiCGSTAB uses the BiCG polynomial and a product of linear factors in an attempt to smoothen the convergence. In many cases, this has proven to be very effective. Unfortunately, the convergence of BiCGSTAB may stall when a linear factor (nearly) degenerates. BiCGstab({ell}) is designed to overcome this degeneration of linear factors. It generalizes BiCGSTAB and uses both the BiCG polynomial and a product of higher order factors. Still, CGS may converge faster than BiCGSTAB or BiCGstab({ell}). So instead of using a product of linear or higher order factors, it may be worthwhile to look for other polynomials. Since the BiCG polynomial is based on a three term recursion, a natural choice would be a polynomial based on another three term recursion. Possibly, a suitable choice of recursion coefficients would result in method that converges faster or as fast as CGS, but less erratic. It turns out that an algorithm for such a method can easily be formulated. One particular choice for the recursion coefficients leads to CGS. Therefore one could call this algorithm generalized CGS. Another choice for the recursion coefficients leads to BiCGSTAB. It is therefore possible to mix linear factors and some polynomial based on a three term recursion. This way one may get the best of both worlds. The authors will report on their findings.
Minimal inversion, command matching and disturbance decoupling in multivariable systems
NASA Technical Reports Server (NTRS)
Seraji, H.
1989-01-01
The present treatment of the related problems of minimal inversion and perfect output control in linear multivariable systems uses a simple analytical expression for the inverse of a square multivariate system's transfer-function matrix to construct a minimal-order inverse of the system. Because the poles of the minimal-order inverse are the transmission zeros of the system, necessary and sufficient conditions for the inverse system's stability are simply stated in terms of the zero polynomial of the original system. A necessary and sufficient condition for the existence of the required controllers is that the plant zero polynomial be neither identical to zero nor unstable.
Non-linear Conjugate Gradient Time-Domain Controlled Inversion Source
Newman, Gregory A.; Commer, Michael
2006-11-16
Software that simulates and inverts time-domain electromagnetic field data for subsurface electrical properties (electrical conductivity) of geological media. The software treats data produced by a step-wise source signal from either galvanic (grounded wires) or inductive (magnetic loops) sources. The inversion process is carried inductive (magnetic loops) sources. The inversion process is carried out using a non-linear conjugate gradient optimization scheme, which minimizes the misfit between field data and model data using a least squares criteria. The software is an upgrade from the code TEM3D ver. 2.0. The upgrade includes the following components: (1) Improved (faster)memory access during gradient computation. (2) Data parellelization scheme: Multiple transmitters (sources) can be distributed accross several banks of processors (daa-planes). Similarly, the receivers of each source are also distributed accross the corresponding data-plane. (3) Improved data-IO.
Recursive inversion of externally defined linear systems by FIR filters
NASA Technical Reports Server (NTRS)
Bach, Ralph E., Jr.; Baram, Yoram
1989-01-01
The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.
Teaching Tip: When a Matrix and Its Inverse Are Stochastic
ERIC Educational Resources Information Center
Ding, J.; Rhee, N. H.
2013-01-01
A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.
Inversion methods for interpretation of asteroid lightcurves
NASA Technical Reports Server (NTRS)
Kaasalainen, Mikko; Lamberg, L.; Lumme, K.
1992-01-01
We have developed methods of inversion that can be used in the determination of the three-dimensional shape or the albedo distribution of the surface of a body from disk-integrated photometry, assuming the shape to be strictly convex. In addition to the theory of inversion methods, we have studied the practical aspects of the inversion problem and applied our methods to lightcurve data of 39 Laetitia and 16 Psyche.
Inverse groundwater modeling with emphasis on model parameterization
NASA Astrophysics Data System (ADS)
Kourakos, George; Mantoglou, Aristotelis
2012-05-01
This study develops an inverse method aiming to circumvent the subjective decision regarding model parameterization and complexity in inverse groundwater modeling. The number of parameters is included as a decision variable along with parameter values. A parameterization based on B-spline surfaces (BSS) is selected to approximate transmissivity, and genetic algorithms were selected to perform error minimization. A transform based on linear least squares (LLS) is developed, so that different parameterizations may be combined by standard genetic algorithm operators. First, three applications, with isotropic, anisotropic, and zoned aquifer parameters, are examined in a single objective optimization problem and the estimated transmissivity is found to be near the true one. Interestingly, in the anisotropic case, the algorithm converged to a solution with an anisotropic distribution of control points. Next, a single objective optimization with regularization, penalizing complex models, is considered, and last, the problem is expressed in a multiobjective optimization framework (MOO), where the goals are simultaneous minimization of calibration error and model complexity. The result of MOO is a Pareto set of potential solutions where the user can examine the tradeoffs between calibration error and model complexity and select the most suitable model. By comparing calibration with prediction errors, it appears, that the most promising models are the ones near a region where the rate of decrease of calibration error as model complexity increases drops (bend of error curve). This is a useful result of practical interest in real inverse modeling applications.
Dielectric square resonator investigated with microwave experiments.
Bittner, S; Bogomolny, E; Dietz, B; Miski-Oglu, M; Richter, A
2014-11-01
We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.
Dynamics of paramagnetic squares in uniform magnetic fields
NASA Astrophysics Data System (ADS)
Du, Di; He, Peng; Zeng, Yongchao; Biswal, Sibani Lisa
2016-11-01
The magnetic forces between paramagnetic squares cannot be calculated using a classic dipolar model because the magnetic field distribution is not uniform within square particles. Here, we present the calculation of magnetic forces and torques on paramagnetic squares in a uniform 2-D magnetic field using a Laplace's equation solver. With these calculations, we simulate the variations in equilibrium configurations as a function of number of interacting squares. For example, a single square orients with its diagonal directed to the external field while a system of multiple squares will assemble into chain-like structures with their edges directed to the external field. Unlike chains of spherical magnetic particles, that easily stagger themselves to aggregate, chains consisting of magnetic squares are unable to aggregate due to interchain repulsion.
Orthogonalizing EM: A design-based least squares algorithm.
Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z G
We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online.
Orthogonalizing EM: A design-based least squares algorithm
Xiong, Shifeng; Dai, Bin; Huling, Jared; Qian, Peter Z. G.
2016-01-01
We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online. PMID:27499558
Sun, Yu; Hou, Zhangshuan; Huang, Maoyi; Tian, Fuqiang; Leung, Lai-Yung R.
2013-12-10
This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.
NASA Astrophysics Data System (ADS)
Cordes, James M.
2006-06-01
The SKA is an observatory for m/cm wavelengths that will provide quantum leaps in studies of the early universe, the high-energy universe, and astrobiology. Key science areas include:(1) Galaxy Evolution and Large-Scale Structure, including Dark Energy;(2) Probing the Dark Ages through studies of highly redshifted hydrogen and carbon monoxide;(3) Cosmic magnetism;(4) Probing Gravity with Pulsars and Black Holes; and(5) The Cradle of Life, including real-time images of protoplanetary disks, inventory of organic molecules, and the search for signals from extraterrestrial intelligence.From a phase-space point of view, the SKA will expand enormously our ability to discover new and known phenomena, including transient sources with time scales from nano-seconds to years. Particular examples include coherent emissions from extrasolar planets and gamma-ray burst afterglows, detectable at levels 100 times smaller than currently. Specifications needed to meet the science requirements are technically quite challenging: a frequency range of approximately 0.1 to 25 GHz; wide field of view, tens of square degrees (frequency dependent); high dynamic range and image fidelity; flexibility in imaging on scales from sub-mas to degrees; and sampling the time-frequency domain as demanded by transient objects. Meeting these specifications requires collaboration of a world-wide group of engineers and scientists. For this and other reasons, the SKA will be realized internationally. Initially, several concepts have been explored for building inexpensive collecting area that provides broad frequency coverage. The Reference Design now specifies an SKA based on a large number of small-diameter dish antennas with "smart feeds." Complementary to the dishes is a phased aperture array that will provide very wide-field capability. I will discuss the Reference Design, along with a timeline for developing the technology, building the first 10% of the SKA, and finishing the full SKA, along with the
An exact inverse method for subsonic flows
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1988-01-01
A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.
NASA Astrophysics Data System (ADS)
Brendlé, E.; Balard, H.; Papirer, E.
1998-07-01
Inverse Gas Chromatography (IGC), at finite concentration conditions, was applied for the evaluation of the surface properties of hematite samples obtained by heat treatment of goethite. From the alkane adsorption isotherms, the distribution of surface sites according to the adsorption energy is determined. It is shown that the surface of hematite undergoes significant changes when heated up to 500 circC. La chromatographie Gazeuse Inverse (CGI), à concentration finie, a été utilisée pour évaluer les propriétés de surface d'échantillons d'hématite obtenus par traitement thermique de la goethite. A partir des isothermes d'adsorption des alcanes, on détermine la courbe de distribution des sites de surface en fonction de l'énergie d'adsorption de molécules sondes. On montre que ces courbes évoluent en fonction du traitement thermique de la goethite et traduisent une importante modification de surface de l'hématite formée après un chauffage à 500 circC.
Statistical inference for inverse problems
NASA Astrophysics Data System (ADS)
Bissantz, Nicolai; Holzmann, Hajo
2008-06-01
In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima of the unknown function. The methods are illustrated in a case study, where we analyze the distribution of heliocentric escape velocities of galaxies in the Centaurus galaxy cluster, and provide statistical evidence for its bimodality.
Eberhard, Wynn L
2017-04-01
The maximum likelihood estimator (MLE) is derived for retrieving the extinction coefficient and zero-range intercept in the lidar slope method in the presence of random and independent Gaussian noise. Least-squares fitting, weighted by the inverse of the noise variance, is equivalent to the MLE. Monte Carlo simulations demonstrate that two traditional least-squares fitting schemes, which use different weights, are less accurate. Alternative fitting schemes that have some positive attributes are introduced and evaluated. The principal factors governing accuracy of all these schemes are elucidated. Applying these schemes to data with Poisson rather than Gaussian noise alters accuracy little, even when the signal-to-noise ratio is low. Methods to estimate optimum weighting factors in actual data are presented. Even when the weighting estimates are coarse, retrieval accuracy declines only modestly. Mathematical tools are described for predicting retrieval accuracy. Least-squares fitting with inverse variance weighting has optimum accuracy for retrieval of parameters from single-wavelength lidar measurements when noise, errors, and uncertainties are Gaussian distributed, or close to optimum when only approximately Gaussian.
1975-04-15
paper is a compromise in the same nature as the 2SLS. We use the Moore - Penrose (MP) generalized inverse to... Moore - Penrose generalized inverse ; Indirect Least Squares; 1’wo Stage Least Squares; Instrumental Variables; Limited Information Maximum L-..clihood...Abstract -In this paper , we propose a procedure based on the use of the Moore - Penrose inverse of matrices for deriving unique Indirect Least Squares
NASA Astrophysics Data System (ADS)
Aso, N.; Ohta, K.; Ide, S.
2014-12-01
Deformation in a small volume of earth interior is expressed by a symmetric moment tensor located on a point source. The tensor contains information of characteristic directions, source amplitude, and source types such as isotropic, double-couple, or compensated-linear-vector-dipole (CLVD). Although we often assume a double couple as the source type of an earthquake, significant non-double-couple component including isotropic component is often reported for induced earthquakes and volcanic earthquakes. For discussions on source types including double-couple and non-double-couple components, it is helpful to display them using some visual diagrams. Since the information of source type has two degrees of freedom, it can be displayed onto a two-dimensional flat plane. Although the diagram developed by Hudson et al. [1989] is popular, the trace corresponding to the mechanism combined by two mechanisms is not always a smooth line. To overcome this problem, Chapman and Leaney [2012] developed a new diagram. This diagram has an advantage that a straight line passing through the center corresponds to the mechanism obtained by a combination of an arbitrary mechanism and a double-couple [Tape and Tape, 2012], but this diagram has some difficulties in use. First, it is slightly difficult to produce the diagram because of its curved shape. Second, it is also difficult to read out the ratios among isotropic, double-couple, and CLVD components, which we want to obtain from the estimated moment tensors, because they do not appear directly on the horizontal or vertical axes. In the present study, we developed another new square diagram that overcomes the difficulties of previous diagrams. This diagram is an orthogonal system of isotropic and deviatoric axes, so it is easy to get the ratios among isotropic, double-couple, and CLVD components. Our diagram has another advantage that the probability density is obtained simply from the area within the diagram if the probability density
Facet growth of self-separated GaN layers through HVPE on large square-patterned template
NASA Astrophysics Data System (ADS)
Sui, Yanping; Wang, Bin; Zhao, Zhide; Xu, Wei; Li, Xiaoliang; Wang, Xinzhong; Yu, Guanghui
2014-05-01
A self-separated GaN layer was prepared by hydride vapor phase epitaxy (HVPE) on a square-patterned template with large periodicity. Self-separation was completed by breakage of the fragile layer because of the thermal stresses generated during the cooling process after HVPE growth. The GaN layer exhibited graphical surface comprising the terrace and the concave, the shapes of which were corresponding with the mask pattern. The terrace came from the growth on window openings, and had Ga-polarity by wet etching and micro-Raman measurement. The concave over the mask was composed of large inclined facets, and was demonstrated to have N-polarity. The growth on large square-patterned template was considered to be facet growth. The polarity inversion was related to dislocation accumulation. The strain distribution regularly varied, which was interpreted based on the facet growth mode.
In Defense of the Chi-Square Continuity Correction.
ERIC Educational Resources Information Center
Veldman, Donald J.; McNemar, Quinn
Published studies of the sampling distribution of chi-square with and without Yates' correction for continuity have been interpreted as discrediting the correction. Yates' correction actually produces a biased chi-square value which in turn yields a better estimate of the exact probability of the discrete event concerned when used in conjunction…
Annibaldi, A; Truzzi, C; Illuminati, S; Bassotti, E; Scarponi, G
2007-02-01
Eight PM10 aerosol samples were collected in the vicinity of the "Mario Zucchelli" Italian Antarctic Station (formerly Terra Nova Bay Station) during the 2000-2001 austral summer using a high-volume sampler and precleaned cellulose filters. The aerosol mass was determined by differential weighing of filters carried out in a clean chemistry laboratory under controlled temperature and humidity. A two-step sequential extraction procedure was used to separate the water-soluble and the insoluble (dilute-HCl-extractable) fractions. Cd, Pb and Cu were determined in the two fractions using an ultrasensitive square wave anodic stripping voltammetric (SWASV) procedure set up for and applied to aerosol samples for the first time. Total extractable metals showed maxima at midsummer for Cd and Pb and a less clear trend for Cu. In particular, particulate metal concentrations ranged as follows: Cd 0.84-9.2 microg g(-1) (average 4.7 microg g(-1)), Pb 13.2-81 microg g(-1) (average 33 microg g(-1)), Cu 126-628 microg g(-1) (average 378 microg g(-1)). In terms of atmospheric concentration, the values were: Cd 0.55-6.3 pg m(-3) (average 3.4 pg m(-3)), Pb 8.7-48 pg m(-3) (average 24 pg m(-3)), Cu 75-365 pg m(-3) (average 266 pg m(-3)). At the beginning of the season the three metals appear widely distributed in the insoluble (HCl-extractable) fraction (higher proportions for Cd and Pb, 90-100%, and lower for Cu, 70-90%) with maxima in the second half of December. The soluble fraction then increases, and at the end of the season Cd and Pb are approximately equidistributed between the two fractions, while for Cu the soluble fraction reaches its maximum level of 36%. Practically negligible contributions are estimated for crustal and sea-spray sources. Low but significant volcanic contributions are estimated for Cd and Pb (approximately 10% and approximately 5%, respectively), while there is an evident although not quantified marine biogenic source, at least for Cd. The estimated natural
Inverse statistics and information content
NASA Astrophysics Data System (ADS)
Ebadi, H.; Bolgorian, Meysam; Jafari, G. R.
2010-12-01
Inverse statistics analysis studies the distribution of investment horizons to achieve a predefined level of return. This distribution provides a maximum investment horizon which determines the most likely horizon for gaining a specific return. There exists a significant difference between inverse statistics of financial market data and a fractional Brownian motion (fBm) as an uncorrelated time-series, which is a suitable criteria to measure information content in financial data. In this paper we perform this analysis for the DJIA and S&P500 as two developed markets and Tehran price index (TEPIX) as an emerging market. We also compare these probability distributions with fBm probability, to detect when the behavior of the stocks are the same as fBm.
Effects of Tape and Exercise on Dynamic Ankle Inversion
Ricard, Mark D.; Sherwood, Stephen M.; Schulthies, Shane S.; Knight, Kenneth L.
2000-01-01
Objective: To compare the effects of tape, with and without prewrap, on dynamic ankle inversion before and after exercise. Design and Setting: Doubly multivariate analyses of variance were used to compare the taping and exercise conditions. Subjects were randomly assigned to a fixed treatment order as determined by a balanced latin square. The independent variables were tape application (no tape, tape with prewrap, tape to skin) and exercise (before and after). The dependent variables were average inversion velocity, total inversion, maximum inversion velocity, and time to maximum inversion. Subjects: Thirty college-age male and female students (17 males, 13 females; mean age = 24.9 ± 4.3 years, range, 19 to 39 years) were tested. Subjects were excluded from the study if they exhibited a painful gait or painful range of motion or had a past history of ankle surgery or an ankle sprain within the past 4 weeks. Measurements: We collected data using electronic goniometers while subjects balanced on the right leg on an inversion platform tilted about the medial-lateral axis to produce 15° of plantar flexion. Sudden ankle inversion was induced by pulling the inversion platform support, allowing the platform support base to rotate 37°. Ten satisfactory trials were recorded on the inversion platform before and after a prescribed exercise bout. We calculated total inversion, time to maximum inversion, average inversion velocity, and maximum inversion velocity after sudden inversion. Results: We found no significant differences between taping to the skin and taping over prewrap for any of the variables measured. There were significant differences between both taping conditions and no-tape postexercise for average inversion velocity, maximum inversion, maximum inversion velocity, and time to maximum inversion. The total inversion mean for no-tape postexercise was 38.8° ± 6.3°, whereas the means for tape and skin and for tape and prewrap were 28.3° ± 4.6° and 29.1°
NASA Astrophysics Data System (ADS)
Luo, Wei-Ping; Li, Hong-Qi; Shi, Ning
2016-06-01
At the early stages of deep-water oil exploration and development, fewer and further apart wells are drilled than in onshore oilfields. Supervised least squares support vector machine algorithms are used to predict the reservoir parameters but the prediction accuracy is low. We combined the least squares support vector machine (LSSVM) algorithm with semi-supervised learning and established a semi-supervised regression model, which we call the semi-supervised least squares support vector machine (SLSSVM) model. The iterative matrix inversion is also introduced to improve the training ability and training time of the model. We use the UCI data to test the generalization of a semi-supervised and a supervised LSSVM models. The test results suggest that the generalization performance of the LSSVM model greatly improves and with decreasing training samples the generalization performance is better. Moreover, for small-sample models, the SLSSVM method has higher precision than the semi-supervised K-nearest neighbor (SKNN) method. The new semisupervised LSSVM algorithm was used to predict the distribution of porosity and sandstone in the Jingzhou study area.
Inverse sequential procedures for the monitoring of time series
NASA Technical Reports Server (NTRS)
Radok, Uwe; Brown, Timothy
1993-01-01
Climate changes traditionally have been detected from long series of observations and long after they happened. The 'inverse sequential' monitoring procedure is designed to detect changes as soon as they occur. Frequency distribution parameters are estimated both from the most recent existing set of observations and from the same set augmented by 1,2,...j new observations. Individual-value probability products ('likelihoods') are then calculated which yield probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set and vice versa. A parameter change is signaled when these probabilities (or a more convenient and robust compound 'no change' probability) show a progressive decrease. New parameters are then estimated from the new observations alone to restart the procedure. The detailed algebra is developed and tested for Gaussian means and variances, Poisson and chi-square means, and linear or exponential trends; a comprehensive and interactive Fortran program is provided in the appendix.
Hybrid least squares multivariate spectral analysis methods
Haaland, David M.
2004-03-23
A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following prediction or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The hybrid method herein means a combination of an initial calibration step with subsequent analysis by an inverse multivariate analysis method. A spectral shape herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The shape can be continuous, discontinuous, or even discrete points illustrative of the particular effect.
ERIC Educational Resources Information Center
Emanouilidis, Emanuel
2008-01-01
Latin squares were first introduced and studied by the famous mathematician Leonhard Euler in the 1700s. Through the years, Latin squares have been used in areas such as statistics, graph theory, coding theory, the generation of random numbers as well as in the design and analysis of experiments. Recently, with the international popularity of…
From Square Dance to Mathematics
ERIC Educational Resources Information Center
Bremer, Zoe
2010-01-01
In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…
An inversion method for cometary atmospheres
NASA Astrophysics Data System (ADS)
Hubert, B.; Opitom, C.; Hutsemékers, D.; Jehin, E.; Munhoven, G.; Manfroid, J.; Bisikalo, D. V.; Shematovich, V. I.
2016-10-01
Remote observation of cometary atmospheres produces a measurement of the cometary emissions integrated along the line of sight. This integration is the so-called Abel transform of the local emission rate. The observation is generally interpreted under the hypothesis of spherical symmetry of the coma. Under that hypothesis, the Abel transform can be inverted. We derive a numerical inversion method adapted to cometary atmospheres using both analytical results and least squares fitting techniques. This method, derived under the usual hypothesis of spherical symmetry, allows us to retrieve the radial distribution of the emission rate of any unabsorbed emission, which is the fundamental, physically meaningful quantity governing the observation. A Tikhonov regularization technique is also applied to reduce the possibly deleterious effects of the noise present in the observation and to warrant that the problem remains well posed. Standard error propagation techniques are included in order to estimate the uncertainties affecting the retrieved emission rate. Several theoretical tests of the inversion techniques are carried out to show its validity and robustness. In particular, we show that the Abel inversion of real data is only weakly sensitive to an offset applied to the input flux, which implies that the method, applied to the study of a cometary atmosphere, is only weakly dependent on uncertainties on the sky background which has to be subtracted from the raw observations of the coma. We apply the method to observations of three different comets observed using the TRAPPIST telescope: 103P/ Hartley 2, F6/ Lemmon and A1/ Siding Spring. We show that the method retrieves realistic emission rates, and that characteristic lengths and production rates can be derived from the emission rate for both CN and C2 molecules. We show that the retrieved characteristic lengths can differ from those obtained from a direct least squares fitting over the observed flux of radiation, and
3D Electromagnetic inversion using conjugate gradients
Newman, G.A.; Alumbaugh, D.L.
1997-06-01
In large scale 3D EM inverse problems it may not be possible to directly invert a full least-squares system matrix involving model sensitivity elements. Thus iterative methods must be employed. For the inverse problem, we favor either a linear or non-linear (NL) CG scheme, depending on the application. In a NL CG scheme, the gradient of the objective function is required at each relaxation step along with a univariate line search needed to determine the optimum model update. Solution examples based on both approaches will be presented.
Monte Carlo inversion of seismic data
NASA Technical Reports Server (NTRS)
Wiggins, R. A.
1972-01-01
The analytic solution to the linear inverse problem provides estimates of the uncertainty of the solution in terms of standard deviations of corrections to a particular solution, resolution of parameter adjustments, and information distribution among the observations. It is shown that Monte Carlo inversion, when properly executed, can provide all the same kinds of information for nonlinear problems. Proper execution requires a relatively uniform sampling of all possible models. The expense of performing Monte Carlo inversion generally requires strategies to improve the probability of finding passing models. Such strategies can lead to a very strong bias in the distribution of models examined unless great care is taken in their application.
Radiation Source Mapping with Bayesian Inverse Methods
NASA Astrophysics Data System (ADS)
Hykes, Joshua Michael
We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system's geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (IP) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of 137Cs and 60Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (MCNP) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution
Locative Inversion in Cantonese.
ERIC Educational Resources Information Center
Mok, Sui-Sang
This study investigates the phenomenon of "Locative Inversion" in Cantonese. The term "Locative Inversion" indicates that the locative phrase (LP) syntactic process in Cantonese and the appears at the sentence-initial position and its logical subject occurs postverbally. It is demonstrated that this Locative Inversion is a…
Normal versus Noncentral Chi-Square Asymptotics of Misspecified Models
ERIC Educational Resources Information Center
Chun, So Yeon; Shapiro, Alexander
2009-01-01
The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…
Hartzell, S.; Liu, P.; Mendoza, C.; Ji, C.; Larson, K.M.
