An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2001-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

Gaussian cloning of coherent states with known phases

International Nuclear Information System (INIS)

Alexanian, Moorad

2006-01-01

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier

Response moments of dynamic systems under non-Gaussian random excitation by the equivalent non-Gaussian excitation method

International Nuclear Information System (INIS)

Tsuchida, Takahiro; Kimura, Koji

2016-01-01

Equivalent non-Gaussian excitation method is proposed to obtain the response moments up to the 4th order of dynamic systems under non-Gaussian random excitation. The non-Gaussian excitation is prescribed by the probability density and the power spectrum, and is described by an Ito stochastic differential equation. Generally, moment equations for the response, which are derived from the governing equations for the excitation and the system, are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation even though the system is linear. In the equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a quadratic polynomial. In numerical examples, a linear system subjected to nonGaussian excitations with bimodal and Rayleigh distributions is analyzed by using the present method. The results show that the method yields the variance, skewness and kurtosis of the response with high accuracy for non-Gaussian excitation with the widely different probability densities and bandwidth. The statistical moments of the equivalent non-Gaussian excitation are also investigated to describe the feature of the method. (paper)

Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis

Directory of Open Access Journals (Sweden)

M. Bocquet

2008-02-01

Full Text Available For a start, recent techniques devoted to the reconstruction of sources of an atmospheric tracer at continental scale are introduced. A first method is based on the principle of maximum entropy on the mean and is briefly reviewed here. A second approach, which has not been applied in this field yet, is based on an exact Bayesian approach, through a maximum a posteriori estimator. The methods share common grounds, and both perform equally well in practice. When specific prior hypotheses on the sources are taken into account such as positivity, or boundedness, both methods lead to purposefully devised cost-functions. These cost-functions are not necessarily quadratic because the underlying assumptions are not Gaussian. As a consequence, several mathematical tools developed in data assimilation on the basis of quadratic cost-functions in order to establish a posteriori analysis, need to be extended to this non-Gaussian framework. Concomitantly, the second-order sensitivity analysis needs to be adapted, as well as the computations of the averaging kernels of the source and the errors obtained in the reconstruction. All of these developments are applied to a real case of tracer dispersion: the European Tracer Experiment [ETEX]. Comparisons are made between a least squares cost function (similar to the so-called 4D-Var approach and a cost-function which is not based on Gaussian hypotheses. Besides, the information content of the observations which is used in the reconstruction is computed and studied on the application case. A connection with the degrees of freedom for signal is also established. As a by-product of these methodological developments, conclusions are drawn on the information content of the ETEX dataset as seen from the inverse modelling point of view.

Binary naive Bayesian classifiers for correlated Gaussian features: a theoretical analysis

CSIR Research Space (South Africa)

Van Dyk, E

2008-11-01

Full Text Available classifier with Gaussian features while using any quadratic decision boundary. Therefore, the analysis is not restricted to Naive Bayesian classifiers alone and can, for instance, be used to calculate the Bayes error performance. We compare the analytical...

An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2003-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

An Extended Quadratic Frobenius Primality Test with Average- and Worst-Case Error Estimate

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2006-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

Non-gaussian turbulence

Energy Technology Data Exchange (ETDEWEB)

Hoejstrup, J [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K S [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B J [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)

1999-03-01

The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)

Aspects of Quadratic Gravity

CERN Document Server

Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

2016-01-01

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

Quadratic time dependent Hamiltonians and separation of variables

International Nuclear Information System (INIS)

Anzaldo-Meneses, A.

2017-01-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.

Non-Gaussian bias: insights from discrete density peaks

CERN Document Server

Desjacques, Vincent; Riotto, Antonio

2013-01-01

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out tha...

When non-Gaussian states are Gaussian: Generalization of nonseparability criterion for continuous variables

International Nuclear Information System (INIS)

McHugh, Derek; Buzek, Vladimir; Ziman, Mario

2006-01-01

We present a class of non-Gaussian two-mode continuous-variable states for which the separability criterion for Gaussian states can be employed to detect whether they are separable or not. These states reduce to the two-mode Gaussian states as a special case

Quantum information with Gaussian states

International Nuclear Information System (INIS)

Wang Xiangbin; Hiroshima, Tohya; Tomita, Akihisa; Hayashi, Masahito

2007-01-01

Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states

Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

International Nuclear Information System (INIS)

Desjacques, Vincent; Jeong, Donghui; Schmidt, Fabian

2011-01-01

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local f NL model. In a separate paper (to be published in PRD rapid communication), the authors compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.

Binary classification posed as a quadratically constrained quadratic ...

Indian Academy of Sciences (India)

Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

Quadratic third-order tensor optimization problem with quadratic constraints

Directory of Open Access Journals (Sweden)

Lixing Yang

2014-05-01

Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

Asymptotic performance of regularized quadratic discriminant analysis based classifiers

KAUST Repository

Elkhalil, Khalil

2017-12-13

This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.

Applications exponential approximation by integer shifts of Gaussian functions

Directory of Open Access Journals (Sweden)

S. M. Sitnik

2013-01-01

Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.

Quadratic tracer dynamical models tobacco growth

International Nuclear Information System (INIS)

Qiang Jiyi; Hua Cuncai; Wang Shaohua

2011-01-01

In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

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

DEFF Research Database (Denmark)

Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

2016-01-01

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...

Sensitivity analysis in Gaussian Bayesian networks using a symbolic-numerical technique

International Nuclear Information System (INIS)

Castillo, Enrique; Kjaerulff, Uffe

2003-01-01

The paper discusses the problem of sensitivity analysis in Gaussian Bayesian networks. The algebraic structure of the conditional means and variances, as rational functions involving linear and quadratic functions of the parameters, are used to simplify the sensitivity analysis. In particular the probabilities of conditional variables exceeding given values and related probabilities are analyzed. Two examples of application are used to illustrate all the concepts and methods

Type-A Worst-Case Uncertainty for Gaussian noise instruments

International Nuclear Information System (INIS)

Arpaia, P.; Baccigalupi, C.; Martino, M.

2015-01-01

An analytical type-A approach is proposed for predicting the Worst-Case Uncertainty of a measurement system. In a set of independent observations of the same measurand, modelled as independent- and identically-distributed random variables, the upcoming extreme values (e.g. peaks) can be forecast by only characterizing the measurement system noise level, assumed to be white and Gaussian. Simulation and experimental results are presented to validate the model for a case study on the worst-case repeatability of a pulsed power supply for the klystron modulators of the Compact LInear Collider at CERN. The experimental validation highlights satisfying results for an acquisition system repeatable in the order of ±25 ppm over a bandwidth of 5 MHz

Type-A Worst-Case Uncertainty for Gaussian noise instruments

CERN Document Server

AUTHOR|(CDS)2087245; Arpaia, Pasquale; Martino, Michele

2015-01-01

An analytical type-A approach is proposed for predicting the Worst-Case Uncertainty of a measurement system. In a set of independent observations of the same measurand, modelled as independent- and identically-distributed random variables, the upcoming extreme values (e.g. peaks) can be forecast by only characterizing the measurement system noise level, assumed to be white and Gaussian. Simulation and experimental results are presented to validate the model for a case study on the worst-case repeatability of a pulsed power supply for the klystron modulators of the Compact LInear Collider at CERN. The experimental validation highlights satisfying results for an acquisition system repeatable in the order of _25 ppm over a bandwidth of 5 MHz.

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

Science.gov (United States)

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Hidden conic quadratic representation of some nonconvex quadratic optimization problems

NARCIS (Netherlands)

Ben-Tal, A.; den Hertog, D.

The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture

International Nuclear Information System (INIS)

Ji, Se-Wan; Nha, Hyunchul; Kim, M S

2015-01-01

It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and here we address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by an N-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements. (paper)

Self-Replicating Quadratics

Science.gov (United States)

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

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

Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

International Nuclear Information System (INIS)

Chingangbam, Pravabati; Park, Changbom

2009-01-01

We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter g NL . The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of g NL and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for g NL > 0 and less of both for g NL NL and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of g NL that are clearly distinct from the quadratic order perturbations, encoded in the parameter f NL . Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between g NL and f NL type non-Gaussianities

A novel multitarget model of radiation-induced cell killing based on the Gaussian distribution.

Science.gov (United States)

Zhao, Lei; Mi, Dong; Sun, Yeqing

2017-05-07

The multitarget version of the traditional target theory based on the Poisson distribution is still used to describe the dose-survival curves of cells after ionizing radiation in radiobiology and radiotherapy. However, noting that the usual ionizing radiation damage is the result of two sequential stochastic processes, the probability distribution of the damage number per cell should follow a compound Poisson distribution, like e.g. Neyman's distribution of type A (N. A.). In consideration of that the Gaussian distribution can be considered as the approximation of the N. A. in the case of high flux, a multitarget model based on the Gaussian distribution is proposed to describe the cell inactivation effects in low linear energy transfer (LET) radiation with high dose-rate. Theoretical analysis and experimental data fitting indicate that the present theory is superior to the traditional multitarget model and similar to the Linear - Quadratic (LQ) model in describing the biological effects of low-LET radiation with high dose-rate, and the parameter ratio in the present model can be used as an alternative indicator to reflect the radiation damage and radiosensitivity of the cells. Copyright © 2017 Elsevier Ltd. All rights reserved.

Special cases of the quadratic shortest path problem

NARCIS (Netherlands)

Sotirov, Renata; Hu, Hao

2017-01-01

The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

International Nuclear Information System (INIS)

Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan

2007-01-01

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

A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

NARCIS (Netherlands)

de Klerk, E.; Pasechnik, D.V.

2005-01-01

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

Quadratic Damping

Science.gov (United States)

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…

Classification of the quantum two dimensional superintegrable systems with quadratic integrals and the Stackel transforms

International Nuclear Information System (INIS)

Dakaloyannis, C.

2006-01-01

Full text: (author)The two dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar as the classical ones multiplied by a quantum coefficient -n 2 plus a quantum deformation of order n 4 and n 6 . The systems inside the classes are transformed using Stackel transforms in the quantum case as in the classical case and general form is discussed. The idea of the Jacobi Hamiltonian corresponding to the Jacobi metric in the classical case is discussed

Detecting the presence of a magnetic field under Gaussian and non-Gaussian noise by adaptive measurement

Energy Technology Data Exchange (ETDEWEB)

Wang, Yuan-Mei; Li, Jun-Gang, E-mail: jungl@bit.edu.cn; Zou, Jian

2017-06-15

Highlights: • Adaptive measurement strategy is used to detect the presence of a magnetic field. • Gaussian Ornstein–Uhlenbeck noise and non-Gaussian noise have been considered. • Weaker magnetic fields may be more easily detected than some stronger ones. - Abstract: By using the adaptive measurement method we study how to detect whether a weak magnetic field is actually present or not under Gaussian noise and non-Gaussian noise. We find that the adaptive measurement method can effectively improve the detection accuracy. For the case of Gaussian noise, we find the stronger the magnetic field strength, the easier for us to detect the magnetic field. Counterintuitively, for non-Gaussian noise, some weaker magnetic fields are more likely to be detected rather than some stronger ones. Finally, we give a reasonable physical interpretation.

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

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

2003-11-01

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

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

International Nuclear Information System (INIS)

Marquette, Ian

2011-01-01

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Optimal Quadratic Programming Algorithms

CERN Document Server

Dostal, Zdenek

2009-01-01

Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers

Linear-quadratic control and quadratic differential forms for multidimensional behaviors

NARCIS (Netherlands)

Napp, D.; Trentelman, H.L.

2011-01-01

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

The halo bispectrum in N-body simulations with non-Gaussian initial conditions

Science.gov (United States)

Sefusatti, E.; Crocce, M.; Desjacques, V.

2012-10-01

We present measurements of the bispectrum of dark matter haloes in numerical simulations with non-Gaussian initial conditions of local type. We show, in the first place, that the overall effect of primordial non-Gaussianity on the halo bispectrum is larger than on the halo power spectrum when all measurable configurations are taken into account. We then compare our measurements with a tree-level perturbative prediction, finding good agreement at large scales when the constant Gaussian bias parameter, both linear and quadratic, and their constant non-Gaussian corrections are fitted for. The best-fitting values of the Gaussian bias factors and their non-Gaussian, scale-independent corrections are in qualitative agreement with the peak-background split expectations. In particular, we show that the effect of non-Gaussian initial conditions on squeezed configurations is fairly large (up to 30 per cent for fNL = 100 at redshift z = 0.5) and results from contributions of similar amplitude induced by the initial matter bispectrum, scale-dependent bias corrections as well as from non-linear matter bispectrum corrections. We show, in addition, that effects at second order in fNL are irrelevant for the range of values allowed by cosmic microwave background and galaxy power spectrum measurements, at least on the scales probed by our simulations (k > 0.01 h Mpc-1). Finally, we present a Fisher matrix analysis to assess the possibility of constraining primordial non-Gaussianity with future measurements of the galaxy bispectrum. We find that a survey with a volume of about 10 h-3 Gpc3 at mean redshift z ≃ 1 could provide an error on fNL of the order of a few. This shows the relevance of a joint analysis of galaxy power spectrum and bispectrum in future redshift surveys.

Rescuing Quadratic Inflation

CERN Document Server

Ellis, John; Sueiro, Maria

2014-01-01

Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

Handbook of Gaussian basis sets

International Nuclear Information System (INIS)

Poirier, R.; Kari, R.; Csizmadia, I.G.

1985-01-01

A collection of a large body of information is presented useful for chemists involved in molecular Gaussian computations. Every effort has been made by the authors to collect all available data for cartesian Gaussian as found in the literature up to July of 1984. The data in this text includes a large collection of polarization function exponents but in this case the collection is not complete. Exponents for Slater type orbitals (STO) were included for completeness. This text offers a collection of Gaussian exponents primarily without criticism. (Auth.)

Feasibility study on the least square method for fitting non-Gaussian noise data

Science.gov (United States)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Monogamy inequality for distributed gaussian entanglement.

