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Sample records for quadratic inference functions

  1. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

  2. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

  3. Integration of the Quadratic Function and Generalization

    ERIC Educational Resources Information Center

    Mitsuma, Kunio

    2011-01-01

    We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

  4. Characterization of a Quadratic Function in Rn

    ERIC Educational Resources Information Center

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  5. Optimal Approximation of Quadratic Interval Functions

    NASA Technical Reports Server (NTRS)

    Koshelev, Misha; Taillibert, Patrick

    1997-01-01

    Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

  6. L -functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field

    NASA Astrophysics Data System (ADS)

    Louboutin, Stephane

    1992-07-01

    Starting from the analytic class number formula involving its L-function, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class number tables. Then, using class field theory, we will construct a periodic character &chi , defined on the ring of integers of a field K that is a quadratic extension of a principal imaginary quadratic field k, such that the zeta function of K is the product of the zeta function of k and of the L-function L(s,χ) . We will then determine an integral representation of this L-function that enables us to calculate the class number of K numerically, as soon as its regulator is known. It will also provide us with an upper bound for these class numbers, showing that Hua's bound for the class numbers of imaginary and real quadratic fields is not the best that one could expect. We give statistical results concerning the class numbers of the first 50000 quadratic extensions of {Q}(i) with prime relative discriminant (and with K/Q a non-Galois quartic extension). Our analytic calculation improves the algebraic calculation used by Lakein in the same way as the analytic calculation of the class numbers of real quadratic fields made by Williams and Broere improved the algebraic calculation consisting in counting the number of cycles of reduced ideals. Finally, we give upper bounds for class numbers of K that is a quadratic extension of an imaginary quadratic field k which is no longer assumed to be of class number one.

  7. Quadratic function approaching method for magnetotelluric soundingdata inversion

    SciTech Connect

    Liangjun, Yan; Wenbao, Hu; Zhang, Keni

    2004-04-05

    The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.

  8. Four Labs to Introduce Quadratic Functions.

    ERIC Educational Resources Information Center

    Malone, Jim

    1989-01-01

    Describes four laboratory activities in algebra and precalculus classes that provide hands-on experiences related to functions: slowing down the acceleration of gravity; calculating the acceleration of gravity; generating a parabola using a steel ball and a tilted board; and photographing projectile motion. (YP)

  9. The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function.

    PubMed

    Hendrickx, Christophe; Araújo, Ricardo; Mateus, Octávio

    2015-01-01

    The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber-invaded by the quadrate diverticulum of the mandibular arch pneumatic system-was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

  10. The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

    PubMed Central

    Araújo, Ricardo; Mateus, Octávio

    2015-01-01

    The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

  11. Hydroxyl functionalized thermosensitive microgels with quadratic crosslinking density distribution.

    PubMed

    Elmas, Begum; Tuncel, Murvet; Senel, Serap; Patir, S; Tuncel, Ali

    2007-09-01

    N-isopropylacrylamide (NIPA) based uniform thermosensitive microgels were synthesized by dispersion polymerization by using relatively hydrophilic crosslinking agents with hydroxyl functionality. Glycerol dimethacrylate (GDMA), pentaerythritol triacrylate (PETA) and pentaerythritol propoxylate triacrylate (PEPTA) were used as crosslinking agents with different hydrophilicities. A protocol was first proposed to determine the crosslinking density distribution in the thermosensitive microgel particles by confocal laser scanning microscopy (CLSM). The microgels were fluorescently labeled by using hydroxyl group of the crosslinking agent. The CLSM observations performed with the microgels synthesized by three different crosslinking agents showed that the crosslinking density exhibited a quadratic decrease with the increasing radial distance in the spherical microgel particles. This structure led to the formation of more loose gel structure on the particle surface with respect to the center. Then the use of hydrophilic crosslinking agents in the dispersion polymerization of NIPA made possible the synthesis of thermosensitive microgels carrying long, flexible and chemically derivatizable (i.e., hydroxyl functionalized) fringes on the surface by a single-stage dispersion polymerization. The microgels with all crosslinking agents exhibited volume phase transition with the increasing temperature. The microgel obtained by the most hydrophilic crosslinking agent, GDMA exhibited higher hydrodynamic diameters in the fully swollen form at low temperatures than those obtained by PETA and PEPTA. Higher hydrodynamic size decrease from fully swollen form to the fully shrunken form was also observed with the same microgel. PMID:17532327

  12. On the connection of the quadratic Lienard equation with an equation for the elliptic functions

    NASA Astrophysics Data System (ADS)

    Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.

    2015-07-01

    The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.

  13. The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system

    NASA Technical Reports Server (NTRS)

    Yeon, Kyu Hwang; Um, Chung IN; George, T. F.

    1994-01-01

    The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.

  14. Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2012-01-01

    In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

  15. Automated calculation of anharmonic vibrational contributions to first hyperpolarizabilities: Quadratic response functions from vibrational configuration interaction wave functions

    NASA Astrophysics Data System (ADS)

    Hansen, Mikkel Bo; Christiansen, Ove; Hättig, Christof

    2009-10-01

    Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.

  16. Quadratic Interaction Functional for General Systems of Conservation Laws

    NASA Astrophysics Data System (ADS)

    Bianchini, Stefano; Modena, Stefano

    2015-09-01

    For the Glimm scheme approximation to the solution of the system of conservation laws in one space dimension with initial data u 0 with small total variation, we prove a quadratic (w.r.t. Tot. Var. ( u 0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux f are made (apart from smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely, we obtain the following results: a new analysis of the interaction estimates of simple waves;

  17. Failures and Inabilities of High School Students about Quadratic Equations and Functions

    ERIC Educational Resources Information Center

    Memnun, Dilek Sezgin; Aydin, Bünyamin; Dinç, Emre; Çoban, Merve; Sevindik, Fatma

    2015-01-01

    In this research study, it was aimed to examine failures and inabilities of eleventh grade students about quadratic equations and functions. For this purpose, these students were asked ten open-ended questions. The analysis of the answers given by the students to these questions indicated that a significant part of these students had failures and…

  18. Emotion suppression moderates the quadratic association between RSA and executive function

    PubMed Central

    Spangler, Derek P.; Bell, Martha Ann; Deater-Deckard, Kirby

    2016-01-01

    There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated: (1) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (2) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a two-minute resting period during which ECG was continually assessed. In the next phase, the women completed an array of executive function and non-executive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. PMID:26018941

  19. The Effects of an Undergraduate Algebra Course on Prospective Middle School Teachers' Understanding of Functions, Especially Quadratic Functions

    ERIC Educational Resources Information Center

    Duarte, Jonathan T.

    2010-01-01

    Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…

  20. Functional network inference of the suprachiasmatic nucleus.

    PubMed

    Abel, John H; Meeker, Kirsten; Granados-Fuentes, Daniel; St John, Peter C; Wang, Thomas J; Bales, Benjamin B; Doyle, Francis J; Herzog, Erik D; Petzold, Linda R

    2016-04-19

    In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure. PMID:27044085

  1. On the use of the OCM's quadratic objective function as a pilot rating metric

    NASA Technical Reports Server (NTRS)

    Schmidt, D. K.

    1981-01-01

    A correlation between the magnitude of the quadratic objective function from an optimal control pilot model and the subjective rating of the vehicle and task provides a valuable tool for handling qualities research and flight control synthesis. An analysis of simulation results for fourteen aircraft configurations flight tested earlier was conducted. A fixed set of pilot model parameters, are found for all cases in modeling the simulated regulation task. The agreement obtained between performance statistics is shown and a strong correlation was obtained between the cost function and rating.

  2. Quadratic and rate-independent limits for a large-deviations functional

    NASA Astrophysics Data System (ADS)

    Bonaschi, Giovanni A.; Peletier, Mark A.

    2016-07-01

    We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers' law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ` L log L' gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.

  3. An efficient ensemble of radial basis functions method based on quadratic programming

    NASA Astrophysics Data System (ADS)

    Shi, Renhe; Liu, Li; Long, Teng; Liu, Jian

    2016-07-01

    Radial basis function (RBF) surrogate models have been widely applied in engineering design optimization problems to approximate computationally expensive simulations. Ensemble of radial basis functions (ERBF) using the weighted sum of stand-alone RBFs improves the approximation performance. To achieve a good trade-off between the accuracy and efficiency of the modelling process, this article presents a novel efficient ERBF method to determine the weights through solving a quadratic programming subproblem, denoted ERBF-QP. Several numerical benchmark functions are utilized to test the performance of the proposed ERBF-QP method. The results show that ERBF-QP can significantly improve the modelling efficiency compared with several existing ERBF methods. Moreover, ERBF-QP also provides satisfactory performance in terms of approximation accuracy. Finally, the ERBF-QP method is applied to a satellite multidisciplinary design optimization problem to illustrate its practicality and effectiveness for real-world engineering applications.

  4. Regularized quadratic cost-function for integrating wave-front gradient fields.

    PubMed

    Villa, Jesús; Rodríguez, Gustavo; Ivanov, Rumen; González, Efrén

    2016-05-15

    From the Bayesian regularization theory we derive a quadratic cost-function for integrating wave-front gradient fields. In the proposed cost-function, the term of conditional distribution uses a central-differences model to make the estimated function well consistent with the observed gradient field. As will be shown, the results obtained with the central-differences model are superior to the results obtained with the backward-differences model, commonly used in other integration techniques. As a regularization term we use an isotropic first-order differences Markov Random-Field model, which acts as a low-pass filter reducing the errors caused by the noise. We present simulated and real experiments of the proposal applied in the Foucault test, obtaining good results. PMID:27176991

  5. Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

    NASA Technical Reports Server (NTRS)

    Turso, James A.; Litt, Jonathan S.

    2004-01-01

    A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

  6. Functional neuroanatomy of intuitive physical inference.

    PubMed

    Fischer, Jason; Mikhael, John G; Tenenbaum, Joshua B; Kanwisher, Nancy

    2016-08-23

    To engage with the world-to understand the scene in front of us, plan actions, and predict what will happen next-we must have an intuitive grasp of the world's physical structure and dynamics. How do the objects in front of us rest on and support each other, how much force would be required to move them, and how will they behave when they fall, roll, or collide? Despite the centrality of physical inferences in daily life, little is known about the brain mechanisms recruited to interpret the physical structure of a scene and predict how physical events will unfold. Here, in a series of fMRI experiments, we identified a set of cortical regions that are selectively engaged when people watch and predict the unfolding of physical events-a "physics engine" in the brain. These brain regions are selective to physical inferences relative to nonphysical but otherwise highly similar scenes and tasks. However, these regions are not exclusively engaged in physical inferences per se or, indeed, even in scene understanding; they overlap with the domain-general "multiple demand" system, especially the parts of that system involved in action planning and tool use, pointing to a close relationship between the cognitive and neural mechanisms involved in parsing the physical content of a scene and preparing an appropriate action. PMID:27503892

  7. Robustness of the Quadratic Discriminant Function to correlated and uncorrelated normal training samples.

    PubMed

    Adebanji, Atinuke; Asamoah-Boaheng, Michael; Osei-Tutu, Olivia

    2016-01-01

    This study investigates the asymptotic performance of the Quadratic Discriminant Function (QDF) under correlated and uncorrelated normal training samples. This paper specifically examines the effect of correlation, uncorrelation considering different sample size ratios, number of variables and varying group centroid separators ([Formula: see text], [Formula: see text]) on classification accuracy of the QDF using simulated data from three populations ([Formula: see text]). The three populations differs with respect to their mean vector and covariance matrices. The results show the correlated normal distribution exhibits high coefficient of variation as [Formula: see text] increased. The QDF performed better when the training samples were correlated than when they were under uncorrelated normal distribution. The QDF performed better resulting in the reduction in misclassification error rates as group centroid separator increases with non increasing sample size under correlated training samples. PMID:26877900

  8. A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

    PubMed Central

    Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang

    2015-01-01

    It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. PMID:26381742

  9. Quadratic response functions in the time-dependent four-component Hartree-Fock approximation.

    PubMed

    Norman, Patrick; Jensen, Hans Jørgen Aa

    2004-10-01

    The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process beta(-2omega;omega,omega). It is shown that relativistic corrections to property values are substantial in these cases--the orientationally averaged hyperpolarizabilities in the static limit beta(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown. PMID:15446908

  10. Quadratic response functions in the time-dependent four-component Hartree-Fock approximation

    NASA Astrophysics Data System (ADS)

    Norman, Patrick; Jensen, Hans Jørgen Aa.

    2004-10-01

    The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process β(-2ω;ω,ω). It is shown that relativistic corrections to property values are substantial in these cases—the orientationally averaged hyperpolarizabilities in the static limit β¯(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown.

  11. High School Teachers' Use of Graphing Calculators When Teaching Linear and Quadratic Functions: Professed Beliefs and Observed Practice

    ERIC Educational Resources Information Center

    Molenje, Levi

    2012-01-01

    This study was designed to explore secondary mathematics teachers' beliefs about graphing calculators, their practices with the graphing calculators when teaching linear and quadratic functions, and the relationship between the teachers' beliefs and their practices. The study was conducted in two phases. In the first phase, 81 teachers…

  12. Nonparametric inference on median residual life function.

    PubMed

    Jeong, Jong-Hyeon; Jung, Sin-Ho; Costantino, Joseph P

    2008-03-01

    A simple approach to the estimation of the median residual lifetime is proposed for a single group by inverting a function of the Kaplan-Meier estimators. A test statistic is proposed to compare two median residual lifetimes at any fixed time point. The test statistic does not involve estimation of the underlying probability density function of failure times under censoring. Extensive simulation studies are performed to validate the proposed test statistic in terms of type I error probabilities and powers at various time points. One of the oldest data sets from the National Surgical Adjuvant Breast and Bowel Project (NSABP), which has more than a quarter century of follow-up, is used to illustrate the method. The analysis results indicate that, without systematic post-operative therapy, a significant difference in median residual lifetimes between node-negative and node-positive breast cancer patients persists for about 10 years after surgery. The new estimates of the median residual lifetime could serve as a baseline for physicians to explain any incremental effects of post-operative treatments in terms of delaying breast cancer recurrence or prolonging remaining lifetimes of breast cancer patients. PMID:17501936

  13. Functional inferences of environmental coccolithovirus biodiversity.

    PubMed

    Nissimov, Jozef I; Jones, Mark; Napier, Johnathan A; Munn, Colin B; Kimmance, Susan A; Allen, Michael J

    2013-10-01

    The cosmopolitan calcifying alga Emiliania huxleyi is one of the most abundant bloom forming coccolithophore species in the oceans and plays an important role in global biogeochemical cycling. Coccolithoviruses are a major cause of coccolithophore bloom termination and have been studied in laboratory, mesocosm and open ocean studies. However, little is known about the dynamic interactions between the host and its viruses, and less is known about the natural diversity and role of functionally important genes within natural coccolithovirus communities. Here, we investigate the temporal and spatial distribution of coccolithoviruses by the use of molecular fingerprinting techniques PCR, DGGE and genomic sequencing. The natural biodiversity of the virus genes encoding the major capsid protein (MCP) and serine palmitoyltransferase (SPT) were analysed in samples obtained from the Atlantic Meridional Transect (AMT), the North Sea and the L4 site in the Western Channel Observatory. We discovered nine new coccolithovirus genotypes across the AMT and L4 site, with the majority of MCP sequences observed at the deep chlorophyll maximum layer of the sampled sites on the transect. We also found four new SPT gene variations in the North Sea and at L4. Their translated fragments and the full protein sequence of SPT from laboratory strains EhV-86 and EhV-99B1 were modelled and revealed that the theoretical fold differs among strains. Variation identified in the structural distance between the two domains of the SPT protein may have an impact on the catalytic capabilities of its active site. In summary, the combined use of 'standard' markers (i.e. MCP), in combination with metabolically relevant markers (i.e. SPT) are useful in the study of the phylogeny and functional biodiversity of coccolithoviruses, and can provide an interesting intracellular insight into the evolution of these viruses and their ability to infect and replicate within their algal hosts. PMID:24006045

  14. Students' Understanding of the Concept of Vertex of Quadratic Functions in Relation to Their Personal Meaning of the Concept of Vertex

    ERIC Educational Resources Information Center

    Childers, Annie Burns; Vidakovic, Draga

    2014-01-01

    This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or…

  15. Quadratic Damping

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  16. A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

    NASA Astrophysics Data System (ADS)

    Xu, Jiuping; Li, Jun

    2002-09-01

    In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

  17. Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

    NASA Astrophysics Data System (ADS)

    Landsman, Zinoviy

    2008-10-01

    We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

  18. Classical methods for interpreting objective function minimization as intelligent inference

    SciTech Connect

    Golden, R.M.

    1996-12-31

    Most recognition algorithms and neural networks can be formally viewed as seeking a minimum value of an appropriate objective function during either classification or learning phases. The goal of this paper is to argue that in order to show a recognition algorithm is making intelligent inferences, it is not sufficient to show that the recognition algorithm is computing (or trying to compute) the global minimum of some objective function. One must explicitly define a {open_quotes}relational system{close_quotes} for the recognition algorithm or neural network which identifies the: (i) sample space, (ii) the relevant sigmafield of events generated by the sample space, and (iii) the {open_quotes}relation{close_quotes} for that relational system. Only when such a {open_quotes}relational system{close_quotes} is properly defined, is it possible to formally establish the sense in which computing the global minimum of an objective function is an intelligent, inference.

  19. Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1984-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  20. Legendre-tau approximation for functional differential equations. II - The linear quadratic optimal control problem

    NASA Technical Reports Server (NTRS)

    Ito, Kazufumi; Teglas, Russell

    1987-01-01

    The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

  1. Receiver function deconvolution using transdimensional hierarchical Bayesian inference

    NASA Astrophysics Data System (ADS)

    Kolb, J. M.; Lekić, V.

    2014-06-01

    Teleseismic waves can convert from shear to compressional (Sp) or compressional to shear (Ps) across impedance contrasts in the subsurface. Deconvolving the parent waveforms (P for Ps or S for Sp) from the daughter waveforms (S for Ps or P for Sp) generates receiver functions which can be used to analyse velocity structure beneath the receiver. Though a variety of deconvolution techniques have been developed, they are all adversely affected by background and signal-generated noise. In order to take into account the unknown noise characteristics, we propose a method based on transdimensional hierarchical Bayesian inference in which both the noise magnitude and noise spectral character are parameters in calculating the likelihood probability distribution. We use a reversible-jump implementation of a Markov chain Monte Carlo algorithm to find an ensemble of receiver functions whose relative fits to the data have been calculated while simultaneously inferring the values of the noise parameters. Our noise parametrization is determined from pre-event noise so that it approximates observed noise characteristics. We test the algorithm on synthetic waveforms contaminated with noise generated from a covariance matrix obtained from observed noise. We show that the method retrieves easily interpretable receiver functions even in the presence of high noise levels. We also show that we can obtain useful estimates of noise amplitude and frequency content. Analysis of the ensemble solutions produced by our method can be used to quantify the uncertainties associated with individual receiver functions as well as with individual features within them, providing an objective way for deciding which features warrant geological interpretation. This method should make possible more robust inferences on subsurface structure using receiver function analysis, especially in areas of poor data coverage or under noisy station conditions.

  2. Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

    SciTech Connect

    Validi, AbdoulAhad

    2014-03-01

    This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

  3. Beyond the bounds of orthology: functional inference from metagenomic context.

    PubMed

    Vey, Gregory; Moreno-Hagelsieb, Gabriel

    2010-07-01

    The effectiveness of the computational inference of function by genomic context is bounded by the diversity of known microbial genomes. Although metagenomes offer access to previously inaccessible organisms, their fragmentary nature prevents the conventional establishment of orthologous relationships required for reliably predicting functional interactions. We introduce a protocol for the prediction of functional interactions using data sources without information about orthologous relationships. To illustrate this process, we use the Sargasso Sea metagenome to construct a functional interaction network for the Escherichia coli K12 genome. We identify two reliability metrics, target intergenic distance and source interaction count, and apply them to selectively filter the predictions retained to construct the network of functional interactions. The resulting network contains 2297 nodes with 10 072 edges with a positive predictive value of 0.80. The metagenome yielded 8423 functional interactions beyond those found using only the genomic orthologs as a data source. This amounted to a 134% increase in the total number of functional interactions that are predicted by combining the metagenome and the genomic orthologs versus the genomic orthologs alone. In the absence of detectable orthologous relationships it remains feasible to derive a reliable set of predicted functional interactions. This offers a strategy for harnessing other metagenomes and homologs in general. Because metagenomes allow access to previously unreachable microorganisms, this will result in expanding the universe of known functional interactions thus furthering our understanding of functional organization. PMID:20419183

  4. Network inference from functional experimental data (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Desrosiers, Patrick; Labrecque, Simon; Tremblay, Maxime; Bélanger, Mathieu; De Dorlodot, Bertrand; Côté, Daniel C.

    2016-03-01

    Functional connectivity maps of neuronal networks are critical tools to understand how neurons form circuits, how information is encoded and processed by neurons, how memory is shaped, and how these basic processes are altered under pathological conditions. Current light microscopy allows to observe calcium or electrical activity of thousands of neurons simultaneously, yet assessing comprehensive connectivity maps directly from such data remains a non-trivial analytical task. There exist simple statistical methods, such as cross-correlation and Granger causality, but they only detect linear interactions between neurons. Other more involved inference methods inspired by information theory, such as mutual information and transfer entropy, identify more accurately connections between neurons but also require more computational resources. We carried out a comparative study of common connectivity inference methods. The relative accuracy and computational cost of each method was determined via simulated fluorescence traces generated with realistic computational models of interacting neurons in networks of different topologies (clustered or non-clustered) and sizes (10-1000 neurons). To bridge the computational and experimental works, we observed the intracellular calcium activity of live hippocampal neuronal cultures infected with the fluorescent calcium marker GCaMP6f. The spontaneous activity of the networks, consisting of 50-100 neurons per field of view, was recorded from 20 to 50 Hz on a microscope controlled by a homemade software. We implemented all connectivity inference methods in the software, which rapidly loads calcium fluorescence movies, segments the images, extracts the fluorescence traces, and assesses the functional connections (with strengths and directions) between each pair of neurons. We used this software to assess, in real time, the functional connectivity from real calcium imaging data in basal conditions, under plasticity protocols, and epileptic

  5. Visualization of group inference data in functional neuroimaging.

    PubMed

    Gläscher, Jan

    2009-01-01

    While thresholded statistical parametric maps can convey an accurate account for the location and spatial extent of an effect in functional neuroimaging studies, their use is somewhat limited for characterizing more complex experimental effects, such as interactions in a factorial design. The resulting necessity for plotting the underlying data has long been recognized. Statistical Parametric Mapping (SPM) is a widely used software package for analyzing functional neuroimaging data that offers a variety of options for visualizing data from first level analyses. However, nowadays, the thrust of the statistical inference lies at the second level thus allowing for population inference. Unfortunately, the options for visualizing data from second level analyses are quite sparse. rfxplot is a new toolbox designed to alleviate this problem by providing a comprehensive array of options for plotting data from within second level analyses in SPM. These include graphs of average effect sizes (across subjects), averaged fitted responses and event-related blood oxygen level-dependent (BOLD) time courses. All data are retrieved from the underlying first level analyses and voxel selection can be tailored to the maximum effect in each subject within a defined search volume. All plot configurations can be easily configured via a graphical user-interface as well as non-interactively via a script. The large variety of plot options renders rfxplot suitable both for data exploration as well as producing high-quality figures for publications. PMID:19140033

  6. Explanation and inference: mechanistic and functional explanations guide property generalization

    PubMed Central

    Lombrozo, Tania; Gwynne, Nicholas Z.