2007-01-01
The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.
NASA Astrophysics Data System (ADS)
Chugunov, Svyatoslav; Li, Changying
2015-09-01
Parallel implementation of two numerical tools popular in optical studies of biological materials-Inverse Adding-Doubling (IAD) program and Monte Carlo Multi-Layered (MCML) program-was developed and tested in this study. The implementation was based on Message Passing Interface (MPI) and standard C-language. Parallel versions of IAD and MCML programs were compared to their sequential counterparts in validation and performance tests. Additionally, the portability of the programs was tested using a local high performance computing (HPC) cluster, Penguin-On-Demand HPC cluster, and Amazon EC2 cluster. Parallel IAD was tested with up to 150 parallel cores using 1223 input datasets. It demonstrated linear scalability and the speedup was proportional to the number of parallel cores (up to 150x). Parallel MCML was tested with up to 1001 parallel cores using problem sizes of 104-109 photon packets. It demonstrated classical performance curves featuring communication overhead and performance saturation point. Optimal performance curve was derived for parallel MCML as a function of problem size. Typical speedup achieved for parallel MCML (up to 326x) demonstrated linear increase with problem size. Precision of MCML results was estimated in a series of tests - problem size of 106 photon packets was found optimal for calculations of total optical response and 108 photon packets for spatially-resolved results. The presented parallel versions of MCML and IAD programs are portable on multiple computing platforms. The parallel programs could significantly speed up the simulation for scientists and be utilized to their full potential in computing systems that are readily available without additional costs.
Least-squares Gaussian beam migration
NASA Astrophysics Data System (ADS)
Yuan, Maolin; Huang, Jianping; Liao, Wenyuan; Jiang, Fuyou
2017-02-01
A theory of least-squares Gaussian beam migration (LSGBM) is presented to optimally estimate a subsurface reflectivity. In the iterative inversion scheme, a Gaussian beam (GB) propagator is used as the kernel of linearized forward modeling (demigration) and its adjoint (migration). Born approximation based GB demigration relies on the calculation of Green’s function by a Gaussian-beam summation for the downward and upward wavefields. The adjoint operator of GB demigration accounts for GB prestack depth migration under the cross-correlation imaging condition, where seismic traces are processed one by one for each shot. A numerical test on the point diffractors model suggests that GB demigration can successfully simulate primary scattered data, while migration (adjoint) can yield a corresponding image. The GB demigration/migration algorithms are used for the least-squares migration scheme to deblur conventional migrated images. The proposed LSGBM is illustrated with two synthetic data for a four-layer model and the Marmousi2 model. Numerical results show that LSGBM, compared to migration (adjoint) with GBs, produces images with more balanced amplitude, higher resolution and even fewer artifacts. Additionally, the LSGBM shows a robust convergence rate.
Counting Triangles to Sum Squares
ERIC Educational Resources Information Center
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
AKLSQF - LEAST SQUARES CURVE FITTING
NASA Technical Reports Server (NTRS)
Kantak, A. V.
1994-01-01
The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.
Least Squares Estimation Without Priors or Supervision
Raphan, Martin; Simoncelli, Eero P.
2011-01-01
Selection of an optimal estimator typically relies on either supervised training samples (pairs of measurements and their associated true values) or a prior probability model for the true values. Here, we consider the problem of obtaining a least squares estimator given a measurement process with known statistics (i.e., a likelihood function) and a set of unsupervised measurements, each arising from a corresponding true value drawn randomly from an unknown distribution. We develop a general expression for a nonparametric empirical Bayes least squares (NEBLS) estimator, which expresses the optimal least squares estimator in terms of the measurement density, with no explicit reference to the unknown (prior) density. We study the conditions under which such estimators exist and derive specific forms for a variety of different measurement processes. We further show that each of these NEBLS estimators may be used to express the mean squared estimation error as an expectation over the measurement density alone, thus generalizing Stein’s unbiased risk estimator (SURE), which provides such an expression for the additive gaussian noise case. This error expression may then be optimized over noisy measurement samples, in the absence of supervised training data, yielding a generalized SURE-optimized parametric least squares (SURE2PLS) estimator. In the special case of a linear parameterization (i.e., a sum of nonlinear kernel functions), the objective function is quadratic, and we derive an incremental form for learning this estimator from data. We also show that combining the NEBLS form with its corresponding generalized SURE expression produces a generalization of the score-matching procedure for parametric density estimation. Finally, we have implemented several examples of such estimators, and we show that their performance is comparable to their optimal Bayesian or supervised regression counterparts for moderate to large amounts of data. PMID:21105827
Error handling strategies in multiphase inverse modeling
Finsterle, S.; Zhang, Y.
2010-12-01
Parameter estimation by inverse modeling involves the repeated evaluation of a function of residuals. These residuals represent both errors in the model and errors in the data. In practical applications of inverse modeling of multiphase flow and transport, the error structure of the final residuals often significantly deviates from the statistical assumptions that underlie standard maximum likelihood estimation using the least-squares method. Large random or systematic errors are likely to lead to convergence problems, biased parameter estimates, misleading uncertainty measures, or poor predictive capabilities of the calibrated model. The multiphase inverse modeling code iTOUGH2 supports strategies that identify and mitigate the impact of systematic or non-normal error structures. We discuss these approaches and provide an overview of the error handling features implemented in iTOUGH2.
Inversion strategies for visco-acoustic waveform inversion
NASA Astrophysics Data System (ADS)
Kamei, R.; Pratt, R. G.
2013-08-01
Visco-acoustic waveform inversion can potentially yield quantitative images of the distribution of both velocity and the attenuation parameters from seismic data. Intrinsic P-wave attenuation has been of particular interest, but has also proven challenging. Frequency-domain inversion allows attenuation and velocity relations to be easily incorporated, and allows a natural multiscale approach. The Laplace-Fourier approach extends this to allow the natural damping of waveforms to enhance early arrivals. Nevertheless, simultaneous inversion of velocity and attenuation leads to significant `cross-talk' between the resulting images, reflecting a lack of parameter resolution and indicating the need for pre-conditioning and regularization of the inverse problem. We analyse the cross-talk issue by partitioning the inversion parameters into two classes; the velocity parameter class, and the attenuation parameter class. Both parameters are defined at a reference frequency, and a dispersion relation is assumed that describes these parameters at any other frequency. We formulate the model gradients at a forward modelling frequency, and convert them to the reference frequency by employing the Jacobian of the coordinate change represented by the dispersion relation. We show that at a given modelling frequency, the Fréchet derivatives corresponding to these two parameter classes differ only by a 90° phase shift, meaning that the magnitudes of resulting model updates will be unscaled, and will not reflect the expected magnitudes in realistic (Q-1 ≪ 1) media. Due to the lack of scaling, cross-talk will be enhanced by poor subsurface illumination, by errors in kinematics, and by data noise. To solve these issues, we introduce an attenuation scaling term (the inverse of a penalty term) that is used to pre-condition the gradient by controlling the magnitudes of the updates to the attenuation parameters. Initial results from a suite of synthetic cross-hole tests using a three
MEERSCHAERT, MARK M.; STRAKA, PETER
2013-01-01
The inverse stable subordinator provides a probability model for time-fractional differential equations, and leads to explicit solution formulae. This paper reviews properties of the inverse stable subordinator, and applications to a variety of problems in mathematics and physics. Several different governing equations for the inverse stable subordinator have been proposed in the literature. This paper also shows how these equations can be reconciled. PMID:25045216
Joint inversion of high-frequency surface waves with fundamental and higher modes
Luo, Y.; Xia, J.; Liu, J.; Liu, Q.; Xu, S.
2007-01-01
Joint inversion of multimode surface waves for estimating the shear (S)-wave velocity has received much attention in recent years. In this paper, we first analyze sensitivity of phase velocities of multimodes of surface waves for a six-layer earth model, and then we invert surface-wave dispersion curves of the theoretical model and a real-world example. Sensitivity analysis shows that fundamental mode data are more sensitive to the S-wave velocities of shallow layers and are concentrated on a very narrow frequency band, while higher mode data are more sensitive to the parameters of relatively deeper layers and are distributed over a wider frequency band. These properties provide a foundation of using a multimode joint inversion to define S-wave velocities. Inversion results of both synthetic data and a real-world example demonstrate that joint inversion with the damped least-square method and the singular-value decomposition technique to invert high-frequency surface waves with fundamental and higher mode data simultaneously can effectively reduce the ambiguity and improve the accuracy of S-wave velocities. ?? 2007.
Dibrov, Sergey M.; McLean, Jaime; Parsons, Jerod; Hermann, Thomas
2011-12-22
The three-dimensional structures of noncoding RNA molecules reveal recurring architectural motifs that have been exploited for the design of artificial RNA nanomaterials. Programmed assembly of RNA nanoobjects from autonomously folding tetraloop-receptor complexes as well as junction motifs has been achieved previously through sequence-directed hybridization of complex sets of long oligonucleotides. Due to size and complexity, structural characterization of artificial RNA nanoobjects has been limited to low-resolution microscopy studies. Here we present the design, construction, and crystal structure determination at 2.2 {angstrom} of the smallest yet square-shaped nanoobject made entirely of double-stranded RNA. The RNA square is comprised of 100 residues and self-assembles from four copies each of two oligonucleotides of 10 and 15 bases length. Despite the high symmetry on the level of secondary structure, the three-dimensional architecture of the square is asymmetric, with all four corners adopting distinct folding patterns. We demonstrate the programmed self-assembly of RNA squares from complex mixtures of corner units and establish a concept to exploit the RNA square as a combinatorial nanoscale platform.
Magnetotelluric inversion based on mutual information
NASA Astrophysics Data System (ADS)
Mandolesi, Eric; Jones, Alan G.
2014-10-01
Joint inversion of different geophysical data sets is becoming a more popular and powerful tool, and it has been performed on data sensitive both to the same physical parameter and to different physical parameters. Joint inversion is undertaken to reduce acceptable model space and to increase sensitivity to model parameters that one method alone is unable to resolve adequately. We examine and implement a novel hybrid joint inversion approach. In our inversion scheme a model-the reference model-is fixed, and the information shared with the subsurface structure obtained from another method will be maximized; in our case conductivity structures from magnetotelluric (MT) inversion. During inversion, the joint probability distribution of the MT and the specified reference model is estimated and its entropy minimized in order to guide the inversion result towards a solution that is statistically compatible with the reference model. The powerful feature of this technique is that no explicit relationships between estimated model parameters and reference model ones are presumed: if a link exists in data then it is highlighted in the estimation of the joint probability distribution, if no link is required, then none is enforced. Tests performed verify the robustness of this method and the advantages of it in a 1-D anisotropic scenario are demonstrated. A case study was performed with data from Central Germany, effectively fitting an MT data set from a single station within as minimal an amount of anisotropy as required.
A Solution to Weighted Sums of Squares as a Square
ERIC Educational Resources Information Center
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
For n = 1, 2, ... , we give a solution (x[subscript 1], ... , x[subscript n], N) to the Diophantine integer equation [image omitted]. Our solution has N of the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given n and given integer weights m[subscript…
A Weighted Least Squares Approach To Robustify Least Squares Estimates.
ERIC Educational Resources Information Center
Lin, Chowhong; Davenport, Ernest C., Jr.
This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…
Full waveform inversion of seismic waves reflected in a stratified porous medium
NASA Astrophysics Data System (ADS)
De Barros, Louis; Dietrich, Michel; Valette, Bernard
2010-09-01
In reservoir geophysics applications, seismic imaging techniques are expected to provide as much information as possible on fluid-filled reservoir rocks. Since seismograms are, to some degree, sensitive to the mechanical parameters and fluid properties of porous media, inversion methods can be devised to directly estimate these quantities from the waveforms obtained in seismic reflection experiments. An inversion algorithm that uses a generalized least-squares, quasi-Newton approach is described to determine the porosity, permeability, interstitial fluid properties and mechanical parameters of porous media. The proposed algorithm proceeds by iteratively minimizing a misfit function between observed data and synthetic wavefields computed with the Biot theory. Simple models consisting of plane-layered, fluid-saturated and poro-elastic media are considered to demonstrate the concept and evaluate the performance of such a full waveform inversion scheme. Numerical experiments show that, when applied to synthetic data, the inversion procedure can accurately reconstruct the vertical distribution of a single model parameter, if all other parameters are perfectly known. However, the coupling between some of the model parameters does not permit the reconstruction of several model parameters at the same time. To get around this problem, we consider composite parameters defined from the original model properties and from a priori information, such as the fluid saturation rate or the lithology, to reduce the number of unknowns. Another possibility is to apply this inversion algorithm to time-lapse surveys carried out for fluid substitution problems, such as CO2 injection, since in this case only a few parameters may vary as a function of time. We define a two-step differential inversion approach which allows us to reconstruct the fluid saturation rate in reservoir layers, even though the medium properties are poorly known.
High-resolution Geostatistical Inversion of the Transient Richards Equation
NASA Astrophysics Data System (ADS)
Klein, Ole; Bastian, Peter; Ippisch, Olaf
2015-04-01
The vadose zone and the complex physical processes in it play a vital role in our understanding of the environment. The production of most food is directly or indirectly linked to the growth of organic matter sustained by subsurface flow. For a reliable assessment of the influence of natural and anthropogenic changes to such a coupled system detailed knowledge about the flow patterns and dynamics is important, but the high spatial variability of subsurface hydraulic parameters makes reliable predictions about flow patterns difficult. Direct measurement of these properties is not possible, making indirect observations through dependent quantities and parameter estimation a necessity. The geostatistical approach characterizes these hydraulic parameters without predetermined zonation. The parameter fields are treated as stochastic processes, optionally incorporating a priori information in the probability distribution. Maximizing the likelihood of the parameters with regard to the given observations yields a parameter estimate with high spatial resolution. This approach naturally leads to non-linear least squares optimization problems that may theoretically be solved using standard techniques. However, the accurate numerical representation of the Richards equation necessitates high spatio-temporal resolution and therefore a large number of parameters, while time series of observed physical quantities typically lead to many data points to invert. This high dimensionality in both the parameter and observation space makes standard techniques infeasible. We present an extension of one of these existing inversion methods, developed for stationary flow in confined aquifers, to instationary flow regimes in partially saturated porous media. Our approach uses a Conjugate Gradients scheme preconditioned with the prior covariance matrix to avoid both multiplications with its inverse and the explicit assembly of the sensitivity matrix. Instead, one combined adjoint model run is
ERIC Educational Resources Information Center
Bedard, Catherine; Belin, Pascal
2004-01-01
Voice is the carrier of speech but is also an ''auditory face'' rich in information on the speaker's identity and affective state. Three experiments explored the possibility of a ''voice inversion effect,'' by analogy to the classical ''face inversion effect,'' which could support the hypothesis of a voice-specific module. Experiment 1 consisted…
Teaching about Inverse Functions
ERIC Educational Resources Information Center
Esty, Warren
2005-01-01
In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…
Dewpoint temperature inversions analyzed
NASA Technical Reports Server (NTRS)
Ashby, W. C.; Bogner, M. A.; Moses, H.
1969-01-01
Dewpoint temperature inversion, with regard to other simultaneous meteorological conditions, was examined to establish the influence of meteorological variables on the variation of dewpoint temperature with height. This report covers instrumentation and available data, all the climatological features of dewpoint inversions, and specific special cases.
ERIC Educational Resources Information Center
Bowers, Wayne A.
This monograph was written for the Conference of the New Instructional Materials in Physics, held at the University of Washington in summer, 1965. It is intended for students who have had an introductory college physics course. It seeks to provide an introduction to the idea of distributions in general, and to some aspects of the subject in…
Source Localization using Stochastic Approximation and Least Squares Methods
Sahyoun, Samir S.; Djouadi, Seddik M.; Qi, Hairong; Drira, Anis
2009-03-05
This paper presents two approaches to locate the source of a chemical plume; Nonlinear Least Squares and Stochastic Approximation (SA) algorithms. Concentration levels of the chemical measured by special sensors are used to locate this source. Non-linear Least Squares technique is applied at different noise levels and compared with the localization using SA. For a noise corrupted data collected from a distributed set of chemical sensors, we show that SA methods are more efficient than Least Squares method. SA methods are often better at coping with noisy input information than other search methods.
Liu, Tian; Spincemaille, Pascal; de Rochefort, Ludovic; Kressler, Bryan; Wang, Yi
2009-01-01
Magnetic susceptibility differs among tissues based on their contents of iron, calcium, contrast agent, and other molecular compositions. Susceptibility modifies the magnetic field detected in the MR signal phase. The determination of an arbitrary susceptibility distribution from the induced field shifts is a challenging, ill-posed inverse problem. A method called "calculation of susceptibility through multiple orientation sampling" (COSMOS) is proposed to stabilize this inverse problem. The field created by the susceptibility distribution is sampled at multiple orientations with respect to the polarization field, B(0), and the susceptibility map is reconstructed by weighted linear least squares to account for field noise and the signal void region. Numerical simulations and phantom and in vitro imaging validations demonstrated that COSMOS is a stable and precise approach to quantify a susceptibility distribution using MRI.
Norm-square localization for Hamiltonian LG-spaces
NASA Astrophysics Data System (ADS)
Loizides, Yiannis
2017-04-01
We prove a formula for twisted Duistermaat-Heckman distributions associated to a Hamiltonian LG-space. The terms of the formula are localized at the critical points of the norm-square of the moment map, and can be computed in cross-sections. Our main tools are the theory of quasi-Hamiltonian G-spaces, as well as the Hamiltonian cobordism approach to norm-square localization introduced recently by Harada and Karshon.
Weighted total least squares formulated by standard least squares theory
NASA Astrophysics Data System (ADS)
Amiri-Simkooei, A.; Jazaeri, S.
2012-01-01
This contribution presents a simple, attractive, and flexible formulation for the weighted total least squares (WTLS) problem. It is simple because it is based on the well-known standard least squares theory; it is attractive because it allows one to directly use the existing body of knowledge of the least squares theory; and it is flexible because it can be used to a broad field of applications in the error-invariable (EIV) models. Two empirical examples using real and simulated data are presented. The first example, a linear regression model, takes the covariance matrix of the coefficient matrix as
Beam shaping to provide round and square-shaped beams in optical systems of high-power lasers
NASA Astrophysics Data System (ADS)
Laskin, Alexander; Laskin, Vadim
2016-05-01
Optical systems of modern high-power lasers require control of irradiance distribution: round or square-shaped flat-top or super-Gaussian irradiance profiles are optimum for amplification in MOPA lasers and for thermal load management while pumping of crystals of solid-state ultra-short pulse lasers to control heat and minimize its impact on the laser power and beam quality while maximizing overall laser efficiency, variable profiles are also important in irradiating of photocathode of Free Electron lasers (FEL). It is suggested to solve the task of irradiance re-distribution using field mapping refractive beam shapers like piShaper. The operational principle of these devices presumes transformation of laser beam intensity from Gaussian to flat-top one with high flatness of output wavefront, saving of beam consistency, providing collimated output beam of low divergence, high transmittance, extended depth of field, negligible residual wave aberration, and achromatic design provides capability to work with ultra-short pulse lasers having broad spectrum. Using the same piShaper device it is possible to realize beams with flat-top, inverse Gauss or super Gauss irradiance distribution by simple variation of input beam diameter, and the beam shape can be round or square with soft edges. This paper will describe some design basics of refractive beam shapers of the field mapping type and optical layouts of their applying in optical systems of high-power lasers. Examples of real implementations and experimental results will be presented as well.
Inverse planning incorporating organ motion.
Li, J G; Xing, L
2000-07-01
Accurate targeting is important in intensity-modulated radiation therapy (IMRT). The positional uncertainties of structures with respect to the external beams arise in part from random organ motion and patient setup errors. While it is important to improve immobilization and reduce the influence of organ motion, the residual effects should be included in the IMRT plan design. Current inverse planning algorithms follow the conventional approach and include uncertainties by assuming population-based margins to the target and sensitive structures. Margin around a structure represents a "hard boundary" and the fact that a structure has a spatial probability distribution has been completely ignored. With increasing understanding of spatial uncertainties of structures and the technical capability of fine-tuning the dose distribution on an individual beamlet level in IMRT, it seems timely and important to fully utilize the information in the planning process. This will reduce the "effective" margins of the structures and facilitate dose escalation. Instead of specifying a "hard margin," we describe an inverse planning algorithm which takes into consideration positional uncertainty in terms of spatial probability distribution. The algorithm was demonstrated by assuming that the random organ motion can be represented by a three-dimensional Gaussian distribution function. Other probability distributions can be dealt with similarly. In particular, the commonly used "hard margin" is a special case of the current approach with a uniform probability distribution within a specified range. The algorithm was applied to plan treatment for a prostate case and a pancreatic case. The results were compared with those obtained by adding a margin to the clinical target volume. Better sparing of the sensitive structures were obtained in both cases using the proposed method for approximately the same target coverage.
Square ice in graphene nanocapillaries.
Algara-Siller, G; Lehtinen, O; Wang, F C; Nair, R R; Kaiser, U; Wu, H A; Geim, A K; Grigorieva, I V
2015-03-26
Bulk water exists in many forms, including liquid, vapour and numerous crystalline and amorphous phases of ice, with hexagonal ice being responsible for the fascinating variety of snowflakes. Much less noticeable but equally ubiquitous is water adsorbed at interfaces and confined in microscopic pores. Such low-dimensional water determines aspects of various phenomena in materials science, geology, biology, tribology and nanotechnology. Theory suggests many possible phases for adsorbed and confined water, but it has proved challenging to assess its crystal structure experimentally. Here we report high-resolution electron microscopy imaging of water locked between two graphene sheets, an archetypal example of hydrophobic confinement. The observations show that the nanoconfined water at room temperature forms 'square ice'--a phase having symmetry qualitatively different from the conventional tetrahedral geometry of hydrogen bonding between water molecules. Square ice has a high packing density with a lattice constant of 2.83 Å and can assemble in bilayer and trilayer crystallites. Molecular dynamics simulations indicate that square ice should be present inside hydrophobic nanochannels independently of their exact atomic nature.
A New Class of Pandiagonal Squares
ERIC Educational Resources Information Center
Loly, P. D.; Steeds, M. J.
2005-01-01
An interesting class of purely pandiagonal, i.e. non-magic, whole number (integer) squares of orders (row/column dimension) of the powers of two which are related to Gray codes and square Karnaugh maps has been identified. Treated as matrices these squares possess just two non-zero eigenvalues. The construction of these squares has been automated…
NASA Astrophysics Data System (ADS)
Mohapatra, S. K.; Maity, K. P.
2016-02-01
The effect of various process parameters for determining extrusion load has been studied for square to square extrusion of Al-6061 alloy, a most used aluminium alloy series in forming industries. Parameters like operating temperature, friction condition, ram velocity, extrusion ratio and die length have been chosen as an input variable for the above study. Twenty five combinations of parameters were set for the investigation by considering aforementioned five parameters in five levels. The simulations have been carried out by Deform-3D software for predicting maximum load requirement for the complete extrusion process. Effective stress and strain distribution across the billet has been checked. Operating temperature, extrusion ratio, friction factor, ram velocity and die length have the significant effect in decreasing order on the maximum load requirement.
Analytic semigroups: Applications to inverse problems for flexible structures
NASA Technical Reports Server (NTRS)
Banks, H. T.; Rebnord, D. A.
1990-01-01
Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.
Recursive Inversion By Finite-Impulse-Response Filters
NASA Technical Reports Server (NTRS)
Bach, Ralph E., Jr.; Baram, Yoram
1991-01-01
Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.
Non-LTE Inversion of Line Profiles
NASA Astrophysics Data System (ADS)
Socas-Navarro, H.; Ruiz Cobo, B.; Trujillo Bueno, J.
1998-11-01
In this paper we address the problem of the non-LTE (NLTE) inversion of line profiles by means of a nonlinear least-squares minimization procedure combined with very efficient multilevel transfer methods. Our approach is based on the concept of response functions, which measure the first-order response of the emergent profiles to changes in the atmospheric conditions. We introduce the fixed departure coefficients (FDC) approximation in order to compute these response functions in a fast and straightforward manner. The accuracy of this approximation is checked comparing FDC response functions with those obtained from full NLTE computations. An NLTE inversion code based on these response functions has been developed and extensively tested. Reference synthetic profiles, similar to those expected from real observations, are given as input to the inversion algorithm and the recovered models are shown to be compatible with the reference models within the error bars. Our NLTE inversion code thus provides a new tool for the investigation of the chromospheres of the Sun and other stars.