Science.gov (United States)

Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio

2007-02-02

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.

Faithfully quadratic rings

CERN Document Server

Dickmann, M

2015-01-01

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

Gravitation and quadratic forms

International Nuclear Information System (INIS)

Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

2017-01-01

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Gravitation and quadratic forms

Energy Technology Data Exchange (ETDEWEB)

Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

2017-03-31

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

Optimal unitary dilation for bosonic Gaussian channels

International Nuclear Information System (INIS)

Caruso, Filippo; Eisert, Jens; Giovannetti, Vittorio; Holevo, Alexander S.

2011-01-01

A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

Science.gov (United States)

Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

2006-06-01

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Directory of Open Access Journals (Sweden)

Phil Diamond

2003-01-01

Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

MCEM algorithm for the log-Gaussian Cox process

OpenAIRE

Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis

2014-01-01

Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...

Nonclassicality by Local Gaussian Unitary Operations for Gaussian States

Directory of Open Access Journals (Sweden)

Yangyang Wang

2018-04-01

Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.

Quadratic time dependent Hamiltonians and separation of variables

Science.gov (United States)

Anzaldo-Meneses, A.

2017-06-01

Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review

Science.gov (United States)

Falsone, G.

2018-03-01

In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable with many difficulties. Here all the principal approaches solving the SDEs are reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible.

Event rate and reaction time performance in ADHD: Testing predictions from the state regulation deficit hypothesis using an ex-Gaussian model.

Science.gov (United States)

Metin, Baris; Wiersema, Jan R; Verguts, Tom; Gasthuys, Roos; van Der Meere, Jacob J; Roeyers, Herbert; Sonuga-Barke, Edmund

2014-12-06

According to the state regulation deficit (SRD) account, ADHD is associated with a problem using effort to maintain an optimal activation state under demanding task settings such as very fast or very slow event rates. This leads to a prediction of disrupted performance at event rate extremes reflected in higher Gaussian response variability that is a putative marker of activation during motor preparation. In the current study, we tested this hypothesis using ex-Gaussian modeling, which distinguishes Gaussian from non-Gaussian variability. Twenty-five children with ADHD and 29 typically developing controls performed a simple Go/No-Go task under four different event-rate conditions. There was an accentuated quadratic relationship between event rate and Gaussian variability in the ADHD group compared to the controls. The children with ADHD had greater Gaussian variability at very fast and very slow event rates but not at moderate event rates. The results provide evidence for the SRD account of ADHD. However, given that this effect did not explain all group differences (some of which were independent of event rate) other cognitive and/or motivational processes are also likely implicated in ADHD performance deficits.

Fundamental quadratic variational principle underlying general relativity

International Nuclear Information System (INIS)

Atkins, W.K.

1983-01-01

The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed

Investigating Students' Mathematical Difficulties with Quadratic Equations

Science.gov (United States)

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…

Loop corrections to primordial non-Gaussianity

Science.gov (United States)

Boran, Sibel; Kahya, E. O.

2018-02-01

We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.

Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space

International Nuclear Information System (INIS)

Daszkiewicz, Marcin; Walczyk, Cezary J.

2008-01-01

The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces

Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

DEFF Research Database (Denmark)

Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

2016-01-01

We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

Optimal cloning of mixed Gaussian states

International Nuclear Information System (INIS)

Guta, Madalin; Matsumoto, Keiji

2006-01-01

We construct the optimal one to two cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states

Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

Directory of Open Access Journals (Sweden)

Królak Andrzej

2005-03-01

Full Text Available The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, F-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

Directory of Open Access Journals (Sweden)

Piotr Jaranowski

2012-03-01

Full Text Available The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, ℱ-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration

Directory of Open Access Journals (Sweden)

Fei Xu

2016-01-01

Full Text Available Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF. A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD, probability density function (PDF, and loading cycle distribution (LCD as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS and the extreme response spectrum (ERS and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.

Phase space eigenfunctions of multidimensional quadratic Hamiltonians

International Nuclear Information System (INIS)

Dodonov, V.V.; Man'ko, V.I.

1986-01-01

We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

Science.gov (United States)

Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal

2017-03-01

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

Quadratic interaction effect on the dark energy density in the universe

International Nuclear Information System (INIS)

Deveci, Derya G; Aydiner, Ekrem

2017-01-01

In this study, we deal with the holographic model of interacting dark components of dark energy and dark matter quadratic case of the equation of state parameter (EoS). The effective equations of states for the interacting holographic energy density are derived and the results are analyzed and compared with the solution of the linear form in the literature. The result of our work shows that the value of interaction term between dark components affects the fixed points at far future in the DE-dominated universe in the case of quadratic EoS parameter; it is a different result from the linear case in the theoretical results in the literature, and as the Quintom scenario the equations of state had coincidence at the cosmological constant boundary of –1 from above to below. (paper)

Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

International Nuclear Information System (INIS)

Rekab, S.; Zenine, N.

2006-01-01

We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

Revisiting non-Gaussianity from non-attractor inflation models

Science.gov (United States)

Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

2018-05-01

Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.

On Characterization of Quadratic Splines

DEFF Research Database (Denmark)

Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

2005-01-01

that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

Scale dependence of the halo bias in general local-type non-Gaussian models I: analytical predictions and consistency relations

International Nuclear Information System (INIS)

Nishimichi, Takahiro

2012-01-01

The large-scale clustering pattern of biased tracers is known to be a powerful probe of the non-Gaussianities in the primordial fluctuations. The so-called scale-dependent bias has been reported in various type of models of primordial non-Gaussianities. We focus on local-type non-Gaussianities, and unify the derivations in the literature of the scale-dependent bias in the presence of multiple Gaussian source fields as well as higher-order coupling to cover the models described by frequently-discussed f NL , g NL and t NL parameterization. We find that the resultant power spectrum is characterized by two parameters responsible for the shape and the amplitude of the scale-dependent bias in addition to the Gaussian bias factor. We show how (a generalized version of) Suyama-Yamaguchi inequality between f NL and t NL can directly be accessible from the observed power spectrum through the dependence on our new parameter which controls the shape of the scale-dependent bias. The other parameter for the amplitude of the scale-dependent bias is shown to be useful to distinguish the simplest quadratic non-Gaussianities (i.e., f NL -type) from higher-order ones (g NL and higher), if one measures it from multiple species of galaxies or clusters of galaxies. We discuss the validity and limitations of our analytic results by comparison with numerical simulations in an accompanying paper

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.

Science.gov (United States)

Yokoyama, Jun'ichi

2014-01-01

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student's t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.

Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

Science.gov (United States)

Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

2017-12-01

Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

An L∞/L1-Constrained Quadratic Optimization Problem with Applications to Neural Networks

International Nuclear Information System (INIS)

Leizarowitz, Arie; Rubinstein, Jacob

2003-01-01

Pattern formation in associative neural networks is related to a quadratic optimization problem. Biological considerations imply that the functional is constrained in the L ∞ norm and in the L 1 norm. We consider such optimization problems. We derive the Euler-Lagrange equations, and construct basic properties of the maximizers. We study in some detail the case where the kernel of the quadratic functional is finite-dimensional. In this case the optimization problem can be fully characterized by the geometry of a certain convex and compact finite-dimensional set

Interconversion of pure Gaussian states requiring non-Gaussian operations

Science.gov (United States)

Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.

2015-01-01

We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.

Integration of non-Gaussian fields

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille

1996-01-01

The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast....... and Randrup-Thomsen, S. Reliability of silo ring under lognormal stochastic pressure using stochastic interpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: Advances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin...

Quadratic theory and feedback controllers for linear time delay systems

International Nuclear Information System (INIS)

Lee, E.B.

1976-01-01

Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)

Gaussian vs non-Gaussian turbulence: impact on wind turbine loads

DEFF Research Database (Denmark)

Berg, Jacob; Natarajan, Anand; Mann, Jakob

2016-01-01

taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...

Extending the Scope of Robust Quadratic Optimization

NARCIS (Netherlands)

Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

Gaussian discriminating strength

Science.gov (United States)

Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.

2015-10-01

We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.

Vacuum solutions of Bianchi cosmologies in quadratic gravity

International Nuclear Information System (INIS)

Deus, Juliano Alves de; Muller, Daniel

2011-01-01

Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

Quadratic residues and non-residues selected topics

CERN Document Server

Wright, Steve

2016-01-01

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution

DEFF Research Database (Denmark)

Stentoft, Lars Peter

In this paper we propose a feasible way to price American options in a model with time varying volatility and conditional skewness and leptokurtosis using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk neutral dynamics can be obtained in this model, we interpret...... properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model outperforms the Gaussian case for pricing options on three large US stocks as well as a major index...

Students' Understanding of Quadratic Equations

Science.gov (United States)

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…

Quadratic integrals of motion for identical particle systems in quantum case

International Nuclear Information System (INIS)

Brije, I.; Gonera, S.; Kosinski, P.; Maslanka, P.; Giller, S.

2005-01-01

One studied quantum dynamic systems of identical particles allowing for additional integral of motion being quadratic in pulses. It was found that there was an appropriate way to ensure order that enabled to convert the classical integrals of motion into their quantum analogues. One analyzed relation of the mentioned integrals with splitting of the variables in the Schroedinger equation [ru

Non-chaotic behaviour for a class of quadratic jerk equations

International Nuclear Information System (INIS)

Malasoma, J.-M.

2009-01-01

It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

On the Issue of the ζ series convergence and loop corrections in the generation of observable primordial non-Gaussianity in slow-roll inflation. II. The trispectrum

International Nuclear Information System (INIS)

Rodriguez, Yeinzon; Valenzuela-Toledo, Cesar A.

2010-01-01

We calculate the trispectrum T ζ of the primordial curvature perturbation ζ, generated during a slow-roll inflationary epoch by considering a two-field quadratic model of inflation with canonical kinetic terms. We consider loop contributions as well as tree-level terms, and show that it is possible to attain very high, including observable, values for the level of non-Gaussianity τ NL if T ζ is dominated by the one-loop contribution. Special attention is paid to the claim in J. Cosmol. Astropart. Phys. 02 (2009) 017 that, in the model studied in this paper and for the specific inflationary trajectory we choose, the quantum fluctuations of the fields overwhelm the classical evolution. We argue that such a claim actually does not apply to our model, although more research is needed in order to understand the role of quantum diffusion. We also consider the probability that an observer in an ensemble of realizations of the density field sees a non-Gaussian distribution. In that respect, we show that the probability associated to the chosen inflationary trajectory is non-negligible. Finally, the levels of non-Gaussianity f NL and τ NL in the bispectrum B ζ and trispectrum T ζ of ζ, respectively, are also studied for the case in which ζ is not generated during inflation.

Dynamical invariants for variable quadratic Hamiltonians

International Nuclear Information System (INIS)

Suslov, Sergei K

2010-01-01

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

Quadratic Hamiltonians on non-symmetric Poisson structures

International Nuclear Information System (INIS)

Arribas, M.; Blesa, F.; Elipe, A.

2007-01-01

Many dynamical systems may be represented in a set of non-canonical coordinates that generate an su(2) algebraic structure. The topology of the phase space is the one of the S 2 sphere, the Poisson structure is the one of the rigid body, and the Hamiltonian is a parametric quadratic form in these 'spherical' coordinates. However, there are other problems in which the Poisson structure losses its symmetry. In this paper we analyze this case and, we show how the loss of the spherical symmetry affects the phase flow and parametric bifurcations for the bi-parametric cases

Orthogonality preserving infinite dimensional quadratic stochastic operators

International Nuclear Information System (INIS)

Akın, Hasan; Mukhamedov, Farrukh

2015-01-01

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

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2006-01-01

This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaël

2017-06-23

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaë l; Opitz, Thomas; Thibaud, Emeric

2017-01-01

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Rotating quantum Gaussian packets

International Nuclear Information System (INIS)

Dodonov, V V

2015-01-01

We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions. (paper)

Quadratically convergent MCSCF scheme using Fock operators

International Nuclear Information System (INIS)

Das, G.

1981-01-01

A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

Quadratic brackets from symplectic forms

International Nuclear Information System (INIS)

Alekseev, Anton Yu.; Todorov, Ivan T.

1994-01-01

We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

Gaussian entanglement revisited

Science.gov (United States)

Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo

2018-02-01

We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of m versus n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for: (i) Gaussian states of 1 versus n modes; and (ii) isotropic Gaussian states. In passing, we also retrieve (iii) the recently established equivalence between separability of a Gaussian state and and its complete Gaussian extendability. Our techniques are then applied to progress beyond the state of the art. We prove that: (iv) Gaussian states that are invariant under partial transposition are necessarily separable; (v) the PPT criterion is necessary and sufficient for separability for Gaussian states of m versus n modes that are symmetric under the exchange of any two modes belonging to one of the parties; and (vi) Gaussian states which remain PPT under passive optical operations can not be entangled by them either. This is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.

Management of linear quadratic regulator optimal control with full-vehicle control case study

Directory of Open Access Journals (Sweden)

Rodrigue Tchamna

2016-09-01

Full Text Available Linear quadratic regulator is a powerful technique for dealing with the control design of any linear and nonlinear system after linearization of the system around an operating point. For small systems, which have fewer state variables, the transformation of the performance index from scalar to matrix form can be straightforward. On the other hand, as the system becomes large with many state variables and controllers, appropriate design and notations should be defined to make it easy to automatically implement the technique for any large system without the need to redesign from scratch every time one requires a new system. The main aim of this article was to deal with this issue. This article shows how to automatically obtain the matrix form of the performance index matrices from the scalar version of the performance index. Control of a full-vehicle in cornering was taken as a case study in this article.

Non-Gaussian Methods for Causal Structure Learning.