    2014-01-01

    The ability to generalize from the known to the unknown is central to learning and inference. Two experiments explore the relationship between how a property is explained and how that property is generalized to novel species and artifacts. The experiments contrast the consequences of explaining a property mechanistically, by appeal to parts and processes, with the consequences of explaining the property functionally, by appeal to functions and goals. The findings suggest that properties that are explained functionally are more likely to be generalized on the basis of shared functions, with a weaker relationship between mechanistic explanations and generalization on the basis of shared parts and processes. The influence of explanation type on generalization holds even though all participants are provided with the same mechanistic and functional information, and whether an explanation type is freely generated (Experiment 1), experimentally provided (Experiment 2), or experimentally induced (Experiment 2). The experiments also demonstrate that explanations and generalizations of a particular type (mechanistic or functional) can be experimentally induced by providing sample explanations of that type, with a comparable effect when the sample explanations come from the same domain or from a different domains. These results suggest that explanations serve as a guide to generalization, and contribute to a growing body of work supporting the value of distinguishing mechanistic and functional explanations. PMID:25309384

  7. Medical-Legal Inferences From Functional Neuroimaging Evidence.

    PubMed

    Mayberg

    1996-07-01

    Positron emission (PET) and single-photon emission tomography (SPECT) are validated functional imaging techniques for the in vivo measurement of many neuro-phsyiological and neurochemical parameters. Research studies of patients with a broad range of neurological and psychiatric illness have been published. Reproducible and specific patterns of altered cerebral blood flow and glucose metabolism, however, have been demonstrated and confirmed for only a limited number of specific illnesses. The association of functional scan patterns with specific deficits is less conclusive. Correlations of regional abnormalities with clinical symptoms such as motor weakness, aphasia, and visual spatial dysfunction are the most reproducible but are more poorly localized than lesion-deficit studies would suggest. Findings are even less consistent for nonlocalizing behavioral symptoms such as memory difficulties, poor concentration, irritability, or chronic pain, and no reliable patterns have been demonstrated. In a forensic context, homicidal and sadistic tendencies, aberrant sexual drive, violent impulsivity, psychopathic and sociopathic personality traits, as well as impaired judgement and poor insight, have no known PET or SPECT patterns, and their presence in an individual with any PET or SPECT scan finding cannot be inferred or concluded. Furthermore, the reliable prediction of any specific neurological, psychiatric, or behavioral deficits from specific scan findings has not been demonstrated. Unambiguous results from experiments designed to specifically examine the causative relationships between regional brain dysfunction and these types of complex behaviors are needed before any introduction of functional scans into the courts can be considered scientifically justified or legally admissible. PMID:10320420

  8. Constructing a Flexible Likelihood Function for Spectroscopic Inference

    NASA Astrophysics Data System (ADS)

    Czekala, Ian; Andrews, Sean M.; Mandel, Kaisey S.; Hogg, David W.; Green, Gregory M.

    2015-10-01

    We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. For the high signal-to-noise data with large spectral range that is commonly employed in stellar astrophysics, that covariant structure can lead to dramatically underestimated parameter uncertainties (and, in some cases, biases). We construct a likelihood function that accounts for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. This framework specifically addresses the common problem of mismatches in model spectral line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic/molecular databases or opacity prescriptions) by developing a novel local covariance kernel formalism that identifies and self-consistently downweights pathological spectral line “outliers.” By fitting many spectra in a hierarchical manner, these local kernels provide a mechanism to learn about and build data-driven corrections to synthetic spectral libraries. An open-source software implementation of this approach is available at http://iancze.github.io/Starfish, including a sophisticated probabilistic scheme for spectral interpolation when using model libraries that are sparsely sampled in the stellar parameters. We demonstrate some salient features of the framework by fitting the high-resolution V-band spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate-resolution K-band spectrum of Gliese 51, an M5 field dwarf.

  9. Time domain simulation of tandem silicon solar cells with optimal textured light trapping enabled by the quadratic complex rational function.

    PubMed

    Chung, H; Jung, K-Y; Tee, X T; Bermel, P

    2014-05-01

    Amorphous silicon/crystalline silicon (a-Si/c-Si) micromorph tandem cells, with best confirmed efficiency of 12.3%, have yet to fully approach their theoretical performance limits. In this work, we consider a strategy for improving the light trapping and charge collection of a-Si/c-Si micromorph tandem cells using random texturing with adjustable short-range correlations and long-range periodicity. In order to consider the full-spectrum absorption of a-Si and c-Si, a novel dispersion model known as a quadratic complex rational function (QCRF) is applied to photovoltaic materials (e.g., a-Si, c-Si and silver). It has the advantage of accurately modeling experimental semiconductor dielectric values over the entire relevant solar bandwidth from 300-1000 nm in a single simulation. This wide-band dispersion model is then used to model a silicon tandem cell stack (ITO/a-Si:H/c-Si:H/silver), as two parameters are varied: maximum texturing height h and correlation parameter f. Even without any other light trapping methods, our front texturing method demonstrates 12.37% stabilized cell efficiency and 12.79 mA/cm² in a 2 μm-thick active layer. PMID:24922389

  10. Analytic derivative couplings in time-dependent density functional theory: Quadratic response theory versus pseudo-wavefunction approach

    SciTech Connect

    Zhang, Xing; Herbert, John M.

    2015-02-14

    We revisit the formalism for analytic derivative couplings between excited states in time-dependent density functional theory (TDDFT). We derive and implement these couplings using quadratic response theory, then numerically compare this response-theory formulation to couplings implemented previously based on a pseudo-wavefunction formalism and direct differentiation of the Kohn-Sham determinant. Numerical results, including comparison to full configuration interaction calculations, suggest that the two approaches perform equally well for many molecular systems, provided that the underlying DFT method affords accurate potential energy surfaces. The response contributions are found to be important for certain systems with high symmetry, but can be calculated with only a moderate increase in computational cost beyond what is required for the pseudo-wavefunction approach. In the case of spin-flip TDDFT, we provide a formal proof that the derivative couplings obtained using response theory are identical to those obtained from the pseudo-wavefunction formulation, which validates our previous implementation based on the latter formalism.

  11. Structure-based inference of molecular functions of proteins of unknown function from Berkeley Structural Genomics Center

    SciTech Connect

    Kim, Sung-Hou; Shin, Dong Hae; Hou, Jingtong; Chandonia, John-Marc; Das, Debanu; Choi, In-Geol; Kim, Rosalind; Kim, Sung-Hou

    2007-09-02

    Advances in sequence genomics have resulted in an accumulation of a huge number of protein sequences derived from genome sequences. However, the functions of a large portion of them cannot be inferred based on the current methods of sequence homology detection to proteins of known functions. Three-dimensional structure can have an important impact in providing inference of molecular function (physical and chemical function) of a protein of unknown function. Structural genomics centers worldwide have been determining many 3-D structures of the proteins of unknown functions, and possible molecular functions of them have been inferred based on their structures. Combined with bioinformatics and enzymatic assay tools, the successful acceleration of the process of protein structure determination through high throughput pipelines enables the rapid functional annotation of a large fraction of hypothetical proteins. We present a brief summary of the process we used at the Berkeley Structural Genomics Center to infer molecular functions of proteins of unknown function.

  12. OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE

    PubMed Central

    Xie, Xianchao; Kou, S. C.; Brown, Lawrence

    2015-01-01

    This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results. PMID:27041778

  13. Self-Replicating Quadratics

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  14. Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

    PubMed

    Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

    2016-01-01

    This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come. PMID:27034708

  15. Bayesian Inference for Functional Dynamics Exploring in fMRI Data

    PubMed Central

    Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao

    2016-01-01

    This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come. PMID:27034708

  16. Role of Utility and Inference in the Evolution of Functional Information

    PubMed Central

    Sharov, Alexei A.

    2009-01-01

    Functional information means an encoded network of functions in living organisms from molecular signaling pathways to an organism’s behavior. It is represented by two components: code and an interpretation system, which together form a self-sustaining semantic closure. Semantic closure allows some freedom between components because small variations of the code are still interpretable. The interpretation system consists of inference rules that control the correspondence between the code and the function (phenotype) and determines the shape of the fitness landscape. The utility factor operates at multiple time scales: short-term selection drives evolution towards higher survival and reproduction rate within a given fitness landscape, and long-term selection favors those fitness landscapes that support adaptability and lead to evolutionary expansion of certain lineages. Inference rules make short-term selection possible by shaping the fitness landscape and defining possible directions of evolution, but they are under control of the long-term selection of lineages. Communication normally occurs within a set of agents with compatible interpretation systems, which I call communication system. Functional information cannot be directly transferred between communication systems with incompatible inference rules. Each biological species is a genetic communication system that carries unique functional information together with inference rules that determine evolutionary directions and constraints. This view of the relation between utility and inference can resolve the conflict between realism/positivism and pragmatism. Realism overemphasizes the role of inference in evolution of human knowledge because it assumes that logic is embedded in reality. Pragmatism substitutes usefulness for truth and therefore ignores the advantage of inference. The proposed concept of evolutionary pragmatism rejects the idea that logic is embedded in reality; instead, inference rules are

  17. Craniofacial biomechanics and functional and dietary inferences in hominin paleontology.

    PubMed

    Grine, Frederick E; Judex, Stefan; Daegling, David J; Ozcivici, Engin; Ungar, Peter S; Teaford, Mark F; Sponheimer, Matt; Scott, Jessica; Scott, Robert S; Walker, Alan

    2010-04-01

    Finite element analysis (FEA) is a potentially powerful tool by which the mechanical behaviors of different skeletal and dental designs can be investigated, and, as such, has become increasingly popular for biomechanical modeling and inferring the behavior of extinct organisms. However, the use of FEA to extrapolate from characterization of the mechanical environment to questions of trophic or ecological adaptation in a fossil taxon is both challenging and perilous. Here, we consider the problems and prospects of FEA applications in paleoanthropology, and provide a critical examination of one such study of the trophic adaptations of Australopithecus africanus. This particular FEA is evaluated with regard to 1) the nature of the A. africanus cranial composite, 2) model validation, 3) decisions made with respect to model parameters, 4) adequacy of data presentation, and 5) interpretation of the results. Each suggests that the results reflect methodological decisions as much as any underlying biological significance. Notwithstanding these issues, this model yields predictions that follow from the posited emphasis on premolar use by A. africanus. These predictions are tested with data from the paleontological record, including a phylogenetically-informed consideration of relative premolar size, and postcanine microwear fabrics and antemortem enamel chipping. In each instance, the data fail to conform to predictions from the model. This model thus serves to emphasize the need for caution in the application of FEA in paleoanthropological enquiry. Theoretical models can be instrumental in the construction of testable hypotheses; but ultimately, the studies that serve to test these hypotheses - rather than data from the models - should remain the source of information pertaining to hominin paleobiology and evolution. PMID:20227747

  18. Generalised partition functions: inferences on phase space distributions

    NASA Astrophysics Data System (ADS)

    Treumann, Rudolf A.; Baumjohann, Wolfgang

    2016-06-01

    It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

  19. On the functional equivalence of fuzzy inference systems and spline-based networks.

    PubMed

    Hunt, K J; Haas, R; Brown, M

    1995-06-01

    The conditions under which spline-based networks are functionally equivalent to the Takagi-Sugeno-model of fuzzy inference are formally established. We consider a generalized form of basis function network whose basis functions are splines. The result admits a wide range of fuzzy membership functions which are commonly encountered in fuzzy systems design. We use the theoretical background of functional equivalence to develop a hybrid fuzzy-spline net for inverse dynamic modeling of a hydraulically driven robot manipulator. PMID:7496588

  20. Denoising inferred functional association networks obtained by gene fusion analysis

    PubMed Central

    Kamburov, Atanas; Goldovsky, Leon; Freilich, Shiri; Kapazoglou, Aliki; Kunin, Victor; Enright, Anton J; Tsaftaris, Athanasios; Ouzounis, Christos A

    2007-01-01

    Background Gene fusion detection – also known as the 'Rosetta Stone' method – involves the identification of fused composite genes in a set of reference genomes, which indicates potential interactions between its un-fused counterpart genes in query genomes. The precision of this method typically improves with an ever-increasing number of reference genomes. Results In order to explore the usefulness and scope of this approach for protein interaction prediction and generate a high-quality, non-redundant set of interacting pairs of proteins across a wide taxonomic range, we have exhaustively performed gene fusion analysis for 184 genomes using an efficient variant of a previously developed protocol. By analyzing interaction graphs and applying a threshold that limits the maximum number of possible interactions within the largest graph components, we show that we can reduce the number of implausible interactions due to the detection of promiscuous domains. With this generally applicable approach, we generate a robust set of over 2 million distinct and testable interactions encompassing 696,894 proteins in 184 species or strains, most of which have never been the subject of high-throughput experimental proteomics. We investigate the cumulative effect of increasing numbers of genomes on the fidelity and quantity of predictions, and show that, for large numbers of genomes, predictions do not become saturated but continue to grow linearly, for the majority of the species. We also examine the percentage of component (and composite) proteins with relation to the number of genes and further validate the functional categories that are highly represented in this robust set of detected genome-wide interactions. Conclusion We illustrate the phylogenetic and functional diversity of gene fusion events across genomes, and their usefulness for accurate prediction of protein interaction and function. PMID:18081932

  1. Structure and function of the mammalian middle ear. II: Inferring function from structure.

    PubMed

    Mason, Matthew J

    2016-02-01

    Anatomists and zoologists who study middle ear morphology are often interested to know what the structure of an ear can reveal about the auditory acuity and hearing range of the animal in question. This paper represents an introduction to middle ear function targetted towards biological scientists with little experience in the field of auditory acoustics. Simple models of impedance matching are first described, based on the familiar concepts of the area and lever ratios of the middle ear. However, using the Mongolian gerbil Meriones unguiculatus as a test case, it is shown that the predictions made by such 'ideal transformer' models are generally not consistent with measurements derived from recent experimental studies. Electrical analogue models represent a better way to understand some of the complex, frequency-dependent responses of the middle ear: these have been used to model the effects of middle ear subcavities, and the possible function of the auditory ossicles as a transmission line. The concepts behind such models are explained here, again aimed at those with little background knowledge. Functional inferences based on middle ear anatomy are more likely to be valid at low frequencies. Acoustic impedance at low frequencies is dominated by compliance; expanded middle ear cavities, found in small desert mammals including gerbils, jerboas and the sengi Macroscelides, are expected to improve low-frequency sound transmission, as long as the ossicular system is not too stiff. PMID:26100915

  2. An Unexpected Influence on a Quadratic

    ERIC Educational Resources Information Center

    Davis, Jon D.

    2013-01-01

    Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

  3. Crustal structure beneath northeast India inferred from receiver function modeling

    NASA Astrophysics Data System (ADS)

    Borah, Kajaljyoti; Bora, Dipok K.; Goyal, Ayush; Kumar, Raju

    2016-09-01

    We estimated crustal shear velocity structure beneath ten broadband seismic stations of northeast India, by using H-Vp/Vs stacking method and a non-linear direct search approach, Neighbourhood Algorithm (NA) technique followed by joint inversion of Rayleigh wave group velocity and receiver function, calculated from teleseismic earthquakes data. Results show significant variations of thickness, shear velocities (Vs) and Vp/Vs ratio in the crust of the study region. The inverted shear wave velocity models show crustal thickness variations of 32-36 km in Shillong Plateau (North), 36-40 in Assam Valley and ∼44 km in Lesser Himalaya (South). Average Vp/Vs ratio in Shillong Plateau is less (1.73-1.77) compared to Assam Valley and Lesser Himalaya (∼1.80). Average crustal shear velocity beneath the study region varies from 3.4 to 3.5 km/s. Sediment structure beneath Shillong Plateau and Assam Valley shows 1-2 km thick sediment layer with low Vs (2.5-2.9 km/s) and high Vp/Vs ratio (1.8-2.1), while it is observed to be of greater thickness (4 km) with similar Vs and high Vp/Vs (∼2.5) in RUP (Lesser Himalaya). Both Shillong Plateau and Assam Valley show thick upper and middle crust (10-20 km), and thin (4-9 km) lower crust. Average Vp/Vs ratio in Assam Valley and Shillong Plateau suggest that the crust is felsic-to-intermediate and intermediate-to-mafic beneath Shillong Plateau and Assam Valley, respectively. Results show that lower crust rocks beneath the Shillong Plateau and Assam Valley lies between mafic granulite and mafic garnet granulite.

  4. Quadratic eigenvalue problems.

    SciTech Connect

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  5. Pragmatic Inference Abilities in Individuals with Asperger Syndrome or High-Functioning Autism. A Review

    ERIC Educational Resources Information Center

    Loukusa, Soile; Moilanen, Irma

    2009-01-01

    This review summarizes studies involving pragmatic language comprehension and inference abilities in individuals with Asperger syndrome or high-functioning autism. Systematic searches of three electronic databases, selected journals, and reference lists identified 20 studies meeting the inclusion criteria. These studies were evaluated in terms of:…

  6. Sufficient Conditions for Global Minimality of Metastable States in a Class of Non-convex Functionals: A Simple Approach Via Quadratic Lower Bounds

    NASA Astrophysics Data System (ADS)

    Shirokoff, David; Choksi, Rustum; Nave, Jean-Christophe

    2015-06-01

    We consider mass-constrained minimizers for a class of non-convex energy functionals involving a double-well potential. Based upon global quadratic lower bounds to the energy, we introduce a simple strategy to find sufficient conditions on a given critical point (metastable state) to be a global minimizer. We show that this strategy works well for the one exact and known metastable state: the constant state. In doing so, we numerically derive an almost optimal lower bound for both the order-disorder transition curve of the Ohta-Kawasaki energy and the liquid-solid interface of the phase-field crystal energy. We discuss how this strategy extends to non-constant computed metastable states, and the resulting symmetry issues that one must overcome. We give a preliminary analysis of these symmetry issues by addressing the global optimality of a computed lamellar structure for the Ohta-Kawasaki energy in one (1D) and two (2D) space dimensions. We also consider global optimality of a non-constant state for a spatially in-homogenous perturbation of the 2D Ohta-Kawasaki energy. Finally we use one of our simple quadratic lower bounds to rigorously prove that for certain values of the Ohta-Kawasaki parameter and aspect ratio of an asymmetric torus, any global minimizer for the 1D problem is automatically a global minimizer for the 2D problem on the asymmetric torus.

  7. Function Formula Oriented Construction of Bayesian Inference Nets for Diagnosis of Cardiovascular Disease

    PubMed Central

    Sekar, Booma Devi; Dong, Mingchui

    2014-01-01

    An intelligent cardiovascular disease (CVD) diagnosis system using hemodynamic parameters (HDPs) derived from sphygmogram (SPG) signal is presented to support the emerging patient-centric healthcare models. To replicate clinical approach of diagnosis through a staged decision process, the Bayesian inference nets (BIN) are adapted. New approaches to construct a hierarchical multistage BIN using defined function formulas and a method employing fuzzy logic (FL) technology to quantify inference nodes with dynamic values of statistical parameters are proposed. The suggested methodology is validated by constructing hierarchical Bayesian fuzzy inference nets (HBFIN) to diagnose various heart pathologies from the deduced HDPs. The preliminary diagnostic results show that the proposed methodology has salient validity and effectiveness in the diagnosis of cardiovascular disease. PMID:25247174

  8. Function formula oriented construction of Bayesian inference nets for diagnosis of cardiovascular disease.

    PubMed

    Sekar, Booma Devi; Dong, Mingchui

    2014-01-01

    An intelligent cardiovascular disease (CVD) diagnosis system using hemodynamic parameters (HDPs) derived from sphygmogram (SPG) signal is presented to support the emerging patient-centric healthcare models. To replicate clinical approach of diagnosis through a staged decision process, the Bayesian inference nets (BIN) are adapted. New approaches to construct a hierarchical multistage BIN using defined function formulas and a method employing fuzzy logic (FL) technology to quantify inference nodes with dynamic values of statistical parameters are proposed. The suggested methodology is validated by constructing hierarchical Bayesian fuzzy inference nets (HBFIN) to diagnose various heart pathologies from the deduced HDPs. The preliminary diagnostic results show that the proposed methodology has salient validity and effectiveness in the diagnosis of cardiovascular disease. PMID:25247174

  9. Self-replicating quadratics

    NASA Astrophysics Data System (ADS)

    Withers, Christopher S.; Nadarajah, Saralees

    2012-06-01

    We show that there are exactly four quadratic polynomials, Q(x) = x 2 + ax + b, such that For n = 1, 2, … , these quadratic polynomials can be written as the product of N = 2 n quadratic polynomials in x 1/N , namely, ? , where w N is the Nth root of 1.

  10. A Model-Based Analysis to Infer the Functional Content of a Gene List

    PubMed Central

    Newton, Michael A.; He, Qiuling; Kendziorski, Christina

    2012-01-01

    An important challenge in statistical genomics concerns integrating experimental data with exogenous information about gene function. A number of statistical methods are available to address this challenge, but most do not accommodate complexities in the functional record. To infer activity of a functional category (e.g., a gene ontology term), most methods use gene-level data on that category, but do not use other functional properties of the same genes. Not doing so creates undue errors in inference. Recent developments in model-based category analysis aim to overcome this difficulty, but in attempting to do so they are faced with serious computational problems. This paper investigates statistical properties and the structure of posterior computation in one such model for the analysis of functional category data. We examine the graphical structures underlying posterior computation in the original parameterization and in a new parameterization aimed at leveraging elements of the model. We characterize identifiability of the underlying activation states, describe a new prior distribution, and introduce approximations that aim to support numerical methods for posterior inference. PMID:22499692

  11. Vikodak - A Modular Framework for Inferring Functional Potential of Microbial Communities from 16S Metagenomic Datasets

    PubMed Central

    Nagpal, Sunil; Haque, Mohammed Monzoorul; Mande, Sharmila S.

    2016-01-01

    Background The overall metabolic/functional potential of any given environmental niche is a function of the sum total of genes/proteins/enzymes that are encoded and expressed by various interacting microbes residing in that niche. Consequently, prior (collated) information pertaining to genes, enzymes encoded by the resident microbes can aid in indirectly (re)constructing/ inferring the metabolic/ functional potential of a given microbial community (given its taxonomic abundance profile). In this study, we present Vikodak—a multi-modular package that is based on the above assumption and automates inferring and/ or comparing the functional characteristics of an environment using taxonomic abundance generated from one or more environmental sample datasets. With the underlying assumptions of co-metabolism and independent contributions of different microbes in a community, a concerted effort has been made to accommodate microbial co-existence patterns in various modules incorporated in Vikodak. Results Validation experiments on over 1400 metagenomic samples have confirmed the utility of Vikodak in (a) deciphering enzyme abundance profiles of any KEGG metabolic pathway, (b) functional resolution of distinct metagenomic environments, (c) inferring patterns of functional interaction between resident microbes, and (d) automating statistical comparison of functional features of studied microbiomes. Novel features incorporated in Vikodak also facilitate automatic removal of false positives and spurious functional predictions. Conclusions With novel provisions for comprehensive functional analysis, inclusion of microbial co-existence pattern based algorithms, automated inter-environment comparisons; in-depth analysis of individual metabolic pathways and greater flexibilities at the user end, Vikodak is expected to be an important value addition to the family of existing tools for 16S based function prediction. Availability and Implementation A web implementation of Vikodak

  12. Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference

    NASA Technical Reports Server (NTRS)

    Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah

    1998-01-01

    Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.

