The derivative and tangent operators of a motion in Lorentzian space

NASA Astrophysics Data System (ADS)

Durmaz, Olgun; Aktaş, Buşra; Gündoğan, Hali˙t

In this paper, by using Lorentzian matrix multiplication, L-Tangent operator is obtained in Lorentzian space. The L-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. L-Tangent operators are related to vectors. Some illustrative examples for applications of L-Tangent operators are also presented.

Application of the Double-Tangent Construction of Coexisting Phases to Any Type of Phase Equilibrium for Binary Systems Modeled with the Gamma-Phi Approach

ERIC Educational Resources Information Center

Jaubert, Jean-Noël; Privat, Romain

2014-01-01

The double-tangent construction of coexisting phases is an elegant approach to visualize all the multiphase binary systems that satisfy the equality of chemical potentials and to select the stable state. In this paper, we show how to perform the double-tangent construction of coexisting phases for binary systems modeled with the gamma-phi…

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low

Examining Students' Generalizations of the Tangent Concept: A Theoretical Perspective

ERIC Educational Resources Information Center

Çekmez, Erdem; Baki, Adnan

2016-01-01

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

Tangent-ogive nose cones

NASA Technical Reports Server (NTRS)

Wing, L. D.

1976-01-01

Program calculates aerodynamic heating and shear stresses at wall for tangent-ogive noses that are slender enough to maintain an attached nose shock during portion of flight when heat transfer from boundary layer to wall is significant.

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

NASA Technical Reports Server (NTRS)

Chin, S.; Lan, C. Edward

1988-01-01

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

Linear strain sensor made of multi-walled carbon nanotube/epoxy composite

NASA Astrophysics Data System (ADS)

Tong, Shuying; Yuan, Weifeng; Liu, Haidong; Alamusi; Hu, Ning; Zhao, Chaoyang; Zhao, Yangzhou

2017-11-01

In this study, a fabrication process was developed to make the multi-walled carbon nanotubes/epoxy (MWCNT/EP) composite films. The electrical-strain behaviour of the films in direct and alternating current circuits were both tested. It is found that the direct current resistance and the dielectric loss tangent of the MWCNT/EP composite films are dependent on the strain and the weight fraction of the carbon nanotubes. In an alternating current circuit, the test frequency affects the impedance and the phase angle of the composite film, but it has nothing to do with the change ratio of the dielectric loss tangent of the film in tension. This phenomenon can be interpreted by a proposed equivalent circuit model. Experiment results show that the change rate of the dielectric loss tangent of the MWCNT/EP sensor is linearly proportional to the strain. The findings obtained in the present study provide a promising method to develop ultrasensitive linear strain gauges.

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

NASA Astrophysics Data System (ADS)

Nguyen, Van-Dung; Wu, Ling; Noels, Ludovic

2017-03-01

This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time.

Designing worked examples for learning tangent lines to circles

NASA Astrophysics Data System (ADS)

Retnowati, E.; Marissa

2018-03-01

Geometry is a branch of mathematics that deals with shape and space, including the circle. A difficult topic in the circle may be the tangent line to circle. This is considered a complex material since students have to simultaneously apply several principles to solve the problems, these are the property of circle, definition of the tangent, measurement and Pythagorean theorem. This paper discusses designs of worked examples for learning tangent line to circles and how to apply this design to an effective and efficient instructional activity. When students do not have sufficient prior knowledge, solving tangent problems might be clumsy, and as a consequence, the problem-solving activity hinders learning. According to a Cognitive Load Theory, learning occurs when students can construct new knowledge based on the relevant knowledge previously learned. When the relevant knowledge is unavailable, providing students with the worked example is suggested. Worked example may reduce unproductive process during learning that causes extraneous cognitive load. Nevertheless, worked examples must be created in such a way facilitate learning.

Tangent Lines without Derivatives for Quadratic and Cubic Equations

ERIC Educational Resources Information Center

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Numerical calculation of thermo-mechanical problems at large strains based on complex step derivative approximation of tangent stiffness matrices

NASA Astrophysics Data System (ADS)

Balzani, Daniel; Gandhi, Ashutosh; Tanaka, Masato; Schröder, Jörg

2015-05-01

In this paper a robust approximation scheme for the numerical calculation of tangent stiffness matrices is presented in the context of nonlinear thermo-mechanical finite element problems and its performance is analyzed. The scheme extends the approach proposed in Kim et al. (Comput Methods Appl Mech Eng 200:403-413, 2011) and Tanaka et al. (Comput Methods Appl Mech Eng 269:454-470, 2014 and bases on applying the complex-step-derivative approximation to the linearizations of the weak forms of the balance of linear momentum and the balance of energy. By incorporating consistent perturbations along the imaginary axis to the displacement as well as thermal degrees of freedom, we demonstrate that numerical tangent stiffness matrices can be obtained with accuracy up to computer precision leading to quadratically converging schemes. The main advantage of this approach is that contrary to the classical forward difference scheme no round-off errors due to floating-point arithmetics exist within the calculation of the tangent stiffness. This enables arbitrarily small perturbation values and therefore leads to robust schemes even when choosing small values. An efficient algorithmic treatment is presented which enables a straightforward implementation of the method in any standard finite-element program. By means of thermo-elastic and thermo-elastoplastic boundary value problems at finite strains the performance of the proposed approach is analyzed.

Teachers' Conceptions of Tangent Line

ERIC Educational Resources Information Center

Paez Murillo, Rosa Elvira; Vivier, Laurent

2013-01-01

In order to study the conceptions, and their evolutions, of the tangent line to a curve an updating workshop which took place in Mexico was designed for upper secondary school teachers. This workshop was planned using the methodology of cooperative learning, scientific debate and auto reflection (ACODESA) and the conception-knowing-concept model…

Measurement of corneal tangent modulus using ultrasound indentation.

PubMed

Wang, Li-Ke; Huang, Yan-Ping; Tian, Lei; Kee, Chea-Su; Zheng, Yong-Ping

2016-09-01

Biomechanical properties are potential information for the diagnosis of corneal pathologies. An ultrasound indentation probe consisting of a load cell and a miniature ultrasound transducer as indenter was developed to detect the force-indentation relationship of the cornea. The key idea was to utilize the ultrasound transducer to compress the cornea and to ultrasonically measure the corneal deformation with the eyeball overall displacement compensated. Twelve corneal silicone phantoms were fabricated with different stiffness for the validation of measurement with reference to an extension test. In addition, fifteen fresh porcine eyes were measured by the developed system in vitro. The tangent moduli of the corneal phantoms calculated using the ultrasound indentation data agreed well with the results from the tensile test of the corresponding phantom strips (R(2)=0.96). The mean tangent moduli of the porcine corneas measured by the proposed method were 0.089±0.026MPa at intraocular pressure (IOP) of 15mmHg and 0.220±0.053MPa at IOP of 30mmHg, respectively. The coefficient of variation (CV) and intraclass correlation coefficient (ICC) of tangent modulus were 14.4% and 0.765 at 15mmHg, and 8.6% and 0.870 at 30mmHg, respectively. The preliminary study showed that ultrasound indentation could be applied to the measurement of corneal tangent modulus with good repeatability and improved measurement accuracy compared to conventional surface displacement-based measurement method. The ultrasound indentation can be a potential tool for the corneal biomechanical properties measurement in vivo. Copyright © 2016 Elsevier B.V. All rights reserved.

Internal mammary lymph node inclusion in standard tangent breast fields: effects of body habitus.

PubMed

Proulx, G M; Lee, R J; Stomper, P C

2001-01-01

The purpose of this study was to determine the variability of internal mammary node (IMN) coverage with standard breast tangent fields using surface anatomy as determined by computed tomography (CT) planning for patients treated with either breast-conserving treatment or postmastectomy, and to evaluate the influence of body habitus and shape on IMN coverage with standard tangent fields. This prospective study included consecutive women with breast cancer who underwent either local excision or mastectomy and had standard tangent fields intended to cover the breast plus a margin simulated using surface anatomy. CT planning determined the location of the IMN with respect to the tangent fields designed from surface anatomy. The internal mammary vessels were used as surrogates for the IMNs. CT measurements of the presternal fat thickness and anteroposterior (AP) and transverse skeletal diameters were made to determine their relationship to the inclusion of IMNs within the tangent fields. Only seven patients (14%) had their IMNs completely within the tangent fields. Twenty patients (40%) had partial coverage of their IMNs, and 23 (46%) had their IMNs completely outside the fields. IMN inclusion was inversely correlated with presternal fat thickness. Thoracic skeletal shape was not associated with IMN inclusion. Standard tangent fields generally do not cover the IMNs completely but may cover them at least partially in a majority of patients. The presternal fat thickness is inversely correlated with IMN inclusion in the tangent fields.

Tangent linear super-parameterization: attributable, decomposable moist processes for tropical variability studies

NASA Astrophysics Data System (ADS)

Mapes, B. E.; Kelly, P.; Song, S.; Hu, I. K.; Kuang, Z.

2015-12-01

An economical 10-layer global primitive equation solver is driven by time-independent forcing terms, derived from a training process, to produce a realisting eddying basic state with a tracer q trained to act like water vapor mixing ratio. Within this basic state, linearized anomaly moist physics in the column are applied in the form of a 20x20 matrix. The control matrix was derived from the results of Kuang (2010, 2012) who fitted a linear response function from a cloud resolving model in a state of deep convecting equilibrium. By editing this matrix in physical space and eigenspace, scaling and clipping its action, and optionally adding terms for processes that do not conserve moist statice energy (radiation, surface fluxes), we can decompose and explain the model's diverse moist process coupled variability. Recitified effects of this variability on the general circulation and climate, even in strictly zero-mean centered anomaly physic cases, also are sometimes surprising.

Catalog of Observed Tangents to the Spiral Arms in the Milky Way Galaxy

NASA Astrophysics Data System (ADS)

Vallée, Jacques P.

2014-11-01

From the Sun's location in the Galactic disk, one can use different arm tracers (CO, H I, thermal or ionized or relativistic electrons, masers, cold and hot dust, etc.) to locate a tangent to each spiral arm in the disk of the Milky Way. We present a master catalog of the astronomically observed tangents to the Galaxy's spiral arms, using different arm tracers from the literature. Some arm tracers can have slightly divergent results from several papers, so a mean value is taken—see the Appendix for CO, H II, and masers. The catalog of means currently consists of 63 mean tracer entries, spread over many arms (Carina, Crux-Centaurus, Norma, Perseus origin, near 3 kpc, Scutum, Sagittarius), stemming from 107 original arm tracer entries. Additionally, we updated and revised a previous statistical analysis of the angular offset and linear separation from the mid-arm for each different mean arm tracer. Given enough arm tracers, and summing and averaging over all four spiral arms, one could determine if arm tracers have separate and parallel lanes in the Milky Way. This statistical analysis allows a cross-cut of a Galactic spiral arm to be made, confirming a recent discovery of a linear separation between arm tracers. Here, from the mid-arm's CO to the inner edge's hot dust, the arm halfwidth is about 340 pc doubling would yield a full arm width of 680 pc. We briefly compare these observations with the predictions of many spiral arm theories, notably the density wave theory.

CATALOG OF OBSERVED TANGENTS TO THE SPIRAL ARMS IN THE MILKY WAY GALAXY

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

Vallée, Jacques P., E-mail: jacques.vallee@nrc-cnrc.gc.ca

2014-11-01

From the Sun's location in the Galactic disk, one can use different arm tracers (CO, H I, thermal or ionized or relativistic electrons, masers, cold and hot dust, etc.) to locate a tangent to each spiral arm in the disk of the Milky Way. We present a master catalog of the astronomically observed tangents to the Galaxy's spiral arms, using different arm tracers from the literature. Some arm tracers can have slightly divergent results from several papers, so a mean value is taken—see the Appendix for CO, H II, and masers. The catalog of means currently consists of 63 meanmore » tracer entries, spread over many arms (Carina, Crux-Centaurus, Norma, Perseus origin, near 3 kpc, Scutum, Sagittarius), stemming from 107 original arm tracer entries. Additionally, we updated and revised a previous statistical analysis of the angular offset and linear separation from the mid-arm for each different mean arm tracer. Given enough arm tracers, and summing and averaging over all four spiral arms, one could determine if arm tracers have separate and parallel lanes in the Milky Way. This statistical analysis allows a cross-cut of a Galactic spiral arm to be made, confirming a recent discovery of a linear separation between arm tracers. Here, from the mid-arm's CO to the inner edge's hot dust, the arm halfwidth is about 340 pc; doubling would yield a full arm width of 680 pc. We briefly compare these observations with the predictions of many spiral arm theories, notably the density wave theory.« less

Reverse-Tangent Injection in a Centrifugal Compressor

NASA Technical Reports Server (NTRS)

Skoch, Gary J.

2007-01-01

Injection of working fluid into a centrifugal compressor in the reverse tangent direction has been invented as a way of preventing flow instabilities (stall and surge) or restoring stability when stall or surge has already commenced. The invention applies, in particular, to a centrifugal compressor, the diffuser of which contains vanes that divide the flow into channels oriented partly radially and partly tangentially. In reverse-tangent injection, a stream or jet of the working fluid (the fluid that is compressed) is injected into the vaneless annular region between the blades of the impeller and the vanes of the diffuser. As used here, "reverse" signifies that the injected flow opposes (and thereby reduces) the tangential component of the velocity of the impeller discharge. At the same time, the injected jet acts to increase the radial component of the velocity of the impeller discharge.

A new method to approximate load-displacement relationships of spinal motion segments for patient-specific multi-body models of scoliotic spine.

PubMed

Jalalian, Athena; Tay, Francis E H; Arastehfar, Soheil; Liu, Gabriel

2017-06-01

Load-displacement relationships of spinal motion segments are crucial factors in characterizing the stiffness of scoliotic spine models to mimic the spine responses to loads. Although nonlinear approach to approximation of the relationships can be superior to linear ones, little mention has been made to deriving personalized nonlinear load-displacement relationships in previous studies. A method is developed for nonlinear approximation of load-displacement relationships of spinal motion segments to assist characterizing in vivo the stiffness of spine models. We propose approximation by tangent functions and focus on rotational displacements in lateral direction. The tangent functions are characterized using lateral bending test. A multi-body model was characterized to 18 patients and utilized to simulate four spine positions; right bending, left bending, neutral, and traction. The same was done using linear functions to assess the performance of the proposed tangent function in comparison with the linear function. Root-mean-square error (RMSE) of the displacements estimated by the tangent functions was 44 % smaller than the linear functions. This shows the ability of our tangent function in approximation of the relationships for a range of infinitesimal to large displacements involved in the spine movement to the four positions. In addition, the models based on the tangent functions yielded 67, 55, and 39 % smaller RMSEs of Ferguson angles, locations of vertebrae, and orientations of vertebrae, respectively, implying better estimates of spine responses to loads. Overall, it can be concluded that our method for approximating load-displacement relationships of spinal motion segments can offer good estimates of scoliotic spine stiffness.

Generic Equations for Constructing Smooth Paths Along Circles and Tangent Lines With Application to Airport Ground Paths

NASA Technical Reports Server (NTRS)

Barker, L. Keith

1998-01-01

The primary purpose of this publication is to develop a mathematical model to describe smooth paths along any combination of circles and tangent lines. Two consecutive circles in a path are either tangent (externally or internally) or they appear on the same (lateral) or opposite (transverse) sides of a connecting tangent line. A path may start or end on either a segment or circle. The approach is to use mathematics common to robotics to design the path as a multilink manipulator. This approach allows a hierarchical view of the problem and keeps the notation manageable. A user simply specifies a few parameters to configure a path. Necessary and sufficient conditions automatically ensure the consistency of the inputs for a smooth path. Two example runway exit paths are given, and an angle to go assists in knowing when to switch from one path element to the next.

Transformation formulas relating geodetic coordinates to a tangent to Earth, plane coordinate system

NASA Technical Reports Server (NTRS)

Credeur, L.

1981-01-01

Formulas and their approximation were developed to map geodetic position to an Earth tangent plane with an airport centered rectangular coordinate system. The transformations were developed for use in a terminal area air traffic model with deterministic aircraft traffic. The exact configured vehicle's approximation equations used in their precision microwave landing system navigation experiments.

Measurement of the loss tangent of low-density polyethylene with a nanoindentation technique

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

Loubet, J. L.; Oliver, W. C.; Lucas, B. N.

2000-05-01

This paper describes experimental measurements of the linear viscoelastic behavior of the surface of low-density (LD) polyethylene in contact with a pyramidal Berkovich diamond indenter. The experiments were carried out at two different temperatures, 15.9 and 27.2 degree sign C, between frequencies of 0.1 and 800 Hz. Using the shift of the loss tangent between the two temperatures at frequencies lower than 20 Hz and an Arrhenius equation, an activation energy of 105{+-}2 kJ/mol was obtained. This value is in good agreement with the bulk value of the {alpha} relaxation of LD polyethylene reported in the literature. (c) 2000 Materialsmore » Research Society.« less

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Stiffness optimization of non-linear elastic structures

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

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Tangent function transformation of the Abbreviated Injury Scale improves accuracy and simplifies scoring.

PubMed

Wang, Muding; Qiu, Wusi; Qiu, Fang; Mo, Yinan; Fan, Wenhui

2015-03-16

The Injury Severity Score (ISS) and the New Injury Severity Score (NISS) are widely used for anatomic severity assessments after trauma. We present here the Tangent Injury Severity Score (TISS), which transforms the Abbreviated Injury Scale (AIS) as a predictor of mortality. The TISS is defined as the sum of the tangent function of AIS/6 to the power 3.04 multiplied by 18.67 of a patient's three most severe AIS injuries regardless of body regions. TISS values were calculated for every patient in two large independent data sets: 3,908 and 4,171 patients treated during a 6-year period at level-3 first-class comprehensive hospitals: the Affiliated Hospital of Hangzhou Normal University and Fengtian Hospital Affiliated to Shenyang Medical College, China. The power of TISS to predict mortality was compared with previously calculated NISS values for the same patients in each data set. The TISS is more predictive of survival than NISS (Hangzhou: receiver operating characteristic (ROC): NISS = 0.929, TISS = 0.949; p = 0.002; Shenyang: ROC: NISS = 0.924, TISS = 0.942; p = 0.008). Moreover, TISS provides a better fit throughout its entire range of prediction (Hosmer Lemeshow statistic for Hangzhou NISS = 29.71; p < 0.001, TISS = 19.59; p = 0.003; Hosmer Lemeshow statistic for Shenyang NISS = 33.49; p < 0.001, TISS = 21.19; p = 0.002). The TISS shows more accurate prediction of prognosis and a linear relation to mortality. The TISS might be a better injury scoring tool with simple computation.

Dielectric response of high permittivity polymer ceramic composite with low loss tangent

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

Subodh, G.; 1.Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, Stuttgart 70550; Deepu, V.

2009-08-10

The present communication investigates the dielectric response of the Sr{sub 9}Ce{sub 2}Ti{sub 12}O{sub 36} ceramics loaded high density polyethylene and epoxy resin. Sr{sub 9}Ce{sub 2}Ti{sub 12}O{sub 36} ceramic filled polyethylene and epoxy composites were prepared using hot blending and mechanical mixing, respectively. 40 vol % ceramic loaded polyethylene has relative permittivity of 12.1 and loss tangent of 0.004 at 8 GHz, whereas the corresponding composite using epoxy as matrix has permittivity and loss tangent of 14.1 and 0.022, respectively. The effective medium theory fits relatively well for the observed permittivity of these composites.

The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: An analytical equation of state

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Vlugt, Thijs J. H.; Gross, Joachim

2014-01-01

An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the

Toward more accurate loss tangent measurements in reentrant cavities

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

Moyer, R. D.

1980-05-01

Karpova has described an absolute method for measurement of dielectric properties of a solid in a coaxial reentrant cavity. His cavity resonance equation yields very accurate results for dielectric constants. However, he presented only approximate expressions for the loss tangent. This report presents more exact expressions for that quantity and summarizes some experimental results.

SCIPUFF Tangent-Linear/Adjoint Model for Release Source Location from Observational Data

DTIC Science & Technology

2011-01-18

magnitudes, times? Inverse model based on SCIPUFF (AIMS) 1/17/2011 Aerodyne Research, Inc. W911NF-06-C-0161 5 (1981), Daescu and Carmichael (2003...Defined Choice- Situations” The Journal of the Operational Research Society, Vol. 32, No. 2 (1981) Daescu, D. N., and Carmichael , G. R., “An Adjoint...Intelligence Applications to Environmental Sciences at AMS Annual Meeting, Atlanta, GA, Jan 17-21 (2010 ) N. Platt, S. Warner and S. M. Nunes, ’Plan for

Tangent linear superparameterization of convection in a 10 layer global atmosphere with calibrated climatology

DOE PAGES

Kelly, Patrick; Mapes, Brian; Hu, I-Kuan; ...

2017-04-03

This study describes a new intermediate global atmosphere model in which synoptic and planetary dynamics including the advection of water vapor are explicit, the time mean flow is centered near a realistic state through the calibration of time-independent 3D forcings, and temporal anomalies of convective tendencies of heat and moisture in each column are represented as a linear matrix acting on the anomalous temperature and moisture profiles in the GCM. This matrix was devised from Kuang’s [2010] linear response function (LRF) of a cooled cyclic convection-permitting model (CCPM) with 256 km periodic domain and 1km mesh, measured around an equilibriummore » state with a mean rainrate of 3.5 mm/d. The goal of this effort was to cleanly test the role of convection’s free-tropospheric moisture sensitivity in tropical waves, without incurring large changes of mean climate that confuse the interpretation of experiments with entrainment rates in the convection schemes of full-physics GCMs. As the sensitivity to free tropospheric moisture (columns 12-20 of the matrix, representing sensitivity to humidity above 900 hPa altitude) is multiplied by a factor ranging from 0 to 2, the model’s variability ranges from: (1) moderately strong convectively coupled waves with speeds near 20 m s -1; to (0) weak waves, but still slowed by convective coupling; to (2) wave variability that is greater in amplitude as the water vapor field plays an increasingly important role. Longitudinal structure in the model’s time-mean tropical flow is not fully realistic, and does change significantly with matrix edits, disappointing initial hopes that the Madden-Julian oscillation would be well simulated in the control and could be convincingly decomposed, but further work could improve this class of models.« less

Tangent linear superparameterization of convection in a 10 layer global atmosphere with calibrated climatology

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

Kelly, Patrick; Mapes, Brian; Hu, I-Kuan

This study describes a new intermediate global atmosphere model in which synoptic and planetary dynamics including the advection of water vapor are explicit, the time mean flow is centered near a realistic state through the calibration of time-independent 3D forcings, and temporal anomalies of convective tendencies of heat and moisture in each column are represented as a linear matrix acting on the anomalous temperature and moisture profiles in the GCM. This matrix was devised from Kuang’s [2010] linear response function (LRF) of a cooled cyclic convection-permitting model (CCPM) with 256 km periodic domain and 1km mesh, measured around an equilibriummore » state with a mean rainrate of 3.5 mm/d. The goal of this effort was to cleanly test the role of convection’s free-tropospheric moisture sensitivity in tropical waves, without incurring large changes of mean climate that confuse the interpretation of experiments with entrainment rates in the convection schemes of full-physics GCMs. As the sensitivity to free tropospheric moisture (columns 12-20 of the matrix, representing sensitivity to humidity above 900 hPa altitude) is multiplied by a factor ranging from 0 to 2, the model’s variability ranges from: (1) moderately strong convectively coupled waves with speeds near 20 m s -1; to (0) weak waves, but still slowed by convective coupling; to (2) wave variability that is greater in amplitude as the water vapor field plays an increasingly important role. Longitudinal structure in the model’s time-mean tropical flow is not fully realistic, and does change significantly with matrix edits, disappointing initial hopes that the Madden-Julian oscillation would be well simulated in the control and could be convincingly decomposed, but further work could improve this class of models.« less

An arc tangent function demodulation method of fiber-optic Fabry-Perot high-temperature pressure sensor

NASA Astrophysics Data System (ADS)

Ren, Qianyu; Li, Junhong; Hong, Yingping; Jia, Pinggang; Xiong, Jijun

2017-09-01

A new demodulation algorithm of the fiber-optic Fabry-Perot cavity length based on the phase generated carrier (PGC) is proposed in this paper, which can be applied in the high-temperature pressure sensor. This new algorithm based on arc tangent function outputs two orthogonal signals by utilizing an optical system, which is designed based on the field-programmable gate array (FPGA) to overcome the range limit of the original PGC arc tangent function demodulation algorithm. The simulation and analysis are also carried on. According to the analysis of demodulation speed and precision, the simulation of different numbers of sampling points, and measurement results of the pressure sensor, the arc tangent function demodulation method has good demodulation results: 1 MHz processing speed of single data and less than 1% error showing practical feasibility in the fiber-optic Fabry-Perot cavity length demodulation of the Fabry-Perot high-temperature pressure sensor.

Introduction to Adjoint Models

NASA Technical Reports Server (NTRS)

Errico, Ronald M.

2015-01-01

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

Internal friction between fluid particles of MHD tangent hyperbolic fluid with heat generation: Using coefficients improved by Cash and Karp

NASA Astrophysics Data System (ADS)

Salahuddin, T.; Khan, Imad; Malik, M. Y.; Khan, Mair; Hussain, Arif; Awais, Muhammad

2017-05-01

The present work examines the internal resistance between fluid particles of tangent hyperbolic fluid flow due to a non-linear stretching sheet with heat generation. Using similarity transformations, the governing system of partial differential equations is transformed into a coupled non-linear ordinary differential system with variable coefficients. Unlike the current analytical works on the flow problems in the literature, the main concern here is to numerically work out and find the solution by using Runge-Kutta-Fehlberg coefficients improved by Cash and Karp (Naseer et al., Alexandria Eng. J. 53, 747 (2014)). To determine the relevant physical features of numerous mechanisms acting on the deliberated problem, it is sufficient to have the velocity profile and temperature field and also the drag force and heat transfer rate all as given in the current paper.

LINEAR - DERIVATION AND DEFINITION OF A LINEAR AIRCRAFT MODEL

NASA Technical Reports Server (NTRS)

Duke, E. L.

1994-01-01

The Derivation and Definition of a Linear Model program, LINEAR, provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models. LINEAR was developed to provide a standard, documented, and verified tool to derive linear models for aircraft stability analysis and control law design. Linear system models define the aircraft system in the neighborhood of an analysis point and are determined by the linearization of the nonlinear equations defining vehicle dynamics and sensors. LINEAR numerically determines a linear system model using nonlinear equations of motion and a user supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. LINEAR is capable of extracting both linearized engine effects, such as net thrust, torque, and gyroscopic effects and including these effects in the linear system model. The point at which this linear model is defined is determined either by completely specifying the state and control variables, or by specifying an analysis point on a trajectory and directing the program to determine the control variables and the remaining state variables. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to provide easy selection of state, control, and observation variables to be used in a particular model. Thus, the order of the system model is completely under user control. Further, the program provides the flexibility of allowing alternate formulations of both the state and observation equations. Data describing the aircraft and the test case is input to the program through a terminal or formatted data files. All data can be modified interactively from case to case. The aerodynamic model can be defined in two ways: a set of nondimensional stability and control derivatives for the flight point of

The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Oyarzún, Bernardo; Vlugt, Thijs J. H.; Gross, Joachim

2013-07-01

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.

A new analytical method for estimating lumped parameter constants of linear viscoelastic models from strain rate tests

NASA Astrophysics Data System (ADS)

Mattei, G.; Ahluwalia, A.

2018-04-01

We introduce a new function, the apparent elastic modulus strain-rate spectrum, E_{app} ( \\dot{ɛ} ), for the derivation of lumped parameter constants for Generalized Maxwell (GM) linear viscoelastic models from stress-strain data obtained at various compressive strain rates ( \\dot{ɛ}). The E_{app} ( \\dot{ɛ} ) function was derived using the tangent modulus function obtained from the GM model stress-strain response to a constant \\dot{ɛ} input. Material viscoelastic parameters can be rapidly derived by fitting experimental E_{app} data obtained at different strain rates to the E_{app} ( \\dot{ɛ} ) function. This single-curve fitting returns similar viscoelastic constants as the original epsilon dot method based on a multi-curve global fitting procedure with shared parameters. Its low computational cost permits quick and robust identification of viscoelastic constants even when a large number of strain rates or replicates per strain rate are considered. This method is particularly suited for the analysis of bulk compression and nano-indentation data of soft (bio)materials.

Modelling female fertility traits in beef cattle using linear and non-linear models.

PubMed

Naya, H; Peñagaricano, F; Urioste, J I

2017-06-01

Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2  < 0.08 and r < 0.13, for linear models; h 2  > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.