Science.gov (United States)

Shimizu, Shohei

2018-05-22

Causal structure learning is one of the most exciting new topics in the fields of machine learning and statistics. In many empirical sciences including prevention science, the causal mechanisms underlying various phenomena need to be studied. Nevertheless, in many cases, classical methods for causal structure learning are not capable of estimating the causal structure of variables. This is because it explicitly or implicitly assumes Gaussianity of data and typically utilizes only the covariance structure. In many applications, however, non-Gaussian data are often obtained, which means that more information may be contained in the data distribution than the covariance matrix is capable of containing. Thus, many new methods have recently been proposed for using the non-Gaussian structure of data and inferring the causal structure of variables. This paper introduces prevention scientists to such causal structure learning methods, particularly those based on the linear, non-Gaussian, acyclic model known as LiNGAM. These non-Gaussian data analysis tools can fully estimate the underlying causal structures of variables under assumptions even in the presence of unobserved common causes. This feature is in contrast to other approaches. A simulated example is also provided.

Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states

International Nuclear Information System (INIS)

Adesso, Gerardo; Illuminati, Fabrizio

2005-01-01

We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they

Information sets as permutation cycles for quadratic residue codes

Directory of Open Access Journals (Sweden)

Richard A. Jenson

1982-01-01

Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1,   (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

Science.gov (United States)

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

Integrable quadratic classical Hamiltonians on so(4) and so(3, 1)

International Nuclear Information System (INIS)

Sokolov, Vladimir V; Wolf, Thomas

2006-01-01

We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree

How Gaussian can our Universe be?

Energy Technology Data Exchange (ETDEWEB)

Cabass, G. [Physics Department and INFN, Università di Roma ' ' La Sapienza' ' , P.le Aldo Moro 2, 00185, Rome (Italy); Pajer, E. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Schmidt, F., E-mail: giovanni.cabass@roma1.infn.it, E-mail: e.pajer@uu.nl, E-mail: fabians@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)

2017-01-01

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of k {sub ℓ}{sup 2}/ k {sub s} {sup 2}, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × ( n {sub s}−1).

How Gaussian can our Universe be?

Science.gov (United States)

Cabass, G.; Pajer, E.; Schmidt, F.

2017-01-01

Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is controlled by two observables: the tensor-to-scalar ratio, which is uncertain by more than fifty orders of magnitude; and the scalar spectral index, or tilt, which is relatively well measured. It is well known that to leading and next-to-leading order in derivatives, the contributions proportional to the tilt disappear from any local observable, and suspicion has been raised that this might happen to all orders, allowing for an arbitrarily low amount of primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show explicitly that this is not the case. Instead, a contribution of order the tilt appears in local observables. In summary, the floor of physical primordial non-Gaussianity in our Universe has a squeezed-limit scaling of kl2/ks2, similar to equilateral and orthogonal shapes, and a dimensionless amplitude of order 0.1 × (ns-1).

Quadratic Term Structure Models in Discrete Time

OpenAIRE

Marco Realdon

2006-01-01

This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

Science.gov (United States)

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example

A revisit to quadratic programming with fuzzy parameters

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

Quadratic Boost A-Source Impedance Network

DEFF Research Database (Denmark)

Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

2016-01-01

A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

Quadratic spatial soliton interactions

Science.gov (United States)

Jankovic, Ladislav

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

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

Science.gov (United States)

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

2016-03-01

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.

Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.

Science.gov (United States)

Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel

2009-11-01

A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.

Investigation of non-Gaussian effects in the Brazilian option market

Science.gov (United States)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

The quadratic-form identity for constructing the Hamiltonian structure of integrable systems

International Nuclear Information System (INIS)

Guo Fukui; Zhang Yufeng

2005-01-01

A usual loop algebra, not necessarily the matrix form of the loop algebra A-tilde n-1 , is also made use of for constructing linear isospectral problems, whose compatibility conditions exhibit a zero-curvature equation from which integrable systems are derived. In order to look for the Hamiltonian structure of such integrable systems, a quadratic-form identity is created in the present paper whose special case is just the trace identity; that is, when taking the loop algebra A-tilde 1 , the quadratic-form identity presented in this paper is completely consistent with the trace identity

Improved effective potential by nonlinear canonical transformations

International Nuclear Information System (INIS)

Ritschel, U.

1990-01-01

We generalize the familiar gaussian-effective-potential formalism to a class of non-gaussian trial states. With the help of exact nonlinear canonical transformations, expectation values can be calculated analytically and in closed form. A detailed description of our method, particularly for quadratic and cubic transformations, and of the related renormalization procedure is given. Applications to φ 4 -models in various dimensionalities are treated. We find the expected critical behaviour in two space-time dimensions. In three and four dimensions we observe instabilities which go back the incompleteness of the gaussian-based renormalization. In the appendices it is shown that the quadratic transformation leads to a coherent state in a certain limiting case, and the generalization to systems at finite temperature is performed. (orig.)

Mode entanglement of Gaussian fermionic states

Science.gov (United States)

Spee, C.; Schwaiger, K.; Giedke, G.; Kraus, B.

2018-04-01

We investigate the entanglement of n -mode n -partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique, two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow one to partially order the entanglement contained in states. We show, however, that there are no nontrivial Gaussian LOCC (GLOCC) among pure n -partite (fully entangled) states. That is, any such GLOCC transformation can also be accomplished via GLU. To obtain further insight into the entanglement properties of such GFS, we investigate the richer class of Gaussian stochastic local operations assisted by classical communication (SLOCC). We characterize Gaussian SLOCC classes of pure n -mode n -partite states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set of pure n -mode n -partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure m -mode n -partite (for m >n ) case.

Quadratic reactivity fuel cycle model

International Nuclear Information System (INIS)

Lewins, J.D.

1985-01-01

For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

Quadratic Diophantine equations

CERN Document Server

Andreescu, Titu

2015-01-01

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

Decay rates of Gaussian-type I-balls and Bose-enhancement effects in 3+1 dimensions

International Nuclear Information System (INIS)

Kawasaki, Masahiro; Yamada, Masaki

2014-01-01

I-balls/oscillons are long-lived spatially localized lumps of a scalar field which may be formed after inflation. In the scalar field theory with monomial potential nearly and shallower than quadratic, which is motivated by chaotic inflationary models and supersymmetric theories, the scalar field configuration of I-balls is approximately Gaussian. If the I-ball interacts with another scalar field, the I-ball eventually decays into radiation. Recently, it was pointed out that the decay rate of I-balls increases exponentially by the effects of Bose enhancement under some conditions and a non-perturbative method to compute the exponential growth rate has been derived. In this paper, we apply the method to the Gaussian-type I-ball in 3+1 dimensions assuming spherical symmetry, and calculate the partial decay rates into partial waves, labelled by the angular momentum of daughter particles. We reveal the conditions that the I-ball decays exponentially, which are found to depend on the mass and angular momentum of daughter particles and also be affected by the quantum uncertainty in the momentum of daughter particles

An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...

Quantum information theory with Gaussian systems

Energy Technology Data Exchange (ETDEWEB)

Krueger, O.

2006-04-06

This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)

Quantum information theory with Gaussian systems

International Nuclear Information System (INIS)

Krueger, O.

2006-01-01

This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)

Scalable Gaussian Processes and the search for exoplanets

CERN Multimedia

CERN. Geneva

2015-01-01

Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.

Resource theory of non-Gaussian operations

Science.gov (United States)

Zhuang, Quntao; Shor, Peter W.; Shapiro, Jeffrey H.

2018-05-01

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

Directory of Open Access Journals (Sweden)

Xue-Gang Zhou

2014-01-01

Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

Gaussian density matrices: Quantum analogs of classical states

International Nuclear Information System (INIS)

Mann, A.; Revzen, M.

1993-01-01

We study quantum analogs of clasical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space. (orig.)

Interaction of Airy–Gaussian beams in saturable media

International Nuclear Information System (INIS)

Zhou Meiling; Peng Yulian; Chen Chidao; Chen Bo; Peng Xi; Deng Dongmei

2016-01-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. (paper)

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

Science.gov (United States)

Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

2016-06-27

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Realistic continuous-variable quantum teleportation with non-Gaussian resources

International Nuclear Information System (INIS)

Dell'Anno, F.; De Siena, S.; Illuminati, F.

2010-01-01

We present a comprehensive investigation of nonideal continuous-variable quantum teleportation implemented with entangled non-Gaussian resources. We discuss in a unified framework the main decoherence mechanisms, including imperfect Bell measurements and propagation of optical fields in lossy fibers, applying the formalism of the characteristic function. By exploiting appropriate displacement strategies, we compute analytically the success probability of teleportation for input coherent states and two classes of non-Gaussian entangled resources: two-mode squeezed Bell-like states (that include as particular cases photon-added and photon-subtracted de-Gaussified states), and two-mode squeezed catlike states. We discuss the optimization procedure on the free parameters of the non-Gaussian resources at fixed values of the squeezing and of the experimental quantities determining the inefficiencies of the nonideal protocol. It is found that non-Gaussian resources enhance significantly the efficiency of teleportation and are more robust against decoherence than the corresponding Gaussian ones. Partial information on the alphabet of input states allows further significant improvement in the performance of the nonideal teleportation protocol.

A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

1999-01-01

The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

Quadratic programming with fuzzy parameters: A membership function approach

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

Analytic methods to find beating transitions of asymmetric Gaussian beams in GNLS equations

Science.gov (United States)

Ianetz, David; Schiff, Jeremy

2018-01-01

In a simple model of propagation of asymmetric Gaussian beams in nonlinear waveguides, described by a reduction to ordinary differential equations of generalized nonlinear Schrödinger equations with cubic-quintic (CQ) and saturable (SAT) nonlinearities and a graded-index profile, the beam widths exhibit two different types of beating behavior, with transitions between them. We present an analytic model to explain these phenomena, which originate in a 1:1 resonance in a 2 degree-of-freedom Hamiltonian system. We show how small oscillations near a fixed point close to 1:1 resonance in such a system can be approximated using an integrable Hamiltonian and, ultimately, a single first order differential equation. In particular, the beating transitions can be located from coincidences of roots of a pair of quadratic equations, with coefficients determined (in a highly complex manner) by the internal parameters and initial conditions of the original system. The results of the analytic model agree with the numerics of the original system over large parameter ranges, and allow new predictions that can be verified directly. In the CQ case, we identify a band of beam energies for which there is only a single beating transition (as opposed to 0 or 2) as the eccentricity is increased. In the SAT case, we explain the sudden (dis)appearance of beating transitions for certain values of the other parameters as the grade-index is changed.

A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

KAUST Repository

Dutta, Subhajit

2014-07-28

Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.

A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families

KAUST Repository

Dutta, Subhajit; Genton, Marc G.

2014-01-01

Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.

Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere.

Science.gov (United States)

Eyyuboğlu, Halil Tanyer

2005-08-01

Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.

Stability in quadratic torsion theories

Energy Technology Data Exchange (ETDEWEB)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

2017-11-15

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability in quadratic torsion theories

International Nuclear Information System (INIS)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

2017-01-01

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Cosmological information in Gaussianized weak lensing signals

Science.gov (United States)

Joachimi, B.; Taylor, A. N.; Kiessling, A.

2011-11-01

Gaussianizing the one-point distribution of the weak gravitational lensing convergence has recently been shown to increase the signal-to-noise ratio contained in two-point statistics. We investigate the information on cosmology that can be extracted from the transformed convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimized Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianizing the convergence, but both yield very similar results for the signal-to-noise ratio. None of the transformations is capable of eliminating correlations of the power spectra between different angular frequencies, which we demonstrate to have a significant impact on the errors in cosmology. Analytic models of the Gaussianized power spectrum yield good fits to the simulations and produce unbiased parameter estimates in the majority of cases, where the exceptions can be traced back to the limitations in modelling the higher order correlations of the original convergence. In the ideal case, without galaxy shape noise, we find an increase in the cumulative signal-to-noise ratio by a factor of 2.6 for angular frequencies up to ℓ= 1500, and a decrease in the area of the confidence region in the Ωm-σ8 plane, measured in terms of q-values, by a factor of 4.4 for the best performing transformation. When adding a realistic level of shape noise, all transformations perform poorly with little decorrelation of angular frequencies, a maximum increase in signal-to-noise ratio of 34 per cent, and even slightly degraded errors on cosmological parameters. We argue that to find Gaussianizing transformations of practical use, it will be necessary to go beyond transformations of the one-point distribution of the convergence, extend the analysis deeper into the non

Visualising the Complex Roots of Quadratic Equations with Real Coefficients

Science.gov (United States)

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…

Non normal and non quadratic anisotropic plasticity coupled with ductile damage in sheet metal forming: Application to the hydro bulging test

International Nuclear Information System (INIS)

Badreddine, Houssem; Saanouni, Khemaies; Dogui, Abdelwaheb

2007-01-01

In this work an improved material model is proposed that shows good agreement with experimental data for both hardening curves and plastic strain ratios in uniaxial and equibiaxial proportional loading paths for steel metal until the final fracture. This model is based on non associative and non normal flow rule using two different orthotropic equivalent stresses in both yield criterion and plastic potential functions. For the plastic potential the classical Hill 1948 quadratic equivalent stress is considered while for the yield criterion the Karafillis and Boyce 1993 non quadratic equivalent stress is used taking into account the non linear mixed (kinematic and isotropic) hardening. Applications are made to hydro bulging tests using both circular and elliptical dies. The results obtained with different particular cases of the model such as the normal quadratic and the non normal non quadratic cases are compared and discussed with respect to the experimental results

An example in linear quadratic optimal control

NARCIS (Netherlands)

Weiss, George; Zwart, Heiko J.

1998-01-01

We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

Radiotherapy treatment planning linear-quadratic radiobiology

CERN Document Server

Chapman, J Donald

2015-01-01

Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

Expert Strategies in Solving Algebraic Structure Sense Problems: The Case of Quadratic Equations

Science.gov (United States)

Jupri, Al; Sispiyati, R.

