#### 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. 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.

4. Some Aspects of Quadratic Generalized White Noise Functionals

Si, Si; Hida, Takeyuki

2009-02-01

We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.

5. Finding the Best Quadratic Approximation of a Function

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2011-01-01

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

6. 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

7. 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)

8. Optimization with quadratic support functions in nonconvex smooth optimization

Khamisov, O. V.

2016-10-01

Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.

9. Revealing Ozgur's Thoughts of a Quadratic Function with a Clinical Interview: Concepts and Their Underlying Reasons

ERIC Educational Resources Information Center

Ozaltun Celik, Aytug; Bukova Guzel, Esra

2017-01-01

The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…

10. Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations

ERIC Educational Resources Information Center

2008-01-01

This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…

11. 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…

12. 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.

13. Robust and reliable control via quadratic Lyapunov functions

Alt, Terry Robert

In this dissertation we present a new approach to design robust and reliable controllers. Our results are used to find control laws for systems that are subject to (1) real polytopic and norm bounded uncertainties, (2) actuator and sensor variations and (3) actuator and sensor failure. In addition, we present conditions that can be added to the control design problem to constrain the controller to be stable or strictly positive real, further strengthening the robustness and reliability of the control design. The basic framework relies on the use of quadratic Lyapunov functions to accommodate potentially time varying uncertainty. Conditions are derived that, when satisfied, allow a robust control design to be obtained by performing two convex optimizations. These controllers recover the performance robustness of either state feedback or full information controllers. Sufficient conditions are presented that remove the non-convexity in terms of the control design variables. This allows a robust control design to be obtained by solving a set of linear matrix inequalities. These general robustness results are then applied to the reliability problem. Actuator and sensor variations are modeled using real polytopic uncertainties. It is shown that under some simplifying assumptions the state feedback problem reduces to a single linear matrix inequality. It also shows that the Riccati equations for standard LQR and Hsb{infty} need only a slight modification to obtain a control law that is reliable with respect to actuator variability. For the output feedback case, convex conditions are presented that yield controllers which are reliable to actuator and sensor variations. Utilizing the simultaneous Lyapunov function approach, we further extend these results to include actuator or sensor failure. Additionally, when applicable, stronger reliability guaranties may be obtained by constraining the controller to be strictly positive real. This guarantees stability for positive real

14. Can orangutans (Pongo abelii) infer tool functionality?

PubMed

Mulcahy, Nicholas J; Schubiger, Michèle N

2014-05-01

It is debatable whether apes can reason about the unobservable properties of tools. We tested orangutans for this ability with a range of tool tasks that they could solve by using observational cues to infer tool functionality. In experiment 1, subjects successfully chose an unbroken tool over a broken one when each tool's middle section was hidden. This prevented seeing which tool was functional but it could be inferred by noting the tools' visible ends that were either disjointed (broken tool) or aligned (unbroken tool). We investigated whether success in experiment 1 was best explained by inferential reasoning or by having a preference per se for a hidden tool with an aligned configuration. We conducted a similar task to experiment 1 and included a functional bent tool that could be arranged to have the same disjointed configuration as the broken tool. The results suggested that subjects had a preference per se for the aligned tool by choosing it regardless of whether it was paired with the broken tool or the functional bent tool. However, further experiments with the bent tool task suggested this preference was a result of additional demands of having to attend to and remember the properties of the tools from the beginning of the task. In our last experiment, we removed these task demands and found evidence that subjects could infer the functionality of a broken tool and an unbroken tool that both looked identical at the time of choice.

15. A plasticity integration algorithm motivated by analytical integration of a generalized quadratic function

SciTech Connect

Becker, R

2006-03-03

The goal is to examine the dependence of the plastic flow direction as a function of strain increment for a generalized quadratic flow potential; and from that, extract a scheme for constructing a plastic flow direction for a more general class of yield and flow surfaces.

16. 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…

17. Exact evaluation of the quadratic longitudinal response function for an unmagnetized Maxwellian plasma

SciTech Connect

Layden, B.; Cairns, Iver H.; Robinson, P. A.; Percival, D. J.

2012-07-15

The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.

18. Neural Circuit Inference from Function to Structure.

PubMed

Real, Esteban; Asari, Hiroki; Gollisch, Tim; Meister, Markus

2017-01-23

Advances in technology are opening new windows on the structural connectivity and functional dynamics of brain circuits. Quantitative frameworks are needed that integrate these data from anatomy and physiology. Here, we present a modeling approach that creates such a link. The goal is to infer the structure of a neural circuit from sparse neural recordings, using partial knowledge of its anatomy as a regularizing constraint. We recorded visual responses from the output neurons of the retina, the ganglion cells. We then generated a systematic sequence of circuit models that represents retinal neurons and connections and fitted them to the experimental data. The optimal models faithfully recapitulated the ganglion cell outputs. More importantly, they made predictions about dynamics and connectivity among unobserved neurons internal to the circuit, and these were subsequently confirmed by experiment. This circuit inference framework promises to facilitate the integration and understanding of big data in neuroscience.

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

PubMed

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

2015-09-01

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 (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) 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 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive 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.

20. 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

1. Range and flight time of quadratic resisted projectile motion using the Lambert W function

2014-09-01

We study projectile motion with air resistance quadratic in speed. An approximation of a low-angle trajectory is considered where the horizontal velocity, v x , is assumed to be much larger than the vertical velocity, v y . The explicit solutions for the range and flight time are expressed in terms of the secondary branch of the Lambert function, {{W}_{-1}}. In addition to their theoretical importance, the results obtained will be of interest to teachers involved in undergraduate physics courses.

2. 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.

3. Functional network inference of the suprachiasmatic nucleus

PubMed Central

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.

2016-01-01

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

4. Functional network inference of the suprachiasmatic nucleus

SciTech Connect

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.

2016-04-04

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.

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

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.

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

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.

7. 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.

8. 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.

9. Functional neuroanatomy of intuitive physical inference

PubMed Central

Mikhael, John G.; Tenenbaum, Joshua B.; Kanwisher, Nancy

2016-01-01

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

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

PubMed

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.

11. 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

12. Detection of spatial variations in temporal trends with a quadratic function.

PubMed

Moraga, Paula; Kulldorff, Martin

2016-08-01

Methods for the assessment of spatial variations in temporal trends (SVTT) are important tools for disease surveillance, which can help governments to formulate programs to prevent diseases, and measure the progress, impact, and efficacy of preventive efforts already in operation. The linear SVTT method is designed to detect areas with unusual different disease linear trends. In some situations, however, its estimation trend procedure can lead to wrong conclusions. In this article, the quadratic SVTT method is proposed as alternative of the linear SVTT method. The quadratic method provides better estimates of the real trends, and increases the power of detection in situations where the linear SVTT method fails. A performance comparison between the linear and quadratic methods is provided to help illustrate their respective properties. The quadratic method is applied to detect unusual different cervical cancer trends in white women in the United States, over the period 1969 to 1995.

13. 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 minimum…

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…

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

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.

16. Quantitative evaluation of statistical inference in resting state functional MRI.

PubMed

Yang, Xue; Kang, Hakmook; Newton, Allen; Landman, Bennett A

2012-01-01

Modern statistical inference techniques may be able to improve the sensitivity and specificity of resting state functional MRI (rs-fMRI) connectivity analysis through more realistic characterization of distributional assumptions. In simulation, the advantages of such modern methods are readily demonstrable. However quantitative empirical validation remains elusive in vivo as the true connectivity patterns are unknown and noise/artifact distributions are challenging to characterize with high fidelity. Recent innovations in capturing finite sample behavior of asymptotically consistent estimators (i.e., SIMulation and EXtrapolation - SIMEX) have enabled direct estimation of bias given single datasets. Herein, we leverage the theoretical core of SIMEX to study the properties of inference methods in the face of diminishing data (in contrast to increasing noise). The stability of inference methods with respect to synthetic loss of empirical data (defined as resilience) is used to quantify the empirical performance of one inference method relative to another. We illustrate this new approach in a comparison of ordinary and robust inference methods with rs-fMRI.

17. Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score

PubMed Central

Zhang, Zhongheng; Ji, Xuqing

2016-01-01

Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO2) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO2 and its interaction with other covariates were explored. A total of 199,125 PaO2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO2 on mortality risk was in quadratic form. There was significant interaction between PaO2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO2 on SOFA score was nonlinear. The study shows that the effect of PaO2 on mortality risk is in quadratic function form, and there is significant interaction between PaO2 and severity of illness. PMID:27734905

18. Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score.

PubMed

Zhang, Zhongheng; Ji, Xuqing

2016-10-13

Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO2) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO2 and its interaction with other covariates were explored. A total of 199,125 PaO2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO2 on mortality risk was in quadratic form. There was significant interaction between PaO2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO2 on SOFA score was nonlinear. The study shows that the effect of PaO2 on mortality risk is in quadratic function form, and there is significant interaction between PaO2 and severity of illness.

19. Differential Expression and Network Inferences through Functional Data Modeling

PubMed Central

Telesca, Donatello; Inoue, Lurdes Y.T.; Neira, Mauricio; Etzioni, Ruth; Gleave, Martin; Nelson, Colleen

2010-01-01

Time–course microarray data consist of mRNA expression from a common set of genes collected at different time points. Such data are thought to reflect underlying biological processes developing over time. In this article we propose a model that allows us to examine differential expression and gene network relationships using time course microarray data. We model each gene expression profile as a random functional transformation of the scale, amplitude and phase of a common curve. Inferences about the gene–specific amplitude parameters allow us to examine differential gene expression. Inferences about measures of functional similarity based on estimated time transformation functions allow us to examine gene networks while accounting for features of the gene expression profiles. We discuss applications to simulated data as well as to microarray data on prostate cancer progression. PMID:19053995

20. Estimation and Inference of Directionally Differentiable Functions: Theory and Applications

Fang, Zheng

This dissertation addresses a large class of irregular models in economics and statistics -- settings in which the parameters of interest take the form φ(theta 0), where φ is a known directionally differentiable function and theta 0 is estimated by thetan. Chapter 1 provides a tractable framework for conducting inference, Chapter 2 focuses on optimality of estimation, and Chapter 3 applies the developed theory to construct a test whether a Hilbert space valued parameter belongs to a convex set and to derive the uniform weak convergence of the Grenander distribution function -- i.e. the least concave majorant of the empirical distribution function -- under minimal assumptions.

1. Inferring consistent functional interaction patterns from natural stimulus FMRI data.

PubMed

Sun, Jiehuan; Hu, Xintao; Huang, Xiu; Liu, Yang; Li, Kaiming; Li, Xiang; Han, Junwei; Guo, Lei; Liu, Tianming; Zhang, Jing

2012-07-16

There has been increasing interest in how the human brain responds to natural stimulus such as video watching in the neuroimaging field. Along this direction, this paper presents our effort in inferring consistent and reproducible functional interaction patterns under natural stimulus of video watching among known functional brain regions identified by task-based fMRI. Then, we applied and compared four statistical approaches, including Bayesian network modeling with searching algorithms: greedy equivalence search (GES), Peter and Clark (PC) analysis, independent multiple greedy equivalence search (IMaGES), and the commonly used Granger causality analysis (GCA), to infer consistent and reproducible functional interaction patterns among these brain regions. It is interesting that a number of reliable and consistent functional interaction patterns were identified by the GES, PC and IMaGES algorithms in different participating subjects when they watched multiple video shots of the same semantic category. These interaction patterns are meaningful given current neuroscience knowledge and are reasonably reproducible across different brains and video shots. In particular, these consistent functional interaction patterns are supported by structural connections derived from diffusion tensor imaging (DTI) data, suggesting the structural underpinnings of consistent functional interactions. Our work demonstrates that specific consistent patterns of functional interactions among relevant brain regions might reflect the brain's fundamental mechanisms of online processing and comprehension of video messages.

USGS Publications Warehouse

Rasmussen, Lowell A.

1982-01-01

A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

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

SciTech Connect

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.

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

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. Inference of gene regulation functions from dynamic transcriptome data

PubMed Central

Hillenbrand, Patrick; Maier, Kerstin C; Cramer, Patrick; Gerland, Ulrich

2016-01-01

To quantify gene regulation, a function is required that relates transcription factor binding to DNA (input) to the rate of mRNA synthesis from a target gene (output). Such a ‘gene regulation function’ (GRF) generally cannot be measured because the experimental titration of inputs and simultaneous readout of outputs is difficult. Here we show that GRFs may instead be inferred from natural changes in cellular gene expression, as exemplified for the cell cycle in the yeast S. cerevisiae. We develop this inference approach based on a time series of mRNA synthesis rates from a synchronized population of cells observed over three cell cycles. We first estimate the functional form of how input transcription factors determine mRNA output and then derive GRFs for target genes in the CLB2 gene cluster that are expressed during G2/M phase. Systematic analysis of additional GRFs suggests a network architecture that rationalizes transcriptional cell cycle oscillations. We find that a transcription factor network alone can produce oscillations in mRNA expression, but that additional input from cyclin oscillations is required to arrive at the native behaviour of the cell cycle oscillator. DOI: http://dx.doi.org/10.7554/eLife.12188.001 PMID:27652904

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

PubMed

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.

7. 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

8. Computational approaches for inferring the functions of intrinsically disordered proteins

PubMed Central

Varadi, Mihaly; Vranken, Wim; Guharoy, Mainak; Tompa, Peter

2015-01-01

Intrinsically disordered proteins (IDPs) are ubiquitously involved in cellular processes and often implicated in human pathological conditions. The critical biological roles of these proteins, despite not adopting a well-defined fold, encouraged structural biologists to revisit their views on the protein structure-function paradigm. Unfortunately, investigating the characteristics and describing the structural behavior of IDPs is far from trivial, and inferring the function(s) of a disordered protein region remains a major challenge. Computational methods have proven particularly relevant for studying IDPs: on the sequence level their dependence on distinct characteristics determined by the local amino acid context makes sequence-based prediction algorithms viable and reliable tools for large scale analyses, while on the structure level the in silico integration of fundamentally different experimental data types is essential to describe the behavior of a flexible protein chain. Here, we offer an overview of the latest developments and computational techniques that aim to uncover how protein function is connected to intrinsic disorder. PMID:26301226

9. Quadratic functions used in the estimation of projections of antique maps

Molnar, Gabor

2010-05-01

"Substituting projection" is a projection defined by a set of projection parameters in GIS systems, for a map, whose "true" projection parameters are not known. Defining "substituting projection" is easy for maps with overprinted meridians and parallels. In this case any projection is acceptable as a "substituting projection" that has a same shape for geographic coordinates, as it is printed on the map. This makes it possible to find out the projection type at least (conic, cylindrical or azimuthal) using basic cartometry rules. After defining the "substituting projection", a linear or a Helmert transformation can be used to transform the image into this projection. If we do not have geographic coordinates overprinted on the map, we still can estimate them, using map features as ground control points (GCPs), and using the geographic coordinates of these GCPs. Some GIS software applied for georeferencing raster maps are capable to show the transformed grid defined by the GGPs' coordinates on the raster image. If we use second or third order polynomial (quadratic or cubic) transformation, the transformed geographical coordinate grid can be regarded as an overprinted geographical grid. In this case this "overprint" can be used for finding out the projection type and parameters. In this case, the root-mean-square (RMS) of the residual error of the GCPs measured and transformed coordinates is not negligible. We get similar RMS errors if we use modern coordinate system coordinates as GCP coordinates. In this case the magnitude of the RMS errors is almost independent of the system chosen. This RMS error is due to by the inaccurate measurement of location coordinates during the mapping process, and can not be reduced choosing another projection. If we found out a good parameter set for "substituting projection" this RMS error is the same magnitude, even if we use a linear or Helmert-type transformation. This can be used as a criteria for selecting between projection types

10. 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.

11. Steepest descent with momentum for quadratic functions is a version of the conjugate gradient method.

PubMed

Bhaya, Amit; Kaszkurewicz, Eugenius

2004-01-01

It is pointed out that the so called momentum method, much used in the neural network literature as an acceleration of the backpropagation method, is a stationary version of the conjugate gradient method. Connections with the continuous optimization method known as heavy ball with friction are also made. In both cases, adaptive (dynamic) choices of the so called learning rate and momentum parameters are obtained using a control Liapunov function analysis of the system.

SciTech Connect

Jian Jinbao Hu Qingjie; Tang Chunming; Zheng Haiyan

2007-12-15

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.

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

PubMed

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.

14. 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.

15. Constructing a Flexible Likelihood Function for Spectroscopic Inference

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.

16. CONSTRUCTING A FLEXIBLE LIKELIHOOD FUNCTION FOR SPECTROSCOPIC INFERENCE

SciTech Connect

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

2015-10-20

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.

17. On the Inference of Functional Circadian Networks Using Granger Causality.

PubMed

Pourzanjani, Arya; Herzog, Erik D; Petzold, Linda R

2015-01-01

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals.

18. Properties of surjective real quadratic maps

Arutyunov, A. V.; Zhukovskiy, S. E.

2016-09-01

The properties of surjective real quadratic maps are investigated. Sufficient conditions for the property of surjectivity to be stable under various perturbations are obtained. Examples of surjective quadratic maps whose surjectivity breaks down after an arbitrarily small perturbation are constructed. Sufficient conditions for quadratic maps to have nontrivial zeros are obtained. For a smooth even map in a neighbourhood of the origin an inverse function theorem in terms of the degree of the corresponding quadratic map is obtained. A canonical form of surjective quadratic maps from {R}^3 to {R}^3 is constructed. Bibliography: 27 titles.

19. 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.

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

PubMed

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

2007-09-01

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.

1. 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

ERIC Educational Resources Information Center

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…

3. 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

4. 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.

5. Executive Functions in Adolescence: Inferences from Brain and Behavior

ERIC Educational Resources Information Center

Crone, Eveline A.

2009-01-01

Despite the advances in understanding cognitive improvements in executive function in adolescence, much less is known about the influence of affective and social modulators on executive function and the biological underpinnings of these functions and sensitivities. Here, recent behavioral and neuroscientific studies are summarized that have used…

6. 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

7. 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.

8. Bayesian inference of nonpositive spectral functions in quantum field theory

Rothkopf, Alexander

2017-03-01

We present the generalization to nonpositive definite spectral functions of a recently proposed Bayesian deconvolution approach (BR method). The novel prior used here retains many of the beneficial analytic properties of the original method; in particular, it allows us to integrate out the hyperparameter α directly. To preserve the underlying axiom of scale invariance, we introduce a second default-model related function, whose role is discussed. Our reconstruction prescription is contrasted with existing direct methods, as well as with an approach where shift functions are introduced to compensate for negative spectral features. A mock spectrum analysis inspired by the study of gluon spectral functions in QCD illustrates the capabilities of this new approach.

9. Generalised partition functions: inferences on phase space distributions

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.

10. Actively Learning Specific Function Properties with Applications to Statistical Inference

DTIC Science & Technology

2007-12-01

which are distant from their nearest neigh- bors . However, when searching for level-sets, we are less interested in the function away from the level...34 excludes openly gay , lesbian and bisexual students from receiving ROTC scholarships or serving in the military. Nevertheless, all ROTC classes at

11. Network-based inference of protein activity helps functionalize the genetic landscape of cancer

PubMed Central

Alvarez, Mariano J.; Shen, Yao; Giorgi, Federico M.; Lachmann, Alexander; Ding, B. Belinda; Ye, B. Hilda; Califano, Andrea

2016-01-01

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. To address this problem we introduce and experimentally validate a new algorithm, VIPER (Virtual Inference of Protein-activity by Enriched Regulon analysis), for the accurate assessment of protein activity from gene expression data. We use VIPER to evaluate the functional relevance of genetic alterations in regulatory proteins across all TCGA samples. In addition to accurately inferring aberrant protein activity induced by established mutations, we also identify a significant fraction of tumors with aberrant activity of druggable oncoproteins—despite a lack of mutations, and vice-versa. In vitro assays confirmed that VIPER-inferred protein activity outperforms mutational analysis in predicting sensitivity to targeted inhibitors. PMID:27322546

12. Communicative functions of directional verbal probabilities: Speaker's choice, listener's inference, and reference points.

PubMed

Honda, Hidehito; Yamagishi, Kimihiko

2016-09-09

Verbal probabilities have directional communicative functions, and most can be categorized as positive (e.g., "it is likely") or negative (e.g., "it is doubtful"). We examined the communicative functions of verbal probabilities based on the reference point hypothesis According to this hypothesis, listeners are sensitive to and can infer a speaker's reference points based on the speaker's selected directionality. In four experiments (two of which examined speakers' choice of directionality and two of which examined listeners' inferences about a speaker's reference point), we found that listeners could make inferences about speakers' reference points based on the stated directionality of verbal probability. Thus, the directionality of verbal probabilities serves the communicative function of conveying information about a speaker's reference point.

13. 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.

14. Inferring Functional Relationships from Conservation of Gene Order.

PubMed

Moreno-Hagelsieb, Gabriel

2017-01-01

Predicting functional associations using the Gene Neighbor Method depends on the simple idea that if genes are conserved next to each other in evolutionarily distant prokaryotes they might belong to a polycistronic transcription unit. The procedure presented in this chapter starts with the organization of the genes within genomes into pairs of adjacent genes. Then, the pairs of adjacent genes in a genome of interest are mapped to their corresponding orthologs in other, informative, genomes. The final step is to verify if the mapped orthologs are also pairs of adjacent genes in the informative genomes.

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.

16. Functional Inference of Complex Anatomical Tendinous Networks at a Macroscopic Scale via Sparse Experimentation

PubMed Central

Saxena, Anupam; Lipson, Hod; Valero-Cuevas, Francisco J.

2012-01-01

In systems and computational biology, much effort is devoted to functional identification of systems and networks at the molecular-or cellular scale. However, similarly important networks exist at anatomical scales such as the tendon network of human fingers: the complex array of collagen fibers that transmits and distributes muscle forces to finger joints. This network is critical to the versatility of the human hand, and its function has been debated since at least the 16th century. Here, we experimentally infer the structure (both topology and parameter values) of this network through sparse interrogation with force inputs. A population of models representing this structure co-evolves in simulation with a population of informative future force inputs via the predator-prey estimation-exploration algorithm. Model fitness depends on their ability to explain experimental data, while the fitness of future force inputs depends on causing maximal functional discrepancy among current models. We validate our approach by inferring two known synthetic Latex networks, and one anatomical tendon network harvested from a cadaver's middle finger. We find that functionally similar but structurally diverse models can exist within a narrow range of the training set and cross-validation errors. For the Latex networks, models with low training set error [<4%] and resembling the known network have the smallest cross-validation errors [∼5%]. The low training set [<4%] and cross validation [<7.2%] errors for models for the cadaveric specimen demonstrate what, to our knowledge, is the first experimental inference of the functional structure of complex anatomical networks. This work expands current bioinformatics inference approaches by demonstrating that sparse, yet informative interrogation of biological specimens holds significant computational advantages in accurate and efficient inference over random testing, or assuming model topology and only inferring parameters values. These

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

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.

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

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.

19. 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:…

20. Specificity of Emotion Inferences as a Function of Emotional Contextual Support

ERIC Educational Resources Information Center

Gillioz, Christelle; Gygax, Pascal M.

2017-01-01

Research on emotion inferences has shown that readers include a representation of the main character's emotional state in their mental representations of the text. We examined the specificity of emotion representations as a function of the emotion content of short narratives, in terms of the quantity and quality of emotion components included in…

1. An estimating function approach to inference for inhomogeneous Neyman-Scott processes.

PubMed

Waagepetersen, Rasmus Plenge

2007-03-01

This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Scott process tends to infinity. Clustering parameter estimates are obtained using minimum contrast estimation based on the K-function. The approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot.

2. Transcriptional network inference from functional similarity and expression data: a global supervised approach.

PubMed

Ambroise, Jérôme; Robert, Annie; Macq, Benoit; Gala, Jean-Luc

2012-01-06

An important challenge in system biology is the inference of biological networks from postgenomic data. Among these biological networks, a gene transcriptional regulatory network focuses on interactions existing between transcription factors (TFs) and and their corresponding target genes. A large number of reverse engineering algorithms were proposed to infer such networks from gene expression profiles, but most current methods have relatively low predictive performances. In this paper, we introduce the novel TNIFSED method (Transcriptional Network Inference from Functional Similarity and Expression Data), that infers a transcriptional network from the integration of correlations and partial correlations of gene expression profiles and gene functional similarities through a supervised classifier. In the current work, TNIFSED was applied to predict the transcriptional network in Escherichia coli and in Saccharomyces cerevisiae, using datasets of 445 and 170 affymetrix arrays, respectively. Using the area under the curve of the receiver operating characteristics and the F-measure as indicators, we showed the predictive performance of TNIFSED to be better than unsupervised state-of-the-art methods. TNIFSED performed slightly worse than the supervised SIRENE algorithm for the target genes identification of the TF having a wide range of yet identified target genes but better for TF having only few identified target genes. Our results indicate that TNIFSED is complementary to the SIRENE algorithm, and particularly suitable to discover target genes of "orphan" TFs.

3. 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

4. A variance components model for statistical inference on functional connectivity networks.

PubMed

Fiecas, Mark; Cribben, Ivor; Bahktiari, Reyhaneh; Cummine, Jacqueline

2017-01-24

We propose a variance components linear modeling framework to conduct statistical inference on functional connectivity networks that directly accounts for the temporal autocorrelation inherent in functional magnetic resonance imaging (fMRI) time series data and for the heterogeneity across subjects in the study. The novel method estimates the autocorrelation structure in a nonparametric and subject-specific manner, and estimates the variance due to the heterogeneity using iterative least squares. We apply the new model to a resting-state fMRI study to compare the functional connectivity networks in both typical and reading impaired young adults in order to characterize the resting state networks that are related to reading processes. We also compare the performance of our model to other methods of statistical inference on functional connectivity networks that do not account for the temporal autocorrelation or heterogeneity across the subjects using simulated data, and show that by accounting for these sources of variation and covariation results in more powerful tests for statistical inference.

5. Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Stankovski, Tomislav

2017-02-01

Interactions in nature can be described by their coupling strength, direction of coupling, and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems; however, there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here: synchronization transition occurs only due to the time variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brain waves extracted from the electroencephalography recording of a healthy human subject in a free-running resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions, and it should be taken into account when detecting biological or other interactions from data.

6. Time-varying coupling functions: Dynamical inference and cause of synchronization transitions.

PubMed

Stankovski, Tomislav

2017-02-01

Interactions in nature can be described by their coupling strength, direction of coupling, and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems; however, there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here: synchronization transition occurs only due to the time variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brain waves extracted from the electroencephalography recording of a healthy human subject in a free-running resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions, and it should be taken into account when detecting biological or other interactions from data.

7. 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.

8. 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

9. Statistical inference for assessing functional connectivity of neuronal ensembles with sparse spiking data.

PubMed

Chen, Zhe; Putrino, David F; Ghosh, Soumya; Barbieri, Riccardo; Brown, Emery N

2011-04-01

The ability to accurately infer functional connectivity between ensemble neurons using experimentally acquired spike train data is currently an important research objective in computational neuroscience. Point process generalized linear models and maximum likelihood estimation have been proposed as effective methods for the identification of spiking dependency between neurons. However, unfavorable experimental conditions occasionally results in insufficient data collection due to factors such as low neuronal firing rates or brief recording periods, and in these cases, the standard maximum likelihood estimate becomes unreliable. The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data. Four inference methods were compared: maximum likelihood estimation, penalized maximum likelihood estimation, using either l(2) or l(1) regularization, and hierarchical Bayesian estimation based on a variational Bayes algorithm. Algorithmic performances were compared using well-established goodness-of-fit measures in benchmark simulation studies, and the hierarchical Bayesian approach performed favorably when compared with the other algorithms, and this approach was then successfully applied to real spiking data recorded from the cat motor cortex. The identification of spiking dependencies in physiologically acquired data was encouraging, since their sparse nature would have previously precluded them from successful analysis using traditional methods.

10. Diverse Effects, Complex Causes: Children Use Information About Machines' Functional Diversity to Infer Internal Complexity.

PubMed

Ahl, Richard E; Keil, Frank C

2016-09-26

Four studies explored the abilities of 80 adults and 180 children (4-9 years), from predominantly middle-class families in the Northeastern United States, to use information about machines' observable functional capacities to infer their internal, "hidden" mechanistic complexity. Children as young as 4 and 5 years old used machines' numbers of functions as indications of complexity and matched machines performing more functions with more complex "insides" (Study 1). However, only older children (6 and older) and adults used machines' functional diversity alone as an indication of complexity (Studies 2-4). The ability to use functional diversity as a complexity cue therefore emerges during the early school years, well before the use of diversity in most categorical induction tasks.

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)

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]…

13. Asymptotic Normality of Quadratic Estimators.

PubMed

Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad

2016-12-01

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

14. De novo inference of protein function from coarse-grained dynamics.

PubMed

2014-10-01

Inference of molecular function of proteins is the fundamental task in the quest for understanding cellular processes. The task is getting increasingly difficult with thousands of new proteins discovered each day. The difficulty arises primarily due to lack of high-throughput experimental technique for assessing protein molecular function, a lacunae that computational approaches are trying hard to fill. The latter too faces a major bottleneck in absence of clear evidence based on evolutionary information. Here we propose a de novo approach to annotate protein molecular function through structural dynamics match for a pair of segments from two dissimilar proteins, which may share even <10% sequence identity. To screen these matches, corresponding 1 µs coarse-grained (CG) molecular dynamics trajectories were used to compute normalized root-mean-square-fluctuation graphs and select mobile segments, which were, thereafter, matched for all pairs using unweighted three-dimensional autocorrelation vectors. Our in-house custom-built forcefield (FF), extensively validated against dynamics information obtained from experimental nuclear magnetic resonance data, was specifically used to generate the CG dynamics trajectories. The test for correspondence of dynamics-signature of protein segments and function revealed 87% true positive rate and 93.5% true negative rate, on a dataset of 60 experimentally validated proteins, including moonlighting proteins and those with novel functional motifs. A random test against 315 unique fold/function proteins for a negative test gave >99% true recall. A blind prediction on a novel protein appears consistent with additional evidences retrieved therein. This is the first proof-of-principle of generalized use of structural dynamics for inferring protein molecular function leveraging our custom-made CG FF, useful to all.