A Linearized Prognostic Cloud Scheme in NASAs Goddard Earth Observing System Data Assimilation Tools

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Errico, Ronald M.; Gelaro, Ronald; Kim, Jong G.; Mahajan, Rahul

2015-01-01

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA's Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

Without derivatives or limits: from visual and geometrical points of view to algebraic methods for identifying tangent lines

NASA Astrophysics Data System (ADS)

Vivier, L.

2013-07-01

Usually, the tangent line is considered to be a calculus notion. However, it is also a graphical and an algebraic notion. The graphical frame, where our primary conceptions are conceived, could give rise to algebraic methods to obtain the tangent line to a curve. In this pre-calculus perspective, two methods are described and discussed according to their potential for secondary students and teacher training.

Multiband tangent space mapping and feature selection for classification of EEG during motor imagery.

PubMed

Islam, Md Rabiul; Tanaka, Toshihisa; Molla, Md Khademul Islam

2018-05-08

When designing multiclass motor imagery-based brain-computer interface (MI-BCI), a so-called tangent space mapping (TSM) method utilizing the geometric structure of covariance matrices is an effective technique. This paper aims to introduce a method using TSM for finding accurate operational frequency bands related brain activities associated with MI tasks. A multichannel electroencephalogram (EEG) signal is decomposed into multiple subbands, and tangent features are then estimated on each subband. A mutual information analysis-based effective algorithm is implemented to select subbands containing features capable of improving motor imagery classification accuracy. Thus obtained features of selected subbands are combined to get feature space. A principal component analysis-based approach is employed to reduce the features dimension and then the classification is accomplished by a support vector machine (SVM). Offline analysis demonstrates the proposed multiband tangent space mapping with subband selection (MTSMS) approach outperforms state-of-the-art methods. It acheives the highest average classification accuracy for all datasets (BCI competition dataset 2a, IIIa, IIIb, and dataset JK-HH1). The increased classification accuracy of MI tasks with the proposed MTSMS approach can yield effective implementation of BCI. The mutual information-based subband selection method is implemented to tune operation frequency bands to represent actual motor imagery tasks.

Linear models: permutation methods

USGS Publications Warehouse

Cade, B.S.; Everitt, B.S.; Howell, D.C.

2005-01-01

Permutation tests (see Permutation Based Inference) for the linear model have applications in behavioral studies when traditional parametric assumptions about the error term in a linear model are not tenable. Improved validity of Type I error rates can be achieved with properly constructed permutation tests. Perhaps more importantly, increased statistical power, improved robustness to effects of outliers, and detection of alternative distributional differences can be achieved by coupling permutation inference with alternative linear model estimators. For example, it is well-known that estimates of the mean in linear model are extremely sensitive to even a single outlying value of the dependent variable compared to estimates of the median [7, 19]. Traditionally, linear modeling focused on estimating changes in the center of distributions (means or medians). However, quantile regression allows distributional changes to be estimated in all or any selected part of a distribution or responses, providing a more complete statistical picture that has relevance to many biological questions [6]...

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

NASA Astrophysics Data System (ADS)

Triantafyllopoulos, A.; Stavrinos, P. C.

2018-04-01

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of general relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4‑velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein–Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.

Population response to climate change: linear vs. non-linear modeling approaches.

PubMed

Ellis, Alicia M; Post, Eric

2004-03-31

Research on the ecological consequences of global climate change has elicited a growing interest in the use of time series analysis to investigate population dynamics in a changing climate. Here, we compare linear and non-linear models describing the contribution of climate to the density fluctuations of the population of wolves on Isle Royale, Michigan from 1959 to 1999. The non-linear self excitatory threshold autoregressive (SETAR) model revealed that, due to differences in the strength and nature of density dependence, relatively small and large populations may be differentially affected by future changes in climate. Both linear and non-linear models predict a decrease in the population of wolves with predicted changes in climate. Because specific predictions differed between linear and non-linear models, our study highlights the importance of using non-linear methods that allow the detection of non-linearity in the strength and nature of density dependence. Failure to adopt a non-linear approach to modelling population response to climate change, either exclusively or in addition to linear approaches, may compromise efforts to quantify ecological consequences of future warming.

Local electron tomography using angular variations of surface tangents: Stomo version 2

NASA Astrophysics Data System (ADS)

Petersen, T. C.; Ringer, S. P.

2012-03-01

In a recent publication, we investigated the prospect of measuring the outer three-dimensional (3D) shapes of nano-scale atom probe specimens from tilt-series of images collected in the transmission electron microscope. For this purpose alone, an algorithm and simplified reconstruction theory were developed to circumvent issues that arise in commercial "back-projection" computations in this context. In our approach, we give up the difficult task of computing the complete 3D continuum structure and instead seek only the 3D morphology of internal and external scattering interfaces. These interfaces can be described as embedded 2D surfaces projected onto each image in a tilt series. Curves and other features in the images are interpreted as inscribed sets of tangent lines, which intersect the scattering interfaces at unknown locations along the direction of the incident electron beam. Smooth angular variations of the tangent line abscissa are used to compute the surface tangent intersections and hence the 3D morphology as a "point cloud". We have published the explicit details of our alternative algorithm along with the source code entitled "stomo_version_1". For this work, we have further modified the code to efficiently handle rectangular image sets, perform much faster tangent-line "edge detection" and smoother tilt-axis image alignment using simple bi-linear interpolation. We have also adapted the algorithm to detect tangent lines as "ridges", based upon 2nd order partial derivatives of the image intensity; the magnitude and orientation of which is described by a Hessian matrix. Ridges are more appropriate descriptors for tangent-line curves in phase contrast images outlined by Fresnel fringes or absorption contrast data from fine-scale objects. Improved accuracy, efficiency and speed for "stomo_version_2" is demonstrated in this paper using both high resolution electron tomography data of a nano-sized atom probe tip and simulated absorption-contrast images

Application of Hierarchical Linear Models/Linear Mixed-Effects Models in School Effectiveness Research

ERIC Educational Resources Information Center

Ker, H. W.

2014-01-01

Multilevel data are very common in educational research. Hierarchical linear models/linear mixed-effects models (HLMs/LMEs) are often utilized to analyze multilevel data nowadays. This paper discusses the problems of utilizing ordinary regressions for modeling multilevel educational data, compare the data analytic results from three regression…

CSP-TSM: Optimizing the performance of Riemannian tangent space mapping using common spatial pattern for MI-BCI.

PubMed

Kumar, Shiu; Mamun, Kabir; Sharma, Alok

2017-12-01

Classification of electroencephalography (EEG) signals for motor imagery based brain computer interface (MI-BCI) is an exigent task and common spatial pattern (CSP) has been extensively explored for this purpose. In this work, we focused on developing a new framework for classification of EEG signals for MI-BCI. We propose a single band CSP framework for MI-BCI that utilizes the concept of tangent space mapping (TSM) in the manifold of covariance matrices. The proposed method is named CSP-TSM. Spatial filtering is performed on the bandpass filtered MI EEG signal. Riemannian tangent space is utilized for extracting features from the spatial filtered signal. The TSM features are then fused with the CSP variance based features and feature selection is performed using Lasso. Linear discriminant analysis (LDA) is then applied to the selected features and finally classification is done using support vector machine (SVM) classifier. The proposed framework gives improved performance for MI EEG signal classification in comparison with several competing methods. Experiments conducted shows that the proposed framework reduces the overall classification error rate for MI-BCI by 3.16%, 5.10% and 1.70% (for BCI Competition III dataset IVa, BCI Competition IV Dataset I and BCI Competition IV Dataset IIb, respectively) compared to the conventional CSP method under the same experimental settings. The proposed CSP-TSM method produces promising results when compared with several competing methods in this paper. In addition, the computational complexity is less compared to that of TSM method. Our proposed CSP-TSM framework can be potentially used for developing improved MI-BCI systems. Copyright © 2017 Elsevier Ltd. All rights reserved.

Is the local linearity of space-time inherited from the linearity of probabilities?

NASA Astrophysics Data System (ADS)

Müller, Markus P.; Carrozza, Sylvain; Höhn, Philipp A.

2017-02-01

The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the physicist, most computer scientists would argue that something like a ‘local linear tangent space’ is not very typical and in fact a quite surprising property of any conceivable world or algorithm. In this paper, we take the perspective of the computer scientist seriously, and ask whether there could be any inherently information-theoretic reason to expect this notion of linearity to appear in physics. We give a series of simple arguments, spanning quantum information theory, group representation theory, and renormalization in quantum gravity, that supports a surprising thesis: namely, that the local linearity of space-time might ultimately be a consequence of the linearity of probabilities. While our arguments involve a fair amount of speculation, they have the virtue of being independent of any detailed assumptions on quantum gravity, and they are in harmony with several independent recent ideas on emergent space-time in high-energy physics.

From Spiking Neuron Models to Linear-Nonlinear Models

PubMed Central

Ostojic, Srdjan; Brunel, Nicolas

2011-01-01

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates. PMID:21283777

From spiking neuron models to linear-nonlinear models.

PubMed

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

A Family of Ellipse Methods for Solving Non-Linear Equations

ERIC Educational Resources Information Center

Gupta, K. C.; Kanwar, V.; Kumar, Sanjeev

2009-01-01

This note presents a method for the numerical approximation of simple zeros of a non-linear equation in one variable. In order to do so, the method uses an ellipse rather than a tangent approach. The main advantage of our method is that it does not fail even if the derivative of the function is either zero or very small in the vicinity of the…

Numerical prediction of rail roughness growth on tangent railway tracks

NASA Astrophysics Data System (ADS)

Nielsen, J. C. O.

2003-10-01

Growth of railhead roughness (irregularities, waviness) is predicted through numerical simulation of dynamic train-track interaction on tangent track. The hypothesis is that wear is caused by longitudinal slip due to driven wheelsets, and that wear is proportional to the longitudinal frictional power in the contact patch. Emanating from an initial roughness spectrum corresponding to a new or a recent ground rail, an initial roughness profile is determined. Wheel-rail contact forces, creepages and wear for one wheelset passage are calculated in relation to location along a discretely supported track model. The calculated wear is scaled by a chosen number of wheelset passages, and is then added to the initial roughness profile. Field observations of rail corrugation on a Dutch track are used to validate the simulation model. Results from the simulations predict a large roughness growth rate for wavelengths around 30-40 mm. The large growth in this wavelength interval is explained by a low track receptance near the sleepers around the pinned-pinned resonance frequency, in combination with a large number of driven passenger wheelset passages at uniform speed. The agreement between simulations and field measurements is good with respect to dominating roughness wavelength and annual wear rate. Remedies for reducing roughness growth are discussed.

Computing Linear Mathematical Models Of Aircraft

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1991-01-01

Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

Modelling and Predicting Backstroke Start Performance Using Non-Linear and Linear Models

PubMed Central

de Jesus, Karla; Ayala, Helon V. H.; de Jesus, Kelly; Coelho, Leandro dos S.; Medeiros, Alexandre I.A.; Abraldes, José A.; Vaz, Mário A.P.; Fernandes, Ricardo J.; Vilas-Boas, João Paulo

2018-01-01

Abstract Our aim was to compare non-linear and linear mathematical model responses for backstroke start performance prediction. Ten swimmers randomly completed eight 15 m backstroke starts with feet over the wedge, four with hands on the highest horizontal and four on the vertical handgrip. Swimmers were videotaped using a dual media camera set-up, with the starts being performed over an instrumented block with four force plates. Artificial neural networks were applied to predict 5 m start time using kinematic and kinetic variables and to determine the accuracy of the mean absolute percentage error. Artificial neural networks predicted start time more robustly than the linear model with respect to changing training to the validation dataset for the vertical handgrip (3.95 ± 1.67 vs. 5.92 ± 3.27%). Artificial neural networks obtained a smaller mean absolute percentage error than the linear model in the horizontal (0.43 ± 0.19 vs. 0.98 ± 0.19%) and vertical handgrip (0.45 ± 0.19 vs. 1.38 ± 0.30%) using all input data. The best artificial neural network validation revealed a smaller mean absolute error than the linear model for the horizontal (0.007 vs. 0.04 s) and vertical handgrip (0.01 vs. 0.03 s). Artificial neural networks should be used for backstroke 5 m start time prediction due to the quite small differences among the elite level performances. PMID:29599857

Modelling and Predicting Backstroke Start Performance Using Non-Linear and Linear Models.

PubMed

de Jesus, Karla; Ayala, Helon V H; de Jesus, Kelly; Coelho, Leandro Dos S; Medeiros, Alexandre I A; Abraldes, José A; Vaz, Mário A P; Fernandes, Ricardo J; Vilas-Boas, João Paulo

2018-03-01

Our aim was to compare non-linear and linear mathematical model responses for backstroke start performance prediction. Ten swimmers randomly completed eight 15 m backstroke starts with feet over the wedge, four with hands on the highest horizontal and four on the vertical handgrip. Swimmers were videotaped using a dual media camera set-up, with the starts being performed over an instrumented block with four force plates. Artificial neural networks were applied to predict 5 m start time using kinematic and kinetic variables and to determine the accuracy of the mean absolute percentage error. Artificial neural networks predicted start time more robustly than the linear model with respect to changing training to the validation dataset for the vertical handgrip (3.95 ± 1.67 vs. 5.92 ± 3.27%). Artificial neural networks obtained a smaller mean absolute percentage error than the linear model in the horizontal (0.43 ± 0.19 vs. 0.98 ± 0.19%) and vertical handgrip (0.45 ± 0.19 vs. 1.38 ± 0.30%) using all input data. The best artificial neural network validation revealed a smaller mean absolute error than the linear model for the horizontal (0.007 vs. 0.04 s) and vertical handgrip (0.01 vs. 0.03 s). Artificial neural networks should be used for backstroke 5 m start time prediction due to the quite small differences among the elite level performances.

User's manual for LINEAR, a FORTRAN program to derive linear aircraft models

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Patterson, Brian P.; Antoniewicz, Robert F.

1987-01-01

This report documents a FORTRAN program that provides a powerful and flexible tool for the linearization of aircraft models. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.

Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots

ERIC Educational Resources Information Center

Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.

2013-01-01

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…

Inclusion of Linearized Moist Physics in Nasa's Goddard Earth Observing System Data Assimilation Tools

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Errico, Ronald; Gelaro, Ronaldo; Kim, Jong G.

2013-01-01

Inclusion of moist physics in the linearized version of a weather forecast model is beneficial in terms of variational data assimilation. Further, it improves the capability of important tools, such as adjoint-based observation impacts and sensitivity studies. A linearized version of the relaxed Arakawa-Schubert (RAS) convection scheme has been developed and tested in NASA's Goddard Earth Observing System data assimilation tools. A previous study of the RAS scheme showed it to exhibit reasonable linearity and stability. This motivates the development of a linearization of a near-exact version of the RAS scheme. Linearized large-scale condensation is included through simple conversion of supersaturation into precipitation. The linearization of moist physics is validated against the full nonlinear model for 6- and 24-h intervals, relevant to variational data assimilation and observation impacts, respectively. For a small number of profiles, sudden large growth in the perturbation trajectory is encountered. Efficient filtering of these profiles is achieved by diagnosis of steep gradients in a reduced version of the operator of the tangent linear model. With filtering turned on, the inclusion of linearized moist physics increases the correlation between the nonlinear perturbation trajectory and the linear approximation of the perturbation trajectory. A month-long observation impact experiment is performed and the effect of including moist physics on the impacts is discussed. Impacts from moist-sensitive instruments and channels are increased. The effect of including moist physics is examined for adjoint sensitivity studies. A case study examining an intensifying Northern Hemisphere Atlantic storm is presented. The results show a significant sensitivity with respect to moisture.

A Tangent Bundle Theory for Visual Curve Completion.

PubMed

Ben-Yosef, Guy; Ben-Shahar, Ohad

2012-07-01

Visual curve completion is a fundamental perceptual mechanism that completes the missing parts (e.g., due to occlusion) between observed contour fragments. Previous research into the shape of completed curves has generally followed an "axiomatic" approach, where desired perceptual/geometrical properties are first defined as axioms, followed by mathematical investigation into curves that satisfy them. However, determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place. Instead, here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle R(2) × S(1), which abstracts the primary visual cortex (V1) and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed. Exploring here the elementary principle of least action in V1, we show how the problem becomes one of finding minimum-length admissible curves in R(2) × S(1). We formalize the problem in variational terms, we analyze it theoretically, and we formulate practical algorithms for the reconstruction of these completed curves. We then explore their induced visual properties vis-à-vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature. Finally, we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models.

Determination of loss tangent of human tear film at 9.8 GHz

NASA Astrophysics Data System (ADS)

Bansal, Namita; Dhaliwal, A. S.; Mann, K. S.

2015-08-01

Basal (non-stimulated) tears that are produced by accessory lacrimal glands located in conjunctiva of human eye, form tear film which in turn keeps the eye moist and lubricate; nourishes the eye; protects the eye from dust, bacterial infection and shear forces generated during eye movements and blinking; and provides a refractive surface on the corneal epithelium. Film is known to contain water, mucin, lipids, lysozyme, glucose, urea, sodium etc. In present communication, loss tangent of human tear film has been determined at 9.8 GHz microwaves by employing cavity perturbation technique at a temperature of 37°C. The basal tears from a small population comprising six subjects were collected and average value of loss tangent is reported. Slater's technique was used to reduce the error caused in measuring the volume of sample. The determined values are useful to study the biological effects of microwaves on tear film as well as other parts of human eye such as eye lens and lens epithelial cells. To the best of author's knowledge, no such study is available in literature at any radio as well as microwave frequencies; therefore present determinations are first of its kind.

Overview of TANGENT (Tandem Aerosol Nucleation and Growth ENvironment Tube) 2017 IOP Study

NASA Astrophysics Data System (ADS)

Tiszenkel, L.

2017-12-01

New particle formation consists of two steps: nucleation and growth of nucleated particles. However, most laboratory studies have been conducted under conditions where these two processes are convoluted together, thereby hampering the detailed understanding of the effect of chemical species and atmospheric conditions on two processes. The objective of the Tandem Aerosol Nucleation and Growth ENvironment Tube (TANGENT) laboratory study is to investigate aerosol nucleation and growth properties independently by separating these two processes in two different flow tubes. This research is a collaboration between the University of Alabama in Huntsville and the University of Delaware. In this poster we will present the experimental setup of TANGENT and summarize the key results from the first IOP (intense observation period) experiments undertaken during Summer 2017. Nucleation takes place in a temperature- and RH-controlled fast flow reactor (FT-1) where sulfuric acid forms from OH radicals and sulfur dioxide. Sulfuric acid and impurity base compounds are detected with chemical ionization mass spectrometers (CIMS). Particle sizes and number concentrations of newly nucleated particles are measured with a scanning mobility particle sizer (SMPS) and particle size magnifier (PSM), providing concentrations of particles between 1-100 nm. The nucleation particles are transferred directly to the growth tube (FT-2) where oxidants and biogenic organic precursors are added to grow nucleated nanoparticles. Sizes of particles after growth are analyzed with an additional SMPS and elemental chemical composition of 50 nm and above particles detected with a nano-aerosol mass spectrometer (NAMS). TANGENT provides the unique ability to conduct experiments that can monitor and control reactant concentrations, aerosol size and aerosol chemical composition during nucleation and growth. Experiments during this first IOP study have elucidated the effects of sulfur dioxide, particle size

User's manual for interactive LINEAR: A FORTRAN program to derive linear aircraft models

NASA Technical Reports Server (NTRS)

Antoniewicz, Robert F.; Duke, Eugene L.; Patterson, Brian P.

1988-01-01

An interactive FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models is documented in this report. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.

Simplified aerosol modeling for variational data assimilation

NASA Astrophysics Data System (ADS)

Huneeus, N.; Boucher, O.; Chevallier, F.

2009-11-01

We have developed a simplified aerosol model together with its tangent linear and adjoint versions for the ultimate aim of optimizing global aerosol and aerosol precursor emission using variational data assimilation. The model was derived from the general circulation model LMDz; it groups together the 24 aerosol species simulated in LMDz into 4 species, namely gaseous precursors, fine mode aerosols, coarse mode desert dust and coarse mode sea salt. The emissions have been kept as in the original model. Modifications, however, were introduced in the computation of aerosol optical depth and in the processes of sedimentation, dry and wet deposition and sulphur chemistry to ensure consistency with the new set of species and their composition. The simplified model successfully manages to reproduce the main features of the aerosol distribution in LMDz. The largest differences in aerosol load are observed for fine mode aerosols and gaseous precursors. Differences between the original and simplified models are mainly associated to the new deposition and sedimentation velocities consistent with the definition of species in the simplified model and the simplification of the sulphur chemistry. Furthermore, simulated aerosol optical depth remains within the variability of monthly AERONET observations for all aerosol types and all sites throughout most of the year. Largest differences are observed over sites with strong desert dust influence. In terms of the daily aerosol variability, the model is less able to reproduce the observed variability from the AERONET data with larger discrepancies in stations affected by industrial aerosols. The simplified model however, closely follows the daily simulation from LMDz. Sensitivity analyses with the tangent linear version show that the simplified sulphur chemistry is the dominant process responsible for the strong non-linearity of the model.

Parameterized Linear Longitudinal Airship Model

NASA Technical Reports Server (NTRS)

Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph

2010-01-01

A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics

Cable Effects Study. Tangents, Rabbit Holes, Dead Ends, and Valuable Results

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

Ardelean, Emil V.; Babuška, Vít; Goodding, James C.

Lessons learned during a study on the effects that electrical power and signal wiring harness cables introduce on the dynamic response of precision spacecraft is presented, along with the most significant results. Our study was a three year effort to discover a set of practical approaches for updating well-defined dynamic models of harness-free structures where knowledge of the cable type, position, and tie-down method are known. Although cables are found on every satellite, the focus was on precision, low damping, and very flexible structures. Obstacles encountered, classified as tangents, rabbit holes, and dead ends, offer practical lessons for structural dynamicsmore » research. The paper traces the historical, experiential progression of the project, describing how the obstacles affected the project. Methods were developed to estimate cable properties. Problems were encountered because of the flexible, highly damped nature of cables. A beam was used as a test article to validate experimentally derived cable properties and to refine the assumptions regarding boundary conditions. Furthermore, a spacecraft bus-like panel with cables attached was designed, and finite element models were developed and validated through experiment. Various paths were investigated at each stage before a consistent test and analysis methodology was developed« less

Cable Effects Study. Tangents, Rabbit Holes, Dead Ends, and Valuable Results

DOE PAGES

Ardelean, Emil V.; Babuška, Vít; Goodding, James C.; ...

2014-08-04

Lessons learned during a study on the effects that electrical power and signal wiring harness cables introduce on the dynamic response of precision spacecraft is presented, along with the most significant results. Our study was a three year effort to discover a set of practical approaches for updating well-defined dynamic models of harness-free structures where knowledge of the cable type, position, and tie-down method are known. Although cables are found on every satellite, the focus was on precision, low damping, and very flexible structures. Obstacles encountered, classified as tangents, rabbit holes, and dead ends, offer practical lessons for structural dynamicsmore » research. The paper traces the historical, experiential progression of the project, describing how the obstacles affected the project. Methods were developed to estimate cable properties. Problems were encountered because of the flexible, highly damped nature of cables. A beam was used as a test article to validate experimentally derived cable properties and to refine the assumptions regarding boundary conditions. Furthermore, a spacecraft bus-like panel with cables attached was designed, and finite element models were developed and validated through experiment. Various paths were investigated at each stage before a consistent test and analysis methodology was developed« less

Convex set and linear mixing model

NASA Technical Reports Server (NTRS)

Xu, P.; Greeley, R.

1993-01-01

A major goal of optical remote sensing is to determine surface compositions of the earth and other planetary objects. For assessment of composition, single pixels in multi-spectral images usually record a mixture of the signals from various materials within the corresponding surface area. In this report, we introduce a closed and bounded convex set as a mathematical model for linear mixing. This model has a clear geometric implication because the closed and bounded convex set is a natural generalization of a triangle in n-space. The endmembers are extreme points of the convex set. Every point in the convex closure of the endmembers is a linear mixture of those endmembers, which is exactly how linear mixing is defined. With this model, some general criteria for selecting endmembers could be described. This model can lead to a better understanding of linear mixing models.

Linear Logistic Test Modeling with R

ERIC Educational Resources Information Center

Baghaei, Purya; Kubinger, Klaus D.

2015-01-01

The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…

Comparison of linear and non-linear models for predicting energy expenditure from raw accelerometer data.

PubMed

Montoye, Alexander H K; Begum, Munni; Henning, Zachary; Pfeiffer, Karin A

2017-02-01

This study had three purposes, all related to evaluating energy expenditure (EE) prediction accuracy from body-worn accelerometers: (1) compare linear regression to linear mixed models, (2) compare linear models to artificial neural network models, and (3) compare accuracy of accelerometers placed on the hip, thigh, and wrists. Forty individuals performed 13 activities in a 90 min semi-structured, laboratory-based protocol. Participants wore accelerometers on the right hip, right thigh, and both wrists and a portable metabolic analyzer (EE criterion). Four EE prediction models were developed for each accelerometer: linear regression, linear mixed, and two ANN models. EE prediction accuracy was assessed using correlations, root mean square error (RMSE), and bias and was compared across models and accelerometers using repeated-measures analysis of variance. For all accelerometer placements, there were no significant differences for correlations or RMSE between linear regression and linear mixed models (correlations: r  =  0.71-0.88, RMSE: 1.11-1.61 METs; p  >  0.05). For the thigh-worn accelerometer, there were no differences in correlations or RMSE between linear and ANN models (ANN-correlations: r  =  0.89, RMSE: 1.07-1.08 METs. Linear models-correlations: r  =  0.88, RMSE: 1.10-1.11 METs; p  >  0.05). Conversely, one ANN had higher correlations and lower RMSE than both linear models for the hip (ANN-correlation: r  =  0.88, RMSE: 1.12 METs. Linear models-correlations: r  =  0.86, RMSE: 1.18-1.19 METs; p  <  0.05), and both ANNs had higher correlations and lower RMSE than both linear models for the wrist-worn accelerometers (ANN-correlations: r  =  0.82-0.84, RMSE: 1.26-1.32 METs. Linear models-correlations: r  =  0.71-0.73, RMSE: 1.55-1.61 METs; p  <  0.01). For studies using wrist-worn accelerometers, machine learning models offer a significant improvement in EE prediction

Linear and non-linear perturbations in dark energy models

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

Escamilla-Rivera, Celia; Casarini, Luciano; Fabris, Júlio C.

2016-11-01

In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state w ( z ). In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected w ( z ) parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard ΛCDM model.

Latent log-linear models for handwritten digit classification.

PubMed

Deselaers, Thomas; Gass, Tobias; Heigold, Georg; Ney, Hermann

2012-06-01

We present latent log-linear models, an extension of log-linear models incorporating latent variables, and we propose two applications thereof: log-linear mixture models and image deformation-aware log-linear models. The resulting models are fully discriminative, can be trained efficiently, and the model complexity can be controlled. Log-linear mixture models offer additional flexibility within the log-linear modeling framework. Unlike previous approaches, the image deformation-aware model directly considers image deformations and allows for a discriminative training of the deformation parameters. Both are trained using alternating optimization. For certain variants, convergence to a stationary point is guaranteed and, in practice, even variants without this guarantee converge and find models that perform well. We tune the methods on the USPS data set and evaluate on the MNIST data set, demonstrating the generalization capabilities of our proposed models. Our models, although using significantly fewer parameters, are able to obtain competitive results with models proposed in the literature.

Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

PubMed

Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad

2016-02-01

In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.

Quantum particles in general spacetimes: A tangent bundle formalism

NASA Astrophysics Data System (ADS)

Wohlfarth, Mattias N. R.

2018-06-01

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new type of nonminimal coupling of the fields and is shown to admit a canonical quantization procedure. For the resulting quantum theory we demonstrate the emergence of a particle interpretation, fully consistent with general relativistic geometry. The path dependency of parallel transport forces each observer to carry their own quantum state; we find that the communication of the corresponding quantum information may generate extra particles on curved spacetimes. A speculative link between quantum information and spacetime curvature is discussed which might lead to novel explanations for quantum decoherence and vanishing interference in double-slit or interaction-free measurement scenarios, in the mere presence of additional observers.

Study on Remote Monitoring System of Crossing and Spanning Tangent Tower

NASA Astrophysics Data System (ADS)

Chen, Da-bing; Zhang, Nai-long; Zhang, Meng-ge; Wang, Ze-hua; Zhang, Yan

2017-05-01

In order to grasp the vibration state of overhead transmission line and ensure the operational security of transmission line, the remote monitoring system of crossing and spanning tangent tower was studied. By use of this system, the displacement, velocity and acceleration of the tower, and the local weather data are collected automatically, displayed on computer of remote monitoring centre through wireless network, real-time collection and transmission of vibration signals are realized. The applying results show that the system is excellent in reliability and accuracy and so on. The system can be used to remote monitoring of transmission tower of UHV power transmission lines and in large spanning areas.