2017-02-01

Structure sense, an intuitive ability towards symbolic expressions, including skills to interpret, to manipulate, and to perceive symbols in different roles, is considered as a key success in learning algebra. In this article, we report results of three phases of a case study on solving algebraic structure sense problems aiming at testing the appropriateness of algebraic structure sense tasks and at investigating expert strategies dealing with the tasks. First, we developed three tasks on quadratic equations based on the characteristics of structure sense for high school algebra. Next, we validated the tasks to seven experts. In the validation process, we requested these experts to solve each task using two different strategies. Finally, we analyzing expert solution strategies in the light of structure sense characteristics. We found that even if eventual expert strategies are in line with the characteristics of structure sense; some of their initial solution strategies used standard procedures which might pay less attention to algebraic structures. This finding suggests that experts have reconsidered their procedural work and have provided more efficient solution strategies. For further investigation, we consider to test the tasks to high school algebra students and to see whether they produce similar results as experts.

Partial summations of stationary sequences of non-Gaussian random variables

DEFF Research Database (Denmark)

Mohr, Gunnar; Ditlevsen, Ove Dalager

1996-01-01

The distribution of the sum of a finite number of identically distributed random variables is in many cases easily determined given that the variables are independent. The moments of any order of the sum can always be expressed by the moments of the single term without computational problems...... of convergence of the distribution of a sum (or an integral) of mutually dependent random variables to the Gaussian distribution. The paper is closely related to the work in Ditlevsen el al. [Ditlevsen, O., Mohr, G. & Hoffmeyer, P. Integration of non-Gaussian fields. Prob. Engng Mech 11 (1996) 15-23](2)....... lognormal variables or polynomials of standard Gaussian variables. The dependency structure is induced by specifying the autocorrelation structure of the sequence of standard Gaussian variables. Particularly useful polynomials are the Winterstein approximations that distributionally fit with non...

Invariant measures on multimode quantum Gaussian states

Science.gov (United States)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-12-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Invariant measures on multimode quantum Gaussian states

International Nuclear Information System (INIS)

Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.

2012-01-01

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom—the symplectic eigenvalues—which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Invariant measures on multimode quantum Gaussian states

Energy Technology Data Exchange (ETDEWEB)

Lupo, C. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Mancini, S. [School of Science and Technology, Universita di Camerino, I-62032 Camerino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia (Italy); De Pasquale, A. [NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy); Facchi, P. [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Florio, G. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Piazza del Viminale 1, I-00184 Roma (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); Pascazio, S. [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy)

2012-12-15

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom-the symplectic eigenvalues-which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

Science.gov (United States)

Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

2016-03-01

To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

International Nuclear Information System (INIS)

Mestel, B D; Osbaldestin, A H

2004-01-01

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case

A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

Energy Technology Data Exchange (ETDEWEB)

Mestel, B D [Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA (United Kingdom); Osbaldestin, A H [Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HE (United Kingdom)

2004-10-01

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.

Quadratic independence of coordinate functions of certain ...

Indian Academy of Sciences (India)

... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

Estimators for local non-Gaussianities

International Nuclear Information System (INIS)

Creminelli, P.; Senatore, L.; Zaldarriaga, M.

2006-05-01

We study the Likelihood function of data given f NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f NL and show that for small values of f NL the 3- point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f NL , the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f NL only decrease as 1/ln N pix rather than N pix -1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non- Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as N pix -1/2 even for large f NL , asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f NL . In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f NL . (author)

A generalization of Baker's quadratic formulae for hyperelliptic p-functions

International Nuclear Information System (INIS)

Athorne, Chris

2011-01-01

We present a generalization of a compact form, due to Baker, for quadratic identities satisfied by the three-index p-functions on curves of genus g=2, and a further generalization of a new result in genus g=3. The compact forms involve a bordered determinant containing 2(g-1)(g+1) free parameters. -- Highlights: → Properties of Weierstrass P-functions for hyperelliptic curves. → Generalization of result of H.F. Baker for genus two case. → Compact formulae with maximal number of parameters in genus two and three cases.

Analysis of multi-species point patterns using multivariate log Gaussian Cox processes

DEFF Research Database (Denmark)

Waagepetersen, Rasmus; Guan, Yongtao; Jalilian, Abdollah

Multivariate log Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far only been applied in bivariate cases. In this paper we move beyond the bivariate case in order to model multi-species point patterns of tree locations. In particular we address t...... of the data. The selected number of common latent fields provides an index of complexity of the multivariate covariance structure. Hierarchical clustering is used to identify groups of species with similar patterns of dependence on the common latent fields.......Multivariate log Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far only been applied in bivariate cases. In this paper we move beyond the bivariate case in order to model multi-species point patterns of tree locations. In particular we address...... the problems of identifying parsimonious models and of extracting biologically relevant information from the fitted models. The latent multivariate Gaussian field is decomposed into components given in terms of random fields common to all species and components which are species specific. This allows...

Exact cancellation of quadratic divergences in top condensation models

International Nuclear Information System (INIS)

Blumhofer, A.

1995-01-01

We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

International Nuclear Information System (INIS)

Aquilanti, V; Marinelli, D; Marzuoli, A

2014-01-01

Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed

Equation for disentangling time-ordered exponentials with arbitrary quadratic generators

International Nuclear Information System (INIS)

Budanov, V.G.

1987-01-01

In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function

Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

African Journals Online (AJOL)

Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

Off-Axis Gaussian Beams with Random Displacement in Atmospheric Turbulence

Directory of Open Access Journals (Sweden)

Yahya Baykal

2006-10-01

Full Text Available Our recent work in which we study the propagation of the general Hermite-sinusoidal-Gaussian laser beams in wireless broadband access telecommunication systems is elaborated in this paper to cover the special case of an off-axis Gaussian beam. We mainly investigate the propagation characteristics in atmospheric turbulence of an off-axis Gaussian beam possessing Gaussian distributed random displacement parameters. Our interest is to search for different types of laser beams that will improve the performance of a wireless broadband access system when atmospheric turbulence is considered. Our formulation is based on the basic solution of the second order mutual coherence function evaluated at the receiver plane. For fixed turbulence strength, the coherence length calculated at the receiver plane is found to decrease as the variance of the random displacement is increased. It is shown that as the turbulence becomes stronger, coherence lengths due to off-axis Gaussian beams tend to approach the same value, irrespective of the variance of the random displacement. As expected, the beam spreading is found to be pronounced for larger variance of displacement parameter. Average intensity profiles when atmospheric turbulence is present are plotted for different values of the variance of the random displacement parameter of the off-axis Gaussian beam.

GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.

Science.gov (United States)

Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi

2017-05-24

As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.

Teleportation of squeezing: Optimization using non-Gaussian resources

International Nuclear Information System (INIS)

Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio; Adesso, Gerardo

2010-01-01

We study the continuous-variable quantum teleportation of states, statistical moments of observables, and scale parameters such as squeezing. We investigate the problem both in ideal and imperfect Vaidman-Braunstein-Kimble protocol setups. We show how the teleportation fidelity is maximized and the difference between output and input variances is minimized by using suitably optimized entangled resources. Specifically, we consider the teleportation of coherent squeezed states, exploiting squeezed Bell states as entangled resources. This class of non-Gaussian states, introduced by Illuminati and co-workers [F. Dell'Anno, S. De Siena, L. Albano, and F. Illuminati, Phys. Rev. A 76, 022301 (2007); F. Dell'Anno, S. De Siena, and F. Illuminati, ibid. 81, 012333 (2010)], includes photon-added and photon-subtracted squeezed states as special cases. At variance with the case of entangled Gaussian resources, the use of entangled non-Gaussian squeezed Bell resources allows one to choose different optimization procedures that lead to inequivalent results. Performing two independent optimization procedures, one can either maximize the state teleportation fidelity, or minimize the difference between input and output quadrature variances. The two different procedures are compared depending on the degrees of displacement and squeezing of the input states and on the working conditions in ideal and nonideal setups.

Solitons in quadratic nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2001-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1981-01-01

Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

Quadratic gravity in first order formalism

Energy Technology Data Exchange (ETDEWEB)

Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)

2017-10-01

We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

Science.gov (United States)

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…

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

Time-optimal thermalization of single-mode Gaussian states

Science.gov (United States)

Carlini, Alberto; Mari, Andrea; Giovannetti, Vittorio

2014-11-01

We consider the problem of time-optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one-mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e., arbitrary phase rotations, bounded squeezing, and unlimited displacements. In the ideal ansatz of unconstrained quantum control (i.e., when the unitary phase rotations, squeezing, and displacement of the mode can be performed instantaneously), we study how control can be optimized for speeding up the relaxation towards the fixed point of the dynamics and we analytically derive the optimal relaxation time. Our model has potential and interesting applications to the control of modes of electromagnetic radiation and of trapped levitated nanospheres.

A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems

Energy Technology Data Exchange (ETDEWEB)

Weerakkody, Sean [Carnegie Mellon Univ., Pittsburgh, PA (United States); Ozel, Omur [Carnegie Mellon Univ., Pittsburgh, PA (United States); Sinopoli, Bruno [Carnegie Mellon Univ., Pittsburgh, PA (United States)

2017-11-02

We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the other hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.

Bound constrained quadratic programming via piecewise

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.

1999-01-01

of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...

Analysis of regularized inversion of data corrupted by white Gaussian noise

International Nuclear Information System (INIS)

Kekkonen, Hanne; Lassas, Matti; Siltanen, Samuli

2014-01-01

Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function u(x) is m(x) = Au(x) + δ ε (x), where δ > 0 is the noise magnitude. If ε was an L 2 -function, Tikhonov regularization gives an estimate T α (m) = u∈H r arg min { ||Au-m|| L 2 2 + α||u|| H r 2 } for u where α = α(δ) is the regularization parameter. Here penalization of the Sobolev norm ||u|| H r covers the cases of standard Tikhonov regularization (r = 0) and first derivative penalty (r = 1). Realizations of white Gaussian noise are almost never in L 2 , but do belong to H s with probability one if s < 0 is small enough. A modification of Tikhonov regularization theory is presented, covering the case of white Gaussian measurement noise. Furthermore, the convergence of regularized reconstructions to the correct solution as δ → 0 is proven in appropriate function spaces using microlocal analysis. The convergence of the related finite-dimensional problems to the infinite-dimensional problem is also analysed. (paper)

AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

International Nuclear Information System (INIS)

2005-01-01

Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Vortices in Gaussian beams

CSIR Research Space (South Africa)

Roux, FS

2009-01-01

Full Text Available , t0)} = P(du, dv) {FR{g(u, v, t0)}} Replacement: u→ du = t− t0 i2 ∂ ∂u′ v → dv = t− t0 i2 ∂ ∂v′ CSIR National Laser Centre – p.13/30 Differentiation i.s.o integration Evaluate the integral over the Gaussian beam (once and for all). Then, instead... . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...

AUTONOMOUS GAUSSIAN DECOMPOSITION

International Nuclear Information System (INIS)

Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John

2015-01-01

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes

AUTONOMOUS GAUSSIAN DECOMPOSITION

Energy Technology Data Exchange (ETDEWEB)

Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)

2015-04-15

We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.

Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

KAUST Repository

Yan, Yuan; Genton, Marc G.

2017-01-01

Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.

Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

KAUST Repository

Yan, Yuan

2017-07-13

Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.

Renormalization of correlations in a quasiperiodically forced two-level system: quadratic irrationals

International Nuclear Information System (INIS)

Mestel, B D; Osbaldestin, A H

2004-01-01

Generalizing from the case of golden mean frequency to a wider class of quadratic irrationals, we extend our renormalization analysis of the self-similarity of correlation functions in a quasiperiodically forced two-level system. We give a description of all piecewise-constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case. We establish a criterion for periodic orbits to be globally bounded, and also calculate the asymptotic height of the main peaks in the correlation function

Teleportation of squeezing: Optimization using non-Gaussian resources

Science.gov (United States)

Dell'Anno, Fabio; de Siena, Silvio; Adesso, Gerardo; Illuminati, Fabrizio

2010-12-01

We study the continuous-variable quantum teleportation of states, statistical moments of observables, and scale parameters such as squeezing. We investigate the problem both in ideal and imperfect Vaidman-Braunstein-Kimble protocol setups. We show how the teleportation fidelity is maximized and the difference between output and input variances is minimized by using suitably optimized entangled resources. Specifically, we consider the teleportation of coherent squeezed states, exploiting squeezed Bell states as entangled resources. This class of non-Gaussian states, introduced by Illuminati and co-workers [F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.022301 76, 022301 (2007); F. Dell’Anno, S. De Siena, and F. Illuminati, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.81.012333 81, 012333 (2010)], includes photon-added and photon-subtracted squeezed states as special cases. At variance with the case of entangled Gaussian resources, the use of entangled non-Gaussian squeezed Bell resources allows one to choose different optimization procedures that lead to inequivalent results. Performing two independent optimization procedures, one can either maximize the state teleportation fidelity, or minimize the difference between input and output quadrature variances. The two different procedures are compared depending on the degrees of displacement and squeezing of the input states and on the working conditions in ideal and nonideal setups.

Orthogonal and Scaling Transformations of Quadratic Functions with ...

African Journals Online (AJOL)

In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

Geometry of Gaussian quantum states

International Nuclear Information System (INIS)

Link, Valentin; Strunz, Walter T

2015-01-01

We study the Hilbert–Schmidt measure on the manifold of mixed Gaussian states in multi-mode continuous variable quantum systems. An analytical expression for the Hilbert–Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert–Schmidt measure. (paper)

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

Science.gov (United States)

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems

A Quadratic Spring Equation

Science.gov (United States)

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]…

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

On orthogonality preserving quadratic stochastic operators

Energy Technology Data Exchange (ETDEWEB)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

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.

On orthogonality preserving quadratic stochastic operators

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-01-01

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

Quadratic Twists of Rigid Calabi–Yau Threefolds Over

DEFF Research Database (Denmark)

Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

2013-01-01

of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

Chimera states in Gaussian coupled map lattices

Science.gov (United States)

Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian

2018-04-01

We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.

Extended Linear Models with Gaussian Priors

DEFF Research Database (Denmark)

Quinonero, Joaquin

2002-01-01

In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....