  13. Study of static and dynamic first hyperpolarizabilities using time-dependent density functional quadratic response theory with local contribution and natural bond orbital analysis.

    PubMed

    Ye, Aijun; Autschbach, Jochen

    2006-12-21

    We apply time-dependent density-functional quadratic response theory to investigate the static and dynamic second-order polarizabilities (first hyperpolarizability) beta. A new implementation using Slater-type basis functions, numerical integration, and density fitting techniques is reported. The second order coupled perturbed Kohn-Sham equations are solved and the second-order perturbed charge density is obtained. It is useful to highlight atomic and bond contributions to understand the relation between molecular structure and properties. Four moderately sized molecules (para-nitroaniline and derivatives thereof) are investigated to assess the accuracy of the time-dependent density-functional theory computations and to investigate the distribution of the second-order charge density as well as the "beta density." Our results highlight the contributions from atoms and bonds on different functional groups to the total value of beta with Mulliken-type and natural bond orbital (NBO) analyses, and demonstrate in some cases how contributions from a particular bond may be identified easily by visual inspection of the beta density. In addition, the position of side group substitution on carbon-carbon bonds significantly affects the hyperpolarizability. A contribution analysis as performed here might be helpful for the design of new materials with desired properties. PMID:17190541

  14. INTEGRATING EVOLUTIONARY AND FUNCTIONAL APPROACHES TO INFER ADAPTATION AT SPECIFIC LOCI

    PubMed Central

    Storz, Jay F.; Wheat, Christopher W.

    2010-01-01

    Inferences about adaptation at specific loci are often exclusively based on the static analysis of DNA sequence variation. Ideally, population-genetic evidence for positive selection serves as a stepping-off point for experimental studies to elucidate the functional significance of the putatively adaptive variation. We argue that inferences about adaptation at specific loci are best achieved by integrating the indirect, retrospective insights provided by population-genetic analyses with the more direct, mechanistic insights provided by functional experiments. Integrative studies of adaptive genetic variation may sometimes be motivated by experimental insights into molecular function, which then provide the impetus to perform population genetic tests to evaluate whether the functional variation is of adaptive significance. In other cases, studies may be initiated by genome scans of DNA variation to identify candidate loci for recent adaptation. Results of such analyses can then motivate experimental efforts to test whether the identified candidate loci do in fact contribute to functional variation in some fitness-related phenotype. Functional studies can provide corroborative evidence for positive selection at particular loci, and can potentially reveal specific molecular mechanisms of adaptation. PMID:20500215

  15. Weight of quadratic forms and graph states

    NASA Astrophysics Data System (ADS)

    Cosentino, Alessandro; Severini, Simone

    2009-11-01

    We prove a connection between Schmidt rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results concerning the weight of quadratic forms in terms of graph states properties. As a byproduct, we obtain a straightforward characterization of the weight of functions associated with pivot-minor of bipartite graphs.

  16. Using evolutionary sequence variation to make inferences about protein structure and function

    NASA Astrophysics Data System (ADS)

    Colwell, Lucy

    2015-03-01

    The evolutionary trajectory of a protein through sequence space is constrained by its function. Collections of sequence homologs record the outcomes of millions of evolutionary experiments in which the protein evolves according to these constraints. The explosive growth in the number of available protein sequences raises the possibility of using the natural variation present in homologous protein sequences to infer these constraints and thus identify residues that control different protein phenotypes. Because in many cases phenotypic changes are controlled by more than one amino acid, the mutations that separate one phenotype from another may not be independent, requiring us to understand the correlation structure of the data. To address this we build a maximum entropy probability model for the protein sequence. The parameters of the inferred model are constrained by the statistics of a large sequence alignment. Pairs of sequence positions with the strongest interactions accurately predict contacts in protein tertiary structure, enabling all atom structural models to be constructed. We describe development of a theoretical inference framework that enables the relationship between the amount of available input data and the reliability of structural predictions to be better understood.

  17. The Mystical "Quadratic Formula."

    ERIC Educational Resources Information Center

    March, Robert H.

    1993-01-01

    Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

  18. A Quadratic Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  19. Impact of Prematurity and Perinatal Antibiotics on the Developing Intestinal Microbiota: A Functional Inference Study

    PubMed Central

    Arboleya, Silvia; Sánchez, Borja; Solís, Gonzalo; Fernández, Nuria; Suárez, Marta; Hernández-Barranco, Ana M.; Milani, Christian; Margolles, Abelardo; de los Reyes-Gavilán, Clara G.; Ventura, Marco; Gueimonde, Miguel

    2016-01-01

    Background: The microbial colonization of the neonatal gut provides a critical stimulus for normal maturation and development. This process of early microbiota establishment, known to be affected by several factors, constitutes an important determinant for later health. Methods: We studied the establishment of the microbiota in preterm and full-term infants and the impact of perinatal antibiotics upon this process in premature babies. To this end, 16S rRNA gene sequence-based microbiota assessment was performed at phylum level and functional inference analyses were conducted. Moreover, the levels of the main intestinal microbial metabolites, the short-chain fatty acids (SCFA) acetate, propionate and butyrate, were measured by Gas-Chromatography Flame ionization/Mass spectrometry detection. Results: Prematurity affects microbiota composition at phylum level, leading to increases of Proteobacteria and reduction of other intestinal microorganisms. Perinatal antibiotic use further affected the microbiota of the preterm infant. These changes involved a concomitant alteration in the levels of intestinal SCFA. Moreover, functional inference analyses allowed for identifying metabolic pathways potentially affected by prematurity and perinatal antibiotics use. Conclusion: A deficiency or delay in the establishment of normal microbiota function seems to be present in preterm infants. Perinatal antibiotic use, such as intrapartum prophylaxis, affected the early life microbiota establishment in preterm newborns, which may have consequences for later health. PMID:27136545

  20. Inferring the functional effect of gene expression changes in signaling pathways.

    PubMed

    Sebastián-León, Patricia; Carbonell, José; Salavert, Francisco; Sanchez, Rubén; Medina, Ignacio; Dopazo, Joaquín

    2013-07-01

    Signaling pathways constitute a valuable source of information that allows interpreting the way in which alterations in gene activities affect to particular cell functionalities. There are web tools available that allow viewing and editing pathways, as well as representing experimental data on them. However, few methods aimed to identify the signaling circuits, within a pathway, associated to the biological problem studied exist and none of them provide a convenient graphical web interface. We present PATHiWAYS, a web-based signaling pathway visualization system that infers changes in signaling that affect cell functionality from the measurements of gene expression values in typical expression microarray case-control experiments. A simple probabilistic model of the pathway is used to estimate the probabilities for signal transmission from any receptor to any final effector molecule (taking into account the pathway topology) using for this the individual probabilities of gene product presence/absence inferred from gene expression values. Significant changes in these probabilities allow linking different cell functionalities triggered by the pathway to the biological problem studied. PATHiWAYS is available at: http://pathiways.babelomics.org/. PMID:23748960

  1. Inferring deep-brain activity from cortical activity using functional near-infrared spectroscopy

    PubMed Central

    Liu, Ning; Cui, Xu; Bryant, Daniel M.; Glover, Gary H.; Reiss, Allan L.

    2015-01-01

    Functional near-infrared spectroscopy (fNIRS) is an increasingly popular technology for studying brain function because it is non-invasive, non-irradiating and relatively inexpensive. Further, fNIRS potentially allows measurement of hemodynamic activity with high temporal resolution (milliseconds) and in naturalistic settings. However, in comparison with other imaging modalities, namely fMRI, fNIRS has a significant drawback: limited sensitivity to hemodynamic changes in deep-brain regions. To overcome this limitation, we developed a computational method to infer deep-brain activity using fNIRS measurements of cortical activity. Using simultaneous fNIRS and fMRI, we measured brain activity in 17 participants as they completed three cognitive tasks. A support vector regression (SVR) learning algorithm was used to predict activity in twelve deep-brain regions using information from surface fNIRS measurements. We compared these predictions against actual fMRI-measured activity using Pearson’s correlation to quantify prediction performance. To provide a benchmark for comparison, we also used fMRI measurements of cortical activity to infer deep-brain activity. When using fMRI-measured activity from the entire cortex, we were able to predict deep-brain activity in the fusiform cortex with an average correlation coefficient of 0.80 and in all deep-brain regions with an average correlation coefficient of 0.67. The top 15% of predictions using fNIRS signal achieved an accuracy of 0.7. To our knowledge, this study is the first to investigate the feasibility of using cortical activity to infer deep-brain activity. This new method has the potential to extend fNIRS applications in cognitive and clinical neuroscience research. PMID:25798327

  2. Inferring deep biosphere function and diversity through (near) surface biosphere portals (Invited)

    NASA Astrophysics Data System (ADS)

    Meyer-Dombard, D. R.; Cardace, D.; Woycheese, K. M.; Swingley, W.; Schubotz, F.; Shock, E.

    2013-12-01

    The consideration of surface expressions of the deep subsurface- such as springs- remains one of the most economically viable means to query the deep biosphere's diversity and function. Hot spring source pools are ideal portals for accessing and inferring the taxonomic and functional diversity of related deep subsurface microbial communities. Consideration of the geochemical composition of deep vs. surface fluids provides context for interpretation of community function. Further, parallel assessment of 16S rRNA data, metagenomic sequencing, and isotopic compositions of biomass in surface springs allows inference of the functional capacities of subsurface ecosystems. Springs in Yellowstone National Park (YNP), the Philippines, and Turkey are considered here, incorporating near-surface, transition, and surface ecosystems to identify 'legacy' taxa and functions of the deep biosphere. We find that source pools often support functional capacity suited to subsurface ecosystems. For example, in hot ecosystems, source pools are strictly chemosynthetic, and surface environments with measureable dissolved oxygen may contain evidence of community functions more favorable under anaerobic conditions. Metagenomic reads from a YNP ecosystem indicate the genetic capacity for sulfate reduction at high temperature. However, inorganic sulfate reduction is only minimally energy-yielding in these surface environments suggesting the potential that sulfate reduction is a 'legacy' function of deeper biosphere ecosystems. Carbon fixation tactics shift with increased surface exposure of the thermal fluids. Genes related to the rTCA cycle and the acetyl co-A pathway are most prevalent in highest temperature, anaerobic sites. At lower temperature sites, fewer total carbon fixation genes were observed, perhaps indicating an increase in heterotrophic metabolism with increased surface exposure. In hydrogen and methane rich springs in the Philippines and Turkey, methanogenic taxa dominate source

  3. LncRNA ontology: inferring lncRNA functions based on chromatin states and expression patterns

    PubMed Central

    Li, Yongsheng; Chen, Hong; Pan, Tao; Jiang, Chunjie; Zhao, Zheng; Wang, Zishan; Zhang, Jinwen; Xu, Juan; Li, Xia

    2015-01-01

    Accumulating evidences suggest that long non-coding RNAs (lncRNAs) perform important functions. Genome-wide chromatin-states area rich source of information about cellular state, yielding insights beyond what is typically obtained by transcriptome profiling. We propose an integrative method for genome-wide functional predictions of lncRNAs by combining chromatin states data with gene expression patterns. We first validated the method using protein-coding genes with known function annotations. Our validation results indicated that our integrative method performs better than co-expression analysis, and is accurate across different conditions. Next, by applying the integrative model genome-wide, we predicted the probable functions for more than 97% of human lncRNAs. The putative functions inferred by our method match with previously annotated by the targets of lncRNAs. Moreover, the linkage from the cellular processes influenced by cancer-associated lncRNAs to the cancer hallmarks provided a “lncRNA point-of-view” on tumor biology. Our approach provides a functional annotation of the lncRNAs, which we developed into a web-based application, LncRNA Ontology, to provide visualization, analysis, and downloading of lncRNA putative functions. PMID:26485761

  4. Inferring modules of functionally interacting proteins using the Bond Energy Algorithm

    PubMed Central

    Watanabe, Ryosuke LA; Morett, Enrique; Vallejo, Edgar E

    2008-01-01

    Background Non-homology based methods such as phylogenetic profiles are effective for predicting functional relationships between proteins with no considerable sequence or structure similarity. Those methods rely heavily on traditional similarity metrics defined on pairs of phylogenetic patterns. Proteins do not exclusively interact in pairs as the final biological function of a protein in the cellular context is often hold by a group of proteins. In order to accurately infer modules of functionally interacting proteins, the consideration of not only direct but also indirect relationships is required. In this paper, we used the Bond Energy Algorithm (BEA) to predict functionally related groups of proteins. With BEA we create clusters of phylogenetic profiles based on the associations of the surrounding elements of the analyzed data using a metric that considers linked relationships among elements in the data set. Results Using phylogenetic profiles obtained from the Cluster of Orthologous Groups of Proteins (COG) database, we conducted a series of clustering experiments using BEA to predict (upper level) relationships between profiles. We evaluated our results by comparing with COG's functional categories, And even more, with the experimentally determined functional relationships between proteins provided by the DIP and ECOCYC databases. Our results demonstrate that BEA is capable of predicting meaningful modules of functionally related proteins. BEA outperforms traditionally used clustering methods, such as k-means and hierarchical clustering by predicting functional relationships between proteins with higher accuracy. Conclusion This study shows that the linked relationships of phylogenetic profiles obtained by BEA is useful for detecting functional associations between profiles and extending functional modules not found by traditional methods. BEA is capable of detecting relationship among phylogenetic patterns by linking them through a common element shared in

  5. Brain imaging and cognitive neuroscience. Toward strong inference in attributing function to structure.

    PubMed

    Sarter, M; Berntson, G G; Cacioppo, J T

    1996-01-01

    Cognitive neuroscience has emerged from the neurosciences and cognitive psychology as a scientific discipline that aims at the determination of "how brain function gives rise to mental activity" (S. M. Kosslyn & L. M. Shin, 1992, p. 146). While research in cognitive neuroscience combines many levels of neuroscientific and psychological analyses, modern imaging techniques that monitor brain activity during behavioral or cognitive operations have significantly contributed to the emergence of this discipline. The conclusions deduced from these studies are inherently localizationistic in nature; in other words, they describe cognitive functions as being localized in focal brain regions (brain activity in a defined brain region, phi, is involved in specific cognitive function, psi). A broad discussion about the virtues and limitations of such conclusions may help avoid the emergence of a mentalistic localizationism (i.e., the attribution of mentalistic concepts such as happiness, morality, or consciousness to brain structure) and illustrates the importance of a convergence with information generated by different research strategies (such as, for example, evidence generated by studies in which the effects of experimental manipulations of local neuronal processes on cognitive functions are assessed). Progress in capitalizing on brain-imaging studies to investigate questions of the form "brain structure or event phi is associated with cognitive function psi" may be impeded because of the way in which inferences are typically formulated in the brain imaging literature. A conceptual framework to advance the interpretation of data describing the relationships between cognitive phenomena and brain structure activity is provided. PMID:8585670

  6. On the inference of function from structure using biomechanical modelling and simulation of extinct organisms.

    PubMed

    Hutchinson, John R

    2012-02-23

    Biomechanical modelling and simulation techniques offer some hope for unravelling the complex inter-relationships of structure and function perhaps even for extinct organisms, but have their limitations owing to this complexity and the many unknown parameters for fossil taxa. Validation and sensitivity analysis are two indispensable approaches for quantifying the accuracy and reliability of such models or simulations. But there are other subtleties in biomechanical modelling that include investigator judgements about the level of simplicity versus complexity in model design or how uncertainty and subjectivity are dealt with. Furthermore, investigator attitudes toward models encompass a broad spectrum between extreme credulity and nihilism, influencing how modelling is conducted and perceived. Fundamentally, more data and more testing of methodology are required for the field to mature and build confidence in its inferences. PMID:21666064

  7. Pragmatic inferences in high-functioning adults with autism and Asperger syndrome.

    PubMed

    Pijnacker, Judith; Hagoort, Peter; Buitelaar, Jan; Teunisse, Jan-Pieter; Geurts, Bart

    2009-04-01

    Although people with autism spectrum disorders (ASD) often have severe problems with pragmatic aspects of language, little is known about their pragmatic reasoning. We carried out a behavioral study on high-functioning adults with autistic disorder (n = 11) and Asperger syndrome (n = 17) and matched controls (n = 28) to investigate whether they are capable of deriving scalar implicatures, which are generally considered to be pragmatic inferences. Participants were presented with underinformative sentences like "Some sparrows are birds". This sentence is logically true, but pragmatically inappropriate if the scalar implicature "Not all sparrows are birds" is derived. The present findings indicate that the combined ASD group was just as likely as controls to derive scalar implicatures, yet there was a difference between participants with autistic disorder and Asperger syndrome, suggesting a potential differentiation between these disorders in pragmatic reasoning. Moreover, our results suggest that verbal intelligence is a constraint for task performance in autistic disorder but not in Asperger syndrome. PMID:19052858

  8. Solitons in quadratic media

    NASA Astrophysics Data System (ADS)

    Colin, M.; Di Menza, L.; Saut, J. C.

    2016-03-01

    In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.

  9. LC-MS/MS based proteomic analysis and functional inference of hypothetical proteins in Desulfovibrio vulgaris

    SciTech Connect

    Zhang, Weiwen; Culley, David E.; Gritsenko, Marina A.; Moore, Ronald J.; Nie, Lei; Scholten, Johannes C.; Petritis, Konstantinos; Strittmatter, Eric F.; Camp, David G.; Smith, Richard D.; Brockman, Fred J.

    2006-11-03

    ABSTRACT In the previous study, the whole-genome gene expression profiles of D. vulgaris in response to oxidative stress and heat shock were determined. The results showed 24-28% of the responsive genes were hypothetical proteins that have not been experimentally characterized or whose function can not be deduced by simple sequence comparison. To further explore the protecting mechanisms employed in D. vulgaris against the oxidative stress and heat shock, attempt was made in this study to infer functions of these hypothetical proteins by phylogenomic profiling along with detailed sequence comparison against various publicly available databases. By this approach we were ableto assign possible functions to 25 responsive hypothetical proteins. The findings included that DVU0725, induced by oxidative stress, may be involved in lipopolysaccharide biosynthesis, implying that the alternation of lipopolysaccharide on cell surface might service as a mechanism against oxidative stress in D. vulgaris. In addition, two responsive proteins, DVU0024 encoding a putative transcriptional regulator and DVU1670 encoding predicted redox protein, were sharing co-evolution atterns with rubrerythrin in Archaeoglobus fulgidus and Clostridium perfringens, respectively, implying that they might be part of the stress response and protective systems in D. vulgaris. The study demonstrated that phylogenomic profiling is a useful tool in interpretation of experimental genomics data, and also provided further insight on cellular response to oxidative stress and heat shock in D. vulgaris.

  10. Guises and disguises of quadratic divergences

    SciTech Connect

    Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  11. Quadratic spatial soliton interactions

    NASA Astrophysics Data System (ADS)

    Jankovic, Ladislav

    Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

  12. Quadratic soliton self-reflection at a quadratically nonlinear interface

    NASA Astrophysics Data System (ADS)

    Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

    2003-11-01

    The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

  13. Inferring muscle functional roles of the ostrich pelvic limb during walking and running using computer optimization.

    PubMed

    Rankin, Jeffery W; Rubenson, Jonas; Hutchinson, John R

    2016-05-01

    Owing to their cursorial background, ostriches (Struthio camelus) walk and run with high metabolic economy, can reach very fast running speeds and quickly execute cutting manoeuvres. These capabilities are believed to be a result of their ability to coordinate muscles to take advantage of specialized passive limb structures. This study aimed to infer the functional roles of ostrich pelvic limb muscles during gait. Existing gait data were combined with a newly developed musculoskeletal model to generate simulations of ostrich walking and running that predict muscle excitations, force and mechanical work. Consistent with previous avian electromyography studies, predicted excitation patterns showed that individual muscles tended to be excited primarily during only stance or swing. Work and force estimates show that ostrich gaits are partially hip-driven with the bi-articular hip-knee muscles driving stance mechanics. Conversely, the knee extensors acted as brakes, absorbing energy. The digital extensors generated large amounts of both negative and positive mechanical work, with increased magnitudes during running, providing further evidence that ostriches make extensive use of tendinous elastic energy storage to improve economy. The simulations also highlight the need to carefully consider non-muscular soft tissues that may play a role in ostrich gait. PMID:27146688

  14. Inferring muscle functional roles of the ostrich pelvic limb during walking and running using computer optimization

    PubMed Central

    Rubenson, Jonas

    2016-01-01

    Owing to their cursorial background, ostriches (Struthio camelus) walk and run with high metabolic economy, can reach very fast running speeds and quickly execute cutting manoeuvres. These capabilities are believed to be a result of their ability to coordinate muscles to take advantage of specialized passive limb structures. This study aimed to infer the functional roles of ostrich pelvic limb muscles during gait. Existing gait data were combined with a newly developed musculoskeletal model to generate simulations of ostrich walking and running that predict muscle excitations, force and mechanical work. Consistent with previous avian electromyography studies, predicted excitation patterns showed that individual muscles tended to be excited primarily during only stance or swing. Work and force estimates show that ostrich gaits are partially hip-driven with the bi-articular hip–knee muscles driving stance mechanics. Conversely, the knee extensors acted as brakes, absorbing energy. The digital extensors generated large amounts of both negative and positive mechanical work, with increased magnitudes during running, providing further evidence that ostriches make extensive use of tendinous elastic energy storage to improve economy. The simulations also highlight the need to carefully consider non-muscular soft tissues that may play a role in ostrich gait. PMID:27146688

  15. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  16. Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses

    NASA Astrophysics Data System (ADS)

    Vegetti, S.; Koopmans, L. V. E.; Auger, M. W.; Treu, T.; Bolton, A. S.

    2014-08-01

    We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey by Bolton et al. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift ˜ 0.2 and an average velocity dispersion <σeff> ˜ 270 km s-1. We perform a Bayesian inference on the substructure mass function, within a median region of about 32 kpc2 around the Einstein radius ( ˜ 4.2 kpc). We infer a mean projected substructure mass fraction f = 0.0076_{-0.0052}^{+0.0208} at the 68 per cent confidence level and a substructure mass function slope α < 2.93 at the 95 per cent confidence level for a uniform prior probability density on α. For a Gaussian prior based on cold dark matter (CDM) simulations, we infer f = 0.0064^{+0.0080}_{-0.0042} and a slope of α = 1.90^{+0.098}_{-0.098} at the 68 per cent confidence level. Since only one substructure was detected in the full sample, we have little information on the mass function slope, which is therefore poorly constrained (i.e. the Bayes factor shows no positive preference for any of the two models). The inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at the 68 per cent confidence level.