Robust video copy detection approach based on local tangent space alignment

NASA Astrophysics Data System (ADS)

Nie, Xiushan; Qiao, Qianping

2012-04-01

We propose a robust content-based video copy detection approach based on local tangent space alignment (LTSA), which is an efficient dimensionality reduction algorithm. The idea is motivated by the fact that the content of video becomes richer and the dimension of content becomes higher. It does not give natural tools for video analysis and understanding because of the high dimensionality. The proposed approach reduces the dimensionality of video content using LTSA, and then generates video fingerprints in low dimensional space for video copy detection. Furthermore, a dynamic sliding window is applied to fingerprint matching. Experimental results show that the video copy detection approach has good robustness and discrimination.

Deformation-Aware Log-Linear Models

NASA Astrophysics Data System (ADS)

Gass, Tobias; Deselaers, Thomas; Ney, Hermann

In this paper, we present a novel deformation-aware discriminative model for handwritten digit recognition. Unlike previous approaches our model directly considers image deformations and allows discriminative training of all parameters, including those accounting for non-linear transformations of the image. This is achieved by extending a log-linear framework to incorporate a latent deformation variable. The resulting model has an order of magnitude less parameters than competing approaches to handling image deformations. We tune and evaluate our approach on the USPS task and show its generalization capabilities by applying the tuned model to the MNIST task. We gain interesting insights and achieve highly competitive results on both tasks.

The Cretaceous superchron geodynamo: Observations near the tangent cylinder

PubMed Central

Tarduno, John A.; Cottrell, Rory D.; Smirnov, Alexei V.

2002-01-01

If relationships exist between the frequency of geomagnetic reversals and the morphology, secular variation, and intensity of Earth's magnetic field, they should be best expressed during superchrons, intervals tens of millions of years long lacking reversals. Here we report paleomagnetic and paleointensity data from lavas of the Cretaceous Normal Polarity Superchron that formed at high latitudes near the tangent cylinder that surrounds the solid inner core. The time-averaged field recorded by these lavas is remarkably strong and stable. When combined with global results available from lower latitudes, these data define a time-averaged field that is overwhelmingly dominated by the axial dipole (octupole components are insignificant). These observations suggest that the basic features of the geomagnetic field are intrinsically related. Superchrons may reflect times when the nature of core–mantle boundary heat flux allows the geodynamo to operate at peak efficiency. PMID:12388778

On some approaches to model reversible magnetization processes

NASA Astrophysics Data System (ADS)

Chwastek, K.; Baghel, A. P. S.; Sai Ram, B.; Borowik, B.; Daniel, L.; Kulkarni, S. V.

2018-04-01

This paper focuses on the problem of how reversible magnetization processes are taken into account in contemporary descriptions of hysteresis curves. For comparison, three versions of the phenomenological T(x) model based on hyperbolic tangent mapping are considered. Two of them are based on summing the output of the hysteresis operator with a linear or nonlinear mapping. The third description is inspired by the concept of the product Preisach model. Total susceptibility is modulated with a magnetization-dependent function. The models are verified using measurement data for grain-oriented electrical steel. The proposed third description represents minor loops most accurately.

Linear Models for Systematics and Nuisances

NASA Astrophysics Data System (ADS)

Luger, Rodrigo; Foreman-Mackey, Daniel; Hogg, David W.

2017-12-01

The target of many astronomical studies is the recovery of tiny astrophysical signals living in a sea of uninteresting (but usually dominant) noise. In many contexts (i.e., stellar time-series, or high-contrast imaging, or stellar spectroscopy), there are structured components in this noise caused by systematic effects in the astronomical source, the atmosphere, the telescope, or the detector. More often than not, evaluation of the true physical model for these nuisances is computationally intractable and dependent on too many (unknown) parameters to allow rigorous probabilistic inference. Sometimes, housekeeping data---and often the science data themselves---can be used as predictors of the systematic noise. Linear combinations of simple functions of these predictors are often used as computationally tractable models that can capture the nuisances. These models can be used to fit and subtract systematics prior to investigation of the signals of interest, or they can be used in a simultaneous fit of the systematics and the signals. In this Note, we show that if a Gaussian prior is placed on the weights of the linear components, the weights can be marginalized out with an operation in pure linear algebra, which can (often) be made fast. We illustrate this model by demonstrating the applicability of a linear model for the non-linear systematics in K2 time-series data, where the dominant noise source for many stars is spacecraft motion and variability.

The incidence and effect of fatty atrophy, positive tangent sign, and rotator cuff tears on outcomes after total shoulder arthroplasty.

PubMed

Choate, W Stephen; Shanley, Ellen; Washburn, Richard; Tolan, Stefan J; Salim, Tariq I; Tadlock, Josh; Shealy, Elizabeth C; Long, Catherine D; Crawford, Ashley E; Kissenberth, Michael J; Lonergan, Keith T; Hawkins, Richard J; Tokish, John M

2017-12-01

Treatment choices for total shoulder arthroplasty (TSA) in the absence of full-thickness rotator cuff tears (RCTs) are not clearly defined in current literature. This study investigated the prevalence and effect of preoperative partial-thickness RCTs and muscular degenerative changes on postoperative outcomes after TSA. Medical records and magnetic resonance imaging studies were reviewed for patients who underwent TSA for primary glenohumeral osteoarthritis with minimum 2-year follow-up to determine preoperative tear classification, Goutallier grade, and supraspinatus tangent sign. Postoperative pain on the visual analog scale, range of motion, and patient outcomes scores were obtained to correlate preoperative RCT status, Goutallier grading, tangent sign, and postoperative outcomes. Patients with full-thickness RCT on preoperative magnetic resonance imaging were excluded. Forty-five patients met all inclusion criteria (average age, 65 ± 10 years; average follow-up, 43 months). Of the patients undergoing TSA, 40% had a significant (>50% thickness) partial RCT. Grade 3 to 4 Goutallier changes were noted in 22% of all patients, and 13% demonstrated grade 3 to 4 changes in the context of no tear. Positive tangent sign was present in 7% of all patients. The preoperative Goutallier grade of the infraspinatus was significantly negatively correlated with postoperative forward elevation (P = .02) and external rotation (P = .05), but rotator cuff pathology, including tear status, Goutallier grade, and the presence of a tangent sign, did not correlate with postoperative functional outcome scores. Even in the absence of a full-thickness RCT, rotator cuff atrophy, fatty infiltration, and partial thickness tearing are common findings. Although postoperative range of motion is correlated to Goutallier changes of the infraspinatus, rotator cuff pathology is not correlated to outcomes after TSA; therefore, one may proceed with TSA without concern of their effect on

Diffusion tensor analysis with invariant gradients and rotation tangents.

PubMed

Kindlmann, Gordon; Ennis, Daniel B; Whitaker, Ross T; Westin, Carl-Fredrik

2007-11-01

Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

Classical Testing in Functional Linear Models.

PubMed

Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

2016-01-01

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

Classical Testing in Functional Linear Models

PubMed Central

Kong, Dehan; Staicu, Ana-Maria; Maity, Arnab

2016-01-01

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications. PMID:28955155

Composite Linear Models | Division of Cancer Prevention

Cancer.gov

By Stuart G. Baker The composite linear models software is a matrix approach to compute maximum likelihood estimates and asymptotic standard errors for models for incomplete multinomial data. It implements the method described in Baker SG. Composite linear models for incomplete multinomial data. Statistics in Medicine 1994;13:609-622. The software includes a library of thirty

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Dynamic Geometry Software and Tracing Tangents in the Context of the Mean Value Theorem: Technique and Theory Production

ERIC Educational Resources Information Center

Martínez-Hernández, Cesar; Ulloa-Azpeitia, Ricardo

2017-01-01

Based on the theoretical elements of the instrumental approach to tool use known as Task-Technique-Theory (Artigue, 2002), this paper analyses and discusses the performance of graduate students enrolled in a Teacher Training program. The latter performance relates to tracing tangent lines to the curve of a quadratic function in Dynamic Geometry…

Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

PubMed

Sahin, Rubina; Tapadia, Kavita

2015-01-01

The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG < 0) and endothermic (ΔH > 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses.

NASA Technical Reports Server (NTRS)

Wing, L. D.

1973-01-01

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN IV for an IBM 360/91 computer.

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses

NASA Technical Reports Server (NTRS)

Wing, L. D.

1972-01-01

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN 4 for an IBM 360/91 computer.

Genetic parameters for racing records in trotters using linear and generalized linear models.

PubMed

Suontama, M; van der Werf, J H J; Juga, J; Ojala, M

2012-09-01

Heritability and repeatability and genetic and phenotypic correlations were estimated for trotting race records with linear and generalized linear models using 510,519 records on 17,792 Finnhorses and 513,161 records on 25,536 Standardbred trotters. Heritability and repeatability were estimated for single racing time and earnings traits with linear models, and logarithmic scale was used for racing time and fourth-root scale for earnings to correct for nonnormality. Generalized linear models with a gamma distribution were applied for single racing time and with a multinomial distribution for single earnings traits. In addition, genetic parameters for annual earnings were estimated with linear models on the observed and fourth-root scales. Racing success traits of single placings, winnings, breaking stride, and disqualifications were analyzed using generalized linear models with a binomial distribution. Estimates of heritability were greatest for racing time, which ranged from 0.32 to 0.34. Estimates of heritability were low for single earnings with all distributions, ranging from 0.01 to 0.09. Annual earnings were closer to normal distribution than single earnings. Heritability estimates were moderate for annual earnings on the fourth-root scale, 0.19 for Finnhorses and 0.27 for Standardbred trotters. Heritability estimates for binomial racing success variables ranged from 0.04 to 0.12, being greatest for winnings and least for breaking stride. Genetic correlations among racing traits were high, whereas phenotypic correlations were mainly low to moderate, except correlations between racing time and earnings were high. On the basis of a moderate heritability and moderate to high repeatability for racing time and annual earnings, selection of horses for these traits is effective when based on a few repeated records. Because of high genetic correlations, direct selection for racing time and annual earnings would also result in good genetic response in racing success.

TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS

PubMed Central

Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.

2017-01-01

Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions. PMID:29332971

Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations

NASA Astrophysics Data System (ADS)

Huck, Thierry; Vallis, Geoffrey K.

2001-08-01

What can we learn from performing a linear stability analysis of the large-scale ocean circulation? Can we predict from the basic state the occurrence of interdecadal oscillations, such as might be found in a forward integration of the full equations of motion? If so, do the structure and period of the linearly unstable modes resemble those found in a forward integration? We pursue here a preliminary study of these questions for a case in idealized geometry, in which the full nonlinear behavior can also be explored through forward integrations. Specifically, we perform a three-dimensional linear stability analysis of the thermally-driven circulation of the planetary geostrophic equations. We examine the resulting eigenvalues and eigenfunctions, comparing them with the structure of the interdecadal oscillations found in the fully nonlinear model in various parameter regimes. We obtain a steady state by running the time-dependent, nonlinear model to equilibrium using restoring boundary conditions on surface temperature. If the surface heat fluxes are then diagnosed, and these values applied as constant flux boundary conditions, the nonlinear model switches into a state of perpetual, finite amplitude, interdecadal oscillations. We construct a linearized version of the model by empirically evaluating the tangent linear matrix at the steady state, under both restoring and constant-flux boundary conditions. An eigen-analysis shows there are no unstable eigenmodes of the linearized model with restoring conditions. In contrast, under constant flux conditions, we find a single unstable eigenmode that shows a striking resemblance to the fully-developed oscillations in terms of three-dimensional structure, period and growth rate. The mode may be damped through either surface restoring boundary conditions or sufficiently large horizontal tracer diffusion. The success of this simple numerical method in idealized geometry suggests applications in the study of the stability of

Estimation of the linear mixed integrated Ornstein–Uhlenbeck model

PubMed Central

Hughes, Rachael A.; Kenward, Michael G.; Sterne, Jonathan A. C.; Tilling, Kate

2017-01-01

ABSTRACT The linear mixed model with an added integrated Ornstein–Uhlenbeck (IOU) process (linear mixed IOU model) allows for serial correlation and estimation of the degree of derivative tracking. It is rarely used, partly due to the lack of available software. We implemented the linear mixed IOU model in Stata and using simulations we assessed the feasibility of fitting the model by restricted maximum likelihood when applied to balanced and unbalanced data. We compared different (1) optimization algorithms, (2) parameterizations of the IOU process, (3) data structures and (4) random-effects structures. Fitting the model was practical and feasible when applied to large and moderately sized balanced datasets (20,000 and 500 observations), and large unbalanced datasets with (non-informative) dropout and intermittent missingness. Analysis of a real dataset showed that the linear mixed IOU model was a better fit to the data than the standard linear mixed model (i.e. independent within-subject errors with constant variance). PMID:28515536

Development of a Linear Stirling Model with Varying Heat Inputs

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.

2007-01-01

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Non-linear Growth Models in Mplus and SAS

PubMed Central

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Particle orbits in two-dimensional equilibrium models for the magnetotail

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Pritchett, P. L.; Coroniti, F. V.

1990-01-01

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

Ionized gas clouds near the Sagittarius Arm tangent

NASA Astrophysics Data System (ADS)

Hou, Li-Gang; Dong, Jian; Gao, Xu-Yang; Han, Jin-Lin

2017-04-01

Radio recombination lines (RRLs) are the best tracers of ionized gas. Simultaneous observations of multi-transitions of RRLs can significantly improve survey sensitivity. We conducted pilot RRL observations near the Sagittarius Arm tangent by using the 65-m Shanghai Tian Ma Radio Telescope (TMRT) equipped with broadband feeds and a digital backend. Six hydrogen RRLs (H96 α - H101α) at C band (6289 MHz-7319 MHz) were observed simultaneously toward a sky area of 2° × 1.2° by using on-the-fly mapping mode. These transitions were then stacked together for detection of ionized gas. Star forming complexes G48.6+0.1 and G49.5-0.3 were detected in the integrated intensity map. We found agreements between our measured centroid velocities and previous results for the 21 known HII regions in the mapped area. For more than 80 cataloged HII region candidates without previous RRL measurements, we obtained new RRL spectra at 30 targeted positions. In addition, we detected 25 new discrete RRL sources with spectral S/N > 5 σ, and they were not listed in the catalogs of previously known HII regions. The distances for 44 out of these 55 new RRL sources were estimated.

Extending Linear Models to Non-Linear Contexts: An In-Depth Study about Two University Students' Mathematical Productions

ERIC Educational Resources Information Center

Esteley, Cristina; Villarreal, Monica; Alagia, Humberto

2004-01-01

This research report presents a study of the work of agronomy majors in which an extension of linear models to non-linear contexts can be observed. By linear models we mean the model y=a.x+b, some particular representations of direct proportionality and the diagram for the rule of three. Its presence and persistence in different types of problems…

Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum.

PubMed

Ramírez-Neria, M; Sira-Ramírez, H; Garrido-Moctezuma, R; Luviano-Juárez, A

2014-07-01

An Active Disturbance Rejection Control (ADRC) scheme is proposed for a trajectory tracking problem defined on a nonfeedback linearizable Furuta Pendulum example. A desired rest to rest angular position reference trajectory is to be tracked by the horizontal arm while the unactuated vertical pendulum arm stays around its unstable vertical position without falling down during the entire maneuver and long after it concludes. A linear observer-based linear controller of the ADRC type is designed on the basis of the flat tangent linearization of the system around an arbitrary equilibrium. The advantageous combination of flatness and the ADRC method makes it possible to on-line estimate and cancels the undesirable effects of the higher order nonlinearities disregarded by the linearization. These effects are triggered by fast horizontal arm tracking maneuvers driving the pendulum substantially away from the initial equilibrium point. Convincing experimental results, including a comparative test with a sliding mode controller, are presented. © 2013 ISA. Published by ISA. All rights reserved.

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Descriptive Linear modeling of steady-state visual evoked response

NASA Technical Reports Server (NTRS)

Levison, W. H.; Junker, A. M.; Kenner, K.

1986-01-01

A study is being conducted to explore use of the steady state visual-evoke electrocortical response as an indicator of cognitive task loading. Application of linear descriptive modeling to steady state Visual Evoked Response (VER) data is summarized. Two aspects of linear modeling are reviewed: (1) unwrapping the phase-shift portion of the frequency response, and (2) parsimonious characterization of task-loading effects in terms of changes in model parameters. Model-based phase unwrapping appears to be most reliable in applications, such as manual control, where theoretical models are available. Linear descriptive modeling of the VER has not yet been shown to provide consistent and readily interpretable results.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

The determination of third order linear models from a seventh order nonlinear jet engine model

NASA Technical Reports Server (NTRS)

Lalonde, Rick J.; Hartley, Tom T.; De Abreu-Garcia, J. Alex

1989-01-01

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

Linear network representation of multistate models of transport.

PubMed Central

Sandblom, J; Ring, A; Eisenman, G

1982-01-01

By introducing external driving forces in rate-theory models of transport we show how the Eyring rate equations can be transformed into Ohm's law with potentials that obey Kirchhoff's second law. From such a formalism the state diagram of a multioccupancy multicomponent system can be directly converted into linear network with resistors connecting nodal (branch) points and with capacitances connecting each nodal point with a reference point. The external forces appear as emf or current generators in the network. This theory allows the algebraic methods of linear network theory to be used in solving the flux equations for multistate models and is particularly useful for making proper simplifying approximation in models of complex membrane structure. Some general properties of linear network representation are also deduced. It is shown, for instance, that Maxwell's reciprocity relationships of linear networks lead directly to Onsager's relationships in the near equilibrium region. Finally, as an example of the procedure, the equivalent circuit method is used to solve the equations for a few transport models. PMID:7093425

Learning in fully recurrent neural networks by approaching tangent planes to constraint surfaces.

PubMed

May, P; Zhou, E; Lee, C W

2012-10-01

In this paper we present a new variant of the online real time recurrent learning algorithm proposed by Williams and Zipser (1989). Whilst the original algorithm utilises gradient information to guide the search towards the minimum training error, it is very slow in most applications and often gets stuck in local minima of the search space. It is also sensitive to the choice of learning rate and requires careful tuning. The new variant adjusts weights by moving to the tangent planes to constraint surfaces. It is simple to implement and requires no parameters to be set manually. Experimental results show that this new algorithm gives significantly faster convergence whilst avoiding problems like local minima. Copyright © 2012 Elsevier Ltd. All rights reserved.

Acoustic contrast control in an arc-shaped area using a linear loudspeaker array.

PubMed

Zhao, Sipei; Qiu, Xiaojun; Burnett, Ian

2015-02-01

This paper proposes a method of creating acoustic contrast control in an arc-shaped area using a linear loudspeaker array. The boundary of the arc-shaped area is treated as the envelope of the tangent lines that can be formed by manipulating the phase profile of the loudspeakers in the array. When compared with the existing acoustic contrast control method, the proposed method is able to generate sound field inside an arc-shaped area and achieve a trade-off between acoustic uniformity and acoustic contrast. The acoustic contrast created by the proposed method increases while the acoustic uniformity decreases with frequency.

Linear time-varying models can reveal non-linear interactions of biomolecular regulatory networks using multiple time-series data.

PubMed

Kim, Jongrae; Bates, Declan G; Postlethwaite, Ian; Heslop-Harrison, Pat; Cho, Kwang-Hyun

2008-05-15

Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. The software used in this article is available from http://sbie.kaist.ac.kr/software

Effective connectivity between superior temporal gyrus and Heschl's gyrus during white noise listening: linear versus non-linear models.

PubMed

Hamid, Ka; Yusoff, An; Rahman, Mza; Mohamad, M; Hamid, Aia

2012-04-01

This fMRI study is about modelling the effective connectivity between Heschl's gyrus (HG) and the superior temporal gyrus (STG) in human primary auditory cortices. MATERIALS #ENTITYSTARTX00026; Ten healthy male participants were required to listen to white noise stimuli during functional magnetic resonance imaging (fMRI) scans. Statistical parametric mapping (SPM) was used to generate individual and group brain activation maps. For input region determination, two intrinsic connectivity models comprising bilateral HG and STG were constructed using dynamic causal modelling (DCM). The models were estimated and inferred using DCM while Bayesian Model Selection (BMS) for group studies was used for model comparison and selection. Based on the winning model, six linear and six non-linear causal models were derived and were again estimated, inferred, and compared to obtain a model that best represents the effective connectivity between HG and the STG, balancing accuracy and complexity. Group results indicated significant asymmetrical activation (p(uncorr) < 0.001) in bilateral HG and STG. Model comparison results showed strong evidence of STG as the input centre. The winning model is preferred by 6 out of 10 participants. The results were supported by BMS results for group studies with the expected posterior probability, r = 0.7830 and exceedance probability, ϕ = 0.9823. One-sample t-tests performed on connection values obtained from the winning model indicated that the valid connections for the winning model are the unidirectional parallel connections from STG to bilateral HG (p < 0.05). Subsequent model comparison between linear and non-linear models using BMS prefers non-linear connection (r = 0.9160, ϕ = 1.000) from which the connectivity between STG and the ipsi- and contralateral HG is gated by the activity in STG itself. We are able to demonstrate that the effective connectivity between HG and STG while listening to white noise for the respective participants can

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

ERIC Educational Resources Information Center

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

Recent Updates to the GEOS-5 Linear Model

NASA Technical Reports Server (NTRS)

Holdaway, Dan; Kim, Jong G.; Errico, Ron; Gelaro, Ronald; Mahajan, Rahul

2014-01-01

Global Modeling and Assimilation Office (GMAO) is close to having a working 4DVAR system and has developed a linearized version of GEOS-5.This talk outlines a series of improvements made to the linearized dynamics, physics and trajectory.Of particular interest is the development of linearized cloud microphysics, which provides the framework for 'all-sky' data assimilation.

Development of a Linear Stirling System Model with Varying Heat Inputs

NASA Technical Reports Server (NTRS)

Regan, Timothy F.; Lewandowski, Edward J.

2007-01-01

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

[From clinical judgment to linear regression model.

PubMed

Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O

2013-01-01

When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.

Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

ERIC Educational Resources Information Center

Henson, Robert A.; Templin, Jonathan L.; Willse, John T.

2009-01-01

This paper uses log-linear models with latent variables (Hagenaars, in "Loglinear Models with Latent Variables," 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for…

Simple linear and multivariate regression models.

PubMed

Rodríguez del Águila, M M; Benítez-Parejo, N

2011-01-01

In biomedical research it is common to find problems in which we wish to relate a response variable to one or more variables capable of describing the behaviour of the former variable by means of mathematical models. Regression techniques are used to this effect, in which an equation is determined relating the two variables. While such equations can have different forms, linear equations are the most widely used form and are easy to interpret. The present article describes simple and multiple linear regression models, how they are calculated, and how their applicability assumptions are checked. Illustrative examples are provided, based on the use of the freely accessible R program. Copyright © 2011 SEICAP. Published by Elsevier Espana. All rights reserved.

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Wear-caused deflection evolution of a slide rail, considering linear and non-linear wear models

NASA Astrophysics Data System (ADS)

Kim, Dongwook; Quagliato, Luca; Park, Donghwi; Murugesan, Mohanraj; Kim, Naksoo; Hong, Seokmoo

2017-05-01

The research presented in this paper details an experimental-numerical approach for the quantitative correlation between wear and end-point deflection in a slide rail. Focusing the attention on slide rail utilized in white-goods applications, the aim is to evaluate the number of cycles the slide rail can operate, under different load conditions, before it should be replaced due to unacceptable end-point deflection. In this paper, two formulations are utilized to describe the wear: Archard model for the linear wear and Lemaitre damage model for the nonlinear wear. The linear wear gradually reduces the surface of the slide rail whereas the nonlinear one accounts for the surface element deletion (i.e. due to pitting). To determine the constants to use in the wear models, simple tension test and sliding wear test, by utilizing a designed and developed experiment machine, have been carried out. A full slide rail model simulation has been implemented in ABAQUS including both linear and non-linear wear models and the results have been compared with those of the real rails under different load condition, provided by the rail manufacturer. The comparison between numerically estimated and real rail results proved the reliability of the developed numerical model, limiting the error in a ±10% range. The proposed approach allows predicting the displacement vs cycle curves, parametrized for different loads and, based on a chosen failure criterion, to predict the lifetime of the rail.

Boundary layer flow of MHD tangent hyperbolic nanofluid over a stretching sheet: A numerical investigation

NASA Astrophysics Data System (ADS)

Khan, Mair; Hussain, Arif; Malik, M. Y.; Salahuddin, T.; Khan, Farzana

This article presents the two-dimensional flow of MHD hyperbolic tangent fluid with nanoparticles towards a stretching surface. The mathematical modelling of current flow analysis yields the nonlinear set of partial differential equations which then are reduce to ordinary differential equations by using suitable scaling transforms. Then resulting equations are solved by using shooting technique. The behaviour of the involved physical parameters (Weissenberg number We , Hartmann number M , Prandtl number Pr , Brownian motion parameter Nb , Lewis number Le and thermophoresis number Nt) on velocity, temperature and concentration are interpreted in detail. Additionally, local skin friction, local Nusselt number and local Sherwood number are computed and analyzed. It has been explored that Weissenberg number and Hartmann number are decelerate fluid motion. Brownian motion and thermophoresis both enhance the fluid temperature. Local Sherwood number is increasing function whereas Nusselt number is reducing function for increasing values of Brownian motion parameter Nb , Prandtl number Pr , thermophoresis parameter Nt and Lewis number Le . Additionally, computed results are compared with existing literature to validate the accuracy of solution, one can see that present results have quite resemblance with reported data.

A variational data assimilation system for the range dependent acoustic model using the representer method: Theoretical derivations.

PubMed

Ngodock, Hans; Carrier, Matthew; Fabre, Josette; Zingarelli, Robert; Souopgui, Innocent

2017-07-01

This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.

Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.

PubMed

Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J

2016-10-03

Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

NASA Astrophysics Data System (ADS)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Confirming the Lanchestrian linear-logarithmic model of attrition

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

Hartley, D.S. III.

1990-12-01

This paper is the fourth in a series of reports on the breakthrough research in historical validation of attrition in conflict. Significant defense policy decisions, including weapons acquisition and arms reduction, are based in part on models of conflict. Most of these models are driven by their attrition algorithms, usually forms of the Lanchester square and linear laws. None of these algorithms have been validated. The results of this paper confirm the results of earlier papers, using a large database of historical results. The homogeneous linear-logarithmic Lanchestrian attrition model is validated to the extent possible with current initial and finalmore » force size data and is consistent with the Iwo Jima data. A particular differential linear-logarithmic model is described that fits the data very well. A version of Helmbold's victory predicting parameter is also confirmed, with an associated probability function. 37 refs., 73 figs., 68 tabs.« less

Linear Mixed Models: Gum and Beyond

NASA Astrophysics Data System (ADS)

Arendacká, Barbora; Täubner, Angelika; Eichstädt, Sascha; Bruns, Thomas; Elster, Clemens

2014-04-01

In Annex H.5, the Guide to the Evaluation of Uncertainty in Measurement (GUM) [1] recognizes the necessity to analyze certain types of experiments by applying random effects ANOVA models. These belong to the more general family of linear mixed models that we focus on in the current paper. Extending the short introduction provided by the GUM, our aim is to show that the more general, linear mixed models cover a wider range of situations occurring in practice and can be beneficial when employed in data analysis of long-term repeated experiments. Namely, we point out their potential as an aid in establishing an uncertainty budget and as means for gaining more insight into the measurement process. We also comment on computational issues and to make the explanations less abstract, we illustrate all the concepts with the help of a measurement campaign conducted in order to challenge the uncertainty budget in calibration of accelerometers.

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

PubMed

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Numerical study of a thermally stratified flow of a tangent hyperbolic fluid induced by a stretching cylindrical surface

NASA Astrophysics Data System (ADS)

Ur Rehman, Khali; Ali Khan, Abid; Malik, M. Y.; Hussain, Arif

2017-09-01

The effects of temperature stratification on a tangent hyperbolic fluid flow over a stretching cylindrical surface are studied. The fluid flow is achieved by taking the no-slip condition into account. The mathematical modelling of the physical problem yields a nonlinear set of partial differential equations. These obtained partial differential equations are converted in terms of ordinary differential equations. Numerical investigation is done to identify the effects of the involved physical parameters on the dimensionless velocity and temperature profiles. In the presence of temperature stratification it is noticed that the curvature parameter makes both the fluid velocity and fluid temperature increase. In addition, positive variations in the thermal stratification parameter produce retardation with respect to the fluid flow, as a result the fluid temperature drops. The skin friction coefficient shows a decreasing nature for increasing value of both power law index and Weissenberg number, whereas the local Nusselt number is an increasing function of the Prandtl number, but opposite trends are found with respect to the thermal stratification parameter. The obtained results are validated by making a comparison with the existing literature which brings support to the presently developed model.