On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

Hybrid algorithm of ensemble transform and importance sampling for assimilation of non-Gaussian observations

Directory of Open Access Journals (Sweden)

Shin'ya Nakano

2014-05-01

Full Text Available A hybrid algorithm that combines the ensemble transform Kalman filter (ETKF and the importance sampling approach is proposed. Since the ETKF assumes a linear Gaussian observation model, the estimate obtained by the ETKF can be biased in cases with nonlinear or non-Gaussian observations. The particle filter (PF is based on the importance sampling technique, and is applicable to problems with nonlinear or non-Gaussian observations. However, the PF usually requires an unrealistically large sample size in order to achieve a good estimation, and thus it is computationally prohibitive. In the proposed hybrid algorithm, we obtain a proposal distribution similar to the posterior distribution by using the ETKF. A large number of samples are then drawn from the proposal distribution, and these samples are weighted to approximate the posterior distribution according to the importance sampling principle. Since the importance sampling provides an estimate of the probability density function (PDF without assuming linearity or Gaussianity, we can resolve the bias due to the nonlinear or non-Gaussian observations. Finally, in the next forecast step, we reduce the sample size to achieve computational efficiency based on the Gaussian assumption, while we use a relatively large number of samples in the importance sampling in order to consider the non-Gaussian features of the posterior PDF. The use of the ETKF is also beneficial in terms of the computational simplicity of generating a number of random samples from the proposal distribution and in weighting each of the samples. The proposed algorithm is not necessarily effective in case that the ensemble is located distant from the true state. However, monitoring the effective sample size and tuning the factor for covariance inflation could resolve this problem. In this paper, the proposed hybrid algorithm is introduced and its performance is evaluated through experiments with non-Gaussian observations.

The Model and Quadratic Stability Problem of Buck Converter in DCM

Directory of Open Access Journals (Sweden)

Li Xiaojing

2016-01-01

Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.

Operator-sum representation for bosonic Gaussian channels

International Nuclear Information System (INIS)

Ivan, J. Solomon; Sabapathy, Krishna Kumar; Simon, R.

2011-01-01

Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted D(κ) in the Holevo classification. The matrix transposition channels D(κ), D(κ -1 ) turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor κ and the beam-splitter channel with attenuation factor κ -1 turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank 1 Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of

Treatment of non-Gaussian tails of multiple Coulomb scattering in track fitting with a Gaussian-sum filter

International Nuclear Information System (INIS)

Strandlie, A.; Wroldsen, J.

2006-01-01

If any of the probability densities involved in track fitting deviate from the Gaussian assumption, it is plausible that a non-linear estimator which better takes the actual shape of the distribution into account can do better. One such non-linear estimator is the Gaussian-sum filter, which is adequate if the distributions under consideration can be approximated by Gaussian mixtures. The main purpose of this paper is to present a Gaussian-sum filter for track fitting, based on a two-component approximation of the distribution of angular deflections due to multiple scattering. In a simulation study within a linear track model the Gaussian-sum filter is shown to be a competitive alternative to the Kalman filter. Scenarios at various momenta and with various maximum number of components in the Gaussian-sum filter are considered. Particularly at low momenta the Gaussian-sum filter yields a better estimate of the uncertainties than the Kalman filter, and it is also slightly more precise than the latter

Palm distributions for log Gaussian Cox processes

DEFF Research Database (Denmark)

Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus Plenge

2017-01-01

This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new...... result is used to study functional summaries for log Gaussian Cox processes....

High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.

Science.gov (United States)

Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei

2017-07-01

Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.

Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition

Science.gov (United States)

Huo, Xiaoming; Elad, Michael; Flesia, Ana G.; Muise, Robert R.; Stanfill, S. Robert; Friedman, Jerome; Popescu, Bogdan; Chen, Jihong; Mahalanobis, Abhijit; Donoho, David L.

2003-09-01

In target recognition applications of discriminant of classification analysis, each 'feature' is a result of a convolution of an imagery with a filter, which may be derived from a feature vector. It is important to use relatively few features. We analyze an optimal reduced-rank classifier under the two-class situation. Assuming each population is Gaussian and has zero mean, and the classes differ through the covariance matrices: ∑1 and ∑2. The following matrix is considered: Λ=(∑1+∑2)-1/2∑1(∑1+∑2)-1/2. We show that the k eigenvectors of this matrix whose eigenvalues are most different from 1/2 offer the best rank k approximation to the maximum likelihood classifier. The matrix Λ and its eigenvectors have been introduced by Fukunaga and Koontz; hence this analysis gives a new interpretation of the well known Fukunaga-Koontz transform. The optimality that is promised in this method hold if the two populations are exactly Guassian with the same means. To check the applicability of this approach to real data, an experiment is performed, in which several 'modern' classifiers were used on an Infrared ATR data. In these experiments, a reduced-rank classifier-Tuned Basis Functions-outperforms others. The competitive performance of the optimal reduced-rank quadratic classifier suggests that, at least for classification purposes, the imagery data behaves in a nearly-Gaussian fashion.

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2002-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2003-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2004-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Linear quadratic optimization for positive LTI system

Science.gov (United States)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Directory of Open Access Journals (Sweden)

Madjid Eshaghi Gordji

2012-01-01

Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

Comparison between linear quadratic and early time dose models

International Nuclear Information System (INIS)

Chougule, A.A.; Supe, S.J.

1993-01-01

During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

Science.gov (United States)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

Guises and disguises of quadratic divergences

Energy Technology Data Exchange (ETDEWEB)

Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

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.

PSQP: Puzzle Solving by Quadratic Programming.

Science.gov (United States)

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.

Visualising the Roots of Quadratic Equations with Complex Coefficients

Science.gov (United States)

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…

Non-Gaussianity and cross-scale coupling in interplanetary magnetic field turbulence during a rope-rope magnetic reconnection event

Science.gov (United States)

Miranda, Rodrigo A.; Schelin, Adriane B.; Chian, Abraham C.-L.; Ferreira, José L.

2018-03-01

In a recent paper (Chian et al., 2016) it was shown that magnetic reconnection at the interface region between two magnetic flux ropes is responsible for the genesis of interplanetary intermittent turbulence. The normalized third-order moment (skewness) and the normalized fourth-order moment (kurtosis) display a quadratic relation with a parabolic shape that is commonly observed in observational data from turbulence in fluids and plasmas, and is linked to non-Gaussian fluctuations due to coherent structures. In this paper we perform a detailed study of the relation between the skewness and the kurtosis of the modulus of the magnetic field |B| during a triple interplanetary magnetic flux rope event. In addition, we investigate the skewness-kurtosis relation of two-point differences of |B| for the same event. The parabolic relation displays scale dependence and is found to be enhanced during magnetic reconnection, rendering support for the generation of non-Gaussian coherent structures via rope-rope magnetic reconnection. Our results also indicate that a direct coupling between the scales of magnetic flux ropes and the scales within the inertial subrange occurs in the solar wind.

On the Computation of Optimal Monotone Mean-Variance Portfolios via Truncated Quadratic Utility

OpenAIRE

Ales Cerný; Fabio Maccheroni; Massimo Marinacci; Aldo Rustichini

2008-01-01

We report a surprising link between optimal portfolios generated by a special type of variational preferences called divergence preferences (cf. [8]) and optimal portfolios generated by classical expected utility. As a special case we connect optimization of truncated quadratic utility (cf. [2]) to the optimal monotone mean-variance portfolios (cf. [9]), thus simplifying the computation of the latter.

Breaking Gaussian incompatibility on continuous variable quantum systems

Energy Technology Data Exchange (ETDEWEB)

Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk [Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ (United Kingdom); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)

2015-08-15

We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.

Interaction of Airy-Gaussian beams in saturable media

Science.gov (United States)

Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei

2016-08-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy-Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy-Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy-Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.

Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

DEFF Research Database (Denmark)

Sørensen, Dan Erik Krarup

1996-01-01

We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

Scale-Invariant Rotating Black Holes in Quadratic Gravity

Directory of Open Access Journals (Sweden)

Guido Cognola

2015-07-01

Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

Learning non-Gaussian Time Series using the Box-Cox Gaussian Process

OpenAIRE

Rios, Gonzalo; Tobar, Felipe

2018-01-01

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired with an expressive covariance kernel and then fed into a nonlinear transformation (or warping). However, overparametrising the kernel and the warping is known to, respectively, hin...

Parametric estimation of covariance function in Gaussian-process based Kriging models. Application to uncertainty quantification for computer experiments

International Nuclear Information System (INIS)

Bachoc, F.

2013-01-01

The parametric estimation of the covariance function of a Gaussian process is studied, in the framework of the Kriging model. Maximum Likelihood and Cross Validation estimators are considered. The correctly specified case, in which the covariance function of the Gaussian process does belong to the parametric set used for estimation, is first studied in an increasing-domain asymptotic framework. The sampling considered is a randomly perturbed multidimensional regular grid. Consistency and asymptotic normality are proved for the two estimators. It is then put into evidence that strong perturbations of the regular grid are always beneficial to Maximum Likelihood estimation. The incorrectly specified case, in which the covariance function of the Gaussian process does not belong to the parametric set used for estimation, is then studied. It is shown that Cross Validation is more robust than Maximum Likelihood in this case. Finally, two applications of the Kriging model with Gaussian processes are carried out on industrial data. For a validation problem of the friction model of the thermal-hydraulic code FLICA 4, where experimental results are available, it is shown that Gaussian process modeling of the FLICA 4 code model error enables to considerably improve its predictions. Finally, for a meta modeling problem of the GERMINAL thermal-mechanical code, the interest of the Kriging model with Gaussian processes, compared to neural network methods, is shown. (author) [fr

A non-Gaussian approach to risk measures

Science.gov (United States)

Bormetti, Giacomo; Cisana, Enrica; Montagna, Guido; Nicrosini, Oreste

2007-03-01

Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modelling the power-law tails of the returns distribution in terms of a Student- t distribution. Non-Gaussian closed-form solutions for value-at-risk and expected shortfall are obtained and standard formulae known in the literature under the normality assumption are recovered as a special case. The implications of the approach for risk management are demonstrated through an empirical analysis of financial time series from the Italian stock market and in comparison with the results of the most widely used procedures of quantitative finance. Particular attention is paid to quantify the size of the errors affecting the market risk measures obtained according to different methodologies, by employing a bootstrap technique.

Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models

Science.gov (United States)

Wen, Xian-Huan; Gómez-Hernández, J. Jaime

1998-03-01

The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than

Geometric Approaches to Quadratic Equations from Other Times and Places.

Science.gov (United States)

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)

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

Directory of Open Access Journals (Sweden)

Park Choonkil

2011-01-01

Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

Non-Gaussian halo assembly bias

International Nuclear Information System (INIS)

Reid, Beth A.; Verde, Licia; Dolag, Klaus; Matarrese, Sabino; Moscardini, Lauro

2010-01-01

The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f NL , offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ∼ 23% and ∼ 48% for galaxies at z = 1 selected by stellar mass and star formation rate, respectively

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

Science.gov (United States)

Jacquet, O.; Leymarie, N.; Cassereau, D.

2018-05-01

The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.

Area of isodensity contours in Gaussian and non-Gaussian fields

International Nuclear Information System (INIS)

Ryden, B.S.

1988-01-01

The area of isodensity contours in a smoothed density field can be measured by the contour-crossing statistic N1, the number of times per unit length that a line drawn through the density field pierces an isodensity contour. The contour-crossing statistic distinguishes between Gaussian and non-Gaussian fields and provides a measure of the effective slope of the power spectrum. The statistic is easy to apply and can be used on pencil beams and slices as well as on a three-dimensional field. 10 references

Analysis of Students' Error in Learning of Quadratic Equations

Science.gov (United States)

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…

Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

Directory of Open Access Journals (Sweden)

Javier Amezcua

2014-09-01

Full Text Available The analysis step of the (ensemble Kalman filter is optimal when (1 the distribution of the background is Gaussian, (2 state variables and observations are related via a linear operator, and (3 the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state-variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1–(3 are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

Lambda-lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, O.; Schultz, U.P.

2004-01-01

-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

Sketching the General Quadratic Equation Using Dynamic Geometry Software

Science.gov (United States)

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…

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

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.)

Case studies in Gaussian process modelling of computer codes

International Nuclear Information System (INIS)

Kennedy, Marc C.; Anderson, Clive W.; Conti, Stefano; O'Hagan, Anthony

2006-01-01

In this paper we present a number of recent applications in which an emulator of a computer code is created using a Gaussian process model. Tools are then applied to the emulator to perform sensitivity analysis and uncertainty analysis. Sensitivity analysis is used both as an aid to model improvement and as a guide to how much the output uncertainty might be reduced by learning about specific inputs. Uncertainty analysis allows us to reflect output uncertainty due to unknown input parameters, when the finished code is used for prediction. The computer codes themselves are currently being developed within the UK Centre for Terrestrial Carbon Dynamics

Predictive Active Set Selection Methods for Gaussian Processes

DEFF Research Database (Denmark)

Henao, Ricardo; Winther, Ole

2012-01-01

We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal...... high impact to the classifier decision process while removing those that are less relevant. We introduce two active set rules based on different criteria, the first one prefers a model with interpretable active set parameters whereas the second puts computational complexity first, thus a model...... with active set parameters that directly control its complexity. We also provide both theoretical and empirical support for our active set selection strategy being a good approximation of a full Gaussian process classifier. Our extensive experiments show that our approach can compete with state...