15. 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

16. Homology-based inference sets the bar high for protein function prediction

PubMed Central

2013-01-01

Background Any method that de novo predicts protein function should do better than random. More challenging, it also ought to outperform simple homology-based inference. Methods Here, we describe a few methods that predict protein function exclusively through homology. Together, they set the bar or lower limit for future improvements. Results and conclusions During the development of these methods, we faced two surprises. Firstly, our most successful implementation for the baseline ranked very high at CAFA1. In fact, our best combination of homology-based methods fared only slightly worse than the top-of-the-line prediction method from the Jones group. Secondly, although the concept of homology-based inference is simple, this work revealed that the precise details of the implementation are crucial: not only did the methods span from top to bottom performers at CAFA, but also the reasons for these differences were unexpected. In this work, we also propose a new rigorous measure to compare predicted and experimental annotations. It puts more emphasis on the details of protein function than the other measures employed by CAFA and may best reflect the expectations of users. Clearly, the definition of proper goals remains one major objective for CAFA. PMID:23514582

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

PubMed

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

2015-03-01

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.

18. Statistical inference of dynamic resting-state functional connectivity using hierarchical observation modeling.

PubMed

2016-12-01

Spontaneous fluctuations of blood-oxygenation level-dependent functional magnetic resonance imaging (BOLD fMRI) signals are highly synchronous between brain regions that serve similar functions. This provides a means to investigate functional networks; however, most analysis techniques assume functional connections are constant over time. This may be problematic in the case of neurological disease, where functional connections may be highly variable. Recently, several methods have been proposed to determine moment-to-moment changes in the strength of functional connections over an imaging session (so called dynamic connectivity). Here a novel analysis framework based on a hierarchical observation modeling approach was proposed, to permit statistical inference of the presence of dynamic connectivity. A two-level linear model composed of overlapping sliding windows of fMRI signals, incorporating the fact that overlapping windows are not independent was described. To test this approach, datasets were synthesized whereby functional connectivity was either constant (significant or insignificant) or modulated by an external input. The method successfully determines the statistical significance of a functional connection in phase with the modulation, and it exhibits greater sensitivity and specificity in detecting regions with variable connectivity, when compared with sliding-window correlation analysis. For real data, this technique possesses greater reproducibility and provides a more discriminative estimate of dynamic connectivity than sliding-window correlation analysis. Hum Brain Mapp 37:4566-4580, 2016. © 2016 Wiley Periodicals, Inc.

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

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

20. Testing two mechanisms by which rational and irrational beliefs may affect the functionality of inferences.

PubMed

Bond, F W; Dryden, W; Briscoe, R

1999-12-01

This article describes a role playing experiment that examined the sufficiency hypothesis of Rational Emotive Behaviour Therapy (REBT). This proposition states that it is sufficient for rational and irrational beliefs to refer to preferences and musts, respectively, if those beliefs are to affect the functionality of inferences (FI). Consistent with the REBT literature (e.g. Dryden, 1994; Dryden & Ellis, 1988; Palmer, Dryden, Ellis & Yapp, 1995) results from this experiment showed that rational and irrational beliefs, as defined by REBT, do affect FI. Specifically, results showed that people who hold a rational belief form inferences that are significantly more functional than those that are formed by people who hold an irrational belief. Contrary to REBT theory, the sufficiency hypothesis was not supported. Thus, results indicated that it is not sufficient for rational and irrational beliefs to refer to preferences and musts, respectively, if those beliefs are to affect the FI. It appears, then, that preferences and musts are not sufficient mechanisms by which rational and irrational beliefs, respectively, affect the FI. Psychotherapeutic implications of these findings are considered.

1. Bayesian Inference of Two-Dimensional Contrast Sensitivity Function from Data Obtained with Classical One-Dimensional Algorithms Is Efficient

PubMed Central

Wang, Xiaoxiao; Wang, Huan; Huang, Jinfeng; Zhou, Yifeng; Tzvetanov, Tzvetomir

2017-01-01

The contrast sensitivity function that spans the two dimensions of contrast and spatial frequency is crucial in predicting functional vision both in research and clinical applications. In this study, the use of Bayesian inference was proposed to determine the parameters of the two-dimensional contrast sensitivity function. Two-dimensional Bayesian inference was extensively simulated in comparison to classical one-dimensional measures. Its performance on two-dimensional data gathered with different sampling algorithms was also investigated. The results showed that the two-dimensional Bayesian inference method significantly improved the accuracy and precision of the contrast sensitivity function, as compared to the more common one-dimensional estimates. In addition, applying two-dimensional Bayesian estimation to the final data set showed similar levels of reliability and efficiency across widely disparate and established sampling methods (from classical one-dimensional sampling, such as Ψ or staircase, to more novel multi-dimensional sampling methods, such as quick contrast sensitivity function and Fisher information gain). Furthermore, the improvements observed following the application of Bayesian inference were maintained even when the prior poorly matched the subject's contrast sensitivity function. Simulation results were confirmed in a psychophysical experiment. The results indicated that two-dimensional Bayesian inference of contrast sensitivity function data provides similar estimates across a wide range of sampling methods. The present study likely has implications for the measurement of contrast sensitivity function in various settings (including research and clinical settings) and would facilitate the comparison of existing data from previous studies. PMID:28119563

2. Bayesian Inference of Two-Dimensional Contrast Sensitivity Function from Data Obtained with Classical One-Dimensional Algorithms Is Efficient.

PubMed

Wang, Xiaoxiao; Wang, Huan; Huang, Jinfeng; Zhou, Yifeng; Tzvetanov, Tzvetomir

2016-01-01

The contrast sensitivity function that spans the two dimensions of contrast and spatial frequency is crucial in predicting functional vision both in research and clinical applications. In this study, the use of Bayesian inference was proposed to determine the parameters of the two-dimensional contrast sensitivity function. Two-dimensional Bayesian inference was extensively simulated in comparison to classical one-dimensional measures. Its performance on two-dimensional data gathered with different sampling algorithms was also investigated. The results showed that the two-dimensional Bayesian inference method significantly improved the accuracy and precision of the contrast sensitivity function, as compared to the more common one-dimensional estimates. In addition, applying two-dimensional Bayesian estimation to the final data set showed similar levels of reliability and efficiency across widely disparate and established sampling methods (from classical one-dimensional sampling, such as Ψ or staircase, to more novel multi-dimensional sampling methods, such as quick contrast sensitivity function and Fisher information gain). Furthermore, the improvements observed following the application of Bayesian inference were maintained even when the prior poorly matched the subject's contrast sensitivity function. Simulation results were confirmed in a psychophysical experiment. The results indicated that two-dimensional Bayesian inference of contrast sensitivity function data provides similar estimates across a wide range of sampling methods. The present study likely has implications for the measurement of contrast sensitivity function in various settings (including research and clinical settings) and would facilitate the comparison of existing data from previous studies.

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. 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

Direct liquid chromatography-tandem mass spectrometry (LC-MS/MS) was used to examine the proteins extracted from Desulfovibrio vulgaris cells. While our previous study provided a proteomic overview of the cellular metabolism based on proteins with known functions (Zhang et al., 2006a, Proteomics, 6: 4286-4299), this study describes the global detection and functional inference for hypothetical D. vulgaris proteins. Across six growth conditions, 15,841 tryptic peptides were identified with high confidence. Using a criterion of peptide identification from at least two out of three independent LC-MS/MS analyses per protein, 176 open reading frames (ORFs) originally annotated as hypothetical proteins were found to encode expressed proteins. These proteins ranged from 6.0 to 153 kDa, and had calculated pI values ranging from 3.7 to 11.5. Based on homology search results (with E value <= 0.01 as a cutoff), 159 proteins were defined as conserved hypothetical proteins, and 17 proteins were unique to the D. vulgaris genome. Functional inference of the conserved hypothetical proteins was performed by a combination of several non-homology based methods: genomic context analysis, phylogenomic profiling, and analysis of a combination of experimental information including peptide detection in cells grown under specific culture conditions and cellular location of the proteins. Using this approach we were able to assign possible functions to 27 conserved hypothetical proteins. This study demonstrated that a combination of proteomics and bioinformatics methodologies can provide verification for the authenticity of hypothetical proteins and improve annotation for the D. vulgaris genome.

5. Phase diagram of electronic systems with quadratic Fermi nodes in 2 functional renormalization group

Janssen, Lukas; Herbut, Igor F.

2017-02-01

Several materials in the regime of strong spin-orbit interaction such as HgTe, the pyrochlore iridate Pr2Ir2O7 , and the half-Heusler compound LaPtBi, as well as various systems related to these three prototype materials, are believed to host a quadratic band touching point at the Fermi level. Recently, it has been proposed that such a three-dimensional gapless state is unstable to a Mott-insulating ground state at low temperatures when the number of band touching points N at the Fermi level is smaller than a certain critical number Nc. We further substantiate and quantify this scenario by various approaches. Using ɛ expansion near two spatial dimensions, we show that Nc=64 /(25 ɛ2) +O (1 /ɛ ) and demonstrate that the instability for N functional renormalization group equations in the dynamical bosonization scheme which we show to agree to one-loop order with the results from ɛ expansion both near two as well as near four dimensions, and which smoothly interpolates between these two perturbatively accessible limits for general 2

6. 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

7. Using quadratic simplicial elements for hierarchical approximation and visualization

Wiley, David F.; Childs, Henry R.; Hamann, Bernd; Joy, Kenneth I.; Max, Nelson

2002-03-01

Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.

8. Inferring functional constraints and divergence in protein families using 3D mapping of phylogenetic information

PubMed Central

Blouin, Christian; Boucher, Yan; Roger, Andrew J.

2003-01-01

Comparative sequence analysis has been used to study specific questions about the structure and function of proteins for many years. Here we propose a knowledge-based framework in which the maximum likelihood rate of evolution is used to quantify the level of constraint on the identity of a site. We demonstrate that site-rate mapping on 3D structures using datasets of rhodopsin-like G-protein receptors and α- and β-tubulins provides an excellent tool for pinpointing the functional features shared between orthologous and paralogous proteins. In addition, functional divergence within protein families can be inferred by examining the differences in the site rates, the differences in the chemical properties of the side chains or amino acid usage between aligned sites. Two novel analytical methods are introduced to characterize rate- independent functional divergence. These are tested using a dataset of two classes of HMG-CoA reductases for which only one class can perform both the forward and reverse reaction. We show that functionally divergent sites occur in a cluster of sites interacting with the catalytic residues and that this information should facilitate the design of experimental strategies to directly test functional properties of residues. PMID:12527789

9. Inferring functional constraints and divergence in protein families using 3D mapping of phylogenetic information.

PubMed

Blouin, Christian; Boucher, Yan; Roger, Andrew J

2003-01-15

Comparative sequence analysis has been used to study specific questions about the structure and function of proteins for many years. Here we propose a knowledge-based framework in which the maximum likelihood rate of evolution is used to quantify the level of constraint on the identity of a site. We demonstrate that site-rate mapping on 3D structures using datasets of rhodopsin-like G-protein receptors and alpha- and beta-tubulins provides an excellent tool for pinpointing the functional features shared between orthologous and paralogous proteins. In addition, functional divergence within protein families can be inferred by examining the differences in the site rates, the differences in the chemical properties of the side chains or amino acid usage between aligned sites. Two novel analytical methods are introduced to characterize rate- independent functional divergence. These are tested using a dataset of two classes of HMG-CoA reductases for which only one class can perform both the forward and reverse reaction. We show that functionally divergent sites occur in a cluster of sites interacting with the catalytic residues and that this information should facilitate the design of experimental strategies to directly test functional properties of residues.

10. Structure-based function inference using protein family-specific fingerprints

PubMed Central

Bandyopadhyay, Deepak; Huan, Jun; Liu, Jinze; Prins, Jan; Snoeyink, Jack; Wang, Wei; Tropsha, Alexander

2006-01-01

We describe a method to assign a protein structure to a functional family using family-specific fingerprints. Fingerprints represent amino acid packing patterns that occur in most members of a family but are rare in the background, a nonredundant subset of PDB; their information is additional to sequence alignments, sequence patterns, structural superposition, and active-site templates. Fingerprints were derived for 120 families in SCOP using Frequent Subgraph Mining. For a new structure, all occurrences of these family-specific fingerprints may be found by a fast algorithm for subgraph isomorphism; the structure can then be assigned to a family with a confidence value derived from the number of fingerprints found and their distribution in background proteins. In validation experiments, we infer the function of new members added to SCOP families and we discriminate between structurally similar, but functionally divergent TIM barrel families. We then apply our method to predict function for several structural genomics proteins, including orphan structures. Some predictions have been corroborated by other computational methods and some validated by subsequent functional characterization. PMID:16731985

11. Unleashing the power of meta-threading for evolution/structure-based function inference of proteins.

PubMed

Brylinski, Michal

2013-01-01

12. 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.

13. PSQP -- Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda; Taubin, Gabriel; Goldenstein, Siome

2016-03-25

In this article we present the first effective global method for the reconstruction of image puzzles comprising rectangle pieces - Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

14. PSQP: Puzzle Solving by Quadratic Programming.

PubMed

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

15. 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.

16. Guises and disguises of quadratic divergences

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

2014-12-01

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.

17. Target manifold formation using a quadratic SDF

Hester, Charles F.; Risko, Kelly K. D.

2013-05-01

Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.

18. 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.

19. Inference of Functionally-Relevant N-acetyltransferase Residues Based on Statistical Correlations.

PubMed

Neuwald, Andrew F; Altschul, Stephen F

2016-12-01

Over evolutionary time, members of a superfamily of homologous proteins sharing a common structural core diverge into subgroups filling various functional niches. At the sequence level, such divergence appears as correlations that arise from residue patterns distinct to each subgroup. Such a superfamily may be viewed as a population of sequences corresponding to a complex, high-dimensional probability distribution. Here we model this distribution as hierarchical interrelated hidden Markov models (hiHMMs), which describe these sequence correlations implicitly. By characterizing such correlations one may hope to obtain information regarding functionally-relevant properties that have thus far evaded detection. To do so, we infer a hiHMM distribution from sequence data using Bayes' theorem and Markov chain Monte Carlo (MCMC) sampling, which is widely recognized as the most effective approach for characterizing a complex, high dimensional distribution. Other routines then map correlated residue patterns to available structures with a view to hypothesis generation. When applied to N-acetyltransferases, this reveals sequence and structural features indicative of functionally important, yet generally unknown biochemical properties. Even for sets of proteins for which nothing is known beyond unannotated sequences and structures, this can lead to helpful insights. We describe, for example, a putative coenzyme-A-induced-fit substrate binding mechanism mediated by arginine residue switching between salt bridge and π-π stacking interactions. A suite of programs implementing this approach is available (psed.igs.umaryland.edu).

20. Constrained parametric model for simultaneous inference of two cumulative incidence functions.

PubMed

Shi, Haiwen; Cheng, Yu; Jeong, Jong-Hyeon

2013-01-01

We propose a parametric regression model for the cumulative incidence functions (CIFs) commonly used for competing risks data. The model adopts a modified logistic model as the baseline CIF and a generalized odds-rate model for covariate effects, and it explicitly takes into account the constraint that a subject with any given prognostic factors should eventually fail from one of the causes such that the asymptotes of the CIFs should add up to one. This constraint intrinsically holds in a nonparametric analysis without covariates, but is easily overlooked in a semiparametric or parametric regression setting. We hence model the CIF from the primary cause assuming the generalized odds-rate transformation and the modified logistic function as the baseline CIF. Under the additivity constraint, the covariate effects on the competing cause are modeled by a function of the asymptote of the baseline distribution and the covariate effects on the primary cause. The inference procedure is straightforward by using the standard maximum likelihood theory. We demonstrate desirable finite-sample performance of our model by simulation studies in comparison with existing methods. Its practical utility is illustrated in an analysis of a breast cancer dataset to assess the treatment effect of tamoxifen, adjusting for age and initial pathological tumor size, on breast cancer recurrence that is subject to dependent censoring by second primary cancers and deaths.

1. Inference of Functionally-Relevant N-acetyltransferase Residues Based on Statistical Correlations

PubMed Central

Neuwald, Andrew F.

2016-01-01

Over evolutionary time, members of a superfamily of homologous proteins sharing a common structural core diverge into subgroups filling various functional niches. At the sequence level, such divergence appears as correlations that arise from residue patterns distinct to each subgroup. Such a superfamily may be viewed as a population of sequences corresponding to a complex, high-dimensional probability distribution. Here we model this distribution as hierarchical interrelated hidden Markov models (hiHMMs), which describe these sequence correlations implicitly. By characterizing such correlations one may hope to obtain information regarding functionally-relevant properties that have thus far evaded detection. To do so, we infer a hiHMM distribution from sequence data using Bayes’ theorem and Markov chain Monte Carlo (MCMC) sampling, which is widely recognized as the most effective approach for characterizing a complex, high dimensional distribution. Other routines then map correlated residue patterns to available structures with a view to hypothesis generation. When applied to N-acetyltransferases, this reveals sequence and structural features indicative of functionally important, yet generally unknown biochemical properties. Even for sets of proteins for which nothing is known beyond unannotated sequences and structures, this can lead to helpful insights. We describe, for example, a putative coenzyme-A-induced-fit substrate binding mechanism mediated by arginine residue switching between salt bridge and π-π stacking interactions. A suite of programs implementing this approach is available (psed.igs.umaryland.edu). PMID:28002465

2. Inferring Hypotheses on Functional Relationships of Genes: Analysis of the Arabidopsis thaliana Subtilase Gene Family

PubMed Central

Büssis, Dirk; Stintzi, Annick; Schaller, Andreas; Kopka, Joachim; Altmann, Thomas

2005-01-01

The gene family of subtilisin-like serine proteases (subtilases) in Arabidopsis thaliana comprises 56 members, divided into six distinct subfamilies. Whereas the members of five subfamilies are similar to pyrolysins, two genes share stronger similarity to animal kexins. Mutant screens confirmed 144 T-DNA insertion lines with knockouts for 55 out of the 56 subtilases. Apart from SDD1, none of the confirmed homozygous mutants revealed any obvious visible phenotypic alteration during growth under standard conditions. Apart from this specific case, forward genetics gave us no hints about the function of the individual 54 non-characterized subtilase genes. Therefore, the main objective of our work was to overcome the shortcomings of the forward genetic approach and to infer alternative experimental approaches by using an integrative bioinformatics and biological approach. Computational analyses based on transcriptional co-expression and co-response pattern revealed at least two expression networks, suggesting that functional redundancy may exist among subtilases with limited similarity. Furthermore, two hubs were identified, which may be involved in signalling or may represent higher-order regulatory factors involved in responses to environmental cues. A particular enrichment of co-regulated genes with metabolic functions was observed for four subtilases possibly representing late responsive elements of environmental stress. The kexin homologs show stronger associations with genes of transcriptional regulation context. Based on the analyses presented here and in accordance with previously characterized subtilases, we propose three main functions of subtilases: involvement in (i) control of development, (ii) protein turnover, and (iii) action as downstream components of signalling cascades. Supplemental material is available in the Plant Subtilase Database (PSDB) (http://csbdb.mpimp-golm.mpg.de/psdb.html) , as well as from the CSB.DB (http

3. 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…

4. Phydbac2: improved inference of gene function using interactive phylogenomic profiling and chromosomal location analysis.

PubMed

Enault, François; Suhre, Karsten; Poirot, Olivier; Abergel, Chantal; Claverie, Jean-Michel

2004-07-01

Phydbac (phylogenomic display of bacterial genes) implemented a method of phylogenomic profiling using a distance measure based on normalized BLAST scores. This method was able to increase the predictive power of phylogenomic profiling by about 25% when compared to the classical approach based on Hamming distances. Here we present a major extension of Phydbac (named here Phydbac2), that extends both the concept and the functionality of the original web-service. While phylogenomic profiles remain the central focus of Phydbac2, it now integrates chromosomal proximity and gene fusion analyses as two additional non-similarity-based indicators for inferring pairwise gene functional relationships. Moreover, all presently available (January 2004) fully sequenced bacterial genomes and those of three lower eukaryotes are now included in the profiling process, thus increasing the initial number of reference genomes (71 in Phydbac) to 150 in Phydbac2. Using the KEGG metabolic pathway database as a benchmark, we show that the predictive power of Phydbac2 is improved by 27% over the previous version. This gain is accounted for on one hand, by the increased number of reference genomes (11%) and on the other hand, as a result of including chromosomal proximity into the distance measure (16%). The expanded functionality of Phydbac2 now allows the user to query more than 50 different genomes, including at least one member of each major bacterial group, most major pathogens and potential bio-terrorism agents. The search for co-evolving genes based on consensus profiles from multiple organisms, the display of Phydbac2 profiles side by side with COG information, the inclusion of KEGG metabolic pathway maps the production of chromosomal proximity maps, and the possibility of collecting and processing results from different Phydbac queries in a common shopping cart are the main new features of Phydbac2. The Phydbac2 web server is available at http://igs-server.cnrs-mrs.fr/phydbac/.

5. Inference of gene function based on gene fusion events: the rosetta-stone method.

PubMed

Suhre, Karsten

2007-01-01

The method described in this chapter can be used to infer putative functional links between two proteins. The basic idea is based on the principle of "guilt by association." It is assumed that two proteins, which are found to be transcribed by a single transcript in one (or several) genomes are likely to be functionally linked, for example by acting in a same metabolic pathway or by forming a multiprotein complex. This method is of particular interest for studying genes that exhibit no, or only remote, homologies with already well-characterized proteins. Combined with other non-homology based methods, gene fusion events may yield valuable information for hypothesis building on protein function, and may guide experimental characterization of the target protein, for example by suggesting potential ligands or binding partners. This chapter uses the FusionDB database (http://www.igs.cnrs-mrs.fr/FusionDB/) as source of information. FusionDB provides a characterization of a large number of gene fusion events at hand of multiple sequence alignments. Orthologous genes are included to yield a comprehensive view of the structure of a gene fusion event. Phylogenetic tree reconstruction is provided to evaluate the history of a gene fusion event, and three-dimensional protein structure information is used, where available, to further characterize the nature of the gene fusion. For genes that are not comprised in FusionDB, some instructions are given as how to generate a similar type of information, based solely on publicly available web tools that are listed here.

6. Comparative internal anatomy of Staurozoa (Cnidaria), with functional and evolutionary inferences.

PubMed

Miranda, Lucília S; Collins, Allen G; Hirano, Yayoi M; Mills, Claudia E; Marques, Antonio C

2016-01-01

Comparative efforts to understand the body plan evolution of stalked jellyfishes are scarce. Most characters, and particularly internal anatomy, have neither been explored for the class Staurozoa, nor broadly applied in its taxonomy and classification. Recently, a molecular phylogenetic hypothesis was derived for Staurozoa, allowing for the first broad histological comparative study of staurozoan taxa. This study uses comparative histology to describe the body plans of nine staurozoan species, inferring functional and evolutionary aspects of internal morphology based on the current phylogeny of Staurozoa. We document rarely-studied structures, such as ostia between radial pockets, intertentacular lobules, gametoducts, pad-like adhesive structures, and white spots of nematocysts (the last four newly proposed putative synapomorphies for Staurozoa). Two different regions of nematogenesis are documented. This work falsifies the view that the peduncle region of stauromedusae only retains polypoid characters; metamorphosis from stauropolyp to stauromedusa occurs both at the apical region (calyx) and basal region (peduncle). Intertentacular lobules, observed previously in only a small number of species, are shown to be widespread. Similarly, gametoducts were documented in all analyzed genera, both in males and females, thereby elucidating gamete release. Finally, ostia connecting adjacent gastric radial pockets appear to be universal for Staurozoa. Detailed histological studies of medusozoan polyps and medusae are necessary to further understand the relationships between staurozoan features and those of other medusozoan cnidarians.

7. Comparative internal anatomy of Staurozoa (Cnidaria), with functional and evolutionary inferences

PubMed Central

Collins, Allen G.; Hirano, Yayoi M.; Mills, Claudia E.

2016-01-01

Comparative efforts to understand the body plan evolution of stalked jellyfishes are scarce. Most characters, and particularly internal anatomy, have neither been explored for the class Staurozoa, nor broadly applied in its taxonomy and classification. Recently, a molecular phylogenetic hypothesis was derived for Staurozoa, allowing for the first broad histological comparative study of staurozoan taxa. This study uses comparative histology to describe the body plans of nine staurozoan species, inferring functional and evolutionary aspects of internal morphology based on the current phylogeny of Staurozoa. We document rarely-studied structures, such as ostia between radial pockets, intertentacular lobules, gametoducts, pad-like adhesive structures, and white spots of nematocysts (the last four newly proposed putative synapomorphies for Staurozoa). Two different regions of nematogenesis are documented. This work falsifies the view that the peduncle region of stauromedusae only retains polypoid characters; metamorphosis from stauropolyp to stauromedusa occurs both at the apical region (calyx) and basal region (peduncle). Intertentacular lobules, observed previously in only a small number of species, are shown to be widespread. Similarly, gametoducts were documented in all analyzed genera, both in males and females, thereby elucidating gamete release. Finally, ostia connecting adjacent gastric radial pockets appear to be universal for Staurozoa. Detailed histological studies of medusozoan polyps and medusae are necessary to further understand the relationships between staurozoan features and those of other medusozoan cnidarians. PMID:27812408

8. Fracture in teeth: a diagnostic for inferring bite force and tooth function.

PubMed

Lee, James J-W; Constantino, Paul J; Lucas, Peter W; Lawn, Brian R

2011-11-01

Teeth are brittle and highly susceptible to cracking. We propose that observations of such cracking can be used as a diagnostic tool for predicting bite force and inferring tooth function in living and fossil mammals. Laboratory tests on model tooth structures and extracted human teeth in simulated biting identify the principal fracture modes in enamel. Examination of museum specimens reveals the presence of similar fractures in a wide range of vertebrates, suggesting that cracks extended during ingestion or mastication. The use of 'fracture mechanics' from materials engineering provides elegant relations for quantifying critical bite forces in terms of characteristic tooth size and enamel thickness. The role of enamel microstructure in determining how cracks initiate and propagate within the enamel (and beyond) is discussed. The picture emerges of teeth as damage-tolerant structures, full of internal weaknesses and defects and yet able to contain the expansion of seemingly precarious cracks and fissures within the enamel shell. How the findings impact on dietary pressures forms an undercurrent of the study.

9. 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

10. Quadratic algebras for three-dimensional superintegrable systems

SciTech Connect

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.

11. Dichoptic Metacontrast Masking Functions to Infer Transmission Delay in Optic Neuritis

PubMed Central

Bruchmann, Maximilian; Korsukewitz, Catharina; Krämer, Julia; Wiendl, Heinz; Meuth, Sven G.

2016-01-01

Optic neuritis (ON) has detrimental effects on the transmission of neuronal signals generated at the earliest stages of visual information processing. The amount, as well as the speed of transmitted visual signals is impaired. Measurements of visual evoked potentials (VEP) are often implemented in clinical routine. However, the specificity of VEPs is limited because multiple cortical areas are involved in the generation of P1 potentials, including feedback signals from higher cortical areas. Here, we show that dichoptic metacontrast masking can be used to estimate the temporal delay caused by ON. A group of 15 patients with unilateral ON, nine of which had sufficient visual acuity and volunteered to participate, and a group of healthy control subjects (N = 8) were presented with flashes of gray disks to one eye and flashes of gray annuli to the corresponding retinal location of the other eye. By asking subjects to report the subjective visibility of the target (i.e. the disk) while varying the stimulus onset asynchrony (SOA) between disk and annulus, we obtained typical U-shaped masking functions. From these functions we inferred the critical SOAmax at which the mask (i.e. the annulus) optimally suppressed the visibility of the target. ON-associated transmission delay was estimated by comparing the SOAmax between conditions in which the disk had been presented to the affected and the mask to the other eye, and vice versa. SOAmax differed on average by 28 ms, suggesting a reduction in transmission speed in the affected eye. Compared to previously reported methods assessing perceptual consequences of altered neuronal transmission speed the presented method is more accurate as it is not limited by the observers’ ability to judge subtle variations in perceived synchrony. PMID:27711139

12. Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement

PubMed Central

Duchesne, Thierry; Fortin, Daniel; Rivest, Louis-Paul

2015-01-01

Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis. PMID:25898019

13. Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement.

PubMed

Duchesne, Thierry; Fortin, Daniel; Rivest, Louis-Paul

2015-01-01

Animal movement has a fundamental impact on population and community structure and dynamics. Biased correlated random walks (BCRW) and step selection functions (SSF) are commonly used to study movements. Because no studies have contrasted the parameters and the statistical properties of their estimators for models constructed under these two Lagrangian approaches, it remains unclear whether or not they allow for similar inference. First, we used the Weak Law of Large Numbers to demonstrate that the log-likelihood function for estimating the parameters of BCRW models can be approximated by the log-likelihood of SSFs. Second, we illustrated the link between the two approaches by fitting BCRW with maximum likelihood and with SSF to simulated movement data in virtual environments and to the trajectory of bison (Bison bison L.) trails in natural landscapes. Using simulated and empirical data, we found that the parameters of a BCRW estimated directly from maximum likelihood and by fitting an SSF were remarkably similar. Movement analysis is increasingly used as a tool for understanding the influence of landscape properties on animal distribution. In the rapidly developing field of movement ecology, management and conservation biologists must decide which method they should implement to accurately assess the determinants of animal movement. We showed that BCRW and SSF can provide similar insights into the environmental features influencing animal movements. Both techniques have advantages. BCRW has already been extended to allow for multi-state modeling. Unlike BCRW, however, SSF can be estimated using most statistical packages, it can simultaneously evaluate habitat selection and movement biases, and can easily integrate a large number of movement taxes at multiple scales. SSF thus offers a simple, yet effective, statistical technique to identify movement taxis.

14. Causal inference in cross-lagged panel analysis: a reciprocal causal relationship between cognitive function and depressive symptoms.