Model Selection with the Linear Mixed Model for Longitudinal Data

ERIC Educational Resources Information Center

Ryoo, Ji Hoon

2011-01-01

Model building or model selection with linear mixed models (LMMs) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are codependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multilevel or…

Non-linear modeling of RF in fusion grade plasmas

NASA Astrophysics Data System (ADS)

Austin, Travis; Smithe, David; Hakim, Ammar; Jenkins, Thomas

2011-10-01

We are seeking to model nonlinear effects, particularly parametric decay instability in the vicinity of the edge plasma and RF launchers, which is thought to be a potential parasitic loss mechanism. We will use time-domain approaches which treat the full spectrum of modes. Two approaches are being tested for feasibility, a non-linear delta-f particle approach, and a higher order many-fluid closure approach. Our particle approach builds on extensive previous work demonstrating the ability to model IBW waves (one of the PDI daughter waves) with a linear delta-f particle model. Here we report on the performance of such simulations when the linear constraint is relaxed, and in particular on the ability of the low-noise loading scheme, specially developed for RF and ion-time scale physics, to operate and maintain low noise in the non-linear regime. Similarly, a novel high-order closure of the fluid equations is necessary to model the IBW and higher harmonics. We will report on the benchmarking of the fluid closure, and its ability to model the anticipated pump and daughter waves in a PDI scenario. This research supported by US DOE Grant # DE-SC0006242.

Genomic prediction based on data from three layer lines using non-linear regression models.

PubMed

Huang, Heyun; Windig, Jack J; Vereijken, Addie; Calus, Mario P L

2014-11-06

Most studies on genomic prediction with reference populations that include multiple lines or breeds have used linear models. Data heterogeneity due to using multiple populations may conflict with model assumptions used in linear regression methods. In an attempt to alleviate potential discrepancies between assumptions of linear models and multi-population data, two types of alternative models were used: (1) a multi-trait genomic best linear unbiased prediction (GBLUP) model that modelled trait by line combinations as separate but correlated traits and (2) non-linear models based on kernel learning. These models were compared to conventional linear models for genomic prediction for two lines of brown layer hens (B1 and B2) and one line of white hens (W1). The three lines each had 1004 to 1023 training and 238 to 240 validation animals. Prediction accuracy was evaluated by estimating the correlation between observed phenotypes and predicted breeding values. When the training dataset included only data from the evaluated line, non-linear models yielded at best a similar accuracy as linear models. In some cases, when adding a distantly related line, the linear models showed a slight decrease in performance, while non-linear models generally showed no change in accuracy. When only information from a closely related line was used for training, linear models and non-linear radial basis function (RBF) kernel models performed similarly. The multi-trait GBLUP model took advantage of the estimated genetic correlations between the lines. Combining linear and non-linear models improved the accuracy of multi-line genomic prediction. Linear models and non-linear RBF models performed very similarly for genomic prediction, despite the expectation that non-linear models could deal better with the heterogeneous multi-population data. This heterogeneity of the data can be overcome by modelling trait by line combinations as separate but correlated traits, which avoids the occasional

Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis

ERIC Educational Resources Information Center

Luo, Wen; Azen, Razia

2013-01-01

Dominance analysis (DA) is a method used to evaluate the relative importance of predictors that was originally proposed for linear regression models. This article proposes an extension of DA that allows researchers to determine the relative importance of predictors in hierarchical linear models (HLM). Commonly used measures of model adequacy in…

A Vernacular for Linear Latent Growth Models

ERIC Educational Resources Information Center

Hancock, Gregory R.; Choi, Jaehwa

2006-01-01

In its most basic form, latent growth modeling (latent curve analysis) allows an assessment of individuals' change in a measured variable X over time. For simple linear models, as with other growth models, parameter estimates associated with the a construct (amount of X at a chosen temporal reference point) and b construct (growth in X per unit…

Model checking for linear temporal logic: An efficient implementation

NASA Technical Reports Server (NTRS)

Sherman, Rivi; Pnueli, Amir

1990-01-01

This report provides evidence to support the claim that model checking for linear temporal logic (LTL) is practically efficient. Two implementations of a linear temporal logic model checker is described. One is based on transforming the model checking problem into a satisfiability problem; the other checks an LTL formula for a finite model by computing the cross-product of the finite state transition graph of the program with a structure containing all possible models for the property. An experiment was done with a set of mutual exclusion algorithms and tested safety and liveness under fairness for these algorithms.

A penalized framework for distributed lag non-linear models.

PubMed

Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G

2017-09-01

Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Derivation and definition of a linear aircraft model

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1988-01-01

A linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth is derived and defined. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.

Generation of linear dynamic models from a digital nonlinear simulation

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.

1979-01-01

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Mixed models, linear dependency, and identification in age-period-cohort models.

PubMed

O'Brien, Robert M

2017-07-20

This paper examines the identification problem in age-period-cohort models that use either linear or categorically coded ages, periods, and cohorts or combinations of these parameterizations. These models are not identified using the traditional fixed effect regression model approach because of a linear dependency between the ages, periods, and cohorts. However, these models can be identified if the researcher introduces a single just identifying constraint on the model coefficients. The problem with such constraints is that the results can differ substantially depending on the constraint chosen. Somewhat surprisingly, age-period-cohort models that specify one or more of ages and/or periods and/or cohorts as random effects are identified. This is the case without introducing an additional constraint. I label this identification as statistical model identification and show how statistical model identification comes about in mixed models and why which effects are treated as fixed and which are treated as random can substantially change the estimates of the age, period, and cohort effects. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Linear regression crash prediction models : issues and proposed solutions.

DOT National Transportation Integrated Search

2010-05-01

The paper develops a linear regression model approach that can be applied to : crash data to predict vehicle crashes. The proposed approach involves novice data aggregation : to satisfy linear regression assumptions; namely error structure normality ...

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

The Tangent Linear and Adjoint of the FV3 Dynamical Core: Development and Applications

NASA Technical Reports Server (NTRS)

Holdaway, Daniel

2018-01-01

GMAO (NASA's Global Modeling and Assimilation Office) has developed a highly sophisticated adjoint modeling system based on the most recent version of the finite volume cubed sphere (FV3) dynamical core. This provides a mechanism for investigating sensitivity to initial conditions and examining observation impacts. It also allows for the computation of singular vectors and for the implementation of hybrid 4DVAR (4-Dimensional Variational Assimilation). In this work we will present the scientific assessment of the new adjoint system and show results from a number of research application of the adjoint system.

Functional linear models for association analysis of quantitative traits.

PubMed

Fan, Ruzong; Wang, Yifan; Mills, James L; Wilson, Alexander F; Bailey-Wilson, Joan E; Xiong, Momiao

2013-11-01

Functional linear models are developed in this paper for testing associations between quantitative traits and genetic variants, which can be rare variants or common variants or the combination of the two. By treating multiple genetic variants of an individual in a human population as a realization of a stochastic process, the genome of an individual in a chromosome region is a continuum of sequence data rather than discrete observations. The genome of an individual is viewed as a stochastic function that contains both linkage and linkage disequilibrium (LD) information of the genetic markers. By using techniques of functional data analysis, both fixed and mixed effect functional linear models are built to test the association between quantitative traits and genetic variants adjusting for covariates. After extensive simulation analysis, it is shown that the F-distributed tests of the proposed fixed effect functional linear models have higher power than that of sequence kernel association test (SKAT) and its optimal unified test (SKAT-O) for three scenarios in most cases: (1) the causal variants are all rare, (2) the causal variants are both rare and common, and (3) the causal variants are common. The superior performance of the fixed effect functional linear models is most likely due to its optimal utilization of both genetic linkage and LD information of multiple genetic variants in a genome and similarity among different individuals, while SKAT and SKAT-O only model the similarities and pairwise LD but do not model linkage and higher order LD information sufficiently. In addition, the proposed fixed effect models generate accurate type I error rates in simulation studies. We also show that the functional kernel score tests of the proposed mixed effect functional linear models are preferable in candidate gene analysis and small sample problems. The methods are applied to analyze three biochemical traits in data from the Trinity Students Study. © 2013 WILEY

Variability simulations with a steady, linearized primitive equations model

NASA Technical Reports Server (NTRS)

Kinter, J. L., III; Nigam, S.

1985-01-01

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

PubMed

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth

Multicollinearity in hierarchical linear models.

PubMed

Yu, Han; Jiang, Shanhe; Land, Kenneth C

2015-09-01

This study investigates an ill-posed problem (multicollinearity) in Hierarchical Linear Models from both the data and the model perspectives. We propose an intuitive, effective approach to diagnosing the presence of multicollinearity and its remedies in this class of models. A simulation study demonstrates the impacts of multicollinearity on coefficient estimates, associated standard errors, and variance components at various levels of multicollinearity for finite sample sizes typical in social science studies. We further investigate the role multicollinearity plays at each level for estimation of coefficient parameters in terms of shrinkage. Based on these analyses, we recommend a top-down method for assessing multicollinearity in HLMs that first examines the contextual predictors (Level-2 in a two-level model) and then the individual predictors (Level-1) and uses the results for data collection, research problem redefinition, model re-specification, variable selection and estimation of a final model. Copyright © 2015 Elsevier Inc. All rights reserved.

Smoothed Residual Plots for Generalized Linear Models. Technical Report #450.

ERIC Educational Resources Information Center

Brant, Rollin

Methods for examining the viability of assumptions underlying generalized linear models are considered. By appealing to the likelihood, a natural generalization of the raw residual plot for normal theory models is derived and is applied to investigating potential misspecification of the linear predictor. A smooth version of the plot is also…

Linear Power-Flow Models in Multiphase Distribution Networks: Preprint

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

Bernstein, Andrey; Dall'Anese, Emiliano

This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- frommore » advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.« less

Modeling containment of large wildfires using generalized linear mixed-model analysis

Treesearch

Mark Finney; Isaac C. Grenfell; Charles W. McHugh

2009-01-01

Billions of dollars are spent annually in the United States to contain large wildland fires, but the factors contributing to suppression success remain poorly understood. We used a regression model (generalized linear mixed-model) to model containment probability of individual fires, assuming that containment was a repeated-measures problem (fixed effect) and...

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

USGS Publications Warehouse

Ng, G.-H.C.; McLaughlin, D.; Entekhabi, D.; Ahanin, A.

2011-01-01

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or 'diverging', when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter's update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as non-linearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics. ?? 2011 The Authors Tellus A ?? 2011 John Wiley & Sons A/S.

Frequency response of synthetic vocal fold models with linear and nonlinear material properties.

PubMed

Shaw, Stephanie M; Thomson, Scott L; Dromey, Christopher; Smith, Simeon

2012-10-01

The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F0) during anterior-posterior stretching. Three materially linear and 3 materially nonlinear models were created and stretched up to 10 mm in 1-mm increments. Phonation onset pressure (Pon) and F0 at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1-mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Nonlinear synthetic models appear to more accurately represent the human vocal folds than do linear models, especially with respect to F0 response.

Comparison of linear and nonlinear models for coherent hemodynamics spectroscopy (CHS)

NASA Astrophysics Data System (ADS)

Sassaroli, Angelo; Kainerstorfer, Jana; Fantini, Sergio

2015-03-01

A recently proposed linear time-invariant hemodynamic model for coherent hemodynamics spectroscopy1 (CHS) relates the tissue concentrations of oxy- and deoxy-hemoglobin (outputs of the system) to given dynamics of the tissue blood volume, blood flow and rate constant of oxygen diffusion (inputs of the system). This linear model was derived in the limit of "small" perturbations in blood flow velocity. We have extended this model to a more general model (which will be referred to as the nonlinear extension to the original model) that yields the time-dependent changes of oxy and deoxy-hemoglobin concentrations in response to arbitrary dynamic changes in capillary blood flow velocity. The nonlinear extension to the model relies on a general solution of the partial differential equation that governs the spatio-temporal behavior of oxygen saturation of hemoglobin in capillaries and venules on the basis of dynamic (or time resolved) blood transit time. We show preliminary results where the CHS spectra obtained from the linear and nonlinear models are compared to quantify the limits of applicability of the linear model.

A position-aware linear solid constitutive model for peridynamics

DOE PAGES

Mitchell, John A.; Silling, Stewart A.; Littlewood, David J.

2015-11-06

A position-aware linear solid (PALS) peridynamic constitutive model is proposed for isotropic elastic solids. The PALS model addresses problems that arise, in ordinary peridynamic material models such as the linear peridynamic solid (LPS), due to incomplete neighborhoods near the surface of a body. We improved model behavior in the vicinity of free surfaces through the application of two influence functions that correspond, respectively, to the volumetric and deviatoric parts of the deformation. Furthermore, the model is position-aware in that the influence functions vary over the body and reflect the proximity of each material point to free surfaces. Demonstration calculations onmore » simple benchmark problems show a sharp reduction in error relative to the LPS model.« less

A position-aware linear solid constitutive model for peridynamics

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

Mitchell, John A.; Silling, Stewart A.; Littlewood, David J.

A position-aware linear solid (PALS) peridynamic constitutive model is proposed for isotropic elastic solids. The PALS model addresses problems that arise, in ordinary peridynamic material models such as the linear peridynamic solid (LPS), due to incomplete neighborhoods near the surface of a body. We improved model behavior in the vicinity of free surfaces through the application of two influence functions that correspond, respectively, to the volumetric and deviatoric parts of the deformation. Furthermore, the model is position-aware in that the influence functions vary over the body and reflect the proximity of each material point to free surfaces. Demonstration calculations onmore » simple benchmark problems show a sharp reduction in error relative to the LPS model.« less

Nonlinear Modeling by Assembling Piecewise Linear Models

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2013-01-01

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

NASA Technical Reports Server (NTRS)

Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

1993-01-01

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Portfolio optimization by using linear programing models based on genetic algorithm

NASA Astrophysics Data System (ADS)

Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.

2018-01-01

In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.

Estimating linear-nonlinear models using Renyi divergences.

PubMed

Kouh, Minjoon; Sharpee, Tatyana O

2009-01-01

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

The development of global GRAPES 4DVAR

NASA Astrophysics Data System (ADS)

Liu, Yongzhu

2017-04-01

Four-dimensional variation data assimilation (4DVAR) has given a great contribution to the improvement of NWP system over the past twenty years. Therefore, our strategy is to develop an operational global 4D-Var system from the outset. The aim at the paper is to introduce the development of the global GRAPES four-dimensional variation data assimilation (4DVAR) using incremental analysis schemes and to presents results of a comparison between 4DVAR using 6-hour assimilation window and simplified physics during the minimization with three-dimensional variation data assimilation (3DVAR). The dynamical cores of the tangent-linear and adjoint models are developed directly based on the non-hydrostatic forecast model. In addition, the standard correctness checks have been performed. As well as the development adjoint codes, most of our work is focused on improving the computational efficiency since the bulk of the computational cost of 4D-Var is in the integration of the tangent-linear and adjoint models. In terms of tangent-linear model, the wall-clock time is reduced to about 1.2 times as much as one of nonlinear model through the optimizing of the software framework. The significant computational cost savings on adjoint model result from the removing the redundant recompilations of model trajectories. It is encouraging that the wall-clock time of adjoint model is less than 1.5 times as much as one of nonlinear model. The current difficulty is that the numerical scheme used within the linear model is based on strategically on the numeric of the corresponding nonlinear model. Further computational acceleration should be expected from the improvement on nonlinear numerical algorithm. A series of linearized physical parameterization schemes has been developed to improve the representation of perturbed fields in the linear model. It consists of horizontal and vertical diffusion, sub-grid scale orographic gravity wave drag, large-scale condensation and cumulus convection

Linear and Nonlinear Thinking: A Multidimensional Model and Measure

ERIC Educational Resources Information Center

Groves, Kevin S.; Vance, Charles M.

2015-01-01

Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…

Laboratory Studies of Temperature and Relative Humidity Dependence of Aerosol Nucleation during the TANGENT 2017 IOP Study

NASA Astrophysics Data System (ADS)

Ouyang, Q.; Tiszenkel, L.; Stangl, C. M.; Krasnomowitz, J.; Johnston, M. V.; Lee, S.

2017-12-01

In this poster, we will present recent measurements of temperature and relative humidity dependence of aerosol nucleation of sulfuric acid under the conditions representative of the ground level to the free troposphere. Aerosol nucleation is critically dependent on temperature, but the current global aerosol models use nucleation algorithms that are independent of temperature and relative humidity due to the lack of experimental data. Thus, these models fail to simulate nucleation in a wide range of altitude and latitude conditions. We are currently conducting the Tandem Aerosol Nucleation and Growth Environment Tube (TANGENT) the intense observation period (IOP) experiments to investigate the aerosol nucleation and growth properties independently, during nucleation and growth. Nucleation takes place from sulfuric acid, water and some base compounds in a fast flow nucleation tube (FT-1). Nucleation precursors are detected with two chemical ionization mass spectrometers (CIMS) and newly nucleated particles are measured with a particle size magnifier (PSM) and a scanning mobility particle sizers (SMPS). Then these particles grow further in the second flow tube (FT-2) in the presence of oxidants of biogenic organic compounds. Chemical compositions of grown particles are further analyzed with a nano-aerosol mass spectrometer (NAMS). Our experimental results will provide a robust algorithm for aerosol nucleation and growth rates as a function of temperature and relative humidity.

Driver Gaze Behavior Is Different in Normal Curve Driving and when Looking at the Tangent Point

PubMed Central

Itkonen, Teemu; Pekkanen, Jami; Lappi, Otto

2015-01-01

Several steering models in the visual science literature attempt to capture the visual strategies in curve driving. Some of them are based on steering points on the future path (FP), others on tangent points (TP). It is, however, challenging to differentiate between the models’ predictions in real–world contexts. Analysis of optokinetic nystagmus (OKN) parameters is one useful measure, as the different strategies predict measurably different OKN patterns. Here, we directly test this prediction by asking drivers to either a) “drive as they normally would” or b) to “look at the TP”. The design of the experiment is similar to a previous study by Kandil et al., but uses more sophisticated methods of eye–movement analysis. We find that the eye-movement patterns in the “normal” condition are indeed markedly different from the “tp” condition, and consistent with drivers looking at waypoints on the future path. This is the case for both overall fixation distribution, as well as the more informative fixation–by–fixation analysis of OKN. We find that the horizontal gaze speed during OKN corresponds well to the quantitative prediction of the future path models. The results also definitively rule out the alternative explanation that the OKN is produced by an involuntary reflex even while the driver is “trying” to look at the TP. The results are discussed in terms of the sequential organization of curve driving. PMID:26287914

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

PubMed Central

Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

2014-01-01

Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

An experimental study of the effects of aft blowing on a 3.0 caliber tangent ogive body at high angles of attack

NASA Technical Reports Server (NTRS)

Gittner, Nathan M.; Chokani, Ndaona

1991-01-01

An experimental study of the effects of aft blowing on the forebody vortex asymmetry over a 3.0 caliber tangent ogive body at high angles of attack was conducted. The tip of the ogive body was equipped with a single blowing nozzle whose position could be adjusted. The tests were conducted in a subsonic wind tunnel at laminar flow conditions. The effects of model roll, angle of attack, blowing coefficient, and blowing nozzle axial position were independently studied. Surface pressure measurements and flow visualization results were obtained. Aft blowing was observed to alleviate the degree of vortex asymmetry at all angles of attack. The blowing was found to be more effective at the higher angles of attack. However, proportional control of the degree of vortex asymmetry was not observed, because the initial flowfield was highly asymmetric.

The Simplest Complete Model of Choice Response Time: Linear Ballistic Accumulation

ERIC Educational Resources Information Center

Brown, Scott D.; Heathcote, Andrew

2008-01-01

We propose a linear ballistic accumulator (LBA) model of decision making and reaction time. The LBA is simpler than other models of choice response time, with independent accumulators that race towards a common response threshold. Activity in the accumulators increases in a linear and deterministic manner. The simplicity of the model allows…

Robust Linear Models for Cis-eQTL Analysis.

PubMed

Rantalainen, Mattias; Lindgren, Cecilia M; Holmes, Christopher C

2015-01-01

Expression Quantitative Trait Loci (eQTL) analysis enables characterisation of functional genetic variation influencing expression levels of individual genes. In outbread populations, including humans, eQTLs are commonly analysed using the conventional linear model, adjusting for relevant covariates, assuming an allelic dosage model and a Gaussian error term. However, gene expression data generally have noise that induces heavy-tailed errors relative to the Gaussian distribution and often include atypical observations, or outliers. Such departures from modelling assumptions can lead to an increased rate of type II errors (false negatives), and to some extent also type I errors (false positives). Careful model checking can reduce the risk of type-I errors but often not type II errors, since it is generally too time-consuming to carefully check all models with a non-significant effect in large-scale and genome-wide studies. Here we propose the application of a robust linear model for eQTL analysis to reduce adverse effects of deviations from the assumption of Gaussian residuals. We present results from a simulation study as well as results from the analysis of real eQTL data sets. Our findings suggest that in many situations robust models have the potential to provide more reliable eQTL results compared to conventional linear models, particularly in respect to reducing type II errors due to non-Gaussian noise. Post-genomic data, such as that generated in genome-wide eQTL studies, are often noisy and frequently contain atypical observations. Robust statistical models have the potential to provide more reliable results and increased statistical power under non-Gaussian conditions. The results presented here suggest that robust models should be considered routinely alongside other commonly used methodologies for eQTL analysis.

Linear modeling of steady-state behavioral dynamics.

PubMed Central

Palya, William L; Walter, Donald; Kessel, Robert; Lucke, Robert

2002-01-01

The observed steady-state behavioral dynamics supported by unsignaled periods of reinforcement within repeating 2,000-s trials were modeled with a linear transfer function. These experiments employed improved schedule forms and analytical methods to improve the precision of the measured transfer function, compared to previous work. The refinements include both the use of multiple reinforcement periods that improve spectral coverage and averaging of independently determined transfer functions. A linear analysis was then used to predict behavior observed for three different test schedules. The fidelity of these predictions was determined. PMID:11831782

Reasons for Hierarchical Linear Modeling: A Reminder.

ERIC Educational Resources Information Center

Wang, Jianjun

1999-01-01

Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)

Effect of non-linearity in predicting doppler waveforms through a novel model

PubMed Central

Gayasen, Aman; Dua, Sunil Kumar; Sengupta, Amit; Nagchoudhuri, D

2003-01-01

Background In pregnancy, the uteroplacental vascular system develops de novo locally in utero and a systemic haemodynamic & bio-rheological alteration accompany it. Any abnormality in the non-linear vascular system is believed to trigger the onset of serious morbid conditions like pre-eclampsia and/or intrauterine growth restriction (IUGR). Exact Aetiopathogenesis is unknown. Advancement in the field of non-invasive doppler image analysis and simulation incorporating non-linearities may unfold the complexities associated with the inaccessible uteroplacental vessels. Earlier modeling approaches approximate it as a linear system. Method We proposed a novel electrical model for the uteroplacental system that uses MOSFETs as non-linear elements in place of traditional linear transmission line (TL) model. The model to simulate doppler FVW's was designed by including the inputs from our non-linear mathematical model. While using the MOSFETs as voltage-controlled switches, a fair degree of controlled-non-linearity has been introduced in the model. Comparative analysis was done between the simulated data and the actual doppler FVW's waveforms. Results & Discussion Normal pregnancy has been successfully modeled and the doppler output waveforms are simulated for different gestation time using the model. It is observed that the dicrotic notch disappears and the S/D ratio decreases as the pregnancy matures. Both these results are established clinical facts. Effects of blood density, viscosity and the arterial wall elasticity on the blood flow velocity profile were also studied. Spectral analysis on the output of the model (blood flow velocity) indicated that the Total Harmonic Distortion (THD) falls during the mid-gestation. Conclusion Total harmonic distortion (THD) is found to be informative in determining the Feto-maternal health. Effects of the blood density, the viscosity and the elasticity changes on the blood FVW are simulated. Future works are expected to concentrate

B-737 Linear Autoland Simulink Model

NASA Technical Reports Server (NTRS)

Belcastro, Celeste (Technical Monitor); Hogge, Edward F.

2004-01-01

The Linear Autoland Simulink model was created to be a modular test environment for testing of control system components in commercial aircraft. The input variables, physical laws, and referenced frames used are summarized. The state space theory underlying the model is surveyed and the location of the control actuators described. The equations used to realize the Dryden gust model to simulate winds and gusts are derived. A description of the pseudo-random number generation method used in the wind gust model is included. The longitudinal autopilot, lateral autopilot, automatic throttle autopilot, engine model and automatic trim devices are considered as subsystems. The experience in converting the Airlabs FORTRAN aircraft control system simulation to a graphical simulation tool (Matlab/Simulink) is described.

Predicting musically induced emotions from physiological inputs: linear and neural network models.

PubMed

Russo, Frank A; Vempala, Naresh N; Sandstrom, Gillian M

2013-01-01

Listening to music often leads to physiological responses. Do these physiological responses contain sufficient information to infer emotion induced in the listener? The current study explores this question by attempting to predict judgments of "felt" emotion from physiological responses alone using linear and neural network models. We measured five channels of peripheral physiology from 20 participants-heart rate (HR), respiration, galvanic skin response, and activity in corrugator supercilii and zygomaticus major facial muscles. Using valence and arousal (VA) dimensions, participants rated their felt emotion after listening to each of 12 classical music excerpts. After extracting features from the five channels, we examined their correlation with VA ratings, and then performed multiple linear regression to see if a linear relationship between the physiological responses could account for the ratings. Although linear models predicted a significant amount of variance in arousal ratings, they were unable to do so with valence ratings. We then used a neural network to provide a non-linear account of the ratings. The network was trained on the mean ratings of eight of the 12 excerpts and tested on the remainder. Performance of the neural network confirms that physiological responses alone can be used to predict musically induced emotion. The non-linear model derived from the neural network was more accurate than linear models derived from multiple linear regression, particularly along the valence dimension. A secondary analysis allowed us to quantify the relative contributions of inputs to the non-linear model. The study represents a novel approach to understanding the complex relationship between physiological responses and musically induced emotion.

Robust Bounded Influence Tests in Linear Models

DTIC Science & Technology

1988-11-01

sensitivity analysis and bounded influence estimation. In: Evaluation of Econometric Models, J. Kmenta and J.B. Ramsey (eds.) Academic Press, New York...1R’OBUST bOUNDED INFLUENCE TESTS IN LINEA’ MODELS and( I’homas P. [lettmansperger* Tim [PennsylvanLa State UJniversity A M i0d fix pu111 rsos.p JJ 1 0...November 1988 ROBUST BOUNDED INFLUENCE TESTS IN LINEAR MODELS Marianthi Markatou The University of Iowa and Thomas P. Hettmansperger* The Pennsylvania

A simplified approach to quasi-linear viscoelastic modeling

PubMed Central

Nekouzadeh, Ali; Pryse, Kenneth M.; Elson, Elliot L.; Genin, Guy M.

2007-01-01

The fitting of quasi-linear viscoelastic (QLV) constitutive models to material data often involves somewhat cumbersome numerical convolution. A new approach to treating quasi-linearity in one dimension is described and applied to characterize the behavior of reconstituted collagen. This approach is based on a new principle for including nonlinearity and requires considerably less computation than other comparable models for both model calibration and response prediction, especially for smoothly applied stretching. Additionally, the approach allows relaxation to adapt with the strain history. The modeling approach is demonstrated through tests on pure reconstituted collagen. Sequences of “ramp-and-hold” stretching tests were applied to rectangular collagen specimens. The relaxation force data from the “hold” was used to calibrate a new “adaptive QLV model” and several models from literature, and the force data from the “ramp” was used to check the accuracy of model predictions. Additionally, the ability of the models to predict the force response on a reloading of the specimen was assessed. The “adaptive QLV model” based on this new approach predicts collagen behavior comparably to or better than existing models, with much less computation. PMID:17499254

A hierarchical linear model for tree height prediction.

Treesearch

Vicente J. Monleon

2003-01-01

Measuring tree height is a time-consuming process. Often, tree diameter is measured and height is estimated from a published regression model. Trees used to develop these models are clustered into stands, but this structure is ignored and independence is assumed. In this study, hierarchical linear models that account explicitly for the clustered structure of the data...

Modeling exposure–lag–response associations with distributed lag non-linear models

PubMed Central

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

Biochemical methane potential prediction of plant biomasses: Comparing chemical composition versus near infrared methods and linear versus non-linear models.

PubMed

Godin, Bruno; Mayer, Frédéric; Agneessens, Richard; Gerin, Patrick; Dardenne, Pierre; Delfosse, Philippe; Delcarte, Jérôme

2015-01-01

The reliability of different models to predict the biochemical methane potential (BMP) of various plant biomasses using a multispecies dataset was compared. The most reliable prediction models of the BMP were those based on the near infrared (NIR) spectrum compared to those based on the chemical composition. The NIR predictions of local (specific regression and non-linear) models were able to estimate quantitatively, rapidly, cheaply and easily the BMP. Such a model could be further used for biomethanation plant management and optimization. The predictions of non-linear models were more reliable compared to those of linear models. The presentation form (green-dried, silage-dried and silage-wet form) of biomasses to the NIR spectrometer did not influence the performances of the NIR prediction models. The accuracy of the BMP method should be improved to enhance further the BMP prediction models. Copyright © 2014 Elsevier Ltd. All rights reserved.