  17. Dissociable functions of reward inference in the lateral prefrontal cortex and the striatum

    PubMed Central

    Tanaka, Shingo; Pan, Xiaochuan; Oguchi, Mineki; Taylor, Jessica E.; Sakagami, Masamichi

    2015-01-01

    In a complex and uncertain world, how do we select appropriate behavior? One possibility is that we choose actions that are highly reinforced by their probabilistic consequences (model-free processing). However, we may instead plan actions prior to their actual execution by predicting their consequences (model-based processing). It has been suggested that the brain contains multiple yet distinct systems involved in reward prediction. Several studies have tried to allocate model-free and model-based systems to the striatum and the lateral prefrontal cortex (LPFC), respectively. Although there is much support for this hypothesis, recent research has revealed discrepancies. To understand the nature of the reward prediction systems in the LPFC and the striatum, a series of single-unit recording experiments were conducted. LPFC neurons were found to infer the reward associated with the stimuli even when the monkeys had not yet learned the stimulus-reward (SR) associations directly. Striatal neurons seemed to predict the reward for each stimulus only after directly experiencing the SR contingency. However, the one exception was “Exclusive Or” situations in which striatal neurons could predict the reward without direct experience. Previous single-unit studies in monkeys have reported that neurons in the LPFC encode category information, and represent reward information specific to a group of stimuli. Here, as an extension of these, we review recent evidence that a group of LPFC neurons can predict reward specific to a category of visual stimuli defined by relevant behavioral responses. We suggest that the functional difference in reward prediction between the LPFC and the striatum is that while LPFC neurons can utilize abstract code, striatal neurons can code individual associations between stimuli and reward but cannot utilize abstract code. PMID:26236266

  18. Dissociable functions of reward inference in the lateral prefrontal cortex and the striatum.

    PubMed

    Tanaka, Shingo; Pan, Xiaochuan; Oguchi, Mineki; Taylor, Jessica E; Sakagami, Masamichi

    2015-01-01

    In a complex and uncertain world, how do we select appropriate behavior? One possibility is that we choose actions that are highly reinforced by their probabilistic consequences (model-free processing). However, we may instead plan actions prior to their actual execution by predicting their consequences (model-based processing). It has been suggested that the brain contains multiple yet distinct systems involved in reward prediction. Several studies have tried to allocate model-free and model-based systems to the striatum and the lateral prefrontal cortex (LPFC), respectively. Although there is much support for this hypothesis, recent research has revealed discrepancies. To understand the nature of the reward prediction systems in the LPFC and the striatum, a series of single-unit recording experiments were conducted. LPFC neurons were found to infer the reward associated with the stimuli even when the monkeys had not yet learned the stimulus-reward (SR) associations directly. Striatal neurons seemed to predict the reward for each stimulus only after directly experiencing the SR contingency. However, the one exception was "Exclusive Or" situations in which striatal neurons could predict the reward without direct experience. Previous single-unit studies in monkeys have reported that neurons in the LPFC encode category information, and represent reward information specific to a group of stimuli. Here, as an extension of these, we review recent evidence that a group of LPFC neurons can predict reward specific to a category of visual stimuli defined by relevant behavioral responses. We suggest that the functional difference in reward prediction between the LPFC and the striatum is that while LPFC neurons can utilize abstract code, striatal neurons can code individual associations between stimuli and reward but cannot utilize abstract code. PMID:26236266

  19. Quadratic algebras for three-dimensional superintegrable systems

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2010-02-15

    The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

  20. Quadratic Programming for Allocating Control Effort

    NASA Technical Reports Server (NTRS)

    Singh, Gurkirpal

    2005-01-01

    A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

  1. A phylogeny-based benchmarking test for orthology inference reveals the limitations of function-based validation.

    PubMed

    Trachana, Kalliopi; Forslund, Kristoffer; Larsson, Tomas; Powell, Sean; Doerks, Tobias; von Mering, Christian; Bork, Peer

    2014-01-01

    Accurate orthology prediction is crucial for many applications in the post-genomic era. The lack of broadly accepted benchmark tests precludes a comprehensive analysis of orthology inference. So far, functional annotation between orthologs serves as a performance proxy. However, this violates the fundamental principle of orthology as an evolutionary definition, while it is often not applicable due to limited experimental evidence for most species. Therefore, we constructed high quality "gold standard" orthologous groups that can serve as a benchmark set for orthology inference in bacterial species. Herein, we used this dataset to demonstrate 1) why a manually curated, phylogeny-based dataset is more appropriate for benchmarking orthology than other popular practices and 2) how it guides database design and parameterization through careful error quantification. More specifically, we illustrate how function-based tests often fail to identify false assignments, misjudging the true performance of orthology inference methods. We also examined how our dataset can instruct the selection of a "core" species repertoire to improve detection accuracy. We conclude that including more genomes at the proper evolutionary distances can influence the overall quality of orthology detection. The curated gene families, called Reference Orthologous Groups, are publicly available at http://eggnog.embl.de/orthobench2. PMID:25369365

  2. A Phylogeny-Based Benchmarking Test for Orthology Inference Reveals the Limitations of Function-Based Validation

    PubMed Central

    Larsson, Tomas; Powell, Sean; Doerks, Tobias; von Mering, Christian

    2014-01-01

    Accurate orthology prediction is crucial for many applications in the post-genomic era. The lack of broadly accepted benchmark tests precludes a comprehensive analysis of orthology inference. So far, functional annotation between orthologs serves as a performance proxy. However, this violates the fundamental principle of orthology as an evolutionary definition, while it is often not applicable due to limited experimental evidence for most species. Therefore, we constructed high quality "gold standard" orthologous groups that can serve as a benchmark set for orthology inference in bacterial species. Herein, we used this dataset to demonstrate 1) why a manually curated, phylogeny-based dataset is more appropriate for benchmarking orthology than other popular practices and 2) how it guides database design and parameterization through careful error quantification. More specifically, we illustrate how function-based tests often fail to identify false assignments, misjudging the true performance of orthology inference methods. We also examined how our dataset can instruct the selection of a “core” species repertoire to improve detection accuracy. We conclude that including more genomes at the proper evolutionary distances can influence the overall quality of orthology detection. The curated gene families, called Reference Orthologous Groups, are publicly available at http://eggnog.embl.de/orthobench2. PMID:25369365

  3. Inference of S-system models of genetic networks by solving one-dimensional function optimization problems.

    PubMed

    Kimura, S; Araki, D; Matsumura, K; Okada-Hatakeyama, M

    2012-02-01

    Voit and Almeida have proposed the decoupling approach as a method for inferring the S-system models of genetic networks. The decoupling approach defines the inference of a genetic network as a problem requiring the solutions of sets of algebraic equations. The computation can be accomplished in a very short time, as the approach estimates S-system parameters without solving any of the differential equations. Yet the defined algebraic equations are non-linear, which sometimes prevents us from finding reasonable S-system parameters. In this study, we propose a new technique to overcome this drawback of the decoupling approach. This technique transforms the problem of solving each set of algebraic equations into a one-dimensional function optimization problem. The computation can still be accomplished in a relatively short time, as the problem is transformed by solving a linear programming problem. We confirm the effectiveness of the proposed approach through numerical experiments. PMID:22155075

  4. Students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  5. A quadratic analog-to-digital converter

    NASA Technical Reports Server (NTRS)

    Harrison, D. C.; Staples, M. H.

    1980-01-01

    An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.

  6. Inferring gene function from evolutionary change in signatures of translation efficiency

    PubMed Central

    2014-01-01

    Background The genetic code is redundant, meaning that most amino acids can be encoded by more than one codon. Highly expressed genes tend to use optimal codons to increase the accuracy and speed of translation. Thus, codon usage biases provide a signature of the relative expression levels of genes, which can, uniquely, be quantified across the domains of life. Results Here we describe a general statistical framework to exploit this phenomenon and to systematically associate genes with environments and phenotypic traits through changes in codon adaptation. By inferring evolutionary signatures of translation efficiency in 911 bacterial and archaeal genomes while controlling for confounding effects of phylogeny and inter-correlated phenotypes, we linked 187 gene families to 24 diverse phenotypic traits. A series of experiments in Escherichia coli revealed that 13 of 15, 19 of 23, and 3 of 6 gene families with changes in codon adaptation in aerotolerant, thermophilic, or halophilic microbes. Respectively, confer specific resistance to, respectively, hydrogen peroxide, heat, and high salinity. Further, we demonstrate experimentally that changes in codon optimality alone are sufficient to enhance stress resistance. Finally, we present evidence that multiple genes with altered codon optimality in aerobes confer oxidative stress resistance by controlling the levels of iron and NAD(P)H. Conclusions Taken together, these results provide experimental evidence for a widespread connection between changes in translation efficiency and phenotypic adaptation. As the number of sequenced genomes increases, this novel genomic context method for linking genes to phenotypes based on sequence alone will become increasingly useful. PMID:24580753

  7. Effect of taxonomic resolution on ecological and palaeoecological inference - a test using testate amoeba water table depth transfer functions

    NASA Astrophysics Data System (ADS)

    Mitchell, Edward A. D.; Lamentowicz, Mariusz; Payne, Richard J.; Mazei, Yuri

    2014-05-01

    Sound taxonomy is a major requirement for quantitative environmental reconstruction using biological data. Transfer function performance should theoretically be expected to decrease with reduced taxonomic resolution. However for many groups of organisms taxonomy is imperfect and species level identification not always possible. We conducted numerical experiments on five testate amoeba water table (DWT) transfer function data sets. We sequentially reduced the number of taxonomic groups by successively merging morphologically similar species and removing inconspicuous species. We then assessed how these changes affected model performance and palaeoenvironmental reconstruction using two fossil data sets. Model performance decreased with decreasing taxonomic resolution, but this had only limited effects on patterns of inferred DWT, at least to detect major dry/wet shifts. Higher-resolution taxonomy may however still be useful to detect more subtle changes, or for reconstructed shifts to be significant.

  8. A Genome-Scale Investigation of How Sequence, Function, and Tree-Based Gene Properties Influence Phylogenetic Inference

    PubMed Central

    Shen, Xing-Xing; Salichos, Leonidas; Rokas, Antonis

    2016-01-01

    Molecular phylogenetic inference is inherently dependent on choices in both methodology and data. Many insightful studies have shown how choices in methodology, such as the model of sequence evolution or optimality criterion used, can strongly influence inference. In contrast, much less is known about the impact of choices in the properties of the data, typically genes, on phylogenetic inference. We investigated the relationships between 52 gene properties (24 sequence-based, 19 function-based, and 9 tree-based) with each other and with three measures of phylogenetic signal in two assembled data sets of 2,832 yeast and 2,002 mammalian genes. We found that most gene properties, such as evolutionary rate (measured through the percent average of pairwise identity across taxa) and total tree length, were highly correlated with each other. Similarly, several gene properties, such as gene alignment length, Guanine-Cytosine content, and the proportion of tree distance on internal branches divided by relative composition variability (treeness/RCV), were strongly correlated with phylogenetic signal. Analysis of partial correlations between gene properties and phylogenetic signal in which gene evolutionary rate and alignment length were simultaneously controlled, showed similar patterns of correlations, albeit weaker in strength. Examination of the relative importance of each gene property on phylogenetic signal identified gene alignment length, alongside with number of parsimony-informative sites and variable sites, as the most important predictors. Interestingly, the subsets of gene properties that optimally predicted phylogenetic signal differed considerably across our three phylogenetic measures and two data sets; however, gene alignment length and RCV were consistently included as predictors of all three phylogenetic measures in both yeasts and mammals. These results suggest that a handful of sequence-based gene properties are reliable predictors of phylogenetic signal

  9. Tectonomagmatic origin of Precambrian rocks of Mexico and Argentina inferred from multi-dimensional discriminant-function based discrimination diagrams

    NASA Astrophysics Data System (ADS)

    Pandarinath, Kailasa

    2014-12-01

    Several new multi-dimensional tectonomagmatic discrimination diagrams employing log-ratio variables of chemical elements and probability based procedure have been developed during the last 10 years for basic-ultrabasic, intermediate and acid igneous rocks. There are numerous studies on extensive evaluations of these newly developed diagrams which have indicated their successful application to know the original tectonic setting of younger and older as well as sea-water and hydrothermally altered volcanic rocks. In the present study, these diagrams were applied to Precambrian rocks of Mexico (southern and north-eastern) and Argentina. The study indicated the original tectonic setting of Precambrian rocks from the Oaxaca Complex of southern Mexico as follows: (1) dominant rift (within-plate) setting for rocks of 1117-988 Ma age; (2) dominant rift and less-dominant arc setting for rocks of 1157-1130 Ma age; and (3) a combined tectonic setting of collision and rift for Etla Granitoid Pluton (917 Ma age). The diagrams have indicated the original tectonic setting of the Precambrian rocks from the north-eastern Mexico as: (1) a dominant arc tectonic setting for the rocks of 988 Ma age; and (2) an arc and collision setting for the rocks of 1200-1157 Ma age. Similarly, the diagrams have indicated the dominant original tectonic setting for the Precambrian rocks from Argentina as: (1) with-in plate (continental rift-ocean island) and continental rift (CR) setting for the rocks of 800 Ma and 845 Ma age, respectively; and (2) an arc setting for the rocks of 1174-1169 Ma and of 1212-1188 Ma age. The inferred tectonic setting for these Precambrian rocks are, in general, in accordance to the tectonic setting reported in the literature, though there are some inconsistence inference of tectonic settings by some of the diagrams. The present study confirms the importance of these newly developed discriminant-function based diagrams in inferring the original tectonic setting of

  10. A Genome-Scale Investigation of How Sequence, Function, and Tree-Based Gene Properties Influence Phylogenetic Inference.

    PubMed

    Shen, Xing-Xing; Salichos, Leonidas; Rokas, Antonis

    2016-01-01

    Molecular phylogenetic inference is inherently dependent on choices in both methodology and data. Many insightful studies have shown how choices in methodology, such as the model of sequence evolution or optimality criterion used, can strongly influence inference. In contrast, much less is known about the impact of choices in the properties of the data, typically genes, on phylogenetic inference. We investigated the relationships between 52 gene properties (24 sequence-based, 19 function-based, and 9 tree-based) with each other and with three measures of phylogenetic signal in two assembled data sets of 2,832 yeast and 2,002 mammalian genes. We found that most gene properties, such as evolutionary rate (measured through the percent average of pairwise identity across taxa) and total tree length, were highly correlated with each other. Similarly, several gene properties, such as gene alignment length, Guanine-Cytosine content, and the proportion of tree distance on internal branches divided by relative composition variability (treeness/RCV), were strongly correlated with phylogenetic signal. Analysis of partial correlations between gene properties and phylogenetic signal in which gene evolutionary rate and alignment length were simultaneously controlled, showed similar patterns of correlations, albeit weaker in strength. Examination of the relative importance of each gene property on phylogenetic signal identified gene alignment length, alongside with number of parsimony-informative sites and variable sites, as the most important predictors. Interestingly, the subsets of gene properties that optimally predicted phylogenetic signal differed considerably across our three phylogenetic measures and two data sets; however, gene alignment length and RCV were consistently included as predictors of all three phylogenetic measures in both yeasts and mammals. These results suggest that a handful of sequence-based gene properties are reliable predictors of phylogenetic signal

  11. Bayesian inverse modeling of vadose zone hydraulic properties in a layered soil profile with data-driven likelihood function inference

    NASA Astrophysics Data System (ADS)

    Over, M. W.; Wollschlaeger, U.; Osorio-Murillo, C. A.; Ames, D. P.; Rubin, Y.

    2013-12-01

    Good estimates for water retention and hydraulic conductivity functions are essential for accurate modeling of the nonlinear water dynamics of unsaturated soils. Parametric mathematical models for these functions are utilized in numerical applications of vadose zone dynamics; therefore, characterization of the model parameters to represent in situ soil properties is the goal of many inversion or calibration techniques. A critical, statistical challenge of existing approaches is the subjective, user-definition of a likelihood function or objective function - a step known to introduce bias in the results. We present a methodology for Bayesian inversion where the likelihood function is inferred directly from the simulation data, which eliminates subjectivity. Additionally, our approach assumes that there is no one parameterization that is appropriate for soils, but rather that the parameters are randomly distributed. This introduces the familiar concept from groundwater hydrogeology of structural models into vadose zone applications, but without attempting to apply geostatistics, which is extremely difficult in unsaturated problems. We validate our robust statistical approach on field data obtained during a multi-layer, natural boundary condition experiment and compare with previous optimizations using the same data. Our confidence intervals for the water retention and hydraulic conductivity functions as well as joint posterior probability distributions of the Mualem-van Genuchten parameters compare well with the previous work. The entire analysis was carried out using the free, open-source MAD# software available at http://mad.codeplex.com/.

  12. Inferring Functional Interaction and Transition Patterns via Dynamic Bayesian Variable Partition Models

    PubMed Central

    Zhang, Jing; Li, Xiang; Li, Cong; Lian, Zhichao; Huang, Xiu; Zhong, Guocheng; Zhu, Dajiang; Li, Kaiming; Jin, Changfeng; Hu, Xintao; Han, Junwei; Guo, Lei; Hu, Xiaoping; Li, Lingjiang; Liu, Tianming

    2014-01-01

    Multivariate connectivity and functional dynamics have been of wide interest in the neuroimaging field, and a variety of methods have been developed to study functional interactions and dynamics. In contrast, the temporal dynamic transitions of multivariate functional interactions among brain networks, in particular, in resting state, have been much less explored. This paper presents a novel dynamic Bayesian variable partition model (DBVPM) that simultaneously considers and models multivariate functional interactions and their dynamics via a unified Bayesian framework. The basic idea is to detect the temporal boundaries of piecewise quasi-stable functional interaction patterns, which are then modeled by representative signature patterns and whose temporal transitions are characterized by finite-state transition machines. Results on both simulated and experimental datasets demonstrated the effectiveness and accuracy of the DBVPM in dividing temporally transiting functional interaction patterns. The application of DBVPM on a post-traumatic stress disorder (PTSD) dataset revealed substantially different multivariate functional interaction signatures and temporal transitions in the default mode and emotion networks of PTSD patients, in comparison with those in healthy controls. This result demonstrated the utility of DBVPM in elucidating salient features that cannot be revealed by static pair-wise functional connectivity analysis. PMID:24222313

  13. INFERRING FUNCTIONAL NETWORK-BASED SIGNATURES VIA STRUCTURALLY-WEIGHTED LASSO MODEL

    PubMed Central

    Zhu, Dajiang; Shen, Dinggang; Liu, Tianming

    2014-01-01

    Most current research approaches for functional/effective connectivity analysis focus on pair-wise connectivity and cannot deal with network-scale functional interactions. In this paper, we propose a structurally-weighted LASSO (SW-LASSO) regression model to represent the functional interaction among multiple regions of interests (ROIs) based on resting state fMRI (R-fMRI) data. The structural connectivity constraints derived from diffusion tenor imaging (DTI) data will guide the selection of the weights which adjust the penalty levels of different coefficients corresponding to different ROIs. Using the Default Mode Network (DMN) as a test-bed, our results indicate that the learned SW-LASSO has good capability of differentiating Mild Cognitive Impairment (MCI) subjects from their normal controls and has promising potential to characterize the brain functions among different condition, thus serving as the functional network-based signature. PMID:25002915

  14. Orthogonality preserving infinite dimensional quadratic stochastic operators

    SciTech Connect

    Akın, Hasan; Mukhamedov, Farrukh

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  15. Ecological Inference

    NASA Astrophysics Data System (ADS)

    King, Gary; Rosen, Ori; Tanner, Martin A.

    2004-09-01

    This collection of essays brings together a diverse group of scholars to survey the latest strategies for solving ecological inference problems in various fields. The last half-decade has witnessed an explosion of research in ecological inference--the process of trying to infer individual behavior from aggregate data. Although uncertainties and information lost in aggregation make ecological inference one of the most problematic types of research to rely on, these inferences are required in many academic fields, as well as by legislatures and the Courts in redistricting, by business in marketing research, and by governments in policy analysis.

  16. Preliminary Results of the Lithospheric Structure Beneath the Aeolian Archipelago (Italy) Inferred from Teleseismic Receiver Functions

    NASA Astrophysics Data System (ADS)

    Musumeci, C.; Martinez-Arevalo, C.; de Lis Mancilla3, F.; Patanè, D.

    2009-12-01

    The Aeolian archipelago (Italy) represents an approximately one-million-year-old volcanic arc related to the subduction of the Ionian oceanic plate beneath the Calabrian continental crust. The objective of this work is to develop a better understanding of the regional structure of the whole archipelago. The crustal structure under each station was obtained applying P-receiver function technique to the teleseismic P-coda data recorded by the broadband seismic network (10 stations) installed by the Istituto Nazionale di Geofisica e Volcanologia (INGV-CT). Receiver functions were computed by using the Extended-Time Multitaper Frequency Domain Cross-Correlation Receiver Function (ET-MTRF) method. The preliminary results suggest a very similar listhospheric structure below all the islands of the Aeolian archipelago, with the exception of Stromboli. The boundary between the subducting ocean crust of the Ionian plate and the Thyrrenian mantle is clearly observed below all the stations.

  17. Phylogenetic Gaussian Process Model for the Inference of Functionally Important Regions in Protein Tertiary Structures

    PubMed Central

    Huang, Yi-Fei; Golding, G. Brian

    2014-01-01

    A critical question in biology is the identification of functionally important amino acid sites in proteins. Because functionally important sites are under stronger purifying selection, site-specific substitution rates tend to be lower than usual at these sites. A large number of phylogenetic models have been developed to estimate site-specific substitution rates in proteins and the extraordinarily low substitution rates have been used as evidence of function. Most of the existing tools, e.g. Rate4Site, assume that site-specific substitution rates are independent across sites. However, site-specific substitution rates may be strongly correlated in the protein tertiary structure, since functionally important sites tend to be clustered together to form functional patches. We have developed a new model, GP4Rate, which incorporates the Gaussian process model with the standard phylogenetic model to identify slowly evolved regions in protein tertiary structures. GP4Rate uses the Gaussian process to define a nonparametric prior distribution of site-specific substitution rates, which naturally captures the spatial correlation of substitution rates. Simulations suggest that GP4Rate can potentially estimate site-specific substitution rates with a much higher accuracy than Rate4Site and tends to report slowly evolved regions rather than individual sites. In addition, GP4Rate can estimate the strength of the spatial correlation of substitution rates from the data. By applying GP4Rate to a set of mammalian B7-1 genes, we found a highly conserved region which coincides with experimental evidence. GP4Rate may be a useful tool for the in silico prediction of functionally important regions in the proteins with known structures. PMID:24453956

  18. STATISTICAL INFERENCE PROCEDURES FOR PROBABILITY SELECTION FUNCTIONS IN LONG-TERM MONITORING PROGRAMS

    EPA Science Inventory

    This report develops the theory and illustrates the use of selection functions to describe changes over time in the distributions of environmentally important variables at sites sampled as part of environmental monitoring programs. he first part of the report provides a review of...