PubMed

Yoon, Ju Young; Brown, Roger L

2014-01-01

Cross-lagged panel analysis (CLPA) is a method of examining one-way or reciprocal causal inference between longitudinally changing variables. It has been used in the social sciences for many years, but not much in nursing research. This article introduces the conceptual and statistical background of CLPA and provides an exemplar of CLPA that examines the reciprocal causal relationship between depression and cognitive function over time in older adults. The 2-year cross-lagged effects of depressive symptoms (T1) on cognitive function (T2) and cognitive function (T1) on depressive symptoms (T2) were significant, which demonstrated a reciprocal causal relationship between cognitive function and depressive mood over time. Although CLPA is a methodologically strong approach to examine the reciprocal causal inferences over time, it is necessary to consider potential sources of spuriousness to lead to false causal relationship and a reasonable time frame to detect the change of the variables.

Lovejoy, S.; Schertzer, D.; Addor, J. B.

Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.

16. Function inferences from a molecular structural model of bacterial ParE toxin

PubMed Central

Barbosa, Luiz Carlos Bertucci; Garrido, Saulo Santesso; Garcia, Anderson; Delfino, Davi Barbosa; Marchetto, Reinaldo

2010-01-01

Toxin-antitoxin (TA) systems contribute to plasmid stability by a mechanism that relies on the differential stabilities of the toxin and antitoxin proteins and leads to the killing of daughter bacteria that did not receive a plasmid copy at the cell division. ParE is the toxic component of a TA system that constitutes along with RelE an important class of bacterial toxin called RelE/ParE superfamily. For ParE toxin, no crystallographic structure is available so far and rare in vitro studies demonstrated that the target of toxin activity is E. coli DNA gyrase. Here, a 3D Model for E. coli ParE toxin by molecular homology modeling was built using MODELLER, a program for comparative modeling. The Model was energy minimized by CHARMM and validated using PROCHECK and VERIFY3D programs. Resulting Ramachandran plot analysis it was found that the portion residues failing into the most favored and allowed regions was 96.8%. Structural similarity search employing DALI server showed as the best matches RelE and YoeB families. The Model also showed similarities with other microbial ribonucleases but in a small score. A possible homologous deep cleft active site was identified in the Model using CASTp program. Additional studies to investigate the nuclease activity in members of ParE family as well as to confirm the inhibitory replication activity are needed. The predicted Model allows initial inferences about the unexplored 3D structure of the ParE toxin and may be further used in rational design of molecules for structure­function studies. PMID:20975905

17. Stochastic Linear Quadratic Optimal Control Problems

SciTech Connect

Chen, S.; Yong, J.

2001-07-01

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

18. Leveraging enzyme structure-function relationships for functional inference and experimental design: the structure-function linkage database.

PubMed

Pegg, Scott C-H; Brown, Shoshana D; Ojha, Sunil; Seffernick, Jennifer; Meng, Elaine C; Morris, John H; Chang, Patricia J; Huang, Conrad C; Ferrin, Thomas E; Babbitt, Patricia C

2006-02-28

The study of mechanistically diverse enzyme superfamilies-collections of enzymes that perform different overall reactions but share both a common fold and a distinct mechanistic step performed by key conserved residues-helps elucidate the structure-function relationships of enzymes. We have developed a resource, the structure-function linkage database (SFLD), to analyze these structure-function relationships. Unique to the SFLD is its hierarchical classification scheme based on linking the specific partial reactions (or other chemical capabilities) that are conserved at the superfamily, subgroup, and family levels with the conserved structural elements that mediate them. We present the results of analyses using the SFLD in correcting misannotations, guiding protein engineering experiments, and elucidating the function of recently solved enzyme structures from the structural genomics initiative. The SFLD is freely accessible at http://sfld.rbvi.ucsf.edu.

19. 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.

20. Quadratic optimization in ill-posed problems

Ben Belgacem, F.; Kaber, S.-M.

2008-10-01

Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.

1. 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

2. 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.

3. Students' understanding of quadratic equations

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.

4. Robust modeling based on optimized EEG bands for functional brain state inference.

PubMed

Podlipsky, Ilana; Ben-Simon, Eti; Hendler, Talma; Intrator, Nathan

2012-01-30

The need to infer brain states in a data driven approach is crucial for BCI applications as well as for neuroscience research. In this work we present a novel classification framework based on Regularized Linear Regression classifier constructed from time-frequency decomposition of an EEG (electro-encephalography) signal. The regression is then used to derive a model of frequency distributions that identifies brain states. The process of classifier construction, preprocessing and selection of optimal regularization parameter by means of cross-validation is presented and discussed. The framework and the feature selection technique are demonstrated on EEG data recorded from 10 healthy subjects while requested to open and close their eyes every 30 s. This paradigm is well known in inducing Alpha power modulations that differ from low power (during eyes opened) to high (during eyes closed). The classifier was trained to infer eyes opened or eyes closed states and achieved higher than 90% classification accuracy. Furthermore, our findings reveal interesting patterns of relations between experimental conditions, EEG frequencies, regularization parameters and classifier choice. This viable tool enables identification of the most contributing frequency bands to any given brain state and their optimal combination in inferring this state. These features allow for much greater detail than the standard Fourier Transform power analysis, making it an essential method for both BCI proposes and neuroimaging research.

5. 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.

6. The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

7. Concretising Factorisation of Quadratic Expressions

ERIC Educational Resources Information Center

Hoong, Leong Yew; Fwe, Yap Sook; Yvonne, Teo Mei Lin; Subramaniam, Thilagam d/o; Zaini, Irni Karen Bte Mohd; Chiew, Quek Eng; Karen, Tan Kang Ling

2010-01-01

The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers…

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.

9. 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.

10. Inferring the Early Evolution of Translation: Ancestral Reconstruction, Compositional Analysis, and Functional Specificity

Fournier, G. P.; Gogarten, J. P.

2010-04-01

Using ancestral sequence reconstruction and compositional analysis, it is possible to reconstruct the ancestral functions of many enzymes involved in protein synthesis, elucidating the early functional evolution of the translation machinery and genetic code.

11. Inference of functional properties from large-scale analysis of enzyme superfamilies.

PubMed

Brown, Shoshana D; Babbitt, Patricia C

2012-01-02

As increasingly large amounts of data from genome and other sequencing projects become available, new approaches are needed to determine the functions of the proteins these genes encode. We show how large-scale computational analysis can help to address this challenge by linking functional information to sequence and structural similarities using protein similarity networks. Network analyses using three functionally diverse enzyme superfamilies illustrate the use of these approaches for facile updating and comparison of available structures for a large superfamily, for creation of functional hypotheses for metagenomic sequences, and to summarize the limits of our functional knowledge about even well studied superfamilies.

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

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.

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

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

14. Inferring biological functions and associated transcriptional regulators using gene set expression coherence analysis

PubMed Central

Kim, Tae-Min; Chung, Yeun-Jun; Rhyu, Mun-Gan; Ho Jung, Myeong

2007-01-01

Background Gene clustering has been widely used to group genes with similar expression pattern in microarray data analysis. Subsequent enrichment analysis using predefined gene sets can provide clues on which functional themes or regulatory sequence motifs are associated with individual gene clusters. In spite of the potential utility, gene clustering and enrichment analysis have been used in separate platforms, thus, the development of integrative algorithm linking both methods is highly challenging. Results In this study, we propose an algorithm for discovery of molecular functions and elucidation of transcriptional logics using two kinds of gene information, functional and regulatory motif gene sets. The algorithm, termed gene set expression coherence analysis first selects functional gene sets with significantly high expression coherences. Those candidate gene sets are further processed into a number of functionally related themes or functional clusters according to the expression similarities. Each functional cluster is then, investigated for the enrichment of transcriptional regulatory motifs using modified gene set enrichment analysis and regulatory motif gene sets. The method was tested for two publicly available expression profiles representing murine myogenesis and erythropoiesis. For respective profiles, our algorithm identified myocyte- and erythrocyte-related molecular functions, along with the putative transcriptional regulators for the corresponding molecular functions. Conclusion As an integrative and comprehensive method for the analysis of large-scaled gene expression profiles, our method is able to generate a set of testable hypotheses: the transcriptional regulator X regulates function Y under cellular condition Z. GSECA algorithm is implemented into freely available software package. PMID:18021416

15. A probabilistic framework to infer brain functional connectivity from anatomical connections.

PubMed

Deligianni, Fani; Varoquaux, Gael; Thirion, Bertrand; Robinson, Emma; Sharp, David J; Edwards, A David; Rueckert, Daniel

2011-01-01

We present a novel probabilistic framework to learn across several subjects a mapping from brain anatomical connectivity to functional connectivity, i.e. the covariance structure of brain activity. This prediction problem must be formulated as a structured-output learning task, as the predicted parameters are strongly correlated. We introduce a model selection framework based on cross-validation with a parametrization-independent loss function suitable to the manifold of covariance matrices. Our model is based on constraining the conditional independence structure of functional activity by the anatomical connectivity. Subsequently, we learn a linear predictor of a stationary multivariate autoregressive model. This natural parameterization of functional connectivity also enforces the positive-definiteness of the predicted covariance and thus matches the structure of the output space. Our results show that functional connectivity can be explained by anatomical connectivity on a rigorous statistical basis, and that a proper model of functional connectivity is essential to assess this link.

16. Nebulon: a system for the inference of functional relationships of gene products from the rearrangement of predicted operons

PubMed Central

Janga, Sarath Chandra; Collado-Vides, Julio; Moreno-Hagelsieb, Gabriel

2005-01-01

Since operons are unstable across Prokaryotes, it has been suggested that perhaps they re-combine in a conservative manner. Thus, genes belonging to a given operon in one genome might re-associate in other genomes revealing functional relationships among gene products. We developed a system to build networks of functional relationships of gene products based on their organization into operons in any available genome. The operon predictions are based on inter-genic distances. Our system can use different kinds of thresholds to accept a functional relationship, either related to the prediction of operons, or to the number of non-redundant genomes that support the associations. We also work by shells, meaning that we decide on the number of linking iterations to allow for the complementation of related gene sets. The method shows high reliability benchmarked against knowledge-bases of functional interactions. We also illustrate the use of Nebulon in finding new members of regulons, and of other functional groups of genes. Operon rearrangements produce thousands of high-quality new interactions per prokaryotic genome, and thousands of confirmations per genome to other predictions, making it another important tool for the inference of functional interactions from genomic context. PMID:15867197

17. The interval testing procedure: A general framework for inference in functional data analysis.

PubMed

Pini, Alessia; Vantini, Simone

2016-09-01

We introduce in this work the Interval Testing Procedure (ITP), a novel inferential technique for functional data. The procedure can be used to test different functional hypotheses, e.g., distributional equality between two or more functional populations, equality of mean function of a functional population to a reference. ITP involves three steps: (i) the representation of data on a (possibly high-dimensional) functional basis; (ii) the test of each possible set of consecutive basis coefficients; (iii) the computation of the adjusted p-values associated to each basis component, by means of a new strategy here proposed. We define a new type of error control, the interval-wise control of the family wise error rate, particularly suited for functional data. We show that ITP is provided with such a control. A simulation study comparing ITP with other testing procedures is reported. ITP is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology. ITP is implemented in the fdatest R package.

18. Phylogenetic approach for inferring the origin and functional evolution of bacterial ADP-ribosylation superfamily.

PubMed

Chellapandi, P; Sakthishree, S; Bharathi, M

2013-09-01

19. Ecological Inference

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.

20. 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.

1. Inference of Functional Relations in Predicted Protein Networks with a Machine Learning Approach

PubMed Central

Ezkurdia, Iakes; Andrés-León, Eduardo; Valencia, Alfonso

2010-01-01

Background Molecular biology is currently facing the challenging task of functionally characterizing the proteome. The large number of possible protein-protein interactions and complexes, the variety of environmental conditions and cellular states in which these interactions can be reorganized, and the multiple ways in which a protein can influence the function of others, requires the development of experimental and computational approaches to analyze and predict functional associations between proteins as part of their activity in the interactome. Methodology/Principal Findings We have studied the possibility of constructing a classifier in order to combine the output of the several protein interaction prediction methods. The AODE (Averaged One-Dependence Estimators) machine learning algorithm is a suitable choice in this case and it provides better results than the individual prediction methods, and it has better performances than other tested alternative methods in this experimental set up. To illustrate the potential use of this new AODE-based Predictor of Protein InterActions (APPIA), when analyzing high-throughput experimental data, we show how it helps to filter the results of published High-Throughput proteomic studies, ranking in a significant way functionally related pairs. Availability: All the predictions of the individual methods and of the combined APPIA predictor, together with the used datasets of functional associations are available at http://ecid.bioinfo.cnio.es/. Conclusions We propose a strategy that integrates the main current computational techniques used to predict functional associations into a unified classifier system, specifically focusing on the evaluation of poorly characterized protein pairs. We selected the AODE classifier as the appropriate tool to perform this task. AODE is particularly useful to extract valuable information from large unbalanced and heterogeneous data sets. The combination of the information provided by five

2. Some Randomized Algorithms for Convex Quadratic Programming

SciTech Connect

Goldbach, R.

1999-01-15

We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.

3. Phylogenetic Gaussian process model for the inference of functionally important regions in protein tertiary structures.

PubMed

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.

4. Binary black hole merger rates inferred from luminosity function of ultra-luminous X-ray sources

Inoue, Yoshiyuki; Tanaka, Yasuyuki T.; Isobe, Naoki

2016-10-01

The Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) has detected direct signals of gravitational waves (GWs) from GW150914. The event was a merger of binary black holes whose masses are 36^{+5}_{-4} M_{{⊙}} and 29^{+4}_{-4} M_{{⊙}}. Such binary systems are expected to be directly evolved from stellar binary systems or formed by dynamical interactions of black holes in dense stellar environments. Here we derive the binary black hole merger rate based on the nearby ultra-luminous X-ray source (ULX) luminosity function (LF) under the assumption that binary black holes evolve through X-ray emitting phases. We obtain the binary black hole merger rate as 5.8(tULX/0.1 Myr)- 1λ- 0.6exp ( - 0.30λ) Gpc- 3 yr- 1, where tULX is the typical duration of the ULX phase and λ is the Eddington ratio in luminosity. This is coincident with the event rate inferred from the detection of GW150914 as well as the predictions based on binary population synthesis models. Although we are currently unable to constrain the Eddington ratio of ULXs in luminosity due to the uncertainties of our models and measured binary black hole merger event rates, further X-ray and GW data will allow us to narrow down the range of the Eddington ratios of ULXs. We also find the cumulative merger rate for the mass range of 5 M⊙ ≤ MBH ≤ 100 M⊙ inferred from the ULX LF is consistent with that estimated by the aLIGO collaboration considering various astrophysical conditions such as the mass function of black holes.

5. The cost of misremembering: Inferring the loss function in visual working memory.

PubMed

Sims, Chris R

2015-03-04

Visual working memory (VWM) is a highly limited storage system. A basic consequence of this fact is that visual memories cannot perfectly encode or represent the veridical structure of the world. However, in natural tasks, some memory errors might be more costly than others. This raises the intriguing possibility that the nature of memory error reflects the costs of committing different kinds of errors. Many existing theories assume that visual memories are noise-corrupted versions of afferent perceptual signals. However, this additive noise assumption oversimplifies the problem. Implicit in the behavioral phenomena of visual working memory is the concept of a loss function: a mathematical entity that describes the relative cost to the organism of making different types of memory errors. An optimally efficient memory system is one that minimizes the expected loss according to a particular loss function, while subject to a constraint on memory capacity. This paper describes a novel theoretical framework for characterizing visual working memory in terms of its implicit loss function. Using inverse decision theory, the empirical loss function is estimated from the results of a standard delayed recall visual memory experiment. These results are compared to the predicted behavior of a visual working memory system that is optimally efficient for a previously identified natural task, gaze correction following saccadic error. Finally, the approach is compared to alternative models of visual working memory, and shown to offer a superior account of the empirical data across a range of experimental datasets.

6. Topological Inference of Teleology: Deriving Function from Structure via Evidential Reasoning

DTIC Science & Technology

1999-06-10

His system, DUDU , takes as input Pascal- like pseudo-code and either verifies its correctness or produces an explanation of the problems it finds. The...explicit representation of function in DUDU enables the program to focus its efforts on buggy parts of the input code rather than constructing a proof

7. 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…

8. The Luminosity Function at z ~ 8 from 97 Y-band Dropouts: Inferences about Reionization

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

2014-05-01

We present the largest search to date for Y-band dropout galaxies (z ~ 8 Lyman break galaxies, LBGs) based on 350 arcmin2 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 arcmin2 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 <= mJ <= 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^\\star = -20.15^{+0.29}_{-0.38}, a faint-end slope of \\alpha = -1.87^{+0.26}_{-0.26}, and a number density of log _{10} \\phi ^\\star [{Mpc}^{-3}] = -3.24^{+0.25}_{-0.24}. Integrated down to M = -17.7, this luminosity function yields a luminosity density log _{10} \\epsilon [erg\\, s^{-1\\, Hz^{-1}\\, Mpc^{-3}}] = 25.52^{+0.05}_{-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 reionization. By assuming theoretically motivated priors on the clumping

9. Bayesian inference for functional response in a stochastic predator-prey system.

PubMed

Gilioli, Gianni; Pasquali, Sara; Ruggeri, Fabrizio

2008-02-01

We present a Bayesian method for functional response parameter estimation starting from time series of field data on predator-prey dynamics. Population dynamics is described by a system of stochastic differential equations in which behavioral stochasticities are represented by noise terms affecting each population as well as their interaction. We focus on the estimation of a behavioral parameter appearing in the functional response of predator to prey abundance when a small number of observations is available. To deal with small sample sizes, latent data are introduced between each pair of field observations and are considered as missing data. The method is applied to both simulated and observational data. The results obtained using different numbers of latent data are compared with those achieved following a frequentist approach. As a case study, we consider an acarine predator-prey system relevant to biological control problems.

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

PubMed

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

2014-04-30

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.

11. 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.

12. Convergence properties of the softassign quadratic assignment algorithm.

PubMed

Rangarajan, A; Vuille, A; Mjolsness, E

1999-08-15

The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.

13. 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.

14. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

SciTech Connect

Fernández, Francisco M.

2016-06-15

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. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.

15. 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.

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

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.

17. The use of structural modelling to infer structure and function in biocontrol agents.

PubMed

Berry, Colin; Board, Jason

2017-01-01

Homology modelling can provide important insights into the structures of proteins when a related protein structure has already been solved. However, for many proteins, including a number of invertebrate-active toxins and accessory proteins, no such templates exist. In these cases, techniques of ab initio, template-independent modelling can be employed to generate models that may give insight into structure and function. In this overview, examples of both the problems and the potential benefits of ab initio techniques are illustrated. Consistent modelling results may indicate useful approximations to actual protein structures and can thus allow the generation of hypotheses regarding activity that can be tested experimentally.

18. A Nearly Universal Solar-Wind Magnetosphere Coupling Function Inferred from Ten Magnetospheric State Variables

Newell, P. T.; Sotirelis, T.; Liou, K.; Meng, C. I.; Rich, F. J.

2006-12-01

We investigated whether one or a few coupling functions can represent best the interaction between the solar wind and the magnetosphere. Ten characterizations of the magnetosphere five from ground-based magnetometers, including Dst, Kp, AE, AU, and AL, and five from other sources, including auroral power (Polar UVI), cusp latitude and b2i (both DMSP), geosynchronous magnetic inclination angle (GOES), and polar cap size (SuperDARN) were correlated with more than 20 candidate solar wind coupling functions. A single coupling function, representing the rate magnetic flux is opened at the magnetopause, correlated best with 9 out of 10 indices of magnetospheric condition. This is dFMP/dt = v4/3BT2/3sin8/3(tc/2), calculated from (rate IMF field lines approach the magnetopause, v)(percent of IMF lines which merge, sin8/3(tc/2))(magnitude of magnetopause field, Bmp, v)(merging line length, (BT/Bmp)2/3). The merging line length is based on flux matching between the solar wind and a dipole field, and agrees with a superposed IMF on a vacuum dipole. The IMF clock angle dependence matches the merging rate reported at high altitude. The non-linearities of the magnetospheric response to BT and v are evident when the mean values of indices are plotted, as well as in the superior correlations from dFMP/dt. A wide variety of magnetospheric phenomena can ths be accurately predicted ab initio by just a single function, estimating the rate magnetic flux is opened on the dayside magnetopause. Across all state variables studied dFMP/dt accounts for about 57.2 percent of the variance, compared to 50.9 for EKL, and 48.8 for vBs. All data sets included thousands of points over many years, up to two solar cycles. The sole index which does not correlate best with dFMP/dt is Dst, which correlates best (r=0.87) with p1/2dFMP/dt. If dFMP/dt were credited with this success, its average score would be even higher.

19. A nearly universal solar wind-magnetosphere coupling function inferred from 10 magnetospheric state variables

Newell, P. T.; Sotirelis, T.; Liou, K.; Meng, C.-I.; Rich, F. J.

2007-01-01

We investigated whether one or a few coupling functions can represent best the interaction between the solar wind and the magnetosphere over a wide variety of magnetospheric activity. Ten variables which characterize the state of the magnetosphere were studied. Five indices from ground-based magnetometers were selected, namely Dst, Kp, AE, AU, and AL, and five from other sources, namely auroral power (Polar UVI), cusp latitude (sin(Λc)), b2i (both DMSP), geosynchronous magnetic inclination angle (GOES), and polar cap size (SuperDARN). These indices were correlated with more than 20 candidate solar wind coupling functions. One function, representing the rate magnetic flux is opened at the magnetopause, correlated best with 9 out of 10 indices of magnetospheric activity. This is dΦMP/dt = v4/3BT2/3sin8/3(θc/2), calculated from (rate IMF field lines approach the magnetopause, ˜v)(% of IMF lines which merge, sin8/3(θc/2))(interplanetary field magnitude, BT)(merging line length, ˜(BMP/BT)1/3). The merging line length is based on flux matching between the solar wind and a dipole field and agrees with a superposed IMF on a vacuum dipole. The IMF clock angle dependence matches the merging rate reported (albeit with limited statistics) at high altitude. The nonlinearities of the magnetospheric response to BT and v are evident when the mean values of indices are plotted, in scatterplots, and in the superior correlations from dΦMP/dt. Our results show that a wide variety of magnetospheric phenomena can be predicted with reasonable accuracy (r > 0.80 in several cases) ab initio, that is without the time history of the target index, by a single function, estimating the dayside merging rate. Across all state variables studied (including AL, which is hard to predict, and polar cap size, which is hard to measure), dΦMP/dt accounts for about 57.2% of the variance, compared to 50.9% for EKL and 48.8% for vBs. All data sets included at least thousands of points over many

20. 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.

1. 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

2016-07-05

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.

2. 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

3. A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

SciTech Connect

Orsi, R. J.; Mahony, R. E.; Moore, J. B.

1999-09-15

This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

4. Alpha values as a function of sample size, effect size, and power: accuracy over inference.

PubMed

2013-06-01

Tables of alpha values as a function of sample size, effect size, and desired power were presented. The tables indicated expected alphas for small, medium, and large effect sizes given a variety of sample sizes. It was evident that sample sizes for most psychological studies are adequate for large effect sizes defined at .8. The typical alpha level of .05 and desired power of 90% can be achieved with 70 participants in two groups. It was perhaps doubtful if these ideal levels of alpha and power have generally been achieved for medium effect sizes in actual research, since 170 participants would be required. Small effect sizes have rarely been tested with an adequate number of participants or power. Implications were discussed.

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

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

6. Digital image restoration using quadratic programming.

PubMed

Abdelmalek, N N; Kasvand, T

1980-10-01

The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given.

7. On Coupled Rate Equations with Quadratic Nonlinearities

PubMed Central

Montroll, Elliott W.

1972-01-01

Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013

8. Inferring parrotfish (Teleostei: Scaridae) pharyngeal mill function from dental morphology, wear, and microstructure.

PubMed

Carr, Andrew; Tibbetts, Ian R; Kemp, Anne; Truss, Rowan; Drennan, John

2006-10-01

Morphology, occlusal surface topography, macrowear, and microwear features of parrotfish pharyngeal teeth were investigated to relate microstructural characteristics to the function of the pharyngeal mill using scanning electron microscopy of whole and sectioned pharyngeal jaws and teeth. Pharyngeal tooth migration is anterior in the lower jaw (fifth ceratobranchial) and posterior in the upper jaw (paired third pharyngobranchials), making the interaction of occlusal surfaces and wear-generating forces complex. The extent of wear can be used to define three regions through which teeth migrate: a region containing newly erupted teeth showing little or no wear; a midregion in which the apical enameloid is swiftly worn; and a region containing teeth with only basal enameloid remaining, which shows low to moderate wear. The shape of the occlusal surface alters as the teeth progress along the pharyngeal jaw, generating conditions that appear suited to the reduction of coral particles. It is likely that the interaction between these particles and algal cells during the process of the rendering of the former is responsible for the rupture of the latter, with the consequent liberation of cell contents from which parrotfish obtain their nutrients.

9. An expression atlas of human primary cells: inference of gene function from coexpression networks

PubMed Central

2013-01-01

Background The specialisation of mammalian cells in time and space requires genes associated with specific pathways and functions to be co-ordinately expressed. Here we have combined a large number of publically available microarray datasets derived from human primary cells and analysed large correlation graphs of these data. Results Using the network analysis tool BioLayout Express3D we identify robust co-associations of genes expressed in a wide variety of cell lineages. We discuss the biological significance of a number of these associations, in particular the coexpression of key transcription factors with the genes that they are likely to control. Conclusions We consider the regulation of genes in human primary cells and specifically in the human mononuclear phagocyte system. Of particular note is the fact that these data do not support the identity of putative markers of antigen-presenting dendritic cells, nor classification of M1 and M2 activation states, a current subject of debate within immunological field. We have provided this data resource on the BioGPS web site (http://biogps.org/dataset/2429/primary-cell-atlas/) and on macrophages.com (http://www.macrophages.com/hu-cell-atlas). PMID:24053356

10. The Random Quadratic Assignment Problem

Paul, Gerald; Shao, Jia; Stanley, H. Eugene

2011-11-01

The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.

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

12. 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.

13. Open chromatin profiling of human postmortem brain infers functional roles for non-coding schizophrenia loci.

PubMed

Fullard, John F; Giambartolomei, Claudia; Hauberg, Mads E; Xu, Ke; Voloudakis, Georgios; Shao, Zhiping; Bare, Christopher; Dudley, Joel T; Mattheisen, Manuel; Robakis, Nikolaos K; Haroutunian, Vahram; Roussos, Panos

2017-03-14

Open chromatin provides access to DNA binding proteins for the correct spatiotemporal regulation of gene expression. Mapping chromatin accessibility has been widely used to identify the location of cis regulatory elements (CREs) including promoters and enhancers. CREs show tissue- and cell-type specificity and disease-associated variants are often enriched for CREs in the tissues and cells that pertain to a given disease. To better understand the role of CREs in neuropsychiatric disorders we applied the Assay for Transposase Accessible Chromatin followed by sequencing (ATAC-seq) to neuronal and non-neuronal nuclei isolated from frozen postmortem human brain by fluorescence-activated nuclear sorting (FANS). Most of the identified open chromatin regions (OCRs) are differentially accessible between neurons and non-neurons, and show enrichment with known cell type markers, promoters and enhancers. Relative to those of non-neurons, neuronal OCRs are more evolutionarily conserved and are enriched in distal regulatory elements. Transcription factor (TF) footprinting analysis identifies differences in the regulome between neuronal and non-neuronal cells and ascribes putative functional roles to a number of non-coding schizophrenia (SCZ) risk variants. Among the identified variants is a Single Nucleotide Polymorphism (SNP) proximal to the gene encoding SNX19. In vitro experiments reveal that this SNP leads to an increase in transcriptional activity. As elevated expression of SNX19 has been associated with SCZ, our data provides evidence that the identified SNP contributes to disease. These results represent the first analysis of OCRs and TF binding sites in distinct populations of postmortem human brain cells and further our understanding of the regulome and the impact of neuropsychiatric disease-associated genetic risk variants.

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

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.

15. Receiver-Function Stacking Methods to Infer Crustal Anisotropic Structure with Application to the Turkish-Anatolian Plateau

Kaviani, A.; Rumpker, G.

2015-12-01

To account for the presence of seismic anisotropy within the crust and to estimate the relevant parameters, we first discuss a robust technique for the analysis of shear-wave splitting in layered anisotropic media by using converted shear phases. We use a combined approach that involves time-shifting and stacking of radial receiver functions and energy-minimization of transverse receiver functions to constrain the splitting parameters (i.e. the fast-polarization direction and the delay time) for an anisotropic layer. In multi-layered anisotropic media, the splitting parameters for the individual layers can be inferred by a layer-stripping approach, where the splitting effects due to shallower layers on converted phases from deeper discontinuities are successively corrected. The effect of anisotropy on the estimates of crustal thickness and average bulk Vp/Vs ratio can be significant. Recently, we extended the approach of Zhu & Kanamori (2000) to include P-to-S converted waves and their crustal reverberations generated in the anisotropic case. The anisotropic parameters of the medium are first estimated using the splitting analysis of the Ps-phase as described above. Then, a grid-search is performed over layer thickness and Vp/Vs ratio, while accounting for all relevant arrivals (up to 20 phases) in the anisotropic medium. We apply these techniques to receiver-function data from seismological stations across the Turkish-Anatolian Plateau to study seismic anisotropy in the crust and its relationship to crustal tectonics. Preliminary results reveal significant crustal anisotropy and indicate that the strength and direction of the anisotropy vary across the main tectonic boundaries. We also improve the estimates of the crustal thickness and the bulk Vp/Vs ratio by accounting for the presence of crustal anisotropy beneath the station. ReferenceZhu, L. & H. Kanamori (2000), Moho depth variation in southern California from teleseismic receiver functions, J. Geophys. Res

16. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

PubMed

Wang, Di; Kleinberg, Robert D

2009-11-28

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

17. On Quantization of Quadratic Poisson Structures

Manchon, D.; Masmoudi, M.; Roux, A.

Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.