Some comparisons of complexity in dictionary-based and linear computational models.

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. Copyright © 2010 Elsevier Ltd. All rights reserved.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

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

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

A Search for Mountain Waves in MLS Stratospheric Limb Radiances from the Winter Northern Hemisphere: Data Analysis and Global Mountain Wave Modeling

DTIC Science & Technology

2004-02-11

the general circulation of the middle atmosphere, Philos. Trans. R. Soc. London, Ser. A, 323, 693–705. Anton , H. (2000), Elementary Linear Algebra ...Because the saturated radiances may depend slightly on tangent height as the limb path length decreases, a linear trend (described by parameters a and b...track days and interpolated onto the same limb-track orbits. The color bar scale for radiance variance is linear . (b) Digital elevations of northern

An R2 statistic for fixed effects in the linear mixed model.

PubMed

Edwards, Lloyd J; Muller, Keith E; Wolfinger, Russell D; Qaqish, Bahjat F; Schabenberger, Oliver

2008-12-20

Statisticians most often use the linear mixed model to analyze Gaussian longitudinal data. The value and familiarity of the R(2) statistic in the linear univariate model naturally creates great interest in extending it to the linear mixed model. We define and describe how to compute a model R(2) statistic for the linear mixed model by using only a single model. The proposed R(2) statistic measures multivariate association between the repeated outcomes and the fixed effects in the linear mixed model. The R(2) statistic arises as a 1-1 function of an appropriate F statistic for testing all fixed effects (except typically the intercept) in a full model. The statistic compares the full model with a null model with all fixed effects deleted (except typically the intercept) while retaining exactly the same covariance structure. Furthermore, the R(2) statistic leads immediately to a natural definition of a partial R(2) statistic. A mixed model in which ethnicity gives a very small p-value as a longitudinal predictor of blood pressure (BP) compellingly illustrates the value of the statistic. In sharp contrast to the extreme p-value, a very small R(2) , a measure of statistical and scientific importance, indicates that ethnicity has an almost negligible association with the repeated BP outcomes for the study.

Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes.

PubMed

Casellas, J; Bach, R

2012-06-01

Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.

On classical mechanical systems with non-linear constraints

NASA Astrophysics Data System (ADS)

Terra, Gláucio; Kobayashi, Marcelo H.

2004-03-01

In the present work, we analyze classical mechanical systems with non-linear constraints in the velocities. We prove that the d'Alembert-Chetaev trajectories of a constrained mechanical system satisfy both Gauss' principle of least constraint and Hölder's principle. In the case of a free mechanics, they also satisfy Hertz's principle of least curvature if the constraint manifold is a cone. We show that the Gibbs-Maggi-Appell (GMA) vector field (i.e. the second-order vector field which defines the d'Alembert-Chetaev trajectories) conserves energy for any potential energy if, and only if, the constraint is homogeneous (i.e. if the Liouville vector field is tangent to the constraint manifold). We introduce the Jacobi-Carathéodory metric tensor and prove Jacobi-Carathéodory's theorem assuming that the constraint manifold is a cone. Finally, we present a version of Liouville's theorem on the conservation of volume for the flow of the GMA vector field.

Mixed convection and heat generation/absorption aspects in MHD flow of tangent-hyperbolic nanoliquid with Newtonian heat/mass transfer

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed

2018-03-01

This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.

Estimation of group means when adjusting for covariates in generalized linear models.

PubMed

Qu, Yongming; Luo, Junxiang

2015-01-01

Generalized linear models are commonly used to analyze categorical data such as binary, count, and ordinal outcomes. Adjusting for important prognostic factors or baseline covariates in generalized linear models may improve the estimation efficiency. The model-based mean for a treatment group produced by most software packages estimates the response at the mean covariate, not the mean response for this treatment group for the studied population. Although this is not an issue for linear models, the model-based group mean estimates in generalized linear models could be seriously biased for the true group means. We propose a new method to estimate the group mean consistently with the corresponding variance estimation. Simulation showed the proposed method produces an unbiased estimator for the group means and provided the correct coverage probability. The proposed method was applied to analyze hypoglycemia data from clinical trials in diabetes. Copyright © 2014 John Wiley & Sons, Ltd.

Identifiability Results for Several Classes of Linear Compartment Models.

PubMed

Meshkat, Nicolette; Sullivant, Seth; Eisenberg, Marisa

2015-08-01

Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.

A non-linear model of economic production processes

NASA Astrophysics Data System (ADS)

Ponzi, A.; Yasutomi, A.; Kaneko, K.

2003-06-01

We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

The linearized multistage model and the future of quantitative risk assessment.

PubMed

Crump, K S

1996-10-01

The linearized multistage (LMS) model has for over 15 years been the default dose-response model used by the U.S. Environmental Protection Agency (USEPA) and other federal and state regulatory agencies in the United States for calculating quantitative estimates of low-dose carcinogenic risks from animal data. The LMS model is in essence a flexible statistical model that can describe both linear and non-linear dose-response patterns, and that produces an upper confidence bound on the linear low-dose slope of the dose-response curve. Unlike its namesake, the Armitage-Doll multistage model, the parameters of the LMS do not correspond to actual physiological phenomena. Thus the LMS is 'biological' only to the extent that the true biological dose response is linear at low dose and that low-dose slope is reflected in the experimental data. If the true dose response is non-linear the LMS upper bound may overestimate the true risk by many orders of magnitude. However, competing low-dose extrapolation models, including those derived from 'biologically-based models' that are capable of incorporating additional biological information, have not shown evidence to date of being able to produce quantitative estimates of low-dose risks that are any more accurate than those obtained from the LMS model. Further, even if these attempts were successful, the extent to which more accurate estimates of low-dose risks in a test animal species would translate into improved estimates of human risk is questionable. Thus, it does not appear possible at present to develop a quantitative approach that would be generally applicable and that would offer significant improvements upon the crude bounding estimates of the type provided by the LMS model. Draft USEPA guidelines for cancer risk assessment incorporate an approach similar to the LMS for carcinogens having a linear mode of action. However, under these guidelines quantitative estimates of low-dose risks would not be developed for

Item Purification in Differential Item Functioning Using Generalized Linear Mixed Models

ERIC Educational Resources Information Center

Liu, Qian

2011-01-01

For this dissertation, four item purification procedures were implemented onto the generalized linear mixed model for differential item functioning (DIF) analysis, and the performance of these item purification procedures was investigated through a series of simulations. Among the four procedures, forward and generalized linear mixed model (GLMM)…

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

A Method for Generating Reduced-Order Linear Models of Multidimensional Supersonic Inlets

NASA Technical Reports Server (NTRS)

Chicatelli, Amy; Hartley, Tom T.

1998-01-01

Simulation of high speed propulsion systems may be divided into two categories, nonlinear and linear. The nonlinear simulations are usually based on multidimensional computational fluid dynamics (CFD) methodologies and tend to provide high resolution results that show the fine detail of the flow. Consequently, these simulations are large, numerically intensive, and run much slower than real-time. ne linear simulations are usually based on large lumping techniques that are linearized about a steady-state operating condition. These simplistic models often run at or near real-time but do not always capture the detailed dynamics of the plant. Under a grant sponsored by the NASA Lewis Research Center, Cleveland, Ohio, a new method has been developed that can be used to generate improved linear models for control design from multidimensional steady-state CFD results. This CFD-based linear modeling technique provides a small perturbation model that can be used for control applications and real-time simulations. It is important to note the utility of the modeling procedure; all that is needed to obtain a linear model of the propulsion system is the geometry and steady-state operating conditions from a multidimensional CFD simulation or experiment. This research represents a beginning step in establishing a bridge between the controls discipline and the CFD discipline so that the control engineer is able to effectively use multidimensional CFD results in control system design and analysis.

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PubMed

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were

Available pressure amplitude of linear compressor based on phasor triangle model

NASA Astrophysics Data System (ADS)

Duan, C. X.; Jiang, X.; Zhi, X. Q.; You, X. K.; Qiu, L. M.

2017-12-01

The linear compressor for cryocoolers possess the advantages of long-life operation, high efficiency, low vibration and compact structure. It is significant to study the match mechanisms between the compressor and the cold finger, which determines the working efficiency of the cryocooler. However, the output characteristics of linear compressor are complicated since it is affected by many interacting parameters. The existing matching methods are simplified and mainly focus on the compressor efficiency and output acoustic power, while neglecting the important output parameter of pressure amplitude. In this study, a phasor triangle model basing on analyzing the forces of the piston is proposed. It can be used to predict not only the output acoustic power, the efficiency, but also the pressure amplitude of the linear compressor. Calculated results agree well with the measurement results of the experiment. By this phasor triangle model, the theoretical maximum output pressure amplitude of the linear compressor can be calculated simply based on a known charging pressure and operating frequency. Compared with the mechanical and electrical model of the linear compressor, the new model can provide an intuitionistic understanding on the match mechanism with faster computational process. The model can also explain the experimental phenomenon of the proportional relationship between the output pressure amplitude and the piston displacement in experiments. By further model analysis, such phenomenon is confirmed as an expression of the unmatched design of the compressor. The phasor triangle model may provide an alternative method for the compressor design and matching with the cold finger.

The Overgeneralization of Linear Models among University Students' Mathematical Productions: A Long-Term Study

ERIC Educational Resources Information Center

Esteley, Cristina B.; Villarreal, Monica E.; Alagia, Humberto R.

2010-01-01

Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase,…

Free-piston engine linear generator for hybrid vehicles modeling study

NASA Astrophysics Data System (ADS)

Callahan, T. J.; Ingram, S. K.

1995-05-01

Development of a free piston engine linear generator was investigated for use as an auxiliary power unit for a hybrid electric vehicle. The main focus of the program was to develop an efficient linear generator concept to convert the piston motion directly into electrical power. Computer modeling techniques were used to evaluate five different designs for linear generators. These designs included permanent magnet generators, reluctance generators, linear DC generators, and two and three-coil induction generators. The efficiency of the linear generator was highly dependent on the design concept. The two-coil induction generator was determined to be the best design, with an efficiency of approximately 90 percent.

Managing Clustered Data Using Hierarchical Linear Modeling

ERIC Educational Resources Information Center

Warne, Russell T.; Li, Yan; McKyer, E. Lisako J.; Condie, Rachel; Diep, Cassandra S.; Murano, Peter S.

2012-01-01

Researchers in nutrition research often use cluster or multistage sampling to gather participants for their studies. These sampling methods often produce violations of the assumption of data independence that most traditional statistics share. Hierarchical linear modeling is a statistical method that can overcome violations of the independence…

Non-linear models for the detection of impaired cerebral blood flow autoregulation.

PubMed

Chacón, Max; Jara, José Luis; Miranda, Rodrigo; Katsogridakis, Emmanuel; Panerai, Ronney B

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Estimating population trends with a linear model

USGS Publications Warehouse

Bart, Jonathan; Collins, Brian D.; Morrison, R.I.G.

2003-01-01

We describe a simple and robust method for estimating trends in population size. The method may be used with Breeding Bird Survey data, aerial surveys, point counts, or any other program of repeated surveys at permanent locations. Surveys need not be made at each location during each survey period. The method differs from most existing methods in being design based, rather than model based. The only assumptions are that the nominal sampling plan is followed and that sample size is large enough for use of the t-distribution. Simulations based on two bird data sets from natural populations showed that the point estimate produced by the linear model was essentially unbiased even when counts varied substantially and 25% of the complete data set was missing. The estimating-equation approach, often used to analyze Breeding Bird Survey data, performed similarly on one data set but had substantial bias on the second data set, in which counts were highly variable. The advantages of the linear model are its simplicity, flexibility, and that it is self-weighting. A user-friendly computer program to carry out the calculations is available from the senior author.

Analysis of baseline, average, and longitudinally measured blood pressure data using linear mixed models.

PubMed

Hossain, Ahmed; Beyene, Joseph

2014-01-01

This article compares baseline, average, and longitudinal data analysis methods for identifying genetic variants in genome-wide association study using the Genetic Analysis Workshop 18 data. We apply methods that include (a) linear mixed models with baseline measures, (b) random intercept linear mixed models with mean measures outcome, and (c) random intercept linear mixed models with longitudinal measurements. In the linear mixed models, covariates are included as fixed effects, whereas relatedness among individuals is incorporated as the variance-covariance structure of the random effect for the individuals. The overall strategy of applying linear mixed models decorrelate the data is based on Aulchenko et al.'s GRAMMAR. By analyzing systolic and diastolic blood pressure, which are used separately as outcomes, we compare the 3 methods in identifying a known genetic variant that is associated with blood pressure from chromosome 3 and simulated phenotype data. We also analyze the real phenotype data to illustrate the methods. We conclude that the linear mixed model with longitudinal measurements of diastolic blood pressure is the most accurate at identifying the known single-nucleotide polymorphism among the methods, but linear mixed models with baseline measures perform best with systolic blood pressure as the outcome.

Scoring and staging systems using cox linear regression modeling and recursive partitioning.

PubMed

Lee, J W; Um, S H; Lee, J B; Mun, J; Cho, H

2006-01-01

Scoring and staging systems are used to determine the order and class of data according to predictors. Systems used for medical data, such as the Child-Turcotte-Pugh scoring and staging systems for ordering and classifying patients with liver disease, are often derived strictly from physicians' experience and intuition. We construct objective and data-based scoring/staging systems using statistical methods. We consider Cox linear regression modeling and recursive partitioning techniques for censored survival data. In particular, to obtain a target number of stages we propose cross-validation and amalgamation algorithms. We also propose an algorithm for constructing scoring and staging systems by integrating local Cox linear regression models into recursive partitioning, so that we can retain the merits of both methods such as superior predictive accuracy, ease of use, and detection of interactions between predictors. The staging system construction algorithms are compared by cross-validation evaluation of real data. The data-based cross-validation comparison shows that Cox linear regression modeling is somewhat better than recursive partitioning when there are only continuous predictors, while recursive partitioning is better when there are significant categorical predictors. The proposed local Cox linear recursive partitioning has better predictive accuracy than Cox linear modeling and simple recursive partitioning. This study indicates that integrating local linear modeling into recursive partitioning can significantly improve prediction accuracy in constructing scoring and staging systems.

Computation of linear acceleration through an internal model in the macaque cerebellum

PubMed Central

Laurens, Jean; Meng, Hui; Angelaki, Dora E.

2013-01-01

A combination of theory and behavioral findings has supported a role for internal models in the resolution of sensory ambiguities and sensorimotor processing. Although the cerebellum has been proposed as a candidate for implementation of internal models, concrete evidence from neural responses is lacking. Here we exploit un-natural motion stimuli, which induce incorrect self-motion perception and eye movements, to explore the neural correlates of an internal model proposed to compensate for Einstein’s equivalence principle and generate neural estimates of linear acceleration and gravity. We show that caudal cerebellar vermis Purkinje cells and cerebellar nuclei neurons selective for actual linear acceleration also encode erroneous linear acceleration, as expected from the internal model hypothesis, even when no actual linear acceleration occurs. These findings provide strong evidence that the cerebellum might be involved in the implementation of internal models that mimic physical principles to interpret sensory signals, as previously hypothesized by theorists. PMID:24077562

On Discontinuous Piecewise Linear Models for Memristor Oscillators

NASA Astrophysics Data System (ADS)

Amador, Andrés; Freire, Emilio; Ponce, Enrique; Ros, Javier

2017-06-01

In this paper, we provide for the first time rigorous mathematical results regarding the rich dynamics of piecewise linear memristor oscillators. In particular, for each nonlinear oscillator given in [Itoh & Chua, 2008], we show the existence of an infinite family of invariant manifolds and that the dynamics on such manifolds can be modeled without resorting to discontinuous models. Our approach provides topologically equivalent continuous models with one dimension less but with one extra parameter associated to the initial conditions. It is possible to justify the periodic behavior exhibited by three-dimensional memristor oscillators, by taking advantage of known results for planar continuous piecewise linear systems. The analysis developed not only confirms the numerical results contained in previous works [Messias et al., 2010; Scarabello & Messias, 2014] but also goes much further by showing the existence of closed surfaces in the state space which are foliated by periodic orbits. The important role of initial conditions that justify the infinite number of periodic orbits exhibited by these models, is stressed. The possibility of unsuspected bistable regimes under specific configurations of parameters is also emphasized.

Non-linear duality invariant partially massless models?

DOE PAGES

Cherney, D.; Deser, S.; Waldron, A.; ...

2015-12-15

We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Lastly, our models mimic Dirac–Born–Infeld theory but it is unclear whether they are Lagrangian.

A tangent-ring optical TWDM-MAN enabling three-level transregional reconfigurations and shared protections by multipoint distributed control

NASA Astrophysics Data System (ADS)

Gou, Kaiyu; Gan, Chaoqin; Zhang, Xiaoyu; Zhang, Yuchao

2018-03-01

An optical time-and-wavelength-division-multiplexing metro-access network (TWDM-MAN) is proposed and demonstrated in this paper. By the reuse of tangent-ring optical distribution network and the design of distributed control mechanism, ONUs needing to communicate with each other can be flexibly accessed to successfully make up three kinds of reconfigurable networks. By the nature advantage of ring topology in protection, three-level comprehensive protections covering both feeder and distribution fibers are also achieved. Besides, a distributed wavelength allocation (DWA) is designed to support efficient parallel upstream transmission. The analyses including capacity, congestion and transmission simulation show that this network has a great performance.

Development of the WRF-CO2 4D-Var assimilation system v1.0

NASA Astrophysics Data System (ADS)

Zheng, Tao; French, Nancy H. F.; Baxter, Martin

2018-05-01

Regional atmospheric CO2 inversions commonly use Lagrangian particle trajectory model simulations to calculate the required influence function, which quantifies the sensitivity of a receptor to flux sources. In this paper, an adjoint-based four-dimensional variational (4D-Var) assimilation system, WRF-CO2 4D-Var, is developed to provide an alternative approach. This system is developed based on the Weather Research and Forecasting (WRF) modeling system, including the system coupled to chemistry (WRF-Chem), with tangent linear and adjoint codes (WRFPLUS), and with data assimilation (WRFDA), all in version 3.6. In WRF-CO2 4D-Var, CO2 is modeled as a tracer and its feedback to meteorology is ignored. This configuration allows most WRF physical parameterizations to be used in the assimilation system without incurring a large amount of code development. WRF-CO2 4D-Var solves for the optimized CO2 flux scaling factors in a Bayesian framework. Two variational optimization schemes are implemented for the system: the first uses the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization algorithm (L-BFGS-B) and the second uses the Lanczos conjugate gradient (CG) in an incremental approach. WRFPLUS forward, tangent linear, and adjoint models are modified to include the physical and dynamical processes involved in the atmospheric transport of CO2. The system is tested by simulations over a domain covering the continental United States at 48 km × 48 km grid spacing. The accuracy of the tangent linear and adjoint models is assessed by comparing against finite difference sensitivity. The system's effectiveness for CO2 inverse modeling is tested using pseudo-observation data. The results of the sensitivity and inverse modeling tests demonstrate the potential usefulness of WRF-CO2 4D-Var for regional CO2 inversions.

A Linear Viscoelastic Model Calibration of Sylgard 184.

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

Long, Kevin Nicholas; Brown, Judith Alice

2017-04-01

We calibrate a linear thermoviscoelastic model for solid Sylgard 184 (90-10 formulation), a lightly cross-linked, highly flexible isotropic elastomer for use both in Sierra / Solid Mechanics via the Universal Polymer Model as well as in Sierra / Structural Dynamics (Salinas) for use as an isotropic viscoelastic material. Material inputs for the calibration in both codes are provided. The frequency domain master curve of oscillatory shear was obtained from a report from Los Alamos National Laboratory (LANL). However, because the form of that data is different from the constitutive models in Sierra, we also present the mapping of the LANLmore » data onto Sandia’s constitutive models. Finally, blind predictions of cyclic tension and compression out to moderate strains of 40 and 20% respectively are compared with Sandia’s legacy cure schedule material. Although the strain rate of the data is unknown, the linear thermoviscoelastic model accurately predicts the experiments out to moderate strains for the slower strain rates, which is consistent with the expectation that quasistatic test procedures were likely followed. This good agreement comes despite the different cure schedules between the Sandia and LANL data.« less

Estimating linear-nonlinear models using Rényi divergences

PubMed Central

Kouh, Minjoon; Sharpee, Tatyana O.

2009-01-01

This paper compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramér-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data. PMID:19568981

Interpreting linear support vector machine models with heat map molecule coloring

PubMed Central

2011-01-01

Background Model-based virtual screening plays an important role in the early drug discovery stage. The outcomes of high-throughput screenings are a valuable source for machine learning algorithms to infer such models. Besides a strong performance, the interpretability of a machine learning model is a desired property to guide the optimization of a compound in later drug discovery stages. Linear support vector machines showed to have a convincing performance on large-scale data sets. The goal of this study is to present a heat map molecule coloring technique to interpret linear support vector machine models. Based on the weights of a linear model, the visualization approach colors each atom and bond of a compound according to its importance for activity. Results We evaluated our approach on a toxicity data set, a chromosome aberration data set, and the maximum unbiased validation data sets. The experiments show that our method sensibly visualizes structure-property and structure-activity relationships of a linear support vector machine model. The coloring of ligands in the binding pocket of several crystal structures of a maximum unbiased validation data set target indicates that our approach assists to determine the correct ligand orientation in the binding pocket. Additionally, the heat map coloring enables the identification of substructures important for the binding of an inhibitor. Conclusions In combination with heat map coloring, linear support vector machine models can help to guide the modification of a compound in later stages of drug discovery. Particularly substructures identified as important by our method might be a starting point for optimization of a lead compound. The heat map coloring should be considered as complementary to structure based modeling approaches. As such, it helps to get a better understanding of the binding mode of an inhibitor. PMID:21439031

Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

NASA Astrophysics Data System (ADS)

Morén, B.; Larsson, T.; Carlsson Tedgren, Å.

2018-03-01

High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

A Technique of Fuzzy C-Mean in Multiple Linear Regression Model toward Paddy Yield

NASA Astrophysics Data System (ADS)

Syazwan Wahab, Nur; Saifullah Rusiman, Mohd; Mohamad, Mahathir; Amira Azmi, Nur; Che Him, Norziha; Ghazali Kamardan, M.; Ali, Maselan

2018-04-01

In this paper, we propose a hybrid model which is a combination of multiple linear regression model and fuzzy c-means method. This research involved a relationship between 20 variates of the top soil that are analyzed prior to planting of paddy yields at standard fertilizer rates. Data used were from the multi-location trials for rice carried out by MARDI at major paddy granary in Peninsular Malaysia during the period from 2009 to 2012. Missing observations were estimated using mean estimation techniques. The data were analyzed using multiple linear regression model and a combination of multiple linear regression model and fuzzy c-means method. Analysis of normality and multicollinearity indicate that the data is normally scattered without multicollinearity among independent variables. Analysis of fuzzy c-means cluster the yield of paddy into two clusters before the multiple linear regression model can be used. The comparison between two method indicate that the hybrid of multiple linear regression model and fuzzy c-means method outperform the multiple linear regression model with lower value of mean square error.

A comparison of linear versus non-linear models of aversive self-awareness, dissociation, and non-suicidal self-injury among young adults.

PubMed

Armey, Michael F; Crowther, Janis H

2008-02-01

Research has identified a significant increase in both the incidence and prevalence of non-suicidal self-injury (NSSI). The present study sought to test both linear and non-linear cusp catastrophe models by using aversive self-awareness, which was operationalized as a composite of aversive self-relevant affect and cognitions, and dissociation as predictors of NSSI. The cusp catastrophe model evidenced a better fit to the data, accounting for 6 times the variance (66%) of a linear model (9%-10%). These results support models of NSSI implicating emotion regulation deficits and experiential avoidance in the occurrence of NSSI and provide preliminary support for the use of cusp catastrophe models to study certain types of low base rate psychopathology such as NSSI. These findings suggest novel approaches to prevention and treatment of NSSI as well.

Generalized linear mixed models with varying coefficients for longitudinal data.

PubMed

Zhang, Daowen

2004-03-01

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.

Linear score tests for variance components in linear mixed models and applications to genetic association studies.

PubMed

Qu, Long; Guennel, Tobias; Marshall, Scott L

2013-12-01

Following the rapid development of genome-scale genotyping technologies, genetic association mapping has become a popular tool to detect genomic regions responsible for certain (disease) phenotypes, especially in early-phase pharmacogenomic studies with limited sample size. In response to such applications, a good association test needs to be (1) applicable to a wide range of possible genetic models, including, but not limited to, the presence of gene-by-environment or gene-by-gene interactions and non-linearity of a group of marker effects, (2) accurate in small samples, fast to compute on the genomic scale, and amenable to large scale multiple testing corrections, and (3) reasonably powerful to locate causal genomic regions. The kernel machine method represented in linear mixed models provides a viable solution by transforming the problem into testing the nullity of variance components. In this study, we consider score-based tests by choosing a statistic linear in the score function. When the model under the null hypothesis has only one error variance parameter, our test is exact in finite samples. When the null model has more than one variance parameter, we develop a new moment-based approximation that performs well in simulations. Through simulations and analysis of real data, we demonstrate that the new test possesses most of the aforementioned characteristics, especially when compared to existing quadratic score tests or restricted likelihood ratio tests. © 2013, The International Biometric Society.

On the Relation between the Linear Factor Model and the Latent Profile Model

ERIC Educational Resources Information Center

Halpin, Peter F.; Dolan, Conor V.; Grasman, Raoul P. P. P.; De Boeck, Paul

2011-01-01

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the…

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

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

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

A note on probabilistic models over strings: the linear algebra approach.

PubMed

Bouchard-Côté, Alexandre

2013-12-01

Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems.

Predicting recycling behaviour: Comparison of a linear regression model and a fuzzy logic model.

PubMed

Vesely, Stepan; Klöckner, Christian A; Dohnal, Mirko

2016-03-01

In this paper we demonstrate that fuzzy logic can provide a better tool for predicting recycling behaviour than the customarily used linear regression. To show this, we take a set of empirical data on recycling behaviour (N=664), which we randomly divide into two halves. The first half is used to estimate a linear regression model of recycling behaviour, and to develop a fuzzy logic model of recycling behaviour. As the first comparison, the fit of both models to the data included in estimation of the models (N=332) is evaluated. As the second comparison, predictive accuracy of both models for "new" cases (hold-out data not included in building the models, N=332) is assessed. In both cases, the fuzzy logic model significantly outperforms the regression model in terms of fit. To conclude, when accurate predictions of recycling and possibly other environmental behaviours are needed, fuzzy logic modelling seems to be a promising technique. Copyright © 2015 Elsevier Ltd. All rights reserved.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

PubMed Central

2011-01-01

Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task. PMID:21867520

Non-linear models for the detection of impaired cerebral blood flow autoregulation

PubMed Central

Miranda, Rodrigo; Katsogridakis, Emmanuel

2018-01-01

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model’s derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired. PMID:29381724

Modeling the frequency of opposing left-turn conflicts at signalized intersections using generalized linear regression models.

PubMed

Zhang, Xin; Liu, Pan; Chen, Yuguang; Bai, Lu; Wang, Wei

2014-01-01

The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation.

Side forces on forebodies at high angles of attack and Mach numbers from 0.1 to 0.7: two tangent ogives, paraboloid and cone

NASA Technical Reports Server (NTRS)

Keener, E. R.; Chapman, G. T.; Taleghani, J.; Cohen, L.

1977-01-01

An experimental investigation was conducted in the Ames 12-Foot Wind Tunnel to determine the subsonic aerodynamic characteristics of four forebodies at high angles of attack. The forebodies tested were a tangent ogive with fineness ratio of 5, a paraboloid with fineness ratio of 3.5, a 20 deg cone, and a tangent ogive with an elliptic cross section. The investigation included the effects of nose bluntness and boundary-layer trips. The tangent-ogive forebody was also tested in the presence of a short afterbody and with the afterbody attached. Static longitudinal and lateral/directional stability data were obtained. The investigation was conducted to investigate the existence of large side forces and yawing moments at high angles of attack and zero sideslip. It was found that all of the forebodies experience steady side forces that start at angles of attack of from 20 deg to 35 deg and exist to as high as 80 deg, depending on forebody shape. The side is as large as 1.6 times the normal force and is generally repeatable with increasing and decreasing angle of attack and, also, from test to test. The side force is very sensitive to the nature of the boundary layer, as indicated by large changes with boundary trips. The maximum side force caries considerably with Reynolds number and tends to decrease with increasing Mach number. The direction of the side force is sensitive to the body geometry near the nose. The angle of attack of onset of side force is not strongly influenced by Reynolds number or Mach number but varies with forebody shape. Maximum normal force often occurs at angles of attack near 60 deg. The effect of the elliptic cross section is to reduce the angle of onset by about 10 deg compared to that of an equivalent circular forebody with the same fineness ratio. The short afterbody reduces the angle of onset by about 5 deg.