Estimating nuisance parameters in inverse problems
NASA Astrophysics Data System (ADS)
Aravkin, Aleksandr Y.; van Leeuwen, Tristan
2012-11-01
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. The structure of these problems allows efficient optimization strategies—a well-known example is variable projection, where nonlinear least-squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood and maximum a posteriori likelihood problems with nuisance parameters, such as variance or degrees of freedom (d.o.f.). As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, d.o.f. parameter estimation in the context of robust inverse problems, and automatic calibration. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large-scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.
Uncertainty estimates of a GRACE inversion modelling technique over Greenland using a simulation
NASA Astrophysics Data System (ADS)
Bonin, Jennifer; Chambers, Don
2013-07-01
The low spatial resolution of GRACE causes leakage, where signals in one location spread out into nearby regions. Because of this leakage, using simple techniques such as basin averages may result in an incorrect estimate of the true mass change in a region. A fairly simple least squares inversion technique can be used to more specifically localize mass changes into a pre-determined set of basins of uniform internal mass distribution. However, the accuracy of these higher resolution basin mass amplitudes has not been determined, nor is it known how the distribution of the chosen basins affects the results. We use a simple `truth' model over Greenland as an example case, to estimate the uncertainties of this inversion method and expose those design parameters which may result in an incorrect high-resolution mass distribution. We determine that an appropriate level of smoothing (300-400 km) and process noise (0.30 cm2 of water) gets the best results. The trends of the Greenland internal basins and Iceland can be reasonably estimated with this method, with average systematic errors of 3.5 cm yr-1 per basin. The largest mass losses found from GRACE RL04 occur in the coastal northwest (-19.9 and -33.0 cm yr-1) and southeast (-24.2 and -27.9 cm yr-1), with small mass gains (+1.4 to +7.7 cm yr-1) found across the northern interior. Acceleration of mass change is measurable at the 95 per cent confidence level in four northwestern basins, but not elsewhere in Greenland. Due to an insufficiently detailed distribution of basins across internal Canada, the trend estimates of Baffin and Ellesmere Islands are expected to be incorrect due to systematic errors caused by the inversion technique.
Finite Element Based Anisotropic 3D Inversion of Marine CSEM Data
NASA Astrophysics Data System (ADS)
Chung, Y.; Byun, J.
2015-12-01
In order to interpret three-dimensional (3D) marine controlled-source electromagnetic (MCSEM) data, it is critical to accurately determine electrical anisotropy because ignoring anisotropy can produce misleading artifacts. In this study, we present an inversion method for 3D subsurface imaging in media with an inhomogeneous and anisotropic conductivity distribution. Direct solvers are incorporated both in the forward and inverse problems, For the forward problem, the vector Helmholtz equation for the secondary electric field is discretized on a hexahedral mesh using edge finite elements, then a direct sparse-matrix solver is chosen to effectively reuse its factorization both in the survey simulation and Jacobian computation. The inversion method is formulated as a functional optimization with an objective functional containing terms measuring data misfit and model structure by means of smoothness and anisotropy. These measures are efficiently incorporated through the use of an iteratively reweighted least-squares scheme. The objective functional is minimized by a Gauss-Newton approach using a direct dense-matrix solver. We demonstrate the accuracy and applicability of the algorithm by testing it on synthetic data sets.
ERIC Educational Resources Information Center
Dalton, Starrett
The amount of variance accounted for by treatment can be estimated with omega squared or with the squared multiple correlation coefficient. Monte Carlo methods were employed to compare omega squared, the squared multiple correlation coefficient, and the squared multiple correlation coefficient to which a shrinkage formula had been applied, in…
Inverse Bremsstrahlung in Shocked Astrophysical Plasmas
NASA Technical Reports Server (NTRS)
Baring, Matthew G.; Jones, Frank C.; Ellison, Donald C.
2000-01-01
There has recently been interest in the role of inverse bremsstrahlung, the emission of photons by fast suprathermal ions in collisions with ambient electrons possessing relatively low velocities, in tenuous plasmas in various astrophysical contexts. This follows a long hiatus in the application of suprathermal ion bremsstrahlung to astrophysical models since the early 1970s. The potential importance of inverse bremsstrahlung relative to normal bremsstrahlung, i.e. where ions are at rest, hinges upon the underlying velocity distributions of the interacting species. In this paper, we identify the conditions under which the inverse bremsstrahlung emissivity is significant relative to that for normal bremsstrahlung in shocked astrophysical plasmas. We determine that, since both observational and theoretical evidence favors electron temperatures almost comparable to, and certainly not very deficient relative to proton temperatures in shocked plasmas, these environments generally render inverse bremsstrahlung at best a minor contributor to the overall emission. Hence inverse bremsstrahlung can be safely neglected in most models invoking shock acceleration in discrete sources such as supernova remnants. However, on scales approximately > 100 pc distant from these sources, Coulomb collisional losses can deplete the cosmic ray electrons, rendering inverse bremsstrahlung, and perhaps bremsstrahlung from knock-on electrons, possibly detectable.
Full waveform inversion with an auxiliary bump functional
NASA Astrophysics Data System (ADS)
Bharadwaj, Pawan; Mulder, Wim; Drijkoningen, Guy
2016-08-01
Least-squares inversion of seismic arrivals can provide remarkably detailed models of the Earth's subsurface. However, cycle skipping associated with these oscillatory arrivals is the main cause for local minima in the least-squares objective function. Therefore, it is often difficult for descent methods to converge to the solution without an accurate initial large-scale velocity estimate. The low frequencies in the arrivals, needed to update the large-scale components in the velocity model, are usually unreliable or absent. To overcome this difficulty, we propose a multi-objective inversion scheme that uses the conventional least-squares functional along with an auxiliary data-domain objective. As the auxiliary objective effectively replaces the seismic arrivals by bumps, we call it the bump functional. The bump functional minimization can be made far less sensitive to cycle skipping and can deal with multiple arrivals in the data. However, it can only be used as an auxiliary objective since it usually does not provide a unique model after minimization even when the regularized-least-squares functional has a unique global minimum and hence a unique solution. The role of the bump functional during the multi-objective inversion is to guide the optimization towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. The computational complexity of the bump functional is equivalent to that of the least-squares functional. In this paper, we describe various characteristics of the bump functional using simple and illustrative numerical examples. We also demonstrate the effectiveness of the proposed multi-objective inversion scheme by considering more realistic examples. These include synthetic and field data from a cross-well experiment, surface-seismic synthetic data with reflections and synthetic data with refracted arrivals at long offsets.
Abazov, V M; Abbott, B; Abolins, M; Acharya, B S; Adams, M; Adams, T; Aguilo, E; Ahn, S H; Ahsan, M; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Anastasoaie, M; Ancu, L S; Andeen, T; Anderson, S; Andrieu, B; Anzelc, M S; Arnoud, Y; Arov, M; Arthaud, M; Askew, A; Asman, B; Jesus, A C S Assis; Atramentov, O; Autermann, C; Avila, C; Ay, C; Badaud, F; Baden, A; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, S; Banerjee, P; Barberis, E; Barfuss, A-F; Bargassa, P; Baringer, P; Barreto, J; Bartlett, J F; Bassler, U; Bauer, D; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Bellavance, A; Benitez, J A; Beri, S B; Bernardi, G; Bernhard, R; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Biscarat, C; Blazey, G; Blekman, F; Blessing, S; Bloch, D; Bloom, K; Boehnlein, A; Boline, D; Bolton, T A; Borissov, G; Bose, T; Brandt, A; Brock, R; Brooijmans, G; Bross, A; Brown, D; Buchanan, N J; Buchholz, D; Buehler, M; Buescher, V; Bunichev, V; Burdin, S; Burke, S; Burnett, T H; Buszello, C P; Butler, J M; Calfayan, P; Calvet, S; Cammin, J; Carvalho, W; Casey, B C K; Cason, N M; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chan, K; Chandra, A; Charles, F; Cheu, E; Chevallier, F; Cho, D K; Choi, S; Choudhary, B; Christofek, L; Christoudias, T; Cihangir, S; Claes, D; Coadou, Y; Cooke, M; Cooper, W E; Corcoran, M; Couderc, F; Cousinou, M-C; Crépé-Renaudin, S; Cutts, D; Cwiok, M; da Motta, H; Das, A; Davies, G; De, K; de Jong, S J; De La Cruz-Burelo, E; De Oliveira Martins, C; Degenhardt, J D; Déliot, F; Demarteau, M; Demina, R; Denisov, D; Denisov, S P; Desai, S; Diehl, H T; Diesburg, M; Dominguez, A; Dong, H; Dudko, L V; Duflot, L; Dugad, S R; Duggan, D; Duperrin, A; Dyer, J; Dyshkant, A; Eads, M; Edmunds, D; Ellison, J; Elvira, V D; Enari, Y; Eno, S; Ermolov, P; Evans, H; Evdokimov, A; Evdokimov, V N; Ferapontov, A V; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Ford, M; Fortner, M; Fox, H; Fu, S; Fuess, S; Gadfort, T; Galea, C F; Gallas, E; Galyaev, E; Garcia, C; Garcia-Bellido, A; Gavrilov, V; Gay, P; Geist, W; Gelé, D; Gerber, C E; Gershtein, Y; Gillberg, D; Ginther, G; Gollub, N; Gómez, B; Goussiou, A; Grannis, P D; Greenlee, H; Greenwood, Z D; Gregores, E M; Grenier, G; Gris, Ph; Grivaz, J-F; Grohsjean, A; Grünendahl, S; Grünewald, M W; Guo, J; Guo, F; Gutierrez, P; Gutierrez, G; Haas, A; Hadley, N J; Haefner, P; Hagopian, S; Haley, J; Hall, I; Hall, R E; Han, L; Hanagaki, K; Hansson, P; Harder, K; Harel, A; Harrington, R; Hauptman, J M; Hauser, R; Hays, J; Hebbeker, T; Hedin, D; Hegeman, J G; Heinmiller, J M; Heinson, A P; Heintz, U; Hensel, C; Herner, K; Hesketh, G; Hildreth, M D; Hirosky, R; Hobbs, J D; Hoeneisen, B; Hoeth, H; Hohlfeld, M; Hong, S J; Hossain, S; Houben, P; Hu, Y; Hubacek, Z; Hynek, V; Iashvili, I; Illingworth, R; Ito, A S; Jabeen, S; Jaffré, M; Jain, S; Jakobs, K; Jarvis, C; Jesik, R; Johns, K; Johnson, C; Johnson, M; Jonckheere, A; Jonsson, P; Juste, A; Käfer, D; Kajfasz, E; Kalinin, A M; Kalk, J R; Kalk, J M; Kappler, S; Karmanov, D; Kasper, P; Katsanos, I; Kau, D; Kaur, R; Kaushik, V; Kehoe, R; Kermiche, S; Khalatyan, N; Khanov, A; Kharchilava, A; Kharzheev, Y M; Khatidze, D; Kim, H; Kim, T J; Kirby, M H; Kirsch, M; Klima, B; Kohli, J M; Konrath, J-P; Kopal, M; Korablev, V M; Kozelov, A V; Krop, D; Kuhl, T; Kumar, A; Kunori, S; Kupco, A; Kurca, T; Kvita, J; Lacroix, F; Lam, D; Lammers, S; Landsberg, G; Lebrun, P; Lee, W M; Leflat, A; Lehner, F; Lellouch, J; Leveque, J; Lewis, P; Li, J; Li, Q Z; Li, L; Lietti, S M; Lima, J G R; Lincoln, D; Linnemann, J; Lipaev, V V; Lipton, R; Liu, Y; Liu, Z; Lobo, L; Lobodenko, A; Lokajicek, M; Love, P; Lubatti, H J; Lyon, A L; Maciel, A K A; Mackin, D; Madaras, R J; Mättig, P; Magass, C; Magerkurth, A; Mal, P K; Malbouisson, H B; Malik, S; Malyshev, V L; Mao, H S; Maravin, Y; Martin, B; McCarthy, R; Melnitchouk, A; Mendes, A; Mendoza, L; Mercadante, P G; Merkin, M; Merritt, K W; Meyer, J; Meyer, A; Millet, T; Mitrevski, J; Molina, J; Mommsen, R K; Mondal, N K; Moore, R W; Moulik, T; Muanza, G S; Mulders, M; Mulhearn, M; Mundal, O; Mundim, L; Nagy, E; Naimuddin, M; Narain, M; Naumann, N A; Neal, H A; Negret, J P; Neustroev, P; Nilsen, H; Nogima, H; Nomerotski, A; Novaes, S F; Nunnemann, T; O'Dell, V; O'Neil, D C; Obrant, G; Ochando, C; Onoprienko, D; Oshima, N; Osta, J; Otec, R; Y Garzón, G J Otero; Owen, M; Padley, P; Pangilinan, M; Parashar, N; Park, S-J; Park, S K; Parsons, J; Partridge, R; Parua, N; Patwa, A; Pawloski, G; Penning, B; Perfilov, M; Peters, K; Peters, Y; Pétroff, P; Petteni, M; Piegaia, R; Piper, J; Pleier, M-A; Podesta-Lerma, P L M; Podstavkov, V M; Pogorelov, Y; Pol, M-E; Polozov, P; Pope, B G; Popov, A V; Potter, C; da Silva, W L Prado; Prosper, H B; Protopopescu, S; Qian, J; Quadt, A; Quinn, B; Rakitine, A; Rangel, M S; Ranjan, K; Ratoff, P N; Renkel, P; Reucroft, S; Rich, P; Rijssenbeek, M; Ripp-Baudot, I; Rizatdinova, F; Robinson, S; Rodrigues, R F; Rominsky, M; Royon, C; Rubinov, P; Ruchti, R; Safronov, G; Sajot, G; Sánchez-Hernández, A; Sanders, M P; Santoro, A; Savage, G; Sawyer, L; Scanlon, T; Schaile, D; Schamberger, R D; Scheglov, Y; Schellman, H; Schieferdecker, P; Schliephake, T; Schwanenberger, C; Schwartzman, A; Schwienhorst, R; Sekaric, J; Severini, H; Shabalina, E; Shamim, M; Shary, V; Shchukin, A A; Shivpuri, R K; Siccardi, V; Simak, V; Sirotenko, V; Skubic, P; Slattery, P; Smirnov, D; Snow, J; Snow, G R; Snyder, S; Söldner-Rembold, S; Sonnenschein, L; Sopczak, A; Sosebee, M; Soustruznik, K; Souza, M; Spurlock, B; Stark, J; Steele, J; Stolin, V; Stoyanova, D A; Strandberg, J; Strandberg, S; Strang, M A; Strauss, M; Strauss, E; Ströhmer, R; Strom, D; Stutte, L; Sumowidagdo, S; Svoisky, P; Sznajder, A; Talby, M; Tamburello, P; Tanasijczuk, A; Taylor, W; Temple, J; Tiller, B; Tissandier, F; Titov, M; Tokmenin, V V; Toole, T; Torchiani, I; Trefzger, T; Tsybychev, D; Tuchming, B; Tully, C; Tuts, P M; Unalan, R; Uvarov, S; Uvarov, L; Uzunyan, S; Vachon, B; van den Berg, P J; Van Kooten, R; van Leeuwen, W M; Varelas, N; Varnes, E W; Vasilyev, I A; Vaupel, M; Verdier, P; Vertogradov, L S; Verzocchi, M; Villeneuve-Seguier, F; Vint, P; Vokac, P; Von Toerne, E; Voutilainen, M; Wagner, R; Wahl, H D; Wang, L; Wang, M H L S; Warchol, J; Watts, G; Wayne, M; Weber, M; Weber, G; Wenger, A; Wermes, N; Wetstein, M; White, A; Wicke, D; Wilson, G W; Wimpenny, S J; Wobisch, M; Wood, D R; Wyatt, T R; Xie, Y; Yacoob, S; Yamada, R; Yan, M; Yasuda, T; Yatsunenko, Y A; Yip, K; Yoo, H D; Youn, S W; Yu, J; Zatserklyaniy, A; Zeitnitz, C; Zhao, T; Zhou, B; Zhu, J; Zielinski, M; Zieminska, D; Zieminski, A; Zivkovic, L; Zutshi, V; Zverev, E G
2008-03-14
We present a measurement of the shape of the Z/gamma* boson transverse momentum (q(T)) distribution in pp --> Z/gamma* --> e(+)e(-) + X events at a center-of-mass energy of 1.96 TeV using 0.98 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low q(T), but above the perturbative QCD calculation in the region of q(T)>30 GeV/c. Using events with q(T)<30 GeV/c, we extract the value of g(2), one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.
An inverse method with regularity condition for transonic airfoil design
NASA Technical Reports Server (NTRS)
Zhu, Ziqiang; Xia, Zhixun; Wu, Liyi
1991-01-01
It is known from Lighthill's exact solution of the incompressible inverse problem that in the inverse design problem, the surface pressure distribution and the free stream speed cannot both be prescribed independently. This implies the existence of a constraint on the prescribed pressure distribution. The same constraint exists at compressible speeds. Presented here is an inverse design method for transonic airfoils. In this method, the target pressure distribution contains a free parameter that is adjusted during the computation to satisfy the regularity condition. Some design results are presented in order to demonstrate the capabilities of the method.
MAP Estimators for Piecewise Continuous Inversion
2016-08-08
tomography. We take a Bayesian approach, placing a prior distribution on ua and determining the conditional distribution on ua given the data y. It is...with recent work on MAP estimators for linear pro- blems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which...any correspondence should be addressed. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence
Integrable operators and the squares of Hankel operators
NASA Astrophysics Data System (ADS)
Blower, Gordon
2008-04-01
Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Bessel and Whittaker functions.
Latin-square three-dimensional gage master
Jones, L.
1981-05-12
A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.
Multi-ring performance of the Kendall square multiprocessor
Dunigan, T.H.
1994-03-01
Performance of the hierarchical shared-memory system of the Kendall Square Research multiprocessor is measured and characterized. The performance of prefetch is measured. Latency, bandwidth, and contention are analyzed on a 4-ring, 128 processor system. Scalability comparisons are made with other shared-memory and distributed-memory multiprocessors.
Two TI-83 Chi-Square Programs for Elementary Statistics.
ERIC Educational Resources Information Center
Thomas, John P.
2000-01-01
Presents two programs for the TI-83 to conduct the chi-square goodness-of-fit test in an elementary statistics course or any other course that might require students to conduct hypothesis tests relative to some frequency distribution. (ASK)
Sun, Chenhang; Berg, John C
2003-04-15
Inverse gas chromatography (IGC) at infinite dilution has been widely used to access the nonspecific surface free energy of solid materials. Since most practical surfaces are heterogeneous, the effective surface energy given by IGC at infinite dilution is somehow averaged over the whole sample surface, but the rule of averaging has thus far not been established. To address this problem, infinite dilution IGC analysis was carried out on mixtures of known heterogeneity. These materials are obtained by mixing two types of solid particles with significantly different surface energies as characterized individually with IGC, and results are obtained for binary combinations in varying proportions. It is found that when all surface components have the same accessibility by probe molecules, the effective surface energy of such a heterogeneous surface is related to the surface energy distribution by a square root linear relationship, square root sigma(eff)(LW)= summation operator (i)phi(i) square root sigma(i)(LW), where sigma(i)(LW) refers to the nonspecific (Lifshitz-van der Waals) surface energy of patches i, and phi(i) to their area fraction.
MODEL SELECTION FOR SPECTROPOLARIMETRIC INVERSIONS
Asensio Ramos, A.; Manso Sainz, R.; Martinez Gonzalez, M. J.; Socas-Navarro, H.; Viticchie, B.
2012-04-01
Inferring magnetic and thermodynamic information from spectropolarimetric observations relies on the assumption of a parameterized model atmosphere whose parameters are tuned by comparison with observations. Often, the choice of the underlying atmospheric model is based on subjective reasons. In other cases, complex models are chosen based on objective reasons (for instance, the necessity to explain asymmetries in the Stokes profiles) but it is not clear what degree of complexity is needed. The lack of an objective way of comparing models has, sometimes, led to opposing views of the solar magnetism because the inferred physical scenarios are essentially different. We present the first quantitative model comparison based on the computation of the Bayesian evidence ratios for spectropolarimetric observations. Our results show that there is not a single model appropriate for all profiles simultaneously. Data with moderate signal-to-noise ratios (S/Ns) favor models without gradients along the line of sight. If the observations show clear circular and linear polarization signals above the noise level, models with gradients along the line are preferred. As a general rule, observations with large S/Ns favor more complex models. We demonstrate that the evidence ratios correlate well with simple proxies. Therefore, we propose to calculate these proxies when carrying out standard least-squares inversions to allow for model comparison in the future.
Mroczka, Janusz; Szczuczyński, Damian
2012-04-10
We present further results of the simulation research on the constrained regularized least squares (CRLS) solution of the ill-conditioned inverse problem in spectral extinction (turbidimetric) measurements, which we originally presented in this journal [Appl. Opt. 49, 4591 (2010)]. The inverse problem consists of determining the particle size distribution (PSD) function of a particulate system on the basis of a measured extinction coefficient as a function of wavelength. In our previous paper, it was shown that under assumed conditions the problem can be formulated in terms of the discretized Fredholm integral equation of the first kind. The CRLS method incorporates two constraints, which the PSD sought will satisfy: nonnegativity of the PSD values and normalization of the PSD to unity when integrated over the whole range of particle size, into the regularized least squares (RLS) method. This leads to the quadratic programming problem, which is solved by means of the active set algorithm within the research. The simulation research that is the subject of the present paper is a continuation and extension of the research described in our previous paper. In the present research, the performance of the CRLS method variants is compared not only to the corresponding RLS method variants but also to other regularization techniques: the truncated generalized singular value decomposition and the filtered generalized singular value decomposition, as well as nonlinear iterative algorithms: The Twomey algorithm and the Twomey-Markowski algorithm. Moreover, two methods of selecting the optimum value of the regularization parameter are considered: The L-curve method and the generalized cross validation method. The results of our simulation research provide even stronger proof that the CRLS method performs considerably better with reconstruction of PSD than other inversing methods, in terms of better fidelity and smaller uncertainty.
Semiautomatic and Automatic Cooperative Inversion of Seismic and Magnetotelluric Data
NASA Astrophysics Data System (ADS)
Le, Cuong V. A.; Harris, Brett D.; Pethick, Andrew M.; Takam Takougang, Eric M.; Howe, Brendan
2016-09-01
Natural source electromagnetic methods have the potential to recover rock property distributions from the surface to great depths. Unfortunately, results in complex 3D geo-electrical settings can be disappointing, especially where significant near-surface conductivity variations exist. In such settings, unconstrained inversion of magnetotelluric data is inexorably non-unique. We believe that: (1) correctly introduced information from seismic reflection can substantially improve MT inversion, (2) a cooperative inversion approach can be automated, and (3) massively parallel computing can make such a process viable. Nine inversion strategies including baseline unconstrained inversion and new automated/semiautomated cooperative inversion approaches are applied to industry-scale co-located 3D seismic and magnetotelluric data sets. These data sets were acquired in one of the Carlin gold deposit districts in north-central Nevada, USA. In our approach, seismic information feeds directly into the creation of sets of prior conductivity model and covariance coefficient distributions. We demonstrate how statistical analysis of the distribution of selected seismic attributes can be used to automatically extract subvolumes that form the framework for prior model 3D conductivity distribution. Our cooperative inversion strategies result in detailed subsurface conductivity distributions that are consistent with seismic, electrical logs and geochemical analysis of cores. Such 3D conductivity distributions would be expected to provide clues to 3D velocity structures that could feed back into full seismic inversion for an iterative practical and truly cooperative inversion process. We anticipate that, with the aid of parallel computing, cooperative inversion of seismic and magnetotelluric data can be fully automated, and we hold confidence that significant and practical advances in this direction have been accomplished.