18. 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

19. IntNetLncSim: an integrative network analysis method to infer human lncRNA functional similarity

PubMed Central

Hu, Yang; Yang, Haixiu; Zhou, Chen; Sun, Jie; Zhou, Meng

2016-01-01

Increasing evidence indicated that long non-coding RNAs (lncRNAs) were involved in various biological processes and complex diseases by communicating with mRNAs/miRNAs each other. Exploiting interactions between lncRNAs and mRNA/miRNAs to lncRNA functional similarity (LFS) is an effective method to explore function of lncRNAs and predict novel lncRNA-disease associations. In this article, we proposed an integrative framework, IntNetLncSim, to infer LFS by modeling the information flow in an integrated network that comprises both lncRNA-related transcriptional and post-transcriptional information. The performance of IntNetLncSim was evaluated by investigating the relationship of LFS with the similarity of lncRNA-related mRNA sets (LmRSets) and miRNA sets (LmiRSets). As a result, LFS by IntNetLncSim was significant positively correlated with the LmRSet (Pearson correlation γ2=0.8424) and LmiRSet (Pearson correlation γ2=0.2601). Particularly, the performance of IntNetLncSim is superior to several previous methods. In the case of applying the LFS to identify novel lncRNA-disease relationships, we achieved an area under the ROC curve (0.7300) in experimentally verified lncRNA-disease associations based on leave-one-out cross-validation. Furthermore, highly-ranked lncRNA-disease associations confirmed by literature mining demonstrated the excellent performance of IntNetLncSim. Finally, a web-accessible system was provided for querying LFS and potential lncRNA-disease relationships: http://www.bio-bigdata.com/IntNetLncSim. PMID:27323856

20. IntNetLncSim: an integrative network analysis method to infer human lncRNA functional similarity.

PubMed

Cheng, Liang; Shi, Hongbo; Wang, Zhenzhen; Hu, Yang; Yang, Haixiu; Zhou, Chen; Sun, Jie; Zhou, Meng

2016-07-26

Increasing evidence indicated that long non-coding RNAs (lncRNAs) were involved in various biological processes and complex diseases by communicating with mRNAs/miRNAs each other. Exploiting interactions between lncRNAs and mRNA/miRNAs to lncRNA functional similarity (LFS) is an effective method to explore function of lncRNAs and predict novel lncRNA-disease associations. In this article, we proposed an integrative framework, IntNetLncSim, to infer LFS by modeling the information flow in an integrated network that comprises both lncRNA-related transcriptional and post-transcriptional information. The performance of IntNetLncSim was evaluated by investigating the relationship of LFS with the similarity of lncRNA-related mRNA sets (LmRSets) and miRNA sets (LmiRSets). As a result, LFS by IntNetLncSim was significant positively correlated with the LmRSet (Pearson correlation γ2=0.8424) and LmiRSet (Pearson correlation γ2=0.2601). Particularly, the performance of IntNetLncSim is superior to several previous methods. In the case of applying the LFS to identify novel lncRNA-disease relationships, we achieved an area under the ROC curve (0.7300) in experimentally verified lncRNA-disease associations based on leave-one-out cross-validation. Furthermore, highly-ranked lncRNA-disease associations confirmed by literature mining demonstrated the excellent performance of IntNetLncSim. Finally, a web-accessible system was provided for querying LFS and potential lncRNA-disease relationships: http://www.bio-bigdata.com/IntNetLncSim.

1. Entanglement entropy of fermionic quadratic band touching model

Chen, Xiao; Cho, Gil Young; Fradkin, Eduardo

2014-03-01

The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in (2 + 1) dimension. This is a fermionic spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit LlogL violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. This work was supported in part by the NSF grant DMR-1064319.

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

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

3. 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

4. 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)

5. 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.

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.

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

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

8. WHAT IS A SATISFACTORY QUADRATIC EQUATION SOLVER?

DTIC Science & Technology

The report discusses precise requirements for a satisfactory computer program to solve a quadratic equation with floating - point coefficients. The principal practical problem is coping with overflow and underflow.

9. 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.)

10. Linear quadratic optimal control for symmetric systems

NASA Technical Reports Server (NTRS)

Lewis, J. H.; Martin, C. F.

1983-01-01

Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.

11. Test spaces and characterizations of quadratic spaces

Dvurečenskij, Anatolij

1996-10-01

We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.

12. 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.

13. Statistical Inference

Khan, Shahjahan

Often scientific information on various data generating processes are presented in the from of numerical and categorical data. Except for some very rare occasions, generally such data represent a small part of the population, or selected outcomes of any data generating process. Although, valuable and useful information is lurking in the array of scientific data, generally, they are unavailable to the users. Appropriate statistical methods are essential to reveal the hidden "jewels" in the mess of the row data. Exploratory data analysis methods are used to uncover such valuable characteristics of the observed data. Statistical inference provides techniques to make valid conclusions about the unknown characteristics or parameters of the population from which scientifically drawn sample data are selected. Usually, statistical inference includes estimation of population parameters as well as performing test of hypotheses on the parameters. However, prediction of future responses and determining the prediction distributions are also part of statistical inference. Both Classical or Frequentists and Bayesian approaches are used in statistical inference. The commonly used Classical approach is based on the sample data alone. In contrast, increasingly popular Beyesian approach uses prior distribution on the parameters along with the sample data to make inferences. The non-parametric and robust methods are also being used in situations where commonly used model assumptions are unsupported. In this chapter,we cover the philosophical andmethodological aspects of both the Classical and Bayesian approaches.Moreover, some aspects of predictive inference are also included. In the absence of any evidence to support assumptions regarding the distribution of the underlying population, or if the variable is measured only in ordinal scale, non-parametric methods are used. Robust methods are employed to avoid any significant changes in the results due to deviations from the model

14. Statistical Inference

Khan, Shahjahan

Often scientific information on various data generating processes are presented in the from of numerical and categorical data. Except for some very rare occasions, generally such data represent a small part of the population, or selected outcomes of any data generating process. Although, valuable and useful information is lurking in the array of scientific data, generally, they are unavailable to the users. Appropriate statistical methods are essential to reveal the hidden “jewels” in the mess of the row data. Exploratory data analysis methods are used to uncover such valuable characteristics of the observed data. Statistical inference provides techniques to make valid conclusions about the unknown characteristics or parameters of the population from which scientifically drawn sample data are selected. Usually, statistical inference includes estimation of population parameters as well as performing test of hypotheses on the parameters. However, prediction of future responses and determining the prediction distributions are also part of statistical inference. Both Classical or Frequentists and Bayesian approaches are used in statistical inference. The commonly used Classical approach is based on the sample data alone. In contrast, increasingly popular Beyesian approach uses prior distribution on the parameters along with the sample data to make inferences. The non-parametric and robust methods are also being used in situations where commonly used model assumptions are unsupported. In this chapter,we cover the philosophical andmethodological aspects of both the Classical and Bayesian approaches.Moreover, some aspects of predictive inference are also included. In the absence of any evidence to support assumptions regarding the distribution of the underlying population, or if the variable is measured only in ordinal scale, non-parametric methods are used. Robust methods are employed to avoid any significant changes in the results due to deviations from the model

15. Statistical Mechanics of Optimal Convex Inference in High Dimensions

2016-07-01

A fundamental problem in modern high-dimensional data analysis involves efficiently inferring a set of P unknown model parameters governing the relationship between the inputs and outputs of N noisy measurements. Various methods have been proposed to regress the outputs against the inputs to recover the P parameters. What are fundamental limits on the accuracy of regression, given finite signal-to-noise ratios, limited measurements, prior information, and computational tractability requirements? How can we optimally combine prior information with measurements to achieve these limits? Classical statistics gives incisive answers to these questions as the measurement density α =(N /P )→∞ . However, these classical results are not relevant to modern high-dimensional inference problems, which instead occur at finite α . We employ replica theory to answer these questions for a class of inference algorithms, known in the statistics literature as M-estimators. These algorithms attempt to recover the P model parameters by solving an optimization problem involving minimizing the sum of a loss function that penalizes deviations between the data and model predictions, and a regularizer that leverages prior information about model parameters. Widely cherished algorithms like maximum likelihood (ML) and maximum-a posteriori (MAP) inference arise as special cases of M-estimators. Our analysis uncovers fundamental limits on the inference accuracy of a subclass of M-estimators corresponding to computationally tractable convex optimization problems. These limits generalize classical statistical theorems like the Cramer-Rao bound to the high-dimensional setting with prior information. We further discover the optimal M-estimator for log-concave signal and noise distributions; we demonstrate that it can achieve our high-dimensional limits on inference accuracy, while ML and MAP cannot. Intriguingly, in high dimensions, these optimal algorithms become computationally simpler than

16. Quadratic nonlinear Klein-Gordon equation in one dimension

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)].

17. Primal-Dual Interior Methods for Quadratic Programming

Shustrova, Anna

Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted "barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of

18. 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,…

19. Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game

Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed

This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

20. Large-scale inference of gene function through phylogenetic annotation of Gene Ontology terms: case study of the apoptosis and autophagy cellular processes

PubMed Central

Feuermann, Marc; Gaudet, Pascale; Mi, Huaiyu; Lewis, Suzanna E.; Thomas, Paul D.

2016-01-01

We previously reported a paradigm for large-scale phylogenomic analysis of gene families that takes advantage of the large corpus of experimentally supported Gene Ontology (GO) annotations. This ‘GO Phylogenetic Annotation’ approach integrates GO annotations from evolutionarily related genes across ∼100 different organisms in the context of a gene family tree, in which curators build an explicit model of the evolution of gene functions. GO Phylogenetic Annotation models the gain and loss of functions in a gene family tree, which is used to infer the functions of uncharacterized (or incompletely characterized) gene products, even for human proteins that are relatively well studied. Here, we report our results from applying this paradigm to two well-characterized cellular processes, apoptosis and autophagy. This revealed several important observations with respect to GO annotations and how they can be used for function inference. Notably, we applied only a small fraction of the experimentally supported GO annotations to infer function in other family members. The majority of other annotations describe indirect effects, phenotypes or results from high throughput experiments. In addition, we show here how feedback from phylogenetic annotation leads to significant improvements in the PANTHER trees, the GO annotations and GO itself. Thus GO phylogenetic annotation both increases the quantity and improves the accuracy of the GO annotations provided to the research community. We expect these phylogenetically based annotations to be of broad use in gene enrichment analysis as well as other applications of GO annotations. Database URL: http://amigo.geneontology.org/amigo PMID:28025345

1. 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

2. Limit cycles near hyperbolas in quadratic systems

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.

3. 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.

4. 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.

5. 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.

6. Investigating Students' Mathematical Difficulties with Quadratic Equations

ERIC Educational Resources Information Center

O'Connor, Bronwyn Reid; Norton, Stephen

2016-01-01

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

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. Multi-attribute utility function or statistical inference models: a comparison of health state valuation models using the HUI2 health state classification system.

PubMed

Stevens, Katherine; McCabe, Christopher; Brazier, John; Roberts, Jennifer

2007-09-01

A key issue in health state valuation modelling is the choice of functional form. The two most frequently used preference based instruments adopt different approaches; one based on multi-attribute utility theory (MAUT), the other on statistical analysis. There has been no comparison of these alternative approaches in the context of health economics. We report a comparison of these approaches for the health utilities index mark 2. The statistical inference model predicts more accurately than the one based on MAUT. We discuss possible explanations for the differences in performance, the importance of the findings, and implications for future research.

9. Bayesian inferences of galaxy formation from the K-band luminosity and H I mass functions of galaxies: constraining star formation and feedback

Lu, Yu; Mo, H. J.; Lu, Zhankui; Katz, Neal; Weinberg, Martin D.

2014-09-01

We infer mechanisms of galaxy formation for a broad family of semi-analytic models (SAMs) constrained by the K-band luminosity function and H I mass function of local galaxies using tools of Bayesian analysis. Even with a broad search in parameter space the whole model family fails to match to constraining data. In the best-fitting models, the star formation and feedback parameters in low-mass haloes are tightly constrained by the two data sets, and the analysis reveals several generic failures of models that similarly apply to other existing SAMs. First, based on the assumption that baryon accretion follows the dark matter accretion, large mass-loading factors are required for haloes with circular velocities lower than 200 km s-1, and most of the wind mass must be expelled from the haloes. Second, assuming that the feedback is powered by Type II supernovae with a Chabrier initial mass function, the outflow requires more than 25 per cent of the available supernova kinetic energy. Finally, the posterior predictive distributions for the star formation history are dramatically inconsistent with observations for masses similar to or smaller than the Milky Way mass. The inferences suggest that the current model family is still missing some key physical processes that regulate the gas accretion and star formation in galaxies with masses below that of the Milky Way.

10. System-level insights into the cellular interactome of a non-model organism: inferring, modelling and analysing functional gene network of soybean (Glycine max).

PubMed

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

11. Projected sequential quadratic programming methods

SciTech Connect

Heinkenschloss, M.

1994-12-31

In this talk we investigate projected SQP methods for the solution of min f(y, u). s.t. c(y, u) = 0 a {<=} u {<=} b. These methods combine the ideas of (reduced) SQP methods and projected Newton methods. The problem formulation and the design of these solution methods is motivated by optimal control problems. In this case y and u are the state and the control, respectively, and c(y, u) = 0 represents the state equation. Projected SQP methods use the simple projection onto the set {l_brace}a {<=} u {<=} b{r_brace} and maintain feasibility with respect to the inequality constraints. In each iteration only linearized constraint equations need to be solved. Global convergence of the method is enforced using a constrained merit function and an Armijo-like line search. We discuss global and local convergence properties of these methods, the identification of active indices, and implementation details for optimal control problems. Numerical examples of projected SQP methods applied to optimal control problems are presented.

12. Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses

Bryc, Włodek; Wesołowski, Jacek

2017-02-01

We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.

13. Geometric Approaches to Quadratic Equations from Other Times and Places.

ERIC Educational Resources Information Center

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

14. Towards General Algorithms for Grammatical Inference

Clark, Alexander

Many algorithms for grammatical inference can be viewed as instances of a more general algorithm which maintains a set of primitive elements, which distributionally define sets of strings, and a set of features or tests that constrain various inference rules. Using this general framework, which we cast as a process of logical inference, we re-analyse Angluin's famous lstar algorithm and several recent algorithms for the inference of context-free grammars and multiple context-free grammars. Finally, to illustrate the advantages of this approach, we extend it to the inference of functional transductions from positive data only, and we present a new algorithm for the inference of finite state transducers.

15. Use of quadratic components for buckling calculations

SciTech Connect

Dohrmann, C.R.; Segalman, D.J.

1996-12-31

A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the systems stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.

16. Bifurcations in biparametric quadratic potentials. II.

PubMed

Lanchares, V.; Elipe, A.

1995-09-01

Quadratic Hamiltonians with the phase space on the S (2) sphere represent numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane for one of these classes, thus complementing the work done in a previous paper where the other class was analyzed. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by four types of bifurcations: namely the pitchfork, the butterfly, the oyster and the pentadent bifurcations. We find also values where the system is degenerate, that is, there are nonisolated equilibria. (c) 1995 American Institute of Physics.

17. Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories

Adamson, L. N. C.; Osbaldestin, A. H.

2014-03-01

We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.

18. 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…

19. 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...

20. 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.

1. Monotone and convex quadratic spline interpolation

NASA Technical Reports Server (NTRS)

Lam, Maria H.

1990-01-01

A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.

2. 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…

3. 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…

4. An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

5. 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.

6. Inferring Aggregated Functional Traits from Metagenomic Data Using Constrained Non-negative Matrix Factorization: Application to Fiber Degradation in the Human Gut Microbiota

PubMed Central

Raguideau, Sébastien; Plancade, Sandra; Pons, Nicolas; Leclerc, Marion

2016-01-01

Whole Genome Shotgun (WGS) metagenomics is increasingly used to study the structure and functions of complex microbial ecosystems, both from the taxonomic and functional point of view. Gene inventories of otherwise uncultured microbial communities make the direct functional profiling of microbial communities possible. The concept of community aggregated trait has been adapted from environmental and plant functional ecology to the framework of microbial ecology. Community aggregated traits are quantified from WGS data by computing the abundance of relevant marker genes. They can be used to study key processes at the ecosystem level and correlate environmental factors and ecosystem functions. In this paper we propose a novel model based approach to infer combinations of aggregated traits characterizing specific ecosystemic metabolic processes. We formulate a model of these Combined Aggregated Functional Traits (CAFTs) accounting for a hierarchical structure of genes, which are associated on microbial genomes, further linked at the ecosystem level by complex co-occurrences or interactions. The model is completed with constraints specifically designed to exploit available genomic information, in order to favor biologically relevant CAFTs. The CAFTs structure, as well as their intensity in the ecosystem, is obtained by solving a constrained Non-negative Matrix Factorization (NMF) problem. We developed a multicriteria selection procedure for the number of CAFTs. We illustrated our method on the modelling of ecosystemic functional traits of fiber degradation by the human gut microbiota. We used 1408 samples of gene abundances from several high-throughput sequencing projects and found that four CAFTs only were needed to represent the fiber degradation potential. This data reduction highlighted biologically consistent functional patterns while providing a high quality preservation of the original data. Our method is generic and can be applied to other metabolic processes in

7. Sites Inferred by Metabolic Background Assertion Labeling (SIMBAL): adapting the Partial Phylogenetic Profiling algorithm to scan sequences for signatures that predict protein function

PubMed Central

2010-01-01

Background Comparative genomics methods such as phylogenetic profiling can mine powerful inferences from inherently noisy biological data sets. We introduce Sites Inferred by Metabolic Background Assertion Labeling (SIMBAL), a method that applies the Partial Phylogenetic Profiling (PPP) approach locally within a protein sequence to discover short sequence signatures associated with functional sites. The approach is based on the basic scoring mechanism employed by PPP, namely the use of binomial distribution statistics to optimize sequence similarity cutoffs during searches of partitioned training sets. Results Here we illustrate and validate the ability of the SIMBAL method to find functionally relevant short sequence signatures by application to two well-characterized protein families. In the first example, we partitioned a family of ABC permeases using a metabolic background property (urea utilization). Thus, the TRUE set for this family comprised members whose genome of origin encoded a urea utilization system. By moving a sliding window across the sequence of a permease, and searching each subsequence in turn against the full set of partitioned proteins, the method found which local sequence signatures best correlated with the urea utilization trait. Mapping of SIMBAL "hot spots" onto crystal structures of homologous permeases reveals that the significant sites are gating determinants on the cytosolic face rather than, say, docking sites for the substrate-binding protein on the extracellular face. In the second example, we partitioned a protein methyltransferase family using gene proximity as a criterion. In this case, the TRUE set comprised those methyltransferases encoded near the gene for the substrate RF-1. SIMBAL identifies sequence regions that map onto the substrate-binding interface while ignoring regions involved in the methyltransferase reaction mechanism in general. Neither method for training set construction requires any prior experimental

8. Two simple approximations to the distributions of quadratic forms.

PubMed

Yuan, Ke-Hai; Bentler, Peter M

2010-05-01

Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to T = sigma(d)(i=1) lambda(i)z(i)(2) with z(i) being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of the lambda(i) and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the lambda(i) is small, the rescaled statistic T(R) = dT/(sigma(d)(i=1) lambda(i)) is also adequate for practical model inference. But comparing T(R) against chi2(d) will inflate type I errors when substantial differences exist among the lambda(i), especially, when d is also large.

9. Why Are "Dunkels" Sticky? Preschoolers Infer Functionality and Intentional Creation for Artifact Properties Learned from Generic Language

ERIC Educational Resources Information Center

2010-01-01

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…

10. 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.

11. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

SciTech Connect

Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

2011-06-23

This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.

12. Constrained neural approaches to quadratic assignment problems.

PubMed

Ishii, S; Sato, M

1998-08-01

In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.

13. Quadratic finite elements and incompressible viscous flows.

SciTech Connect

Dohrmann, Clark R.; Gartling, David K.

2005-01-01

Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.

14. Application of a generalized likelihood function for parameter inference of a carbon balance model using multiple, joint constraints

Hammerle, Albin; Wohlfahrt, Georg; Schoups, Gerrit

2014-05-01

Advances in automated data collection systems enabled ecologists to collect enormous amounts of varied data. Data assimilation (or data model synthesis) is one way to make sense of this mass of data. Given a process model designed to learn about ecological processes these data can be integrated within a statistical framework for data interpretation and extrapolation. Results of such a data assimilation framework clearly depend on the information content of the observed data, on the associated uncertainties (data uncertainties, model structural uncertainties and parameter uncertainties) and underlying assumptions. Parameter estimation is usually done by minimizing a simple least squares objective function with respect to the model parameters - presuming Gaussian, independent and homoscedastic errors (formal approach). Recent contributions to the (ecological) literature, however, have questioned the validity of this approach when confronted with significant errors and uncertainty in the model forcing (inputs) and model structure. Very often residual errors are non-Gaussian, correlated and heteroscedastic. Thus these error sources have to be considered and residual-errors have to be described in a statistically correct fashion order to draw statistically sound conclusions about parameter- and model predictive-uncertainties. We examined the effects of a generalized likelihood (GL) function on the parameter estimation of a carbon balance model. Compared with the formal approach, the GL function allows for correlation, non-stationarity and non-normality of model residuals. Carbon model parameters have been constrained using three different datasets, each of them modelled by its own GL function. As shown in literature the use of different datasets for parameter estimation reduces the uncertainty in model parameters and model predictions and does allow for a better quantification and for more insights into model processes.

15. Application of Heisenberg's S matrix program to the angular scattering of the H + D2(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction: piecewise S matrix elements using linear, quadratic, step-function, and top-hat parametrizations.

PubMed

Shan, Xiao; Connor, J N L

2012-11-26

A previous paper by Shan and Connor (Phys. Chem. Chem. Phys. 2011, 13, 8392) reported the surprising result that four simple parametrized S matrices can reproduce the forward-angle glory scattering of the H + D(2)(v(i)=0,j(i)=0) → HD(v(f)=3,j(f)=0) + D reaction, whose differential cross section (DCS) had been computed in a state-of-the-art scattering calculation for a state-of-the-art potential energy surface. Here, v and j are vibrational and rotational quantum numbers, respectively, and the translational energy is 1.81 eV. This paper asks the question: Can we replace the analytic functions (of class C(ω)) used by Shan-Connor with simpler mathematical functions and still reproduce the forward-angle glory scattering? We first construct S matrix elements (of class C(0)) using a quadratic phase and a piecewise-continuous pre-exponential factor consisting of three pieces. Two of the pieces are constants, with one taking the value N (a real normalization constant) at small values of the total angular momentum number, J; the other piece has the value 0 at large J. These two pieces are joined at intermediate values of J by either a straight line, giving rise to the linear parametrization (denoted param L), or a quadratic curve, which defines the quadratic parametrization (param Q). We find that both param L and param Q can reproduce the glory scattering for center-of-mass reactive scattering angles, θ(R) ≲ 30°. Second, we use a piecewise-discontinuous pre-exponential factor and a quadratic phase, giving rise to a step-function parametrization (param SF) and a top-hat parametrization (param TH). We find that both param SF and param TH can reproduce the forward-angle scattering, even though these class C(-1) parametrizations are usually considered too simplistic to be useful for calculations of DCSs. We find that an ultrasimplistic param THz, which is param TH with a phase of zero, can also reproduce the glory scattering at forward angles. The S matrix elements for

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

PubMed

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

2015-09-01

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 measure of bridging inferences of physical causation, mental states, and emotional states was administered to older children, adolescents, and adults with and without ASD. The ASD group had more difficulty making inferences, particularly related to emotional understanding. Results suggest that individuals with ASD may not have the stored experiential knowledge that specific inferences depend upon or have difficulties accessing relevant experiences due to linguistic limitations. Further research is needed to tease these elements apart.

17. Making inferences: Comprehension of physical causality, intentionality, and emotions in discourse by high-functioning older children, adolescents, and adults with autism

PubMed Central

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

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 experience or the nature of social information have received less consideration. A measure of bridging inferences of physical causation, mental states, and emotional states was administered to older children, adolescents, and adults with and without ASD. The ASD group had more difficulty making inferences, particularly related to emotional understanding. Results suggest that individuals with ASD may not have the stored experiential knowledge that specific inferences depend upon or have difficulties accessing relevant experiences due to linguistic limitations. Further research is needed to tease these elements apart. PMID:25821925

18. Blind deconvolution estimation of fluorescence measurements through quadratic programming

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.

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

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

20. A new one-layer neural network for linear and quadratic programming.

PubMed

Gao, Xingbao; Liao, Li-Zhi

2010-06-01

In this paper, we present a new neural network for solving linear and quadratic programming problems in real time by introducing some new vectors. The proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem when the objective function is convex on the set defined by equality constraints. Compared with existing one-layer neural networks for quadratic programming problems, the proposed neural network has the least neurons and requires weak stability conditions. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.

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

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.

2. Robust partial quadratic eigenvalue assignment with time delay using the receptance and the system matrices

Bai, Zheng-Jian; Yang, Jin-Ku; Datta, Biswa Nath

2016-12-01

In this paper, we consider the robust partial quadratic eigenvalue assignment problem in vibration by active feedback control. Based on the receptance measurements and the system matrices, we propose an optimization method for the robust and minimum norm partial quadratic eigenvalue assignment problem. We provide a new cost function and the closed-loop eigenvalue sensitivity and the feedback norms can be minimized simultaneously. Our method is also extended to the case of time delay between measurements of state and actuation of control. Numerical tests demonstrate the effectiveness of our method.

3. Neutron Distribution in the Nuclear Fuel Cell using Collision Probability Method with Quadratic Flux Approach

Shafii, M. A.; Fitriyani, D.; Tongkukut, S. H. J.; Abdullah, A. G.

2017-03-01

To solve the integral neutron transport equation using collision probability (CP) method usually requires flat flux (FF) approach. In this research, it has been carried out in the cylindrical nuclear fuel cell with the spatial of mesh with quadratic flux approach. This means that the neutron flux at any region of the nuclear fuel cell is forced to follow the pattern of a quadratic function. The mechanism may be referred to as the process of non-flat flux (NFF) approach. The parameters that calculated in this study are the k-eff and the distribution of neutron flux. The result shows that all parameters are in accordance with the result of SRAC.

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

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.

5. General functions to transform associate data to host data, and their use in phylogenetic inference from sequences with intra-individual variability

PubMed Central

2008-01-01

Background Amongst the most commonly used molecular markers for plant phylogenetic studies are the nuclear ribosomal internal transcribed spacers (ITS). Intra-individual variability of these multicopy regions is a very common phenomenon in plants, the causes of which are debated in literature. Phylogenetic reconstruction under these conditions is inherently difficult. Our approach is to consider this problem as a special case of the general biological question of how to infer the characteristics of hosts (represented here by plant individuals) from features of their associates (represented by cloned sequences here). Results Six general transformation functions are introduced, covering the transformation of associate characters to discrete and continuous host characters, and the transformation of associate distances to host distances. A pure distance-based framework is established in which these transformation functions are applied to ITS sequences collected from the angiosperm genera Acer, Fagus and Zelkova. The formulae are also applied to allelic data of three different loci obtained from Rosa spp. The functions are validated by (1) phylogeny-independent measures of treelikeness; (2) correlation with independent host characters; (3) visualization using splits graphs and comparison with published data on the test organisms. The results agree well with these three measures and the datasets examined as well as with the theoretical predictions and previous results in the literature. High-quality distance matrices are obtained with four of the six transformation formulae. We demonstrate that one of them represents a generalization of the Sørensen coefficient, which is widely applied in ecology. Conclusion Because of their generality, the transformation functions may be applied to a wide range of biological problems that are interpretable in terms of hosts and associates. Regarding cloned sequences, the formulae have a high potential to accurately reflect evolutionary

6. The quadratic relationship between difficulty of intelligence test items and their correlations with working memory

PubMed Central

2015-01-01

Fluid intelligence (Gf) is a crucial cognitive ability that involves abstract reasoning in order to solve novel problems. Recent research demonstrated that Gf strongly depends on the individual effectiveness of working memory (WM). We investigated a popular claim that if the storage capacity underlay the WM–Gf correlation, then such a correlation should increase with an increasing number of items or rules (load) in a Gf-test. As often no such link is observed, on that basis the storage-capacity account is rejected, and alternative accounts of Gf (e.g., related to executive control or processing speed) are proposed. Using both analytical inference and numerical simulations, we demonstrated that the load-dependent change in correlation is primarily a function of the amount of floor/ceiling effect for particular items. Thus, the item-wise WM correlation of a Gf-test depends on its overall difficulty, and the difficulty distribution across its items. When the early test items yield huge ceiling, but the late items do not approach floor, that correlation will increase throughout the test. If the early items locate themselves between ceiling and floor, but the late items approach floor, the respective correlation will decrease. For a hallmark Gf-test, the Raven-test, whose items span from ceiling to floor, the quadratic relationship is expected, and it was shown empirically using a large sample and two types of WMC tasks. In consequence, no changes in correlation due to varying WM/Gf load, or lack of them, can yield an argument for or against any theory of WM/Gf. Moreover, as the mathematical properties of the correlation formula make it relatively immune to ceiling/floor effects for overall moderate correlations, only minor changes (if any) in the WM–Gf correlation should be expected for many psychological tests. PMID:26379594

7. On the failure indices of quadratic failure criteria for optimal stacking sequence design of laminated plate

Kim, C. W.; Song, S. R.; Hwang, W.; Park, H. C.; Han, K. S.

1994-01-01

The quadratic failure criterion, which is intended to predict fracture, may be used as an object function for optimal stacking sequence design of laminated plate. However, calculations using a symmetric laminated plate demonstrate that Tsai-Wu theory may give incorrect optimum predictions under uniaxial loading.

8. 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.

9. Transcription Factor Binding Probabilities in Orthologous Promoters: An Alignment-Free Approach to the Inference of Functional Regulatory Targets

Liu, Xiao; Clarke, Neil D.