An approximate generalized linear model with random effects for informative missing data.

PubMed

Follmann, D; Wu, M

1995-03-01

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

MULTIVARIATE LINEAR MIXED MODELS FOR MULTIPLE OUTCOMES. (R824757)

EPA Science Inventory

We propose a multivariate linear mixed (MLMM) for the analysis of multiple outcomes, which generalizes the latent variable model of Sammel and Ryan. The proposed model assumes a flexible correlation structure among the multiple outcomes, and allows a global test of the impact of ...

MAGDM linear-programming models with distinct uncertain preference structures.

PubMed

Xu, Zeshui S; Chen, Jian

2008-10-01

Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.

Effect of heteroscedasticity treatment in residual error models on model calibration and prediction uncertainty estimation

NASA Astrophysics Data System (ADS)

Sun, Ruochen; Yuan, Huiling; Liu, Xiaoli

2017-11-01

The heteroscedasticity treatment in residual error models directly impacts the model calibration and prediction uncertainty estimation. This study compares three methods to deal with the heteroscedasticity, including the explicit linear modeling (LM) method and nonlinear modeling (NL) method using hyperbolic tangent function, as well as the implicit Box-Cox transformation (BC). Then a combined approach (CA) combining the advantages of both LM and BC methods has been proposed. In conjunction with the first order autoregressive model and the skew exponential power (SEP) distribution, four residual error models are generated, namely LM-SEP, NL-SEP, BC-SEP and CA-SEP, and their corresponding likelihood functions are applied to the Variable Infiltration Capacity (VIC) hydrologic model over the Huaihe River basin, China. Results show that the LM-SEP yields the poorest streamflow predictions with the widest uncertainty band and unrealistic negative flows. The NL and BC methods can better deal with the heteroscedasticity and hence their corresponding predictive performances are improved, yet the negative flows cannot be avoided. The CA-SEP produces the most accurate predictions with the highest reliability and effectively avoids the negative flows, because the CA approach is capable of addressing the complicated heteroscedasticity over the study basin.

Nonlinearity measure and internal model control based linearization in anti-windup design

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

Perev, Kamen

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequencymore » ranges.« less

Log-Linear Models for Gene Association

PubMed Central

Hu, Jianhua; Joshi, Adarsh; Johnson, Valen E.

2009-01-01

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens’ sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in a microarray study for which it was possible to obtain biological confirmation of detected interactions. PMID:19655032

An analytically linearized helicopter model with improved modeling accuracy

NASA Technical Reports Server (NTRS)

Jensen, Patrick T.; Curtiss, H. C., Jr.; Mckillip, Robert M., Jr.

1991-01-01

An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.

Effect of linear and non-linear blade modelling techniques on simulated fatigue and extreme loads using Bladed

NASA Astrophysics Data System (ADS)

Beardsell, Alec; Collier, William; Han, Tao

2016-09-01

There is a trend in the wind industry towards ever larger and more flexible turbine blades. Blade tip deflections in modern blades now commonly exceed 10% of blade length. Historically, the dynamic response of wind turbine blades has been analysed using linear models of blade deflection which include the assumption of small deflections. For modern flexible blades, this assumption is becoming less valid. In order to continue to simulate dynamic turbine performance accurately, routine use of non-linear models of blade deflection may be required. This can be achieved by representing the blade as a connected series of individual flexible linear bodies - referred to in this paper as the multi-part approach. In this paper, Bladed is used to compare load predictions using single-part and multi-part blade models for several turbines. The study examines the impact on fatigue and extreme loads and blade deflection through reduced sets of load calculations based on IEC 61400-1 ed. 3. Damage equivalent load changes of up to 16% and extreme load changes of up to 29% are observed at some turbine load locations. It is found that there is no general pattern in the loading differences observed between single-part and multi-part blade models. Rather, changes in fatigue and extreme loads with a multi-part blade model depend on the characteristics of the individual turbine and blade. Key underlying causes of damage equivalent load change are identified as differences in edgewise- torsional coupling between the multi-part and single-part models, and increased edgewise rotor mode damping in the multi-part model. Similarly, a causal link is identified between torsional blade dynamics and changes in ultimate load results.

Artificial Neural Network versus Linear Models Forecasting Doha Stock Market

NASA Astrophysics Data System (ADS)

Yousif, Adil; Elfaki, Faiz

2017-12-01

The purpose of this study is to determine the instability of Doha stock market and develop forecasting models. Linear time series models are used and compared with a nonlinear Artificial Neural Network (ANN) namely Multilayer Perceptron (MLP) Technique. It aims to establish the best useful model based on daily and monthly data which are collected from Qatar exchange for the period starting from January 2007 to January 2015. Proposed models are for the general index of Qatar stock exchange and also for the usages in other several sectors. With the help of these models, Doha stock market index and other various sectors were predicted. The study was conducted by using various time series techniques to study and analyze data trend in producing appropriate results. After applying several models, such as: Quadratic trend model, double exponential smoothing model, and ARIMA, it was concluded that ARIMA (2,2) was the most suitable linear model for the daily general index. However, ANN model was found to be more accurate than time series models.

A new adaptive multiple modelling approach for non-linear and non-stationary systems

NASA Astrophysics Data System (ADS)

Chen, Hao; Gong, Yu; Hong, Xia

2016-07-01

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

Modelling non-linear effects of dark energy

NASA Astrophysics Data System (ADS)

Bose, Benjamin; Baldi, Marco; Pourtsidou, Alkistis

2018-04-01

We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving w models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter ξ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter σv. To quantify the importance of modelling the interaction, we create mock data sets for varying values of ξ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a ξ=0 modelling, ignoring the interaction. We find the fiducial growth parameter f is generally recovered even for very large values of ξ both at z=0.5 and z=1. The ξ=0 modelling is most biased in its estimation of f for the phantom w=‑1.1 case.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant.

PubMed

Eidi, Zahra; Mohammad-Rafiee, Farshid; Khorrami, Mohammad; Gholami, Azam

2017-11-15

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

Log-Linear Modeling of Agreement among Expert Exposure Assessors

PubMed Central

Hunt, Phillip R.; Friesen, Melissa C.; Sama, Susan; Ryan, Louise; Milton, Donald

2015-01-01

Background: Evaluation of expert assessment of exposure depends, in the absence of a validation measurement, upon measures of agreement among the expert raters. Agreement is typically measured using Cohen’s Kappa statistic, however, there are some well-known limitations to this approach. We demonstrate an alternate method that uses log-linear models designed to model agreement. These models contain parameters that distinguish between exact agreement (diagonals of agreement matrix) and non-exact associations (off-diagonals). In addition, they can incorporate covariates to examine whether agreement differs across strata. Methods: We applied these models to evaluate agreement among expert ratings of exposure to sensitizers (none, likely, high) in a study of occupational asthma. Results: Traditional analyses using weighted kappa suggested potential differences in agreement by blue/white collar jobs and office/non-office jobs, but not case/control status. However, the evaluation of the covariates and their interaction terms in log-linear models found no differences in agreement with these covariates and provided evidence that the differences observed using kappa were the result of marginal differences in the distribution of ratings rather than differences in agreement. Differences in agreement were predicted across the exposure scale, with the likely moderately exposed category more difficult for the experts to differentiate from the highly exposed category than from the unexposed category. Conclusions: The log-linear models provided valuable information about patterns of agreement and the structure of the data that were not revealed in analyses using kappa. The models’ lack of dependence on marginal distributions and the ease of evaluating covariates allow reliable detection of observational bias in exposure data. PMID:25748517

Wavefront Sensing for WFIRST with a Linear Optical Model

NASA Technical Reports Server (NTRS)

Jurling, Alden S.; Content, David A.

2012-01-01

In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

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

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

Nonlinear extension of a hemodynamic linear model for coherent hemodynamics spectroscopy.

PubMed

Sassaroli, Angelo; Kainerstorfer, Jana M; Fantini, Sergio

2016-01-21

In this work, we are proposing an extension of a recent hemodynamic model (Fantini, 2014a), which was developed within the framework of a novel approach to the study of tissue hemodynamics, named coherent hemodynamics spectroscopy (CHS). The previous hemodynamic model, from a signal processing viewpoint, treats the tissue microvasculature as a linear time-invariant system, and considers changes of blood volume, capillary blood flow velocity and the rate of oxygen diffusion as inputs, and the changes of oxy-, deoxy-, and total hemoglobin concentrations (measured in near infrared spectroscopy) as outputs. The model has been used also as a forward solver in an inversion procedure to retrieve quantitative parameters that assess physiological and biological processes such as microcirculation, cerebral autoregulation, tissue metabolic rate of oxygen, and oxygen extraction fraction. Within the assumption of "small" capillary blood flow velocity oscillations the model showed that the capillary and venous compartments "respond" to this input as low pass filters, characterized by two distinct impulse response functions. In this work, we do not make the assumption of "small" perturbations of capillary blood flow velocity by solving without approximations the partial differential equation that governs the spatio-temporal behavior of hemoglobin saturation in capillary and venous blood. Preliminary comparison between the linear time-invariant model and the extended model (here identified as nonlinear model) are shown for the relevant parameters measured in CHS as a function of the oscillation frequency (CHS spectra). We have found that for capillary blood flow velocity oscillations with amplitudes up to 10% of the baseline value (which reflect typical scenarios in CHS), the discrepancies between CHS spectra obtained with the linear and nonlinear models are negligible. For larger oscillations (~50%) the linear and nonlinear models yield CHS spectra with differences within typical

Linear diffusion model dating of cinder cones in Central Anatolia, Turkey

NASA Astrophysics Data System (ADS)

O'Sadnick, L. G.; Reid, M. R.; Cline, M. L.; Cosca, M. A.; Kuscu, G.

2013-12-01

The progressive decrease in slope angle, cone height and cone height/width ratio over time provides the basis for geomorphic dating of cinder cones using linear diffusion models. Previous research using diffusion models to date cinder cones has focused on the cone height/width ratio as the basis for dating cones of unknown age [1,2]. Here we apply linear diffusion models to dating cinder cones. A suite of 16 cinder cones from the Hasandağ volcano area of the Neogene-Quaternary Central Anatolian Volcanic Zone, for which samples are available, were selected for morphologic dating analysis. New 40Ar/39Ar dates for five of these cones range from 62 × 4 to 517 × 9 ka. Linear diffusion models were used to model the erosional degradation of each cone. Diffusion coefficients (κ) for the 5 cinder cones with known ages were constrained by comparing various modeled slope profiles to the current slope profile. The resulting κ is 7.5×0.5 m2kyr-1. Using this κ value, eruption ages were modeled for the remaining 11 cinder cones and range from 53×3 to 455×30 ka. These ages are within the range of ages previously reported for cinder cones in the Hasandağ region. The linear diffusion model-derived ages are being compared to additional new 40Ar/39Ar dates in order to further assess the applicability of morphological dating to constrain the ages of cinder cones. The relatively well-constrained κ value we obtained by applying the linear diffusion model to cinder cones that range in age by nearly 500 ka suggests that this model can be used to date cinder cones. This κ value is higher than the well-established value of κ =3.9 for a cinder cone in a similar climate [3]. Therefore our work confirms the importance of determining appropriate κ values from nearby cones with known ages. References 1. C.A. Wood, J. Volcanol. Geotherm. Res. 8, 137 (1980) 2. D.M. Wood, M.F. Sheridan, J. Volcanol. Geotherm. Res. 83, 241 (1998) 3. J.D. Pelletier, M.L. Cline, Geology 35, 1067 (2007)

Locally Dependent Linear Logistic Test Model with Person Covariates

ERIC Educational Resources Information Center

Ip, Edward H.; Smits, Dirk J. M.; De Boeck, Paul

2009-01-01

The article proposes a family of item-response models that allow the separate and independent specification of three orthogonal components: item attribute, person covariate, and local item dependence. Special interest lies in extending the linear logistic test model, which is commonly used to measure item attributes, to tests with embedded item…

Optical linear algebra processors: noise and error-source modeling.

PubMed

Casasent, D; Ghosh, A

1985-06-01

The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

Optical linear algebra processors - Noise and error-source modeling

NASA Technical Reports Server (NTRS)

Casasent, D.; Ghosh, A.

1985-01-01

The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

OPLS statistical model versus linear regression to assess sonographic predictors of stroke prognosis.

PubMed

Vajargah, Kianoush Fathi; Sadeghi-Bazargani, Homayoun; Mehdizadeh-Esfanjani, Robab; Savadi-Oskouei, Daryoush; Farhoudi, Mehdi

2012-01-01

The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.

Procedures for generation and reduction of linear models of a turbofan engine

NASA Technical Reports Server (NTRS)

Seldner, K.; Cwynar, D. S.

1978-01-01

A real time hybrid simulation of the Pratt & Whitney F100-PW-F100 turbofan engine was used for linear-model generation. The linear models were used to analyze the effect of disturbances about an operating point on the dynamic performance of the engine. A procedure that disturbs, samples, and records the state and control variables was developed. For large systems, such as the F100 engine, the state vector is large and may contain high-frequency information not required for control. This, reducing the full-state to a reduced-order model may be a practicable approach to simplifying the control design. A reduction technique was developed to generate reduced-order models. Selected linear and nonlinear output responses to exhaust-nozzle area and main-burner fuel flow disturbances are presented for comparison.

Using Quartile-Quartile Lines as Linear Models

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2015-01-01

This article introduces the notion of the quartile-quartile line as an alternative to the regression line and the median-median line to produce a linear model based on a set of data. It is based on using the first and third quartiles of a set of (x, y) data. Dynamic spreadsheets are used as exploratory tools to compare the different approaches and…

Low-lying scalars in an extended linear σ model

NASA Astrophysics Data System (ADS)

Mukherjee, Tamal K.; Huang, Mei; Yan, Qi-Shu

2012-12-01

We formulate an extended linear σ model of a quarkonia nonet and a tetraquark nonet as well as a complex isosinglet (glueball) by virtue of chiral symmetry SUL(3)×SUR(3) and UA(1) symmetry. In the linear realization formalism, we study the mass spectra and components of the low-lying scalars and pseudoscalars in this model. The mass matrices for physical states are obtained and the glueball candidates are examined. We find that the model can accommodate the mass spectra of low-lying states quite well. Our fits indicate that the most glueball-like scalar should be 2 GeV or higher while the glueball pseudoscalar is η(1756). We also examine the parameter region where the lightest isoscalar f0(600) can be the glueball and quarkonia dominant but find such a parameter region may be confronted with the problem of the unbounded vacuum from below.

Running vacuum cosmological models: linear scalar perturbations

NASA Astrophysics Data System (ADS)

Perico, E. L. D.; Tamayo, D. A.

2017-08-01

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ(H2) or Λ(R). Such models assume an equation of state for the vacuum given by bar PΛ = - bar rhoΛ, relating its background pressure bar PΛ with its mean energy density bar rhoΛ ≡ Λ/8πG. This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely bar rhoΛ = Σibar rhoΛi. Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ(H2) scenario the vacuum is coupled with every matter component, whereas the Λ(R) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.

Light propagation in linearly perturbed ΛLTB models

NASA Astrophysics Data System (ADS)

Meyer, Sven; Bartelmann, Matthias

2017-11-01

We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and perform a suitable spherical harmonic decomposition. This allows to map the abstract gauge-invariant perturbation variables to well-known quantities from weak gravitational lensing like convergence or cosmic shear. The resulting set of differential equations can effectively be solved by a Green's function approach leading to line-of-sight integrals sourced by the perturbation variables on the backward lightcone. The resulting spherical harmonic coefficients of the lensing observables are presented and the shear field is decomposed into its E- and B-modes. Results of this work are an essential tool to add information from linear structure formation to the analysis of spherically symmetric dust models with the purpose of testing the Copernican Principle with multiple cosmological probes.

Weighted functional linear regression models for gene-based association analysis.

PubMed

Belonogova, Nadezhda M; Svishcheva, Gulnara R; Wilson, James F; Campbell, Harry; Axenovich, Tatiana I

2018-01-01

Functional linear regression models are effectively used in gene-based association analysis of complex traits. These models combine information about individual genetic variants, taking into account their positions and reducing the influence of noise and/or observation errors. To increase the power of methods, where several differently informative components are combined, weights are introduced to give the advantage to more informative components. Allele-specific weights have been introduced to collapsing and kernel-based approaches to gene-based association analysis. Here we have for the first time introduced weights to functional linear regression models adapted for both independent and family samples. Using data simulated on the basis of GAW17 genotypes and weights defined by allele frequencies via the beta distribution, we demonstrated that type I errors correspond to declared values and that increasing the weights of causal variants allows the power of functional linear models to be increased. We applied the new method to real data on blood pressure from the ORCADES sample. Five of the six known genes with P < 0.1 in at least one analysis had lower P values with weighted models. Moreover, we found an association between diastolic blood pressure and the VMP1 gene (P = 8.18×10-6), when we used a weighted functional model. For this gene, the unweighted functional and weighted kernel-based models had P = 0.004 and 0.006, respectively. The new method has been implemented in the program package FREGAT, which is freely available at https://cran.r-project.org/web/packages/FREGAT/index.html.

A simple method for identifying parameter correlations in partially observed linear dynamic models.

PubMed

Li, Pu; Vu, Quoc Dong

2015-12-14

Parameter estimation represents one of the most significant challenges in systems biology. This is because biological models commonly contain a large number of parameters among which there may be functional interrelationships, thus leading to the problem of non-identifiability. Although identifiability analysis has been extensively studied by analytical as well as numerical approaches, systematic methods for remedying practically non-identifiable models have rarely been investigated. We propose a simple method for identifying pairwise correlations and higher order interrelationships of parameters in partially observed linear dynamic models. This is made by derivation of the output sensitivity matrix and analysis of the linear dependencies of its columns. Consequently, analytical relations between the identifiability of the model parameters and the initial conditions as well as the input functions can be achieved. In the case of structural non-identifiability, identifiable combinations can be obtained by solving the resulting homogenous linear equations. In the case of practical non-identifiability, experiment conditions (i.e. initial condition and constant control signals) can be provided which are necessary for remedying the non-identifiability and unique parameter estimation. It is noted that the approach does not consider noisy data. In this way, the practical non-identifiability issue, which is popular for linear biological models, can be remedied. Several linear compartment models including an insulin receptor dynamics model are taken to illustrate the application of the proposed approach. Both structural and practical identifiability of partially observed linear dynamic models can be clarified by the proposed method. The result of this method provides important information for experimental design to remedy the practical non-identifiability if applicable. The derivation of the method is straightforward and thus the algorithm can be easily implemented into a

Null tests of the standard model using the linear model formalism

NASA Astrophysics Data System (ADS)

Marra, Valerio; Sapone, Domenico

2018-04-01

We test both the Friedmann-Lemaître-Robertson-Walker geometry and Λ CDM cosmology in a model-independent way by reconstructing the Hubble function H (z ), the comoving distance D (z ), and the growth of structure f σ8(z ) using the most recent data available. We use the linear model formalism in order to optimally reconstruct the above cosmological functions, together with their derivatives and integrals. We then evaluate four of the null tests available in the literature that probe both background and perturbation assumptions. For all the four tests, we find agreement, within the errors, with the standard cosmological model.

Wavelet-linear genetic programming: A new approach for modeling monthly streamflow

NASA Astrophysics Data System (ADS)

Ravansalar, Masoud; Rajaee, Taher; Kisi, Ozgur

2017-06-01

The streamflows are important and effective factors in stream ecosystems and its accurate prediction is an essential and important issue in water resources and environmental engineering systems. A hybrid wavelet-linear genetic programming (WLGP) model, which includes a discrete wavelet transform (DWT) and a linear genetic programming (LGP) to predict the monthly streamflow (Q) in two gauging stations, Pataveh and Shahmokhtar, on the Beshar River at the Yasuj, Iran were used in this study. In the proposed WLGP model, the wavelet analysis was linked to the LGP model where the original time series of streamflow were decomposed into the sub-time series comprising wavelet coefficients. The results were compared with the single LGP, artificial neural network (ANN), a hybrid wavelet-ANN (WANN) and Multi Linear Regression (MLR) models. The comparisons were done by some of the commonly utilized relevant physical statistics. The Nash coefficients (E) were found as 0.877 and 0.817 for the WLGP model, for the Pataveh and Shahmokhtar stations, respectively. The comparison of the results showed that the WLGP model could significantly increase the streamflow prediction accuracy in both stations. Since, the results demonstrate a closer approximation of the peak streamflow values by the WLGP model, this model could be utilized for the simulation of cumulative streamflow data prediction in one month ahead.

Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

DTIC Science & Technology

1974-01-01

REGRESSION MODEL - THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January 1974 Nelson Delfino d’Avila Mascarenha;? Image...Report 520 DIGITAL IMAGE RESTORATION UNDER A REGRESSION MODEL THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January...a two- dimensional form adequately describes the linear model . A dis- cretization is performed by using quadrature methods. By trans

A Hierarchical Linear Model for Estimating Gender-Based Earnings Differentials.

ERIC Educational Resources Information Center

Haberfield, Yitchak; Semyonov, Moshe; Addi, Audrey

1998-01-01

Estimates of gender earnings inequality in data from 116,431 Jewish workers were compared using a hierarchical linear model (HLM) and ordinary least squares model. The HLM allows estimation of the extent to which earnings inequality depends on occupational characteristics. (SK)

Modeling Pan Evaporation for Kuwait by Multiple Linear Regression

PubMed Central

Almedeij, Jaber

2012-01-01

Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

PubMed

Lin, Huiming; Fu, Bo; Qin, Guoyou; Zhu, Zhongyi

2017-12-01

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study. © 2017, The International Biometric Society.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

NASA Astrophysics Data System (ADS)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

Linear Sigma Model Toolshed for D-brane Physics

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

Hellerman, Simeon

Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physic complementary to that of recent work of Douglas.

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.

PubMed

Wiedermann, Wolfgang; Artner, Richard; von Eye, Alexander

2017-01-01

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

NASA Technical Reports Server (NTRS)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

Linear summation of outputs in a balanced network model of motor cortex

PubMed Central

Capaday, Charles; van Vreeswijk, Carl

2015-01-01

Given the non-linearities of the neural circuitry's elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis. PMID:26097452

Linear summation of outputs in a balanced network model of motor cortex.

PubMed

Capaday, Charles; van Vreeswijk, Carl

2015-01-01

Given the non-linearities of the neural circuitry's elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis.

Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

ERIC Educational Resources Information Center

Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

2012-01-01

Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

Role of Statistical Random-Effects Linear Models in Personalized Medicine

PubMed Central

Diaz, Francisco J; Yeh, Hung-Wen; de Leon, Jose

2012-01-01

Some empirical studies and recent developments in pharmacokinetic theory suggest that statistical random-effects linear models are valuable tools that allow describing simultaneously patient populations as a whole and patients as individuals. This remarkable characteristic indicates that these models may be useful in the development of personalized medicine, which aims at finding treatment regimes that are appropriate for particular patients, not just appropriate for the average patient. In fact, published developments show that random-effects linear models may provide a solid theoretical framework for drug dosage individualization in chronic diseases. In particular, individualized dosages computed with these models by means of an empirical Bayesian approach may produce better results than dosages computed with some methods routinely used in therapeutic drug monitoring. This is further supported by published empirical and theoretical findings that show that random effects linear models may provide accurate representations of phase III and IV steady-state pharmacokinetic data, and may be useful for dosage computations. These models have applications in the design of clinical algorithms for drug dosage individualization in chronic diseases; in the computation of dose correction factors; computation of the minimum number of blood samples from a patient that are necessary for calculating an optimal individualized drug dosage in therapeutic drug monitoring; measure of the clinical importance of clinical, demographic, environmental or genetic covariates; study of drug-drug interactions in clinical settings; the implementation of computational tools for web-site-based evidence farming; design of pharmacogenomic studies; and in the development of a pharmacological theory of dosage individualization. PMID:23467392

Role of Statistical Random-Effects Linear Models in Personalized Medicine.

PubMed

Diaz, Francisco J; Yeh, Hung-Wen; de Leon, Jose

2012-03-01

Some empirical studies and recent developments in pharmacokinetic theory suggest that statistical random-effects linear models are valuable tools that allow describing simultaneously patient populations as a whole and patients as individuals. This remarkable characteristic indicates that these models may be useful in the development of personalized medicine, which aims at finding treatment regimes that are appropriate for particular patients, not just appropriate for the average patient. In fact, published developments show that random-effects linear models may provide a solid theoretical framework for drug dosage individualization in chronic diseases. In particular, individualized dosages computed with these models by means of an empirical Bayesian approach may produce better results than dosages computed with some methods routinely used in therapeutic drug monitoring. This is further supported by published empirical and theoretical findings that show that random effects linear models may provide accurate representations of phase III and IV steady-state pharmacokinetic data, and may be useful for dosage computations. These models have applications in the design of clinical algorithms for drug dosage individualization in chronic diseases; in the computation of dose correction factors; computation of the minimum number of blood samples from a patient that are necessary for calculating an optimal individualized drug dosage in therapeutic drug monitoring; measure of the clinical importance of clinical, demographic, environmental or genetic covariates; study of drug-drug interactions in clinical settings; the implementation of computational tools for web-site-based evidence farming; design of pharmacogenomic studies; and in the development of a pharmacological theory of dosage individualization.

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

NASA Astrophysics Data System (ADS)

Szalai, Robert; Ehrhardt, David; Haller, George

2017-06-01

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. This model identification utilizes Taken's delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding. The SSMs are then constructed for the sampling map using the parametrization method for invariant manifolds, which assumes that the manifold is an embedding of, rather than a graph over, a spectral subspace. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

PubMed Central

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H

2017-02-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

NASA Astrophysics Data System (ADS)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-10-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

Modeling of non-ideal hard permanent magnets with an affine-linear model, illustrated for a bar and a horseshoe magnet

NASA Astrophysics Data System (ADS)

Glane, Sebastian; Reich, Felix A.; Müller, Wolfgang H.

2017-11-01

This study is dedicated to continuum-scale material modeling of isotropic permanent magnets. An affine-linear extension to the commonly used ideal hard model for permanent magnets is proposed, motivated, and detailed. In order to demonstrate the differences between these models, bar and horseshoe magnets are considered. The structure of the boundary value problem for the magnetic field and related solution techniques are discussed. For the ideal model, closed-form analytical solutions were obtained for both geometries. Magnetic fields of the boundary value problems for both models and differently shaped magnets were computed numerically by using the boundary element method. The results show that the character of the magnetic field is strongly influenced by the model that is used. Furthermore, it can be observed that the shape of an affine-linear magnet influences the near-field significantly. Qualitative comparisons with experiments suggest that both the ideal and the affine-linear models are relevant in practice, depending on the magnetic material employed. Mathematically speaking, the ideal magnetic model is a special case of the affine-linear one. Therefore, in applications where knowledge of the near-field is important, the affine-linear model can yield more accurate results—depending on the magnetic material.

Quantum criticality of the two-channel pseudogap Anderson model: universal scaling in linear and non-linear conductance.

PubMed

Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou

2016-05-05

The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, ρc(ω) proportional |ω − μF|(r) (0 < r < 1) near the Fermi energy μF. At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r = rc < 1. Surprisingly, in the 2CK phase, different power-law scalings from the well-known [Formula: see text] or [Formula: see text] form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.

Adaptive Error Estimation in Linearized Ocean General Circulation Models

NASA Technical Reports Server (NTRS)

Chechelnitsky, Michael Y.

1999-01-01

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large

Study of linear induction motor characteristics : the Mosebach model

DOT National Transportation Integrated Search

1976-05-31

This report covers the Mosebach theory of the double-sided linear induction motor, starting with the ideallized model and accompanying assumptions, and ending with relations for thrust, airgap power, and motor efficiency. Solutions of the magnetic in...

Study of linear induction motor characteristics : the Oberretl model

DOT National Transportation Integrated Search

1975-05-30

The Oberretl theory of the double-sided linear induction motor (LIM) is examined, starting with the idealized model and accompanying assumptions, and ending with relations for predicted thrust, airgap power, and motor efficiency. The effect of varyin...

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

NASA Astrophysics Data System (ADS)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

Linear Reconstruction of Non-Stationary Image Ensembles Incorporating Blur and Noise Models

DTIC Science & Technology

1998-03-01

for phase distortions due to noise which leads to less deblurring as noise increases [41]. In contrast, the vector Wiener filter incorporates some a...AFIT/DS/ENG/98- 06 Linear Reconstruction of Non-Stationary Image Ensembles Incorporating Blur and Noise Models DISSERTATION Stephen D. Ford Captain...Dissertation 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS LINEAR RECONSTRUCTION OF NON-STATIONARY IMAGE ENSEMBLES INCORPORATING BLUR AND NOISE MODELS 6. AUTHOR(S

Linear and nonlinear methods in modeling the aqueous solubility of organic compounds.