Solutions of inverse problems for biodegradation of xenobiotic polymers
NASA Astrophysics Data System (ADS)
Watanabe, Masaji; Kawai, Fusako
2016-02-01
Mathematical techniques are applied to a microbial depolymerization process. A mathematical model for the transition of the weight distribution and the microbial population is described. Inverse problems for a molecular factor and a time factor of a degradation rate are derived. Numerical techniques to solve the inverse problems are illustrated, and numerical results are presented.
Understanding Least Squares through Monte Carlo Calculations
ERIC Educational Resources Information Center
Tellinghuisen, Joel
2005-01-01
The method of least squares (LS) is considered as an important data analysis tool available to physical scientists. The mathematics of linear least squares(LLS) is summarized in a very compact matrix rotation that renders it practically "formulaic".
Least-Squares Curve-Fitting Program
NASA Technical Reports Server (NTRS)
Kantak, Anil V.
1990-01-01
Least Squares Curve Fitting program, AKLSQF, easily and efficiently computes polynomial providing least-squares best fit to uniformly spaced data. Enables user to specify tolerable least-squares error in fit or degree of polynomial. AKLSQF returns polynomial and actual least-squares-fit error incurred in operation. Data supplied to routine either by direct keyboard entry or via file. Written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler.
An Inverse of the Circular Coverage Function
2005-01-01
unlimited. 12b. DISTRIBUTION CODE 13. ABSTRACT (Maximum 200 words) This report describes an algorithm, INCIR , to evaluate an inverse of the...A Fortran 77 subroutine, INVCIR, is available that is based on INCIR , which produces R to eight significant digits for 10–8 ≤ P ≤ 1 – 10–8 and 0 ≤ d...h2 + k2)1/2 ≤ 108. A table of R versus P and d is included. 15. NUMBER OF PAGES 48 14. SUBJECT TERMS algorithm, INCIR , inverse, Circular
Aerosol physical properties from satellite horizon inversion
NASA Technical Reports Server (NTRS)
Gray, C. R.; Malchow, H. L.; Merritt, D. C.; Var, R. E.; Whitney, C. K.
1973-01-01
The feasibility is investigated of determining the physical properties of aerosols globally in the altitude region of 10 to 100 km from a satellite horizon scanning experiment. The investigation utilizes a horizon inversion technique previously developed and extended. Aerosol physical properties such as number density, size distribution, and the real and imaginary components of the index of refraction are demonstrated to be invertible in the aerosol size ranges (0.01-0.1 microns), (0.1-1.0 microns), (1.0-10 microns). Extensions of previously developed radiative transfer models and recursive inversion algorithms are displayed.
Kelvin transformation and inverse multipoles in electrostatics
NASA Astrophysics Data System (ADS)
Amaral, R. L. P. G.; Ventura, O. S.; Lemos, N. A.
2017-03-01
The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are obtained through the mapping from simple highly symmetric systems. In particular, the concept of multipole expansion is revisited from a point of view opposed to the usual one: the sources are distributed in a region far from the origin while the electrostatic potential is described at points close to it.
NASA Astrophysics Data System (ADS)
Wang, Mengyu; Brigham, John C.
2017-03-01
A computationally efficient gradient-based optimization approach for inverse material characterization from incomplete system response measurements that can utilize a generally applicable parameterization (e.g., finite element-type parameterization) is presented and evaluated. The key to this inverse characterization algorithm is the use of a direct inversion strategy with Gappy proper orthogonal decomposition (POD) response field estimation to initialize the inverse solution estimate prior to gradient-based optimization. Gappy POD is used to estimate the complete (i.e., all components over the entire spatial domain) system response field from incomplete (e.g., partial spatial distribution) measurements obtained from some type of system testing along with some amount of a priori information regarding the potential distribution of the unknown material property. The estimated complete system response is used within a physics-based direct inversion procedure with a finite element-type parameterization to estimate the spatial distribution of the desired unknown material property with minimal computational expense. Then, this estimated spatial distribution of the unknown material property is used to initialize a gradient-based optimization approach, which uses the adjoint method for computationally efficient gradient calculations, to produce the final estimate of the material property distribution. The three-step [(1) Gappy POD, (2) direct inversion, and (3) gradient-based optimization] inverse characterization approach is evaluated through simulated test problems based on the characterization of elastic modulus distributions with localized variations (e.g., inclusions) within simple structures. Overall, this inverse characterization approach is shown to efficiently and consistently provide accurate inverse characterization estimates for material property distributions from incomplete response field measurements. Moreover, the solution procedure is shown to be capable
Story Squares. CATESOL Occasional Papers, No. 4.
ERIC Educational Resources Information Center
Sasaki, Ruth A.
A set of specific and practical ideas for teaching language skills are presented, centered around the use of charts or "squares" of pictures that represent ideas that can be expressed in basic English. The focus is a story square, a system of pictures tied together by a plot and presented to the class as a puzzle. Squares for pronunciation can be…
Security Requirements Reusability and the SQUARE Methodology
2010-09-01
Security Requirements Reusability and the SQUARE Methodology Travis Christian Faculty Advisor Nancy Mead September 2010 TECHNICAL NOTE...i Table of Contents Executive Summary vii Abstract ix 1 Introduction 1 2 Security Requirements in Current Practice 2 3 The SQUARE Methodology ...the technical staff at the Software Engineering Institute and principal investigator for the SQUARE methodology . Her expertise and guidance made this
Using Least Squares for Error Propagation
ERIC Educational Resources Information Center
Tellinghuisen, Joel
2015-01-01
The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…
Multivariate Analog of Hays Omega-Squared.
ERIC Educational Resources Information Center
Sachdeva, Darshan
The multivariate analog of Hays omega-squared for estimating the strength of the relationship in the multivariate analysis of variance has been proposed in this paper. The multivariate omega-squared is obtained through the use of Wilks' lambda test criterion. Application of multivariate omega-squared to a numerical example has been provided so as…
Accounting for correlated errors in inverse radiation transport problems.
Mattingly, John K.; Stork, Christopher Lyle; Thomas, Edward Victor
2010-11-01
Inverse radiation transport focuses on identifying the configuration of an unknown radiation source given its observed radiation signatures. The inverse problem is solved by finding the set of transport model variables that minimizes a weighted sum of the squared differences by channel between the observed signature and the signature predicted by the hypothesized model parameters. The weights per channel are inversely proportional to the sum of the variances of the measurement and model errors at a given channel. In the current treatment, the implicit assumption is that the errors (differences between the modeled and observed radiation signatures) are independent across channels. In this paper, an alternative method that accounts for correlated errors between channels is described and illustrated for inverse problems based on gamma spectroscopy.
A Reassessment of the Groundwater Inverse Problem
NASA Astrophysics Data System (ADS)
McLaughlin, Dennis; Townley, Lloyd R.
1996-05-01
This paper presents a functional formulation of the groundwater flow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms. Unknown hydrogeological properties are assumed to be spatial functions that can be represented in terms of a (possibly infinite) basis function expansion with random coefficients. The unknown parameter function is related to the measurements used for estimation by a "forward operator" which describes the measurement process. In the particular case considered here, the parameter of interest is the large-scale log hydraulic conductivity, the measurements are point values of log conductivity and piezometric head, and the forward operator is derived from an upscaled groundwater flow equation. The inverse algorithm seeks the "most probable" or maximum a posteriori estimate of the unknown parameter function. When the measurement errors and parameter function are Gaussian and independent, the maximum a posteriori estimate may be obtained by minimizing a least squares performance index which can be partitioned into goodness-of-fit and prior terms. When the parameter is a stationary random function the prior portion of the performance index is equivalent to a regularization term which imposes a smoothness constraint on the estimate. This constraint tends to make the problem well-posed by limiting the range of admissible solutions. The Gaussian maximum a posteriori problem may be solved with variational methods, using functional generalizations of Gauss-Newton or gradient-based search techniques. Several popular groundwater inverse algorithms are either special cases of, or variants on, the functional maximum a posteriori algorithm. These algorithms differ primarily with respect to the way they describe spatial variability and the type of search technique they use (linear versus nonlinear). The accuracy of estimates produced by both linear and nonlinear inverse algorithms may be measured in terms of a Bayesian
Commer, Michael; Helwig, Stefan, L.; Hordt, Andreas; Scholl,Carsten; Tezkan, Bulent
2006-06-14
Three long-offset transient electromagnetic (LOTEM) surveyswerecarried out at the active volcano Merapi in Central Java (Indonesia)during the years 1998, 2000, and 2001. The measurements focused on thegeneral resistivity structure of the volcanic edifice at depths of 0.5-2km and the further investigation of a southside anomaly. The measurementswere insufficient for a full 3D inversion scheme, which could enable theimaging of finely discretized resistivity distributions. Therefore, astable, damped least-squares joint-inversion approach is used to optimize3D models with a limited number of parameters. The mode ls feature therealistic simulation of topography, a layered background structure, andadditional coarse 3D blocks representing conductivity anomalies.Twenty-eight LOTEM transients, comprising both horizontal and verticalcomponents of the magnetic induction time derivative, were analyzed. Inview of the few unknowns, we were able to achieve reasonable data fits.The inversion results indicate an upwelling conductor below the summit,suggesting hydrothermal activity in the central volcanic complex. Ashallow conductor due to a magma-filled chamber, at depths down to 1 kmbelow the summit, suggested by earlier seismic studies, is not indicatedby the inversion results. In conjunction with an anomalous-density model,derived from arecent gravity study, our inversion results provideinformation about the southern geological structure resulting from amajor sector collapse during the Middle Merapi period. The density modelallows to assess a porosity range andthus an estimated vertical salinityprofile to explain the high conductivities on a larger scale, extendingbeyond the foothills of Merapi.
Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion.
Wyłomańska, A; Kumar, A; Połoczański, R; Vellaisamy, P
2016-10-01
In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.
Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion
NASA Astrophysics Data System (ADS)
Wyłomańska, A.; Kumar, A.; Połoczański, R.; Vellaisamy, P.
2016-10-01
In this paper we study the fractional Brownian motion (FBM) time changed by the inverse Gaussian (IG) process and its inverse, called the inverse to the inverse Gaussian (IIG) process. Some properties of the time-changed processes are similar to those of the classical FBM, such as long-range dependence. However, one can also observe different characteristics that are not satisfied by the FBM. We study the distributional properties of both subordinators, namely, IG and IIG processes, and also that of the FBM time changed by these subordinators. We establish also the connections between the subordinated processes considered and the continuous-time random-walk model. For the application part, we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters. The effectiveness of these methods is checked for simulated trajectories.
A Bayesian method for microseismic source inversion
NASA Astrophysics Data System (ADS)
Pugh, D. J.; White, R. S.; Christie, P. A. F.
2016-08-01
Earthquake source inversion is highly dependent on location determination and velocity models. Uncertainties in both the model parameters and the observations need to be rigorously incorporated into an inversion approach. Here, we show a probabilistic Bayesian method that allows formal inclusion of the uncertainties in the moment tensor inversion. This method allows the combination of different sets of far-field observations, such as P-wave and S-wave polarities and amplitude ratios, into one inversion. Additional observations can be included by deriving a suitable likelihood function from the uncertainties. This inversion produces samples from the source posterior probability distribution, including a best-fitting solution for the source mechanism and associated probability. The inversion can be constrained to the double-couple space or allowed to explore the gamut of moment tensor solutions, allowing volumetric and other non-double-couple components. The posterior probability of the double-couple and full moment tensor source models can be evaluated from the Bayesian evidence, using samples from the likelihood distributions for the two source models, producing an estimate of whether or not a source is double-couple. Such an approach is ideally suited to microseismic studies where there are many sources of uncertainty and it is often difficult to produce reliability estimates of the source mechanism, although this can be true of many other cases. Using full-waveform synthetic seismograms, we also show the effects of noise, location, network distribution and velocity model uncertainty on the source probability density function. The noise has the largest effect on the results, especially as it can affect other parts of the event processing. This uncertainty can lead to erroneous non-double-couple source probability distributions, even when no other uncertainties exist. Although including amplitude ratios can improve the constraint on the source probability
Equipment for the calibration of squareness standards
NASA Astrophysics Data System (ADS)
Hemming, Björn; Korhonen, Antti; Palosuo, Ilkka; Lassila, Antti
2012-09-01
In dimensional metrology, the measurement of squareness is a basic task for many purposes. At the Centre for Metrology and Accreditation (MIKES), a squareness measuring machine for traceable calibration of squares has been developed. The machine is able to measure a squareness standard of 1000 mm × 1000 mm maximum size. The system consists of a rotary table and a tactile displacement transducer with horizontal and vertical linear guides. The error sources of the developed equipment are presented together with a brief description of the calibration procedure. Implemented error compensation of the rotary table and one linear guide is described. The uncertainty estimate is presented for squareness angle measurement. The standard measurement uncertainty for steel or granite squares is 0.2″. We also present the results of an internal comparison of squareness measurements made with the developed machine and a high accuracy coordinate measuring machine. The results show good agreement.
Inverse heat conduction problems
NASA Astrophysics Data System (ADS)
Orlande, Helcio Rangel Barreto
We present the solution of the following inverse problems: (1) Inverse Problem of Estimating Interface Conductance Between Periodically Contacting Surfaces; (2) Inverse Problem of Estimating Interface Conductance During Solidification via Conjugate Gradient Method; (3) Determination of the Reaction Function in a Reaction-Diffusion Parabolic Problem; and (4) Simultaneous Estimation of Thermal Diffusivity and Relaxation Time with Hyperbolic Heat Conduction Model. Also, we present the solution of a direct problem entitled: Transient Thermal Constriction Resistance in a Finite Heat Flux Tube. The Conjugate Gradient Method with Adjoint Equation was used in chapters 1-3. The more general function estimation approach was treated in these chapters. In chapter 1, we solve the inverse problem of estimating the timewise variation of the interface conductance between periodically contacting solids, under quasi-steady-state conditions. The present method is found to be more accurate than the B-Spline approach for situations involving small periods, which are the most difficult on which to perform the inverse analysis. In chapter 2, we estimate the timewise variation of the interface conductance between casting and mold during the solidification of aluminum. The experimental apparatus used in this study is described. In chapter 3, we present the estimation of the reaction function in a one dimensional parabolic problem. A comparison of the present function estimation approach with the parameter estimation technique, wing B-Splines to approximate the reaction function, revealed that the use of function estimation reduces the computer time requirements. In chapter 4 we present a finite difference solution for the transient constriction resistance in a cylinder of finite length with a circular contact surface. A numerical grid generation scheme was used to concentrate grid points in the regions of high temperature gradients in order to reduce discretization errors. In chapter 6, we
Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion
NASA Technical Reports Server (NTRS)
Von Frese, R. R. B.; Hinze, W. J.; Braile, L. W.
1981-01-01
To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.
Deming's General Least Square Fitting
Rinard, Phillip
1992-02-18
DEM4-26 is a generalized least square fitting program based on Deming''s method. Functions built into the program for fitting include linear, quadratic, cubic, power, Howard''s, exponential, and Gaussian; others can easily be added. The program has the following capabilities: (1) entry, editing, and saving of data; (2) fitting of any of the built-in functions or of a user-supplied function; (3) plotting the data and fitted function on the display screen, with error limits if requested, and with the option of copying the plot to the printer; (4) interpolation of x or y values from the fitted curve with error estimates based on error limits selected by the user; and (5) plotting the residuals between the y data values and the fitted curve, with the option of copying the plot to the printer. If the plot is to be copied to a printer, GRAPHICS should be called from the operating system disk before the BASIC interpreter is loaded.
A comparison of direct and iterative finite element inversion techniques in dynamic elastography.
Honarvar, M; Rohling, R; Salcudean, S E
2016-04-21
As part of tissue elasticity imaging or elastography, an inverse problem needs to be solved to find the elasticity distribution from the measured displacements. The finite element method (FEM) is a common method for solving the inverse problem in dynamic elastography. This problem has been solved with both direct and iterative FEM schemes. Each of these methods has its own advantages and disadvantages which are examined in this paper. Choosing the data resolution and the excitation frequency are critical for achieving the best estimation of the tissue elasticity in FEM methods. In this paper we investigate the performance of both direct and iterative FEMs for different ranges of excitation frequency. A new form of iterative method is suggested here which requires a lower mesh density compared to the original form. Also two forms of the direct method are compared in this paper: one using the exact fit for derivatives calculation and the other using the least squares fit. We also perform a study on the spatial resolution of these methods using simulations. The comparison is also validated using a phantom experiment. The results suggest that the direct method with least squares fit is more robust to noise compared to other methods but has slightly lower resolution results. For example, for the homogenous region with 20 dB noise added to the data, the RMS error for the direct method with least squares fit is approximately half of the iterative method. It was observed that the ratio of voxel size to the wavelength should be within a specific range for the results to be reliable. For example for the direct method with least squares fit, for the case of 20 dB noise level, this ratio should be between 0.1 to 0.2. On balance, considering the much higher computational cost of the iterative method, the dependency of the iterative method on the initial guess, and the greater robustness of the direct method to noise, we suggest using the direct method with least squares fit for
A comparison of direct and iterative finite element inversion techniques in dynamic elastography
NASA Astrophysics Data System (ADS)
Honarvar, M.; Rohling, R.; Salcudean, S. E.
2016-04-01
As part of tissue elasticity imaging or elastography, an inverse problem needs to be solved to find the elasticity distribution from the measured displacements. The finite element method (FEM) is a common method for solving the inverse problem in dynamic elastography. This problem has been solved with both direct and iterative FEM schemes. Each of these methods has its own advantages and disadvantages which are examined in this paper. Choosing the data resolution and the excitation frequency are critical for achieving the best estimation of the tissue elasticity in FEM methods. In this paper we investigate the performance of both direct and iterative FEMs for different ranges of excitation frequency. A new form of iterative method is suggested here which requires a lower mesh density compared to the original form. Also two forms of the direct method are compared in this paper: one using the exact fit for derivatives calculation and the other using the least squares fit. We also perform a study on the spatial resolution of these methods using simulations. The comparison is also validated using a phantom experiment. The results suggest that the direct method with least squares fit is more robust to noise compared to other methods but has slightly lower resolution results. For example, for the homogenous region with 20 dB noise added to the data, the RMS error for the direct method with least squares fit is approximately half of the iterative method. It was observed that the ratio of voxel size to the wavelength should be within a specific range for the results to be reliable. For example for the direct method with least squares fit, for the case of 20 dB noise level, this ratio should be between 0.1 to 0.2. On balance, considering the much higher computational cost of the iterative method, the dependency of the iterative method on the initial guess, and the greater robustness of the direct method to noise, we suggest using the direct method with least squares fit for
Cascadia Tremor Spectra from Beamforming Fall Off as Frequency Squared
NASA Astrophysics Data System (ADS)
Gerstoft, P.; Zhang, J.; Shearer, P. M.; Yao, H.; Vidale, J. E.; Ghosh, A.
2010-12-01
The spectral decay of non-volcanic tremor (NVT) contains important information about the physical processes involved in Episodic Tremor and Slip (ETS). Using a small-aperture seismic array deployed on Big Skidder Hill, WA, we employ frequency-domain beamforming to obtain spatiotemporal spectral estimates of NVT activity in Cascadia on May 6-19, 2008. By shooting rays up from the plate boundary, potential tremor source locations are found where they best match the beamformer output. While energy from 2.5 Hz up to 25 Hz can radiate simultaneously from different patches, they often tend to come from the same region and migrate from the south to the north. An advantage of using beamforming for spectral analysis is that we can suppress noise and focus on the tremor phase by deriving the cross-power spectrum. This enables extracting tremor spectra for higher frequencies. We then compute the tremor source spectrum by using nearby small earthquakes to estimate empirical path and attenuation corrections. Our results show that displacement spectral amplitudes of the Cascadia tremor fall off roughly as the inverse of frequency squared over 5-20 Hz, agreeing with standard frequency-squared spectral models for earthquakes, but disagreeing with prior tremor analyses that have indicated a falloff proportional to frequency rather than frequency squared.
Full wave-field reflection coefficient inversion.
Dettmer, Jan; Dosso, Stan E; Holland, Charles W
2007-12-01
This paper develops a Bayesian inversion for recovering multilayer geoacoustic (velocity, density, attenuation) profiles from a full wave-field (spherical-wave) seabed reflection response. The reflection data originate from acoustic time series windowed for a single bottom interaction, which are processed to yield reflection coefficient data as a function of frequency and angle. Replica data for inversion are computed using a wave number-integration model to calculate the full complex acoustic pressure field, which is processed to produce a commensurate seabed response function. To address the high computational cost of calculating short range acoustic fields, the inversion algorithms are parallelized and frequency averaging is replaced by range averaging in the forward model. The posterior probability density is interpreted in terms of optimal parameter estimates, marginal distributions, and credibility intervals. Inversion results for the full wave-field seabed response are compared to those obtained using plane-wave reflection coefficients. A realistic synthetic study indicates that the plane-wave assumption can fail, producing erroneous results with misleading uncertainty bounds, whereas excellent results are obtained with the full-wave reflection inversion.
Inverse Functions and their Derivatives.
ERIC Educational Resources Information Center
Snapper, Ernst
1990-01-01
Presented is a method of interchanging the x-axis and y-axis for viewing the graph of the inverse function. Discussed are the inverse function and the usual proofs that are used for the function. (KR)
Intersections, ideals, and inversion
Vasco, D.W.
1998-10-01
Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.
Vacuum persistence and inversion of spin statistics in strong QED
Hwang, W-Y. Pauchy; Kim, Sang Pyo
2009-09-15
The vacuum persistence can be written as the Bose-Einstein distribution in spinor QED and as the Fermi-Dirac distribution in scalar QED exactly in a constant electric field and approximately in time-dependent electric fields. The inverse temperature is determined by the period of charged particle in the Euclidean time and the negative chemical potential by the ratio of the worldline instanton to the inverse temperature. The negativity of chemical potential is due to the vacuum instability under strong electric fields. The inversion of spin statistics in the vacuum persistence is a consequence of the Bogoliubov relations for fermions and bosons.
Ning, Hanwen; Qing, Guangyan; Jing, Xingjian
2016-11-01
The identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades. Several methods, such as searching principle-based algorithms, partially linear kernel methods, and coupled lattice methods, have been developed to address the identification problems. However, most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains. These are actually not applicable for some practical applications. In this paper, to tackle this issue, a novel kernel-based learning algorithm named integral least square regularization regression (ILSRR) is proposed, which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain. With this technique, a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified. Thereafter, with this novel inverse meshless collocation model, the ILSRR, and a multiple-kernel-based learning algorithm, a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations. Numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method.
Neutron spectrum unfolding using artificial neural network and modified least square method
NASA Astrophysics Data System (ADS)
Hosseini, Seyed Abolfazl
2016-09-01
In the present paper, neutron spectrum is reconstructed using the Artificial Neural Network (ANN) and Modified Least Square (MLSQR) methods. The detector's response (pulse height distribution) as a required data for unfolding of energy spectrum is calculated using the developed MCNPX-ESUT computational code (MCNPX-Energy engineering of Sharif University of Technology). Unlike the usual methods that apply inversion procedures to unfold the energy spectrum from the Fredholm integral equation, the MLSQR method uses the direct procedure. Since liquid organic scintillators like NE-213 are well suited and routinely used for spectrometry of neutron sources, the neutron pulse height distribution is simulated/measured in the NE-213 detector. The response matrix is calculated using the MCNPX-ESUT computational code through the simulation of NE-213 detector's response to monoenergetic neutron sources. For known neutron pulse height distribution, the energy spectrum of the neutron source is unfolded using the MLSQR method. In the developed multilayer perception neural network for reconstruction of the energy spectrum of the neutron source, there is no need for formation of the response matrix. The multilayer perception neural network is developed based on logsig, tansig and purelin transfer functions. The developed artificial neural network consists of two hidden layers of type hyperbolic tangent sigmoid transfer function and a linear transfer function in the output layer. The motivation of applying the ANN method may be explained by the fact that no matrix inversion is needed for energy spectrum unfolding. The simulated neutron pulse height distributions in each light bin due to randomly generated neutron spectrum are considered as the input data of ANN. Also, the randomly generated energy spectra are considered as the output data of the ANN. Energy spectrum of the neutron source is identified with high accuracy using both MLSQR and ANN methods. The results obtained from
Generalized adjustment by least squares ( GALS).
Elassal, A.A.