  19. Microbial manipulation of immune function for asthma prevention: inferences from clinical trials.

    PubMed

    Yoo, Jennifer; Tcheurekdjian, Haig; Lynch, Susan V; Cabana, Michael; Boushey, Homer A

    2007-07-01

    The "hygiene hypothesis" proposes that the increase in allergic diseases in developing countries reflects a decrease in infections during childhood. Cohort studies suggest, however, that the risks of asthma are increased in children who suffer severe illness from a viral respiratory infection in infancy. This apparent inconsistency can be reconciled through consideration of epidemiologic, clinical, and animal studies. The elements of this line of reasoning are that viral infections can predispose to organ-specific expression of allergic sensitization, and that the severity of illness is shaped by the maturity of immune function, which in turn is influenced by previous contact with bacteria and viruses, whether pathogenic or not. Clinical studies of children and interventional studies of animals indeed suggest that the exposure to microbes through the gastrointestinal tract powerfully shapes immune function. Intestinal microbiota differ in infants who later develop allergic diseases, and feeding Lactobacillus casei to infants at risk has been shown to reduce their rate of developing eczema. This has prompted studies of feeding probiotics as a primary prevention strategy for asthma. We propose that the efficacy of this approach depends on its success in inducing maturation of immune function important in defense against viral infection, rather than on its effectiveness in preventing allergic sensitization. It follows that the endpoints of studies of feeding probiotics to infants at risk for asthma should include not simply tests of responsiveness to allergens, but also assessment of intestinal flora, immune function, and the clinical response to respiratory viral infection. PMID:17607013

  20. Pragmatic Inferences in High-Functioning Adults with Autism and Asperger Syndrome

    ERIC Educational Resources Information Center

    Pijnacker, Judith; Hagoort, Peter; Buitelaar, Jan; Teunisse, Jan-Pieter; Geurts, Bart

    2009-01-01

    Although people with autism spectrum disorders (ASD) often have severe problems with pragmatic aspects of language, little is known about their pragmatic reasoning. We carried out a behavioral study on high-functioning adults with autistic disorder (n = 11) and Asperger syndrome (n = 17) and matched controls (n = 28) to investigate whether they…

  1. Using Functional Behavioral Assessment Data to Infer Learning Histories and Guide Interventions: A Consultation Case Study

    ERIC Educational Resources Information Center

    Parker, Megan; Skinner, Christopher; Booher, Joshua

    2010-01-01

    A teacher requested behavioral consultation services to address a first-grade student's disruptive behavior. Functional behavior assessment (FBA) suggested the behavior was being reinforced by "negative" teacher attention (e.g., reprimands, redirections, response cost). Based on this analysis, the teacher and consultant posited that this student…

  2. Inference for the median residual life function in sequential multiple assignment randomized trials

    PubMed Central

    Kidwell, Kelley M.; Ko, Jin H.; Wahed, Abdus S.

    2014-01-01

    In survival analysis, median residual lifetime is often used as a summary measure to assess treatment effectiveness; it is not clear, however, how such a quantity could be estimated for a given dynamic treatment regimen using data from sequential randomized clinical trials. We propose a method to estimate a dynamic treatment regimen-specific median residual life (MERL) function from sequential multiple assignment randomized trials. We present the MERL estimator, which is based on inverse probability weighting, as well as, two variance estimates for the MERL estimator. One variance estimate follows from Lunceford, Davidian and Tsiatis’ 2002 survival function-based variance estimate and the other uses the sandwich estimator. The MERL estimator is evaluated, and its two variance estimates are compared through simulation studies, showing that the estimator and both variance estimates produce approximately unbiased results in large samples. To demonstrate our methods, the estimator has been applied to data from a sequentially randomized leukemia clinical trial. PMID:24254496

  3. PrOnto database : GO term functional dissimilarity inferred from biological data

    PubMed Central

    Chapple, Charles E.; Herrmann, Carl; Brun, Christine

    2015-01-01

    Moonlighting proteins are defined by their involvement in multiple, unrelated functions. The computational prediction of such proteins requires a formal method of assessing the similarity of cellular processes, for example, by identifying dissimilar Gene Ontology terms. While many measures of Gene Ontology term similarity exist, most depend on abstract mathematical analyses of the structure of the GO tree and do not necessarily represent the underlying biology. Here, we propose two metrics of GO term functional dissimilarity derived from biological information, one based on the protein annotations and the other on the interactions between proteins. They have been collected in the PrOnto database, a novel tool which can be of particular use for the identification of moonlighting proteins. The database can be queried via an web-based interface which is freely available at http://tagc.univ-mrs.fr/pronto. PMID:26089836

  4. Simple Math is Enough: Two Examples of Inferring Functional Associations from Genomic Data

    NASA Technical Reports Server (NTRS)

    Liang, Shoudan

    2003-01-01

    Non-random features in the genomic data are usually biologically meaningful. The key is to choose the feature well. Having a p-value based score prioritizes the findings. If two proteins share a unusually large number of common interaction partners, they tend to be involved in the same biological process. We used this finding to predict the functions of 81 un-annotated proteins in yeast.

  5. Inferring functional connectivity in MRI using Bayesian network structure learning with a modified PC algorithm.

    PubMed

    Iyer, Swathi P; Shafran, Izhak; Grayson, David; Gates, Kathleen; Nigg, Joel T; Fair, Damien A

    2013-07-15

    Resting state functional connectivity MRI (rs-fcMRI) is a popular technique used to gauge the functional relatedness between regions in the brain for typical and special populations. Most of the work to date determines this relationship by using Pearson's correlation on BOLD fMRI timeseries. However, it has been recognized that there are at least two key limitations to this method. First, it is not possible to resolve the direct and indirect connections/influences. Second, the direction of information flow between the regions cannot be differentiated. In the current paper, we follow-up on recent work by Smith et al. (2011), and apply PC algorithm to both simulated data and empirical data to determine whether these two factors can be discerned with group average, as opposed to single subject, functional connectivity data. When applied on simulated individual subjects, the algorithm performs well determining indirect and direct connection but fails in determining directionality. However, when applied at group level, PC algorithm gives strong results for both indirect and direct connections and the direction of information flow. Applying the algorithm on empirical data, using a diffusion-weighted imaging (DWI) structural connectivity matrix as the baseline, the PC algorithm outperformed the direct correlations. We conclude that, under certain conditions, the PC algorithm leads to an improved estimate of brain network structure compared to the traditional connectivity analysis based on correlations. PMID:23501054

  6. Epigenetic regulation of human placental function and pregnancy outcome: considerations for causal inference.

    PubMed

    Januar, Vania; Desoye, Gernot; Novakovic, Boris; Cvitic, Silvija; Saffery, Richard

    2015-10-01

    Epigenetic mechanisms, often defined as regulating gene activity independently of underlying DNA sequence, are crucial for healthy development. The sum total of epigenetic marks within a cell or tissue (the epigenome) is sensitive to environmental influence, and disruption of the epigenome in utero has been associated with adverse pregnancy outcomes. Not surprisingly, given its multifaceted functions and important role in regulating pregnancy outcome, the placenta shows unique epigenetic features. Interestingly however, many of these are only otherwise seen in human malignancy (the pseudomalignant placental epigenome). Epigenetic variation in the placenta is now emerging as a candidate mediator of environmental influence on placental functioning and a key regulator of pregnancy outcome. However, replication of findings is generally lacking, most likely due to small sample sizes and a lack of standardization of analytical approaches. Defining DNA methylation "signatures" in the placenta associated with maternal and fetal outcomes offers tremendous potential to improve pregnancy outcomes, but care must be taken in interpretation of findings. Future placental epigenetic research would do well to address the issues present in epigenetic epidemiology more generally, including careful consideration of sample size, potentially confounding factors, issues of tissue heterogeneity, reverse causation, and the role of genetics in modulating epigenetic profile. The importance of animal or in vitro models in establishing a functional role of epigenetic variation identified in human beings, which is key to establishing causation, should not be underestimated. PMID:26428498

  7. A transient, quadratic nodal method for triangular-Z geometry

    SciTech Connect

    DeLorey, T.F.

    1993-06-01

    Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

  8. Coherent states for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Contreras-Astorga, Alonso; Fernández C, David J.; Velázquez, Mercedes

    2011-01-01

    The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

  9. The luminosity function at z ∼ 8 from 97 Y-band dropouts: Inferences about reionization

    SciTech Connect

    Schmidt, Kasper B.; Treu, Tommaso; Kelly, Brandon C.; Trenti, Michele; Bradley, Larry D.; Stiavelli, Massimo; Oesch, Pascal A.; Shull, J. Michael

    2014-05-01

    We present the largest search to date for Y-band dropout galaxies (z ∼ 8 Lyman break galaxies, LBGs) based on 350 arcmin{sup 2} of Hubble Space Telescope observations in the V, Y, J, and H bands from the Brightest of Reionizing Galaxies (BoRG) survey. In addition to previously published data, the BoRG13 data set presented here includes approximately 50 arcmin{sup 2} of new data and deeper observations of two previous BoRG pointings, from which we present 9 new z ∼ 8 LBG candidates, bringing the total number of BoRG Y-band dropouts to 38 with 25.5 ≤ m{sub J} ≤ 27.6 (AB system). We introduce a new Bayesian formalism for estimating the galaxy luminosity function, which does not require binning (and thus smearing) of the data and includes a likelihood based on the formally correct binomial distribution as opposed to the often-used approximate Poisson distribution. We demonstrate the utility of the new method on a sample of 97 Y-band dropouts that combines the bright BoRG galaxies with the fainter sources published in Bouwens et al. from the Hubble Ultra Deep Field and Early Release Science programs. We show that the z ∼ 8 luminosity function is well described by a Schechter function over its full dynamic range with a characteristic magnitude M{sup ⋆}=−20.15{sub −0.38}{sup +0.29}, a faint-end slope of α=−1.87{sub −0.26}{sup +0.26}, and a number density of log{sub 10} ϕ{sup ⋆}[Mpc{sup −3}]=−3.24{sub −0.24}{sup +0.25}. Integrated down to M = –17.7, this luminosity function yields a luminosity density log{sub 10} ϵ[erg s{sup −1} Hz{sup −1} Mpc{sup −3}]=25.52{sub −0.05}{sup +0.05}. Our luminosity function analysis is consistent with previously published determinations within 1σ. The error analysis suggests that uncertainties on the faint-end slope are still too large to draw a firm conclusion about its evolution with redshift. We use our statistical framework to discuss the implication of our study for the physics of

  10. Function of pretribosphenic and tribosphenic mammalian molars inferred from 3D animation.

    PubMed

    Schultz, Julia A; Martin, Thomas

    2014-10-01

    Appearance of the tribosphenic molar in the Late Jurassic (160 Ma) is a crucial innovation for food processing in mammalian evolution. This molar type is characterized by a protocone, a talonid basin and a two-phased chewing cycle, all of which are apomorphic. In this functional study on the teeth of Late Jurassic Dryolestes leiriensis and the living marsupial Monodelphis domestica, we demonstrate that pretribosphenic and tribosphenic molars show fundamental differences of food reduction strategies, representing a shift in dental function during the transition of tribosphenic mammals. By using the Occlusal Fingerprint Analyser (OFA), we simulated the chewing motions of the pretribosphenic Dryolestes that represents an evolutionary precursor condition to such tribosphenic mammals as Monodelphis. Animation of chewing path and detection of collisional contacts between virtual models of teeth suggests that Dryolestes differs from the classical two-phased chewing movement of tribosphenidans, due to the narrowing of the interdental space in cervical (crown-root transition) direction, the inclination angle of the hypoflexid groove, and the unicuspid talonid. The pretribosphenic chewing cycle is equivalent to phase I of the tribosphenic chewing cycle, but the former lacks phase II of the tribosphenic chewing. The new approach can analyze the chewing cycle of the jaw by using polygonal 3D models of tooth surfaces, in a way that is complementary to the electromyography and strain gauge studies of muscle function of living animals. The technique allows alignment and scaling of isolated fossil teeth and utilizes the wear facet orientation and striation of the teeth to reconstruct the chewing path of extinct mammals. PMID:25091547

  11. Function of pretribosphenic and tribosphenic mammalian molars inferred from 3D animation

    NASA Astrophysics Data System (ADS)

    Schultz, Julia A.; Martin, Thomas

    2014-10-01

    Appearance of the tribosphenic molar in the Late Jurassic (160 Ma) is a crucial innovation for food processing in mammalian evolution. This molar type is characterized by a protocone, a talonid basin and a two-phased chewing cycle, all of which are apomorphic. In this functional study on the teeth of Late Jurassic Dryolestes leiriensis and the living marsupial Monodelphis domestica, we demonstrate that pretribosphenic and tribosphenic molars show fundamental differences of food reduction strategies, representing a shift in dental function during the transition of tribosphenic mammals. By using the Occlusal Fingerprint Analyser (OFA), we simulated the chewing motions of the pretribosphenic Dryolestes that represents an evolutionary precursor condition to such tribosphenic mammals as Monodelphis. Animation of chewing path and detection of collisional contacts between virtual models of teeth suggests that Dryolestes differs from the classical two-phased chewing movement of tribosphenidans, due to the narrowing of the interdental space in cervical (crown-root transition) direction, the inclination angle of the hypoflexid groove, and the unicuspid talonid. The pretribosphenic chewing cycle is equivalent to phase I of the tribosphenic chewing cycle, but the former lacks phase II of the tribosphenic chewing. The new approach can analyze the chewing cycle of the jaw by using polygonal 3D models of tooth surfaces, in a way that is complementary to the electromyography and strain gauge studies of muscle function of living animals. The technique allows alignment and scaling of isolated fossil teeth and utilizes the wear facet orientation and striation of the teeth to reconstruct the chewing path of extinct mammals.

  12. Inferring cortical function in the mouse visual system through large-scale systems neuroscience.

    PubMed

    Hawrylycz, Michael; Anastassiou, Costas; Arkhipov, Anton; Berg, Jim; Buice, Michael; Cain, Nicholas; Gouwens, Nathan W; Gratiy, Sergey; Iyer, Ramakrishnan; Lee, Jung Hoon; Mihalas, Stefan; Mitelut, Catalin; Olsen, Shawn; Reid, R Clay; Teeter, Corinne; de Vries, Saskia; Waters, Jack; Zeng, Hongkui; Koch, Christof

    2016-07-01

    The scientific mission of the Project MindScope is to understand neocortex, the part of the mammalian brain that gives rise to perception, memory, intelligence, and consciousness. We seek to quantitatively evaluate the hypothesis that neocortex is a relatively homogeneous tissue, with smaller functional modules that perform a common computational function replicated across regions. We here focus on the mouse as a mammalian model organism with genetics, physiology, and behavior that can be readily studied and manipulated in the laboratory. We seek to describe the operation of cortical circuitry at the computational level by comprehensively cataloging and characterizing its cellular building blocks along with their dynamics and their cell type-specific connectivities. The project is also building large-scale experimental platforms (i.e., brain observatories) to record the activity of large populations of cortical neurons in behaving mice subject to visual stimuli. A primary goal is to understand the series of operations from visual input in the retina to behavior by observing and modeling the physical transformations of signals in the corticothalamic system. We here focus on the contribution that computer modeling and theory make to this long-term effort. PMID:27382147

  13. Bayesian nonparametric inference on quantile residual life function: Application to breast cancer data.

    PubMed

    Park, Taeyoung; Jeong, Jong-Hyeon; Lee, Jae Won

    2012-08-15

    There is often an interest in estimating a residual life function as a summary measure of survival data. For ease in presentation of the potential therapeutic effect of a new drug, investigators may summarize survival data in terms of the remaining life years of patients. Under heavy right censoring, however, some reasonably high quantiles (e.g., median) of a residual lifetime distribution cannot be always estimated via a popular nonparametric approach on the basis of the Kaplan-Meier estimator. To overcome the difficulties in dealing with heavily censored survival data, this paper develops a Bayesian nonparametric approach that takes advantage of a fully model-based but highly flexible probabilistic framework. We use a Dirichlet process mixture of Weibull distributions to avoid strong parametric assumptions on the unknown failure time distribution, making it possible to estimate any quantile residual life function under heavy censoring. Posterior computation through Markov chain Monte Carlo is straightforward and efficient because of conjugacy properties and partial collapse. We illustrate the proposed methods by using both simulated data and heavily censored survival data from a recent breast cancer clinical trial conducted by the National Surgical Adjuvant Breast and Bowel Project. PMID:22437758

  14. Functional morphology of the hallucal metatarsal with implications for inferring grasping ability in extinct primates.

    PubMed

    Goodenberger, Katherine E; Boyer, Doug M; Orr, Caley M; Jacobs, Rachel L; Femiani, John C; Patel, Biren A

    2015-03-01

    Primate evolutionary morphologists have argued that selection for life in a fine branch niche resulted in grasping specializations that are reflected in the hallucal metatarsal (Mt1) morphology of extant "prosimians", while a transition to use of relatively larger, horizontal substrates explains the apparent loss of such characters in anthropoids. Accordingly, these morphological characters-Mt1 torsion, peroneal process length and thickness, and physiological abduction angle-have been used to reconstruct grasping ability and locomotor mode in the earliest fossil primates. Although these characters are prominently featured in debates on the origin and subsequent radiation of Primates, questions remain about their functional significance. This study examines the relationship between these morphological characters of the Mt1 and a novel metric of pedal grasping ability for a large number of extant taxa in a phylogenetic framework. Results indicate greater Mt1 torsion in taxa that engage in hallucal grasping and in those that utilize relatively small substrates more frequently. This study provides evidence that Carpolestes simpsoni has a torsion value more similar to grasping primates than to any scandentian. The results also show that taxa that habitually grasp vertical substrates are distinguished from other taxa in having relatively longer peroneal processes. Furthermore, a longer peroneal process is also correlated with calcaneal elongation, a metric previously found to reflect leaping proclivity. A more refined understanding of the functional associations between Mt1 morphology and behavior in extant primates enhances the potential for using these morphological characters to comprehend primate (locomotor) evolution. PMID:25378276

  15. Inferring cortical function in the mouse visual system through large-scale systems neuroscience

    PubMed Central

    Hawrylycz, Michael; Anastassiou, Costas; Arkhipov, Anton; Berg, Jim; Buice, Michael; Cain, Nicholas; Gouwens, Nathan W.; Gratiy, Sergey; Iyer, Ramakrishnan; Lee, Jung Hoon; Mihalas, Stefan; Mitelut, Catalin; Olsen, Shawn; Reid, R. Clay; Teeter, Corinne; de Vries, Saskia; Waters, Jack; Zeng, Hongkui; Koch, Christof

    2016-01-01

    The scientific mission of the Project MindScope is to understand neocortex, the part of the mammalian brain that gives rise to perception, memory, intelligence, and consciousness. We seek to quantitatively evaluate the hypothesis that neocortex is a relatively homogeneous tissue, with smaller functional modules that perform a common computational function replicated across regions. We here focus on the mouse as a mammalian model organism with genetics, physiology, and behavior that can be readily studied and manipulated in the laboratory. We seek to describe the operation of cortical circuitry at the computational level by comprehensively cataloging and characterizing its cellular building blocks along with their dynamics and their cell type-specific connectivities. The project is also building large-scale experimental platforms (i.e., brain observatories) to record the activity of large populations of cortical neurons in behaving mice subject to visual stimuli. A primary goal is to understand the series of operations from visual input in the retina to behavior by observing and modeling the physical transformations of signals in the corticothalamic system. We here focus on the contribution that computer modeling and theory make to this long-term effort. PMID:27382147

  16. Bayesian inference in an item response theory model with a generalized student t link function

    NASA Astrophysics Data System (ADS)

    Azevedo, Caio L. N.; Migon, Helio S.

    2012-10-01

    In this paper we introduce a new item response theory (IRT) model with a generalized Student t-link function with unknown degrees of freedom (df), named generalized t-link (GtL) IRT model. In this model we consider only the difficulty parameter in the item response function. GtL is an alternative to the two parameter logit and probit models, since the degrees of freedom (df) play a similar role to the discrimination parameter. However, the behavior of the curves of the GtL is different from those of the two parameter models and the usual Student t link, since in GtL the curve obtained from different df's can cross the probit curves in more than one latent trait level. The GtL model has similar proprieties to the generalized linear mixed models, such as the existence of sufficient statistics and easy parameter interpretation. Also, many techniques of parameter estimation, model fit assessment and residual analysis developed for that models can be used for the GtL model. We develop fully Bayesian estimation and model fit assessment tools through a Metropolis-Hastings step within Gibbs sampling algorithm. We consider a prior sensitivity choice concerning the degrees of freedom. The simulation study indicates that the algorithm recovers all parameters properly. In addition, some Bayesian model fit assessment tools are considered. Finally, a real data set is analyzed using our approach and other usual models. The results indicate that our model fits the data better than the two parameter models.

  17. Crustal structure beneath the Japanese Islands inferred from receiver function analysis using similar earthquakes

    NASA Astrophysics Data System (ADS)

    Igarashi, Toshihiro

    2016-04-01

    The stress concentration and strain accumulation process due to inter-plate coupling of the subducting plate should have a large effect on inland shallow earthquakes that occur in the overriding plate. Information on the crustal structure and the crustal thickness is important to understanding their process. In this study, I applied receiver function analysis using similar earthquakes to estimate the crustal velocity structures beneath the Japanese Islands. Because similar earthquakes are caused repeatedly at almost the same place, they are useful for extracting information on spatial distribution and temporal changes of seismic velocity structures beneath the seismic stations. I used telemetric seismographic network data covered the Japanese Islands and moderate-sized similar earthquakes which occurred in the southern Hemisphere with epicentral distances between 30 and 90 degrees for about 26 years from October 1989. Data analysis was performed separately before and after the 2011 Tohoku-Oki earthquake. To identify the spatial distribution of crustal structure, I searched for the best-correlated model between an observed receiver function at each station and synthetic ones by using a grid search method. As results, I clarified the spatial distribution of the crustal velocity structures. The spatial patterns of velocities from the ground surface to 5 km deep are corresponding with basement depth models although the velocities are slower than those of tomography models. They indicate thick sediment layers in several plain and basin areas. The crustal velocity perturbations are consistent with existing tomography models. The active volcanoes correspond low-velocity zones from the upper crust to the crust-mantle transition. A comparison of the crustal structure before and after the 2011 Tohoku-Oki earthquake suggests that the northeastern Japan arc changed to lower velocities in some areas. This kind of velocity changes might be due to other effects such as changes of

  18. Sediment thickness beneath the Indo-Gangetic Plain and Siwalik Himalaya inferred from receiver function modelling

    NASA Astrophysics Data System (ADS)

    Borah, Kajaljyoti; Kanna, Nagaraju; Rai, S. S.; Prakasam, K. S.