PubMed

Catana, Cornel; Gao, Hua; Orrenius, Christian; Stouten, Pieter F W

2005-01-01

Solubility data for 930 diverse compounds have been analyzed using linear Partial Least Square (PLS) and nonlinear PLS methods, Continuum Regression (CR), and Neural Networks (NN). 1D and 2D descriptors from MOE package in combination with E-state or ISIS keys have been used. The best model was obtained using linear PLS for a combination between 22 MOE descriptors and 65 ISIS keys. It has a correlation coefficient (r2) of 0.935 and a root-mean-square error (RMSE) of 0.468 log molar solubility (log S(w)). The model validated on a test set of 177 compounds not included in the training set has r2 0.911 and RMSE 0.475 log S(w). The descriptors were ranked according to their importance, and at the top of the list have been found the 22 MOE descriptors. The CR model produced results as good as PLS, and because of the way in which cross-validation has been done it is expected to be a valuable tool in prediction besides PLS model. The statistics obtained using nonlinear methods did not surpass those got with linear ones. The good statistic obtained for linear PLS and CR recommends these models to be used in prediction when it is difficult or impossible to make experimental measurements, for virtual screening, combinatorial library design, and efficient leads optimization.

Non-linear modelling and control of semi-active suspensions with variable damping

NASA Astrophysics Data System (ADS)

Chen, Huang; Long, Chen; Yuan, Chao-Chun; Jiang, Hao-Bin

2013-10-01

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f-v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief-desire-intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor

2009-01-01

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

A Chain of Modeling Tools For Gas and Aqueous Phase Chemstry

NASA Astrophysics Data System (ADS)

Audiffren, N.; Djouad, R.; Sportisse, B.

Atmospheric chemistry is characterized by the use of large set of chemical species and reactions. Handling with the set of data required for the definition of the model is a quite difficult task. We prsent in this short article a preprocessor for diphasic models (gas phase and aqueous phase in cloud droplets) named SPACK. The main interest of SPACK is the automatic generation of lumped species related to fast equilibria. We also developped a linear tangent model using the automatic differentiation tool named ODYSSEE in order to perform a sensitivity analysis of an atmospheric multi- phase mechanism based on RADM2 kinetic scheme.Local sensitivity coefficients are computed for two different scenarii. We focus in this study on the sensitivity of the ozone,NOx,HOx, system with respect to some aqueous phase reactions and we inves- tigate the influence of the reduction in the photolysis rates in the area below the cloud region.

Derivation of the linear-logistic model and Cox's proportional hazard model from a canonical system description.

PubMed

Voit, E O; Knapp, R G

1997-08-15

The linear-logistic regression model and Cox's proportional hazard model are widely used in epidemiology. Their successful application leaves no doubt that they are accurate reflections of observed disease processes and their associated risks or incidence rates. In spite of their prominence, it is not a priori evident why these models work. This article presents a derivation of the two models from the framework of canonical modeling. It begins with a general description of the dynamics between risk sources and disease development, formulates this description in the canonical representation of an S-system, and shows how the linear-logistic model and Cox's proportional hazard model follow naturally from this representation. The article interprets the model parameters in terms of epidemiological concepts as well as in terms of general systems theory and explains the assumptions and limitations generally accepted in the application of these epidemiological models.

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure

Valid statistical approaches for analyzing sholl data: Mixed effects versus simple linear models.

PubMed

Wilson, Machelle D; Sethi, Sunjay; Lein, Pamela J; Keil, Kimberly P

2017-03-01

The Sholl technique is widely used to quantify dendritic morphology. Data from such studies, which typically sample multiple neurons per animal, are often analyzed using simple linear models. However, simple linear models fail to account for intra-class correlation that occurs with clustered data, which can lead to faulty inferences. Mixed effects models account for intra-class correlation that occurs with clustered data; thus, these models more accurately estimate the standard deviation of the parameter estimate, which produces more accurate p-values. While mixed models are not new, their use in neuroscience has lagged behind their use in other disciplines. A review of the published literature illustrates common mistakes in analyses of Sholl data. Analysis of Sholl data collected from Golgi-stained pyramidal neurons in the hippocampus of male and female mice using both simple linear and mixed effects models demonstrates that the p-values and standard deviations obtained using the simple linear models are biased downwards and lead to erroneous rejection of the null hypothesis in some analyses. The mixed effects approach more accurately models the true variability in the data set, which leads to correct inference. Mixed effects models avoid faulty inference in Sholl analysis of data sampled from multiple neurons per animal by accounting for intra-class correlation. Given the widespread practice in neuroscience of obtaining multiple measurements per subject, there is a critical need to apply mixed effects models more widely. Copyright © 2017 Elsevier B.V. All rights reserved.

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

Analyzing longitudinal data with the linear mixed models procedure in SPSS.

PubMed

West, Brady T

2009-09-01

Many applied researchers analyzing longitudinal data share a common misconception: that specialized statistical software is necessary to fit hierarchical linear models (also known as linear mixed models [LMMs], or multilevel models) to longitudinal data sets. Although several specialized statistical software programs of high quality are available that allow researchers to fit these models to longitudinal data sets (e.g., HLM), rapid advances in general purpose statistical software packages have recently enabled analysts to fit these same models when using preferred packages that also enable other more common analyses. One of these general purpose statistical packages is SPSS, which includes a very flexible and powerful procedure for fitting LMMs to longitudinal data sets with continuous outcomes. This article aims to present readers with a practical discussion of how to analyze longitudinal data using the LMMs procedure in the SPSS statistical software package.

A model of the extent and distribution of woody linear features in rural Great Britain.

PubMed

Scholefield, Paul; Morton, Dan; Rowland, Clare; Henrys, Peter; Howard, David; Norton, Lisa

2016-12-01

Hedges and lines of trees (woody linear features) are important boundaries that connect and enclose habitats, buffer the effects of land management, and enhance biodiversity in increasingly impoverished landscapes. Despite their acknowledged importance in the wider countryside, they are usually not considered in models of landscape function due to their linear nature and the difficulties of acquiring relevant data about their character, extent, and location. We present a model which uses national datasets to describe the distribution of woody linear features along boundaries in Great Britain. The method can be applied for other boundary types and in other locations around the world across a range of spatial scales where different types of linear feature can be separated using characteristics such as height or width. Satellite-derived Land Cover Map 2007 (LCM2007) provided the spatial framework for locating linear features and was used to screen out areas unsuitable for their occurrence, that is, offshore, urban, and forest areas. Similarly, Ordnance Survey Land-Form PANORAMA®, a digital terrain model, was used to screen out where they do not occur. The presence of woody linear features on boundaries was modelled using attributes from a canopy height dataset obtained by subtracting a digital terrain map (DTM) from a digital surface model (DSM). The performance of the model was evaluated against existing woody linear feature data in Countryside Survey across a range of scales. The results indicate that, despite some underestimation, this simple approach may provide valuable information on the extents and locations of woody linear features in the countryside at both local and national scales.

An evaluation of bias in propensity score-adjusted non-linear regression models.

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

The microcomputer scientific software series 2: general linear model--regression.

Treesearch

Harold M. Rauscher

1983-01-01

The general linear model regression (GLMR) program provides the microcomputer user with a sophisticated regression analysis capability. The output provides a regression ANOVA table, estimators of the regression model coefficients, their confidence intervals, confidence intervals around the predicted Y-values, residuals for plotting, a check for multicollinearity, a...

Machinery running state identification based on discriminant semi-supervised local tangent space alignment for feature fusion and extraction

NASA Astrophysics Data System (ADS)

Su, Zuqiang; Xiao, Hong; Zhang, Yi; Tang, Baoping; Jiang, Yonghua

2017-04-01

Extraction of sensitive features is a challenging but key task in data-driven machinery running state identification. Aimed at solving this problem, a method for machinery running state identification that applies discriminant semi-supervised local tangent space alignment (DSS-LTSA) for feature fusion and extraction is proposed. Firstly, in order to extract more distinct features, the vibration signals are decomposed by wavelet packet decomposition WPD, and a mixed-domain feature set consisted of statistical features, autoregressive (AR) model coefficients, instantaneous amplitude Shannon entropy and WPD energy spectrum is extracted to comprehensively characterize the properties of machinery running state(s). Then, the mixed-dimension feature set is inputted into DSS-LTSA for feature fusion and extraction to eliminate redundant information and interference noise. The proposed DSS-LTSA can extract intrinsic structure information of both labeled and unlabeled state samples, and as a result the over-fitting problem of supervised manifold learning and blindness problem of unsupervised manifold learning are overcome. Simultaneously, class discrimination information is integrated within the dimension reduction process in a semi-supervised manner to improve sensitivity of the extracted fusion features. Lastly, the extracted fusion features are inputted into a pattern recognition algorithm to achieve the running state identification. The effectiveness of the proposed method is verified by a running state identification case in a gearbox, and the results confirm the improved accuracy of the running state identification.

Predictive and mechanistic multivariate linear regression models for reaction development

PubMed Central

Santiago, Celine B.; Guo, Jing-Yao

2018-01-01

Multivariate Linear Regression (MLR) models utilizing computationally-derived and empirically-derived physical organic molecular descriptors are described in this review. Several reports demonstrating the effectiveness of this methodological approach towards reaction optimization and mechanistic interrogation are discussed. A detailed protocol to access quantitative and predictive MLR models is provided as a guide for model development and parameter analysis. PMID:29719711

Experimental study of the convection in a rotating tangent cylinder

NASA Astrophysics Data System (ADS)

Aujogue, Kélig; Pothérat, Alban; Sreenivasan, Binod; Debray, François

2018-05-01

This paper experimentally investigates the convection in a fast rotating Tangent Cylinder (TC), for Ekman numbers down to $E=3.36\\times10^{-6}$, in a configuration relevant to the liquid core of the Earth. In the apparatus, the TC results from the Proudman-Taylor constraint incurred by rotating a hemispherical fluid vessel heated in its centre by a protruding heating element of cylindrical shape. The resulting convection that develops above the heater, i.e within the TC, is shown to set in for critical Rayleigh numbers and wavenumbers respectively scaling as $Ra_c\\sim E^{4/3}$ and $a_c\\sim E^{1/3}$ with the Ekman number $E$. Though exhibiting the same exponents as for plane rotating convection, these laws are indicative of much larger convective plumes at onset. The structure and dynamics of these plumes are in fact closer to those found in solid rotating cylinders heated from below, suggesting that the confinement within the TC induced by the Taylor-Proudman constraint influences convection in a similar way as solid walls would do. There is further similarity in that the critical modes in the TC all exhibit a slow retrograde precession at onset. In supercritical regimes, the precession evolves into a thermal wind with a complex structure featuring retrograde rotation at high latitude and either prograde or retrograde rotation at low latitudes (close to the heater), depending on the criticality and the Ekman number. Nevertheless the intensity of the thermal wind measured by the Rossby number scales as $Ro\\sim 0.85(Ra_q^*)^{0.41}$ with the Rayleigh number based on the heat flux $Ra_q^*$. This scaling suggests that the convection in the TC is driven by quasi-geostrophic dynamics, a finding supported by the scaling for the rotation-normalised Nusselt number $Nu^{*} \\sim (Ra_{q}^{*})^{5/9}$.

Linearized aerodynamic and control law models of the X-29A airplane and comparison with flight data

NASA Technical Reports Server (NTRS)

Bosworth, John T.

1992-01-01

Flight control system design and analysis for aircraft rely on mathematical models of the vehicle dynamics. In addition to a six degree of freedom nonlinear simulation, the X-29A flight controls group developed a set of programs that calculate linear perturbation models throughout the X-29A flight envelope. The models include the aerodynamics as well as flight control system dynamics and were used for stability, controllability, and handling qualities analysis. These linear models were compared to flight test results to help provide a safe flight envelope expansion. A description is given of the linear models at three flight conditions and two flight control system modes. The models are presented with a level of detail that would allow the reader to reproduce the linear results if desired. Comparison between the response of the linear model and flight measured responses are presented to demonstrate the strengths and weaknesses of the linear models' ability to predict flight dynamics.

Running vacuum cosmological models: linear scalar perturbations

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

Perico, E.L.D.; Tamayo, D.A., E-mail: elduartep@usp.br, E-mail: tamayo@if.usp.br

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ( H {sup 2}) or Λ( R ). Such models assume an equation of state for the vacuum given by P-bar {sub Λ} = - ρ-bar {sub Λ}, relating its background pressure P-bar {sub Λ} with its mean energy density ρ-bar {sub Λ} ≡ Λ/8π G . This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interactionmore » between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely ρ-bar {sub Λ} = Σ {sub i} ρ-bar {sub Λ} {sub i} . Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ( H {sup 2}) scenario the vacuum is coupled with every matter component, whereas the Λ( R ) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.« less

Linear discrete systems with memory: a generalization of the Langmuir model

NASA Astrophysics Data System (ADS)

Băleanu, Dumitru; Nigmatullin, Raoul R.

2013-10-01

In this manuscript we analyzed a general solution of the linear nonlocal Langmuir model within time scale calculus. Several generalizations of the Langmuir model are presented together with their exact corresponding solutions. The physical meaning of the proposed models are investigated and their corresponding geometries are reported.

Modeling thermal sensation in a Mediterranean climate—a comparison of linear and ordinal models

NASA Astrophysics Data System (ADS)

Pantavou, Katerina; Lykoudis, Spyridon

2014-08-01

A simple thermo-physiological model of outdoor thermal sensation adjusted with psychological factors is developed aiming to predict thermal sensation in Mediterranean climates. Microclimatic measurements simultaneously with interviews on personal and psychological conditions were carried out in a square, a street canyon and a coastal location of the greater urban area of Athens, Greece. Multiple linear and ordinal regression were applied in order to estimate thermal sensation making allowance for all the recorded parameters or specific, empirically selected, subsets producing so-called extensive and empirical models, respectively. Meteorological, thermo-physiological and overall models - considering psychological factors as well - were developed. Predictions were improved when personal and psychological factors were taken into account as compared to meteorological models. The model based on ordinal regression reproduced extreme values of thermal sensation vote more adequately than the linear regression one, while the empirical model produced satisfactory results in relation to the extensive model. The effects of adaptation and expectation on thermal sensation vote were introduced in the models by means of the exposure time, season and preference related to air temperature and irradiation. The assessment of thermal sensation could be a useful criterion in decision making regarding public health, outdoor spaces planning and tourism.

Meshless analysis of shear deformable shells: the linear model

NASA Astrophysics Data System (ADS)

Costa, Jorge C.; Tiago, Carlos M.; Pimenta, Paulo M.

2013-10-01

This work develops a kinematically linear shell model departing from a consistent nonlinear theory. The initial geometry is mapped from a flat reference configuration by a stress-free finite deformation, after which, the actual shell motion takes place. The model maintains the features of a complete stress-resultant theory with Reissner-Mindlin kinematics based on an inextensible director. A hybrid displacement variational formulation is presented, where the domain displacements and kinematic boundary reactions are independently approximated. The resort to a flat reference configuration allows the discretization using 2-D Multiple Fixed Least-Squares (MFLS) on the domain. The consistent definition of stress resultants and consequent plane stress assumption led to a neat formulation for the analysis of shells. The consistent linear approximation, combined with MFLS, made possible efficient computations with a desired continuity degree, leading to smooth results for the displacement, strain and stress fields, as shown by several numerical examples.

The Dangers of Estimating V˙O2max Using Linear, Nonexercise Prediction Models.

PubMed

Nevill, Alan M; Cooke, Carlton B

2017-05-01

This study aimed to compare the accuracy and goodness of fit of two competing models (linear vs allometric) when estimating V˙O2max (mL·kg·min) using nonexercise prediction models. The two competing models were fitted to the V˙O2max (mL·kg·min) data taken from two previously published studies. Study 1 (the Allied Dunbar National Fitness Survey) recruited 1732 randomly selected healthy participants, 16 yr and older, from 30 English parliamentary constituencies. Estimates of V˙O2max were obtained using a progressive incremental test on a motorized treadmill. In study 2, maximal oxygen uptake was measured directly during a fatigue limited treadmill test in older men (n = 152) and women (n = 146) 55 to 86 yr old. In both studies, the quality of fit associated with estimating V˙O2max (mL·kg·min) was superior using allometric rather than linear (additive) models based on all criteria (R, maximum log-likelihood, and Akaike information criteria). Results suggest that linear models will systematically overestimate V˙O2max for participants in their 20s and underestimate V˙O2max for participants in their 60s and older. The residuals saved from the linear models were neither normally distributed nor independent of the predicted values nor age. This will probably explain the absence of a key quadratic age term in the linear models, crucially identified using allometric models. Not only does the curvilinear age decline within an exponential function follow a more realistic age decline (the right-hand side of a bell-shaped curve), but the allometric models identified either a stature-to-body mass ratio (study 1) or a fat-free mass-to-body mass ratio (study 2), both associated with leanness when estimating V˙O2max. Adopting allometric models will provide more accurate predictions of V˙O2max (mL·kg·min) using plausible, biologically sound, and interpretable models.

Predicting birth weight with conditionally linear transformation models.

PubMed

Möst, Lisa; Schmid, Matthias; Faschingbauer, Florian; Hothorn, Torsten

2016-12-01

Low and high birth weight (BW) are important risk factors for neonatal morbidity and mortality. Gynecologists must therefore accurately predict BW before delivery. Most prediction formulas for BW are based on prenatal ultrasound measurements carried out within one week prior to birth. Although successfully used in clinical practice, these formulas focus on point predictions of BW but do not systematically quantify uncertainty of the predictions, i.e. they result in estimates of the conditional mean of BW but do not deliver prediction intervals. To overcome this problem, we introduce conditionally linear transformation models (CLTMs) to predict BW. Instead of focusing only on the conditional mean, CLTMs model the whole conditional distribution function of BW given prenatal ultrasound parameters. Consequently, the CLTM approach delivers both point predictions of BW and fetus-specific prediction intervals. Prediction intervals constitute an easy-to-interpret measure of prediction accuracy and allow identification of fetuses subject to high prediction uncertainty. Using a data set of 8712 deliveries at the Perinatal Centre at the University Clinic Erlangen (Germany), we analyzed variants of CLTMs and compared them to standard linear regression estimation techniques used in the past and to quantile regression approaches. The best-performing CLTM variant was competitive with quantile regression and linear regression approaches in terms of conditional coverage and average length of the prediction intervals. We propose that CLTMs be used because they are able to account for possible heteroscedasticity, kurtosis, and skewness of the distribution of BWs. © The Author(s) 2014.

POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models

PubMed Central

Johnson, Jacqueline L.; Muller, Keith E.; Slaughter, James C.; Gurka, Matthew J.; Gribbin, Matthew J.; Simpson, Sean L.

2014-01-01

The POWERLIB SAS/IML software provides convenient power calculations for a wide range of multivariate linear models with Gaussian errors. The software includes the Box, Geisser-Greenhouse, Huynh-Feldt, and uncorrected tests in the “univariate” approach to repeated measures (UNIREP), the Hotelling Lawley Trace, Pillai-Bartlett Trace, and Wilks Lambda tests in “multivariate” approach (MULTIREP), as well as a limited but useful range of mixed models. The familiar univariate linear model with Gaussian errors is an important special case. For estimated covariance, the software provides confidence limits for the resulting estimated power. All power and confidence limits values can be output to a SAS dataset, which can be used to easily produce plots and tables for manuscripts. PMID:25400516

A Comparison of Linear versus Non-Linear Models of Aversive Self-Awareness, Dissociation, and Non-Suicidal Self-Injury among Young Adults

ERIC Educational Resources Information Center

Armey, Michael F.; Crowther, Janis H.

2008-01-01

Research has identified a significant increase in both the incidence and prevalence of non-suicidal self-injury (NSSI). The present study sought to test both linear and non-linear cusp catastrophe models by using aversive self-awareness, which was operationalized as a composite of aversive self-relevant affect and cognitions, and dissociation as…

Repopulation Kinetics and the Linear-Quadratic Model

NASA Astrophysics Data System (ADS)

O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

2009-08-01

The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

Linear model correction: A method for transferring a near-infrared multivariate calibration model without standard samples.

PubMed

Liu, Yan; Cai, Wensheng; Shao, Xueguang

2016-12-05

Calibration transfer is essential for practical applications of near infrared (NIR) spectroscopy because the measurements of the spectra may be performed on different instruments and the difference between the instruments must be corrected. For most of calibration transfer methods, standard samples are necessary to construct the transfer model using the spectra of the samples measured on two instruments, named as master and slave instrument, respectively. In this work, a method named as linear model correction (LMC) is proposed for calibration transfer without standard samples. The method is based on the fact that, for the samples with similar physical and chemical properties, the spectra measured on different instruments are linearly correlated. The fact makes the coefficients of the linear models constructed by the spectra measured on different instruments are similar in profile. Therefore, by using the constrained optimization method, the coefficients of the master model can be transferred into that of the slave model with a few spectra measured on slave instrument. Two NIR datasets of corn and plant leaf samples measured with different instruments are used to test the performance of the method. The results show that, for both the datasets, the spectra can be correctly predicted using the transferred partial least squares (PLS) models. Because standard samples are not necessary in the method, it may be more useful in practical uses. Copyright © 2016 Elsevier B.V. All rights reserved.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

NASA Astrophysics Data System (ADS)

Falvo, Cyril

2018-02-01

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

Linear and nonlinear stability of periodic orbits in annular billiards.

PubMed

Dettmann, Carl P; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear and nonlinear stability of periodic orbits in annular billiards

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear system identification via backward-time observer models

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Phan, Minh

1993-01-01

This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.

Bayesian uncertainty quantification in linear models for diffusion MRI.

PubMed

Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans

2018-03-29

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.

Technical note: A linear model for predicting δ13 Cprotein.

PubMed

Pestle, William J; Hubbe, Mark; Smith, Erin K; Stevenson, Joseph M

2015-08-01

Development of a model for the prediction of δ(13) Cprotein from δ(13) Ccollagen and Δ(13) Cap-co . Model-generated values could, in turn, serve as "consumer" inputs for multisource mixture modeling of paleodiet. Linear regression analysis of previously published controlled diet data facilitated the development of a mathematical model for predicting δ(13) Cprotein (and an experimentally generated error term) from isotopic data routinely generated during the analysis of osseous remains (δ(13) Cco and Δ(13) Cap-co ). Regression analysis resulted in a two-term linear model (δ(13) Cprotein (%) = (0.78 × δ(13) Cco ) - (0.58× Δ(13) Cap-co ) - 4.7), possessing a high R-value of 0.93 (r(2)  = 0.86, P < 0.01), and experimentally generated error terms of ±1.9% for any predicted individual value of δ(13) Cprotein . This model was tested using isotopic data from Formative Period individuals from northern Chile's Atacama Desert. The model presented here appears to hold significant potential for the prediction of the carbon isotope signature of dietary protein using only such data as is routinely generated in the course of stable isotope analysis of human osseous remains. These predicted values are ideal for use in multisource mixture modeling of dietary protein source contribution. © 2015 Wiley Periodicals, Inc.

Linear and nonlinear models for predicting fish bioconcentration factors for pesticides.

PubMed

Yuan, Jintao; Xie, Chun; Zhang, Ting; Sun, Jinfang; Yuan, Xuejie; Yu, Shuling; Zhang, Yingbiao; Cao, Yunyuan; Yu, Xingchen; Yang, Xuan; Yao, Wu

2016-08-01

This work is devoted to the applications of the multiple linear regression (MLR), multilayer perceptron neural network (MLP NN) and projection pursuit regression (PPR) to quantitative structure-property relationship analysis of bioconcentration factors (BCFs) of pesticides tested on Bluegill (Lepomis macrochirus). Molecular descriptors of a total of 107 pesticides were calculated with the DRAGON Software and selected by inverse enhanced replacement method. Based on the selected DRAGON descriptors, a linear model was built by MLR, nonlinear models were developed using MLP NN and PPR. The robustness of the obtained models was assessed by cross-validation and external validation using test set. Outliers were also examined and deleted to improve predictive power. Comparative results revealed that PPR achieved the most accurate predictions. This study offers useful models and information for BCF prediction, risk assessment, and pesticide formulation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Estimating trajectories of energy intake through childhood and adolescence using linear-spline multilevel models.

PubMed

Anderson, Emma L; Tilling, Kate; Fraser, Abigail; Macdonald-Wallis, Corrie; Emmett, Pauline; Cribb, Victoria; Northstone, Kate; Lawlor, Debbie A; Howe, Laura D

2013-07-01

Methods for the assessment of changes in dietary intake across the life course are underdeveloped. We demonstrate the use of linear-spline multilevel models to summarize energy-intake trajectories through childhood and adolescence and their application as exposures, outcomes, or mediators. The Avon Longitudinal Study of Parents and Children assessed children's dietary intake several times between ages 3 and 13 years, using both food frequency questionnaires (FFQs) and 3-day food diaries. We estimated energy-intake trajectories for 12,032 children using linear-spline multilevel models. We then assessed the associations of these trajectories with maternal body mass index (BMI), and later offspring BMI, and also their role in mediating the relation between maternal and offspring BMIs. Models estimated average and individual energy intake at 3 years, and linear changes in energy intake from age 3 to 7 years and from age 7 to 13 years. By including the exposure (in this example, maternal BMI) in the multilevel model, we were able to estimate the average energy-intake trajectories across levels of the exposure. When energy-intake trajectories are the exposure for a later outcome (in this case offspring BMI) or a mediator (between maternal and offspring BMI), results were similar, whether using a two-step process (exporting individual-level intercepts and slopes from multilevel models and using these in linear regression/path analysis), or a single-step process (multivariate multilevel models). Trajectories were similar when FFQs and food diaries were assessed either separately, or when combined into one model. Linear-spline multilevel models provide useful summaries of trajectories of dietary intake that can be used as an exposure, outcome, or mediator.

Comparing Multiple-Group Multinomial Log-Linear Models for Multidimensional Skill Distributions in the General Diagnostic Model. Research Report. ETS RR-08-35

ERIC Educational Resources Information Center

Xu, Xueli; von Davier, Matthias

2008-01-01

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

Estimation of reflectance from camera responses by the regularized local linear model.

PubMed

Zhang, Wei-Feng; Tang, Gongguo; Dai, Dao-Qing; Nehorai, Arye

2011-10-01

Because of the limited approximation capability of using fixed basis functions, the performance of reflectance estimation obtained by traditional linear models will not be optimal. We propose an approach based on the regularized local linear model. Our approach performs efficiently and knowledge of the spectral power distribution of the illuminant and the spectral sensitivities of the camera is not needed. Experimental results show that the proposed method performs better than some well-known methods in terms of both reflectance error and colorimetric error. © 2011 Optical Society of America

A Linear Regression and Markov Chain Model for the Arabian Horse Registry

DTIC Science & Technology

1993-04-01

as a tax deduction? Yes No T-4367 68 26. Regardless of previous equine tax deductions, do you consider your current horse activities to be... (Mark one...E L T-4367 A Linear Regression and Markov Chain Model For the Arabian Horse Registry Accesion For NTIS CRA&I UT 7 4:iC=D 5 D-IC JA" LI J:13tjlC,3 lO...the Arabian Horse Registry, which needed to forecast its future registration of purebred Arabian horses . A linear regression model was utilized to

Direct use of linear time-domain aerodynamics in aeroservoelastic analysis: Aerodynamic model

NASA Technical Reports Server (NTRS)

Woods, J. A.; Gilbert, Michael G.

1990-01-01

The work presented here is the first part of a continuing effort to expand existing capabilities in aeroelasticity by developing the methodology which is necessary to utilize unsteady time-domain aerodynamics directly in aeroservoelastic design and analysis. The ultimate objective is to define a fully integrated state-space model of an aeroelastic vehicle's aerodynamics, structure and controls which may be used to efficiently determine the vehicle's aeroservoelastic stability. Here, the current status of developing a state-space model for linear or near-linear time-domain indicial aerodynamic forces is presented.

Vestibular coriolis effect differences modeled with three-dimensional linear-angular interactions.

PubMed

Holly, Jan E

2004-01-01

The vestibular coriolis (or "cross-coupling") effect is traditionally explained by cross-coupled angular vectors, which, however, do not explain the differences in perceptual disturbance under different acceleration conditions. For example, during head roll tilt in a rotating chair, the magnitude of perceptual disturbance is affected by a number of factors, including acceleration or deceleration of the chair rotation or a zero-g environment. Therefore, it has been suggested that linear-angular interactions play a role. The present research investigated whether these perceptual differences and others involving linear coriolis accelerations could be explained under one common framework: the laws of motion in three dimensions, which include all linear-angular interactions among all six components of motion (three angular and three linear). The results show that the three-dimensional laws of motion predict the differences in perceptual disturbance. No special properties of the vestibular system or nervous system are required. In addition, simulations were performed with angular, linear, and tilt time constants inserted into the model, giving the same predictions. Three-dimensional graphics were used to highlight the manner in which linear-angular interaction causes perceptual disturbance, and a crucial component is the Stretch Factor, which measures the "unexpected" linear component.