1983-01-01
The least-squares principle is universally accepted as the basis for adjustment procedures in the allied fields of geodesy, photogrammetry and surveying. A prototype software package for Generalized Adjustment by Least Squares (GALS) is described. The package is designed to perform all least-squares-related functions in a typical adjustment program. GALS is capable of supporting development of adjustment programs of any size or degree of complexity. -Author
The Square Light Clock and Special Relativity
ERIC Educational Resources Information Center
Galli, J. Ronald; Amiri, Farhang
2012-01-01
A thought experiment that includes a square light clock is similar to the traditional vertical light beam and mirror clock, except it is made up of four mirrors placed at a 45[degree] angle at each corner of a square of length L[subscript 0], shown in Fig. 1. Here we have shown the events as measured in the rest frame of the square light clock. By…
Sets of Mutually Orthogonal Sudoku Latin Squares
ERIC Educational Resources Information Center
Vis, Timothy; Petersen, Ryan M.
2009-01-01
A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…
40 CFR 761.306 - Sampling 1 meter square surfaces by random selection of halves.
Code of Federal Regulations, 2010 CFR
2010-07-01
..., PROCESSING, DISTRIBUTION IN COMMERCE, AND USE PROHIBITIONS Sampling Non-Porous Surfaces for Measurement-Based... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Sampling 1 meter square surfaces by...(b)(3) § 761.306 Sampling 1 meter square surfaces by random selection of halves. (a) Divide each...
An efficient method for inverse problems
NASA Technical Reports Server (NTRS)
Daripa, Prabir
1987-01-01
A new inverse method for aerodynamic design of subcritical airfoils is presented. The pressure distribution in this method can be prescribed in a natural way, i.e. as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving a single nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this problem determines the airfoil, the free stream Mach number M(sub x) and the upstream flow direction theta(sub x). The existence of a solution for any given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils.
Development of fully Bayesian multiple-time-window source inversion
NASA Astrophysics Data System (ADS)
Kubo, Hisahiko; Asano, Kimiyuki; Iwata, Tomotaka; Aoi, Shin
2016-03-01
In the estimation of spatiotemporal slip models, kinematic source inversions using Akaike's Bayesian Information Criterion (ABIC) and the multiple-time-window method have often been used. However, there are cases in which conventional ABIC-based source inversions do not work well in the determination of hyperparameters when a non-negative slip constraint is used. In order to overcome this problem, a new source inversion method was developed in this study. The new method introduces a fully Bayesian method into the kinematic multiple-time-window source inversion. The multiple-time-window method is one common way of parametrizing a source time function and is highly flexible in terms of the shape of the source time function. The probability distributions of model parameters and hyperparameters can be directly obtained by using the Markov chain Monte Carlo method. These probability distributions are useful for simply evaluating the uniqueness and reliability of the derived model, which is another advantage of a fully Bayesian method. This newly developed source inversion method was applied to the 2011 Ibaraki-oki, Japan, earthquake (Mw 7.9) to demonstrate its usefulness. It was demonstrated that the problem with using the conventional ABIC-based source inversion method for hyperparameter determination appeared in the spatiotemporal source inversion of this event and that the newly developed source inversion could overcome this problem.
The three-body problem with an inverse square law potential
NASA Astrophysics Data System (ADS)
Jiménez-Lara, Lidia; Piña, Eduardo
2003-09-01
We study the motion of three masses in a plane interacting with a central potential proportional to 1/r2 using the coordinates introduced recently by Piña. We show that this problem with four degrees of freedom (three angles and a distance related to the inertia moment of the system in these coordinates) is partially separable, and can be reduced to a problem with two degrees of freedom (two angles) with a new constant of motion. We find a symmetry of reflection (an involution) for this system and we use the symmetry lines to find periodic orbits in the angular coordinates. These orbits will not be periodic in general on the whole phase space because the coordinate of distance type grows as t when t→∞ and it is unbounded. However, if the inertia moment of the system remains constant, they will be periodic on the whole phase space.
Unveiling chameleon fields in tests of the gravitational inverse-square law
Upadhye, Amol; Gubser, Steven S.; Khoury, Justin
2006-11-15
Scalar self-interactions are known to weaken considerably the current constraints on scalar-mediated fifth forces. We consider a scalar field with a quartic self-interaction and gravitation-strength Yukawa couplings to matter particles. After discussing the phenomenology of this scalar field, we assess the ability of ongoing and planned experiments to detect the fifth force mediated by such a field. Assuming that the quartic and matter couplings are of order unity, the current-generation Eoet-Wash experiment at the University of Washington will be able to explore an interesting subset of parameter space. The next-generation Eoet-Wash experiment is expected to be able to detect, or to rule out, the fifth force due to such a scalar with unit quartic and matter couplings at the 3{sigma} confidence level.
Mean-squared-displacement statistical test for fractional Brownian motion
NASA Astrophysics Data System (ADS)
Sikora, Grzegorz; Burnecki, Krzysztof; Wyłomańska, Agnieszka
2017-03-01
Anomalous diffusion in crowded fluids, e.g., in cytoplasm of living cells, is a frequent phenomenon. A common tool by which the anomalous diffusion of a single particle can be classified is the time-averaged mean square displacement (TAMSD). A classical mechanism leading to the anomalous diffusion is the fractional Brownian motion (FBM). A validation of such process for single-particle tracking data is of great interest for experimentalists. In this paper we propose a rigorous statistical test for FBM based on TAMSD. To this end we analyze the distribution of the TAMSD statistic, which is given by the generalized chi-squared distribution. Next, we study the power of the test by means of Monte Carlo simulations. We show that the test is very sensitive for changes of the Hurst parameter. Moreover, it can easily distinguish between two models of subdiffusion: FBM and continuous-time random walk.
Trimming and procrastination as inversion techniques
NASA Astrophysics Data System (ADS)
Backus, George E.
1996-12-01
By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.
The Moore-Penrose Inverse of Block Magic Rectangles
ERIC Educational Resources Information Center
Hakopian, Y. R.; Eloyan, A. N.
2007-01-01
As is known, a semi-magic square is an "n x n" matrix having the sum of entries in each row and each column equal to a constant. This note generalizes this notion and introduce a special class of block matrices called "block magic rectangles." It is proved that the Moore-Penrose inverse of a block magic rectangle is also a block magic rectangle.
Equivalent Ground Conductivity Inversion in Maritime ASF Correction
NASA Astrophysics Data System (ADS)
Pu, Yurong; Xi, Xiaoli; Zhu, Hong
This letter presents an efficient method for the maritime Loran-C additional secondary factor (ASF) correction based on equivalent ground conductivity inversion. Using the proposed method, the accuracy of Loran-C system on maritime positioning, navigation, and timing (PNT) can be improved significantly with a limited number of surveys. Comparison with measured ASF results shows a root-mean-square error (RMSE) of less than 100ns in most areas.
Polynomial compensation, inversion, and approximation of discrete time linear systems
NASA Technical Reports Server (NTRS)
Baram, Yoram
1987-01-01
The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.
Generalized multi-point inverse airfoil design
NASA Technical Reports Server (NTRS)
Selig, Michael S.; Maughmer, Mark D.
1991-01-01
In a rather general sense, inverse airfoil design can be taken to mean the problem of specifying a desired set of airfoil characteristics, such as the airfoil maximum thickness ratio, pitching moment, part of the velocity distribution or boundary-layer development, etc., then from this information determine the corresponding airfoil shape. This paper presents a method which approaches the design problem from this perspective. In particular, the airfoil is divided into segments along which, together with the design conditions, either the velocity distribution or boundary-layer development may be prescribed. In addition to these local desired distributions, single parameters like the airfoil thickness can be specified. The problem of finding the airfoil shape is determined by coupling an incompressible, inviscid, inverse airfoil design method with a direct integral boundary-layer analysis method and solving the resulting nonlinear equations via a multidimensional Newton iteration technique. The approach is fast and easily allows for interactive design. It is also flexible and could be adapted to solving compressible, inverse airfoil design problems.
Efficient Geostatistical Inversion under Transient Flow Conditions in Heterogeneous Porous Media
NASA Astrophysics Data System (ADS)
Klein, Ole; Cirpka, Olaf A.; Bastian, Peter; Ippisch, Olaf
2014-05-01
The assessment of hydraulic aquifer parameters is important for the evaluation of anthropogenic impacts on groundwater resources. The distribution of these parameters determines flow paths and solute travel times and is therefore critical for the successful design and deployment of remediation schemes at contaminated sites. Direct measurement of these properties is not possible, making indirect observations through dependent quantities and parameter estimation a necessity. The geostatistical approach characterizes these hydraulic parameters without predetermined zonation. The parameter fields are treated as stochastic processes, optionally incorporating a priori information in the probability distribution. Maximizing the likelihood of the parameters with regard to the given observations yields a parameter estimate with high spatial resolution. This approach naturally leads to nonlinear least squares optimization problems, namely objective functions of the form L(Y ) = 1(Y ')TQ -Y1YY ' + 1[F(Y) - z]T Q-z1z [F(Y )- z], 2 2 where Y are the parameters, Y ' their deviations from the a priori estimate, QY Y their covariance matrix, z the measurements, Qzz their covariance matrix and F the forward model mapping parameters to observations. In theory, this objective function may be minimized using standard gradient-based techniques like Gauss-Newton. Due to the typically high number of parameters, however, this is not practical. Let nY be the number of parameters and nz the number of observations. Then QY Y and its inverse are both dense nY ×nY matrices, and the sensitivity matrix Hz := δz/δY is a nz ×nY matrix that has to be assembled using forward or adjoint model runs. Specialized schemes have been developed to reduce the dimensionality of the problem and avoid the high cost of handling products with QY Y -1. This enables efficient inversion in the case of a moderate number of observations as encountered in stationary inversion, where the cost of assembling Hz is in
Seismic imaging and inversion based on spectral-element and adjoint methods
NASA Astrophysics Data System (ADS)
Luo, Yang
action of the Hessian on an arbitrarily-chosen model perturbation, and the resolution function, the action of the resolution matrix on the arbitrarily-chosen model perturbation. Inner products between the two functions and the chosen model perturbation (properly normalized) are two scalars—the point-spread parameter and the resolution parameter. The two functions serve as trade-off maps between the chosen model perturbation and all other model parameters, whereas the two parameters indicate whether the chosen model perturbation is well resolved in the inversion. While the point-spread function and the point-spread parameter work in relative sense, the resolution function and the resolution parameter are absolute quantities, regardless of the misfit function used in the inversion. Besides the optimization point of view, we also treat inverse problems from Tarantola's perspective—the Bayesian inference, where each Earth model is associated with certain probability, preferably obeying multivariate normal distribution by choosing Cartesian model parameters, such as the logarithm of wavespeed. With a new limit-memory square root variable metric algorithm, we may sample the a posteriori distribution of model parameters, which allows statistical analysis on the inversion, e.g., addressing uncertainty and non-uniqueness of the inversion. Although, due to limit of time, seismic examples are to be added, analytical examples involving 20,000 model parameters validate our theory and algorithm, and it is promising that they can be easily adapted to real seismic applications. After solving both resolution and non-uniqueness issues, we finally extend capability of seismic inversions to consider noise simulations, i.e., by cross correlating noisy seismograms between pairs of seismic stations, without help of natural earthquakes and man-made explosions. At the end, we talk about implications of our studies on the model parameterization, in terms of both types of model parameters
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Discovering the Magic of Magic Squares
ERIC Educational Resources Information Center
Semanisinova, Ingrid; Trenkler, Marian
2007-01-01
The purpose of this article is to present a collection of problems that allow students to investigate magic squares and Latin squares, formulate their own conjectures about these mathematical objects, look for arguments supporting or disproving their conjectures, and finally establish and prove mathematical assertions. Each problem is completed…
Collinearity in Least-Squares Analysis
ERIC Educational Resources Information Center
de Levie, Robert
2012-01-01
How useful are the standard deviations per se, and how reliable are results derived from several least-squares coefficients and their associated standard deviations? When the output parameters obtained from a least-squares analysis are mutually independent, as is often assumed, they are reliable estimators of imprecision and so are the functions…
Neyman's Restricted Chi-Square Tests.
ERIC Educational Resources Information Center
Timm, Neil H.
Pearson's unrestricted chi-square procedure is reviewed, and an historical presentation of Neyman's restricted chi-square test is introduced with a discussion of its theory and applicability to education. An example of the Neyman procedure is discussed in detail to familiarize researchers with this useful technique for analyzing contingency…
Enhancing Students' Understanding of Square Roots
ERIC Educational Resources Information Center
Wiesman, Jeff L.
2015-01-01
Students enrolled in a middle school prealgebra or algebra course often struggle to conceptualize and understand the meaning of radical notation when it is introduced. For example, although it is important for students to approximate the decimal value of a number such as [square root of] 30 and estimate the value of a square root in the form of…
Three Perspectives on Teaching Least Squares
ERIC Educational Resources Information Center
Scariano, Stephen M.; Calzada, Maria
2004-01-01
The method of Least Squares is the most widely used technique for fitting a straight line to data, and it is typically discussed in several undergraduate courses. This article focuses on three developmentally different approaches for solving the Least Squares problem that are suitable for classroom exposition.
NASA Astrophysics Data System (ADS)
Alkhazov, G. D.; Vorobyov, A. A.; Dobrovolsky, A. V.; Inglessi, A. G.; Korolev, G. A.; Khanzadeev, A. V.
2015-05-01
In order to study the spatial structure of exotic nuclei, it was proposed at the Petersburg Nuclear Physics Institute (PNPI) to measure the differential cross section for small-angle proton elastic scattering in inverse kinematics. Several experiments in beams of 0.7-GeV/nucleon exotic nuclei were performed at the heavy-ion accelerator facility of GSI (Gesellschaft für Schwerionenforschung, Darmstadt, Germany) by using the IKAR ionization spectrometer developed at PNPI. The IKAR ionization chamber filled with hydrogen at a pressure of 10 bar served simultaneously as a target and as a recoil-proton detector, which measured the recoil-proton energy. The beam-particle scattering angle was also measured. The results obtained for the cross sections in question were analyzed on the basis of the Glauber-Sitenko theory using phenomenological nuclear-density distributions with two free parameters. Nuclear-matter distributions and root-mean-square radii were found for the nuclei under investigation. The size of the halo in the 6He, 8He, 11Li, and 14Be nuclei was determined among other things. Information about neutron distributions in nuclei was deduced by combining the data obtained here with the known values of the radii of proton distributions. A sizable neutron skin was revealed in the 8Li, 9Li, and 12Be nuclei.
Alkhazov, G. D.; Vorobyov, A. A.; Dobrovolsky, A. V. Inglessi, A. G.; Korolev, G. A.; Khanzadeev, A. V.
2015-05-15
In order to study the spatial structure of exotic nuclei, it was proposed at the Petersburg Nuclear Physics Institute (PNPI) to measure the differential cross section for small-angle proton elastic scattering in inverse kinematics. Several experiments in beams of 0.7-GeV/nucleon exotic nuclei were performed at the heavy-ion accelerator facility of GSI (Gesellschaft für Schwerionenforschung, Darmstadt, Germany) by using the IKAR ionization spectrometer developed at PNPI. The IKAR ionization chamber filled with hydrogen at a pressure of 10 bar served simultaneously as a target and as a recoil-proton detector, which measured the recoil-proton energy. The beam-particle scattering angle was also measured. The results obtained for the cross sections in question were analyzed on the basis of the Glauber-Sitenko theory using phenomenological nuclear-density distributions with two free parameters. Nuclear-matter distributions and root-mean-square radii were found for the nuclei under investigation. The size of the halo in the {sup 6}He, {sup 8}He, {sup 11}Li, and {sup 14}Be nuclei was determined among other things. Information about neutron distributions in nuclei was deduced by combining the data obtained here with the known values of the radii of proton distributions. A sizable neutron skin was revealed in the {sup 8}Li, {sup 9}Li, and {sup 12}Be nuclei.
NASA Astrophysics Data System (ADS)
Tozer-Loft, Stephen M.; Walton, Lee; Forster, David M. C.; Kemeny, Andras A.
1999-08-01
A function derived from the geometry of brachytherapy dose distributions is applied to stereotactic radiosurgery and an algorithm for the production of a novel dose-volume histogram, the Anderson inverse-square shifted dose-volume histogram (DVH), is proposed. The expected form of the function to be plotted is checked by calculating its value for single focus exposures, and its application to clinical examples of Gamma Knife treatments described. The technique is shown to provide a valuable tool for assessing the adequacy of radiosurgical plans and comparing and reporting dose distributions.
Full-Waveform Inversion Method for Data Measured by the CONSERT Instrument aboard Rosetta
NASA Astrophysics Data System (ADS)
Statz, C.; Plettemeier, D.; Herique, A.; Kofman, W. W.
2014-12-01
The primary scientific objective of the Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT) aboard Rosetta is to perform a dielectric characterization of comet 67P/Chuyurmov-Gerasimenko's nucleus by means of a bi-static sounding between the lander Philae launched onto the comet's surface and the orbiter Rosetta. For the sounding the lander part of CONSERT will receive and process the radio signal emitted by the orbiter part of the instrument and transmit a signal to the orbiter to be received by CONSERT. With data measured during the first science phase, a three-dimensional model of the material distribution with regard to the complex dielectric permittivity of the comet's nucleus is to be reconstructed. In order to perform the 3D characterization of the nucleus we employ a full-waveform least-squares based inversion in time-domain. The reconstruction is performed on the envelope of the received signal. The direct problem of simulating the wave-propagation inside the comet's nucleus is modelled using a wideband nonstandard finite-differences in time-domain approach and a compensation method to account for the differences in free-space path-loss due to the removal of the carrier in the simulation. This approach will yield an approximation of the permittivity distribution including features large compared to the bandwith of the sounding signal. In order to account for restrictions on the measurement positions by the orbitography and limitations on the instrument dynamic range we employ a regularization technique where the permittivity distribution and the gradient with regard to the permittivity is projected in a domain defined by a viable model of the spatial material distribution. The least-squares optimization step of the reconstruction is performed in such domain on a reduced set of parameters. To demonstrate the viability of the proposed approaches we provide reconstruction results based on simulation data and scale-model laboratory
Antarctic Crustal Thickness from Gravity Inversion
NASA Astrophysics Data System (ADS)
Vaughan, A. P.; Kusznir, N. J.; Ferraccioli, F.; Jordan, T. A.
2013-12-01
Using gravity anomaly inversion, we have produced the first comprehensive regional maps of crustal thickness and oceanic lithosphere distribution for Antarctica and the Southern Ocean. We determine Moho depth, crustal basement thickness, continental lithosphere thinning (1-1/β) and ocean-continent transition location using a 3D spectral domain gravity inversion method, which incorporates a lithosphere thermal gravity anomaly correction. The continental lithosphere thinning distribution, used to define the initial thermal model temperature perturbation is derived from the gravity inversion and uses no a priori isochron information; as a consequence the gravity inversion method provides a prediction of ocean-continent transition location, which is independent of ocean isochron information. The gravity anomaly contribution from ice thickness is included in the gravity inversion, as is the contribution from sediments which assumes a compaction controlled sediment density increase with depth. Data used in the gravity inversion are elevation and bathymetry, free-air gravity anomaly, the most recent Bedmap2 ice thickness and bedrock topography compilation south of 60 degrees south (Fretwell et al., 2013) and relatively sparse constraints on sediment thickness. Our gravity inversion study predicts thick crust (> 45 km) under interior East Antarctica penetrated by narrow continental rifts that feature relatively thinner crust. The East Antarctic Rift System (EARS) is a major Permian to Cretaceous age rift system that appears to extend from the continental margin at the Lambert Rift to the South Pole region, a distance of 2500 km. This is comparable in scale to the well-studied East African rift system. Intermediate crustal thickness with an inferred linear rift fabric is predicted under Coates Land. An extensive region of either thick oceanic crust or highly thinned continental crust is predicted offshore Oates Land and north Victoria Land, and also off West Antarctica
An inverse problem by boundary element method
Tran-Cong, T.; Nguyen-Thien, T.; Graham, A.L.
1996-02-01
Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.
Voxel inversion of airborne electromagnetic data for improved model integration
NASA Astrophysics Data System (ADS)
Fiandaca, Gianluca; Auken, Esben; Kirkegaard, Casper; Vest Christiansen, Anders
2014-05-01
Inversion of electromagnetic data has migrated from single site interpretations to inversions including entire surveys using spatial constraints to obtain geologically reasonable results. Though, the model space is usually linked to the actual observation points. For airborne electromagnetic (AEM) surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space, and the geophysical information has to be relocated for integration in (hydro)geological models. We have developed a new geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the soil properties is computed everywhere by means of an interpolation function (e.g. inverse distance or kriging). Given this definition of the voxel model space, the 1D forward responses of the AEM data are computed as follows: 1) a 1D model subdivision, in terms of model thicknesses, is defined for each 1D data set, creating "virtual" layers. 2) the "virtual" 1D models at the sounding positions are finalized by interpolating the soil properties (the resistivity) in the center of the "virtual" layers. 3) the forward response is computed in 1D for each "virtual" model. We tested the new inversion scheme on an AEM survey carried out with the SkyTEM system close to Odder, in Denmark. The survey comprises 106054 dual mode AEM soundings, and covers an area of approximately 13 km X 16 km. The voxel inversion was carried out on a structured grid of 260 X 325 X 29 xyz nodes (50 m xy spacing), for a total of 2450500 inversion parameters. A classical spatially constrained inversion (SCI) was carried out on the same data set, using 106054
Hicks, H.R.; Dory, R.A.; Holmes, J.A.
1983-01-01
We illustrate in some detail a 2D inverse-equilibrium solver that was constructed to analyze tokamak configurations and stellarators (the latter in the context of the average method). To ensure that the method is suitable not only to determine equilibria, but also to provide appropriately represented data for existing stability codes, it is important to be able to control the Jacobian, tilde J is identical to delta(R,Z)/delta(rho, theta). The form chosen is tilde J = J/sub 0/(rho)R/sup l/rho where rho is a flux surface label, and l is an integer. The initial implementation is for a fixed conducting-wall boundary, but the technique can be extended to a free-boundary model.
NASA Technical Reports Server (NTRS)
Ostro, Steven J.; Connelly, Robert
1987-01-01
One of the most fundamental physical properties of any asteroid is its shape. Lightcurves provide the only source of shape information for most asteroids. Unfortunately, the functional form of a lightcurve is determined by the viewing/illumination geometry and the asteroid's light scattering characteristics as well as its shape, and in general it is impossible to determine an asteroid's shape from lightcurves. A technique called convex-profile inversion (CPI) that obtains a convex profile, P, from any lightcurve is introduced. If certain ideal conditions are satisfied, then P is an estimator for the asteroid's mean cross section, C, a convex set defined as the average of all cross sections C(z) cut by planes a distance z above the asteroids's equatorial plane. C is therefore a 2-D average of the asteroid's 3-D shape.
Eta Squared, Partial Eta Squared, and Misreporting of Effect Size in Communication Research.
ERIC Educational Resources Information Center
Levine, Timothy R.; Hullett, Craig R.
2002-01-01
Alerts communication researchers to potential errors stemming from the use of SPSS (Statistical Package for the Social Sciences) to obtain estimates of eta squared in analysis of variance (ANOVA). Strives to clarify issues concerning the development and appropriate use of eta squared and partial eta squared in ANOVA. Discusses the reporting of…
A duct mapping method using least squares support vector machines
NASA Astrophysics Data System (ADS)
Douvenot, RéMi; Fabbro, Vincent; Gerstoft, Peter; Bourlier, Christophe; Saillard, Joseph
2008-12-01
This paper introduces a "refractivity from clutter" (RFC) approach with an inversion method based on a pregenerated database. The RFC method exploits the information contained in the radar sea clutter return to estimate the refractive index profile. Whereas initial efforts are based on algorithms giving a good accuracy involving high computational needs, the present method is based on a learning machine algorithm in order to obtain a real-time system. This paper shows the feasibility of a RFC technique based on the least squares support vector machine inversion method by comparing it to a genetic algorithm on simulated and noise-free data, at 1 and 5 GHz. These data are simulated in the presence of ideal trilinear surface-based ducts. The learning machine is based on a pregenerated database computed using Latin hypercube sampling to improve the efficiency of the learning. The results show that little accuracy is lost compared to a genetic algorithm approach. The computational time of a genetic algorithm is very high, whereas the learning machine approach is real time. The advantage of a real-time RFC system is that it could work on several azimuths in near real time.