    2015-03-01

    The Indo-Gangetic Plain and the adjoining Siwalik Himalaya are the seismically most vulnerable regions due to high density of human population and presence of thick sediments that amplify the seismic waves due to an earthquake in the region. We investigate the sedimentary structure and crustal thickness of the region through joint inversion of the receiver function time series at 14 broadband seismograph locations and the available Rayleigh velocity data for the region. Results show significant variability of sedimentary layer thicknesses from 1.0 to 2.0 km beneath the Delhi region to 2.0-5.0 km beneath the Indo-Gangetic Plain and the Siwalik Himalaya. As we progress from the Delhi to the Indo-Gangetic Plain, we observe a decrease in the shear velocity in sedimentary layer from ∼2.0 km/s to ∼1.3 km/s while the layer thickness increases progressively from ∼1.0 km in south to 2.0-5.0 km in the north. Average S-velocity in the sedimentary layer beneath the Siwalik Himalaya is ∼2.1 km/s. Crustal thicknesses varies from ∼42 in the Delhi region, ∼48 km in the Indo-Gangetic Plain, ∼50 km in the western part of Siwalik Himalaya to ∼60 km in the Kumaon region of Siwalik Himalaya.

  19. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    NASA Astrophysics Data System (ADS)

    Fernández, Francisco M.

    2016-06-01

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.

  20. On Volterra quadratic stochastic operators with continual state space

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-15

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  1. Quadratic expressions by means of `summing all the matchsticks'

    NASA Astrophysics Data System (ADS)

    Faaiz Gierdien, M.

    2012-09-01

    This note presents demonstrations of quadratic expressions that come about when particular problems are posed with respect to matchsticks that form regular triangles, squares, pentagons and so on. Usually when such 'matchstick' problems are used as ways to foster algebraic thinking, the expressions for the number of matchstick quantities are linear and not quadratic. It will be shown that a pedagogy of 'summing all the matchsticks' is central to the emergence of quadratic expressions. This pedagogy involves generational and transformational activities which are considered as some of the main activities of algebra. Key elements to these activities are processes such as recognizing and extending patterns, and specializing and generalizing particular functional relationships. Implications of these processes in terms of algebraic thinking are considered.

  2. On Volterra quadratic stochastic operators with continual state space

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-01

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (V λ )(A ) = ∫X ∫X P (x ,y ,A )d λ (x )d λ (y ), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim n →∞ Vn(λ ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  3. The SWELLS survey - VI. Hierarchical inference of the initial mass functions of bulges and discs

    NASA Astrophysics Data System (ADS)

    Brewer, Brendon J.; Marshall, Philip J.; Auger, Matthew W.; Treu, Tommaso; Dutton, Aaron A.; Barnabè, Matteo

    2014-01-01

    The long-standing assumption that the stellar initial mass function (IMF) is universal has recently been challenged by a number of observations. Several studies have shown that a `heavy' IMF (e.g. with a Salpeter-like abundance of low-mass stars and thus normalization) is preferred for massive early-type galaxies, while this IMF is inconsistent with the properties of less massive, later-type galaxies. These discoveries motivate the hypothesis that the IMF may vary (possibly very slightly) across galaxies and across components of individual galaxies (e.g. bulges versus discs). In this paper, we use a sample of 19 late-type strong gravitational lenses from the Sloan WFC Edge-on Late-type Lens Survey (SWELLS) to investigate the IMFs of the bulges and discs in late-type galaxies. We perform a joint analysis of the galaxies' total masses (constrained by strong gravitational lensing) and stellar masses (constrained by optical and near-infrared colours in the context of a stellar population synthesis model, up to an IMF normalization parameter). Using minimal assumptions apart from the physical constraint that the total stellar mass m* within any aperture must be less than the total mass mtot within the aperture, we find that the bulges of the galaxies cannot have IMFs heavier (i.e. implying high mass per unit luminosity) than Salpeter, while the disc IMFs are not well constrained by this data set. We also discuss the necessity for hierarchical modelling when combining incomplete information about multiple astronomical objects. This modelling approach allows us to place upper limits on the size of any departures from universality. More data, including spatially resolved kinematics (as in Paper V) and stellar population diagnostics over a range of bulge and disc masses, are needed to robustly quantify how the IMF varies within galaxies.

  4. Seismic Discontinuities within the Crust and Mantle Beneath Indonesia as Inferred from P Receiver Functions

    NASA Astrophysics Data System (ADS)

    Woelbern, I.; Rumpker, G.

    2015-12-01

    Indonesia is situated at the southern margin of SE Asia, which comprises an assemblage of Gondwana-derived continental terranes, suture zones and volcanic arcs. The formation of SE Asia is believed to have started in Early Devonian. Its complex history involves the opening and closure of three distinct Tethys oceans, each accompanied by the rifting of continental fragments. We apply the receiver function technique to data of the temporary MERAMEX network operated in Central Java from May to October 2004 by the GeoForschungsZentrum Potsdam. The network consisted of 112 mobile stations with a spacing of about 10 km covering the full width of the island between the southern and northern coast lines. The tectonic history is reflected in a complex crustal structure of Central Java exhibiting strong topography of the Moho discontinuity related to different tectonic units. A discontinuity of negative impedance contrast is observed throughout the mid-crust interpreted as the top of a low-velocity layer which shows no depth correlation with the Moho interface. Converted phases generated at greater depth beneath Indonesia indicate the existence of multiple seismic discontinuities within the upper mantle and even below. The strongest signal originates from the base of the mantle transition zone, i.e. the 660 km discontinuity. The phase related to the 410 km discontinuity is less pronounced, but clearly identifiable as well. The derived thickness of the mantle-transition zone is in good agreement with the IASP91 velocity model. Additional phases are observed at roughly 33 s and 90 s relative to the P onset, corresponding to about 300 km and 920 km, respectively. A signal of reversed polarity indicates the top of a low velocity layer at about 370 km depth overlying the mantle transition zone.

  5. Complex geometry of the subducted Pacific slab inferred from receiver function

    NASA Astrophysics Data System (ADS)

    Zhang, Ruiqing; Wu, Qingju; Zhang, Guangcheng

    2014-05-01

    In recent years, slab tear has received considerable attention and been reported in many arc-arc junctures in Pacific plate subdution zones. From 2009 to 2011, we deployed two portable experiments equipped with CMG-3ESPC seismometers and the recorders of REFTEK-130B in NE China. The two linear seismic arrays were designed nearly parallel, and each of them containing about 60 seismic stations extended about 1200 km from west to east spanning all surface geological terrains of NE China. The south one was firstly set up and continually operated over two year, while the north deployment worked only about one year. By using the teleseismic data collected by these two arrays, we calculate the P receiver functions to map topographic variation of the upper mantle discontinuities. Our sampled region is located where the juncture between the subducting Kuril and Japan slabs reaches the 660-km discontinuity. Distinct variation of the 660-km discontinuity is mapped beneath the regions. A deeper-than-normal 660 km discontinuity is observed locally in the southeastern part of our sampled region. The depression of the 660 km discontinuity may be resulted from an oceanic lithospheric slab deflected in the mantle transition zone, in good agreement with the result of earlier tomographic and other seismic studies in this region. The northeastern portion of our sampled region, however, does not show clearly the deflection of the slab. The variation of the tomography of the 660-km discontinuity in our sampled regions may indicate a complex geometry of the subducted Pacific slab.

  6. Why are dunkels sticky? Preschoolers infer functionality and intentional creation for artifact properties learned from generic language.

    PubMed

    Cimpian, Andrei; Cadena, Cristina

    2010-10-01

    Artifacts pose a potential learning problem for children because the mapping between their features and their functions is often not transparent. In solving this problem, children are likely to rely on a number of information sources (e.g., others' actions, affordances). We argue that children's sensitivity to nuances in the language used to describe artifacts is an important, but so far unacknowledged, piece of this puzzle. Specifically, we hypothesize that children are sensitive to whether an unfamiliar artifact's features are highlighted using generic (e.g., "Dunkels are sticky") or non-generic (e.g., "This dunkel is sticky") language. Across two studies, older-but not younger-preschoolers who heard such features introduced via generic statements inferred that they are a functional part of the artifact's design more often than children who heard the same features introduced via non-generic statements. The ability to pick up on this linguistic cue may expand considerably the amount of conceptual information about artifacts that children derive from conversations with adults. PMID:20656283

  7. A Version of Quadratic Regression with Interpretable Parameters.

    ERIC Educational Resources Information Center

    Cudeck, Robert; du Toit, Stephen H. C.

    2002-01-01

    Suggests an alternative form of the quadratic model that has the same expectation function of the original model but has the useful feature that its parameters are interpretable. Provides examples of a simple regression problem and a nonlinear mixed-effects model. (SLD)

  8. Geometrical and Graphical Solutions of Quadratic Equations.

    ERIC Educational Resources Information Center

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  9. Single-photon quadratic optomechanics

    PubMed Central

    Liao, Jie-Qiao; Nori, Franco

    2014-01-01

    We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128

  10. Large-scale sequential quadratic programming algorithms

    SciTech Connect

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  11. Maximization of Sums of Quotients of Quadratic Forms and Some Generalizations.

    ERIC Educational Resources Information Center

    Kiers, Henk A. L.

    1995-01-01

    Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)

  12. POGs2: A Web Portal to Facilitate Cross-Species Inferences About Protein Architecture and Function in Plants

    PubMed Central

    Tomcal, Michael; Stiffler, Nicholas; Barkan, Alice

    2013-01-01

    The Putative orthologous Groups 2 Database (POGs2) (http://pogs.uoregon.edu/) integrates information about the inferred proteomes of four plant species (Arabidopsis thaliana, Zea mays, Orza sativa, and Populus trichocarpa) in a display that facilitates comparisons among orthologs and extrapolation of annotations among species. A single-page view collates key functional data for members of each Putative Orthologous Group (POG): graphical representations of InterPro domains, predicted and established intracellular locations, and imported gene descriptions. The display incorporates POGs predicted by two different algorithms as well as gene trees, allowing users to evaluate the validity of POG memberships. The web interface provides ready access to sequences and alignments of POG members, as well as sequences, alignments, and domain architectures of closely-related paralogs. A simple and flexible search interface permits queries by BLAST and by any combination of gene identifier, keywords, domain names, InterPro identifiers, and intracellular location. The concurrent display of domain architectures for orthologous proteins highlights errors in gene models and false-negatives in domain predictions. The POGs2 layout is also useful for exploring candidate genes identified by transposon tagging, QTL mapping, map-based cloning, and proteomics, and for navigating between orthologous groups that belong to the same gene family. PMID:24340041

  13. POGs2: a web portal to facilitate cross-species inferences about protein architecture and function in plants.

    PubMed

    Tomcal, Michael; Stiffler, Nicholas; Barkan, Alice

    2013-01-01

    The Putative orthologous Groups 2 Database (POGs2) (http://pogs.uoregon.edu/) integrates information about the inferred proteomes of four plant species (Arabidopsis thaliana, Zea mays, Orza sativa, and Populus trichocarpa) in a display that facilitates comparisons among orthologs and extrapolation of annotations among species. A single-page view collates key functional data for members of each Putative Orthologous Group (POG): graphical representations of InterPro domains, predicted and established intracellular locations, and imported gene descriptions. The display incorporates POGs predicted by two different algorithms as well as gene trees, allowing users to evaluate the validity of POG memberships. The web interface provides ready access to sequences and alignments of POG members, as well as sequences, alignments, and domain architectures of closely-related paralogs. A simple and flexible search interface permits queries by BLAST and by any combination of gene identifier, keywords, domain names, InterPro identifiers, and intracellular location. The concurrent display of domain architectures for orthologous proteins highlights errors in gene models and false-negatives in domain predictions. The POGs2 layout is also useful for exploring candidate genes identified by transposon tagging, QTL mapping, map-based cloning, and proteomics, and for navigating between orthologous groups that belong to the same gene family. PMID:24340041

  14. Entropic Inference

    NASA Astrophysics Data System (ADS)

    Caticha, Ariel

    2011-03-01

    In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme.

  15. Binary Quadratic Forms: A Historical View

    ERIC Educational Resources Information Center

    Khosravani, Azar N.; Beintema, Mark B.

    2006-01-01

    We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

  16. Factorising a Quadratic Expression with Geometric Insights

    ERIC Educational Resources Information Center

    Joarder, Anwar H.

    2015-01-01

    An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

  17. THE PANCHROMATIC HUBBLE ANDROMEDA TREASURY. IV. A PROBABILISTIC APPROACH TO INFERRING THE HIGH-MASS STELLAR INITIAL MASS FUNCTION AND OTHER POWER-LAW FUNCTIONS

    SciTech Connect

    Weisz, Daniel R.; Fouesneau, Morgan; Dalcanton, Julianne J.; Clifton Johnson, L.; Beerman, Lori C.; Williams, Benjamin F.; Hogg, David W.; Foreman-Mackey, Daniel T.; Rix, Hans-Walter; Gouliermis, Dimitrios; Dolphin, Andrew E.; Lang, Dustin; Bell, Eric F.; Gordon, Karl D.; Kalirai, Jason S.; Skillman, Evan D.

    2013-01-10

    We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the

  18. The Panchromatic Hubble Andromeda Treasury. IV. A Probabilistic Approach to Inferring the High-mass Stellar Initial Mass Function and Other Power-law Functions

    NASA Astrophysics Data System (ADS)

    Weisz, Daniel R.; Fouesneau, Morgan; Hogg, David W.; Rix, Hans-Walter; Dolphin, Andrew E.; Dalcanton, Julianne J.; Foreman-Mackey, Daniel T.; Lang, Dustin; Johnson, L. Clifton; Beerman, Lori C.; Bell, Eric F.; Gordon, Karl D.; Gouliermis, Dimitrios; Kalirai, Jason S.; Skillman, Evan D.; Williams, Benjamin F.

    2013-01-01

    We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M >~ 1 M ⊙). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, α, are unbiased and that the uncertainty, Δα, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on α, and provide an analytic approximation for Δα as a function of the observed number of stars and mass range. Comparison with literature studies shows that ~3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield langαrang = 2.46, with a 1σ dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF

  19. Quadratic invariants for discrete clusters of weakly interacting waves

    NASA Astrophysics Data System (ADS)

    Harper, Katie L.; Bustamante, Miguel D.; Nazarenko, Sergey V.

    2013-06-01

    We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix {A} with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N - M* ⩾ N - M, where M* is the number of linearly independent rows in {A}. Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney-Hasegawa-Mima wave model, and by showing a classification of small (up to three-triad) clusters.

  20. Perceptual inference.

    PubMed

    Aggelopoulos, Nikolaos C

    2015-08-01

    Perceptual inference refers to the ability to infer sensory stimuli from predictions that result from internal neural representations built through prior experience. Methods of Bayesian statistical inference and decision theory model cognition adequately by using error sensing either in guiding action or in "generative" models that predict the sensory information. In this framework, perception can be seen as a process qualitatively distinct from sensation, a process of information evaluation using previously acquired and stored representations (memories) that is guided by sensory feedback. The stored representations can be utilised as internal models of sensory stimuli enabling long term associations, for example in operant conditioning. Evidence for perceptual inference is contributed by such phenomena as the cortical co-localisation of object perception with object memory, the response invariance in the responses of some neurons to variations in the stimulus, as well as from situations in which perception can be dissociated from sensation. In the context of perceptual inference, sensory areas of the cerebral cortex that have been facilitated by a priming signal may be regarded as comparators in a closed feedback loop, similar to the better known motor reflexes in the sensorimotor system. The adult cerebral cortex can be regarded as similar to a servomechanism, in using sensory feedback to correct internal models, producing predictions of the outside world on the basis of past experience. PMID:25976632

  1. Quadratic boundedness of uncertain nonlinear dynamic systems

    NASA Astrophysics Data System (ADS)

    Brockman, Mark Lawrence

    Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.

  2. Crustal anisotropy in northeastern Tibetan Plateau inferred from receiver functions: Rock textures caused by metamorphic fluids and lower crust flow?

    NASA Astrophysics Data System (ADS)

    Liu, Zhen; Park, Jeffrey; Rye, Danny M.

    2015-10-01

    The crust of Tibetan Plateau may have formed via shortening/thickening or large-scale underthrusting, and subsequently modified via lower crust channel flows and volatile-mediated regional metamorphism. The amplitude and distribution of crustal anisotropy record the history of continental deformation, offering clues to its formation and later modification. In this study, we first investigate the back-azimuth dependence of Ps converted phases using multitaper receiver functions (RFs). We analyze teleseismic data for 35 temporary broadband stations in the ASCENT experiment located in northeastern Tibet. We stack receiver functions after a moving-window moveout correction. Major features of RFs include: 1) Ps arrivals at 8-10 s on the radial components, suggesting a 70-90-km crustal thickness in the study area; 2) two-lobed back-azimuth variation for intra-crustal Ps phases in the upper crust (< 20 km), consistent with tilted symmetry axis anisotropy or dipping interfaces; 3) significant Ps arrivals with four-lobed back-azimuth variation distributed in distinct layers in the middle and lower crust (up to 60 km), corresponding to (sub)horizontal-axis anisotropy; and 4) weak or no evidence of azimuthal anisotropy in the lowermost crust. To study the anisotropy, we compare the observed RF stacks with one-dimensional reflectivity synthetic seismograms in anisotropic media, and fit major features by "trial and error" forward modeling. Crustal anisotropy offers few clues on plateau formation, but strong evidence of ongoing deformation and metamorphism. We infer strong horizontal-axis anisotropy concentrated in the middle and lower crust, which could be explained by vertically aligned sheet silicates, open cracks filled with magma or other fluid, vertical vein structures or by 1-10-km-scale chimney structures that have focused metamorphic fluids. Simple dynamic models encounter difficulty in generating vertically aligned sheet silicates. Instead, we interpret our data to

  3. Seven Wonders of the Ancient and Modern Quadratic World.

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2001-01-01

    Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

  4. MicroRNA-Target Network Inference and Local Network Enrichment Analysis Identify Two microRNA Clusters with Distinct Functions in Head and Neck Squamous Cell Carcinoma

    PubMed Central

    Sass, Steffen; Pitea, Adriana; Unger, Kristian; Hess, Julia; Mueller, Nikola S.; Theis, Fabian J.

    2015-01-01

    MicroRNAs represent ~22 nt long endogenous small RNA molecules that have been experimentally shown to regulate gene expression post-transcriptionally. One main interest in miRNA research is the investigation of their functional roles, which can typically be accomplished by identification of mi-/mRNA interactions and functional annotation of target gene sets. We here present a novel method “miRlastic”, which infers miRNA-target interactions using transcriptomic data as well as prior knowledge and performs functional annotation of target genes by exploiting the local structure of the inferred network. For the network inference, we applied linear regression modeling with elastic net regularization on matched microRNA and messenger RNA expression profiling data to perform feature selection on prior knowledge from sequence-based target prediction resources. The novelty of miRlastic inference originates in predicting data-driven intra-transcriptome regulatory relationships through feature selection. With synthetic data, we showed that miRlastic outperformed commonly used methods and was suitable even for low sample sizes. To gain insight into the functional role of miRNAs and to determine joint functional properties of miRNA clusters, we introduced a local enrichment analysis procedure. The principle of this procedure lies in identifying regions of high functional similarity by evaluating the shortest paths between genes in the network. We can finally assign functional roles to the miRNAs by taking their regulatory relationships into account. We thoroughly evaluated miRlastic on a cohort of head and neck cancer (HNSCC) patients provided by The Cancer Genome Atlas. We inferred an mi-/mRNA regulatory network for human papilloma virus (HPV)-associated miRNAs in HNSCC. The resulting network best enriched for experimentally validated miRNA-target interaction, when compared to common methods. Finally, the local enrichment step identified two functional clusters of mi

  5. Functional characterization of somatic mutations in cancer using network-based inference of protein activity | Office of Cancer Genomics

    Cancer.gov

    Identifying the multiple dysregulated oncoproteins that contribute to tumorigenesis in a given patient is crucial for developing personalized treatment plans. However, accurate inference of aberrant protein activity in biological samples is still challenging as genetic alterations are only partially predictive and direct measurements of protein activity are generally not feasible.

  6. Quadratic Stochastic Operators with Countable State Space

    NASA Astrophysics Data System (ADS)

    Ganikhodjaev, Nasir

    2016-03-01

    In this paper, we provide the classes of Poisson and Geometric quadratic stochastic operators with countable state space, study the dynamics of these operators and discuss their application to economics.

  7. Schur Stability Regions for Complex Quadratic Polynomials

    ERIC Educational Resources Information Center

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  8. Quantum integrability of quadratic Killing tensors

    SciTech Connect

    Duval, C.; Valent, G.

    2005-05-01

    Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.

  9. Quadratic nonlinear Klein-Gordon equation in one dimension

    NASA Astrophysics Data System (ADS)

    Hayashi, Nakao; Naumkin, Pavel I.

    2012-10-01

    We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = λv2, t ∈ R, x ∈ R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ∈ R, where v0 and v1 are real-valued functions, λ ∈ R. Using the method of normal forms of Shatah ["Normal forms and quadratic nonlinear Klein-Gordon equations," Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort ["Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1," Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

  10. Exploring {{W}}_{∞ } in the quadratic basis

    NASA Astrophysics Data System (ADS)

    Procházka, Tomáš

    2015-09-01

    We study the operator product expansions in the chiral algebra {W}_{∞ } , first using the associativity conditions in the basis of primary generating fields and then using a different basis coming from the free field representation in which the OPE takes a simpler quadratic form. The results in the quadratic basis can be compactly written using certain bilocal combinations of the generating fields and we conjecture a closed-form expression for the complete OPE in this basis. Next we show that the commutation relations as well as correlation functions can be easily computed using properties of these bilocal fields. In the last part we verify the consistency with results derived previously by studying minimal models of {W}_{∞ } and comparing them to known reductions of {W}_{∞ } to {W}_N . The results we obtain illustrate nicely the role of triality symmetry in the representation theory of {W}_{∞ }.

  11. Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators

    NASA Astrophysics Data System (ADS)

    Marquette, Ian

    2011-06-01

    We present a generalized Kaluza-Klein monopole system. We solve this quantum superintegrable system on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schrödinger equation in spherical and parabolic coordinates. We present the integrals of motion of this system, the quadratic algebra generated by these integrals, the realization in terms of a deformed oscillator algebra using the Daskaloyannis construction and the energy spectrum. The structure constants and the Casimir operator are functions not only of the Hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an Abelian subalgebra. We present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators.

  12. The Factorability of Quadratics: Motivation for More Techniques

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2005-01-01

    Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

  13. Biases in the inferred mass-to-light ratio of globular clusters: no need for variations in the stellar mass function

    NASA Astrophysics Data System (ADS)

    Shanahan, Rosemary L.; Gieles, Mark

    2015-03-01

    From a study of the integrated light properties of 200 globular clusters (GCs) in M31, Strader et al. found that the mass-to-light ratios are lower than what is expected from simple stellar population models with a `canonical' stellar initial mass function (IMF), with the discrepancy being larger at high metallicities. We use dynamical multimass models, that include a prescription for equipartition, to quantify the bias in the inferred dynamical mass as the result of the assumption that light follows mass. For a universal IMF and a metallicity-dependent present-day mass function, we find that the inferred mass from integrated light properties systematically underestimates the true mass, and that the bias is more important at high metallicities, as was found for the M31 GCs. We show that mass segregation and a flattening of the mass function have opposing effects of similar magnitude on the mass inferred from integrated properties. This makes the mass-to-light ratio as derived from integrated properties an inadequate probe of the low-mass end of the stellar mass function. There is, therefore, no need for variations in the IMF, nor the need to invoke depletion of low-mass stars, to explain the observations. Finally, we find that the retention fraction of stellar-mass black holes (BHs) is an equally important parameter in understanding the mass segregation bias. We speculatively put forward to idea that kinematical data of GCs can in fact be used to constrain the total mass in stellar-mass BHs in GCs.