Application of conditional moment tests to model checking for generalized linear models.

PubMed

Pan, Wei

2002-06-01

Generalized linear models (GLMs) are increasingly being used in daily data analysis. However, model checking for GLMs with correlated discrete response data remains difficult. In this paper, through a case study on marginal logistic regression using a real data set, we illustrate the flexibility and effectiveness of using conditional moment tests (CMTs), along with other graphical methods, to do model checking for generalized estimation equation (GEE) analyses. Although CMTs provide an array of powerful diagnostic tests for model checking, they were originally proposed in the econometrics literature and, to our knowledge, have never been applied to GEE analyses. CMTs cover many existing tests, including the (generalized) score test for an omitted covariate, as special cases. In summary, we believe that CMTs provide a class of useful model checking tools.

Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.

PubMed

Khazraee, S Hadi; Sáez-Castillo, Antonio Jose; Geedipally, Srinivas Reddy; Lord, Dominique

2015-05-01

The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model. © 2014 Society for Risk Analysis.

Longitudinal data analyses using linear mixed models in SPSS: concepts, procedures and illustrations.

PubMed

Shek, Daniel T L; Ma, Cecilia M S

2011-01-05

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented.

Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

PubMed Central

Shek, Daniel T. L.; Ma, Cecilia M. S.

2011-01-01

Although different methods are available for the analyses of longitudinal data, analyses based on generalized linear models (GLM) are criticized as violating the assumption of independence of observations. Alternatively, linear mixed models (LMM) are commonly used to understand changes in human behavior over time. In this paper, the basic concepts surrounding LMM (or hierarchical linear models) are outlined. Although SPSS is a statistical analyses package commonly used by researchers, documentation on LMM procedures in SPSS is not thorough or user friendly. With reference to this limitation, the related procedures for performing analyses based on LMM in SPSS are described. To demonstrate the application of LMM analyses in SPSS, findings based on six waves of data collected in the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in Hong Kong are presented. PMID:21218263

Nonlinear price impact from linear models

NASA Astrophysics Data System (ADS)

Patzelt, Felix; Bouchaud, Jean-Philippe

2017-12-01

The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators, and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales (Patzelt and Bouchaud 2017 arXiv:1706.04163). Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear ‘propagator’ models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.

A D-vine copula-based model for repeated measurements extending linear mixed models with homogeneous correlation structure.

PubMed

Killiches, Matthias; Czado, Claudia

2018-03-22

We propose a model for unbalanced longitudinal data, where the univariate margins can be selected arbitrarily and the dependence structure is described with the help of a D-vine copula. We show that our approach is an extremely flexible extension of the widely used linear mixed model if the correlation is homogeneous over the considered individuals. As an alternative to joint maximum-likelihood a sequential estimation approach for the D-vine copula is provided and validated in a simulation study. The model can handle missing values without being forced to discard data. Since conditional distributions are known analytically, we easily make predictions for future events. For model selection, we adjust the Bayesian information criterion to our situation. In an application to heart surgery data our model performs clearly better than competing linear mixed models. © 2018, The International Biometric Society.

Convex Optimization Methods for Graphs and Statistical Modeling

DTIC Science & Technology

2011-06-01

of a set obtained by taking nonnegative linear combinations of elements of the set. The cone TC(x) is the set of directions to points in C from the...Proof. The tangent cone at any signed vector x? with respect to the `∞ ball is a rotation of the nonnegative orthant. Thus we only need to compute the...that ξ(B ?) 1−4ξ(B?)µ(A?) < γ in the second inequality. Sec. A.2. Proofs 167 Proof of Proposition 3.4.2 Based on the Perron - Frobenius theorem [82

Advanced statistics: linear regression, part I: simple linear regression.

PubMed

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Equilibrium Phase Behavior of the Square-Well Linear Microphase-Forming Model.

PubMed

Zhuang, Yuan; Charbonneau, Patrick

2016-07-07

We have recently developed a simulation approach to calculate the equilibrium phase diagram of particle-based microphase formers. Here, this approach is used to calculate the phase behavior of the square-well linear model for different strengths and ranges of the linear long-range repulsive component. The results are compared with various theoretical predictions for microphase formation. The analysis further allows us to better understand the mechanism for microphase formation in colloidal suspensions.

Modeling error analysis of stationary linear discrete-time filters

NASA Technical Reports Server (NTRS)

Patel, R.; Toda, M.

1977-01-01

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

On the modelling of linear-assisted DC-DC voltage regulators for photovoltaic solar energy systems

NASA Astrophysics Data System (ADS)

Martínez-García, Herminio; García-Vílchez, Encarna

2017-11-01

This paper shows the modelling of linear-assisted or hybrid (linear & switching) DC/DC voltage regulators. In this kind of regulators, an auxiliary linear regulator is used, which objective is to cancel the ripple at the output voltage and provide fast responses for load variations. On the other hand, a switching DC/DC converter, connected in parallel with the linear regulator, allows to supply almost the whole output current demanded by the load. The objective of this topology is to take advantage of the suitable regulation characteristics that series linear voltage regulators have, but almost achieving the high efficiency that switching DC/DC converters provide. Linear-assisted DC/DC regulators are feedback systems with potential instability. Therefore, their modelling is mandatory in order to obtain design guidelines and assure stability of the implemented power supply system.

The linear transformation model with frailties for the analysis of item response times.

PubMed

Wang, Chun; Chang, Hua-Hua; Douglas, Jeffrey A

2013-02-01

The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi-parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non-parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non-parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees' latent speeds; whereas the non-parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box-Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two-stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non-parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested. © 2012 The British Psychological Society.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Probabilistic modeling of anatomical variability using a low dimensional parameterization of diffeomorphisms.

PubMed

Zhang, Miaomiao; Wells, William M; Golland, Polina

2017-10-01

We present an efficient probabilistic model of anatomical variability in a linear space of initial velocities of diffeomorphic transformations and demonstrate its benefits in clinical studies of brain anatomy. To overcome the computational challenges of the high dimensional deformation-based descriptors, we develop a latent variable model for principal geodesic analysis (PGA) based on a low dimensional shape descriptor that effectively captures the intrinsic variability in a population. We define a novel shape prior that explicitly represents principal modes as a multivariate complex Gaussian distribution on the initial velocities in a bandlimited space. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than the state-of-the-art method such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA) that operate in the high dimensional image space. Copyright © 2017 Elsevier B.V. All rights reserved.

Cross-beam energy transfer: On the accuracy of linear stationary models in the linear kinetic regime

NASA Astrophysics Data System (ADS)

Debayle, A.; Masson-Laborde, P.-E.; Ruyer, C.; Casanova, M.; Loiseau, P.

2018-05-01

We present an extensive numerical study by means of particle-in-cell simulations of the energy transfer that occurs during the crossing of two laser beams. In the linear regime, when ions are not trapped in the potential well induced by the laser interference pattern, a very good agreement is obtained with a simple linear stationary model, provided the laser intensity is sufficiently smooth. These comparisons include different plasma compositions to cover the strong and weak Landau damping regimes as well as the multispecies case. The correct evaluation of the linear Landau damping at the phase velocity imposed by the laser interference pattern is essential to estimate the energy transfer rate between the laser beams, once the stationary regime is reached. The transient evolution obtained in kinetic simulations is also analysed by means of a full analytical formula that includes 3D beam energy exchange coupled with the ion acoustic wave response. Specific attention is paid to the energy transfer when the laser presents small-scale inhomogeneities. In particular, the energy transfer is reduced when the laser inhomogeneities are comparable with the Landau damping characteristic length of the ion acoustic wave.

Analysis of an inventory model for both linearly decreasing demand and holding cost

NASA Astrophysics Data System (ADS)

Malik, A. K.; Singh, Parth Raj; Tomar, Ajay; Kumar, Satish; Yadav, S. K.

2016-03-01

This study proposes the analysis of an inventory model for linearly decreasing demand and holding cost for non-instantaneous deteriorating items. The inventory model focuses on commodities having linearly decreasing demand without shortages. The holding cost doesn't remain uniform with time due to any form of variation in the time value of money. Here we consider that the holding cost decreases with respect to time. The optimal time interval for the total profit and the optimal order quantity are determined. The developed inventory model is pointed up through a numerical example. It also includes the sensitivity analysis.

Avoiding Boundary Estimates in Hierarchical Linear Models through Weakly Informative Priors

ERIC Educational Resources Information Center

Chung, Yeojin; Rabe-Hesketh, Sophia; Gelman, Andrew; Dorie, Vincent; Liu, Jinchen

2012-01-01

Hierarchical or multilevel linear models are widely used for longitudinal or cross-sectional data on students nested in classes and schools, and are particularly important for estimating treatment effects in cluster-randomized trials, multi-site trials, and meta-analyses. The models can allow for variation in treatment effects, as well as…

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

A linear model fails to predict orientation selectivity of cells in the cat visual cortex.

PubMed Central

Volgushev, M; Vidyasagar, T R; Pei, X

1996-01-01

1. Postsynaptic potentials (PSPs) evoked by visual stimulation in simple cells in the cat visual cortex were recorded using in vivo whole-cell technique. Responses to small spots of light presented at different positions over the receptive field and responses to elongated bars of different orientations centred on the receptive field were recorded. 2. To test whether a linear model can account for orientation selectivity of cortical neurones, responses to elongated bars were compared with responses predicted by a linear model from the receptive field map obtained from flashing spots. 3. The linear model faithfully predicted the preferred orientation, but not the degree of orientation selectivity or the sharpness of orientation tuning. The ratio of optimal to non-optimal responses was always underestimated by the model. 4. Thus non-linear mechanisms, which can include suppression of non-optimal responses and/or amplification of optimal responses, are involved in the generation of orientation selectivity in the primary visual cortex. PMID:8930828

Mathematical Model for the Contribution of Individual Organs to Non-Zero Y-Intercepts in Single and Multi-Compartment Linear Models of Whole-Body Energy Expenditure

PubMed Central

Kaiyala, Karl J.

2014-01-01

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit ‘local linearity.’ Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying ‘latent’ allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses. PMID:25068692

Mathematical model for the contribution of individual organs to non-zero y-intercepts in single and multi-compartment linear models of whole-body energy expenditure.

PubMed

Kaiyala, Karl J

2014-01-01

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit 'local linearity.' Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying 'latent' allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses.

Flood Nowcasting With Linear Catchment Models, Radar and Kalman Filters

NASA Astrophysics Data System (ADS)

Pegram, Geoff; Sinclair, Scott

A pilot study using real time rainfall data as input to a parsimonious linear distributed flood forecasting model is presented. The aim of the study is to deliver an operational system capable of producing flood forecasts, in real time, for the Mgeni and Mlazi catchments near the city of Durban in South Africa. The forecasts can be made at time steps which are of the order of a fraction of the catchment response time. To this end, the model is formulated in Finite Difference form in an equation similar to an Auto Regressive Moving Average (ARMA) model; it is this formulation which provides the required computational efficiency. The ARMA equation is a discretely coincident form of the State-Space equations that govern the response of an arrangement of linear reservoirs. This results in a functional relationship between the reservoir response con- stants and the ARMA coefficients, which guarantees stationarity of the ARMA model. Input to the model is a combined "Best Estimate" spatial rainfall field, derived from a combination of weather RADAR and Satellite rainfield estimates with point rain- fall given by a network of telemetering raingauges. Several strategies are employed to overcome the uncertainties associated with forecasting. Principle among these are the use of optimal (double Kalman) filtering techniques to update the model states and parameters in response to current streamflow observations and the application of short term forecasting techniques to provide future estimates of the rainfield as input to the model.

EVALUATING PREDICTIVE ERRORS OF A COMPLEX ENVIRONMENTAL MODEL USING A GENERAL LINEAR MODEL AND LEAST SQUARE MEANS

EPA Science Inventory

A General Linear Model (GLM) was used to evaluate the deviation of predicted values from expected values for a complex environmental model. For this demonstration, we used the default level interface of the Regional Mercury Cycling Model (R-MCM) to simulate epilimnetic total mer...

Predicting Madura cattle growth curve using non-linear model

NASA Astrophysics Data System (ADS)

Widyas, N.; Prastowo, S.; Widi, T. S. M.; Baliarti, E.

2018-03-01

Madura cattle is Indonesian native. It is a composite breed that has undergone hundreds of years of selection and domestication to reach nowadays remarkable uniformity. Crossbreeding has reached the isle of Madura and the Madrasin, a cross between Madura cows and Limousine semen emerged. This paper aimed to compare the growth curve between Madrasin and one type of pure Madura cows, the common Madura cattle (Madura) using non-linear models. Madura cattles are kept traditionally thus reliable records are hardly available. Data were collected from small holder farmers in Madura. Cows from different age classes (<6 months, 6-12 months, 1-2years, 2-3years, 3-5years and >5years) were observed, and body measurements (chest girth, body length and wither height) were taken. In total 63 Madura and 120 Madrasin records obtained. Linear model was built with cattle sub-populations and age as explanatory variables. Body weights were estimated based on the chest girth. Growth curves were built using logistic regression. Results showed that within the same age, Madrasin has significantly larger body compared to Madura (p<0.05). The logistic models fit better for Madura and Madrasin cattle data; with the estimated MSE for these models were 39.09 and 759.28 with prediction accuracy of 99 and 92% for Madura and Madrasin, respectively. Prediction of growth curve using logistic regression model performed well in both types of Madura cattle. However, attempts to administer accurate data on Madura cattle are necessary to better characterize and study these cattle.

A Linear Variable-[theta] Model for Measuring Individual Differences in Response Precision

ERIC Educational Resources Information Center

Ferrando, Pere J.

2011-01-01

Models for measuring individual response precision have been proposed for binary and graded responses. However, more continuous formats are quite common in personality measurement and are usually analyzed with the linear factor analysis model. This study extends the general Gaussian person-fluctuation model to the continuous-response case and…

Computational Tools for Probing Interactions in Multiple Linear Regression, Multilevel Modeling, and Latent Curve Analysis

ERIC Educational Resources Information Center

Preacher, Kristopher J.; Curran, Patrick J.; Bauer, Daniel J.

2006-01-01

Simple slopes, regions of significance, and confidence bands are commonly used to evaluate interactions in multiple linear regression (MLR) models, and the use of these techniques has recently been extended to multilevel or hierarchical linear modeling (HLM) and latent curve analysis (LCA). However, conducting these tests and plotting the…

Probe-level linear model fitting and mixture modeling results in high accuracy detection of differential gene expression.

PubMed

Lemieux, Sébastien

2006-08-25

The identification of differentially expressed genes (DEGs) from Affymetrix GeneChips arrays is currently done by first computing expression levels from the low-level probe intensities, then deriving significance by comparing these expression levels between conditions. The proposed PL-LM (Probe-Level Linear Model) method implements a linear model applied on the probe-level data to directly estimate the treatment effect. A finite mixture of Gaussian components is then used to identify DEGs using the coefficients estimated by the linear model. This approach can readily be applied to experimental design with or without replication. On a wholly defined dataset, the PL-LM method was able to identify 75% of the differentially expressed genes within 10% of false positives. This accuracy was achieved both using the three replicates per conditions available in the dataset and using only one replicate per condition. The method achieves, on this dataset, a higher accuracy than the best set of tools identified by the authors of the dataset, and does so using only one replicate per condition.

Missing Data Treatments at the Second Level of Hierarchical Linear Models

ERIC Educational Resources Information Center

St. Clair, Suzanne W.

2011-01-01

The current study evaluated the performance of traditional versus modern MDTs in the estimation of fixed-effects and variance components for data missing at the second level of an hierarchical linear model (HLM) model across 24 different study conditions. Variables manipulated in the analysis included, (a) number of Level-2 variables with missing…

Non-linear dual-phase-lag model for analyzing heat transfer phenomena in living tissues during thermal ablation.

PubMed

Kumar, P; Kumar, Dinesh; Rai, K N

2016-08-01

In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method. Copyright © 2016 Elsevier Ltd. All rights reserved.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

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

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Linear Analysis.

PubMed

Henley, B C; Shin, D C; Zhang, R; Marmarelis, V Z

Compartmental and data-based modeling of cerebral hemodynamics are alternative approaches that utilize distinct model forms and have been employed in the quantitative study of cerebral hemodynamics. This paper examines the relation between a compartmental equivalent-circuit and a data-based input-output model of dynamic cerebral autoregulation (DCA) and CO2-vasomotor reactivity (DVR). The compartmental model is constructed as an equivalent-circuit utilizing putative first principles and previously proposed hypothesis-based models. The linear input-output dynamics of this compartmental model are compared with data-based estimates of the DCA-DVR process. This comparative study indicates that there are some qualitative similarities between the two-input compartmental model and experimental results.

How linear response shaped models of neural circuits and the quest for alternatives.

PubMed

Herfurth, Tim; Tchumatchenko, Tatjana

2017-10-01

In the past decades, many mathematical approaches to solve complex nonlinear systems in physics have been successfully applied to neuroscience. One of these tools is the concept of linear response functions. However, phenomena observed in the brain emerge from fundamentally nonlinear interactions and feedback loops rather than from a composition of linear filters. Here, we review the successes achieved by applying the linear response formalism to topics, such as rhythm generation and synchrony and by incorporating it into models that combine linear and nonlinear transformations. We also discuss the challenges encountered in the linear response applications and argue that new theoretical concepts are needed to tackle feedback loops and non-equilibrium dynamics which are experimentally observed in neural networks but are outside of the validity regime of the linear response formalism. Copyright © 2017 Elsevier Ltd. All rights reserved.

Predicting oropharyngeal tumor volume throughout the course of radiation therapy from pretreatment computed tomography data using general linear models.

PubMed

Yock, Adam D; Rao, Arvind; Dong, Lei; Beadle, Beth M; Garden, Adam S; Kudchadker, Rajat J; Court, Laurence E

2014-05-01

The purpose of this work was to develop and evaluate the accuracy of several predictive models of variation in tumor volume throughout the course of radiation therapy. Nineteen patients with oropharyngeal cancers were imaged daily with CT-on-rails for image-guided alignment per an institutional protocol. The daily volumes of 35 tumors in these 19 patients were determined and used to generate (1) a linear model in which tumor volume changed at a constant rate, (2) a general linear model that utilized the power fit relationship between the daily and initial tumor volumes, and (3) a functional general linear model that identified and exploited the primary modes of variation between time series describing the changing tumor volumes. Primary and nodal tumor volumes were examined separately. The accuracy of these models in predicting daily tumor volumes were compared with those of static and linear reference models using leave-one-out cross-validation. In predicting the daily volume of primary tumors, the general linear model and the functional general linear model were more accurate than the static reference model by 9.9% (range: -11.6%-23.8%) and 14.6% (range: -7.3%-27.5%), respectively, and were more accurate than the linear reference model by 14.2% (range: -6.8%-40.3%) and 13.1% (range: -1.5%-52.5%), respectively. In predicting the daily volume of nodal tumors, only the 14.4% (range: -11.1%-20.5%) improvement in accuracy of the functional general linear model compared to the static reference model was statistically significant. A general linear model and a functional general linear model trained on data from a small population of patients can predict the primary tumor volume throughout the course of radiation therapy with greater accuracy than standard reference models. These more accurate models may increase the prognostic value of information about the tumor garnered from pretreatment computed tomography images and facilitate improved treatment management.

Observations and High-Resolution Numerical Simulations of a Non-Developing Tropical Disturbance in the Western North Pacific

DTIC Science & Technology

2013-09-01

potential energy CFSR Climate Forecast System Reanalysis COAMPS Coupled Ocean / Atmosphere Mesoscale Prediction System DA data assimilation DART Data...developing (TCS025) tropical disturbance using the adjoint and tangent linear models for the Coupled Ocean – Atmosphere Mesoscale Prediction System (COAMPS...for Medium-range Weather Forecasts ELDORA ELectra DOppler RAdar EOL Earth Observing Laboratory GPS global positioning system GTS Global

Estimation for the Linear Model With Uncertain Covariance Matrices

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

Linear and non-linear quantitative structure-activity relationship models on indole substitution patterns as inhibitors of HIV-1 attachment.

PubMed

Nirouei, Mahyar; Ghasemi, Ghasem; Abdolmaleki, Parviz; Tavakoli, Abdolreza; Shariati, Shahab

2012-06-01

The antiviral drugs that inhibit human immunodeficiency virus (HIV) entry to the target cells are already in different phases of clinical trials. They prevent viral entry and have a highly specific mechanism of action with a low toxicity profile. Few QSAR studies have been performed on this group of inhibitors. This study was performed to develop a quantitative structure-activity relationship (QSAR) model of the biological activity of indole glyoxamide derivatives as inhibitors of the interaction between HIV glycoprotein gp120 and host cell CD4 receptors. Forty different indole glyoxamide derivatives were selected as a sample set and geometrically optimized using Gaussian 98W. Different combinations of multiple linear regression (MLR), genetic algorithms (GA) and artificial neural networks (ANN) were then utilized to construct the QSAR models. These models were also utilized to select the most efficient subsets of descriptors in a cross-validation procedure for non-linear log (1/EC50) prediction. The results that were obtained using GA-ANN were compared with MLR-MLR and MLR-ANN models. A high predictive ability was observed for the MLR, MLR-ANN and GA-ANN models, with root mean sum square errors (RMSE) of 0.99, 0.91 and 0.67, respectively (N = 40). In summary, machine learning methods were highly effective in designing QSAR models when compared to statistical method.

A non-Linear transport model for determining shale rock characteristics

NASA Astrophysics Data System (ADS)

Ali, Iftikhar; Malik, Nadeem

2016-04-01

Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007

SCI Identification (SCIDNT) program user's guide. [maximum likelihood method for linear rotorcraft models

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

Skew-t partially linear mixed-effects models for AIDS clinical studies.

PubMed

Lu, Tao

2016-01-01

We propose partially linear mixed-effects models with asymmetry and missingness to investigate the relationship between two biomarkers in clinical studies. The proposed models take into account irregular time effects commonly observed in clinical studies under a semiparametric model framework. In addition, commonly assumed symmetric distributions for model errors are substituted by asymmetric distribution to account for skewness. Further, informative missing data mechanism is accounted for. A Bayesian approach is developed to perform parameter estimation simultaneously. The proposed model and method are applied to an AIDS dataset and comparisons with alternative models are performed.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Linear time series modeling of GPS-derived TEC observations over the Indo-Thailand region

NASA Astrophysics Data System (ADS)

Suraj, Puram Sai; Kumar Dabbakuti, J. R. K.; Chowdhary, V. Rajesh; Tripathi, Nitin K.; Ratnam, D. Venkata

2017-12-01

This paper proposes a linear time series model to represent the climatology of the ionosphere and to investigate the characteristics of hourly averaged total electron content (TEC). The GPS-TEC observation data at the Bengaluru international global navigation satellite system (GNSS) service (IGS) station (geographic 13.02°N , 77.57°E ; geomagnetic latitude 4.4°N ) have been utilized for processing the TEC data during an extended period (2009-2016) in the 24{th} solar cycle. Solar flux F10.7p index, geomagnetic Ap index, and periodic oscillation factors have been considered to construct a linear TEC model. It is evident from the results that solar activity effect on TEC is high. It reaches the maximum value (˜ 40 TECU) during the high solar activity (HSA) year (2014) and minimum value (˜ 15 TECU) during the low solar activity (LSA) year (2009). The larger magnitudes of semiannual variations are observed during the HSA periods. The geomagnetic effect on TEC is relatively low, with the highest being ˜ 4 TECU (March 2015). The magnitude of periodic variations can be seen more significantly during HSA periods (2013-2015) and less during LSA periods (2009-2011). The correlation coefficient of 0.89 between the observations and model-based estimations has been found. The RMSE between the observed TEC and model TEC values is 4.0 TECU (linear model) and 4.21 TECU (IRI2016 Model). Further, the linear TEC model has been validated at different latitudes over the northern low-latitude region. The solar component (F10.7p index) value decreases with an increase in latitude. The magnitudes of the periodic component become less significant with the increase in latitude. The influence of geomagnetic component becomes less significant at Lucknow GNSS station (26.76°N, 80.88°E) when compared to other GNSS stations. The hourly averaged TEC values have been considered and ionospheric features are well recovered with linear TEC model.

Physical lumping methods for developing linear reduced models for high speed propulsion systems

NASA Technical Reports Server (NTRS)

Immel, S. M.; Hartley, Tom T.; Deabreu-Garcia, J. Alex

1991-01-01

In gasdynamic systems, information travels in one direction for supersonic flow and in both directions for subsonic flow. A shock occurs at the transition from supersonic to subsonic flow. Thus, to simulate these systems, any simulation method implemented for the quasi-one-dimensional Euler equations must have the ability to capture the shock. In this paper, a technique combining both backward and central differencing is presented. The equations are subsequently linearized about an operating point and formulated into a linear state space model. After proper implementation of the boundary conditions, the model order is reduced from 123 to less than 10 using the Schur method of balancing. Simulations comparing frequency and step response of the reduced order model and the original system models are presented.

Linearized Poststall Aerodynamic and Control Law Models of the X-31A Aircraft and Comparison with Flight Data

NASA Technical Reports Server (NTRS)

Stoliker, Patrick C.; Bosworth, John T.; Georgie, Jennifer

1997-01-01

The X-31A aircraft has a unique configuration that uses thrust-vector vanes and aerodynamic control effectors to provide an operating envelope to a maximum 70 deg angle of attack, an inherently nonlinear portion of the flight envelope. This report presents linearized versions of the X-31A longitudinal and lateral-directional control systems, with aerodynamic models sufficient to evaluate characteristics in the poststall envelope at 30 deg, 45 deg, and 60 deg angle of attack. The models are presented with detail sufficient to allow the reader to reproduce the linear results or perform independent control studies. Comparisons between the responses of the linear models and flight data are presented in the time and frequency domains to demonstrate the strengths and weaknesses of the ability to predict high-angle-of-attack flight dynamics using linear models. The X-31A six-degree-of-freedom simulation contains a program that calculates linear perturbation models throughout the X-31A flight envelope. The models include aerodynamics and flight control system dynamics that are used for stability, controllability, and handling qualities analysis. The models presented in this report demonstrate the ability to provide reasonable linear representations in the poststall flight regime.

The importance of being equivalent: Newton's two models of one-body motion

NASA Astrophysics Data System (ADS)

Pourciau, Bruce

2004-05-01

As an undergraduate at Cambridge, Newton entered into his "Waste Book" an assumption that we have named the Equivalence Assumption (The Younger): "If a body move progressively in some crooked line [about a center of motion] ..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent". In this assumption, Newton somewhat imprecisely describes two mathematical models, a "polygonal limit model" and a "tangent deflected model", for "one-body motion", that is, for the motion of a "body in orbit about a fixed center", and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton's work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions

Non-linear homogenized and heterogeneous FE models for FRCM reinforced masonry walls in diagonal compression

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Poggi, Carlo

2016-12-01

Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

Graphing the Model or Modeling the Graph? Not-so-Subtle Problems in Linear IS-LM Analysis.

ERIC Educational Resources Information Center

Alston, Richard M.; Chi, Wan Fu

1989-01-01

Outlines the differences between the traditional and modern theoretical models of demand for money. States that the two models are often used interchangeably in textbooks, causing ambiguity. Argues against the use of linear specifications that imply that income velocity can increase without limit and that autonomous components of aggregate demand…

Foundation stiffness in the linear modeling of wind turbines

NASA Astrophysics Data System (ADS)

Chiang, Chih-Hung; Yu, Chih-Peng; Chen, Yan-Hao; Lai, Jiunnren; Hsu, Keng-Tsang; Cheng, Chia-Chi

2017-04-01

Effects of foundation stiffness on the linear vibrations of wind turbine systems are of concerns for both planning and construction of wind turbine systems. Current study performed numerical modeling for such a problem using linear spectral finite elements. The effects of foundation stiffness were investigated for various combinations of shear wave velocity of soil, size of tower base plate, and pile length. Multiple piles are also included in the models such that the foundation stiffness can be analyzed more realistically. The results indicate that the shear wave velocity of soil and the size of tower base plate have notable effects on the dominant frequency of the turbine-tower system. The larger the lateral dimension, the stiffer the foundation. Large pile cap and multiple spaced piles result in higher stiffness than small pile cap and a mono-pile. The lateral stiffness of a mono-pile mainly depends on the shear wave velocity of soil with the exception for a very short pile that the end constraints may affect the lateral vibration of the superstructure. Effective pile length may be determined by comparing the simulation results of the frictional pile to those of the end-bearing pile.

Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

PubMed

Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

2015-04-01

Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results