NASA Astrophysics Data System (ADS)
Hendricks Franssen, H.-J.; Alcolea, A.; Riva, M.; Bakr, M.; van de Wiel, N.; Stauffer, F.; Guadagnini, A.,
2009-04-01
While several inverse modeling methods for groundwater flow have been developed during the last decades, hardly any comparisons among them have been published. We present a comparison of the performance of seven inverse methods, the Regularized Pilot Points Method (both in its classical estimation (RPPM-CE) and Monte Carlo (MC) simulation (RPPM-CS) variants), the Monte-Carlo variant of the Representer Method (RM), the Sequential-Self Calibration method (SSC), the Zonation Method (ZM), the Moment Equations Method (MEM) and a recently developed Semi-Analytical Method (SAM). The aforementioned methods are applied to a two-dimensional synthetic set-up, depicting the steady-state groundwater flow around an extraction well in the presence of distributed recharge. Their relative performances were assessed in terms of characterization of (a) the log-transmissivity field, (b) the hydraulic head distribution and (c) the well catchment delineation with respect to the reference scenario. Simulations were performed for a mildly and strongly heterogeneous transmissivity field. Adopted comparison measures include the absolute mean error, the root mean square error and the average ensemble standard deviation (whenever a method allows evaluating it) of the log-transmissivity and hydraulic head distributions. In addition, the estimated median and reference well catchments were compared and the uncertainty associated with the estimated catchment was evaluated. We found that the MC-based methods (RPPM-CS, RM and SSC) yield very similar results in all tested scenarios, despite they use different parameterization schemes and different objective functions. The linear correlation coefficient between the estimates obtained by the different MC methods increases with the number of stochastic realizations adopted and attains values up to 0.99 for 500 stochastic realisations. For the mildly heterogeneous case, the other inverse methods (i.e., non MC) yielded results which were consistent with
Investigating bias in squared regression structure coefficients
Nimon, Kim F.; Zientek, Linda R.; Thompson, Bruce
2015-01-01
The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients. PMID:26217273
Investigating bias in squared regression structure coefficients.
Nimon, Kim F; Zientek, Linda R; Thompson, Bruce
2015-01-01
The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.
Spacecraft inertia estimation via constrained least squares
NASA Technical Reports Server (NTRS)
Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.
2006-01-01
This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.
Simultaneous Inversion of Full Data Bandwidth by Tomographic Full Waveform Inversion
NASA Astrophysics Data System (ADS)
Almomin, A. A.; Biondi, B. C.
2015-12-01
The convergence of full-waveform inversion can be improved by extending the velocity model along either the subsurface-offset axis or the time-lag axis. The extension of the velocity model along the time-lag axis enables us to linearly model large time shifts caused by velocity perturbations. This linear modeling was based on a new linearization of the scalar wave equation in which perturbation of the extended slowness squared was convolved in time with the second time derivative of the background wavefield. The linearization was accurate for reflected events and transmitted events. We determined that it can effectively model conventional reflection data as well as modern long-offset data containing diving waves. It also enabled the simultaneous inversion of reflections and diving waves, even when the starting velocity model was far from being accurate. We solved the optimization problem related to the inversion with a nested algorithm. The inner iterations were based on the proposed linearization and on a mixing of scales between the short- and long-wavelength components of the velocity model. We significantly improved the convergence rate by preconditioning the extended model to balance the amplitude-versus-angle behavior of the wave-equation and by imposing wavelength continuation of the gradient in the outer loop. Numerical tests performed on synthetic data modeled on the Marmousi model and on Chevron's FWI blind-test data demonstrated the global convergence properties as well as the high-resolution potential of the proposed method.
[MEG inverse solution using Gauss-Newton algorithm modified by Moore-Penrose inversion].
Li, J
2001-06-01
In magnetoencephalogram(MEG) basic studies, it is an important issue to estimate magnetic source parameters by inverse solution. It is known that the magnetic field equations are nonlinear, thus explicit solutions are difficult to obtain. However optimization methods are available to this parameter estimation. In many usually used nonlinear local optimization algorithms, Gauss-Newton's is of fast convergent speed. When this algorithm is used, the singularity of the Jacobien matrix about the minimum least square error must be considered carefully. If the matrix is singular, the equation for searching direction has no general solution. One way to overcome this problem is to use negative gradient as searching direction, but it may cause descent of convergent speed. Another way is known as Levenberg-Marquardt algorithm which makes the matrix non-singular by adding some improved factors to it. In this paper we utilize Moore-Penrose inversion for the solution of iterative searching direction equation. In appendix we demonstrate that the searching direction obtained by the proposed method is successful. Computer simulation also demonstrates that by reasonable selection of initial iterative values, the modified Gauss-Newton algorithm is effective for MEG inverse solution in the case with one or two source dipoles.
Least squares in calibration: dealing with uncertainty in x.
Tellinghuisen, Joel
2010-08-01
The least-squares (LS) analysis of data with error in x and y is generally thought to yield best results when carried out by minimizing the "total variance" (TV), defined as the sum of the properly weighted squared residuals in x and y. Alternative "effective variance" (EV) methods project the uncertainty in x into an effective contribution to that in y, and though easier to employ are considered to be less reliable. In the case of a linear response function with both sigma(x) and sigma(y) constant, the EV solutions are identically those from ordinary LS; and Monte Carlo (MC) simulations reveal that they can actually yield smaller root-mean-square errors than the TV method. Furthermore, the biases can be predicted from theory based on inverse regression--x upon y when x is error-free and y is uncertain--which yields a bias factor proportional to the ratio sigma(x)(2)/sigma(xm)(2) of the random-error variance in x to the model variance. The MC simulations confirm that the biases are essentially independent of the error in y, hence correctable. With such bias corrections, the better performance of the EV method in estimating the parameters translates into better performance in estimating the unknown (x(0)) from measurements (y(0)) of its response. The predictability of the EV parameter biases extends also to heteroscedastic y data as long as sigma(x) remains constant, but the estimation of x(0) is not as good in this case. When both x and y are heteroscedastic, there is no known way to predict the biases. However, the MC simulations suggest that for proportional error in x, a geometric x-structure leads to small bias and comparable performance for the EV and TV methods.
Inverse statistical mechanics, lattice packings, and glasses
NASA Astrophysics Data System (ADS)
Marcotte, Etienne
Computer simulation methods enable the investigation of systems and properties that are intractable by purely analytical or experimental approaches. Each chapter of this dissertation contains an application of simulation methods to solve complex physical problems consisting of interacting many-particle or many-spin systems. The problems studied in this dissertation can be divided up into the following two broad categories: inverse and forward problems. The inverse problems considered are those in which we construct an interaction potential such that the corresponding ground state is a targeted configuration. In Chapters 2 and 3, we devise convex pair-potential functions that result in low-coordinated ground states. Chapter 2 describes targeted ground states that are the square and honeycomb crystals, while in Chapter 3 the targeted ground state is the diamond crystal. Chapter 4 applies similar techniques to explicitly enumerate all unique ground states up to a given system size, for spin configurations that interact according to generalized isotropic Ising potentials with finite range. We also consider forward statistical-mechanical problems. In Chapter 5, we adapt a linear programming algorithm to find the densest lattice packings across Euclidean space dimensions. In Chapter 6, we demonstrate that for two different glass models a signature of the glass transition is apparent well before the transition temperature is reached. In both models, this signature appears as nonequilibrium length scales that grow upon supercooling.
Inverse problems biomechanical imaging (Conference Presentation)
NASA Astrophysics Data System (ADS)
Oberai, Assad A.
2016-03-01
It is now well recognized that a host of imaging modalities (a list that includes Ultrasound, MRI, Optical Coherence Tomography, and optical microscopy) can be used to "watch" tissue as it deforms in response to an internal or external excitation. The result is a detailed map of the deformation field in the interior of the tissue. This deformation field can be used in conjunction with a material mechanical response to determine the spatial distribution of material properties of the tissue by solving an inverse problem. Images of material properties thus obtained can be used to quantify the health of the tissue. Recently, they have been used to detect, diagnose and monitor cancerous lesions, detect vulnerable plaque in arteries, diagnose liver cirrhosis, and possibly detect the onset of Alzheimer's disease. In this talk I will describe the mathematical and computational aspects of solving this class of inverse problems, and their applications in biology and medicine. In particular, I will discuss the well-posedness of these problems and quantify the amount of displacement data necessary to obtain a unique property distribution. I will describe an efficient algorithm for solving the resulting inverse problem. I will also describe some recent developments based on Bayesian inference in estimating the variance in the estimates of material properties. I will conclude with the applications of these techniques in diagnosing breast cancer and in characterizing the mechanical properties of cells with sub-cellular resolution.
Inverse boundary-layer technique for airfoil design
NASA Technical Reports Server (NTRS)
Henderson, M. L.
1979-01-01
A description is presented of a technique for the optimization of airfoil pressure distributions using an interactive inverse boundary-layer program. This program allows the user to determine quickly a near-optimum subsonic pressure distribution which meets his requirements for lift, drag, and pitching moment at the desired flow conditions. The method employs an inverse turbulent boundary-layer scheme for definition of the turbulent recovery portion of the pressure distribution. Two levels of pressure-distribution architecture are used - a simple roof top for preliminary studies and a more complex four-region architecture for a more refined design. A technique is employed to avoid the specification of pressure distributions which result in unrealistic airfoils, that is, those with negative thickness. The program allows rapid evaluation of a designed pressure distribution off-design in Reynolds number, transition location, and angle of attack, and will compute an airfoil contour for the designed pressure distribution using linear theory.
Seismic Sensor orientation by complex linear least squares
NASA Astrophysics Data System (ADS)
Grigoli, Francesco; Cesca, Simone; Krieger, Lars; Olcay, Manuel; Tassara, Carlos; Sobiesiak, Monika; Dahm, Torsten
2014-05-01
Poorly known orientation of the horizontal components of seismic sensors is a common problem that limits data analysis and interpretation for several acquisition setups, including linear arrays of geophones deployed in borehole installations, ocean bottom seismometers deployed at the sea-floor and surface seismic arrays. To solve this problem we propose an inversion method based on complex linear least squares method. Relative orientation angles, with respect to a reference sensor, are retrieved by minimizing the l2-norm between the complex traces (hodograms) of adjacent pairs of sensors in a least-squares sense. The absolute orientations are obtained in a second step by the polarization analysis of stacked seismograms of a seismic event with known location. This methodology can be applied without restrictions, if the plane wave approximation for wavefields recorded by each pair of sensors is valid. In most cases, it is possible to satisfy this condition by low-pass filtering the recorded waveform. The main advantage of our methodology is that, finding the estimation of the relative orientations of seismic sensors in complex domain is a linear inverse problem, which allows a direct solution corresponding to the global minimum of a misfit function. It is also possible to use simultaneously more than one independent dataset (e.g. using several seismic events simultaneously) to better constrain the solution of the inverse problem itself. Furthermore, by a computational point of view, our method results faster than the relative orientation methods based on waveform cross-correlation. Our methodology can be also applied for testing the correct orientation/alignment of multicomponent land stations in seismological arrays or temporary networks and for determining the absolute orientation of OBS stations and borehole arrays. We first apply our method to real data resembling two different acquisition setups: a borehole sensor array deployed in a gas field located in the
Inverse models: A necessary next step in ground-water modeling
Poeter, E.P.; Hill, M.C.
1997-01-01
Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.
Imaging of stellar surfaces with the Occamian approach and the least-squares deconvolution technique
NASA Astrophysics Data System (ADS)
Järvinen, S. P.; Berdyugina, S. V.
2010-10-01
Context. We present in this paper a new technique for the indirect imaging of stellar surfaces (Doppler imaging, DI), when low signal-to-noise spectral data have been improved by the least-squares deconvolution (LSD) method and inverted into temperature maps with the Occamian approach. We apply this technique to both simulated and real data and investigate its applicability for different stellar rotation rates and noise levels in data. Aims: Our goal is to boost the signal of spots in spectral lines and to reduce the effect of photon noise without loosing the temperature information in the lines. Methods: We simulated data from a test star, to which we added different amounts of noise, and employed the inversion technique based on the Occamian approach with and without LSD. In order to be able to infer a temperature map from LSD profiles, we applied the LSD technique for the first time to both the simulated observations and theoretical local line profiles, which remain dependent on temperature and limb angles. We also investigated how the excitation energy of individual lines effects the obtained solution by using three submasks that have lines with low, medium, and high excitation energy levels. Results: We show that our novel approach enables us to overcome the limitations of the two-temperature approximation, which was previously employed for LSD profiles, and to obtain true temperature maps with stellar atmosphere models. The resulting maps agree well with those obtained using the inversion code without LSD, provided the data are noiseless. However, using LSD is only advisable for poor signal-to-noise data. Further, we show that the Occamian technique, both with and without LSD, approaches the surface temperature distribution reasonably well for an adequate spatial resolution. Thus, the stellar rotation rate has a great influence on the result. For instance, in a slowly rotating star, closely situated spots are usually recovered blurred and unresolved, which
Anomalous structural transition of confined hard squares.
Gurin, Péter; Varga, Szabolcs; Odriozola, Gerardo
2016-11-01
Structural transitions are examined in quasi-one-dimensional systems of freely rotating hard squares, which are confined between two parallel walls. We find two competing phases: one is a fluid where the squares have two sides parallel to the walls, while the second one is a solidlike structure with a zigzag arrangement of the squares. Using transfer matrix method we show that the configuration space consists of subspaces of fluidlike and solidlike phases, which are connected with low probability microstates of mixed structures. The existence of these connecting states makes the thermodynamic quantities continuous and precludes the possibility of a true phase transition. However, thermodynamic functions indicate strong tendency for the phase transition and our replica exchange Monte Carlo simulation study detects several important markers of the first order phase transition. The distinction of a phase transition from a structural change is practically impossible with simulations and experiments in such systems like the confined hard squares.
A spectral mimetic least-squares method
Bochev, Pavel; Gerritsma, Marc
2014-09-01
We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less
A spectral mimetic least-squares method
Bochev, Pavel; Gerritsma, Marc
2014-09-01
We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.
Aquifer Structure Identification Using Stochastic Inversion
Harp, Dylan R; Dai, Zhenxue; Wolfsberg, Andrew V; Vrugt, Jasper A
2008-01-01
This study presents a stochastic inverse method for aquifer structure identification using sparse geophysical and hydraulic response data. The method is based on updating structure parameters from a transition probability model to iteratively modify the aquifer structure and parameter zonation. The method is extended to the adaptive parameterization of facies hydraulic parameters by including these parameters as optimization variables. The stochastic nature of the statistical structure parameters leads to nonconvex objective functions. A multi-method genetically adaptive evolutionary approach (AMALGAM-SO) was selected to perform the inversion given its search capabilities. Results are obtained as a probabilistic assessment of facies distribution based on indicator cokriging simulation of the optimized structural parameters. The method is illustrated by estimating the structure and facies hydraulic parameters of a synthetic example with a transient hydraulic response.
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; Tartakovsky, Daniel M.
2015-06-01
In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
Optical properties of silicon inverse opals
NASA Astrophysics Data System (ADS)
Wei, Hong
Silicon inverse opals are artificial structures in which nearly monodisperse, close-packed air bubbles are embedded in a silicon matrix. If properly tailored, this structure can exhibit a photonic band gap (PBG) in the near infrared spectral region. The PBG can block light propagation in any direction, allowing the control of light flow in the material. Silicon inverse opals can be fabricated by infiltrating amorphous silicon into silica colloidal crystals and then etching away the silica. In this thesis, the structural defects of silica colloidal crystals and the optical properties of silicon inverse opals are studied. First, by using laser-scanning confocal microscopy, the concentration and distribution of stacking faults and vacancies were quantified in silica colloidal crystals. It's shown that silica colloidal crystals show strong tendency toward face-center-cubic structure with the vacancy density as small as 5 x 10-4. Second, by combining optical microscopy and Fourier Transform Infrared (FTIR) spectroscopy, the transmission and reflection spectra of silicon inverse opals along the [111] direction were measured. Combined with the calculation of transmission and reflection spectra by Transfer Matrix Methods, it is concluded that the strong light attenuation in silicon inverse opals is due to the enhanced absorption (>600%) in silicon materials. Third, by using optical pump-probe techniques, the photo-induced ultra-fast reflection changes in silicon inverse opals were examined. The pump-generated free carriers cause the reflection in the band gap region to change after ˜0.5 ps. For the first few ps, the main effect is a decrease in reflectivity due to nonlinear absorption. After ˜5 ps, this effect disappears and an unexpected blue spectral shift is seen in the photonic band gap. The refractive index decreases due to optically-induced strain born the thermal expansion mismatch between silicon and its native oxide. Finally, by infiltrating silicon inverse
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
Deflection And Stress In Preloaded Square Membrane
NASA Technical Reports Server (NTRS)
Hermida, Alfonso
1991-01-01
Theoretical analysis yields equations for transverse deflection of, and stresses in, square membrane subject to both uniform transverse load and tension preloads applied uniformly along the edges. Follows energy/virtual-displacement approach. Basic equation expresses strain energy in membrane as double integral, over x and y coordinates of square, of function of longitudinal strains, shear strain, thickness of membrane, and Young's modulus and Poissons's ratio of membrane material.
Modular theory of inverse systems
NASA Technical Reports Server (NTRS)
1979-01-01
The relationship between multivariable zeros and inverse systems was explored. A definition of zero module is given in such a way that it is basis independent. The existence of essential right and left inverses were established. The way in which the abstract zero module captured previous definitions of multivariable zeros is explained and examples are presented.
Objectified quantification of uncertainties in Bayesian atmospheric inversions
NASA Astrophysics Data System (ADS)
Berchet, A.; Pison, I.; Chevallier, F.; Bousquet, P.; Bonne, J.-L.; Paris, J.-D.
2014-07-01
Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. At the meso-scale, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results and enhance the classical Bayesian inversion framework through a marginalization on all the plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is complicated and not explicitly describable. We then carry out a Monte-Carlo sampling relying on an approximation of the probability of occurence of the error distributions. This approximation is deduced from the well-tested algorithm of the Maximum of Likelihood. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly includes the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of emission aggregation pattern and sampling protocol in order to reduce the computation costs of the method. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the meso-scale with real observation sites in Eurasia. Observing System Simulation Experiments are carried out
Objectified quantification of uncertainties in Bayesian atmospheric inversions
NASA Astrophysics Data System (ADS)
Berchet, A.; Pison, I.; Chevallier, F.; Bousquet, P.; Bonne, J.-L.; Paris, J.-D.
2015-05-01
Classical Bayesian atmospheric inversions process atmospheric observations and prior emissions, the two being connected by an observation operator picturing mainly the atmospheric transport. These inversions rely on prescribed errors in the observations, the prior emissions and the observation operator. When data pieces are sparse, inversion results are very sensitive to the prescribed error distributions, which are not accurately known. The classical Bayesian framework experiences difficulties in quantifying the impact of mis-specified error distributions on the optimized fluxes. In order to cope with this issue, we rely on recent research results to enhance the classical Bayesian inversion framework through a marginalization on a large set of plausible errors that can be prescribed in the system. The marginalization consists in computing inversions for all possible error distributions weighted by the probability of occurrence of the error distributions. The posterior distribution of the fluxes calculated by the marginalization is not explicitly describable. As a consequence, we carry out a Monte Carlo sampling based on an approximation of the probability of occurrence of the error distributions. This approximation is deduced from the well-tested method of the maximum likelihood estimation. Thus, the marginalized inversion relies on an automatic objectified diagnosis of the error statistics, without any prior knowledge about the matrices. It robustly accounts for the uncertainties on the error distributions, contrary to what is classically done with frozen expert-knowledge error statistics. Some expert knowledge is still used in the method for the choice of an emission aggregation pattern and of a sampling protocol in order to reduce the computation cost. The relevance and the robustness of the method is tested on a case study: the inversion of methane surface fluxes at the mesoscale with virtual observations on a realistic network in Eurasia. Observing system
A perturbative density functional theory for square-well fluids.
Jin, Zhehui; Tang, Yiping; Wu, Jianzhong
2011-05-07
We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.
Inverse problem in hydrogeology
NASA Astrophysics Data System (ADS)
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le
Image Appraisal for 2D and 3D Electromagnetic Inversion
Alumbaugh, D.L.; Newman, G.A.
1999-01-28
Linearized methods are presented for appraising image resolution and parameter accuracy in images generated with two and three dimensional non-linear electromagnetic inversion schemes. When direct matrix inversion is employed, the model resolution and posterior model covariance matrices can be directly calculated. A method to examine how the horizontal and vertical resolution varies spatially within the electromagnetic property image is developed by examining the columns of the model resolution matrix. Plotting the square root of the diagonal of the model covariance matrix yields an estimate of how errors in the inversion process such as data noise and incorrect a priori assumptions about the imaged model map into parameter error. This type of image is shown to be useful in analyzing spatial variations in the image sensitivity to the data. A method is analyzed for statistically estimating the model covariance matrix when the conjugate gradient method is employed rather than a direct inversion technique (for example in 3D inversion). A method for calculating individual columns of the model resolution matrix using the conjugate gradient method is also developed. Examples of the image analysis techniques are provided on 2D and 3D synthetic cross well EM data sets, as well as a field data set collected at the Lost Hills Oil Field in Central California.
NASA Astrophysics Data System (ADS)
Liu, Boda; Liang, Yan
2017-04-01
Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.
Creation of identical multiple focal spots with prescribed axial distribution.
Yu, Yanzhong; Zhan, Qiwen
2015-10-01
We present a scheme for the construction of coaxially equidistant multiple focal spots with identical intensity profiles for each individual focus and a predetermined number and spacing. To achieve this, the radiation field from an antenna is reversed and then gathered by high numerical aperture objective lenses. Radiation patterns from three types of line sources, i.e., the electric current, magnetic current and electromagnetic current distributions, with cosine-squared taper are respectively employed to generate predominately longitudinally polarized bright spots, azimuthally polarized doughnuts, and focal spots with a perfect spherically symmetric intensity distribution. The required illuminations at the pupil plane of a 4Pi focusing configuration for the creation of these identical multiple focal spots can be easily derived by solving the inverse problem of the antenna radiation field. These unique focal field distributions may find potential applications in laser direct writing and optical microscopy, as well as multiple-particle trapping, alignment, and acceleration along the optical axis.
NASA Technical Reports Server (NTRS)
Nelson, Michael R.; Mccaffrey, Robert; Molnar, Peter
1987-01-01
The style and the distribution of faulting occurring today in the Tien Shan region were studied, by digitizing long-period World-Wide Standard Seismograph Network P and SH waveforms of 11 of the largest Tien Shan earthquakes between 1965 and 1982 and then using a least squares inversion routine to constrain their fault plane solutions and depths. The results of the examination indicate that north-south shortening is presently occurring in the Tien Shan, with the formation of basement uplifts flanked by moderately dipping thrust faults. The present-day tectonics of the Tien Shan seem to be analogous to those of the Rocky Mountains in Colorado, Wyoming, and Utah during the Laramide orogeny in Late Cretaceous and Early Tertiary time.
A Generalization of the Spherical Inversion
ERIC Educational Resources Information Center
Ramírez, José L.; Rubiano, Gustavo N.