  14. Solution of the Dirac equation with some superintegrable potentials by the quadratic algebra approach

    NASA Astrophysics Data System (ADS)

    Aghaei, S.; Chenaghlou, A.

    2014-02-01

    The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E8 (case (3b)), S4 and S2, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

  15. PHYSICAL FOUNDATIONS OF QUANTUM ELECTRONICS: A study of radiation propagation in a medium with quadratic inhomogeneity

    NASA Astrophysics Data System (ADS)

    Pikulev, A. A.

    2001-09-01

    The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed.

  16. Fast approximate quadratic programming for graph matching.

    PubMed

    Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  17. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  18. Limit cycles near hyperbolas in quadratic systems

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume

    In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.

  19. Quadratic forms of projective spaces over rings

    NASA Astrophysics Data System (ADS)

    Levchuk, V. M.; Starikova, O. A.

    2006-06-01

    In the passage from fields to rings of coefficients quadratic forms with invertible matrices lose their decisive role. It turns out that if all quadratic forms over a ring are diagonalizable, then in effect this is always a local principal ideal ring R with 2\\in R^*. The problem of the construction of a `normal' diagonal form of a quadratic form over a ring R faces obstacles in the case of indices \\vert R^*:R^{*2}\\vert greater than 1. In the case of index 2 this problem has a solution given in Theorem 2.1 for 1+R^{*2}\\subseteq R^{*2} (an extension of the law of inertia for real quadratic forms) and in Theorem 2.2 for 1+R^2 containing an invertible non-square. Under the same conditions on a ring R with nilpotent maximal ideal the number of classes of projectively congruent quadratic forms of the projective space associated with a free R-module of rank n is explicitly calculated (Proposition 3.2). Up to projectivities, the list of forms is presented for the projective plane over R and also (Theorem 3.3) over the local ring F\\lbrack\\lbrack x,y\\rbrack\\rbrack/\\langle x^{2},xy,y^{2}\\rangle with non-principal maximal ideal, where F=2F is a field with an invertible non-square in 1+F^{2} and \\vert F^{*}:F^{*2}\\vert=2. In the latter case the number of classes of non-diagonalizable quadratic forms of rank 0 depends on one's choice of the field F and is not even always finite; all the other forms make up 21 classes.

  20. Quintessence with quadratic coupling to dark matter

    SciTech Connect

    Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy

    2010-04-15

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  1. Heredity in one-dimensional quadratic maps

    NASA Astrophysics Data System (ADS)

    Romera, M.; Pastor, G.; Alvarez, G.; Montoya, F.

    1998-12-01

    In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found, and the ancestral path that joins all its ancestors. The ancestral path holds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the pattern constitute the family tree of the pattern, which is important to study and understand the orbit's ordering.

  2. On orthogonality preserving quadratic stochastic operators

    SciTech Connect

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  3. Quadratic-Like Dynamics of Cubic Polynomials

    NASA Astrophysics Data System (ADS)

    Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen

    2016-02-01

    A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.

  4. Structured Functional Principal Component Analysis

    PubMed Central

    Shou, Haochang; Zipunnikov, Vadim; Crainiceanu, Ciprian M.; Greven, Sonja

    2015-01-01

    Summary Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep. PMID:25327216

  5. Structured functional principal component analysis.

    PubMed

    Shou, Haochang; Zipunnikov, Vadim; Crainiceanu, Ciprian M; Greven, Sonja

    2015-03-01

    Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for high-dimensional data. Methods are used in applications including high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep. PMID:25327216

  6. Quadratic minima and modular forms II

    NASA Astrophysics Data System (ADS)

    Brent, Barry

    We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two even positive-definite quadratic form. These bounds extend partial results in part I.

  7. Curious Consequences of a Miscopied Quadratic

    ERIC Educational Resources Information Center

    Poet, Jeffrey L.; Vestal, Donald L., Jr.

    2005-01-01

    The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

  8. Fourier analysis of quadratic phase interferograms

    NASA Astrophysics Data System (ADS)

    Muñoz-Maciel, Jesús; Mora-González, Miguel; Casillas-Rodríguez, Francisco J.; Peña-Lecona, Francisco G.

    2015-06-01

    A phase demodulation method from a single interferogram with a quadratic phase term is developed. The fringe pattern being analysed may contain circular, elliptic or astigmatic fringes. The Fourier transform of such interferograms is seen to be also a sine or a cosine of a second order polynomial in both the real and imaginary parts. In this work we take a discrete Fourier transform of the fringe patterns and then we take separate inverse discrete transforms of the real and imaginary parts of the frequency spectrum. This results in two new interferograms corresponding to the sine and cosine of the quadratic term of the phase modulated by the sine and cosine of the linear term. The linear term of these interferograms may be recovered with similar procedures of fringe analysis from open fringe interferograms. Once the linear term is retrieved the quadratic phase of the interferogram being analysed can also be calculated. The present approach is also being investigated for interferograms with nearly circularly symmetry given that the phase contains some tilt. The described procedure of Fourier analysis from quadratic phase interferograms of nearly symmetric interferograms could be used instead of complex and time consuming algorithms for phase recovery from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.

  9. Quadratic integrand double-hybrid made spin-component-scaled

    NASA Astrophysics Data System (ADS)

    Brémond, Éric; Savarese, Marika; Sancho-García, Juan C.; Pérez-Jiménez, Ángel J.; Adamo, Carlo

    2016-03-01

    We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.

  10. Improving Students' Ability to Intuitively Infer Resistance from Magnitude of Current and Potential Difference Information: A Functional Learning Approach

    ERIC Educational Resources Information Center

    Chasseigne, Gerard; Giraudeau, Caroline; Lafon, Peggy; Mullet, Etienne

    2011-01-01

    The study examined the knowledge of the functional relations between potential difference, magnitude of current, and resistance among seventh graders, ninth graders, 11th graders (in technical schools), and college students. It also tested the efficiency of a learning device named "functional learning" derived from cognitive psychology on the…

  11. When does brain aging accelerate? Dangers of quadratic fits in cross-sectional studies.

    PubMed

    Fjell, Anders M; Walhovd, Kristine B; Westlye, Lars T; Østby, Ylva; Tamnes, Christian K; Jernigan, Terry L; Gamst, Anthony; Dale, Anders M

    2010-05-01

    Many brain structures show a complex, non-linear pattern of maturation and age-related change. Often, quadratic models (beta(0) + beta(1)age + beta(2)age(2) + epsilon) are used to describe such relationships. Here, we demonstrate that the fitting of quadratic models is substantially affected by seemingly irrelevant factors, such as the age-range sampled. Hippocampal volume was measured in 434 healthy participants between 8 and 85 years of age, and quadratic models were fit to subsets of the sample with different age-ranges. It was found that as the bottom of the age-range increased, the age at which volumes appeared to peak was moved upwards and the estimated decline in the last part of the age-span became larger. Thus, whether children were included or not affected the estimated decline between 60 and 85 years. We conclude that caution should be exerted in inferring age-trajectories from global fit models, e.g. the quadratic model. A nonparametric local smoothing technique (the smoothing spline) was found to be more robust to the effects of different starting ages. The results were replicated in an independent sample of 309 participants. PMID:20109562

  12. Making Inferences: Comprehension of Physical Causality, Intentionality, and Emotions in Discourse by High-Functioning Older Children, Adolescents, and Adults with Autism

    ERIC Educational Resources Information Center

    Bodner, Kimberly E.; Engelhardt, Christopher R.; Minshew, Nancy J.; Williams, Diane L.

    2015-01-01

    Studies investigating inferential reasoning in autism spectrum disorder (ASD) have focused on the ability to make socially-related inferences or inferences more generally. Important variables for intervention planning such as whether inferences depend on physical experiences or the nature of social information have received less consideration. A…

  13. Decoding the Role of the Insula in Human Cognition: Functional Parcellation and Large-Scale Reverse Inference

    PubMed Central

    Yarkoni, Tal; Khaw, Mel Win; Sanfey, Alan G.

    2013-01-01

    Recent work has indicated that the insula may be involved in goal-directed cognition, switching between networks, and the conscious awareness of affect and somatosensation. However, these findings have been limited by the insula’s remarkably high base rate of activation and considerable functional heterogeneity. The present study used a relatively unbiased data-driven approach combining resting-state connectivity-based parcellation of the insula with large-scale meta-analysis to understand how the insula is anatomically organized based on functional connectivity patterns as well as the consistency and specificity of the associated cognitive functions. Our findings support a tripartite subdivision of the insula and reveal that the patterns of functional connectivity in the resting-state analysis appear to be relatively conserved across tasks in the meta-analytic coactivation analysis. The function of the networks was meta-analytically “decoded” using the Neurosynth framework and revealed that while the dorsoanterior insula is more consistently involved in human cognition than ventroanterior and posterior networks, each parcellated network is specifically associated with a distinct function. Collectively, this work suggests that the insula is instrumental in integrating disparate functional systems involved in processing affect, sensory-motor processing, and general cognition and is well suited to provide an interface between feelings, cognition, and action. PMID:22437053

  14. Factorization using the quadratic sieve algorithm

    SciTech Connect

    Davis, J.A.; Holdridge, D.B.

    1983-12-01

    Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

  15. Factorization using the quadratic sieve algorithm

    SciTech Connect

    Davis, J.A.; Holdridge, D.B.

    1983-01-01

    Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories to determine as sharply as possible the current state-of-the-art in factoring. Because all viable attacks on RSA thus far proposed are equivalent to factorization of the modulus, sharper bounds on the computational difficulty of factoring permit improved estimates for the size of RSA parameters needed for given levels of cryptosecurity. Analysis of the Quadratic Sieve indicates that it may be faster than any previously published general purpose algorithm for factoring large integers. The high speed of the CRAY I coupled with the capability of the CRAY to pipeline certain vectorized operations make this algorithm (and code) the front runner in current factoring techniques.

  16. Communications circuit including a linear quadratic estimator

    DOEpatents

    Ferguson, Dennis D.

    2015-07-07

    A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

  17. An alternative method on quadratic programming problems

    NASA Astrophysics Data System (ADS)

    Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.

    2015-05-01

    In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.

  18. Extended Decentralized Linear-Quadratic-Gaussian Control

    NASA Technical Reports Server (NTRS)

    Carpenter, J. Russell

    2000-01-01

    A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.

  19. Comparison of f2/f1 ratio functions in rabbit and gerbil: Ear-canal DPOAEs vs noninvasively inferred intracochlear DPs

    NASA Astrophysics Data System (ADS)

    Martin, Glen K.; Stagner, Barden B.; Dong, Wei; Lonsbury-Martin, Brenda L.

    2015-12-01

    The properties of distortion product otoacoustic emissions (DPOAEs), i.e., distortion products (DPs) measured in the ear canal, have been thoroughly described. However, considerably less is known about the behavior of intracochlear DPs (iDPs). Detailed comparisons of DPOAEs to iDPs would provide valuable insights on the extent to which ear-canal DPOAEs mirror iDPs. Prior studies described a technique whereby the behavior of iDPs could be inferred by interacting a probe tone (f3) with the iDP of interest to produce a `secondary' DPOAE (DPOAÉ). The behavior of DPOAÉ was then used to deduce the characteristics of the iDP. In the present study, this method was used in rabbits and gerbils to simultaneously compare DPOAE f2/f1-ratio functions to their iDP counterparts. The 2f1-f2 and 2f2-f1 DPOAEs were collected with f1 and f2 primary-tone levels varied from 35-75 dB SPL, and with a 50-dB SPL f3 placed at a DP/f3 ratio of 1.25 to evoke a DPOAÉ at 2f3-(2f1-f2) or 2f3-(2f2-f1). Control experiments demonstrated little effect of the f3-probe tone on DPOAE-ratio functions. Substitution experiments were performed to determine any suppressive effects of the f1 and f2 primaries on the generation of DPOAÉ, as well as to infer the intracochlear level of the iDP once the DPOAÉ was corrected for suppression. Results showed that at low primary-tone levels, 2f1-f2 DPOAE f2/f1-ratio functions peaked around f2/f1=1.25, and exhibited an inverted U-shaped function. In contrast, simultaneously measured 2f1-f2 iDP-ratio functions peaked at f2/f1≈1. Similar growth of the inferred iDP was obtained for higher-level primaries when the ratio functions were corrected for suppressive effects. At these higher levels, DPOAE-ratio functions leveled off and no longer showed the steep reduction at narrow f2/f1 ratios. Overall, noninvasive estimates of 2f1-f2 iDP-ratio functions agreed with reports of similar functions directly measured for 2f1-f2 DPs on the basilar membrane (BM) or in

  20. THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

    EPA Science Inventory

    Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

  1. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    ERIC Educational Resources Information Center

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  2. Explorative Learning and Functional Inferences on a Five-Step Means-Means-End Problem in Goffin’s Cockatoos (Cacatua goffini)

    PubMed Central

    Auersperg, Alice M. I.; Kacelnik, Alex; von Bayern, Auguste M. P.

    2013-01-01

    To investigate cognitive operations underlying sequential problem solving, we confronted ten Goffin’s cockatoos with a baited box locked by five different inter-locking devices. Subjects were either naïve or had watched a conspecific demonstration, and either faced all devices at once or incrementally. One naïve subject solved the problem without demonstration and with all locks present within the first five sessions (each consisting of one trial of up to 20 minutes), while five others did so after social demonstrations or incremental experience. Performance was aided by species-specific traits including neophilia, a haptic modality and persistence. Most birds showed a ratchet-like progress, rarely failing to solve a stage once they had done it once. In most transfer tests subjects reacted flexibly and sensitively to alterations of the locks’ sequencing and functionality, as expected from the presence of predictive inferences about mechanical interactions between the locks. PMID:23844247

  3. System-Level Insights into the Cellular Interactome of a Non-Model Organism: Inferring, Modelling and Analysing Functional Gene Network of Soybean (Glycine max)

    PubMed Central

    Xu, Yungang; Guo, Maozu; Zou, Quan; Liu, Xiaoyan; Wang, Chunyu; Liu, Yang

    2014-01-01

    Cellular interactome, in which genes and/or their products interact on several levels, forming transcriptional regulatory-, protein interaction-, metabolic-, signal transduction networks, etc., has attracted decades of research focuses. However, such a specific type of network alone can hardly explain the various interactive activities among genes. These networks characterize different interaction relationships, implying their unique intrinsic properties and defects, and covering different slices of biological information. Functional gene network (FGN), a consolidated interaction network that models fuzzy and more generalized notion of gene-gene relations, have been proposed to combine heterogeneous networks with the goal of identifying functional modules supported by multiple interaction types. There are yet no successful precedents of FGNs on sparsely studied non-model organisms, such as soybean (Glycine max), due to the absence of sufficient heterogeneous interaction data. We present an alternative solution for inferring the FGNs of soybean (SoyFGNs), in a pioneering study on the soybean interactome, which is also applicable to other organisms. SoyFGNs exhibit the typical characteristics of biological networks: scale-free, small-world architecture and modularization. Verified by co-expression and KEGG pathways, SoyFGNs are more extensive and accurate than an orthology network derived from Arabidopsis. As a case study, network-guided disease-resistance gene discovery indicates that SoyFGNs can provide system-level studies on gene functions and interactions. This work suggests that inferring and modelling the interactome of a non-model plant are feasible. It will speed up the discovery and definition of the functions and interactions of other genes that control important functions, such as nitrogen fixation and protein or lipid synthesis. The efforts of the study are the basis of our further comprehensive studies on the soybean functional interactome at the genome

  4. Orbital instability of standing waves for the quadratic-cubic Klein-Gordon-Schrödinger system

    NASA Astrophysics Data System (ADS)

    Natali, Fábio; Pastor, Ademir

    2015-08-01

    We consider the Klein-Gordon-Schrödinger system with quadratic and cubic interactions. Smooth curves of periodic- and solitary-wave solutions are obtained via the implicit function theorem. Orbital instability of such waves is then established.

  5. Horizontal Distance Travelled by a Mobile Experiencing a Quadratic Drag Force: Normalized Distance and Parametrization

    ERIC Educational Resources Information Center

    Vial, Alexandre

    2007-01-01

    We investigate the problem of the horizontal distance travelled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial…

  6. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    PubMed

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

  7. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

    PubMed Central

    RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

    2013-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

  8. AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.

    1994-01-01

    AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user

  9. User's guide for SOL/QPSOL: a Fortran package for quadratic programming

    SciTech Connect

    Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.

    1983-07-01

    This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.

  10. Propagator for the time-dependent charged oscillator via linear and quadratic invariants

    SciTech Connect

    Abdalla, M. Sebawe Choi, Jeong-Ryeol

    2007-12-15

    The problem of a charged particle in the presence of a variable magnetic field is considered. Using the linear and the quadratic invariants as a tool, the wave functions in Fock state as well as in coherent state are obtained. The corresponding propagators which propagate the wave functions in the space-time are derived. Using numerical computations we have managed to draw some plots for the real, imaginary, and absolute values of the propagators. This has been used to analyze the properties of the propagators associated with both of the linear and the quadratic invariants. It has been shown that there is no essential difference between the behavior of the absolute value of the propagators in both of the linear and the quadratic invariants.

  11. A Function for Representing the Biological Challenge to Respiration Posed by Ocean Acidification and the Geochemical Consequences Inferred

    NASA Astrophysics Data System (ADS)

    Peltzer, E. T.; Brewer, P. G.

    2008-12-01

    Increasing levels of dissolved total CO2 in the ocean from the invasion of fossil fuel CO2 via the atmosphere are widely believed to pose challenges to marine life on several fronts. This is most often expressed as a concern from the resulting lower pH, and the impact of this on calcification in marine organisms (coral reefs, calcareous phytoplankton etc.). These concerns are real, but calcification is by no means the only process affected, nor is the fossil fuel CO2 signal the only geochemical driver of the rapidly emerging deep-sea biological stress. Physical climate change is reducing deep-sea ventilation rates, and thereby leading to increasing oxygen deficits and concomitant increased respiratory CO2. We seek to understand the combined effects of the downward penetration of the fossil fuel signal, and the emergence of the depleted O2/increased respiratory CO2 signal at depth. As a first step, we seek to provide a simple function to capture the changing oceanic state. The most basic thermodynamic equation for the functioning of marine animals can be written as Corg + O2 → CO2 , and this results in the simple Gibbs free energy equation: ΔG° = - RT * ln [fCO2]/[Corg]*[fO2], in which the ratio of pO2 to pCO2 emerges as the dominant factor. From this we construct a simple Respiration Index: RI = log10 (pO2/pCO2), which is linear in energy and map this function for key oceanic regions illustrating the expansion of oceanic dead zones. The formal thermodynamic limit for aerobic life is RI = 0; in practice field data shows that at RI ~ 0.7 microbes turn to electron acceptors other than O2, and denitrification begins to occur. This likely represents the lowest limit for the long-term functioning of higher animals, and the zone RI = 0.7 to 1 appears to present challenges to basic functioning of many marine species. In addition, there are large regions of the ocean where denitrification already occurs, and these zones will expand greatly in size as the combined

  12. Bayesian inference in physics

    NASA Astrophysics Data System (ADS)

    von Toussaint, Udo

    2011-07-01

    Bayesian inference provides a consistent method for the extraction of information from physics experiments even in ill-conditioned circumstances. The approach provides a unified rationale for data analysis, which both justifies many of the commonly used analysis procedures and reveals some of the implicit underlying assumptions. This review summarizes the general ideas of the Bayesian probability theory with emphasis on the application to the evaluation of experimental data. As case studies for Bayesian parameter estimation techniques examples ranging from extra-solar planet detection to the deconvolution of the apparatus functions for improving the energy resolution and change point estimation in time series are discussed. Special attention is paid to the numerical techniques suited for Bayesian analysis, with a focus on recent developments of Markov chain Monte Carlo algorithms for high-dimensional integration problems. Bayesian model comparison, the quantitative ranking of models for the explanation of a given data set, is illustrated with examples collected from cosmology, mass spectroscopy, and surface physics, covering problems such as background subtraction and automated outlier detection. Additionally the Bayesian inference techniques for the design and optimization of future experiments are introduced. Experiments, instead of being merely passive recording devices, can now be designed to adapt to measured data and to change the measurement strategy on the fly to maximize the information of an experiment. The applied key concepts and necessary numerical tools which provide the means of designing such inference chains and the crucial aspects of data fusion are summarized and some of the expected implications are highlighted.

  13. Holographic entropy increases in quadratic curvature gravity

    NASA Astrophysics Data System (ADS)

    Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.

    2015-09-01

    Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.

  14. What is it like to have type-2 blindsight? Drawing inferences from residual function in type-1 blindsight.

    PubMed

    Kentridge, Robert W

    2015-03-01

    Controversy surrounds the question of whether the experience sometimes elicited by visual stimuli in blindsight (type-2 blindsight) is visual in nature or whether it is some sort of non-visual experience. The suggestion that the experience is visual seems, at face value, to make sense. I argue here, however, that the residual abilities found in type-1 blindsight (blindsight in which stimuli elicit no conscious experience) are not aspects of normal vision with consciousness deleted, but are based fragments of visual processes that, in themselves, would not be intelligible as visual experiences. If type-2 blindsight is a conscious manifestation of this residual function then it is not obvious that type-2 blindsight would be phenomenally like vision. PMID:25301438

  15. Quadratic Reciprocity and the Group Orders of Particle States

    SciTech Connect

    DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.

    2001-06-01

    The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.

  16. Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

    NASA Technical Reports Server (NTRS)

    Choi, Benjamin B.

    2002-01-01

    Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

  17. Inferences regarding the diet of extinct hominins: structural and functional trends in dental and mandibular morphology within the hominin clade

    PubMed Central

    Lucas, Peter W; Constantino, Paul J; Wood, Bernard A

    2008-01-01

    This contribution investigates the evolution of diet in the Pan–Homo and hominin clades. It does this by focusing on 12 variables (nine dental and three mandibular) for which data are available about extant chimpanzees, modern humans and most extinct hominins. Previous analyses of this type have approached the interpretation of dental and gnathic function by focusing on the identification of the food consumed (i.e. fruits, leaves, etc.) rather than on the physical properties (i.e. hardness, toughness, etc.) of those foods, and they have not specifically addressed the role that the physical properties of foods play in determining dental adaptations. We take the available evidence for the 12 variables, and set out what the expression of each of those variables is in extant chimpanzees, the earliest hominins, archaic hominins, megadont archaic hominins, and an inclusive grouping made up of transitional hominins and pre-modern Homo. We then present hypotheses about what the states of these variables would be in the last common ancestor of the Pan–Homo clade and in the stem hominin. We review the physical properties of food and suggest how these physical properties can be used to investigate the functional morphology of the dentition. We show what aspects of anterior tooth morphology are critical for food preparation (e.g. peeling fruit) prior to its ingestion, which features of the postcanine dentition (e.g. overall and relative size of the crowns) are related to the reduction in the particle size of food, and how information about the macrostructure (e.g. enamel thickness) and microstructure (e.g. extent and location of enamel prism decussation) of the enamel cap might be used to make predictions about the types of foods consumed by extinct hominins. Specifically, we show how thick enamel can protect against the generation and propagation of cracks in the enamel that begin at the enamel–dentine junction and move towards the outer enamel surface. PMID:18380867

  18. A Fixed-Point Iteration Method with Quadratic Convergence

    SciTech Connect

    Walker, Kevin P.; Sham, Sam

    2012-01-01

    The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed.