Impurity solitons with quadratic nonlinearities

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

1998-01-01

We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

Entanglement concentration for two-mode Gaussian states in non-inertial frames

International Nuclear Information System (INIS)

Di Noia, Maurizio; Giraldi, Filippo; Petruccione, Francesco

2017-01-01

Entanglement creation and concentration by means of a beam splitter (BS) is analysed for a generic two-mode bipartite Gaussian state in a relativistic framework. The total correlations, the purity and the entanglement in terms of logarithmic negativity are analytically studied for observers in an inertial state and in a non-inertial state of uniform acceleration. The dependence of entanglement on the BS transmissivity due to the Unruh effect is analysed in the case when one or both observers undergo uniform acceleration. Due to the Unruh effect, depending on the initial Gaussian state parameters and observed accelerations, the best condition for entanglement generation limited to the two modes of the observers in their regions is not always a balanced beam splitter, as it is for the inertial case. (paper)

Cascaded Quadratic Soliton Compression in Waveguide Structures

DEFF Research Database (Denmark)

Guo, Hairun

between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

Calculations of Sobol indices for the Gaussian process metamodel

Energy Technology Data Exchange (ETDEWEB)

Marrel, Amandine [CEA, DEN, DTN/SMTM/LMTE, F-13108 Saint Paul lez Durance (France)], E-mail: amandine.marrel@cea.fr; Iooss, Bertrand [CEA, DEN, DER/SESI/LCFR, F-13108 Saint Paul lez Durance (France); Laurent, Beatrice [Institut de Mathematiques, Universite de Toulouse (UMR 5219) (France); Roustant, Olivier [Ecole des Mines de Saint-Etienne (France)

2009-03-15

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well-known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling.

Calculations of Sobol indices for the Gaussian process metamodel

International Nuclear Information System (INIS)

Marrel, Amandine; Iooss, Bertrand; Laurent, Beatrice; Roustant, Olivier

2009-01-01

Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model evaluations, are often unacceptable for time expensive computer codes. A well-known and widely used decision consists in replacing the computer code by a metamodel, predicting the model responses with a negligible computation time and rending straightforward the estimation of Sobol indices. In this paper, we discuss about the Gaussian process model which gives analytical expressions of Sobol indices. Two approaches are studied to compute the Sobol indices: the first based on the predictor of the Gaussian process model and the second based on the global stochastic process model. Comparisons between the two estimates, made on analytical examples, show the superiority of the second approach in terms of convergence and robustness. Moreover, the second approach allows to integrate the modeling error of the Gaussian process model by directly giving some confidence intervals on the Sobol indices. These techniques are finally applied to a real case of hydrogeological modeling

An approximate fractional Gaussian noise model with computational cost

KAUST Repository

Sørbye, Sigrunn H.

2017-09-18

Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

Science.gov (United States)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

A Trust-region-based Sequential Quadratic Programming Algorithm

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

1995-01-01

The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

Gaussian variable neighborhood search for the file transfer scheduling problem

Directory of Open Access Journals (Sweden)

Dražić Zorica

2016-01-01

Full Text Available This paper presents new modifications of Variable Neighborhood Search approach for solving the file transfer scheduling problem. To obtain better solutions in a small neighborhood of a current solution, we implement two new local search procedures. As Gaussian Variable Neighborhood Search showed promising results when solving continuous optimization problems, its implementation in solving the discrete file transfer scheduling problem is also presented. In order to apply this continuous optimization method to solve the discrete problem, mapping of uncountable set of feasible solutions into a finite set is performed. Both local search modifications gave better results for the large size instances, as well as better average performance for medium and large size instances. One local search modification achieved significant acceleration of the algorithm. The numerical experiments showed that the results obtained by Gaussian modifications are comparable with the results obtained by standard VNS based algorithms, developed for combinatorial optimization. In some cases Gaussian modifications gave even better results. [Projekat Ministarstava nauke Republike Srbije, br. 174010

Application of Gaussian cubature to model two-dimensional population balances

Directory of Open Access Journals (Sweden)

Bałdyga Jerzy

2017-09-01

Full Text Available In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

Analytic matrix elements with shifted correlated Gaussians

DEFF Research Database (Denmark)

Fedorov, D. V.

2017-01-01

Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....

Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data

DEFF Research Database (Denmark)

Bennedsen, Mikkel

Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, α, of a time series. Our setup encompasses a large class of Gaussian...

A Gaussian mixture copula model based localized Gaussian process regression approach for long-term wind speed prediction

International Nuclear Information System (INIS)

Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.

2013-01-01

Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability

Equivalent non-Gaussian excitation method for response moment calculation of systems under non-Gaussian random excitation

International Nuclear Information System (INIS)

Tsuchida, Takahiro; Kimura, Koji

2015-01-01

Equivalent non-Gaussian excitation method is proposed to obtain the moments up to the fourth order of the response of systems under non-Gaussian random excitation. The excitation is prescribed by the probability density and power spectrum. Moment equations for the response can be derived from the stochastic differential equations for the excitation and the system. However, the moment equations are not closed due to the nonlinearity of the diffusion coefficient in the equation for the excitation. In the proposed method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by the second-order polynomial. In order to demonstrate the validity of the method, a linear system to non-Gaussian excitation with generalized Gaussian distribution is analyzed. The results show the method is applicable to non-Gaussian excitation with the widely different kurtosis and bandwidth. (author)

Entanglement in Gaussian matrix-product states

International Nuclear Information System (INIS)

Adesso, Gerardo; Ericsson, Marie

2006-01-01

Gaussian matrix-product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of a harmonic chain. Replacing the projections by associated Gaussian states, the building blocks, we show that the entanglement range in translationally invariant Gaussian matrix-product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix-product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds (M=1). Finally we discuss how these states can be experimentally engineered from N copies of a three-mode building block and N two-mode finitely squeezed states

The quadratic reciprocity law a collection of classical proofs

CERN Document Server

Baumgart, Oswald

2015-01-01

This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

International Nuclear Information System (INIS)

Aristov, Anatoly I

2011-01-01

We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

International Nuclear Information System (INIS)

Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong

2009-01-01

The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation

Non-Gaussianity from isocurvature perturbations

Energy Technology Data Exchange (ETDEWEB)

Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)

2008-11-15

We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.

Rate-distortion in Closed-Loop LTI Systems

DEFF Research Database (Denmark)

Silva, Eduardo; Derpich, Milan; Østergaard, Jan

2013-01-01

We consider a networked LTI system subject to an average data-rate constraint in the feedback path.We provide upper bounds to the minimal source coding rate required to achieve mean square stability and a desired level of performance. In the quadratic Gaussian case, an almost complete rate...

Multipoint propagators for non-Gaussian initial conditions

International Nuclear Information System (INIS)

Bernardeau, Francis; Sefusatti, Emiliano; Crocce, Martin

2010-01-01

We show here how renormalized perturbation theory calculations applied to the quasilinear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce, and Scoccimarro [Phys. Rev. D 78, 103521 (2008)] is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher-order spectra and is based on a reorganization of the contributing terms into the sum of products of multipoint propagators. In case of PNG, new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multipoint propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespective of statistical properties of the initial field. We furthermore show that the high-momentum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multipoint propagators for Gaussian initial conditions. Numerical forms of the cutoff are shown for the so-called local model of PNG.

On quadratic variation of martingales

Indian Academy of Sciences (India)

On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

Quadratic prediction of factor scores

NARCIS (Netherlands)

Wansbeek, T

1999-01-01

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

The regular indefinite linear-quadratic problem with linear endpoint constraints

NARCIS (Netherlands)

Soethoudt, J.M.; Trentelman, H.L.

1989-01-01

This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that

Gaussian capacity of the quantum bosonic memory channel with additive correlated Gaussian noise

International Nuclear Information System (INIS)

Schaefer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.

2011-01-01

We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schaefer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90% of the capacity.

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

Science.gov (United States)

Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

2015-01-01

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating

The bounds of feasible space on constrained nonconvex quadratic programming

Science.gov (United States)

Zhu, Jinghao

2008-03-01

This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

Searching for non-Gaussianity in the WMAP data

International Nuclear Information System (INIS)

Bernui, A.; Reboucas, M. J.

2009-01-01

Some analyses of recent cosmic microwave background (CMB) data have provided hints that there are deviations from Gaussianity in the WMAP CMB temperature fluctuations. Given the far-reaching consequences of such a non-Gaussianity for our understanding of the physics of the early universe, it is important to employ alternative indicators in order to determine whether the reported non-Gaussianity is of cosmological origin, and/or extract further information that may be helpful for identifying its causes. We propose two new non-Gaussianity indicators, based on skewness and kurtosis of large-angle patches of CMB maps, which provide a measure of departure from Gaussianity on large angular scales. A distinctive feature of these indicators is that they provide sky maps of non-Gaussianity of the CMB temperature data, thus allowing a possible additional window into their origins. Using these indicators, we find no significant deviation from Gaussianity in the three and five-year WMAP Internal Linear Combination (ILC) map with KQ75 mask, while the ILC unmasked map exhibits deviation from Gaussianity, quantifying therefore the WMAP team recommendation to employ the new mask KQ75 for tests of Gaussianity. We also use our indicators to test for Gaussianity the single frequency foreground unremoved WMAP three and five-year maps, and show that the K and Ka maps exhibit a clear indication of deviation from Gaussianity even with the KQ75 mask. We show that our findings are robust with respect to the details of the method.

Remarks on second-order quadratic systems in algebras

Directory of Open Access Journals (Sweden)

Art Sagle

2017-10-01

Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

Estimating sample size for a small-quadrat method of botanical ...

African Journals Online (AJOL)

Reports the results of a study conducted to determine an appropriate sample size for a small-quadrat method of botanical survey for application in the Mixed Bushveld of South Africa. Species density and grass density were measured using a small-quadrat method in eight plant communities in the Nylsvley Nature Reserve.

On solutions of stochastic oscillatory quadratic nonlinear equations using different techniques, a comparison study

International Nuclear Information System (INIS)

El-Tawil, M A; Al-Jihany, A S

2008-01-01

In this paper, nonlinear oscillators under quadratic nonlinearity with stochastic inputs are considered. Different methods are used to obtain first order approximations, namely, the WHEP technique, the perturbation method, the Pickard approximations, the Adomian decompositions and the homotopy perturbation method (HPM). Some statistical moments are computed for the different methods using mathematica 5. Comparisons are illustrated through figures for different case-studies

Reproducing kernel Hilbert spaces of Gaussian priors

NARCIS (Netherlands)

Vaart, van der A.W.; Zanten, van J.H.; Clarke, B.; Ghosal, S.

2008-01-01

We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of posterior distributions based on Gaussian priors can be described

Crossover between the Gaussian orthogonal ensemble, the Gaussian unitary ensemble, and Poissonian statistics.

Science.gov (United States)

Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter

2017-11-01

Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.

Gaussian process regression analysis for functional data

CERN Document Server

Shi, Jian Qing

2011-01-01

Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime

Comparison of Gaussian and non-Gaussian Atmospheric Profile Retrievals from Satellite Microwave Data

Science.gov (United States)

Kliewer, A.; Forsythe, J. M.; Fletcher, S. J.; Jones, A. S.

2017-12-01

The Cooperative Institute for Research in the Atmosphere at Colorado State University has recently developed two different versions of a mixed-distribution (lognormal combined with a Gaussian) based microwave temperature and mixing ratio retrieval system as well as the original Gaussian-based approach. These retrieval systems are based upon 1DVAR theory but have been adapted to use different descriptive statistics of the lognormal distribution to minimize the background errors. The input radiance data is from the AMSU-A and MHS instruments on the NOAA series of spacecraft. To help illustrate how the three retrievals are affected by the change in the distribution we are in the process of creating a new website to show the output from the different retrievals. Here we present initial results from different dynamical situations to show how the tool could be used by forecasters as well as for educators. However, as the new retrieved values are from a non-Gaussian based 1DVAR then they will display non-Gaussian behaviors that need to pass a quality control measure that is consistent with this distribution, and these new measures are presented here along with initial results for checking the retrievals.

Quadratic divergences and dimensional regularisation

International Nuclear Information System (INIS)

Jack, I.; Jones, D.R.T.

1990-01-01

We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)

Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2004-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

Electroweak vacuum stability and finite quadratic radiative corrections

Energy Technology Data Exchange (ETDEWEB)

Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)

2015-07-15

If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.

Isotropy of quadratic forms

Indian Academy of Sciences (India)

V. Suresh University Of Hyderabad Hyderabad

2008-10-31

Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...

Unconventional signal detection techniques with Gaussian probability mixtures adaptation in non-AWGN channels: full resolution receiver

Science.gov (United States)

Chabdarov, Shamil M.; Nadeev, Adel F.; Chickrin, Dmitry E.; Faizullin, Rashid R.

2011-04-01

In this paper we discuss unconventional detection technique also known as «full resolution receiver». This receiver uses Gaussian probability mixtures for interference structure adaptation. Full resolution receiver is alternative to conventional matched filter receivers in the case of non-Gaussian interferences. For the DS-CDMA forward channel with presence of complex interferences sufficient performance increasing was shown.

Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives

NARCIS (Netherlands)

Durbin, J.; Koopman, S.J.M.

1998-01-01

The analysis of non-Gaussian time series using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Monte Carlo Markov chain methods are not employed. Non-Gaussian

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

International Nuclear Information System (INIS)

Catalao, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F.

2010-01-01

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.

Gaussian operations and privacy

International Nuclear Information System (INIS)

Navascues, Miguel; Acin, Antonio

2005-01-01

We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states

New robust chaotic system with exponential quadratic term

International Nuclear Information System (INIS)

Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

2008-01-01

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

Local Gaussian approximation in the generator coordinate method

International Nuclear Information System (INIS)

Onishi, Naoki; Une, Tsutomu.

1975-01-01

A transformation from a non-orthogonal representation to an orthogonal representation of wave functions is studied in the generator coordinate method. A differential equation can be obtained by the transformation for a case that the eigenvalue equation of the overlap kernel is solvable. By assuming local Gaussian overlap, we derive a Schroedinger-type equation for the collective motion from the Hill-Wheeler integral equation. (auth.)

Local Gaussian approximation in the generator coordinate method

Energy Technology Data Exchange (ETDEWEB)

Onishi, N [Tokyo Univ. (Japan). Coll. of General Education; Une, Tsutomu

1975-02-01

A transformation from a non-orthogonal representation to an orthogonal representation of wave functions is studied in the generator coordinate method. A differential equation can be obtained by the transformation for a case that the eigenvalue equation of the overlap kernel is solvable. By assuming local Gaussian overlap, we derive a Schroedinger-type equation for the collective motion from the Hill-Wheeler integral equation.