2017-01-01
In the present article, we introduce a generalization of the spherical inversion. In particular, we define an inversion with respect to an ellipsoid, and prove several properties of this new transformation. The inversion in an ellipsoid is the generalization of the elliptic inversion to the three-dimensional space. We also study the inverse images…
NASA Astrophysics Data System (ADS)
Benavente, Roberto; Cummins, Phil; Dettmer, Jan
2016-04-01
Rapid estimation of the spatial and temporal rupture characteristics of large megathrust earthquakes by finite fault inversion is important for disaster mitigation. For example, estimates of the spatio-temporal evolution of rupture can be used to evaluate population exposure to tsunami waves and ground shaking soon after the event by providing more accurate predictions than possible with point source approximations. In addition, rapid inversion results can reveal seismic source complexity to guide additional, more detailed subsequent studies. This work develops a method to rapidly estimate the slip distribution of megathrust events while reducing subjective parameter choices by automation. The method is simple yet robust and we show that it provides excellent preliminary rupture models as soon as 30 minutes for three great earthquakes in the South-American subduction zone. This may slightly change for other regions depending on seismic station coverage but method can be applied to any subduction region. The inversion is based on W-phase data since it is rapidly and widely available and of low amplitude which avoids clipping at close stations for large events. In addition, prior knowledge of the slab geometry (e.g. SLAB 1.0) is applied and rapid W-phase point source information (time delay and centroid location) is used to constrain the fault geometry and extent. Since the linearization by multiple time window (MTW) parametrization requires regularization, objective smoothing is achieved by the discrepancy principle in two fully automated steps. First, the residuals are estimated assuming unknown noise levels, and second, seeking a subsequent solution which fits the data to noise level. The MTW scheme is applied with positivity constraints and a solution is obtained by an efficient non-negative least squares solver. Systematic application of the algorithm to the Maule (2010), Iquique (2014) and Illapel (2015) events illustrates that rapid finite fault inversion with
Vertex micromagnetic energy in artificial square ice
NASA Astrophysics Data System (ADS)
Perrin, Yann; Canals, Benjamin; Rougemaille, Nicolas
2016-10-01
Artificial arrays of interacting magnetic elements provide an uncharted arena in which the physics of magnetic frustration and magnetic monopoles can be observed in real space and in real time. These systems offer the formidable opportunity to investigate a wide range of collective magnetic phenomena with a lab-on-chip approach and to explore various theoretical predictions from spin models. Here, we study artificial square ice systems numerically and use micromagnetic simulations to understand how the geometrical parameters of the individual magnetic elements affect the energy levels of an isolated square vertex. More specifically, we address the question of whether the celebrated square ice model could be made relevant for artificial square ice systems. Our work reveals that tuning the geometry alone should not allow the experimental realization of the square ice model when using nanomagnets coupled through the magnetostatic interaction. However, low-aspect ratios combined with small gaps separating neighboring magnetic elements of moderated thickness might permit approaching the ideal case where the degeneracy of the ice rule states is recovered.
Appraisal of geodynamic inversion results: a data mining approach
NASA Astrophysics Data System (ADS)
Baumann, T. S.
2016-11-01
Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB
MAP estimators for piecewise continuous inversion
NASA Astrophysics Data System (ADS)
Dunlop, M. M.; Stuart, A. M.
2016-10-01
We study the inverse problem of estimating a field u a from data comprising a finite set of nonlinear functionals of u a , subject to additive noise; we denote this observed data by y. Our interest is in the reconstruction of piecewise continuous fields u a in which the discontinuity set is described by a finite number of geometric parameters a. Natural applications include groundwater flow and electrical impedance tomography. We take a Bayesian approach, placing a prior distribution on u a and determining the conditional distribution on u a given the data y. It is then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP estimators can be characterised as minimisers of a generalised Onsager-Machlup functional, in the case where the prior measure is a Gaussian random field. We extend this theory to a more general class of prior distributions which allows for piecewise continuous fields. Specifically, the prior field is assumed to be piecewise Gaussian with random interfaces between the different Gaussians defined by a finite number of parameters. We also make connections with recent work on MAP estimators for linear problems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which employs the notion of Fomin derivative. In showing applicability of our theory we focus on the groundwater flow and EIT models, though the theory holds more generally. Numerical experiments are implemented for the groundwater flow model, demonstrating the feasibility of determining MAP estimators for these piecewise continuous models, but also that the geometric formulation can lead to multiple nearby (local) MAP estimators. We relate these MAP estimators to the behaviour of output from MCMC samples of the posterior, obtained using a state-of-the-art function space Metropolis-Hastings method.
Inverse problems in mathematical physics
NASA Astrophysics Data System (ADS)
Glasko, V. B.
Procedures for the correct formulation and solution of inverse problems, which usually belong to the class of ill-posed problems, are discussed. Attention is given to the concept of the conditionally correct statement of a problem, the concept of quasi-solution, and the fundamentals of regularization theory. The discussion also covers the uniqueness of solutions to inverse problems in mathematical physics, with consideration given to problems involving layered media, impedance problems, gravimetric problems, and inverse problems of heat conduction. The problem of stability and regularizing operators are also discussed.
Finding A Minimally Informative Dirichlet Prior Using Least Squares
Dana Kelly
2011-03-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson \\lambda, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Inverse Statistics and Asset Allocation Efficiency
NASA Astrophysics Data System (ADS)
Bolgorian, Meysam
In this paper using inverse statistics analysis, the effect of investment horizon on the efficiency of portfolio selection is examined. Inverse statistics analysis is a general tool also known as probability distribution of exit time that is used for detecting the distribution of the time in which a stochastic process exits from a zone. This analysis was used in Refs. 1 and 2 for studying the financial returns time series. This distribution provides an optimal investment horizon which determines the most likely horizon for gaining a specific return. Using samples of stocks from Tehran Stock Exchange (TSE) as an emerging market and S&P 500 as a developed market, effect of optimal investment horizon in asset allocation is assessed. It is found that taking into account the optimal investment horizon in TSE leads to more efficiency for large size portfolios while for stocks selected from S&P 500, regardless of portfolio size, this strategy does not only not produce more efficient portfolios, but also longer investment horizons provides more efficiency.
A Bayesian Level-Set Inversion Protocol for Structural Zonation
NASA Astrophysics Data System (ADS)
Cardiff, M.; Kitanidis, P.
2008-12-01
Mapping the variability of subsurface properties via indirect methods is of great importance for problems in contaminant remediation and resource evaluation. In general, methods for inverse modeling commonly assume smooth and/or geostatistical distributions of the parameters being estimated. However, especially for field- and catchment-scale inverse problems, the existence of distinct, separate geologic facies is not consistent with the assumptions of these inversion techniques. Because of this drawback, it is important that we develop inversion methods that are built for imaging so-called "structural" parameter fields accurately. In our presentation, we discuss the use of a facies-based level set method for imaging geologic parameter fields. The level set framework is applicable when subsurface heterogeneity can be adequately represented as a set of relatively homogeneous geologic facies separated by sharp boundaries. During the inversion optimization, the shape of boundaries between facies are optimized in order to improve data fit. Our method can represent boundaries between arbitrary numbers of facies, and extensions to joint inversion can be handled without relying on petrophysical relations. As examples, we present several synthetic inverse problems that cover realistic estimation problems using nonlinear models with multiple datasets. Throughout our work, we adopt a Bayesian perspective which allows integration of prior information as well as linearized estimation of uncertainty in the boundary locations.
CUMPOIS- CUMULATIVE POISSON DISTRIBUTION PROGRAM
NASA Technical Reports Server (NTRS)
Bowerman, P. N.
1994-01-01
The Cumulative Poisson distribution program, CUMPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, CUMPOIS (NPO-17714) and NEWTPOIS (NPO-17715), can be used independently of one another. CUMPOIS determines the approximate cumulative binomial distribution, evaluates the cumulative distribution function (cdf) for gamma distributions with integer shape parameters, and evaluates the cdf for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. CUMPOIS calculates the probability that n or less events (ie. cumulative) will occur within any unit when the expected number of events is given as lambda. Normally, this probability is calculated by a direct summation, from i=0 to n, of terms involving the exponential function, lambda, and inverse factorials. This approach, however, eventually fails due to underflow for sufficiently large values of n. Additionally, when the exponential term is moved outside of the summation for simplification purposes, there is a risk that the terms remaining within the summation, and the summation itself, will overflow for certain values of i and lambda. CUMPOIS eliminates these possibilities by multiplying an additional exponential factor into the summation terms and the partial sum whenever overflow/underflow situations threaten. The reciprocal of this term is then multiplied into the completed sum giving the cumulative probability. The CUMPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting lambda and n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 26K. CUMPOIS was
Fast Gibbs sampling for high-dimensional Bayesian inversion
NASA Astrophysics Data System (ADS)
Lucka, Felix
2016-11-01
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures can be a significant advantage. Alongside theoretical progress, various new computational techniques allow us to sample very high dimensional posterior distributions: in (Lucka 2012 Inverse Problems 28 125012), and a Markov chain Monte Carlo posterior sampler was developed for linear inverse problems with {{\\ell }}1-type priors. In this article, we extend this single component (SC) Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general {{\\ell }}pq priors with additional hard constraints. In addition, a fast computation of the conditional, SC densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography data with the popular isotropic total variation prior.
A passive inverse filter for Green's function retrieval.
Gallot, Thomas; Catheline, Stefan; Roux, Philippe; Campillo, Michel
2012-01-01
Passive methods for the recovery of Green's functions from ambient noise require strong hypotheses, including isotropic distribution of the noise sources. Very often, this distribution is nonisotropic, which introduces bias in the Green's function reconstruction. To minimize this bias, a spatiotemporal inverse filter is proposed. The method is tested on a directive noise field computed from an experimental active seismic data set. The results indicate that the passive inverse filter allows the manipulation of the spatiotemporal degrees of freedom of a complex wave field, and it can efficiently compensate for the noise wavefield directivity.
Joint inversion of surface and borehole magnetic amplitude data
NASA Astrophysics Data System (ADS)
Li, Zelin; Yao, Changli; Zheng, Yuanman; Yuan, Xiaoyu
2016-04-01
3D magnetic inversion for susceptibility distribution is a powerful tool in quantitative interpretation of magnetic data in mineral exploration. However, the inversion and interpretation of such data are faced with two problems. One problem is the poor imaging results of deep sources when only surface data are inverted. The other is the unknown total magnetization directions of sources when strong remanence exists. To deal with these problems simultaneously, we propose a method through the joint inversion of surface and borehole magnetic amplitude data. In this method, we first transform both surface and borehole magnetic data to magnetic amplitude data that are less sensitive to the directions of total magnetization, and then preform a joint inversion of the whole amplitude data to generate a 3D susceptibility distribution. The amplitude inversion algorithm uses Tikhonov regularization and imposes a positivity constraint on the effective susceptibility defined as the ratio of magnetization magnitude over the geomagnetic field strength. In addition, a distance-based weighting function is used to make the algorithm applicable to joint data sets. To solve this positivity-constraint inversion problem efficiently, an appropriate optimization method must be chosen. We first use an interior-point method to incorporate the positivity constraint into the total objective function, and then minimize the objective function via a Gauss-Newton method due to the nonlinearity introduced by the positivity constraint and the amplitude data. To further improve the efficiency of the inversion algorithm, we use a conjugate gradient method to carry out the fast matrix-vector multiplication during the minimization. To verify the utility of the proposed method, we invert the synthetic and field data using three inversion methods, including the joint inversion of surface and borehole three-component magnetic data, the inversion of surface magnetic amplitude data, and the proposed joint
Gravity inversion in spherical coordinates using tesseroids
NASA Astrophysics Data System (ADS)
Uieda, Leonardo; Barbosa, Valeria C. F.
2014-05-01
Satellite observations of the gravity field have provided geophysicists with exceptionally dense and uniform coverage of data over vast areas. This enables regional or global scale high resolution geophysical investigations. Techniques like forward modeling and inversion of gravity anomalies are routinely used to investigate large geologic structures, such as large igneous provinces, suture zones, intracratonic basins, and the Moho. Accurately modeling such large structures requires taking the sphericity of the Earth into account. A reasonable approximation is to assume a spherical Earth and use spherical coordinates. In recent years, efforts have been made to advance forward modeling in spherical coordinates using tesseroids, particularly with respect to speed and accuracy. Conversely, traditional space domain inverse modeling methods have not yet been adapted to use spherical coordinates and tesseroids. In the literature there are a range of inversion methods that have been developed for Cartesian coordinates and right rectangular prisms. These include methods for estimating the relief of an interface, like the Moho or the basement of a sedimentary basin. Another category includes methods to estimate the density distribution in a medium. The latter apply many algorithms to solve the inverse problem, ranging from analytic solutions to random search methods as well as systematic search methods. We present an adaptation for tesseroids of the systematic search method of "planting anomalous densities". This method can be used to estimate the geometry of geologic structures. As prior information, it requires knowledge of the approximate densities and positions of the structures. The main advantage of this method is its computational efficiency, requiring little computer memory and processing time. We demonstrate the shortcomings and capabilities of this approach using applications to synthetic and field data. Performing the inversion of gravity and gravity gradient
William Wilde and 1 Merrion Square.
McEntegart, R
2016-05-01
William Wilde spent the final third of his life, from 1855 to 1876, in 1 Merrion Square. During the first half of his occupancy of the house his career blossomed to its fullest; the second decade, on the other hand, was marked by scandal, personal tragedy, and an unhappy professional and social decline. This paper considers the background to the development of Merrion Square, the architectural history of 1 Merrion Square from its building in 1762 to the arrival of the Wildes in 1855, the attractions and possibilities which the house offered for William Wilde, the major architectural expansion of the building which he commissioned in 1859, and aspects of his and his family's life in the house.
Highly Anisotropic Dirac Fermions in Square Graphynes.
Zhang, L Z; Wang, Z F; Wang, Zhiming M; Du, S X; Gao, H-J; Liu, Feng
2015-08-06
We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.
Comparison of iterative inverse coarse-graining methods
NASA Astrophysics Data System (ADS)
Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.
2016-10-01
Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.
Scaling of Greenwood Peierls conductance on a diluted square lattice
NASA Astrophysics Data System (ADS)
Schwalm, William; Schmitz, Albert
The modified rectangle lattice of Dhar is a bond-diluted square lattice. The structure is self-similar and finitely ramified, like a fractal. Nevertheless certain discrete Schrödinger equation Green functions for the modified rectangle are known in closed form in the infinite lattice limit and the spectrum is continuous. By standard transfer matrix renormalization methods we present a study scaling properties of the Greenwood Peierls conductance distribution across the lattice with one dimensional lead wires attached as a function of lattice size and of additional disorder of several types.
SISYPHUS: A high performance seismic inversion factory
NASA Astrophysics Data System (ADS)
Gokhberg, Alexey; Simutė, Saulė; Boehm, Christian; Fichtner, Andreas
2016-04-01
branches for the static process setup, inversion iterations, and solver runs, each branch specifying information at the event, station and channel levels. The workflow management framework is based on an embedded scripting engine that allows definition of various workflow scenarios using a high-level scripting language and provides access to all available inversion components represented as standard library functions. At present the SES3D wave propagation solver is integrated in the solution; the work is in progress for interfacing with SPECFEM3D. A separate framework is designed for interoperability with an optimization module; the workflow manager and optimization process run in parallel and cooperate by exchanging messages according to a specially designed protocol. A library of high-performance modules implementing signal pre-processing, misfit and adjoint computations according to established good practices is included. Monitoring is based on information stored in the inversion state database and at present implements a command line interface; design of a graphical user interface is in progress. The software design fits well into the common massively parallel system architecture featuring a large number of computational nodes running distributed applications under control of batch-oriented resource managers. The solution prototype has been implemented on the "Piz Daint" supercomputer provided by the Swiss Supercomputing Centre (CSCS).
Disclinations in square and hexagonal patterns.
Golovin, A A; Nepomnyashchy, A A
2003-05-01
We report the observation of defects with fractional topological charges (disclinations) in square and hexagonal patterns as numerical solutions of several generic equations describing many pattern-forming systems: Swift-Hohenberg equation, damped Kuramoto-Sivashinsky equation, as well as nonlinear evolution equations describing large-scale Rayleigh-Benard and Marangoni convection in systems with thermally nearly insulated boundaries. It is found that disclinations in square and hexagonal patterns can be stable when nucleated from special initial conditions. The structure of the disclinations is analyzed by means of generalized Cross-Newell equations.
Square sugars: challenges and synthetic strategies.
Hazelard, Damien; Compain, Philippe
2017-03-31
Square sugars (4-membered ring carbohydrate mimetics) are at the intersection of several important topics concerning the recent emergence, in medicinal chemistry, of glycomimetic drugs and small ring systems. Monosaccharide mimetics containing oxetane, azetidine, thiethane or cyclobutane rings present a number of synthetic challenges that are a powerful driving force for innovation in organic synthesis. In addition to the inherent issues associated with 4-membered rings, the high density of functional groups and asymmetric centres found in glycomimetics further complicates the matter and requires efficient stereoselective methodologies. The purpose of this review is to present an overview of the elegant strategies that have been developed to synthesize the different types of square sugars.
On the Classification of Fractal Squares
NASA Astrophysics Data System (ADS)
Luo, Jun Jason; Liu, Jing-Cheng
2016-01-01
In the previous paper [K. S. Lau, J. J. Luo and H. Rao, Topological structure of fractal squares, Math. Proc. Camb. Phil. Soc. 155 (2013) 73-86], Lau, Luo and Rao completely classified the topological structure of so called fractal square F defined by F = (F + 𝒟)/n, where 𝒟 ⊊ {0, 1,…,n - 1}2,n ≥ 2. In this paper, we further provide simple criteria for the F to be totally disconnected, then we discuss the Lipschitz classification of F in the case n = 3, which is an attempt to consider non-totally disconnected sets.
Mahan, G. D.
2014-09-21
We calculate the binding energy of an electron bound to a donor in a semiconductor inverse opal. Inverse opals have two kinds of cavities, which we call octahedral and tetrahedral, according to their group symmetry. We put the donor in the center of each of these two cavities and obtain the binding energy. The binding energies become very large when the inverse opal is made from templates with small spheres. For spheres less than 50 nm in diameter, the donor binding can increase to several times its unconfined value. Then electrons become tightly bound to the donor and are unlikely to be thermally activated to the semiconductor conduction band. This conclusion suggests that inverse opals will be poor conductors.
NASA Astrophysics Data System (ADS)
Mahan, G. D.
2014-09-01
We calculate the binding energy of an electron bound to a donor in a semiconductor inverse opal. Inverse opals have two kinds of cavities, which we call octahedral and tetrahedral, according to their group symmetry. We put the donor in the center of each of these two cavities and obtain the binding energy. The binding energies become very large when the inverse opal is made from templates with small spheres. For spheres less than 50 nm in diameter, the donor binding can increase to several times its unconfined value. Then electrons become tightly bound to the donor and are unlikely to be thermally activated to the semiconductor conduction band. This conclusion suggests that inverse opals will be poor conductors.
Testing Earthquake Source Inversion Methodologies
NASA Astrophysics Data System (ADS)
Page, Morgan; Mai, P. Martin; Schorlemmer, Danijel
2011-03-01
Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data and the complex rupture process at depth. The resulting earthquake source models quantify the spatiotemporal evolution of ruptures. They are also used to provide a rapid assessment of the severity of an earthquake and to estimate losses. However, because of uncertainties in the data, assumed fault geometry and velocity structure, and chosen rupture parameterization, it is not clear which features of these source models are robust. Improved understanding of the uncertainty and reliability of earthquake source inversions will allow the scientific community to use the robust features of kinematic inversions to more thoroughly investigate the complexity of the rupture process and to better constrain other earthquake-related computations, such as ground motion simulations and static stress change calculations.
Temperature Inversions Have Cold Bottoms.
ERIC Educational Resources Information Center
Bohren, Craig F.; Brown, Gail M.
1982-01-01
Uses discussion and illustrations of several demonstrations on air temperature differences and atmospheric stability to explain the phenomena of temperature inversions. Relates this to the smog in Los Angeles and discusses the implications. (DC)
Inversion layer MOS solar cells
NASA Technical Reports Server (NTRS)
Ho, Fat Duen
1986-01-01
Inversion layer (IL) Metal Oxide Semiconductor (MOS) solar cells were fabricated. The fabrication technique and problems are discussed. A plan for modeling IL cells is presented. Future work in this area is addressed.
Testing earthquake source inversion methodologies
Page, M.; Mai, P.M.; Schorlemmer, D.
2011-01-01
Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data and the complex rupture process at depth. The resulting earthquake source models quantify the spatiotemporal evolution of ruptures. They are also used to provide a rapid assessment of the severity of an earthquake and to estimate losses. However, because of uncertainties in the data, assumed fault geometry and velocity structure, and chosen rupture parameterization, it is not clear which features of these source models are robust. Improved understanding of the uncertainty and reliability of earthquake source inversions will allow the scientific community to use the robust features of kinematic inversions to more thoroughly investigate the complexity of the rupture process and to better constrain other earthquakerelated computations, such as ground motion simulations and static stress change calculations.
Inversion-symmetric topological insulators
NASA Astrophysics Data System (ADS)
Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
2011-06-01
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer N, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is “topological.” We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion
The Estimation and Inversion of Magnetotelluric Data with Static Shift
NASA Astrophysics Data System (ADS)
Wang, X.; Zhou, J.; Zhang, J.; Min, G.; Xia, S.
2015-12-01
IntroductionIn magnetotelluric sounding data processing, the static shift correction is one of the most important steps. Due to the complexity of near-surface inhomogeneous bodies distribution, it is difficult to estimate the static shift of measured data. For this problem, we put forward on the basis of the inversion model for static shift estimation, and reconstructed the initial model with using the original data for 2D or 3D inversion. Estimation and Inversion methodThe magnetotelluric impedance phase has the characteristics of not influenced by the static shift in Two-dimensional electrical structure. The objective function for static shift estimation can be constructed based on impedance phase data. On the basis of normal inversion, utilizing one-dimensional linear search algorithm, combined with the forward modeling, the MT static shift can be estimated.Using estimation results for translation of anomaly measured curve. According to the inversion(1-D) of these translated curve, the initial model for two-dimensional or two-dimensional inversion can be reconstructed. On this basis, we do inversion for the original data, which not only can effectively eliminate the influence of static shift on the deep structure of inversion model, but also can get the right shallow electrical structure in the inversionConclusionThe estimation value of static shift based on impedance phase can be close to the true value. This estimation results can be used to modify the initial model, which makes the deep electric structure of the model more reasonable. On this basis, the inversion of the original data can ensure the correctness of the final inversion results (including shallow and deep).Acknowledgement This paper is supported by National Natural Science Foundation (41274078) and National 863 High Technology Research and Development Program (2014AA06A612).Reference[1] deGroot-Hedlin C. Removal of static shift in two dimensions by regularized inversion[J]. Geophysics, 1991, 56
Computation of inverse magnetic cascades
NASA Technical Reports Server (NTRS)
Montgomery, D.
1981-01-01
Inverse cascades of magnetic quantities for turbulent incompressible magnetohydrodynamics are reviewed, for two and three dimensions. The theory is extended to the Strauss equations, a description intermediate between two and three dimensions appropriate to Tokamak magnetofluids. Consideration of the absolute equilibrium Gibbs ensemble for the system leads to a prediction of an inverse cascade of magnetic helicity, which may manifest itself as a major disruption. An agenda for computational investigation of this conjecture is proposed.
Use of chi square periodogram in the analysis of estrous rhythmicity.
Refinetti, R
1991-02-01
The usefulness of the chi square periodogram procedure for the analysis of estrous rhythmicity was investigated. Sokolove-Bushell's Q statistic was found to have a chi square distribution at the small degrees of freedom involved in estrous rhythmicity in rodents (i.e., rhythmicity with periods of 2-7 days). Consequently, the significance of the peaks in the periodogram can be effectively evaluated. The effects of multiple-period rhythmicity and of random noise added to periodical data were also investigated. Overall, the analysis of simulated as well as empirical data indicated that the chi square periodogram is an excellent tool for the evaluation of estrous rhythmicity.
The face inversion effect in opponent-stimulus rivalry
Persike, Malte; Meinhardt-Injac, Bozana; Meinhardt, Günter
2014-01-01
The face inversion effect is regarded as a hallmark of face-specific processing, and can be observed in a large variety of visual tasks. Face inversion effects are also reported in binocular rivalry. However, it is unclear whether these effects are face-specific, and distinct from the general tendency of visual awareness to privilege upright objects. We studied continuous rivalry across more than 600 dominance epochs for each observer, having faces and houses rival against their inverted counterparts, and letting faces rival against houses in both upright and inverted orientation. We found strong inversion effects for faces and houses in both the frequency of dominance epochs and their duration. Inversion effects for faces, however, were substantially larger, reaching a 70:30 distribution of dominance times for upright versus inverted faces, while a 60:40 distribution was obtained for upright versus inverted houses. Inversion effects for faces reached a Cohen's d of 0.85, compared to a value of 0.33 for houses. Dominance times for rivalry of faces against houses had a 60:40 distribution in favor of faces, independent of the orientation of the objects. These results confirm the general tendency of visual awareness to prefer upright objects, and demonstrate the outstanding role of faces. Since effect size measures clearly distinguish face stimuli in opponent-stimulus rivalry, the method is highly recommended for testing the effects of face manipulations against non-face reference objects. PMID:24860477
Stress inversion method and analysis of GPS array data
NASA Astrophysics Data System (ADS)
Hori, Muneo; Iinuma, Takeshi; Kato, Teruyuki
2008-01-01
The stress inversion method is developed to find a stress field which satisfies the equation of equilibrium for a body in a state of plane stress. When one stress-strain relation is known and data on the strain distribution on the body and traction along the boundary are provided, the method solves a well-posed problem, which is a linear boundary value problem for Airy's stress function, with the governing equation being the Poisson equation and the boundary conditions being of the Neumann type. The stress inversion method is applied to the Global Positioning System (GPS) array data of the Japanese Islands. The stress increment distribution, which is associated with the displacement increment measured by the GPS array, is computed, and it is found that the distribution is not uniform over the islands and that some regions have a relatively large increment. The elasticity inversion method is developed as an alternative to the stress inversion method; it is based on the assumption of linear elastic deformation with unknown elastic moduli and does not need boundary traction data, which are usually difficult to measure. This method is applied to the GPS array data of a small region in Japan to which the stress inversion method is not applicable. To cite this article: M. Hori et al., C. R. Mecanique 336 (2008).