Using a physically principled method of scoring genomic sequences for the potential to be bound by transcription factors, we have developed an algorithm for assessing the conservation of predicted binding occupancy that does not rely on sequence alignment of promoters. The method, which we call ortholog-weighting, assesses the degree to which the predicted binding occupancy of a transcription factor in a reference gene is also predicted in the promoters of orthologous genes. The analysis was performed separately for over 100 different transcription factors in S. cerevisiae. Statistical significance was evaluated by simulation using permuted versions of the position weight matrices. Ortholog-weighting produced about twice as many significantly high scoring genes as were obtained from the S. cerevisiae genome alone. Gene Ontology analysis found a similar two-fold enrichment of genes. Both analyses suggest that ortholog-weighting improves the prediction of true regulatory targets. Interestingly, the method has only a marginal effect on the prediction of binding by chromatin immunoprecipitation (ChIP) assays. We suggest several possibilities for reconciling this result with the improved enrichment that we observe for functionally related promoters and for promoters that are under positive selection.

10. Nonlinear equality constraints in feasible sequential quadratic programming

SciTech Connect

Lawrence, C.; Tits, A.

1994-12-31

In this talk we show that convergence of a feasible sequential quadratic programming algorithm modified to handle smooth nonlinear equality constraints. The modification of the algorithm to incorporate equality constraints is based on a scheme proposed by Mayne and Polak and is implemented in fsqp/cfsqp, an optimization package that generates feasible iterates. Nonlinear equality constraints are treated as {open_quotes}{<=}-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. For example, the problem minimize f(x) s.t. h(x) = 0, with h(x) a scalar, is replaced by minimize f(x) - ch(x) s.t. h(x) {<=} 0. The modified problem is equivalent to the original problem when c is large enough (but finite). Such a value is determined automatically via iterative adjustments.

11. Crustal structure of Tolfa domes complex (northern Latium - Italy) inferred from receiver functions analysis: an interplay between tectonics and magmatism

Buttinelli, M.; Bianchi, I.; Anselmi, M.; Chiarabba, C.; de Rita, D.; Quattrocchi, F.

2010-12-01

The Tolfa-Cerite volcanic district developed along the Tyrrhenian passive margin of central Italy, as part of magmatic processes started during the middle Pliocene. In this area the uncertainties on the deep crustal structures and the definition of the intrusive bodies geometry are focal issues that still need to be addressed. After the onset of the spreading of the Tyrrhenian sea during the Late Miocene, the emplacement of the intrusive bodies of the Tolfa complex (TDC), in a general back-arc geodynamical regime, generally occurred in a low stretching rate, in correspondence of the junctions between major lithospheric discontinuities. Normal faults, located at the edge of Mio-Pliocene basins, were used as preferential pathways for the rising of magmatic masses from the mantle to the surface. We used teleseismic recordings at the TOLF and MAON broad band station of the INGV seismic network (located between the Argentario promontory and Tolfa-Ceriti dome complexes -TDC-) to image the principal seismic velocity discontinuities by receiver function analysis (RF's). Together with RF’s velocity models of the area computed using the teleseismic events recorded by a temporary network of eight stations deployed around the TDC, we achieve a general crustal model of this area. The geometry of the seismic network has been defined to focus on the crustal structure beneath the TDC, trying to define the main velocity changes attributable to the intrusive bodies, the calcareous basal complex, the deep metamorphic basement, the lower crust and the Moho. The analysis of these data show the Moho at a depth of 23 km in the TDC area and 20 km in the Argentario area. Crustal models also show an unexpected velocity decrease between 12 and 18 km, consistent with a slight dropdown of the Vp/Vs ratio, imputable to a regional mid-crustal shear zone inherited from the previous alpine orogenesis, re-activated in extensional tectonic by the early opening phases of the Tyrrhenian sea. Above

12. Inference of Isoforms from Short Sequence Reads

Feng, Jianxing; Li, Wei; Jiang, Tao

13. Security analysis of quadratic phase based cryptography

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

14. Compact stars with quadratic equation of state

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.

15. Forced oscillations in quadratically damped systems

NASA Technical Reports Server (NTRS)

Bayliss, A.

1978-01-01

Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.

16. Analysis of quadratic nonlinearities in hydrodynamic transport systems employing numerical simulations

Bicken, Gurcan

This dissertation deals with the analysis and identification of quadratic non-linearities in hydrodynamic transport problems arising in engineering and science. As representative application areas, homogenous oscillations of electron and ion plasmas in a 1-D periodic domain and the forced voltage-current dynamics of a semiconductor device are considered. The time series data obtained from numerical solutions of the associated hydrodynamic equations are used for the spectral analysis of the quadratic nonlinearities in these respective systems. More specifically, electron plasma oscillations are analyzed using power spectra and cross-bicoherency spectra to gain insight into the quadratic interactions predicted by a simple model of the energy transfer that cascades from lower modes to higher modes within a small amplitude range of oscillations. The efficiency of the bicoherency function in detecting the quadratic wave interactions from the complex time series of the mode amplitudes is observed. The difference in the modal interactions for isentropic and isothermal plasma models are investigated based on numerical 'experiments' simulating the modal dynamics in each case. Furthermore, the concentration oscillations of cold ion plasmas in a Lagrangian frame are analyzed for different Debye lengths. The detailed effects of linear and nonlinear mechanisms in the hydrodynamic model on the power spectra of the oscillations are investigated. Second-order Volterra models are considered for approximating the dynamics of input-output systems with quadratic nonlinear terms. The linear and quadratic kernels of the Volterra model are estimated using multi- tone inputs and least-squares minimization. The implications of the non-orthogonality of the model are investigated in detail. To circumvent the negative effects of non-orthogonality on the accuracy of the kernel estimation, an 'odd-even' separation technique is utilized in the kernel estimation. This approach for estimating an

17. Integrability of Quadratic Non-autonomous Quantum Linear Systems

Lopez, Raquel

The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is

18. Inferring novel lncRNA-disease associations based on a random walk model of a lncRNA functional similarity network.

PubMed

Sun, Jie; Shi, Hongbo; Wang, Zhenzhen; Zhang, Changjian; Liu, Lin; Wang, Letian; He, Weiwei; Hao, Dapeng; Liu, Shulin; Zhou, Meng

2014-08-01

Accumulating evidence demonstrates that long non-coding RNAs (lncRNAs) play important roles in the development and progression of complex human diseases, and predicting novel human lncRNA-disease associations is a challenging and urgently needed task, especially at a time when increasing amounts of lncRNA-related biological data are available. In this study, we proposed a global network-based computational framework, RWRlncD, to infer potential human lncRNA-disease associations by implementing the random walk with restart method on a lncRNA functional similarity network. The performance of RWRlncD was evaluated by experimentally verified lncRNA-disease associations, based on leave-one-out cross-validation. We achieved an area under the ROC curve of 0.822, demonstrating the excellent performance of RWRlncD. Significantly, the performance of RWRlncD is robust to different parameter selections. Predictively highly-ranked lncRNA-disease associations in case studies of prostate cancer and Alzheimer's disease were manually confirmed by literature mining, providing evidence of the good performance and potential value of the RWRlncD method in predicting lncRNA-disease associations.

19. 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.

20. 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.)

ERIC Educational Resources Information Center

Warrens, Matthijs J.

2012-01-01

The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

2. 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…

3. Convexity preserving C2 rational quadratic trigonometric spline

Dube, Mridula; Tiwari, Preeti

2012-09-01

A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.

4. Sketching the General Quadratic Equation Using Dynamic Geometry Software

ERIC Educational Resources Information Center

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

5. 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…

6. 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.

7. 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.

8. Inferring Horizontal Gene Transfer

PubMed Central

Lassalle, Florent; Dessimoz, Christophe

2015-01-01

Horizontal or Lateral Gene Transfer (HGT or LGT) is the transmission of portions of genomic DNA between organisms through a process decoupled from vertical inheritance. In the presence of HGT events, different fragments of the genome are the result of different evolutionary histories. This can therefore complicate the investigations of evolutionary relatedness of lineages and species. Also, as HGT can bring into genomes radically different genotypes from distant lineages, or even new genes bearing new functions, it is a major source of phenotypic innovation and a mechanism of niche adaptation. For example, of particular relevance to human health is the lateral transfer of antibiotic resistance and pathogenicity determinants, leading to the emergence of pathogenic lineages [1]. Computational identification of HGT events relies upon the investigation of sequence composition or evolutionary history of genes. Sequence composition-based ("parametric") methods search for deviations from the genomic average, whereas evolutionary history-based ("phylogenetic") approaches identify genes whose evolutionary history significantly differs from that of the host species. The evaluation and benchmarking of HGT inference methods typically rely upon simulated genomes, for which the true history is known. On real data, different methods tend to infer different HGT events, and as a result it can be difficult to ascertain all but simple and clear-cut HGT events. PMID:26020646

9. How Forgetting Aids Heuristic Inference

ERIC Educational Resources Information Center

Schooler, Lael J.; Hertwig, Ralph

2005-01-01

Some theorists, ranging from W. James (1890) to contemporary psychologists, have argued that forgetting is the key to proper functioning of memory. The authors elaborate on the notion of beneficial forgetting by proposing that loss of information aids inference heuristics that exploit mnemonic information. To this end, the authors bring together 2…

10. Approximate Graph Edit Distance in Quadratic Time.

PubMed

Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

2015-09-14

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

11. Extremal Optimization for Quadratic Unconstrained Binary Problems

Boettcher, S.

We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

12. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method

Bizyaev, I. A.; Kozlov, V. V.

2015-12-01

We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.

13. Statistical inference and string theory

Heckman, Jonathan J.

2015-09-01

In this paper, we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a d-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a nonlinear sigma model in d dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature space-times.

14. Degenerate nonlinear programming with a quadratic growth condition.

SciTech Connect

Anitescu, M.; Mathematics and Computer Science

2000-01-01

We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.

15. Steering of Frequency Standards by the Use of Linear Quadratic Gaussian Control Theory

NASA Technical Reports Server (NTRS)

Koppang, Paul; Leland, Robert

1996-01-01

Linear quadratic Gaussian control is a technique that uses Kalman filtering to estimate a state vector used for input into a control calculation. A control correction is calculated by minimizing a quadratic cost function that is dependent on both the state vector and the control amount. Different penalties, chosen by the designer, are assessed by the controller as the state vector and control amount vary from given optimal values. With this feature controllers can be designed to force the phase and frequency differences between two standards to zero either more or less aggressively depending on the application. Data will be used to show how using different parameters in the cost function analysis affects the steering and the stability of the frequency standards.

16. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

17. Multiple Instance Fuzzy Inference

DTIC Science & Technology

2015-12-02

INFERENCE A novel fuzzy learning framework that employs fuzzy inference to solve the problem of multiple instance learning (MIL) is presented. The...fuzzy learning framework that employs fuzzy inference to solve the problem of multiple instance learning (MIL) is presented. The framework introduces a...or learned from data. In multiple instance problems, the training data is ambiguously labeled. Instances are grouped into bags, labels of bags are

18. Combinatorics of distance-based tree inference

PubMed Central

Pardi, Fabio; Gascuel, Olivier

2012-01-01

Several popular methods for phylogenetic inference (or hierarchical clustering) are based on a matrix of pairwise distances between taxa (or any kind of objects): The objective is to construct a tree with branch lengths so that the distances between the leaves in that tree are as close as possible to the input distances. If we hold the structure (topology) of the tree fixed, in some relevant cases (e.g., ordinary least squares) the optimal values for the branch lengths can be expressed using simple combinatorial formulae. Here we define a general form for these formulae and show that they all have two desirable properties: First, the common tree reconstruction approaches (least squares, minimum evolution), when used in combination with these formulae, are guaranteed to infer the correct tree when given enough data (consistency); second, the branch lengths of all the simple (nearest neighbor interchange) rearrangements of a tree can be calculated, optimally, in quadratic time in the size of the tree, thus allowing the efficient application of hill climbing heuristics. The study presented here is a continuation of that by Mihaescu and Pachter on branch length estimation [Mihaescu R, Pachter L (2008) Proc Natl Acad Sci USA 105:13206–13211]. The focus here is on the inference of the tree itself and on providing a basis for novel algorithms to reconstruct trees from distances. PMID:23012403

19. Combinatorics of distance-based tree inference.

PubMed

Pardi, Fabio; Gascuel, Olivier

2012-10-09

Several popular methods for phylogenetic inference (or hierarchical clustering) are based on a matrix of pairwise distances between taxa (or any kind of objects): The objective is to construct a tree with branch lengths so that the distances between the leaves in that tree are as close as possible to the input distances. If we hold the structure (topology) of the tree fixed, in some relevant cases (e.g., ordinary least squares) the optimal values for the branch lengths can be expressed using simple combinatorial formulae. Here we define a general form for these formulae and show that they all have two desirable properties: First, the common tree reconstruction approaches (least squares, minimum evolution), when used in combination with these formulae, are guaranteed to infer the correct tree when given enough data (consistency); second, the branch lengths of all the simple (nearest neighbor interchange) rearrangements of a tree can be calculated, optimally, in quadratic time in the size of the tree, thus allowing the efficient application of hill climbing heuristics. The study presented here is a continuation of that by Mihaescu and Pachter on branch length estimation [Mihaescu R, Pachter L (2008) Proc Natl Acad Sci USA 105:13206-13211]. The focus here is on the inference of the tree itself and on providing a basis for novel algorithms to reconstruct trees from distances.

SciTech Connect

Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin

2011-04-15

We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.

1. Chaos synchronization based on quadratic optimum regulation and control

Gong, Lihua

2005-03-01

Based on the method of the quadratic optimum control, a quadratic optimal regulator used for synchronizing chaotic systems is constructed to realize chaos synchronization. The synchronization method can maintain the least error with less control energy, and then realize the optimization on both sides of energy and error synthetically. In addition, the control cost can also be reduced by using this method intermittently. The simulation results of the chaotic Chua's circuit and the Rossler chaos system prove that the method is effective.

2. Quadratic bulk viscosity and the topology of space time.

Wolf, C.

1997-12-01

By considering a homogeneous isotropic universe admitting quadratic bulk viscosity the author shows that if the bulk viscosity coefficient is large the effective topology of space time attains an antiintuitive interpretation in the sense that a positive curvature space time is ever-expanding. This is true for all cosmologies studied except in the case of small quadratic bulk viscosity (3γ+1-kβ ≥ 0, 3γ+1 > 0).

3. Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

4. A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

5. Sequential quadratic programming with step control using the Lagrange function

SciTech Connect

Danilin, Yu.M.

1995-01-01

This article examines some methods of solving the problem min f (x), x {epsilon} S {contained_in} E{sup n}, S = (x:g{sub j}(x) = O,j = 1,...,t). These methods construct the iterative sequence x{sub k}+1 = x{sub k} + {alpha}{sub k}p{sub k}, k = 0, 1,..., where the vector p{sub k} is the solution of the problem min [ + 1/2 ], g{sub j}(x{sub k}) + < g{sub j}{prime}(x{sub k}), p > = O, j = 1,...,t, and the multiplier {alpha}{sub k} is chosen as the maximum value of the parameter {alpha} {le} 1 obtained by splitting such that F(x{sub k} + {alpha}p{sub k}, {lambda}{sub k}{sub i} + 1, R{sub k}{sub i}){le}{epsilon} {alpha} < F{prime} {sub x}(x{sub k},{lambda}{sub k}{sub i} + 1, R{sub k}{sub i}), p{sub k} >, O < {epsilon} < 1.

6. Modelling Transformations of Quadratic Functions: A Proposal of Inductive Inquiry

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2013-01-01

This paper presents a study about using scientific simulations to enhance the process of mathematical modelling. The main component of the study is a lesson whose major objective is to have students mathematise a trajectory of a projected object and then apply the model to formulate other trajectories by using the properties of function…

7. The Notion of Reducing Abstraction in Quadratic Functions

ERIC Educational Resources Information Center

Eraslan, Ali

2008-01-01

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

8. A new gradient-based neural network for solving linear and quadratic programming problems.

PubMed

Leung, Y; Chen, K Z; Jiao, Y C; Gao, X B; Leung, K S

2001-01-01

A new gradient-based neural network is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory, and LaSalle invariance principle to solve linear and quadratic programming problems. In particular, a new function F(x, y) is introduced into the energy function E(x, y) such that the function E(x, y) is convex and differentiable, and the resulting network is more efficient. This network involves all the relevant necessary and sufficient optimality conditions for convex quadratic programming problems. For linear programming and quadratic programming (QP) problems with unique and infinite number of solutions, we have proven strictly that for any initial point, every trajectory of the neural network converges to an optimal solution of the QP and its dual problem. The proposed network is different from the existing networks which use the penalty method or Lagrange method, and the inequality constraints are properly handled. The simulation results show that the proposed neural network is feasible and efficient.

9. Quadratic Optimization in the Problems of Active Control of Sound

NASA Technical Reports Server (NTRS)

Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

10. Inference in poor languages

SciTech Connect

Petrov, S.

1996-10-01

Languages with a solvable implication problem but without complete and consistent systems of inference rules (poor languages) are considered. The problem of existence of finite complete and consistent inference rule system for a poor language is stated independently of the language or rules syntax. Several properties of the problem arc proved. An application of results to the language of join dependencies is given.

11. Moments for general quadratic densities in n dimensions

SciTech Connect

Furman, Miguel A.

2002-03-20

We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.

12. Electrochemical reduction of carbon fluorine bond in 4-fluorobenzonitrile Mechanistic analysis employing Marcus Hush quadratic activation-driving force relation

Muthukrishnan, A.; Sangaranarayanan, M. V.

2007-10-01

The reduction of carbon-fluorine bond in 4-fluorobenzonitrile in acetonitrile as the solvent, is analyzed using convolution potential sweep voltammetry and the dependence of the transfer coefficient on potential is investigated within the framework of Marcus-Hush quadratic activation-driving force theory. The validity of stepwise mechanism is inferred from solvent reorganization energy estimates as well as bond length calculations using B3LYP/6-31g(d) method. A novel method of estimating the standard reduction potential of the 4-fluorobenzonitrile in acetonitrile is proposed.

13. KENO-VI: A Monte Carlo Criticality Program with generalized quadratic geometry

SciTech Connect

Hollenbach, D.F.; Petrie, L.M.; Landers, N.F.

1993-07-01

This report discusses KENO-VI which is a new version of the KENO monte Carlo Criticality Safety developed at Oak Ridge National Laboratory. The purpose of KENO-VI is to provide a criticality safety code similar to KENO-V.a that possesses a more general and flexible geometry package. KENO-VI constructs and processes geometry data as sets of quadratic equations. A lengthy set of simple, easy-to-use geometric functions, similar to those provided in KENO-V.a., and the ability to build more complex geometric shapes represented by sets of quadratic equations are the heart of the geometry package in KENO-VI. The code`s flexibility is increased by allowing intersecting geometry regions, hexagonal as well as cuboidal arrays, and the ability to specify an array boundary that intersects the array.

14. Learning control for minimizing a quadratic cost during repetitions of a task

NASA Technical Reports Server (NTRS)

Longman, Richard W.; Chang, Chi-Kuang

1990-01-01

In many applications, control systems are asked to perform the same task repeatedly. Learning control laws have been developed over the last few years that allow the controller to improve its performance each repetition, and to converge to zero error in tracking a desired trajectory. This paper generates a new type of learning control law that learns to minimize a quadratic cost function for tracking. Besides being of interest in its own right, this objective alleviates the need to specify a desired trajectory that can actually be performed by the system. The approach used here is to adapt appropriate methods from numerical optimization theory in order to produce learning control algorithms that adjust the system command from repetition to repetition in order to converge to the quadratic cost optimal trajectory.

15. Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise

Ren, Ruibin; Luo, Maokang; Deng, Ke

2017-02-01

Stochastic resonance of a fractional oscillator subject to an external periodic field as well as to multiplicative and additive noise is investigated. The fluctuations of the eigenfrequency are modeled as the quadratic function of the trichotomous noise. Applying the moment equation method and Shapiro–Loginov formula, we obtain the exact expression of the complex susceptibility and related stability criteria. Theoretical analysis and numerical simulations indicate that the spectral amplification (SPA) depends non-monotonicly both on the external driving frequency and the parameters of the quadratic noise. In addition, the investigations into fractional stochastic systems have suggested that both the noise parameters and the memory effect can induce the phenomenon of stochastic multi-resonance (SMR), which is previously reported and believed to be absent in the case of the multiplicative noise with only a linear term.

16. Fitting timeseries by continuous-time Markov chains: A quadratic programming approach

SciTech Connect

Crommelin, D.T. . E-mail: crommelin@cims.nyu.edu; Vanden-Eijnden, E. . E-mail: eve2@cims.nyu.edu

2006-09-20

Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.

17. The quadratically damped oscillator: A case study of a non-linear equation of motion

Smith, B. R.

2012-09-01

The equation of motion for a quadratically damped oscillator, where the damping is proportional to the square of the velocity, is a non-linear second-order differential equation. Non-linear equations of motion such as this are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions. Like all second-order ordinary differential equations, it has a corresponding first-order partial differential equation, whose independent solutions constitute the constants of the motion. These constants readily provide an approximate solution correct to first order in the damping constant. They also reveal that the quadratically damped oscillator is never critically damped or overdamped, and that to first order in the damping constant the oscillation frequency is identical to the natural frequency. The technique described has close ties to standard tools such as integral curves in phase space and phase portraits.

18. Fitting timeseries by continuous-time Markov chains: A quadratic programming approach

Crommelin, D. T.; Vanden-Eijnden, E.

2006-09-01

Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows.

ERIC Educational Resources Information Center

Baron, Lorraine M.

2015-01-01

As students develop algebraic reasoning in grades 5 to 9, they learn to recognize patterns and understand expressions, equations, and variables. Linear functions are a focus in eighth-grade mathematics, and by algebra 1, students must make sense of functions that are not linear. This article describes how students worked through a classroom task…

20. Anisotropic feature inferred from receiver functions and S-wave splitting in and around the high strain rate zone, central Japan

Shiomi, K.; Takeda, T.; Sekiguchi, S.

2012-12-01

By the recent dense GPS observation, the high strain rate zone (HSRZ) crossing the central Japan was discovered. In the HSRZ, E-W compressive stress field is observed, and large earthquakes with M>6 are frequently occurred. In this study, we try to reveal depth-dependent anisotropic feature in this region by using teleseismic receiver functions (RFs) and S-wave splitting information. As a target, we select NIED Hi-net stations N.TGWH and N.TSTH, which are located inside and outside of the HSRZ respectively. For RF analysis, we choose M>5.5 teleseismic events from October 2000 to November 2011. Low-pass filters with fc = 1 and 2 Hz are applied to estimate RFs. In the radial RFs, we find clear positive phase arrivals at 4 to 4.5 s in delay time for both stations. Since this time delay corresponds to 35 km-depth velocity discontinuity existence, these phases may be the converted phases generated at the Moho discontinuity. Seeing the back-azimuth paste-ups of the transverse RFs, we can find polarity changes of later phases at 4 to 4.5 s in delay time at the N.TSTH station. This polarity change occurs for direction of N0E (north), N180E (south), and N270E (west). Although we have no data in N90E (east) direction, this feature implies that anisotropic rocks may exist around the Moho. In order to check this feature, we consider 6-layered subsurface model and compare synthetic RFs with the observation. The first three layers are for thick sediments and upper crust including a dipping velocity interface. The fourth, fifth and sixth layer corresponds to the mid crust, lower crust and uppermost mantle, respectively. The best model infers that the mid- and lower-crust beneath the N.TSTH station should have strong anisotropy whose fast axis directs to the N-S, though the fast axis in the uppermost mantle seems to show E-W direction. Moreover, to explain the observation, the symmetric axes in the lower crust and the uppermost mantle should be dipping about 20 degrees. To check

1. Effects of classroom instruction on students' understanding of quadratic equations

Vaiyavutjamai, Pongchawee; Clements, M. A. (Ken)

2006-05-01

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 transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed. Using a rubric for assessing students' understanding, the analysis revealed that at the post-teaching stage students improved their performance on quadratic equations and had a better understanding of associated concepts than they had at the pre-teaching stage. However, many were still confused about the concepts of a variable and of a "solution" to a quadratic equation. After the lessons, most students had acquired neither an instrumental nor a relational understanding of the mathematics associated with solving elementary quadratic equations.

2. Linguistic Markers of Inference Generation While Reading.

PubMed

Clinton, Virginia; Carlson, Sarah E; Seipel, Ben

2016-06-01

Words can be informative linguistic markers of psychological constructs. The purpose of this study is to examine associations between word use and the process of making meaningful connections to a text while reading (i.e., inference generation). To achieve this purpose, think-aloud data from third-fifth grade students ([Formula: see text]) reading narrative texts were hand-coded for inferences. These data were also processed with a computer text analysis tool, Linguistic Inquiry and Word Count, for percentages of word use in the following categories: cognitive mechanism words, nonfluencies, and nine types of function words. Findings indicate that cognitive mechanisms were an independent, positive predictor of connections to background knowledge (i.e., elaborative inference generation) and nonfluencies were an independent, negative predictor of connections within the text (i.e., bridging inference generation). Function words did not provide unique variance towards predicting inference generation. These findings are discussed in the context of a cognitive reflection model and the differences between bridging and elaborative inference generation. In addition, potential practical implications for intelligent tutoring systems and computer-based methods of inference identification are presented.

3. A Projection Neural Network for Constrained Quadratic Minimax Optimization.

PubMed

Liu, Qingshan; Wang, Jun

2015-11-01

This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

4. Inferring Centrality from Network Snapshots

Shao, Haibin; Mesbahi, Mehran; Li, Dewei; Xi, Yugeng

2017-01-01

The topology and dynamics of a complex network shape its functionality. However, the topologies of many large-scale networks are either unavailable or incomplete. Without the explicit knowledge of network topology, we show how the data generated from the network dynamics can be utilised to infer the tempo centrality, which is proposed to quantify the influence of nodes in a consensus network. We show that the tempo centrality can be used to construct an accurate estimate of both the propagation rate of influence exerted on consensus networks and the Kirchhoff index of the underlying graph. Moreover, the tempo centrality also encodes the disturbance rejection of nodes in a consensus network. Our findings provide an approach to infer the performance of a consensus network from its temporal data.

5. Network Plasticity as Bayesian Inference

PubMed Central

Legenstein, Robert; Maass, Wolfgang

2015-01-01

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling. PMID:26545099

6. Inferring Centrality from Network Snapshots

PubMed Central

Shao, Haibin; Mesbahi, Mehran; Li, Dewei; Xi, Yugeng

2017-01-01

The topology and dynamics of a complex network shape its functionality. However, the topologies of many large-scale networks are either unavailable or incomplete. Without the explicit knowledge of network topology, we show how the data generated from the network dynamics can be utilised to infer the tempo centrality, which is proposed to quantify the influence of nodes in a consensus network. We show that the tempo centrality can be used to construct an accurate estimate of both the propagation rate of influence exerted on consensus networks and the Kirchhoff index of the underlying graph. Moreover, the tempo centrality also encodes the disturbance rejection of nodes in a consensus network. Our findings provide an approach to infer the performance of a consensus network from its temporal data. PMID:28098166

7. An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity.

PubMed

Culpepper, Steven Andrew

2016-06-01

Standardized tests are frequently used for selection decisions, and the validation of test scores remains an important area of research. This paper builds upon prior literature about the effect of nonlinearity and heteroscedasticity on the accuracy of standard formulas for correcting correlations in restricted samples. Existing formulas for direct range restriction require three assumptions: (1) the criterion variable is missing at random; (2) a linear relationship between independent and dependent variables; and (3) constant error variance or homoscedasticity. The results in this paper demonstrate that the standard approach for correcting restricted correlations is severely biased in cases of extreme monotone quadratic nonlinearity and heteroscedasticity. This paper offers at least three significant contributions to the existing literature. First, a method from the econometrics literature is adapted to provide more accurate estimates of unrestricted correlations. Second, derivations establish bounds on the degree of bias attributed to quadratic functions under the assumption of a monotonic relationship between test scores and criterion measurements. New results are presented on the bias associated with using the standard range restriction correction formula, and the results show that the standard correction formula yields estimates of unrestricted correlations that deviate by as much as 0.2 for high to moderate selectivity. Third, Monte Carlo simulation results demonstrate that the new procedure for correcting restricted correlations provides more accurate estimates in the presence of quadratic and heteroscedastic test score and criterion relationships.

8. CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

9. Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

Bai, Zheng-Jian; Datta, Biswa Nath; Wang, Jinwei

2010-04-01

The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant "no spill-over property" of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show

10. On Bayesian Inductive Inference & Predictive Estimation

NASA Technical Reports Server (NTRS)

Cheeseman, Peter; Stutz, John; Smelyanskiy, Vadim

2004-01-01

We investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.

11. A note on contracts on quadratic variation

PubMed Central

Lindberg, Carl

2017-01-01

Given a Black stochastic volatility model for a future F, and a function g, we show that the price of 12∫0Tg(t,F(t))F2(t)σ2(t)dt can be represented by portfolios of put and call options. This generalizes the classical representation result for the variance swap. Further, in a local volatility model, we give an example based on Dupire’s formula which shows how the theorem can be used to design variance related contracts with desirable characteristics. PMID:28333971

12. Large-Scale Sequential Quadratic Programming Algorithms

DTIC Science & Technology

1992-09-01

KKT conditions for the QP subproblem shows that Pk(gk) = pk(VL). To see why, note that the KKT necessary and sufficient conditions ...number of active functional constraints at x*). Let Z* be a basis for the null space of A* (so that A*Z* = 0). The KKT necessary conditions for (x*, A... optimal (i.e. when the working set has identified the active set). Let g* FkP* +9k and omit the subscript k. Consider the first-order KKT conditions for

13. A Model for Quadratic Outliers in Linear Regression.

ERIC Educational Resources Information Center

Elashoff, Janet Dixon; Elashoff, Robert M.

This paper introduces a model for describing outliers (observations which are extreme in some sense or violate the apparent pattern of other observations) in linear regression which can be viewed as a mixture of a quadratic and a linear regression. The maximum likelihood estimators of the parameters in the model are derived and their asymptotic…

14. Solving quadratic programming problems by delayed projection neural network.

PubMed

Yang, Yongqing; Cao, Jinde

2006-11-01

In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.

15. Unravelling Student Challenges with Quadratics: A Cognitive Approach

ERIC Educational Resources Information Center

Kotsopoulos, Donna

2007-01-01

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

16. Solving the Quadratic Capacitated Facilities Location Problem by Computer.

ERIC Educational Resources Information Center

Cote, Leon C.; Smith, Wayland P.

Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

17. Tuning a fuzzy controller using quadratic response surfaces

NASA Technical Reports Server (NTRS)

Schott, Brian; Whalen, Thomas

1992-01-01

Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

18. Confidence set interference with a prior quadratic bound. [in geophysics

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

19. Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem

Davendra, Donald; Zelinka, Ivan; Senkerik, Roman

2009-08-01

An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.

20. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2012-01-01

The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan

2016-04-01

The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.

2. Evaluating the Contributions of Individual Variables to a Quadratic Form.

PubMed

Garthwaite, Paul H; Koch, Inge

2016-03-01

Quadratic forms capture multivariate information in a single number, making them useful, for example, in hypothesis testing. When a quadratic form is large and hence interesting, it might be informative to partition the quadratic form into contributions of individual variables. In this paper it is argued that meaningful partitions can be formed, though the precise partition that is determined will depend on the criterion used to select it. An intuitively reasonable criterion is proposed and the partition to which it leads is determined. The partition is based on a transformation that maximises the sum of the correlations between individual variables and the variables to which they transform under a constraint. Properties of the partition, including optimality properties, are examined. The contributions of individual variables to a quadratic form are less clear-cut when variables are collinear, and forming new variables through rotation can lead to greater transparency. The transformation is adapted so that it has an invariance property under such rotation, whereby the assessed contributions are unchanged for variables that the rotation does not affect directly. Application of the partition to Hotelling's one- and two-sample test statistics, Mahalanobis distance and discriminant analysis is described and illustrated through examples. It is shown that bootstrap confidence intervals for the contributions of individual variables to a partition are readily obtained.

3. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

ERIC Educational Resources Information Center

Leyendekkers, J. V.; Shannon, A. G.

2004-01-01

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

4. Beam steering and routing in quadratic nonlinear media

SciTech Connect

Aceves, A.B.; Santos, M.C.; Torner, L.

1997-04-01

We show how the spatial phase modulation of weak second-harmonic signals controls the overall direction of propagation of spatial solitons in quadratic nonlinear media. We investigate numerically such a process and discuss its applications to all-optical beam routing. 5 refs., 3 figs.

5. An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems

SciTech Connect

Zhang Jianzhong; Zhang Liwei

2010-02-15

We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC{sup 1}) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/{radical}r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC{sup 1} function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.

6. Optimizing nondecomposable loss functions in structured prediction.

PubMed

Ranjbar, Mani; Lan, Tian; Wang, Yang; Robinovitch, Steven N; Li, Ze-Nian; Mori, Greg

2013-04-01

We develop an algorithm for structured prediction with nondecomposable performance measures. The algorithm learns parameters of Markov Random Fields (MRFs) and can be applied to multivariate performance measures. Examples include performance measures such as Fβ score (natural language processing), intersection over union (object category segmentation), Precision/Recall at k (search engines), and ROC area (binary classifiers). We attack this optimization problem by approximating the loss function with a piecewise linear function. The loss augmented inference forms a Quadratic Program (QP), which we solve using LP relaxation. We apply this approach to two tasks: object class-specific segmentation and human action retrieval from videos. We show significant improvement over baseline approaches that either use simple loss functions or simple scoring functions on the PASCAL VOC and H3D Segmentation datasets, and a nursing home action recognition dataset.

7. The Bayes Inference Engine

SciTech Connect

Hanson, K.M.; Cunningham, G.S.

1996-04-01

The authors are developing a computer application, called the Bayes Inference Engine, to provide the means to make inferences about models of physical reality within a Bayesian framework. The construction of complex nonlinear models is achieved by a fully object-oriented design. The models are represented by a data-flow diagram that may be manipulated by the analyst through a graphical programming environment. Maximum a posteriori solutions are achieved using a general, gradient-based optimization algorithm. The application incorporates a new technique of estimating and visualizing the uncertainties in specific aspects of the model.

8. Statistical inference for inverse problems

Bissantz, Nicolai; Holzmann, Hajo

2008-06-01

In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima of the unknown function. The methods are illustrated in a case study, where we analyze the distribution of heliocentric escape velocities of galaxies in the Centaurus galaxy cluster, and provide statistical evidence for its bimodality.

9. Using convex quadratic programming to model random media with Gaussian random fields

SciTech Connect

Quintanilla, John A.; Jones, W. Max

2007-04-15

Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented.

10. Singular linear quadratic control problem for systems with linear and constant delay

Sesekin, A. N.; Andreeva, I. Yu.; Shlyakhov, A. S.

2016-12-01

This article is devoted to the singular linear-quadratic optimization problem on the trajectories of the linear non-autonomous system of differential equations with linear and constant delay. It should be noted that such task does not solve the class of integrable controls, so to ensure the existence of a solution is needed to expand the class of controls to include the control impulse components. For the problem under consideration, we have built program control containing impulse components in the initial and final moments time. This is done under certain assumptions on the functional and the right side of the control system.

11. Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

12. The dynamics of a symmetric coupling of three modified quadratic maps

Paulo, C. Rech

2013-08-01

We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark—Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.

13. A sequential quadratic programming algorithm using an incomplete solution of the subproblem

SciTech Connect

Murray, W.; Prieto, F.J.

1993-05-01

We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set.

14. Bianchi type-I universe in Lyra manifold with quadratic equation of state

Şen, R.; Aygün, S.

2017-02-01

In this study, we have solved Einstein field equations for Bianchi type I universe model in Lyra manifold with quadratic equation of state (EoS) p = ap(t)2 - ρ(t). Where α ≠0 is an important constant. Cosmic pressure, density and displacement vector (β2) are related with α constant. In this study β2 is a decreasing function of time and behaves like a cosmological constant. These solutions agree with the studies of Halford, Pradhan and Singh, Aygün et al., Agarwal et al., Yadav and Haque as well as SN Ia observations.

15. Inference as Prediction

ERIC Educational Resources Information Center

Watson, Jane

2007-01-01

Inference, or decision making, is seen in curriculum documents as the final step in a statistical investigation. For a formal statistical enquiry this may be associated with sophisticated tests involving probability distributions. For young students without the mathematical background to perform such tests, it is still possible to draw informal…

SciTech Connect

Schneider, Uwe

2009-04-15

A simple mechanistic model for predicting cancer induction after fractionated radiotherapy is developed. The model is based upon the linear-quadratic model. The inductions of carcinomas and sarcomas are modeled separately. The linear-quadratic model of cell kill is applied to normal tissues which are unintentionally irradiated during a cancer treatment with radiotherapy. Tumor induction is modeled such that each transformation process results in a tumor cell. The microscopic transformation parameter was chosen such that in the limit of low dose and acute exposure, the parameters of the linear-no-threshold model for tumor induction were approached. The differential equations describing carcinoma and sarcoma inductions can be solved analytically. Cancer induction in this model is a function of treatment dose, the cell kill parameters ({alpha},{beta}), the tumor induction variable ({mu}), and the repopulation parameter ({xi}). Carcinoma induction shows a bell shaped behavior as long as cell repopulation is small. Assuming large cell repopulation rates, a plateaulike function is approached. In contrast, sarcoma induction is negligible for low doses and increases with increasing dose up to a constant value. The proposed model describes carcinoma and sarcoma inductions after fractionated radiotherapy as an analytical function of four parameters. In the limit of low dose and for an instant irradiation it reproduces the results of the linear-no-threshold model. The obtained dose-response curves for cancer induction can be implemented with other models such as the organ-equivalent dose model to predict second cancers after radiotherapy.

17. Gravitomagnetic effects in quadratic gravity with a scalar field

Finch, Andrew; Said, Jackson Levi

2016-10-01

The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

18. A generalized quadratic flow law for sheet metals

Jones, S. E.; Gillis, P. P.

1984-01-01

A planar quadratic flow law is proposed for anisotropic sheet materials. This law is similar to the anisotropic strength criterion of Tsai and Wu. It has six experimentally determinable coefficients as compared to four in Hill’s flow law and, thus, allows more experimental information to be accommodated. However, the resulting strain increment vector, while unique, is not necessarily normal to the flow surface.

19. Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications

Li, Jibin; Feng, Zhaosheng

We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.

20. Quantum integrals of motion for variable quadratic Hamiltonians

SciTech Connect

Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

2010-09-15

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

1. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

2. Design of Linear Quadratic Regulators and Kalman Filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L.

1986-01-01

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

3. Quadratic performance index generation for optimal regular design.

NASA Technical Reports Server (NTRS)

Bullock, T. E.; Elder, J. M.

1971-01-01

Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.

4. Measurement of quadratic electrogyration effect in castor oil

Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

2015-07-01

This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

5. Optical Inference Machines

DTIC Science & Technology

1988-06-27

de olf nessse end Id e ;-tl Sb ieeI smleo) ,Optical Artificial Intellegence ; Optical inference engines; Optical logic; Optical informationprocessing...common. They arise in areas such as expert systems and other artificial intelligence systems. In recent years, the computer science language PROLOG has...cal processors should in principle be well suited for : I artificial intelligence applications. In recent years, symbolic logic processing. , the

6. Active inference and learning.

PubMed

Friston, Karl; FitzGerald, Thomas; Rigoli, Francesco; Schwartenbeck, Philipp; O'Doherty, John; Pezzulo, Giovanni

2016-09-01

This paper offers an active inference account of choice behaviour and learning. It focuses on the distinction between goal-directed and habitual behaviour and how they contextualise each other. We show that habits emerge naturally (and autodidactically) from sequential policy optimisation when agents are equipped with state-action policies. In active inference, behaviour has explorative (epistemic) and exploitative (pragmatic) aspects that are sensitive to ambiguity and risk respectively, where epistemic (ambiguity-resolving) behaviour enables pragmatic (reward-seeking) behaviour and the subsequent emergence of habits. Although goal-directed and habitual policies are usually associated with model-based and model-free schemes, we find the more important distinction is between belief-free and belief-based schemes. The underlying (variational) belief updating provides a comprehensive (if metaphorical) process theory for several phenomena, including the transfer of dopamine responses, reversal learning, habit formation and devaluation. Finally, we show that active inference reduces to a classical (Bellman) scheme, in the absence of ambiguity.

7. Scene Construction, Visual Foraging, and Active Inference

PubMed Central

Mirza, M. Berk; Adams, Rick A.; Mathys, Christoph D.; Friston, Karl J.

2016-01-01

This paper describes an active inference scheme for visual searches and the perceptual synthesis entailed by scene construction. Active inference assumes that perception and action minimize variational free energy, where actions are selected to minimize the free energy expected in the future. This assumption generalizes risk-sensitive control and expected utility theory to include epistemic value; namely, the value (or salience) of information inherent in resolving uncertainty about the causes of ambiguous cues or outcomes. Here, we apply active inference to saccadic searches of a visual scene. We consider the (difficult) problem of categorizing a scene, based on the spatial relationship among visual objects where, crucially, visual cues are sampled myopically through a sequence of saccadic eye movements. This means that evidence for competing hypotheses about the scene has to be accumulated sequentially, calling upon both prediction (planning) and postdiction (memory). Our aim is to highlight some simple but fundamental aspects of the requisite functional anatomy; namely, the link between approximate Bayesian inference under mean field assumptions and functional segregation in the visual cortex. This link rests upon the (neurobiologically plausible) process theory that accompanies the normative formulation of active inference for Markov decision processes. In future work, we hope to use this scheme to model empirical saccadic searches and identify the prior beliefs that underwrite intersubject variability in the way people forage for information in visual scenes (e.g., in schizophrenia). PMID:27378899

8. Fast source optimization involving quadratic line-contour objectives for the resist image.

PubMed

Yu, Jue-Chin; Yu, Peichen; Chao, Hsueh-Yung

2012-03-26

In Abbe's formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.

9. IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

10. Multimodel inference and adaptive management

USGS Publications Warehouse

Rehme, S.E.; Powell, L.A.; Allen, C.R.

2011-01-01

Ecology is an inherently complex science coping with correlated variables, nonlinear interactions and multiple scales of pattern and process, making it difficult for experiments to result in clear, strong inference. Natural resource managers, policy makers, and stakeholders rely on science to provide timely and accurate management recommendations. However, the time necessary to untangle the complexities of interactions within ecosystems is often far greater than the time available to make management decisions. One method of coping with this problem is multimodel inference. Multimodel inference assesses uncertainty by calculating likelihoods among multiple competing hypotheses, but multimodel inference results are often equivocal. Despite this, there may be pressure for ecologists to provide management recommendations regardless of the strength of their study’s inference. We reviewed papers in the Journal of Wildlife Management (JWM) and the journal Conservation Biology (CB) to quantify the prevalence of multimodel inference approaches, the resulting inference (weak versus strong), and how authors dealt with the uncertainty. Thirty-eight percent and 14%, respectively, of articles in the JWM and CB used multimodel inference approaches. Strong inference was rarely observed, with only 7% of JWM and 20% of CB articles resulting in strong inference. We found the majority of weak inference papers in both journals (59%) gave specific management recommendations. Model selection uncertainty was ignored in most recommendations for management. We suggest that adaptive management is an ideal method to resolve uncertainty when research results in weak inference.

11. Bayesian inference for OPC modeling

Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.

2016-03-01

The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.

12. Dopamine, Affordance and Active Inference

PubMed Central

Friston, Karl J.; Shiner, Tamara; FitzGerald, Thomas; Galea, Joseph M.; Adams, Rick; Brown, Harriet; Dolan, Raymond J.; Moran, Rosalyn; Stephan, Klaas Enno; Bestmann, Sven

2012-01-01

The role of dopamine in behaviour and decision-making is often cast in terms of reinforcement learning and optimal decision theory. Here, we present an alternative view that frames the physiology of dopamine in terms of Bayes-optimal behaviour. In this account, dopamine controls the precision or salience of (external or internal) cues that engender action. In other words, dopamine balances bottom-up sensory information and top-down prior beliefs when making hierarchical inferences (predictions) about cues that have affordance. In this paper, we focus on the consequences of changing tonic levels of dopamine firing using simulations of cued sequential movements. Crucially, the predictions driving movements are based upon a hierarchical generative model that infers the context in which movements are made. This means that we can confuse agents by changing the context (order) in which cues are presented. These simulations provide a (Bayes-optimal) model of contextual uncertainty and set switching that can be quantified in terms of behavioural and electrophysiological responses. Furthermore, one can simulate dopaminergic lesions (by changing the precision of prediction errors) to produce pathological behaviours that are reminiscent of those seen in neurological disorders such as Parkinson's disease. We use these simulations to demonstrate how a single functional role for dopamine at the synaptic level can manifest in different ways at the behavioural level. PMID:22241972

13. A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application.

PubMed

Li, Shuai; Li, Yangming; Wang, Zheng

2013-03-01

This paper presents a class of recurrent neural networks to solve quadratic programming problems. Different from most existing recurrent neural networks for solving quadratic programming problems, the proposed neural network model converges in finite time and the activation function is not required to be a hard-limiting function for finite convergence time. The stability, finite-time convergence property and the optimality of the proposed neural network for solving the original quadratic programming problem are proven in theory. Extensive simulations are performed to evaluate the performance of the neural network with different parameters. In addition, the proposed neural network is applied to solving the k-winner-take-all (k-WTA) problem. Both theoretical analysis and numerical simulations validate the effectiveness of our method for solving the k-WTA problem.

14. Gene-network inference by message passing

Braunstein, A.; Pagnani, A.; Weigt, M.; Zecchina, R.

2008-01-01

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.

15. Inferring protein function from genomic sequence: Giardia lamblia expresses a phosphatidylinositol kinase-related kinase similar to yeast and mammalian TOR.

PubMed

Morrison, Hilary G; Zamora, Gus; Campbell, Robert K; Sogin, Mitchell L

2002-12-01

Functional assays of genes have historically led to insights about the activities of a protein or protein cascade. However, the rapid expansion of genomic and proteomic information for a variety of diverse taxa is an alternative and powerful means of predicting function by comparing the enzymes and metabolic pathways used by different organisms. As part of the Giardia lamblia genome sequencing project, we routinely survey the complement of predicted proteins and compare those found in this putatively early diverging eukaryote with those of prokaryotes and more recently evolved eukaryotic lineages. Such comparisons reveal the minimal composition of conserved metabolic pathways, suggest which proteins may have been acquired by lateral transfer, and, by their absence, hint at functions lost in the transition from a free-living to a parasitic lifestyle. Here, we describe the use of bioinformatic approaches to investigate the complement and conservation of proteins in Giardia involved in the regulation of translation. We compare an FK506 binding protein homologue and phosphatidylinositol kinase-related kinase present in Giardia to those found in other eukaryotes for which complete genomic sequence data are available. Our investigation of the Giardia genome suggests that PIK-related kinases are of ancient origin and are highly conserved.

16. Visual Inference Programming

NASA Technical Reports Server (NTRS)

Wheeler, Kevin; Timucin, Dogan; Rabbette, Maura; Curry, Charles; Allan, Mark; Lvov, Nikolay; Clanton, Sam; Pilewskie, Peter

2002-01-01

The goal of visual inference programming is to develop a software framework data analysis and to provide machine learning algorithms for inter-active data exploration and visualization. The topics include: 1) Intelligent Data Understanding (IDU) framework; 2) Challenge problems; 3) What's new here; 4) Framework features; 5) Wiring diagram; 6) Generated script; 7) Results of script; 8) Initial algorithms; 9) Independent Component Analysis for instrument diagnosis; 10) Output sensory mapping virtual joystick; 11) Output sensory mapping typing; 12) Closed-loop feedback mu-rhythm control; 13) Closed-loop training; 14) Data sources; and 15) Algorithms. This paper is in viewgraph form.

17. Single board system for fuzzy inference

NASA Technical Reports Server (NTRS)

Symon, James R.; Watanabe, Hiroyuki

1991-01-01

The very large scale integration (VLSI) implementation of a fuzzy logic inference mechanism allows the use of rule-based control and decision making in demanding real-time applications. Researchers designed a full custom VLSI inference engine. The chip was fabricated using CMOS technology. The chip consists of 688,000 transistors of which 476,000 are used for RAM memory. The fuzzy logic inference engine board system incorporates the custom designed integrated circuit into a standard VMEbus environment. The Fuzzy Logic system uses Transistor-Transistor Logic (TTL) parts to provide the interface between the Fuzzy chip and a standard, double height VMEbus backplane, allowing the chip to perform application process control through the VMEbus host. High level C language functions hide details of the hardware system interface from the applications level programmer. The first version of the board was installed on a robot at Oak Ridge National Laboratory in January of 1990.

18. Quality of computationally inferred gene ontology annotations.

PubMed

Skunca, Nives; Altenhoff, Adrian; Dessimoz, Christophe

2012-05-01

Gene Ontology (GO) has established itself as the undisputed standard for protein function annotation. Most annotations are inferred electronically, i.e. without individual curator supervision, but they are widely considered unreliable. At the same time, we crucially depend on those automated annotations, as most newly sequenced genomes are non-model organisms. Here, we introduce a methodology to systematically and quantitatively evaluate electronic annotations. By exploiting changes in successive releases of the UniProt Gene Ontology Annotation database, we assessed the quality of electronic annotations in terms of specificity, reliability, and coverage. Overall, we not only found that electronic annotations have significantly improved in recent years, but also that their reliability now rivals that of annotations inferred by curators when they use evidence other than experiments from primary literature. This work provides the means to identify the subset of electronic annotations that can be relied upon-an important outcome given that >98% of all annotations are inferred without direct curation.

19. AESOP: An interactive computer program for the design of linear quadratic regulators and Kalman filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L. C.

1984-01-01

AESOP is a computer program for use in designing feedback controls and state estimators for linear multivariable systems. AESOP is meant to be used in an interactive manner. Each design task that the program performs is assigned a "function" number. The user accesses these functions either (1) by inputting a list of desired function numbers or (2) by inputting a single function number. In the latter case the choice of the function will in general depend on the results obtained by the previously executed function. The most important of the AESOP functions are those that design,linear quadratic regulators and Kalman filters. The user interacts with the program when using these design functions by inputting design weighting parameters and by viewing graphic displays of designed system responses. Supporting functions are provided that obtain system transient and frequency responses, transfer functions, and covariance matrices. The program can also compute open-loop system information such as stability (eigenvalues), eigenvectors, controllability, and observability. The program is written in ANSI-66 FORTRAN for use on an IBM 3033 using TSS 370. Descriptions of all subroutines and results of two test cases are included in the appendixes.

20. Deep Learning for Population Genetic Inference

PubMed Central

Sheehan, Sara; Song, Yun S.

2016-01-01

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme. PMID:27018908

1. Deep Learning for Population Genetic Inference.

PubMed

Sheehan, Sara; Song, Yun S

2016-03-01

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme.

2. Computationally efficient Bayesian inference for inverse problems.

SciTech Connect

Marzouk, Youssef M.; Najm, Habib N.; Rahn, Larry A.

2007-10-01

Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problems - representing indirect estimation of model parameters, inputs, or structural components - can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field. We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties. We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.

3. Vector dark energy models with quadratic terms in the Maxwell tensor derivatives

Haghani, Zahra; Harko, Tiberiu; Sepangi, Hamid Reza; Shahidi, Shahab

2017-03-01

We consider a vector-tensor gravitational model with terms quadratic in the Maxwell tensor derivatives, called the Bopp-Podolsky term. The gravitational field equations of the model and the equations describing the evolution of the vector field are obtained and their Newtonian limit is investigated. The cosmological implications of a Bopp-Podolsky type dark energy term are investigated for a Bianchi type I homogeneous and anisotropic geometry for two models, corresponding to the absence and presence of the self-interacting potential of the field, respectively. The time evolutions of the Hubble function, of the matter energy density, of the shear scalar, of the mean anisotropy parameter, and of the deceleration parameter, respectively, as well as the field potentials are obtained for both cases by numerically integrating the cosmological evolution equations. In the presence of the vector type dark energy with quadratic terms in the Maxwell tensor derivatives, depending on the numerical values of the model parameters, the Bianchi type I Universe experiences a complex dynamical evolution, with the dust Universes ending in an isotropic phase. The presence of the self-interacting potential of the vector field significantly shortens the time interval necessary for the full isotropization of the Universe.

4. Quadratic programming-based approach for autonomous vehicle path planning in space

Chen, Yang; Han, Jianda; Wu, Huaiyu

2012-07-01

Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades. The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one, and also can not solve the inherent constraints arising from the robot body and the exterior environment. To address these difficulties, this research aims to provide a feasible trajectory based on quadratic programming(QP) for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles. First, the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target, as well as the angle between the velocity and the position in the relative velocity coordinates(RVCs). The optimization is in quadratic polynomial form according to QP formulation. Then, the avoidance task is modeled with linear constraints in RVCs. Some other constraints, such as kinematics, dynamics, and sensor range, are included. Last, simulations with typical multiple obstacles are carried out, including in static and dynamic environments and one of human-in-the-loop. The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances. Therefore, the QP model proposed in this paper not only adapts to dynamic environment with uncertainty, but also can satisfy all kinds of constraints, and it provides an efficient approach to solve the problems of path planning in three-dimensional space.

5. Comparing linear and quadratic models of the human auditory system using EEG.

PubMed

Power, Alan J; Reilly, Richard B; Lalor, Edmund C

2011-01-01

Recent studies have highlighted the importance of system identification as an approach for assessing sensory processing in humans using electroencephalography (EEG). These studies typically use linear impulse response estimates of visual and, more recently, auditory function. These methods, which are known as the VESPA and AESPA (Visual/Auditory Evoked Spread Spectrum Analysis) respectively, have been found to be useful for studying sensory processing in both healthy populations and clinical groups and for studying the effects of cognition on sensory processing. While a nonlinear extension of the VESPA has been previously described, no such extension has yet been examined for the AESPA. This paper investigates such an extension and quantifies the relative contribution of linear and quadratic processes to the EEG in response to novel auditory stimuli. While the ability to accurately predict novel EEG is poor, it is highly significant, with a slightly, but again significantly, greater ability to predict using a quadratic model (r=0.0418) over a linear model (r=0.0361).

6. Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

7. Quadratic Zeeman effect and spin-lattice relaxation of Tm3 +:YAG at high magnetic fields

Veissier, Lucile; Thiel, Charles W.; Lutz, Thomas; Barclay, Paul E.; Tittel, Wolfgang; Cone, Rufus L.

2016-11-01

Anisotropy of the quadratic Zeeman effect for the H36→H34 transition at 793 nm wavelength in 3+169Tm-doped Y3Al5O12 is studied, revealing shifts ranging from near zero up to +4.69 GHz/T 2 for ions in magnetically inequivalent sites. This large range of shifts is used to spectrally resolve different subsets of ions and study nuclear spin relaxation as a function of temperature, magnetic field strength, and orientation in a site-selective manner. A rapid decrease in spin lifetime is found at large magnetic fields, revealing the weak contribution of direct phonon absorption and emission to the nuclear spin-lattice relaxation rate. We furthermore confirm theoretical predictions for the phonon coupling strength, finding much smaller values than those estimated in the limited number of past studies of thulium in similar crystals. Finally, we observe a significant—and unexpected—magnetic field dependence of the two-phonon Orbach spin relaxation process at higher field strengths, which we explain through changes in the electronic energy-level splitting arising from the quadratic Zeeman effect.

8. Bioinformatic Analyses of Unique (Orphan) Core Genes of the Genus Acidithiobacillus: Functional Inferences and Use As Molecular Probes for Genomic and Metagenomic/Transcriptomic Interrogation

PubMed Central

González, Carolina; Lazcano, Marcelo; Valdés, Jorge; Holmes, David S.

2016-01-01

Using phylogenomic and gene compositional analyses, five highly conserved gene families have been detected in the core genome of the phylogenetically coherent genus Acidithiobacillus of the class Acidithiobacillia. These core gene families are absent in the closest extant genus Thermithiobacillus tepidarius that subtends the Acidithiobacillus genus and roots the deepest in this class. The predicted proteins encoded by these core gene families are not detected by a BLAST search in the NCBI non-redundant database of more than 90 million proteins using a relaxed cut-off of 1.0e−5. None of the five families has a clear functional prediction. However, bioinformatic scrutiny, using pI prediction, motif/domain searches, cellular location predictions, genomic context analyses, and chromosome topology studies together with previously published transcriptomic and proteomic data, suggests that some may have functions associated with membrane remodeling during cell division perhaps in response to pH stress. Despite the high level of amino acid sequence conservation within each family, there is sufficient nucleotide variation of the respective genes to permit the use of the DNA sequences to distinguish different species of Acidithiobacillus, making them useful additions to the armamentarium of tools for phylogenetic analysis. Since the protein families are unique to the Acidithiobacillus genus, they can also be leveraged as probes to detect the genus in environmental metagenomes and metatranscriptomes, including industrial biomining operations, and acid mine drainage (AMD). PMID:28082953

9. Inferred H⍺ Flux as a Star Formation Rate Indicator at z ~ 4-5: Implications for Dust Properties, Burstiness, and the z = 4-8 Star Formation Rate Functions

Smit, Renske; Bouwens, Rychard J.; Labbé, Ivo; Franx, Marijn; Wilkins, Stephen M.; Oesch, Pascal A.

2016-12-01

We derive Hα fluxes for a large spectroscopic and photometric-redshift-selected sample of sources over GOODS-North and South in the redshift range z = 3.8-5.0 with deep Hubble Space Telescope (HST), Spitzer/IRAC, and ground-based observations. The Hα flux is inferred based on the offset between the IRAC 3.6 μm flux and that predicted from the best-fit spectral energy distribution (SED). We demonstrate that the Hα flux correlates well with dust-corrected UV star formation rate (SFR) and therefore can serve as an independent SFR indicator. However, we also find a systematic offset in the {{SFR}}{{H}α }/{{SFR}}{UV+β } ratios for z ˜ 4-5 galaxies relative to local relations (assuming the same dust corrections for nebular regions and stellar light). We show that we can resolve the modest tension in the inferred SFRs by assuming bluer intrinsic UV slopes (increasing the dust correction), a rising star formation history, or assuming a low-metallicity stellar population with a hard ionizing spectrum (increasing the {L}{{H}α }/{SFR} ratio). Using Hα as an SFR indicator, we find a normalization of the star formation main sequence in good agreement with recent SED-based determinations and also derive the SFR functions at z˜ 4{--}8. In addition, we assess for the first time the burstiness of star formation in z˜ 4 galaxies on <100 Myr timescales by comparing UV and Hα-based sSFRs; their one-to-one relationship argues against significantly bursty star formation histories.

10. Neural network for solving convex quadratic bilevel programming problems.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network.

11. Solving the quadratic assignment problem with clues from nature.

PubMed

Nissen, V

1994-01-01

This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.

12. Rigorous performance bounds for quadratic and nested dynamical decoupling

SciTech Connect

Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.

2011-12-15

We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

13. Restart-Based Genetic Algorithm for the Quadratic Assignment Problem

Misevicius, Alfonsas

The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.

14. Reaction Wheel Control Design Using Linear Quadratic Controller

Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.

2016-01-01

This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.

15. On a quadratic transformation due to Kummer and its generalizations

Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om

2016-05-01

The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.

16. On stability of the Kasner solution in quadratic gravity

Toporensky, A.; Müller, D.

2017-01-01

We consider the dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described—the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter w is bigger, smaller or equals to 1 / 3. Initial conditions for numerical integrations have been chosen near a General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of the coupling constants so that the resulting cosmological singularity is isotropic.

17. Compact stellar models obeying quadratic equation of state

Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj

2016-10-01

In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.

18. Circular inferences in schizophrenia.

PubMed

Jardri, Renaud; Denève, Sophie

2013-11-01

A considerable number of recent experimental and computational studies suggest that subtle impairments of excitatory to inhibitory balance or regulation are involved in many neurological and psychiatric conditions. The current paper aims to relate, specifically and quantitatively, excitatory to inhibitory imbalance with psychotic symptoms in schizophrenia. Considering that the brain constructs hierarchical causal models of the external world, we show that the failure to maintain the excitatory to inhibitory balance results in hallucinations as well as in the formation and subsequent consolidation of delusional beliefs. Indeed, the consequence of excitatory to inhibitory imbalance in a hierarchical neural network is equated to a pathological form of causal inference called 'circular belief propagation'. In circular belief propagation, bottom-up sensory information and top-down predictions are reverberated, i.e. prior beliefs are misinterpreted as sensory observations and vice versa. As a result, these predictions are counted multiple times. Circular inference explains the emergence of erroneous percepts, the patient's overconfidence when facing probabilistic choices, the learning of 'unshakable' causal relationships between unrelated events and a paradoxical immunity to perceptual illusions, which are all known to be associated with schizophrenia.