Simultaneous effect of modified gravity and primordial non-Gaussianity in large scale structure observations

International Nuclear Information System (INIS)

Mirzatuny, Nareg; Khosravi, Shahram; Baghram, Shant; Moshafi, Hossein

2014-01-01

In this work we study the simultaneous effect of primordial non-Gaussianity and the modification of the gravity in f(R) framework on large scale structure observations. We show that non-Gaussianity and modified gravity introduce a scale dependent bias and growth rate functions. The deviation from ΛCDM in the case of primordial non-Gaussian models is in large scales, while the growth rate deviates from ΛCDM in small scales for modified gravity theories. We show that the redshift space distortion can be used to distinguish positive and negative f NL in standard background, while in f(R) theories they are not easily distinguishable. The galaxy power spectrum is generally enhanced in presence of non-Gaussianity and modified gravity. We also obtain the scale dependence of this enhancement. Finally we define galaxy growth rate and galaxy growth rate bias as new observational parameters to constrain cosmology

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

Science.gov (United States)

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

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

Quadratic Functionals with General Boundary Conditions

International Nuclear Information System (INIS)

Dosla, Z.; Dosly, O.

1997-01-01

The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions

Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

International Nuclear Information System (INIS)

Lopez de la Cruz, J.; Gutierrez, M.A.

2008-01-01

This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed

Geometry of perturbed Gaussian states and quantum estimation

International Nuclear Information System (INIS)

Genoni, Marco G; Giorda, Paolo; Paris, Matteo G A

2011-01-01

We address the non-Gaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that the nG of the perturbed state may be written as the quantum Fisher information (QFI) distance minus a term depending on the infinitesimal energy change, i.e. it provides a lower bound to statistical distinguishability. Upon moving on isoenergetic surfaces in a neighbourhood of a Gaussian state, nG thus coincides with a proper distance in the Hilbert space and exactly quantifies the statistical distinguishability of the perturbations. On the other hand, for perturbations leaving the covariance matrix unperturbed, we show that nG provides an upper bound to the QFI. Our results show that the geometry of non-Gaussian states in the neighbourhood of a Gaussian state is definitely not trivial and cannot be subsumed by a differential structure. Nevertheless, the analysis of perturbations to a Gaussian state reveals that nG may be a resource for quantum estimation. The nG of specific families of perturbed Gaussian states is analysed in some detail with the aim of finding the maximally non-Gaussian state obtainable from a given Gaussian one. (fast track communication)

Quadratic Plus Linear Operators which Preserve Pure States of Quantum Systems: Small Dimensions

International Nuclear Information System (INIS)

Saburov, Mansoor

2014-01-01

A mathematical formalism of quantum mechanics says that a pure state of a quantum system corresponds to a vector of norm 1 and an observable is a self-adjoint operator on the space of states. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces. In the nonlinear case, this problem was open. In this paper, in the small dimensional spaces, we shall describe all quadratic plus linear operators which preserve pure states of the quantum system

Temporal quadratic expansion nodal Green's function method

International Nuclear Information System (INIS)

Liu Cong; Jing Xingqing; Xu Xiaolin

2000-01-01

A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

On wave-packet dynamics in a decaying quadratic potential

DEFF Research Database (Denmark)

Møller, Klaus Braagaard; Henriksen, Niels Engholm

1997-01-01

We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....

Burgers' turbulence problem with linear or quadratic external potential

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

2005-01-01

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

Non-Gaussianity in island cosmology

International Nuclear Information System (INIS)

Piao Yunsong

2009-01-01

In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of the island universe by using the second order perturbation equation. We find that for the spectral index n s ≅0.96, which is favored by current observations, the non-Gaussianity level f NL seen in an island will generally lie between 30 and 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense mean the coming observations, especially the measurement of non-Gaussianity, will be significant to clarify how our position in the landscape is populated.

Geometrical and Graphical Solutions of Quadratic Equations.

Science.gov (United States)

Hornsby, E. John, Jr.

1990-01-01

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

Dynamic Algorithm for LQGPC Predictive Control

DEFF Research Database (Denmark)

Hangstrup, M.; Ordys, A.W.; Grimble, M.J.

1998-01-01

In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated into the control......In this paper the optimal control law is derived for a multi-variable state space Linear Quadratic Gaussian Predictive Controller (LQGPC). A dynamic performance index is utilized resulting in an optimal steady state controller. Knowledge of future reference values is incorporated...... into the controller design and the solution is derived using the method of Lagrange multipliers. It is shown how well-known GPC controller can be obtained as a special case of the LQGPC controller design. The important advantage of using the LQGPC framework for designing predictive, e.g. GPS is that LQGPC enables...

Thermodynamics of noncommutative high-dimensional AdS black holes with non-Gaussian smeared matter distributions

CERN Document Server

Miao, Yan-Gang

2016-01-01

Considering non-Gaussian smeared matter distributions, we investigate thermodynamic behaviors of the noncommutative high-dimensional Schwarzschild-Tangherlini anti-de Sitter black hole, and obtain the condition for the existence of extreme black holes. We indicate that the Gaussian smeared matter distribution, which is a special case of non-Gaussian smeared matter distributions, is not applicable for the 6- and higher-dimensional black holes due to the hoop conjecture. In particular, the phase transition is analyzed in detail. Moreover, we point out that the Maxwell equal area law maintains for the noncommutative black hole with the Hawking temperature within a specific range, but fails with the Hawking temperature beyond this range.

Commuting quantum traces for quadratic algebras

International Nuclear Information System (INIS)

Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve

2005-01-01

Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

Energy Technology Data Exchange (ETDEWEB)

Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)

2010-03-15

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach. (author)

Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces

International Nuclear Information System (INIS)

Oyewumi, K.A.; Bangudu, E.A.

2003-01-01

Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)

Delay-enhanced stability and stochastic resonance in perception bistability under non-Gaussian noise

International Nuclear Information System (INIS)

Yang, Tao; Zeng, Chunhua; Liu, Ruifen; Wang, Hua; Mei, Dongcheng

2015-01-01

In this paper we investigate the effect of time delay in an attractor network model of perception bistability driven by non-Gaussian noise. Using delay Langevin and Fokker–Planck approaches, the theoretical analysis of the model is presented. It is found that the mean first-passage time (MFPT) as a function of the time delay exhibits a maximum, which is identified as the characteristic of the delay-enhanced stability of the system. This is different to the case of noise-enhanced stability. The non-Gaussian noise-enhanced stability of the system is also analyzed. The signal-to-noise ratio (SNR) as a function of the noise intensity exhibits a maximum. This maximum implies the identifying characteristic of stochastic resonance (SR), and the time delay and non-Gaussian noise can enhance the SR phenomenon. (paper)

Non-Gaussianity from inflation: theory and observations

Science.gov (United States)

Bartolo, N.; Komatsu, E.; Matarrese, S.; Riotto, A.

2004-11-01

This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.

Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control

OpenAIRE

Härkegård, Ola

2004-01-01

When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...

The Comparison Study of Quadratic Infinite Beam Program on Optimization Instensity Modulated Radiation Therapy Treatment Planning (IMRTP) between Threshold and Exponential Scatter Method with CERR® In The Case of Lung Cancer

International Nuclear Information System (INIS)

Hardiyanti, Y; Haekal, M; Waris, A; Haryanto, F

2016-01-01

This research compares the quadratic optimization program on Intensity Modulated Radiation Therapy Treatment Planning (IMRTP) with the Computational Environment for Radiotherapy Research (CERR) software. We assumed that the number of beams used for the treatment planner was about 9 and 13 beams. The case used the energy of 6 MV with Source Skin Distance (SSD) of 100 cm from target volume. Dose calculation used Quadratic Infinite beam (QIB) from CERR. CERR was used in the comparison study between Gauss Primary threshold method and Gauss Primary exponential method. In the case of lung cancer, the threshold variation of 0.01, and 0.004 was used. The output of the dose was distributed using an analysis in the form of DVH from CERR. The maximum dose distributions obtained were on the target volume (PTV) Planning Target Volume, (CTV) Clinical Target Volume, (GTV) Gross Tumor Volume, liver, and skin. It was obtained that if the dose calculation method used exponential and the number of beam 9. When the dose calculation method used the threshold and the number of beam 13, the maximum dose distributions obtained were on the target volume PTV, GTV, heart, and skin. (paper)

Non-gaussianity versus nonlinearity of cosmological perturbations.

Science.gov (United States)

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Galaxy bias and primordial non-Gaussianity

Energy Technology Data Exchange (ETDEWEB)

Assassi, Valentin; Baumann, Daniel [DAMTP, Cambridge University, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Schmidt, Fabian, E-mail: assassi@ias.edu, E-mail: D.D.Baumann@uva.nl, E-mail: fabians@MPA-Garching.MPG.DE [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching (Germany)

2015-12-01

We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation.

Galaxy bias and primordial non-Gaussianity

International Nuclear Information System (INIS)

Assassi, Valentin; Baumann, Daniel; Schmidt, Fabian

2015-01-01

We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistency check to confirm the primordial origin of any observed scale-dependent bias. Finally, we also discuss the imprints of anisotropic non-Gaussianity as motivated by recent studies of higher-spin fields during inflation

Quadratic Interpolation and Linear Lifting Design

Directory of Open Access Journals (Sweden)

Joel Solé

2007-03-01

Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

Versatile Gaussian probes for squeezing estimation

Science.gov (United States)

Rigovacca, Luca; Farace, Alessandro; Souza, Leonardo A. M.; De Pasquale, Antonella; Giovannetti, Vittorio; Adesso, Gerardo

2017-05-01

We consider an instance of "black-box" quantum metrology in the Gaussian framework, where we aim to estimate the amount of squeezing applied on an input probe, without previous knowledge on the phase of the applied squeezing. By taking the quantum Fisher information (QFI) as the figure of merit, we evaluate its average and variance with respect to this phase in order to identify probe states that yield good precision for many different squeezing directions. We first consider the case of single-mode Gaussian probes with the same energy, and find that pure squeezed states maximize the average quantum Fisher information (AvQFI) at the cost of a performance that oscillates strongly as the squeezing direction is changed. Although the variance can be brought to zero by correlating the probing system with a reference mode, the maximum AvQFI cannot be increased in the same way. A different scenario opens if one takes into account the effects of photon losses: coherent states represent the optimal single-mode choice when losses exceed a certain threshold and, moreover, correlated probes can now yield larger AvQFI values than all single-mode states, on top of having zero variance.

Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows

Directory of Open Access Journals (Sweden)

F. Laio

2004-01-01

Full Text Available Several methods exist for the detection of nonlinearity in univariate time series. In the present work we consider riverflow time series to infer the dynamical characteristics of the rainfall-runoff transformation. It is shown that the non-Gaussian nature of the driving force (rainfall can distort the results of such methods, in particular when surrogate data techniques are used. Deterministic versus stochastic (DVS plots, conditionally applied to the decay phases of the time series, are instead proved to be a suitable tool to detect nonlinearity in processes driven by non-Gaussian (Poissonian noise. An application to daily discharges from three Italian rivers provides important clues to the presence of nonlinearity in the rainfall-runoff transformation.

Selective Linear or Quadratic Optomechanical Coupling via Measurement

Directory of Open Access Journals (Sweden)

Michael R. Vanner

2011-11-01

Full Text Available The ability to engineer both linear and nonlinear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical-displacement coupling can be achieved using the optomechanical interaction that is linearly proportional to the mechanical position. The resulting square-displacement measurement strength is compared to that attainable in the dispersive case that has a direct interaction with the mechanical-displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.

Quadratic Jordan formulation of quantum mechanics and construction of Lie (super)algebras from Jordan (super)algebras

International Nuclear Information System (INIS)

Guenaydin, M.

1979-05-01

Quadratic Jordan formulation of quantum mechanics in terms of Jordan triple product is presented. This formulation extends to the case of octonionic quantum mechanics for which no Hilbert space formulation exists. Using ternary algebraic techniques we then five the constructions of the derivation, structure and Tits-Koecher (Moebius) algebras of Jordan superalgebras. (orig.) [de

Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F{sub N} method

Energy Technology Data Exchange (ETDEWEB)

Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

2017-11-15

One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.

The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

International Nuclear Information System (INIS)

Li, Chengzhi; Llibre, Jaume

2009-01-01

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

Energy Technology Data Exchange (ETDEWEB)

Bai, Dong [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Wu, Yue-Liang [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China)

2017-09-15

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess-Zumino model with soft supersymmetry breaking terms (WZ' model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques. (orig.)

On quadratic residue codes and hyperelliptic curves

Directory of Open Access Journals (Sweden)

David Joyner

2008-01-01

Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

On Power Allocation for Parallel Gaussian Broadcast Channels with Common Information

Directory of Open Access Journals (Sweden)

Gohary RamyH

2009-01-01

Full Text Available This paper considers a broadcast system in which a single transmitter sends a common message and (independent particular messages to receivers over unmatched parallel scalar Gaussian subchannels. For this system the set of all rate tuples that can be achieved via superposition coding and Gaussian signalling (SPCGS can be parameterized by a set of power loads and partitions, and the boundary of this set can be expressed as the solution of an optimization problem. Although that problem is not convex in the general case, it will be shown that it can be used to obtain tight and efficiently computable inner and outer bounds on the SPCGS rate region. The development of these bounds relies on approximating the original optimization problem by a (convex Geometric Program (GP, and in addition to generating the bounds, the GP also generates the corresponding power loads and partitions. There are special cases of the general problem that can be precisely formulated in a convex form. In this paper, explicit convex formulations are given for three such cases, namely, the case of 2 users, the case in which only particular messages are transmitted (in both of which the SPCGS rate region is the capacity region, and the case in which only the SPCGS sum rate is to be maximized.

Toward the detection of gravitational waves under non-Gaussian noises II. Independent component analysis.