An analysis of the least-squares problem for the DSN systematic pointing error model
NASA Technical Reports Server (NTRS)
Alvarez, L. S.
1991-01-01
A systematic pointing error model is used to calibrate antennas in the Deep Space Network. The least squares problem is described and analyzed along with the solution methods used to determine the model's parameters. Specifically studied are the rank degeneracy problems resulting from beam pointing error measurement sets that incorporate inadequate sky coverage. A least squares parameter subset selection method is described and its applicability to the systematic error modeling process is demonstrated on Voyager 2 measurement distribution.
Eta Squared and Partial Eta Squared as Measures of Effect Size in Educational Research
ERIC Educational Resources Information Center
Richardson, John T. E.
2011-01-01
Eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable. Partial eta squared is a similar measure in which the effects of other independent variables and interactions are partialled out. The development of these measures is…
Building Generalized Inverses of Matrices Using Only Row and Column Operations
ERIC Educational Resources Information Center
Stuart, Jeffrey
2010-01-01
Most students complete their first and only course in linear algebra with the understanding that a real, square matrix "A" has an inverse if and only if "rref"("A"), the reduced row echelon form of "A", is the identity matrix I[subscript n]. That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix…
Mathematical Construction of Magic Squares Utilizing Base-N Arithmetic
ERIC Educational Resources Information Center
O'Brien, Thomas D.
2006-01-01
Magic squares have been of interest as a source of recreation for over 4,500 years. A magic square consists of a square array of n[squared] positive and distinct integers arranged so that the sum of any column, row, or main diagonal is the same. In particular, an array of consecutive integers from 1 to n[squared] forming an nxn magic square is…
Products of square-zero operators
NASA Astrophysics Data System (ADS)
Novak, Nika
2008-03-01
We characterize matrices that can be written as a product of two or three square-zero matrices. We also consider the same questions for (bounded) operators on an infinite-dimensional, separable, complex Hilbert space and in the Calkin algebra.
Squaring Matrices: Connecting Mathematics and Science
ERIC Educational Resources Information Center
Horton, Robert M.; Wiegert, Elaine M.; Marshall, Jeff C.
2008-01-01
This article shows how a matrix can be used to represent a food chain and how the square of this matrix represents the indirect food sources for each animal in the chain. By exploring, through mathematics, the implications when the bottom of the food chain is destroyed, students will see an important connection between mathematics and science.…
Meshless Galerkin least-squares method
NASA Astrophysics Data System (ADS)
Pan, X. F.; Zhang, X.; Lu, M. W.
2005-02-01
Collocation method and Galerkin method have been dominant in the existing meshless methods. Galerkin-based meshless methods are computational intensive, whereas collocation-based meshless methods suffer from instability. A new efficient meshless method, meshless Galerkin lest-squares method (MGLS), is proposed in this paper to combine the advantages of Galerkin method and collocation method. The problem domain is divided into two subdomains, the interior domain and boundary domain. Galerkin method is applied in the boundary domain, whereas the least-squares method is applied in the interior domain.The proposed scheme elliminates the posibilities of spurious solutions as that in the least-square method if an incorrect boundary conditions are used. To investigate the accuracy and efficiency of the proposed method, a cantilevered beam and an infinite plate with a central circular hole are analyzed in detail and numerical results are compared with those obtained by Galerkin-based meshless method (GBMM), collocation-based meshless method (CBMM) and meshless weighted least squares method (MWLS). Numerical studies show that the accuracy of the proposed MGLS is much higher than that of CBMM and is close to, even better than, that of GBMM, while the computational cost is much less than that of GBMM.
Non-Circular Wheels: Reuleaux and Squares
ERIC Educational Resources Information Center
Mills, Allan
2011-01-01
Circular wheels are so familiar on vehicles of all types that it is seldom realized that alternatives do exist. This short non-mathematical article describes Reuleaux and square wheels that, rolling along appropriate tracks, can maintain a moving platform at a constant height. Easily made working models lend themselves to demonstrations at science…
Least squares polynomial fits and their accuracy
NASA Technical Reports Server (NTRS)
Lear, W. M.
1977-01-01
Equations are presented which attempt to fit least squares polynomials to tables of date. It is concluded that much data are needed to reduce the measurement error standard deviation by a significant amount, however at certain points great accuracy is attained.
Least squares estimation of avian molt rates
Johnson, D.H.
1989-01-01
A straightforward least squares method of estimating the rate at which birds molt feathers is presented, suitable for birds captured more than once during the period of molt. The date of molt onset can also be estimated. The method is applied to male and female mourning doves.
BLS: Box-fitting Least Squares
NASA Astrophysics Data System (ADS)
Kovács, G.; Zucker, S.; Mazeh, T.
2016-07-01
BLS (Box-fitting Least Squares) is a box-fitting algorithm that analyzes stellar photometric time series to search for periodic transits of extrasolar planets. It searches for signals characterized by a periodic alternation between two discrete levels, with much less time spent at the lower level.
Least-squares fitting Gompertz curve
NASA Astrophysics Data System (ADS)
Jukic, Dragan; Kralik, Gordana; Scitovski, Rudolf
2004-08-01
In this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,...,m, m≥3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples.
Kendall Square multiprocessor: Early experiences and performance
Dunigan, T.H.
1992-04-01
Initial performance results and early experiences are reported for the Kendall Square Research multiprocessor. The basic architecture of the shared-memory multiprocessor is described, and computational and I/O performance is measured for both serial and parallel programs. Experiences in porting various applications are described.
Iterative methods for weighted least-squares
Bobrovnikova, E.Y.; Vavasis, S.A.
1996-12-31
A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.
A Limitation with Least Squares Predictions
ERIC Educational Resources Information Center
Bittner, Teresa L.
2013-01-01
Although researchers have documented that some data make larger contributions than others to predictions made with least squares models, it is relatively unknown that some data actually make no contribution to the predictions produced by these models. This article explores such noncontributory data. (Contains 1 table and 2 figures.)
Inverse air pollution modelling of urban-scale carbon monoxide emissions
NASA Astrophysics Data System (ADS)
Mulholland, Michael; Seinfeld, John H.
A new recursive least-squares technique is developed to give spatial and temporal definition to the adjustments necessary in an emission inventory, to fit ambient concentration observations optimally. The CIT Photochemical Airshed Model is used to compute CO concentration distributions arising from 29 separate source domains in the South Coast Air Basin of California. A Kalman filter integrated within the model matches predictions with CO observations at 27 locations by superposing the computed distributions with optimal weighting factors. The filter structure allows control of the extent to which adjusted emission inventories are allowed to deviate from a base-case, which already has high spatial and temporal definition. Applied to the Southern California Air Quality Study, 27-29 August 1987, strong temporal dependence was noted in the necessary adjustment to the available CO emission inventory, with a peak factor of 3.0 at midday on weekdays. The spatial resolution of the technique revealed new high-emission zones for CO in a corridor between Pasadena and San Bernardino, in the Riverside-Corona area, and along the Pacific coast on Saturday. In this first such application to an urban environment, some success was also achieved in correcting the phasing of emissions for errors arising from the neglect of source-receptor lags in the inverse modelling technique.
Multidimensional NMR inversion without Kronecker products: Multilinear inversion
NASA Astrophysics Data System (ADS)
Medellín, David; Ravi, Vivek R.; Torres-Verdín, Carlos
2016-08-01
Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences with non-separable kernels. Second, in three or more dimensions, the singular value decomposition is not unique; therefore kernel compression is not well-defined for higher dimensions. Without kernel compression, the Kronecker product yields matrices that require large amounts of memory, making the inversion intractable for personal computers. Finally, incorporating arbitrary regularization terms is not possible using the Lawson-Hanson (LH) or the Butler-Reeds-Dawson (BRD) algorithms. We develop a minimization-based inversion method that circumvents the above problems by using multilinear forms to perform multidimensional NMR inversion without using kernel compression or Kronecker products. The new method is memory efficient, requiring less than 0.1% of the memory required by the LH or BRD methods. It can also be extended to arbitrary dimensions and adapted to include non-separable kernels, linear constraints, and arbitrary regularization terms. Additionally, it is easy to implement because only a cost function and its first derivative are required to perform the inversion.
Deformation of square objects and boudins
NASA Astrophysics Data System (ADS)
Treagus, Susan H.; Lan, Labao
2004-08-01
Some geological objects, such as clasts and boudins, may have had original shapes close to square, that have been modified by ductile deformation. We demonstrate through finite element models presented here and in earlier papers that square objects in a matrix with contrasting viscosity can deform to a variety of curved shapes. The maximum shape change is where the square edges are parallel to the principal bulk strains. Competent objects with viscosity ratio to matrix ( m) of 2-20 become barrel shaped, showing concave 'fish mouth' shortened edges. Incompetent objects ( m<1) show a narrower variety of shapes with m, all becoming smoothed to bone, dumb-bell or lobate shapes, and losing the original corners. We compare the results for square objects with linear and non-linear rheology (power law, stress exponent n=1, 3 or 10), and with previous modelling with different object-matrix proportions. Competent objects with higher n values deform slightly less, and more irregularly, than linearly viscous ( n=1) objects, but the distinctions between n=3 and 10 are only slight. The differences are even slighter (in the opposite sense) for incompetent objects. The proportion of object to matrix is as important, if not more, in controlling the deformation and shape of these objects. The results are compared via graphs of object strain and concavity versus bulk strain. The concavity graph for competent square objects with linear viscosity up to very high strain can be compared with examples of ductile boudins with barrel or fish mouth shapes. Subject to a number of assumptions, this provides a method of estimating boudin-matrix viscosity ratios and post-boudinage ductile strain, of potential use in highly deformed rocks lacking other strain markers. The approach may also be suitable for deformed porphyroblasts, but is more difficult to apply to single clasts in breccias and conglomerates.
Constrained optimization schemes for geophysical inversion of seismic data
NASA Astrophysics Data System (ADS)
Sosa Aguirre, Uram Anibal
Many experimental techniques in geophysics advance the understanding of Earth processes by estimating and interpreting Earth structure (e.g., velocity and/or density structure). These techniques use different types of geophysical data which can be collected and analyzed separately, sometimes resulting in inconsistent models of the Earth depending on data quality, methods and assumptions made. This dissertation presents two approaches for geophysical inversion of seismic data based on constrained optimization. In one approach we expand a one dimensional (1-D) joint inversion least-squares (LSQ) algorithm by introducing a constrained optimization methodology. Then we use the 1-D inversion results to produce 3-D Earth velocity structure models. In the second approach, we provide a unified constrained optimization framework for solving a 1-D inverse wave propagation problem. In Chapter 2 we present a constrained optimization framework for joint inversion. This framework characterizes 1-D Earth's structure by using seismic shear wave velocities as a model parameter. We create two geophysical synthetic data sets sensitive to shear velocities, namely receiver function and surface wave dispersion. We validate our approach by comparing our numerical results with a traditional unconstrained method, and also we test our approach robustness in the presence of noise. Chapter 3 extends this framework to include an interpolation technique for creating 3-D Earth velocity structure models of the Rio Grande Rift region. Chapter 5 introduces the joint inversion of multiple data sets by adding delay travel times information in a synthetic setup, and leave the posibility to include more data sets. Finally, in Chapter 4 we pose a 1-D inverse full-waveform propagation problem as a PDE-constrained optimization program, where we invert for the material properties in terms of shear wave velocities throughout the physical domain. We facilitate the implementation and comparison of different
Reconditioning fault slip inversions via InSAR data discretization
NASA Astrophysics Data System (ADS)
Ziv, Alon
2016-10-01
A major difficulty in inverting geodetic data for fault slip distribution is that measurement errors are mapped from the data space onto the solution space. The amplitude of this mapping is sensitive to the condition number of the inverse problem, i.e., the ratio between the largest and smallest singular value of the forward matrix. Thus, unless the problem is well-conditioned, slip inversions cannot reveal the actual fault slip distribution. In this study, we describe a new iterative algorithm that optimizes the condition of the slip inversion through discretization of InSAR data. We present a numerical example that demonstrates the effectiveness of our approach. We show that the condition number of the reconditioned data sets are not only much smaller than those of uniformly spaced data sets with the same dimension but are also much smaller than non-uniformly spaced data sets, with data density that increases towards the model fault.
Hybrid Adaptive Flight Control with Model Inversion Adaptation
NASA Technical Reports Server (NTRS)
Nguyen, Nhan
2011-01-01
This study investigates a hybrid adaptive flight control method as a design possibility for a flight control system that can enable an effective adaptation strategy to deal with off-nominal flight conditions. The hybrid adaptive control blends both direct and indirect adaptive control in a model inversion flight control architecture. The blending of both direct and indirect adaptive control provides a much more flexible and effective adaptive flight control architecture than that with either direct or indirect adaptive control alone. The indirect adaptive control is used to update the model inversion controller by an on-line parameter estimation of uncertain plant dynamics based on two methods. The first parameter estimation method is an indirect adaptive law based on the Lyapunov theory, and the second method is a recursive least-squares indirect adaptive law. The model inversion controller is therefore made to adapt to changes in the plant dynamics due to uncertainty. As a result, the modeling error is reduced that directly leads to a decrease in the tracking error. In conjunction with the indirect adaptive control that updates the model inversion controller, a direct adaptive control is implemented as an augmented command to further reduce any residual tracking error that is not entirely eliminated by the indirect adaptive control.
1-Dimension magnetotelluric data inversion using MOEA/D algorithm
NASA Astrophysics Data System (ADS)
Pramudiana; Sungkono
2017-01-01
Magnetotelluric (MT) data is used to derive resistivity imaging of subsurface. The subsurface resistivity is obtained by inversion of MT data. Generally, MT data contains two parts, namely: apparent resistivity and phase or real and imaginary parts. Inversion of MT data for reconstructing resistivity value of each layer is to minimize single objective (combination two parameters MT data) which used global or local optimization method. Nerveless, single objective optimization method has several disadvantages, such as; (1) weight value to combine two parameters of MT data is needed, where this weigh value depend on the amplitude of both MT data; (2) there is no validation of the inversion results. In this research, Inversion MT data to estimate 1D resistivity of subsurface uses multi-objective evolutionary algorithm based on decomposition (MOEA/D)to minimize root mean square error (RMSE) of calculated and observed data for apparent resistivity and phase data simultaneously. The algorithm has applied to synthetic and field data. This result shows that MOEA/D algorithm is robust and accurate to determine subsurface resistivity and lithology.
A Simplified Scheme for Kinematic Source Inversion
NASA Astrophysics Data System (ADS)
Iglesias, A.; Castro-Artola, O.; Singh, S.; Hjorleifsdottir, V.; Legrand, D.
2013-05-01
It is well known that different kinematic source inversion schemes lead to non-unique solutions. For this reason, a simplified scheme, which yields the main characteristics of the rupture process, rather than the details, may be desirable. In this work we propose a modification of the frequency-domain inversion scheme of Cotton & Campillo (1995) to extract kinematic parameters using simplified geometries (ellipses). The forward problem is re-parameterized by including one or two ellipses in which the displacement is smoothly distributed. For the ellipses we invert for the position of the centers within the fault plane, the major and minor semi-axes, the maximum displacements, the angles of rotation and a parameter that controls the distribution of slip. A simulated annealing scheme is used to invert near-source displacements. We first test the method on synthetic displacement records corresponding to the Guerrero-Oaxaca earthquake (20/03/2012, Mw=7.5) by comparing the results obtained from the modified technique with the original method. In the next step, we use displacements obtained by double numerical integration of recorded accelerograms. We find that, in spite of the simple geometry, the modified method leads to a good fit between observed and synthetic displacements and recovers the main rupture characteristics.
C/C++ Coding for Matrix Pseudo Inverses in Clinical Near Infrared Spectroscopy.
Gagnon, ROY E.; Macnab, ANDREW J.
1998-01-01
Near infrared spectroscopy is used clinically to investigate patterns of change in cerebral oxygenation. We have shown that differences reported between authors are likely the result of computer encoding errors in the manipulation of matrices. Current methods compute the inverse of a non-square matrix to derive chromophore concentration values, and solution of another non-square matrix to derive polynomial coefficients of a least squares best fit curve from which the first derivative can be used to estimate blood flow values. Encoding of these pseudo inverses involves too many nested looping steps to easily identify encoding errors. We have given C/C++ source code along with sample numerical values at the termination of each loop within the algorithm. This provides counter checking for future software development by other programmers, and also permits other investigators to report whether the software used for their experiments agrees with previously published material.
Global inversion for anisotropy during full-waveform inversion
NASA Astrophysics Data System (ADS)
Debens, H. A.; Warner, M.; Umpleby, A.
2015-12-01
Full-waveform inversion (FWI) is a powerful tool for quantitative estimation of high-resolution high-fidelity models of subsurface seismic parameters, typically P-wave velocity. The solution to FWI's posed nonlinear inverse problem is obtained via an iterative series of linearized local updates to a start model, assuming this model lies within the basin of attraction to the global minimum. Thanks to many successful published applications to three-dimensional (3D) field datasets, its advance has been rapid and driven in large-part by the oil and gas industry. The consideration of seismic anisotropy during FWI is of vital importance, as it holds influence over both the kinematics and dynamics of seismic waveforms. If not appropriately taken into account then inadequacies in the anisotropy model are likely to manifest as significant error in the recovered velocity model. Conventionally, anisotropic FWI employs either an a priori anisotropy model, held fixed during FWI, or it uses a multi-parameter local inversion scheme to recover the anisotropy as part of the FWI; both of these methods can be problematic. Constructing an anisotropy model prior to FWI often involves intensive (and hence expensive) iterative procedures, such as travel-time tomography or moveout velocity analysis. On the other hand, introducing multiple parameters to FWI itself increases the complexity of what is already an underdetermined inverse problem. We propose that global rather than local FWI can be used to recover the long-wavelength acoustic anisotropy model, and that this can then be followed by more-conventional local FWI to recover the detailed model. We validate this approach using a full 3D field dataset, demonstrating that it avoids problems associated to crosstalk that can bedevil local inversion schemes, and reconciles well with in situ borehole measurements. Although our approach includes a global inversion for anisotropy, it is nonetheless affordable and practical for 3D field data.
Kolgotin, Alexei; Müller, Detlef; Chemyakin, Eduard; Romanov, Anton
2016-12-01
Multiwavelength Raman/high spectral resolution lidars that measure backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm can be used for the retrieval of particle microphysical parameters, such as effective and mean radius, number, surface-area and volume concentrations, and complex refractive index, from inversion algorithms. In this study, we carry out a correlation analysis in order to investigate the degree of dependence that may exist between the optical data taken with lidar and the underlying microphysical parameters. We also investigate if the correlation properties identified in our study can be used as a priori or a posteriori constraints for our inversion scheme so that the inversion results can be improved. We made the simplifying assumption of error-free optical data in order to find out what correlations exist in the best case situation. Clearly, for practical applications, erroneous data need to be considered too. On the basis of simulations with synthetic optical data, we find the following results, which hold true for arbitrary particle size distributions, i.e., regardless of the modality or the shape of the size distribution function: surface-area concentrations and extinction coefficients are linearly correlated with a correlation coefficient above 0.99. We also find a correlation coefficient above 0.99 for the extinction coefficient versus (1) the ratio of the volume concentration to effective radius and (2) the product of the number concentration times the sum of the squares of the mean radius and standard deviation of the investigated particle size distributions. Besides that, we find that for particles of any mode fraction of the particle size distribution, the complex refractive index is uniquely defined by extinction- and backscatter-related Ångström exponents, lidar ratios at two wavelengths, and an effective radius.
Sutton, G W; Weiner, M M; Mani, S A
1976-09-01
Theoretical Fraunhofer diffraction patterns are presented for uniformly illuminated square apertures with noncentered square obscurations. The energy within a given subtended solid angle in the far field is calculated. It is shown that the cornered-off-axis obscuration provides much more far-field energy in a given spot size than the centered obscuration for the same clear aperture area and total energy, for example, 82% more far-field energy in the first Airy square for 50% obscuration, thus providing superior performance for practical systems.
Wave Propagation and Inversion in Shallow Water and Poroelastic Sediment
1998-01-01
acoustical properties of rigid frame porous media with pore size distributions. K.V. Horoshenkov, K. Attenborough and S.N. Chandler-Wilde, J. Accoust. Soc...for imaging using inverse scattering techniques and Wave-field Energy", Inventors: Steven A. Johnson, James W. Wiskin, David T. Borup, F. Natterer, F
The Validity of the Inverse Scree Test for Cluster Analysis.
ERIC Educational Resources Information Center
Lathrop, Richard G.; Williams, Janice E.
1990-01-01
A Monte Carlo study of the validity of the Inverse Scree Test under conditions where true group membership is known was conducted. Fifty cluster analyses of each distribution involving 2 to 5 true groups of 3,000 simulated subjects were made. Implications for the data analyst are discussed. (SLD)
Mode control and direct modulation for waveguide-coupled square microcavity lasers
NASA Astrophysics Data System (ADS)
Yang, Yue-De; Xiao, Zhi-Xiong; Weng, Hai-Zhong; Xiao, Jin-Long; Huang, Yong-Zhen
2016-11-01
Lasing mode control and direct modulation characteristics have been investigated for waveguide-coupled unidirectional-emission square microcavity lasers. A quasi-analytical model is introduced to analyze the mode field distributions and quality (Q) factors for the confined modes inside the square optical microcavities with directly coupled waveguide, where high-Q whispering-gallery-like (WG-like) modes are induced by the mode coupling between doubly-degenerate modes. AlGaInAs/InP waveguide-coupled unidirectional-emission square microcavity lasers are fabricated by using standard planar technology, and electrically-injected lasing is realized at room temperature. The lasing modes are controlled by properly designing the lasing cavity, output waveguide and injection pattern. Dual-transverse-mode lasing with a tunable wavelength interval from 0.25 to 0.39 nm is realized by using a spatially selective current injection to modulate the refractive index, as the mode field distributions of different transverse are spatially separated. The wavelength interval can be further increased to a few nanometers by reducing the cavity size and replacing the flat sidewalls with circular arcs. The field distributions of WG-like modes distribute uniformly in square microcavity, which avoid the burning-induced carrier diffusion in high-speed direct modulation. A small-signal modulation 3dB bandwidth exceeding 16 GHz, and an open eye diagram at 25 Gb/s are demonstrated for the high-speed direct modulated square microcavity laser.
Operations concept for the Square Kilometre Array
NASA Astrophysics Data System (ADS)
Davis, Gary R.; Bock, Douglas C.; Chrysostomou, Antonio; Taljaard, Cornelius
2016-07-01
The Square Kilometre Array (SKA) is an ambitious project to build the world's largest radio telescope, eventually reaching one square kilometre in collecting area. The first phase of the project, SKA1, will consist of two telescopes: SKA1-LOW, comprising 131,000 dipole antennas at the Murchison Radio Observatory in Western Australia covering the range 50-350 MHz, and SKA1-MID, comprising 200 x 15-m dishes in the Karoo desert in South Africa covering the range 0.35-13.8 GHz. SKA1 is scheduled to commence operations in 2023 and, in order to appropriately influence the design of the system, operational planning has commenced. This paper presents an overview of the operational concept for SKA1.