19. Moment inference from tomograms

USGS Publications Warehouse

Day-Lewis, F. D.; Chen, Y.; Singha, K.

2007-01-01

Time-lapse geophysical tomography can provide valuable qualitative insights into hydrologic transport phenomena associated with aquifer dynamics, tracer experiments, and engineered remediation. Increasingly, tomograms are used to infer the spatial and/or temporal moments of solute plumes; these moments provide quantitative information about transport processes (e.g., advection, dispersion, and rate-limited mass transfer) and controlling parameters (e.g., permeability, dispersivity, and rate coefficients). The reliability of moments calculated from tomograms is, however, poorly understood because classic approaches to image appraisal (e.g., the model resolution matrix) are not directly applicable to moment inference. Here, we present a semi-analytical approach to construct a moment resolution matrix based on (1) the classic model resolution matrix and (2) image reconstruction from orthogonal moments. Numerical results for radar and electrical-resistivity imaging of solute plumes demonstrate that moment values calculated from tomograms depend strongly on plume location within the tomogram, survey geometry, regularization criteria, and measurement error. Copyright 2007 by the American Geophysical Union.

20. Source mechanism of long-period events at Kusatsu-Shirane Volcano, Japan, inferred from waveform inversion of the effective excitation functions

USGS Publications Warehouse

Nakano, M.; Kumagai, H.; Chouet, B.A.

2003-01-01

We investigate the source mechanism of long-period (LP) events observed at Kusatsu-Shirane Volcano, Japan, based on waveform inversions of their effective excitation functions. The effective excitation function, which represents the apparent excitation observed at individual receivers, is estimated by applying an autoregressive filter to the LP waveform. Assuming a point source, we apply this method to seven LP events the waveforms of which are characterized by simple decaying and nearly monochromatic oscillations with frequency in the range 1-3 Hz. The results of the waveform inversions show dominant volumetric change components accompanied by single force components, common to all the events analyzed, and suggesting a repeated activation of a sub-horizontal crack located 300 m beneath the summit crater lakes. Based on these results, we propose a model of the source process of LP seismicity, in which a gradual buildup of steam pressure in a hydrothermal crack in response to magmatic heat causes repeated discharges of steam from the crack. The rapid discharge of fluid causes the collapse of the fluid-filled crack and excites acoustic oscillations of the crack, which produce the characteristic waveforms observed in the LP events. The presence of a single force synchronous with the collapse of the crack is interpreted as the release of gravitational energy that occurs as the slug of steam ejected from the crack ascends toward the surface and is replaced by cooler water flowing downward in a fluid-filled conduit linking the crack and the base of the crater lake. ?? 2003 Elsevier Science B.V. All rights reserved.

1. Optimizing Non-Decomposable Loss Functions in Structured Prediction

PubMed Central

Ranjbar, Mani; Lan, Tian; Wang, Yang; Robinovitch, Steven N.; Li, Ze-Nian; Mori, Greg

2012-01-01

We develop an algorithm for structured prediction with non-decomposable performance measures. The algorithm learns parameters of Markov random fields and can be applied to multivariate performance measures. Examples include performance measures such as Fβ score (natural language processing), intersection over union (object category segmentation), Precision/Recall at k (search engines) and ROC area (binary classifiers). We attack this optimization problem by approximating the loss function with a piecewise linear function. The loss augmented inference forms a quadratic program (QP), which we solve using LP relaxation. We apply this approach to two tasks: object class-specific segmentation and human action retrieval from videos. We show significant improvement over baseline approaches that either use simple loss functions or simple scoring functions on the PASCAL VOC and H3D Segmentation datasets, and a nursing home action recognition dataset. PMID:22868650

2. Modeling and performance analysis of the fractional order quadratic Boost converter in discontinuous conduction mode-discontinuous conduction mode

Tan, Cheng; Liang, Zhi-Shan

2016-03-01

In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM-DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM-DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.

3. Lie algebraic approach of a charged particle in presence of a constant magnetic field via the quadratic invariant

SciTech Connect

Abdalla, M. Sebawe; Elkasapy, A.I.

2010-08-15

In this paper we consider the problem of a charged harmonic oscillator under the influence of a constant magnetic field. The system is assumed to be isotropic and the magnetic field is applied along the z-axis. The canonical transformation is invoked to remove the interaction term and the system is reduced to a model containing the second harmonic generation. Two classes of the real and complex quadratic invariants (constants of motion) are obtained. We have employed the Lie algebraic technique to find the most general solution for the wave function for both real and complex invariants. Some discussions related to the advantage of using the quadratic invariants to solve the Cauchy problem instead of the direct use of the Hamiltonian itself are also given.

4. Crustal structure and configuration of the subducting Philippine Sea plate beneath the Pacific coast industrial zone in Japan inferred from receiver function analysis

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

2012-12-01

We apply receiver function (RF) analyses to estimate the crustal structure and configuration of the subducting Philippine Sea (PHS) plate beneath the Pacific coast industrial zone stretching from Tokyo to Fukuoka in Japan. Destructive earthquakes often occurred at the plate interface of the PHS plate, and seismic activities increase after the 2011 Tohoku earthquake (Mw9.0) around the Tokyo metropolitan area. Investigation on the crustal structure is the key to understanding the stress concentration and strain accumulation process, and information on configuration of the subducting plate is important to mitigate future earthquake disasters. In this study, we searched for the best-correlated velocity structure model between an observed receiver function at each station and synthetic ones by using a grid search method. Synthetic RFs were calculated from many assumed one-dimensional velocity structures that consist of four layers with positive velocity steps. Observed receiver functions were stacked without considering back azimuth or epicentral distance. 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. Telemetric seismographic network data covered on the Japanese Islands including the Metropolitan Seismic Observation network, which constructed under the Special Project for Earthquake Disaster Mitigation in the Tokyo Metropolitan area and maintained by Special Project for Reducing Vulnerability for Urban Mega Earthquake Disasters, are used. We selected events with magnitudes greater or equal to 5.0 and epicentral distance between 30 and 90 degrees based on USGS catalogues. As a result, we clarify spatial distributions of the crustal S-wave velocities. Estimated average one-dimensional S-wave velocity structure is approximately equal to the JMA2011 structural model although the velocity from the ground surface to 5 km in depth is slow. In particular

5. Estimating uncertainty of inference for validation

SciTech Connect

Booker, Jane M; Langenbrunner, James R; Hemez, Francois M; Ross, Timothy J

2010-09-30

We present a validation process based upon the concept that validation is an inference-making activity. This has always been true, but the association has not been as important before as it is now. Previously, theory had been confirmed by more data, and predictions were possible based on data. The process today is to infer from theory to code and from code to prediction, making the role of prediction somewhat automatic, and a machine function. Validation is defined as determining the degree to which a model and code is an accurate representation of experimental test data. Imbedded in validation is the intention to use the computer code to predict. To predict is to accept the conclusion that an observable final state will manifest; therefore, prediction is an inference whose goodness relies on the validity of the code. Quantifying the uncertainty of a prediction amounts to quantifying the uncertainty of validation, and this involves the characterization of uncertainties inherent in theory/models/codes and the corresponding data. An introduction to inference making and its associated uncertainty is provided as a foundation for the validation problem. A mathematical construction for estimating the uncertainty in the validation inference is then presented, including a possibility distribution constructed to represent the inference uncertainty for validation under uncertainty. The estimation of inference uncertainty for validation is illustrated using data and calculations from Inertial Confinement Fusion (ICF). The ICF measurements of neutron yield and ion temperature were obtained for direct-drive inertial fusion capsules at the Omega laser facility. The glass capsules, containing the fusion gas, were systematically selected with the intent of establishing a reproducible baseline of high-yield 10{sup 13}-10{sup 14} neutron output. The deuterium-tritium ratio in these experiments was varied to study its influence upon yield. This paper on validation inference is the

6. The Abundances of Hydrocarbon Functional Groups in the Interstellar Medium Inferred from Laboratory Spectra of Hydrogenated and Methylated Polycyclic Aromatic Hydrocarbons

Steglich, M.; Jäger, C.; Huisken, F.; Friedrich, M.; Plass, W.; Räder, H.-J.; Müllen, K.; Henning, Th.

2013-10-01

Infrared (IR) absorption spectra of individual polycyclic aromatic hydrocarbons (PAHs) containing methyl (\\sbondCH3), methylene (\\protect{\\epsfbox{art/apjs484229un01.eps}}CH2), or diamond-like \\protect{\\epsfbox{art/apjs484229un02.eps}}CH groups and IR spectra of mixtures of methylated and hydrogenated PAHs prepared by gas-phase condensation were measured at room temperature (as grains in pellets) and at low temperature (isolated in Ne matrices). In addition, the PAH blends were subjected to an in-depth molecular structure analysis by means of high-performance liquid chromatography, nuclear magnetic resonance spectroscopy, and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. Supported by calculations at the density functional theory level, the laboratory results were applied to analyze in detail the aliphatic absorption complex of the diffuse interstellar medium at 3.4 μm and to determine the abundances of hydrocarbon functional groups. Assuming that the PAHs are mainly locked in grains, aliphatic CH x groups (x = 1, 2, 3) would contribute approximately in equal quantities to the 3.4 μm feature (N CHx /N H ≈ 10-5-2 × 10-5). The abundances, however, may be two to four times lower if a major contribution to the 3.4 μm feature comes from molecules in the gas phase. Aromatic \\epsfbox{art/apjs484229un03.eps} CH groups seem to be almost absent from some lines of sight, but can be nearly as abundant as each of the aliphatic components in other directions (N_{\\epsfbox{art/apjs484229un03.eps} CH}/N H lsim 2 × 10-5 upper value for grains). Due to comparatively low binding energies, astronomical IR emission sources do not display such heavy excess hydrogenation. At best, especially in protoplanetary nebulae, \\protect{\\epsfbox{art/apjs484229un01.eps}}CH2 groups bound to aromatic molecules, i.e., excess hydrogens on the molecular periphery only, can survive the presence of a nearby star.

7. Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System

Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. Hernández

Alternate quadratic systems A : xn+1 = 1 - axn2,if n is even 1 - a∗xn2,if n is odd andB : xn+1 = 1 - a∗xn2,if n is even 1 - axn2, if n is odd, where a and a∗ are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (“hidden” because it is not visible at normal resolution and “nonstandard” because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.

8. An Instability Index Theory for Quadratic Pencils and Applications

Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

2014-04-01

Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

9. Electric current quadratic in an applied electric field

Deyo, Eric

The theory of the photogalvanic effect in a low frequency electric field is developed. We complete the semiclassical theory of the effect in bulk samples lacking inversion symmetry, taking into account contributions from the asymmetry of scattering, the shift current, and the effect of Berry's phase. We consider the effect in such samples both in the presence and absence of a constant magnetic field. It is found that by experimentally measuring this effect, that Berry's curvature and the average shift of the center of mass of an electron during a scattering event can be extracted. We also investigate the magnetic field dependence of the part of the electrical current which is quadratic in voltage in mesoscopic conductors. We find that the part of the current which is quadratic in bias voltage, and linear in an applied magnetic field can be related to the effective electron-electron interaction strength. We also find that in the case when the magnetic field is oriented parallel to the plane of a two dimensional sample, that the spin-orbit scattering rate can be measured.

10. Identify five kinds of simple super-secondary structures with quadratic discriminant algorithm based on the chemical shifts.

PubMed

Kou, Gaoshan; Feng, Yonge

2015-09-07

The biological function of protein is largely determined by its spatial structure. The research on the relationship between structure and function is the basis of protein structure prediction. However, the prediction of super secondary structure is an important step in the prediction of protein spatial structure. Many algorithms have been proposed for the prediction of protein super secondary structure. However, the parameters used by these methods were primarily based on amino acid sequences. In this paper, we proposed a novel model for predicting five kinds of protein super secondary structures based on the chemical shifts (CSs). Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in five kinds of protein super secondary structures by using the analysis of variance (ANOVA). Secondly, we used chemical shifts of six nuclei as features, and combined with quadratic discriminant analysis (QDA) to predict five kinds of protein super secondary structures. Finally, we achieved the averaged sensitivity, specificity and the overall accuracy of 81.8%, 95.19%, 82.91%, respectively in seven-fold cross-validation. Moreover, we have performed the prediction by combining the five different chemical shifts as features, the maximum overall accuracy up to 89.87% by using the C,Cα,Cβ,N,Hα of Hα chemical shifts, which are clearly superior to that of the quadratic discriminant analysis (QDA) algorithm by using 20 amino acid compositions (AAC) as feature in the seven-fold cross-validation. These results demonstrated that chemical shifts (CSs) are indeed an outstanding parameter for the prediction of five kinds of super secondary structures. In addition, we compared the prediction of the quadratic discriminant analysis (QDA) with that of support vector machine (SVM) by using the same six CSs as features. The result suggested that the quadratic discriminant analysis method by using chemical shifts as features is a good predictor for protein super

11. On the necessity of dissecting sequence similarity scores into segment-specific contributions for inferring protein homology, function prediction and annotation

PubMed Central

2014-01-01

Background Protein sequence similarities to any types of non-globular segments (coiled coils, low complexity regions, transmembrane regions, long loops, etc. where either positional sequence conservation is the result of a very simple, physically induced pattern or rather integral sequence properties are critical) are pertinent sources for mistaken homologies. Regretfully, these considerations regularly escape attention in large-scale annotation studies since, often, there is no substitute to manual handling of these cases. Quantitative criteria are required to suppress events of function annotation transfer as a result of false homology assignments. Results The sequence homology concept is based on the similarity comparison between the structural elements, the basic building blocks for conferring the overall fold of a protein. We propose to dissect the total similarity score into fold-critical and other, remaining contributions and suggest that, for a valid homology statement, the fold-relevant score contribution should at least be significant on its own. As part of the article, we provide the DissectHMMER software program for dissecting HMMER2/3 scores into segment-specific contributions. We show that DissectHMMER reproduces HMMER2/3 scores with sufficient accuracy and that it is useful in automated decisions about homology for instructive sequence examples. To generalize the dissection concept for cases without 3D structural information, we find that a dissection based on alignment quality is an appropriate surrogate. The approach was applied to a large-scale study of SMART and PFAM domains in the space of seed sequences and in the space of UniProt/SwissProt. Conclusions Sequence similarity core dissection with regard to fold-critical and other contributions systematically suppresses false hits and, additionally, recovers previously obscured homology relationships such as the one between aquaporins and formate/nitrite transporters that, so far, was only

12. A preliminary investigation into the morphology of oral papillae and denticles of blue sharks (Prionace glauca) with inferences about its functional significance across life stages.

PubMed

Rangel, Bianca de S; Wosnick, Natascha; Hammerschlag, Neil; Ciena, Adriano P; Kfoury Junior, José Roberto; Rici, Rose E G

2017-03-01

Sensory organs in elasmobranchs (sharks, skates, rays) detect and respond to a different set of biotic and/or abiotic stimuli, through sight, smell, taste, hearing, mechanoreception and electroreception. Although gustation is crucial for survival and essential for growth, mobility, and maintenance of neural activity and the proper functioning of the immune system, comparatively little is known about this sensory system in elasmobranchs. Here we present a preliminary investigation into the structural and dimensional characteristics of the oral papillae and denticles found in the oropharyngeal cavity of the blue shark (Prionace glauca) during embryonic development through adulthood. Samples were obtained from the dorsal and ventral surface of the oropharyngeal cavity collected from embryos at different development stages as well as from adults. Our results suggest that development of papillae occurs early in ontogeny, before the formation of the oral denticles. The diameter of oral papillae gradually increases during development, starting from 25 μm in stage I embryos, to 110 μm in stage IV embryos and 272-300 μm in adults. Embryos exhibit papillae at early developmental stages, suggesting that these structures may be important during early in life. The highest density of papillae was observed in the maxillary and mandibular valve regions, possibly related to the ability to identify, capture and process prey. The oral denticles were observed only in the final embryonic stage as well as in adults. Accordingly, we suggest that oral denticles likely aid in ram ventilation (through reducing the hydrodynamic drag), to protect papillae from injury during prey consumption and assist in the retention and consumption of prey (through adhesion), since these processes are only necessary after birth.

13. On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane. [central processing units

NASA Technical Reports Server (NTRS)

Cooper, D. B.; Yalabik, N.

1975-01-01

Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.

14. BIE: Bayesian Inference Engine

Weinberg, Martin D.

2013-12-01

The Bayesian Inference Engine (BIE) is an object-oriented library of tools written in C++ designed explicitly to enable Bayesian update and model comparison for astronomical problems. To facilitate "what if" exploration, BIE provides a command line interface (written with Bison and Flex) to run input scripts. The output of the code is a simulation of the Bayesian posterior distribution from which summary statistics e.g. by taking moments, or determine confidence intervals and so forth, can be determined. All of these quantities are fundamentally integrals and the Markov Chain approach produces variates heta distributed according to P( heta|D) so moments are trivially obtained by summing of the ensemble of variates.

15. Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

16. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

Neumeyer, S.; Sorokin, V. S.; Thomsen, J. J.

2017-01-01

We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing-Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude-phase characteristics are predicted, supporting previously reported experimental observations.

17. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

18. A formal model of interpersonal inference

PubMed Central

Moutoussis, Michael; Trujillo-Barreto, Nelson J.; El-Deredy, Wael; Dolan, Raymond J.; Friston, Karl J.

2014-01-01

Introduction: We propose that active Bayesian inference—a general framework for decision-making—can equally be applied to interpersonal exchanges. Social cognition, however, entails special challenges. We address these challenges through a novel formulation of a formal model and demonstrate its psychological significance. Method: We review relevant literature, especially with regards to interpersonal representations, formulate a mathematical model and present a simulation study. The model accommodates normative models from utility theory and places them within the broader setting of Bayesian inference. Crucially, we endow people's prior beliefs, into which utilities are absorbed, with preferences of self and others. The simulation illustrates the model's dynamics and furnishes elementary predictions of the theory. Results: (1) Because beliefs about self and others inform both the desirability and plausibility of outcomes, in this framework interpersonal representations become beliefs that have to be actively inferred. This inference, akin to “mentalizing” in the psychological literature, is based upon the outcomes of interpersonal exchanges. (2) We show how some well-known social-psychological phenomena (e.g., self-serving biases) can be explained in terms of active interpersonal inference. (3) Mentalizing naturally entails Bayesian updating of how people value social outcomes. Crucially this includes inference about one's own qualities and preferences. Conclusion: We inaugurate a Bayes optimal framework for modeling intersubject variability in mentalizing during interpersonal exchanges. Here, interpersonal representations are endowed with explicit functional and affective properties. We suggest the active inference framework lends itself to the study of psychiatric conditions where mentalizing is distorted. PMID:24723872

19. Causal Inference and Explaining Away in a Spiking Network

PubMed Central

Moreno-Bote, Rubén; Drugowitsch, Jan

2015-01-01

While the brain uses spiking neurons for communication, theoretical research on brain computations has mostly focused on non-spiking networks. The nature of spike-based algorithms that achieve complex computations, such as object probabilistic inference, is largely unknown. Here we demonstrate that a family of high-dimensional quadratic optimization problems with non-negativity constraints can be solved exactly and efficiently by a network of spiking neurons. The network naturally imposes the non-negativity of causal contributions that is fundamental to causal inference, and uses simple operations, such as linear synapses with realistic time constants, and neural spike generation and reset non-linearities. The network infers the set of most likely causes from an observation using explaining away, which is dynamically implemented by spike-based, tuned inhibition. The algorithm performs remarkably well even when the network intrinsically generates variable spike trains, the timing of spikes is scrambled by external sources of noise, or the network is mistuned. This type of network might underlie tasks such as odor identification and classification. PMID:26621426

20. Bayes factors and multimodel inference

USGS Publications Warehouse

Link, W.A.; Barker, R.J.; Thomson, David L.; Cooch, Evan G.; Conroy, Michael J.

2009-01-01

Multimodel inference has two main themes: model selection, and model averaging. Model averaging is a means of making inference conditional on a model set, rather than on a selected model, allowing formal recognition of the uncertainty associated with model choice. The Bayesian paradigm provides a natural framework for model averaging, and provides a context for evaluation of the commonly used AIC weights. We review Bayesian multimodel inference, noting the importance of Bayes factors. Noting the sensitivity of Bayes factors to the choice of priors on parameters, we define and propose nonpreferential priors as offering a reasonable standard for objective multimodel inference.

1. Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

2. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1988-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

3. Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

NASA Technical Reports Server (NTRS)

Milman, Mark H.

1987-01-01

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

4. SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Choi, J. R.; Nahm, I. H.

2007-01-01

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola-Kanai oscillator. The probability density of these coherent states for the Caldirola-Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed.

5. Singular linear-quadratic control problem for systems with linear delay

SciTech Connect

Sesekin, A. N.

2013-12-18

A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.

6. Automated detection of the choroid boundary within OCT image data using quadratic measure filters

Wagner, Marcus; Scheibe, Patrick; Francke, Mike; Zimmerling, Beatrice; Frey, Katharina; Vogel, Mandy; Luckhaus, Stephan; Wiedemann, Peter; Kiess, Wieland; Rauscher, Franziska G.

2017-02-01

A novel method for the automated detection of the outer choroid boundary within spectral-domain optical coherence tomography image data, based on an image model within the space of functions of bounded variation and the application of quadratic measure filters, is presented. The same method is used for the segmentation of retinal layer boundaries and proves to be suitable even for data generated without special imaging modes and moderate line averaging. Based on the segmentations, an automated determination of the central fovea region and choroidal thickness measurements for this and two adjacent 1-mm regions are provided. The quality of the method is assessed by comparison with manual delineations performed by five trained graders. The study is based on data from 50 children of the ages 8 to 13 that were obtained in the framework of the LIFE Child study at Leipzig University.

7. Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

NASA Technical Reports Server (NTRS)

Natarajan, R.; Brown, R. A.

1986-01-01

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

8. Regions of attraction and ultimate boundedness for linear quadratic regulators with nonlinearities

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

The closed-loop stability of multivariable linear time-invariant systems controlled by optimal linear quadratic (LQ) regulators is investigated for the case when the feedback loops have nonlinearities N(sigma) that violate the standard stability condition, sigma N(sigma) or = 0.5 sigma(2). The violations of the condition are assumed to occur either (1) for values of sigma away from the origin (sigma = 0) or (2) for values of sigma in a neighborhood of the origin. It is proved that there exists a region of attraction for case (1) and a region of ultimate boundedness for case (2), and estimates are obtained for these regions. The results provide methods for selecting the performance function parameters to design LQ regulators with better tolerance to nonlinearities. The results are demonstrated by application to the problem of attitude and vibration control of a large, flexible space antenna in the presence of actuator nonlinearities.

9. Estimation of regions of attraction and ultimate boundedness for multiloop LQ regulators. [Linear Quadratic

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1984-01-01

Closed-loop stability is investigated for multivariable linear time-invariant systems controlled by optimal full state feedback linear quadratic (LQ) regulators, with nonlinear gains present in the feedback channels. Estimates are obtained for the region of attraction when the nonlinearities escape the (0.5, infinity) sector in regions away from the origin and for the region of ultimate boundedness when the nonlinearities escape the sector near the origin. The expressions for these regions also provide methods for selecting the performance function parameters in order to obtain LQ designs with better tolerance for nonlinearities. The analytical results are illustrated by applying them to the problem of controlling the rigid-body pitch angle and elastic motion of a large, flexible space antenna.

10. Schwarz and multilevel methods for quadratic spline collocation

SciTech Connect

Christara, C.C.; Smith, B.

1994-12-31

Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

11. Longitudinal force distribution using quadratically constrained linear programming

Klomp, M.

2011-12-01

In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle-driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.

12. A quadratic-shaped-finger comb parametric resonator

Guo, Congzhong; Fedder, Gary K.

2013-09-01

A large-stroke (8 µm) parametric resonator excited by an in-plane ‘shaped-finger’ electrostatic comb drive is fabricated using a 15 µm thick silicon-on-insulator microelectromechanical systems (SOI-MEMS) process. A quadratic capacitance-engagement response is synthesized by engineering a custom-shaped comb finger profile. A folded-flexure suspension allows lateral motion while constraining rotational modes. The excitation of the nonlinear parametric resonance is realized by selecting an appropriate combination of the linear and cubic electrostatic stiffness coefficients through a specific varying-gap comb-finger design. The large-amplitude parametric resonance promotes high signal-to-noise ratio for potential use in sensitive chemical gravimetric sensors, strain gauges, and mode-matched gyroscope applications.

13. Consultant-Guided Search Algorithms for the Quadratic Assignment Problem

Iordache, Serban

Consultant-Guided Search (CGS) is a recent swarm intelligence metaheuristic for combinatorial optimization problems, inspired by the way real people make decisions based on advice received from consultants. Until now, CGS has been successfully applied to the Traveling Salesman Problem. Because a good metaheuristic should be able to tackle efficiently a large variety of problems, it is important to see how CGS behaves when applied to other classes of problems. In this paper, we propose an algorithm for the Quadratic Assignment Problem (QAP), which hybridizes CGS with a local search procedure. Our experimental results show that CGS is able to compete in terms of solution quality with one of the best Ant Colony Optimization algorithms, the MAX-MIN Ant System.

14. Absence of the Gribov ambiguity in a quadratic gauge

Raval, Haresh

2016-05-01

The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold {S}^3, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.

15. Repopulation Kinetics and the Linear-Quadratic Model

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

2009-08-01

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

16. Wind turbine power tracking using an improved multimodel quadratic approach.

PubMed

2010-07-01

In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables.

17. Cosmology for quadratic gravity in generalized Weyl geometry

SciTech Connect

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

2016-04-26

A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.

18. Qualitative analysis of certain generalized classes of quadratic oscillator systems

SciTech Connect

Bagchi, Bijan Ghosh, Samiran Pal, Barnali Poria, Swarup

2016-02-15

We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.

Delyon, François; Foulon, Patrick

1987-11-01

We consider the adiabatic problem for general time-dependent quadratic Hamiltonians and develop a method quite different from WKB. In particular, we apply our results to the Schrödinger equation in a strip. We show that there exists a first regular step (avoiding resonance problems) providing one adiabatic invariant, bounds on the Liapunov exponents, and estimates on the rotation number at any order of the perturbation theory. The further step is shown to be equivalent to a quantum adiabatic problem, which, by the usual adiabatic techniques, provides the other possible adiabatic invariants. In the special case of the Schrödinger equation our method is simpler and more powerful than the WKB techniques.

20. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

SciTech Connect

Golubkov, A A; Makarov, Vladimir A

2011-11-30

We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

1. Nonparametric inference procedures for multistate life table analysis.

PubMed

Dow, M M

1985-01-01

Recent generalizations of the classical single state life table procedures to the multistate case provide the means to analyze simultaneously the mobility and mortality experience of 1 or more cohorts. This paper examines fairly general nonparametric combinatorial matrix procedures, known as quadratic assignment, as an analysis technic of various transitional patterns commonly generated by cohorts over the life cycle course. To some degree, the output from a multistate life table analysis suggests inference procedures. In his discussion of multstate life table construction features, the author focuses on the matrix formulation of the problem. He then presents several examples of the proposed nonparametric procedures. Data for the mobility and life expectancies at birth matrices come from the 458 member Cayo Santiago rhesus monkey colony. The author's matrix combinatorial approach to hypotheses testing may prove to be a useful inferential strategy in several multidimensional demographic areas.

2. Improving Inferences from Multiple Methods.

ERIC Educational Resources Information Center

Shotland, R. Lance; Mark, Melvin M.

1987-01-01

Multiple evaluation methods (MEMs) can cause an inferential challenge, although there are strategies to strengthen inferences. Practical and theoretical issues involved in the use by social scientists of MEMs, three potential problems in drawing inferences from MEMs, and short- and long-term strategies for alleviating these problems are outlined.…

3. Causal Inference and Developmental Psychology

ERIC Educational Resources Information Center

Foster, E. Michael

2010-01-01

Causal inference is of central importance to developmental psychology. Many key questions in the field revolve around improving the lives of children and their families. These include identifying risk factors that if manipulated in some way would foster child development. Such a task inherently involves causal inference: One wants to know whether…

4. Causal Inference in Retrospective Studies.

ERIC Educational Resources Information Center

Holland, Paul W.; Rubin, Donald B.

1988-01-01

The problem of drawing causal inferences from retrospective case-controlled studies is considered. A model for causal inference in prospective studies is applied to retrospective studies. Limitations of case-controlled studies are formulated concerning relevant parameters that can be estimated in such studies. A coffee-drinking/myocardial…

5. Spectral likelihood expansions for Bayesian inference

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

6. HIERARCHICAL PROBABILISTIC INFERENCE OF COSMIC SHEAR

SciTech Connect

Schneider, Michael D.; Dawson, William A.; Hogg, David W.; Marshall, Philip J.; Bard, Deborah J.; Meyers, Joshua; Lang, Dustin

2015-07-01

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to gravitational lensing inference that has the potential to mitigate the biased inferences in most common point estimators and is practical for upcoming lensing surveys. The first part of our statistical framework requires specification of a likelihood function for the pixel data in an imaging survey given parameterized models for the galaxies in the images. We derive the lensing shear posterior by marginalizing over all intrinsic galaxy properties that contribute to the pixel data (i.e., not limited to galaxy ellipticities) and learn the distributions for the intrinsic galaxy properties via hierarchical inference with a suitably flexible conditional probabilitiy distribution specification. We use importance sampling to separate the modeling of small imaging areas from the global shear inference, thereby rendering our algorithm computationally tractable for large surveys. With simple numerical examples we demonstrate the improvements in accuracy from our importance sampling approach, as well as the significance of the conditional distribution specification for the intrinsic galaxy properties when the data are generated from an unknown number of distinct galaxy populations with different morphological characteristics.