  19. Functional Inference of Methylenetetrahydrofolate Reductase Gene Polymorphisms on Enzyme Stability as a Potential Risk Factor for Down Syndrome in Croatia

    PubMed Central

    Vraneković, Jadranka; Babić Božović, Ivana; Starčević Čizmarević, Nada; Buretić-Tomljanović, Alena; Ristić, Smiljana; Petrović, Oleg; Kapović, Miljenko; Brajenović-Milić, Bojana

    2010-01-01

    Understanding the biochemical structure and function of the methylenetetrahydrofolate reductase gene (MTHFR) provides new evidence in elucidating the risk of having a child with Down syndrome (DS) in association with two common MTHFR polymorphisms, C677T and A1298C. The aim of this study was to evaluate the risk for DS according to the presence of MTHFR C677T and A1298C polymorphisms as well as the stability of the enzyme configuration. This study included mothers from Croatia with a liveborn DS child (n = 102) or DS pregnancy (n = 9) and mothers with a healthy child (n = 141). MTHFR C677T and A1298C polymorphisms were assessed by PCR-RFLP. Allele/genotype frequencies differences were determined using χ2 test. Odds ratio and the 95% confidence intervals were calculated to evaluate the effects of different alleles/genotypes. No statistically significant differences were found between the frequencies of allele/genotype or genotype combinations of the MTHFR C677T and A1298C polymorphisms in the case and the control groups. Additionally, the observed frequencies of the stable (677CC/1298AA, 677CC/1298AC, 677CC/1298CC) and unstable (677CT/1298AA, 677CT/1298AC, 677TT/1298AA) enzyme configurations were not significantly different. We found no evidence to support the possibility that MTHFR polymorphisms and the stability of the enzyme configurations were associated with risk of having a child with DS in Croatian population. PMID:20592453

  20. Water quality functioning of lowland permeable catchments: inferences from an intensive study of the RIVER KENNEt and upper River Thames.

    PubMed

    Nea, Colin; Jarvie, Helen P; Wade, Andrew J; Whitehead, Paul G

    2002-01-23

    This paper brings together information on the water quality functioning of the River Kennet and other parts of the upper River Thames in the south east of England. The Kennet represents a groundwater fed riverine environment impacted by agricultural and sewage sources of nutrient pollution. Descriptions of the general water quality of the area, nutrient sources, sinks and within river processes are provided together with biological responses to driving issues of agriculture, sewage treatment and climatic change. Models are developed and applied to assess the key processes involved for a highly dynamic system and to provide initial estimates of the likely responses to environmental change. Furthermore, the economic aspects of pollution control are reviewed, together with legislation issues, which are presented within the context of a landmark case known as the 'Axford Inquiry', the implications of which extend to regional and national dimensions. The paper concludes with a discussion on the present state of knowledge, key issues and future research on the science and management of groundwater fed nutrient impacted riverine systems. PMID:11846085

  1. Blind deconvolution estimation of fluorescence measurements through quadratic programming

    NASA Astrophysics Data System (ADS)

    Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.

    2015-07-01

    Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.

  2. Melt infiltration of the lower lithosphere beneath the Tanzania craton and the Albertine rift inferred from S receiver functions

    NASA Astrophysics Data System (ADS)

    WöLbern, Ingo; Rümpker, Georg; Link, Klemens; Sodoudi, Forough

    2012-08-01

    The transition between the lithosphere and the asthenosphere is subject to numerous contemporary studies as its nature is still poorly understood. The thickest lithosphere is associated with old cratons and platforms and it has been shown that seismic investigations may fail to image the lithosphere-asthenosphere boundary in these areas. Instead, several recent studies have proposed a mid-lithospheric discontinuity of unknown origin existing under several cratons. In this study we investigate the Tanzania craton in East Africa which is enclosed by the eastern and western branches of the East African Rift System. We present evidence from S receiver functions for two consecutive discontinuities at depths of 50-100 km and 140-200 km, which correspond to significant S wave velocity reductions under the Tanzania craton and the Albert and Edward rift segments. By comparison with synthetic waveforms we show that the lower discontinuity coincides with the LAB exhibiting velocity reductions of 6-9%. The shallower interface reveals a velocity drop that varies from 12% beneath the craton to 24% below the Albert-Edward rift. It is interpreted as an infiltration front marking the upper boundary of altered lithosphere due to ascending asthenospheric melts. This is corroborated by computing S velocity variations based on xenolith samples which exhibit a dense system of crystallized veins acting as pathways of the infiltrating melt. Mineral assemblages in these veins are rich in phlogopite and pyroxenite which can explain the reduced shear wave velocities. Melt infiltration represents a suitable mechanism to form a mid-lithospheric discontinuity within cratonic lithosphere that is underlain by anomalously hot mantle.

  3. Hydrous state of the subducting Philippine Sea plate inferred from receiver function image using onshore and offshore data

    NASA Astrophysics Data System (ADS)

    Akuhara, Takeshi; Mochizuki, Kimihiro

    2015-12-01

    Exploring the hydrous state of subducting oceanic crust is intriguing because it is considered to affect the strength of megathrust faults that cause various types of earthquakes; however, its state beneath offshore regions remains unclear. In this study, we investigated fluid contents along the subducting Philippine Sea plate around the Kii Peninsula by receiver function (RF) analysis using data from both on-land stations and ocean bottom seismometers (OBSs). The vertical component of OBS records contains dominant water reverberations, and thus, conventional methods fail to estimate RFs correctly. We therefore developed a method to calculate RFs that removes such reverberations. The RFs calculated by our method showed considerable improvement for later phase identification, compared with those obtained using a conventional method. Resultant RF amplitudes suggest the existence of low-velocity zones directly beneath the plate interface of both onshore and offshore regions. We interpreted this as evidence of hydrous oceanic crust, which extends from 5 km to 35 km depth to the plate interface. Reduction of RF amplitudes beneath the Kii Peninsula suggests that dehydration of the oceanic crust increases the seismic velocity, and the accompanying densification makes the plate interface permeable. This permeable plate interface may characterize the location of non-volcanic tremors. This contrasts with long-term slow slip events because it is believed that they occur along the sealed plate interface. Comparison between the plate geometry and local earthquakes reveals the paucity of earthquakes in the oceanic crust below a certain depth, which provides further insight into the dehydration process in the oceanic crust.

  4. Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

    NASA Astrophysics Data System (ADS)

    Lee, T.-W.; An, Keju

    2016-06-01

    We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

  5. Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential

    NASA Astrophysics Data System (ADS)

    Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei

    2016-07-01

    In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.

  6. A study of radiation propagation in a medium with quadratic inhomogeneity

    SciTech Connect

    Pikulev, A A

    2001-09-30

    The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed. (physical foundations of quantum electronics)

  7. Seismic velocity discontinuities in the crust and uppermost mantle beneath the Tokyo metropolitan area inferred from receiver function analysis

    NASA Astrophysics Data System (ADS)

    Igarashi, T.; Sakai, S.; Hirata, N.

    2010-12-01

    We apply receiver function (RF) analyses to estimate the seismic velocity structure and seismic velocity discontinuities in the crust and uppermost mantle beneath the Tokyo metropolitan area, central Japan. Destructive earthquakes often occurred at various places including the subducting Philippine Sea plate (PSP), the subducting Pacific plate (PAP), and inland earthquake in this area. Investigation on the crustal structure and configurations of the subducting plates is the key to understanding the stress and strain concentration process and important to mitigate future earthquake disasters. A RF analysis is widely used to estimate velocity discontinuities in the crust and mantle beneath each seismic station. However, crustal structure beneath the Kanto plain could not be analyzed for lack of applicable seismic stations. Recently, comprehensive surveys are conducted as the Special Project for Earthquake Disaster Mitigation in the Tokyo Metropolitan area from 2007. The Metropolitan Seismic Observation network (MeSO-net) is constructed under this project. In this study, we searched for the best correlated velocity structure model between an observed RF at each station and synthetic ones by using a grid search method. Synthetic RFs calculated from assumed many one-dimensional velocity structures which consisting of four layers. We further constructed the vertical cross-sections of depth converted RF images transformed the lapse time of time series to depth by using the estimated structure models. MeSO-net data and telemetric seismographic network data operated by NIED, JMA and ERI are used. We used events with magnitudes greater or equal to 5.0 and epicentral distances between 30 and 90 degrees based on USGS catalogues. As a result, we clarify spatial distributions of the crustal S-wave velocities. The Boso Peninsula and Kanto plain are covered in the thick low-velocity sediment layers. We image standard velocity distributions in the deep crust of the Boso Peninsula

  8. Detection of code spread OFDM based on 0-1 integer quadratic programming

    NASA Astrophysics Data System (ADS)

    Elghariani, Ali; Zoltowski, Michael D.

    2012-05-01

    In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.

  9. Landau-Zener transition in quadratic nonlinear two-state systems

    SciTech Connect

    Ishkhanyan, A. M.

    2010-05-15

    A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula provides a highly accurate approximation for the whole rage of the variation of the Landau-Zener parameter.

  10. Galactic chemical evolution and nucleocosmochronology - Analytic quadratic models

    NASA Technical Reports Server (NTRS)

    Clayton, D. D.

    1985-01-01

    Quadratic models of the chemical evolution of the Galaxy for a star formation rate proportional to the square of the gas mass are studied. The search for analytic solutions to the gas mass and star mass for time-dependent rates of gaseous infall onto the disk is examined. The quadratic models are compared to models having linear star formation rates. The mass, metallicity, number of stars, and U-235/U-238 isotopic ratio for the models which are subjected to the same infall rate, the same initial disk mass, and the same final gas fraction are compared. The results of the comparison indicate that: (1) the average dwarf age is greater in the quadratic model, (2) the metallicity grows initially faster in the quadratic model, (3) the quadratic model has a smaller percentage of low-Z dwarfs, and (4) the U-235/U-238 isotopic ratio indicates a younger quadratic model.

  11. Quadratic relations in continuous and discrete Painlevé equations

    NASA Astrophysics Data System (ADS)

    Ramani, A.; Grammaticos, B.; Tamizhmani, T.

    2000-04-01

    The quadratic relations between the solutions of a Painlevé equation and that of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the quadratic relations existing for the continuous PII , PIII , PV and PVI have analogues as well as consequences in the discrete case. Moreover, the discrete Painlevé equations have quadratic relations of their own without any reference to the continuous case.

  12. Inference of Isoforms from Short Sequence Reads

    NASA Astrophysics Data System (ADS)

    Feng, Jianxing; Li, Wei; Jiang, Tao

    Due to alternative splicing events in eukaryotic species, the identification of mRNA isoforms (or splicing variants) is a difficult problem. Traditional experimental methods for this purpose are time consuming and cost ineffective. The emerging RNA-Seq technology provides a possible effective method to address this problem. Although the advantages of RNA-Seq over traditional methods in transcriptome analysis have been confirmed by many studies, the inference of isoforms from millions of short sequence reads (e.g., Illumina/Solexa reads) has remained computationally challenging. In this work, we propose a method to calculate the expression levels of isoforms and infer isoforms from short RNA-Seq reads using exon-intron boundary, transcription start site (TSS) and poly-A site (PAS) information. We first formulate the relationship among exons, isoforms, and single-end reads as a convex quadratic program, and then use an efficient algorithm (called IsoInfer) to search for isoforms. IsoInfer can calculate the expression levels of isoforms accurately if all the isoforms are known and infer novel isoforms from scratch. Our experimental tests on known mouse isoforms with both simulated expression levels and reads demonstrate that IsoInfer is able to calculate the expression levels of isoforms with an accuracy comparable to the state-of-the-art statistical method and a 60 times faster speed. Moreover, our tests on both simulated and real reads show that it achieves a good precision and sensitivity in inferring isoforms when given accurate exon-intron boundary, TSS and PAS information, especially for isoforms whose expression levels are significantly high.

  13. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-01

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.

  14. Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.

    PubMed

    Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza

    2016-08-12

    We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986

  15. Compact stars with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi

    2015-05-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  16. Quadratic dynamical decoupling with nonuniform error suppression

    SciTech Connect

    Quiroz, Gregory; Lidar, Daniel A.

    2011-10-15

    We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) single-qubit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N{sub 1} and N{sub 2} pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N{sub 1} and N{sub 2}, and near-optimal performance is achieved for general single-qubit interactions when N{sub 1}=N{sub 2}.

  17. The Middle Miocene Ape Pierolapithecus catalaunicus Exhibits Extant Great Ape-Like Morphometric Affinities on Its Patella: Inferences on Knee Function and Evolution

    PubMed Central

    Pina, Marta; Almécija, Sergio; Alba, David M.; O'Neill, Matthew C.; Moyà-Solà, Salvador

    2014-01-01

    The mosaic nature of the Miocene ape postcranium hinders the reconstruction of the positional behavior and locomotion of these taxa based on isolated elements only. The fossil great ape Pierolapithecus catalaunicus (IPS 21350 skeleton; 11.9 Ma) exhibits a relatively wide and shallow thorax with moderate hand length and phalangeal curvature, dorsally-oriented metacarpophalangeal joints, and loss of ulnocarpal articulation. This evidence reveals enhanced orthograde postures without modern ape-like below-branch suspensory adaptations. Therefore, it has been proposed that natural selection enhanced vertical climbing (and not suspension per se) in Pierolapithecus catalaunicus. Although limb long bones are not available for this species, its patella (IPS 21350.37) can potentially provide insights into its knee function and thus on the complexity of its total morphological pattern. Here we provide a detailed description and morphometric analyses of IPS 21350.37, which are based on four external dimensions intended to capture the overall patellar shape. Our results reveal that the patella of Pierolapithecus is similar to that of extant great apes: proximodistally short, mediolaterally broad and anteroposteriorly thin. Previous biomechanical studies of the anthropoid knee based on the same measurements proposed that the modern great ape patella reflects a mobile knee joint while the long, narrow and thick patella of platyrrhine and especially cercopithecoid monkeys would increase the quadriceps moment arm in knee extension during walking, galloping, climbing and leaping. The patella of Pierolapithecus differs not only from that of monkeys and hylobatids, but also from that of basal hominoids (e.g., Proconsul and Nacholapithecus), which display slightly thinner patellae than extant great apes (the previously-inferred plesiomorphic hominoid condition). If patellar shape in Pierolapithecus is related to modern great ape-like knee function, our results suggest that increased

  18. Convergence analysis of a finite element skull model of Herpestes javanicus (Carnivora, Mammalia): implications for robust comparative inferences of biomechanical function.

    PubMed

    Tseng, Zhijie Jack; Flynn, John J

    2015-01-21

    biomechanical attributes from these simulations are used to infer form-function linkage. PMID:25445190

  19. The Middle Miocene ape Pierolapithecus catalaunicus exhibits extant great ape-like morphometric affinities on its patella: inferences on knee function and evolution.

    PubMed

    Pina, Marta; Almécija, Sergio; Alba, David M; O'Neill, Matthew C; Moyà-Solà, Salvador

    2014-01-01

    The mosaic nature of the Miocene ape postcranium hinders the reconstruction of the positional behavior and locomotion of these taxa based on isolated elements only. The fossil great ape Pierolapithecus catalaunicus (IPS 21350 skeleton; 11.9 Ma) exhibits a relatively wide and shallow thorax with moderate hand length and phalangeal curvature, dorsally-oriented metacarpophalangeal joints, and loss of ulnocarpal articulation. This evidence reveals enhanced orthograde postures without modern ape-like below-branch suspensory adaptations. Therefore, it has been proposed that natural selection enhanced vertical climbing (and not suspension per se) in Pierolapithecus catalaunicus. Although limb long bones are not available for this species, its patella (IPS 21350.37) can potentially provide insights into its knee function and thus on the complexity of its total morphological pattern. Here we provide a detailed description and morphometric analyses of IPS 21350.37, which are based on four external dimensions intended to capture the overall patellar shape. Our results reveal that the patella of Pierolapithecus is similar to that of extant great apes: proximodistally short, mediolaterally broad and anteroposteriorly thin. Previous biomechanical studies of the anthropoid knee based on the same measurements proposed that the modern great ape patella reflects a mobile knee joint while the long, narrow and thick patella of platyrrhine and especially cercopithecoid monkeys would increase the quadriceps moment arm in knee extension during walking, galloping, climbing and leaping. The patella of Pierolapithecus differs not only from that of monkeys and hylobatids, but also from that of basal hominoids (e.g., Proconsul and Nacholapithecus), which display slightly thinner patellae than extant great apes (the previously-inferred plesiomorphic hominoid condition). If patellar shape in Pierolapithecus is related to modern great ape-like knee function, our results suggest that increased

  20. Rays of Small Integer Solutions of Homogeneous Ternary Quadratic Equations

    NASA Astrophysics Data System (ADS)

    Mishra, Sudhakara

    1991-02-01

    We have dealt with the general ternary quadratic equation: ax2 + by^ {2} + cz2 + dxy + exz + fyz = 0 with integer coefficients. After giving a matrix-reduction formula for a quadratic equation in any number of variables, of which the reduction of the above ternary equation is an easy consequence, we have devoted our attention to the reduced equation: ax^ {2} + by2 + cz^{2 } = 0. We have devised an algorithm for reducing Dirichlet's possibly larger solutions to this prescribed range of Holzer's. Then we have generalized Holzer's theorem to the case of the ternary equation: ax^{2 } + by2 + cz2 + dxy + exz + fyz = 0, giving in this context a new range called the CM-range, of which the Holzer's range is a particular case when d = e = f = 0. We have described an algorithm for getting a solution of the general ternary within this CM-range. After that we have devised an algorithm for getting all the solutions of the Legendre's equation ax 2 + by2 + cz^ {2} = 0 within the Holzer's range--and have shown that if we regard this Legendre's equation as a double cone, these solutions within the Holzer's range lie along some definite rays, here called the CM-rays, which are completely determined by the prime factors of the coefficients a, b and c. After giving an algorithm for detecting these CM-rays of the reduced equation: ax^2 + by^2 + cz^2 = 0, we have shown how one can produce some similar rays of solutions of the above general ternary quadratic equation: ax2 + by2 + cz2 + dxy + exz + fyz = 0. Note that apart from the method of exhausting all the possibilities, so far there has been no precisely stated algorithm to find the minimum solutions of the above ternary equations. Towards the end, observing in the context of our main result an inequality involving two functions, namely C and PCM from doubz_sp{*} {3} to doubz_+, and simultaneously presenting some tables of these positive CM-rays or PCM-rays lying in the positive octant, we have concluded this work with a number of

  1. Inferring Selection Intensity and Allele Age from Multilocus Haplotype Structure

    PubMed Central

    Chen, Hua; Slatkin, Montgomery

    2013-01-01

    It is a challenging task to infer selection intensity and allele age from population genetic data. Here we present a method that can efficiently estimate selection intensity and allele age from the multilocus haplotype structure in the vicinity of a segregating mutant under positive selection. We use a structured-coalescent approach to model the effect of directional selection on the gene genealogies of neutral markers linked to the selected mutant. The frequency trajectory of the selected allele follows the Wright-Fisher model. Given the position of the selected mutant, we propose a simplified multilocus haplotype model that can efficiently model the dynamics of the ancestral haplotypes under the joint influence of selection and recombination. This model approximates the ancestral genealogies of the sample, which reduces the number of states from an exponential function of the number of single-nucleotide polymorphism loci to a quadratic function. That allows parameter inference from data covering DNA regions as large as several hundred kilo-bases. Importance sampling algorithms are adopted to evaluate the probability of a sample by exploring the space of both allele frequency trajectories of the selected mutation and gene genealogies of the linked sites. We demonstrate by simulation that the method can accurately estimate selection intensity for moderate and strong positive selection. We apply the method to a data set of the G6PD gene in an African population and obtain an estimate of 0.0456 (95% confidence interval 0.0144−0.0769) for the selection intensity. The proposed method is novel in jointly modeling the multilocus haplotype pattern caused by recombination and mutation, allowing the analysis of haplotype data in recombining regions. Moreover, the method is applicable to data from populations under exponential growth and a variety of other demographic histories. PMID:23797107

  2. Inference or Observation?

    ERIC Educational Resources Information Center

    Finson, Kevin D.

    2010-01-01

    Learning about what inferences are, and what a good inference is, will help students become more scientifically literate and better understand the nature of science in inquiry. Students in K-4 should be able to give explanations about what they investigate (NSTA 1997) and that includes doing so through inferring. This article provides some tips…

  3. Quadratic elongation: A quantitative measure of distortion in coordination polyhedra

    USGS Publications Warehouse

    Robinson, Kelly F.; Gibbs, G.V.; Ribbe, P.H.

    1971-01-01

    Quadratic elongation and the variance of bond angles are linearly correlated for distorted octahedral and tetrahedral coordination complexes, both of which show variations in bond length and bond angle. The quadratic elonga tion is dimensionless, giving a quantitative measure of polyhedral distortion which is independent of the effective size of the polyhedron.

  4. Analysis of Students' Error in Learning of Quadratic Equations

    ERIC Educational Resources Information Center

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  5. 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.)

  6. Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    Vaiyavutjamai, Pongchawee; Clements, M. A.

    2006-01-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

  7. Visualising the Roots of Quadratic Equations with Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  8. Geometric quadratic stochastic operator on countable infinite set

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-02-03

    In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

  9. Quadratic divergences and quantum gravitational contributions to gauge coupling constants

    NASA Astrophysics Data System (ADS)

    Toms, David J.

    2011-10-01

    The calculation of quadratic divergences in Einstein-Maxwell theory with a possible cosmological constant is considered. We describe a method of calculation, using the background-field method, that is sensitive to quadratic divergences, is respectful of gauge invariance, and is independent of gauge conditions. A standard renormalization group analysis is applied to the result where it is shown that the quadratic divergences do lead to asymptotic freedom as found in the original paper of Robinson and Wilczek. The role and nature of these quadratic divergences is critically evaluated in light of recent criticism. Within the context of the background-field method, it is shown that it is possible to define the charge in a physically motivated way in which the quadratic divergences do not play a role. This latter view is studied in more depth in a toy model described in an appendix.

  10. Time Domain Identification of an Optimal Control Pilot Model with Emphasis on the Objective Function

    NASA Technical Reports Server (NTRS)

    Schmidt, D. K.

    1982-01-01

    A method for the identification of the pilot's control compensation using time domain techniques is proposed. From this information we hope to infer a quadratic cost function, supported by the data, that represents a reasonable expression for the pilot's control objective in the task being performed, or an inferred piloting strategy. The objectives for this method are: (1) obtain a better understanding of the fundamental piloting techniques in complex tasks, such as landing approach; (2) the development of a metric measurable in simulations and flight test that correlate with subjective pilot opinion; and (3) to further validate pilot models and pilot vehicle analysis methods.