7. Active interoceptive inference and the emotional brain

PubMed Central

Friston, Karl J.

2016-01-01

We review a recent shift in conceptions of interoception and its relationship to hierarchical inference in the brain. The notion of interoceptive inference means that bodily states are regulated by autonomic reflexes that are enslaved by descending predictions from deep generative models of our internal and external milieu. This re-conceptualization illuminates several issues in cognitive and clinical neuroscience with implications for experiences of selfhood and emotion. We first contextualize interoception in terms of active (Bayesian) inference in the brain, highlighting its enactivist (embodied) aspects. We then consider the key role of uncertainty or precision and how this might translate into neuromodulation. We next examine the implications for understanding the functional anatomy of the emotional brain, surveying recent observations on agranular cortex. Finally, we turn to theoretical issues, namely, the role of interoception in shaping a sense of embodied self and feelings. We will draw links between physiological homoeostasis and allostasis, early cybernetic ideas of predictive control and hierarchical generative models in predictive processing. The explanatory scope of interoceptive inference ranges from explanations for autism and depression, through to consciousness. We offer a brief survey of these exciting developments. This article is part of the themed issue ‘Interoception beyond homeostasis: affect, cognition and mental health’. PMID:28080966

8. Social Inference Through Technology

Oulasvirta, Antti

Awareness cues are computer-mediated, real-time indicators of people’s undertakings, whereabouts, and intentions. Already in the mid-1970 s, UNIX users could use commands such as “finger” and “talk” to find out who was online and to chat. The small icons in instant messaging (IM) applications that indicate coconversants’ presence in the discussion space are the successors of “finger” output. Similar indicators can be found in online communities, media-sharing services, Internet relay chat (IRC), and location-based messaging applications. But presence and availability indicators are only the tip of the iceberg. Technological progress has enabled richer, more accurate, and more intimate indicators. For example, there are mobile services that allow friends to query and follow each other’s locations. Remote monitoring systems developed for health care allow relatives and doctors to assess the wellbeing of homebound patients (see, e.g., Tang and Venables 2000). But users also utilize cues that have not been deliberately designed for this purpose. For example, online gamers pay attention to other characters’ behavior to infer what the other players are like “in real life.” There is a common denominator underlying these examples: shared activities rely on the technology’s representation of the remote person. The other human being is not physically present but present only through a narrow technological channel.

9. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-11-01

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

10. Human Inferences about Sequences: A Minimal Transition Probability Model

PubMed Central

2016-01-01

The brain constantly infers the causes of the inputs it receives and uses these inferences to generate statistical expectations about future observations. Experimental evidence for these expectations and their violations include explicit reports, sequential effects on reaction times, and mismatch or surprise signals recorded in electrophysiology and functional MRI. Here, we explore the hypothesis that the brain acts as a near-optimal inference device that constantly attempts to infer the time-varying matrix of transition probabilities between the stimuli it receives, even when those stimuli are in fact fully unpredictable. This parsimonious Bayesian model, with a single free parameter, accounts for a broad range of findings on surprise signals, sequential effects and the perception of randomness. Notably, it explains the pervasive asymmetry between repetitions and alternations encountered in those studies. Our analysis suggests that a neural machinery for inferring transition probabilities lies at the core of human sequence knowledge. PMID:28030543

11. Exploration of Quadratic Expressions through Multiple Representations for Students with Mathematics Difficulties

ERIC Educational Resources Information Center

Strickland, Tricia K.; Maccini, Paula

2013-01-01

The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…

12. Active Inference: A Process Theory.

PubMed

Friston, Karl; FitzGerald, Thomas; Rigoli, Francesco; Schwartenbeck, Philipp; Pezzulo, Giovanni

2017-01-01

This article describes a process theory based on active inference and belief propagation. Starting from the premise that all neuronal processing (and action selection) can be explained by maximizing Bayesian model evidence-or minimizing variational free energy-we ask whether neuronal responses can be described as a gradient descent on variational free energy. Using a standard (Markov decision process) generative model, we derive the neuronal dynamics implicit in this description and reproduce a remarkable range of well-characterized neuronal phenomena. These include repetition suppression, mismatch negativity, violation responses, place-cell activity, phase precession, theta sequences, theta-gamma coupling, evidence accumulation, race-to-bound dynamics, and transfer of dopamine responses. Furthermore, the (approximately Bayes' optimal) behavior prescribed by these dynamics has a degree of face validity, providing a formal explanation for reward seeking, context learning, and epistemic foraging. Technically, the fact that a gradient descent appears to be a valid description of neuronal activity means that variational free energy is a Lyapunov function for neuronal dynamics, which therefore conform to Hamilton's principle of least action.

13. Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach.

PubMed

Zhang, Xian-Ming; Han, Qing-Long

2014-06-01

This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.

14. Optimal piecewise linear schedules for LSGP- and LPGS-decomposed array processors via quadratic programming

Zimmermann, Karl-Heinz; Achtziger, Wolfgang

2001-09-01

The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.

15. Parameter Inference for Biochemical Systems that Undergo a Hopf Bifurcation

PubMed Central

Kirk, Paul D. W.; Toni, Tina; Stumpf, Michael P. H.

2008-01-01

The increasingly widespread use of parametric mathematical models to describe biological systems means that the ability to infer model parameters is of great importance. In this study, we consider parameter inferability in nonlinear ordinary differential equation models that undergo a bifurcation, focusing on a simple but generic biochemical reaction model. We systematically investigate the shape of the likelihood function for the model's parameters, analyzing the changes that occur as the model undergoes a Hopf bifurcation. We demonstrate that there exists an intrinsic link between inference and the parameters' impact on the modeled system's dynamical stability, which we hope will motivate further research in this area. PMID:18456830

16. Bayesian Inference of Galaxy Morphology

Yoon, Ilsang; Weinberg, M.; Katz, N.

2011-01-01

Reliable inference on galaxy morphology from quantitative analysis of ensemble galaxy images is challenging but essential ingredient in studying galaxy formation and evolution, utilizing current and forthcoming large scale surveys. To put galaxy image decomposition problem in broader context of statistical inference problem and derive a rigorous statistical confidence levels of the inference, I developed a novel galaxy image decomposition tool, GALPHAT (GALaxy PHotometric ATtributes) that exploits recent developments in Bayesian computation to provide full posterior probability distributions and reliable confidence intervals for all parameters. I will highlight the significant improvements in galaxy image decomposition using GALPHAT, over the conventional model fitting algorithms and introduce the GALPHAT potential to infer the statistical distribution of galaxy morphological structures, using ensemble posteriors of galaxy morphological parameters from the entire galaxy population that one studies.

17. The empirical accuracy of uncertain inference models

NASA Technical Reports Server (NTRS)

Vaughan, David S.; Yadrick, Robert M.; Perrin, Bruce M.; Wise, Ben P.

1987-01-01

Uncertainty is a pervasive feature of the domains in which expert systems are designed to function. Research design to test uncertain inference methods for accuracy and robustness, in accordance with standard engineering practice is reviewed. Several studies were conducted to assess how well various methods perform on problems constructed so that correct answers are known, and to find out what underlying features of a problem cause strong or weak performance. For each method studied, situations were identified in which performance deteriorates dramatically. Over a broad range of problems, some well known methods do only about as well as a simple linear regression model, and often much worse than a simple independence probability model. The results indicate that some commercially available expert system shells should be used with caution, because the uncertain inference models that they implement can yield rather inaccurate results.

18. Investigation on probing quadratic electro-optic coefficient of tantalum potassium niobate crystal based on Fourier transform

Gao, Ch. Y.; Yu, H. T.; Wen, J.; Zhao, M.; Shang, J. J.; Li, X. L.

2016-02-01

A method for probing quadratic electro-optic(QEO) coefficient of tantalum potassium niobate crystal based on Fourier transform was proposed. We acquired all the independent component of QEO coefficient tensor of crystal, they are h11 = 1.56 ×10-14m2 /V2 , h12 = 1.24 ×10-14m2 /V2 and h44 = 0.160 ×10-14m2 /V2 respectively. With the help of the computer digital image processing technology, this method should have further application prospect in the areas of optical properties parameters measuring to the optical functional materials.

19. Statistical Inference in Graphical Models

DTIC Science & Technology

2008-06-17

Probabilistic Network Library ( PNL ). While not fully mature, PNL does provide the most commonly-used algorithms for inference and learning with the efficiency...of C++, and also offers interfaces for calling the library from MATLAB and R 1361. Notably, both BNT and PNL provide learning and inference algorithms...mature and has been used for research purposes for several years, it is written in MATLAB and thus is not suitable to be used in real-time settings. PNL

20. Statistical Inference: The Big Picture.

PubMed

Kass, Robert E

2011-02-01

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labelled here statistical pragmatism, serves as a foundation for inference. Statistical pragmatism is inclusive and emphasizes the assumptions that connect statistical models with observed data. I argue that introductory courses often mis-characterize the process of statistical inference and I propose an alternative "big picture" depiction.

1. Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

2. Inferring the Why in Images

DTIC Science & Technology

2014-01-01

images. To our knowledge, this challenging problem has not yet been extensively explored in computer vision. We present a novel learning based...automatically infers why people are performing actions in images by learning from visual data and written language. ∗denotes equal contribution 1 Report...explored in computer vision. We present a novel learning based framework that uses high-level visual recognition to infer why people are performing

3. Linear versus quadratic portfolio optimization model with transaction cost

Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

2014-06-01

Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

4. Memetic algorithms for the unconstrained binary quadratic programming problem.

PubMed

Merz, Peter; Katayama, Kengo

2004-12-01

This paper presents a memetic algorithm, a highly effective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a fitness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes--besides a highly effective randomized k-opt local search--a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally different from traditional crossover operators, since new genetic material is included in the offspring which is not contained in one of the parents. The evolutionary heuristic is tested on 35 publicly available BQP instances, and it is shown experimentally that the algorithm is capable of finding best-known solutions to large BQPs in a short time and with a high frequency. In comparison to other approaches for the BQP, the approach appears to be much more effective, particularly for large instances of 1000 or 2500 binary variables.

5. A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.

PubMed

Qin, Sitian; Le, Xinyi; Wang, Jun

2016-08-19

This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.

6. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

NASA Technical Reports Server (NTRS)

Orr, Jeb S.

2012-01-01

A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

7. Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube

Mittelmann, Hans; Peng, Jiming; Wu, Xiaolin

2009-07-01

In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.

8. Linear quadratic optimal controller for cable-driven parallel robots

Abdolshah, Saeed; Shojaei Barjuei, Erfan

2015-12-01

In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

9. Quadratic Fermi node in a 3D strongly correlated semimetal

DOE PAGES

Kondo, Takeshi; Nakayama, M.; Chen, R.; ...

2015-12-07

We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less

10. The Quadratic Spinor Lagrangian, Axial Torsion Current and Generalizations

Da Rocha, R.; Pereira, J. G.

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field — Weyl, Majorana, flagpole, or flag-dipole spinor fields — yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

11. Bright nonlocal quadratic solitons induced by boundary confinement

Zheng, Yizhou; Gao, Yan; Wang, Jing; Lv, Fang; Lu, Daquan; Hu, Wei

2017-01-01

Under the Dirichlet boundary conditions, a family of bright quadratic solitons exists in the regime where the second harmonic can be regarded as the refractive index of the fundamental wave with an oscillatory nonlocal response. By simplifying the governing equations into the Snyder-Mitchell mode, the approximate analytical solutions are obtained. Taking them as the initial guess and using a numerical code, we found two branches of bright solitons, of which the beam width increases (branch I) and decreases (branch II) with the increase of the sample size, respectively. If the nonlocality is fixed and the sample size is varied, the soliton width varies piecewise and approximately periodically. In each period, solitons only exist in a small range of sample size. Single-hump fundamental wave solitons with the same beam width in narrower samples can be, if the second harmonics are connected smoothly, jointed to be a multihump soliton in a wider sample whose size is the sum of those for the narrower ones. The dynamical simulation shows that the found solitons are unstable.

12. Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?

PubMed

Schönberg, C H L

2015-04-01

Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.

13. GR angular momentum in the quadratic spinor Lagrangian formulation

Li, Siao-Jing

2016-08-01

We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.

14. Quadratic Fermi node in a 3D strongly correlated semimetal

SciTech Connect

Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

2015-12-07

We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

15. Junction conditions in quadratic gravity: thin shells and double layers

Reina, Borja; Senovilla, José M. M.; Vera, Raül

2016-05-01

The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.

16. Mechanical cooling in single-photon optomechanics with quadratic nonlinearity

Gu, Wen-ju; Yi, Zhen; Sun, Li-hui; Xu, Da-hai

2015-08-01

In the paper we study the nonlinear mechanical cooling processes in an intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply scattering theory to calculate the transition rates between different mechanical Fock states using the resolvent of the Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in nonclassical mechanical states, and the phonon number fluctuations F to display that the even-phonon transitions favor suppressing the phonon number fluctuations compared to the linear coupling optomechanical system.

17. Quadratic Fermi node in a 3D strongly correlated semimetal

PubMed Central

Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

2015-01-01

Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

18. Pathway network inference from gene expression data

PubMed Central

2014-01-01

Background The development of high-throughput omics technologies enabled genome-wide measurements of the activity of cellular elements and provides the analytical resources for the progress of the Systems Biology discipline. Analysis and interpretation of gene expression data has evolved from the gene to the pathway and interaction level, i.e. from the detection of differentially expressed genes, to the establishment of gene interaction networks and the identification of enriched functional categories. Still, the understanding of biological systems requires a further level of analysis that addresses the characterization of the interaction between functional modules. Results We present a novel computational methodology to study the functional interconnections among the molecular elements of a biological system. The PANA approach uses high-throughput genomics measurements and a functional annotation scheme to extract an activity profile from each functional block -or pathway- followed by machine-learning methods to infer the relationships between these functional profiles. The result is a global, interconnected network of pathways that represents the functional cross-talk within the molecular system. We have applied this approach to describe the functional transcriptional connections during the yeast cell cycle and to identify pathways that change their connectivity in a disease condition using an Alzheimer example. Conclusions PANA is a useful tool to deepen in our understanding of the functional interdependences that operate within complex biological systems. We show the approach is algorithmically consistent and the inferred network is well supported by the available functional data. The method allows the dissection of the molecular basis of the functional connections and we describe the different regulatory mechanisms that explain the network's topology obtained for the yeast cell cycle data. PMID:25032889

19. Active inference, communication and hermeneutics☆

PubMed Central

Friston, Karl J.; Frith, Christopher D.

2015-01-01

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others – during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions – both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then – in principle – they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa. PMID:25957007

20. Active inference, communication and hermeneutics.

PubMed

Friston, Karl J; Frith, Christopher D

2015-07-01

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others--during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions--both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then--in principle--they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa.

1. Causal inference and developmental psychology.

PubMed

Foster, E Michael

2010-11-01

Causal inference is of central importance to developmental psychology. Many key questions in the field revolve around improving the lives of children and their families. These include identifying risk factors that if manipulated in some way would foster child development. Such a task inherently involves causal inference: One wants to know whether the risk factor actually causes outcomes. Random assignment is not possible in many instances, and for that reason, psychologists must rely on observational studies. Such studies identify associations, and causal interpretation of such associations requires additional assumptions. Research in developmental psychology generally has relied on various forms of linear regression, but this methodology has limitations for causal inference. Fortunately, methodological developments in various fields are providing new tools for causal inference-tools that rely on more plausible assumptions. This article describes the limitations of regression for causal inference and describes how new tools might offer better causal inference. This discussion highlights the importance of properly identifying covariates to include (and exclude) from the analysis. This discussion considers the directed acyclic graph for use in accomplishing this task. With the proper covariates having been chosen, many of the available methods rely on the assumption of "ignorability." The article discusses the meaning of ignorability and considers alternatives to this assumption, such as instrumental variables estimation. Finally, the article considers the use of the tools discussed in the context of a specific research question, the effect of family structure on child development.

2. Differential-geometric aspects of a nonholonomic Dirac mechanics: Lessons of a model quadratic in velocities

Pavlov, V. P.

2014-03-01

Faddeev and Vershik proposed the Hamiltonian and Lagrangian formulations of constrained mechanical systems that are invariant from the differential geometry standpoint. In both formulations, the description is based on a nondegenerate symplectic 2-form defined on a cotangent bundle T*Q (in the Hamiltonian formulation) or on a tangent bundle TQ (in the Lagrangian formulation), and constraints are sets of functions in involution on these manifolds. We demonstrate that this technique does not allow "invariantization" of the Dirac procedure of constraint "proliferation." We show this in an example of a typical quantum field model in which the original Lagrange function is a quadratic form in velocities with a degenerate coefficient matrix. We postulate that the initial phase space is a manifold where all arguments of the action functional including the Lagrange multipliers are defined. The Lagrange multipliers can then be naturally interpreted physically as velocities (in the Hamiltonian formulation) or momenta (in the Lagrangian formulation) related to "nonphysical" degrees of freedom. A quasisymplectic 2-form invariantly defined on such a manifold is degenerate. We propose new differential-geometric structures that allow formulating the Dirac procedure invariantly.

3. Optimal inference with suboptimal models: Addiction and active Bayesian inference

PubMed Central

Schwartenbeck, Philipp; FitzGerald, Thomas H.B.; Mathys, Christoph; Dolan, Ray; Wurst, Friedrich; Kronbichler, Martin; Friston, Karl

2015-01-01

When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent’s beliefs – based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment – as opposed to the agent’s beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less ‘optimally’ than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject’s generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described ‘limited offer’ task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work. PMID:25561321

4. Causal inference in biology networks with integrated belief propagation.

PubMed

Chang, Rui; Karr, Jonathan R; Schadt, Eric E

2015-01-01

Inferring causal relationships among molecular and higher order phenotypes is a critical step in elucidating the complexity of living systems. Here we propose a novel method for inferring causality that is no longer constrained by the conditional dependency arguments that limit the ability of statistical causal inference methods to resolve causal relationships within sets of graphical models that are Markov equivalent. Our method utilizes Bayesian belief propagation to infer the responses of perturbation events on molecular traits given a hypothesized graph structure. A distance measure between the inferred response distribution and the observed data is defined to assess the 'fitness' of the hypothesized causal relationships. To test our algorithm, we infer causal relationships within equivalence classes of gene networks in which the form of the functional interactions that are possible are assumed to be nonlinear, given synthetic microarray and RNA sequencing data. We also apply our method to infer causality in real metabolic network with v-structure and feedback loop. We show that our method can recapitulate the causal structure and recover the feedback loop only from steady-state data which conventional method cannot.

5. The fifteen theorem for universal Hermitian lattices over imaginary quadratic fields

Kim, Byeong Moon; Kim, Ji Young; Park, Poo-Sung

2010-04-01

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields Q(√{-m}) for all m . For each imaginary quadratic field Q(√{-m}) , we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13. In addition, we determine the minimal rank of universal Hermitian lattices for all imaginary quadratic fields.

6. Causal inference in obesity research.

PubMed

Franks, P W; Atabaki-Pasdar, N

2017-03-01

Obesity is a risk factor for a plethora of severe morbidities and premature death. Most supporting evidence comes from observational studies that are prone to chance, bias and confounding. Even data on the protective effects of weight loss from randomized controlled trials will be susceptible to confounding and bias if treatment assignment cannot be masked, which is usually the case with lifestyle and surgical interventions. Thus, whilst obesity is widely considered the major modifiable risk factor for many chronic diseases, its causes and consequences are often difficult to determine. Addressing this is important, as the prevention and treatment of any disease requires that interventions focus on causal risk factors. Disease prediction, although not dependent on knowing the causes, is nevertheless enhanced by such knowledge. Here, we provide an overview of some of the barriers to causal inference in obesity research and discuss analytical approaches, such as Mendelian randomization, that can help to overcome these obstacles. In a systematic review of the literature in this field, we found: (i) probable causal relationships between adiposity and bone health/disease, cancers (colorectal, lung and kidney cancers), cardiometabolic traits (blood pressure, fasting insulin, inflammatory markers and lipids), uric acid concentrations, coronary heart disease and venous thrombosis (in the presence of pulmonary embolism), (ii) possible causal relationships between adiposity and gray matter volume, depression and common mental disorders, oesophageal cancer, macroalbuminuria, end-stage renal disease, diabetic kidney disease, nuclear cataract and gall stone disease, and (iii) no evidence for causal relationships between adiposity and Alzheimer's disease, pancreatic cancer, venous thrombosis (in the absence of pulmonary embolism), liver function and periodontitis.

7. Bayesian Inference for Skewed Stable Distributions

2011-03-01

Stable distributions are a class of distributions which allow skewness and heavy tail. Non-Gaussian stable random variables play the role of normal distribution in the central limit theorem, for normalized sums of random variables with infinite variance. The lack of analytic formula for density and distribution functions of stable random variables has been a major drawback to the use of stable distributions, also in the case of inference in Bayesian framework. Buckle introduced priors for the parameters of stable random variables to obtain an analytic form of posterior distribution. However, many researchers tried to solve the problem, through the Markov chain Monte Carlo methods, e.g. [8] and their references. In this paper a new class of heavy-tailed distribution is introduced, called skewed stable. This class has two main advantages: It has many inferential advantages, since it is a member of exponential family, so the Bayesian inference can be drawn similar to the exponential family of distributions and modelling skew data with stable distributions is dominated by this family. Finally, Bayesian inference for skewed stable arc compared to the stable distributions through a few simulations study.

8. Quality of Computationally Inferred Gene Ontology Annotations

PubMed Central

Škunca, Nives; Altenhoff, Adrian; Dessimoz, Christophe

2012-01-01

Gene Ontology (GO) has established itself as the undisputed standard for protein function annotation. Most annotations are inferred electronically, i.e. without individual curator supervision, but they are widely considered unreliable. At the same time, we crucially depend on those automated annotations, as most newly sequenced genomes are non-model organisms. Here, we introduce a methodology to systematically and quantitatively evaluate electronic annotations. By exploiting changes in successive releases of the UniProt Gene Ontology Annotation database, we assessed the quality of electronic annotations in terms of specificity, reliability, and coverage. Overall, we not only found that electronic annotations have significantly improved in recent years, but also that their reliability now rivals that of annotations inferred by curators when they use evidence other than experiments from primary literature. This work provides the means to identify the subset of electronic annotations that can be relied upon—an important outcome given that >98% of all annotations are inferred without direct curation. PMID:22693439

9. Reduced order parameter estimation using quasilinearization and quadratic programming

2012-06-01

The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

10. New type of Weyl semimetal with quadratic double Weyl fermions

PubMed Central

Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid

2016-01-01

Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914

11. Gravity waves from non-minimal quadratic inflation

SciTech Connect

Pallis, Constantinos; Shafi, Qaisar

2015-03-12

We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.

12. A decentralized linear quadratic control design method for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass

13. Stability and monotone convergence of generalised policy iteration for discrete-time linear quadratic regulations

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2016-03-01

In this paper, we analyse the convergence and stability properties of generalised policy iteration (GPI) applied to discrete-time linear quadratic regulation problems. GPI is one kind of the generalised adaptive dynamic programming methods used for solving optimal control problems, and is composed of policy evaluation and policy improvement steps. To analyse the convergence and stability of GPI, the dynamic programming (DP) operator is defined. Then, GPI and its equivalent formulas are presented based on the notation of DP operator. The convergence of the approximate value function to the exact one in policy evaluation is proven based on the equivalent formulas. Furthermore, the positive semi-definiteness, stability, and the monotone convergence (PI-mode and VI-mode convergence) of GPI are presented under certain conditions on the initial value function. The online least square method is also presented for the implementation of GPI. Finally, some numerical simulations are carried out to verify the effectiveness of GPI as well as to further investigate the convergence and stability properties.

14. Cochlear compression: effects of low-frequency biasing on quadratic distortion product otoacoustic emission.

PubMed

Bian, Lin

2004-12-01

Distortion product otoacoustic emissions (DPOAEs) are generated from the nonlinear transduction n cochlear outer hair cells. The transducer function demonstrating a compressive nonlinearity can be estimated from low-frequency modulation of DPOAEs. Experimental results from the gerbils showed that the magnitude of quadratic difference tone (QDT, f2-f1) was either enhanced or suppressed depending on the phase of the low-frequency bias tone. Within one period of the bias tone, QDT magnitudes exhibited two similar modulation patterns, each resembling the absolute value of the second derivative of the transducer function. In the time domain, the center notches of the modulation patterns occurred around the zero crossings of the bias pressure, whereas peaks corresponded to the increase or decrease in bias pressure. Evaluated with respect to the bias pressure, modulated QDT magnitude displayed a double-modulation pattern marked by a separation of the center notches. Loading/unloading of the cochlear transducer or rise/fall in bias pressure shifted the center notch to positive or negative sound pressures, indicating a mechanical hysteresis. These results suggest that QDT arises from the compression that coexists with the active hysteresis in cochlear transduction. Modulation of QDT magnitude reflects the dynamic regulation of cochlear transducer gain and compression.

15. Multiple model inference.

SciTech Connect

Swiler, Laura Painton; Urbina, Angel

2010-07-01

This paper compares three approaches for model selection: classical least squares methods, information theoretic criteria, and Bayesian approaches. Least squares methods are not model selection methods although one can select the model that yields the smallest sum-of-squared error function. Information theoretic approaches balance overfitting with model accuracy by incorporating terms that penalize more parameters with a log-likelihood term to reflect goodness of fit. Bayesian model selection involves calculating the posterior probability that each model is correct, given experimental data and prior probabilities that each model is correct. As part of this calculation, one often calibrates the parameters of each model and this is included in the Bayesian calculations. Our approach is demonstrated on a structural dynamics example with models for energy dissipation and peak force across a bolted joint. The three approaches are compared and the influence of the log-likelihood term in all approaches is discussed.

16. Locative inferences in medical texts.

PubMed

Mayer, P S; Bailey, G H; Mayer, R J; Hillis, A; Dvoracek, J E

1987-06-01

Medical research relies on epidemiological studies conducted on a large set of clinical records that have been collected from physicians recording individual patient observations. These clinical records are recorded for the purpose of individual care of the patient with little consideration for their use by a biostatistician interested in studying a disease over a large population. Natural language processing of clinical records for epidemiological studies must deal with temporal, locative, and conceptual issues. This makes text understanding and data extraction of clinical records an excellent area for applied research. While much has been done in making temporal or conceptual inferences in medical texts, parallel work in locative inferences has not been done. This paper examines the locative inferences as well as the integration of temporal, locative, and conceptual issues in the clinical record understanding domain by presenting an application that utilizes two key concepts in its parsing strategy--a knowledge-based parsing strategy and a minimal lexicon.

17. Minitrack tracking function description, volume 2

NASA Technical Reports Server (NTRS)

Englar, T. S.; Mango, S. A.; Roettcher, C. A.; Watters, D. L.

1973-01-01

The minitrack tracking function is described and specific operations are identified. The subjects discussed are: (1) preprocessor listing, (2) minitrack hardware, (3) system calibration, (4) quadratic listing, and (5) quadratic flow diagram. Detailed information is provided on the construction of the tracking system and its operation. The calibration procedures are supported by mathematical models to show the application of the computer programs.

18. LOWER LEVEL INFERENCE CONTROL IN STATISTICAL DATABASE SYSTEMS

SciTech Connect

Lipton, D.L.; Wong, H.K.T.

1984-02-01

An inference is the process of transforming unclassified data values into confidential data values. Most previous research in inference control has studied the use of statistical aggregates to deduce individual records. However, several other types of inference are also possible. Unknown functional dependencies may be apparent to users who have 'expert' knowledge about the characteristics of a population. Some correlations between attributes may be concluded from 'commonly-known' facts about the world. To counter these threats, security managers should use random sampling of databases of similar populations, as well as expert systems. 'Expert' users of the DATABASE SYSTEM may form inferences from the variable performance of the user interface. Users may observe on-line turn-around time, accounting statistics. the error message received, and the point at which an interactive protocol sequence fails. One may obtain information about the frequency distributions of attribute values, and the validity of data object names from this information. At the back-end of a database system, improved software engineering practices will reduce opportunities to bypass functional units of the database system. The term 'DATA OBJECT' should be expanded to incorporate these data object types which generate new classes of threats. The security of DATABASES and DATABASE SySTEMS must be recognized as separate but related problems. Thus, by increased awareness of lower level inferences, system security managers may effectively nullify the threat posed by lower level inferences.

19. Efficient Exact Inference With Loss Augmented Objective in Structured Learning.

PubMed

Bauer, Alexander; Nakajima, Shinichi; Muller, Klaus-Robert

2016-08-19

Structural support vector machine (SVM) is an elegant approach for building complex and accurate models with structured outputs. However, its applicability relies on the availability of efficient inference algorithms--the state-of-the-art training algorithms repeatedly perform inference to compute a subgradient or to find the most violating configuration. In this paper, we propose an exact inference algorithm for maximizing nondecomposable objectives due to special type of a high-order potential having a decomposable internal structure. As an important application, our method covers the loss augmented inference, which enables the slack and margin scaling formulations of structural SVM with a variety of dissimilarity measures, e.g., Hamming loss, precision and recall, Fβ-loss, intersection over union, and many other functions that can be efficiently computed from the contingency table. We demonstrate the advantages of our approach in natural language parsing and sequence segmentation applications.

20. Bayesian inferences about the self (and others): A review

PubMed Central

Moutoussis, Michael; Fearon, Pasco; El-Deredy, Wael; Dolan, Raymond J.; Friston, Karl J.

2014-01-01

Viewing the brain as an organ of approximate Bayesian inference can help us understand how it represents the self. We suggest that inferred representations of the self have a normative function: to predict and optimise the likely outcomes of social interactions. Technically, we cast this predict-and-optimise as maximising the chance of favourable outcomes through active inference. Here the utility of outcomes can be conceptualised as prior beliefs about final states. Actions based on interpersonal representations can therefore be understood as minimising surprise – under the prior belief that one will end up in states with high utility. Interpersonal representations thus serve to render interactions more predictable, while the affective valence of interpersonal inference renders self-perception evaluative. Distortions of self-representation contribute to major psychiatric disorders such as depression, personality disorder and paranoia. The approach we review may therefore operationalise the study of interpersonal representations in pathological states. PMID:24583455