Science.gov (United States)

Morisaki, Soichiro; Yokoyama, Jun'ichi; Eda, Kazunari; Itoh, Yousuke

2016-01-01

We introduce a new analysis method to deal with stationary non-Gaussian noises in gravitational wave detectors in terms of the independent component analysis. First, we consider the simplest case where the detector outputs are linear combinations of the inputs, consisting of signals and various noises, and show that this method may be helpful to increase the signal-to-noise ratio. Next, we take into account the time delay between the inputs and the outputs. Finally, we extend our method to nonlinearly correlated noises and show that our method can identify the coupling coefficients and remove non-Gaussian noises. Although we focus on gravitational wave data analysis, our methods are applicable to the detection of any signals under non-Gaussian noises.

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

Solving symmetric-definite quadratic lambda-matrix problems without factorization

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1982-01-01

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

Information geometry of Gaussian channels

International Nuclear Information System (INIS)

Monras, Alex; Illuminati, Fabrizio

2010-01-01

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).

Laguerre Gaussian beam multiplexing through turbulence

CSIR Research Space (South Africa)

Trichili, A

2014-08-17

Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...

Phase statistics in non-Gaussian scattering

International Nuclear Information System (INIS)

Watson, Stephen M; Jakeman, Eric; Ridley, Kevin D

2006-01-01

Amplitude weighting can improve the accuracy of frequency measurements in signals corrupted by multiplicative speckle noise. When the speckle field constitutes a circular complex Gaussian process, the optimal function of amplitude weighting is provided by the field intensity, corresponding to the intensity-weighted phase derivative statistic. In this paper, we investigate the phase derivative and intensity-weighted phase derivative returned from a two-dimensional random walk, which constitutes a generic scattering model capable of producing both Gaussian and non-Gaussian fluctuations. Analytical results are developed for the correlation properties of the intensity-weighted phase derivative, as well as limiting probability densities of the scattered field. Numerical simulation is used to generate further probability densities and determine optimal weighting criteria from non-Gaussian fields. The results are relevant to frequency retrieval in radiation scattered from random media

Generalized Gaussian Error Calculus

CERN Document Server

Grabe, Michael

2010-01-01

For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...

Schur Stability Regions for Complex Quadratic Polynomials

Science.gov (United States)

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.)

A Novel Single Switch Transformerless Quadratic DC/DC Buck-Boost Converter

DEFF Research Database (Denmark)

Mostaan, Ali; A. Gorji, Saman; N. Soltani, Mohsen

2017-01-01

A novel quadratic buck-boost DC/DC converter is presented in this study. The proposed converter utilizes only one active switch and can step-up/down the input voltage, while the existing single switch quadratic buck/boost converters can only work in step-up or step-down mode. First, the proposed ...

Thermodynamics of noncommutative high-dimensional AdS black holes with non-Gaussian smeared matter distributions

Energy Technology Data Exchange (ETDEWEB)

Miao, Yan-Gang [Nankai University, School of Physics, Tianjin (China); Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, P.O. Box 2735, Beijing (China); CERN, PH-TH Division, Geneva 23 (Switzerland); Xu, Zhen-Ming [Nankai University, School of Physics, Tianjin (China)

2016-04-15

Considering non-Gaussian smeared matter distributions, we investigate the thermodynamic behaviors of the noncommutative high-dimensional Schwarzschild-Tangherlini anti-de Sitter black hole, and we obtain the condition for the existence of extreme black holes. We indicate that the Gaussian smeared matter distribution, which is a special case of non-Gaussian smeared matter distributions, is not applicable for the six- and higher-dimensional black holes due to the hoop conjecture. In particular, the phase transition is analyzed in detail. Moreover, we point out that the Maxwell equal area law holds for the noncommutative black hole whose Hawking temperature is within a specific range, but fails for one whose the Hawking temperature is beyond this range. (orig.)

Big bang nucleosynthesis with Gaussian inhomogeneous neutrino degeneracy

International Nuclear Information System (INIS)

Stirling, Spencer D.; Scherrer, Robert J.

2002-01-01

We consider the effect of inhomogeneous neutrino degeneracy on big bang nucleosynthesis for the case where the distribution of neutrino chemical potentials is given by a Gaussian. The chemical potential fluctuations are taken to be isocurvature, so that only inhomogeneities in the electron chemical potential are relevant. Then the final element abundances are a function only of the baryon-photon ratio η, the effective number of additional neutrinos ΔN ν , the mean electron neutrino degeneracy parameter ξ-bar, and the rms fluctuation of the degeneracy parameter, σ ξ . We find that for fixed η, ΔN ν , and ξ-bar, the abundances of 4 He, D, and 7 Li are, in general, increasing functions of σ ξ . Hence, the effect of adding a Gaussian distribution for the electron neutrino degeneracy parameter is to decrease the allowed range for η. We show that this result can be generalized to a wide variety of distributions for ξ

Conformal Invariance, Dark Energy, and CMB Non-Gaussianity

CERN Document Server

Antoniadis, Ignatios; Mottola, Emil

2012-01-01

We show that in addition to simple scale invariance, a universe dominated by dark energy naturally gives rise to correlation functions possessing full conformal invariance. This is due to the mathematical isomorphism between the conformal group of certain three dimensional slices of de Sitter space and the de Sitter isometry group SO(4,1). In the standard homogeneous, isotropic cosmological model in which primordial density perturbations are generated during a long vacuum energy dominated de Sitter phase, the embedding of flat spatial R^3 sections in de Sitter space induces a conformal invariant perturbation spectrum and definite prediction for the shape of the non-Gaussian CMB bispectrum. In the case in which the density fluctuations are generated instead on the de Sitter horizon, conformal invariance of the S^2 horizon embedding implies a different but also quite definite prediction for the angular correlations of CMB non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic to the sym...

Measurement of quadratic electrogyration effect in castor oil

Science.gov (United States)

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.

On a quadratic inverse eigenvalue problem

International Nuclear Information System (INIS)

Cai, Yunfeng; Xu, Shufang

2009-01-01

This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

Large N saddle formulation of quadratic building block theories

International Nuclear Information System (INIS)

Halpern, M.B.

1980-01-01

I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)

Functional differential equations for the q-Fourier transform of q-Gaussians

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Functional differential equations for the q-Fourier transform of q-Gaussians

Energy Technology Data Exchange (ETDEWEB)

Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

2010-02-05

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Strong monogamy of bipartite and genuine multipartite entanglement: the Gaussian case.

Science.gov (United States)

Adesso, Gerardo; Illuminati, Fabrizio

2007-10-12

We demonstrate the existence of general constraints on distributed quantum correlations, which impose a trade-off on bipartite and multipartite entanglement at once. For all N-mode Gaussian states under permutation invariance, we establish exactly a monogamy inequality, stronger than the traditional one, that by recursion defines a proper measure of genuine N-partite entanglement. Strong monogamy holds as well for subsystems of arbitrary size, and the emerging multipartite entanglement measure is found to be scale invariant. We unveil its operational connection with the optimal fidelity of continuous variable teleportation networks.

Noise-level determination for discrete spectra with Gaussian or Lorentzian probability density functions

International Nuclear Information System (INIS)

Moriya, Netzer

2010-01-01

A method, based on binomial filtering, to estimate the noise level of an arbitrary, smoothed pure signal, contaminated with an additive, uncorrelated noise component is presented. If the noise characteristics of the experimental spectrum are known, as for instance the type of the corresponding probability density function (e.g., Gaussian), the noise properties can be extracted. In such cases, both the noise level, as may arbitrarily be defined, and a simulated white noise component can be generated, such that the simulated noise component is statistically indistinguishable from the true noise component present in the original signal. In this paper we present a detailed analysis of the noise level extraction when the additive noise is Gaussian or Lorentzian. We show that the statistical parameters in these cases (mainly the variance and the half width at half maximum, respectively) can directly be obtained from the experimental spectrum even when the pure signal is erratic. Further discussion is given for cases where the noise probability density function is initially unknown.

Linking network usage patterns to traffic Gaussianity fit

NARCIS (Netherlands)

de Oliveira Schmidt, R.; Sadre, R.; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko

Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001,

Characterisation of random Gaussian and non-Gaussian stress processes in terms of extreme responses

Directory of Open Access Journals (Sweden)

Colin Bruno

2015-01-01

Full Text Available In the field of military land vehicles, random vibration processes generated by all-terrain wheeled vehicles in motion are not classical stochastic processes with a stationary and Gaussian nature. Non-stationarity of processes induced by the variability of the vehicle speed does not form a major difficulty because the designer can have good control over the vehicle speed by characterising the histogram of instantaneous speed of the vehicle during an operational situation. Beyond this non-stationarity problem, the hard point clearly lies in the fact that the random processes are not Gaussian and are generated mainly by the non-linear behaviour of the undercarriage and the strong occurrence of shocks generated by roughness of the terrain. This non-Gaussian nature is expressed particularly by very high flattening levels that can affect the design of structures under extreme stresses conventionally acquired by spectral approaches, inherent to Gaussian processes and based essentially on spectral moments of stress processes. Due to these technical considerations, techniques for characterisation of random excitation processes generated by this type of carrier need to be changed, by proposing innovative characterisation methods based on time domain approaches as described in the body of the text rather than spectral domain approaches.

The Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Thomadsen, Tommy; Stidsen, Thomas K.

2003-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

On Quadratic Variation of Martingales

Indian Academy of Sciences (India)

where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Hunting for primordial non-Gaussianity in the cosmic microwave background

International Nuclear Information System (INIS)

Komatsu, Eiichiro

2010-01-01

Since the first limit on the (local) primordial non-Gaussianity parameter, f NL , was obtained from the Cosmic Background Explorer (COBE) data in 2002, observations of the cosmic microwave background (CMB) have been playing a central role in constraining the amplitudes of various forms of non-Gaussianity in primordial fluctuations. The current 68% limit from the 7-year data of the Wilkinson Microwave Anisotropy Probe (WMAP) is f NL = 32 ± 21, and the Planck satellite is expected to reduce the uncertainty by a factor of 4 in a few years from now. If f NL >> 1 is found by Planck with high statistical significance, all single-field models of inflation would be ruled out. Moreover, if the Planck satellite finds f NL ∼ 30, then it would be able to test a broad class of multi-field models using the 4-point function (trispectrum) test of τ NL ≥ (6f NL /5) 2 . In this paper, we review the methods (optimal estimator), results (WMAP 7-year) and challenges (secondary anisotropy, second-order effect and foreground) of measuring primordial non-Gaussianity from the CMB data, present a science case for the trispectrum and conclude with future prospects.

Asymptotics of sums of lognormal random variables with Gaussian copula

DEFF Research Database (Denmark)

Asmussen, Søren; Rojas-Nandayapa, Leonardo

2008-01-01

Let (Y1, ..., Yn) have a joint n-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let Xi = eYi, Sn = X1 + ⋯ + Xn. The asymptotics of P (Sn > x) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In part...

Gaussian maximally multipartite-entangled states

Science.gov (United States)

Facchi, Paolo; Florio, Giuseppe; Lupo, Cosmo; Mancini, Stefano; Pascazio, Saverio

2009-12-01

We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7 .

Gaussian maximally multipartite-entangled states

International Nuclear Information System (INIS)

Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Lupo, Cosmo; Mancini, Stefano

2009-01-01

We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing n=2 or 3 modes. We further numerically investigate the structure of these states and their frustration for n≤7.

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

Science.gov (United States)

Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W

2008-09-01

The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.

Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. I. Gaussian-white case

NARCIS (Netherlands)

Steffen, T; Tanimura, Y

The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by

Probing primordial non-Gaussianity via iSW measurements with SKA continuum surveys

Energy Technology Data Exchange (ETDEWEB)

Raccanelli, Alvise; Doré, Olivier, E-mail: alvise@jhu.edu, E-mail: olivier.dore@caltech.edu [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109 (United States); Bacon, David J.; Maartens, Roy, E-mail: David.Bacon@port.ac.uk, E-mail: roy.maartens@gmail.com [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth P01 3FX (United Kingdom); and others

2015-01-01

The Planck CMB experiment has delivered the best constraints so far on primordial non-Gaussianity, ruling out early-Universe models of inflation that generate large non-Gaussianity. Although small improvements in the CMB constraints are expected, the next frontier of precision will come from future large-scale surveys of the galaxy distribution. The advantage of such surveys is that they can measure many more modes than the CMB—in particular, forthcoming radio surveys with the Square Kilometre Array will cover huge volumes. Radio continuum surveys deliver the largest volumes, but with the disadvantage of no redshift information. In order to mitigate this, we use two additional observables. First, the integrated Sachs-Wolfe effect—the cross-correlation of the radio number counts with the CMB temperature anisotropies—helps to reduce systematics on the large scales that are sensitive to non-Gaussianity. Second, optical data allows for cross-identification in order to gain some redshift information. We show that, while the single redshift bin case can provide a σ(f{sub NL}) ∼ 20, and is therefore not competitive with current and future constraints on non-Gaussianity, a tomographic analysis could improve the constraints by an order of magnitude, even with only two redshift bins. A huge improvement is provided by the addition of high-redshift sources, so having cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling very precise measurements of f{sub NL}. We use Fisher matrix forecasts to predict the constraining power in the case of no redshift information and the case where cross-ID allows a tomographic analysis, and we show that the constraints do not improve much with 3 or more bins. Our results show that SKA continuum surveys could provide constraints competitive with CMB and forthcoming optical surveys, potentially allowing a measurement of σ(f{sub NL}) ∼ 1 to be made. Moreover, these measurements would act as a useful check

Variational Gaussian approximation for Poisson data

Science.gov (United States)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Quantum tomography and classical propagator for quadratic quantum systems

International Nuclear Information System (INIS)

Man'ko, O.V.

1999-03-01

The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)

Phase space structure of generalized Gaussian cat states

International Nuclear Information System (INIS)

Nicacio, Fernando; Maia, Raphael N.P.; Toscano, Fabricio; Vallejos, Raul O.

2010-01-01

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states. The structure of the interference term of the Wigner function is always hyperbolic, surviving the action of a thermal reservoir. We also consider certain superpositions of mixed Gaussian states. An application to semiclassical dynamics is discussed.

Prediction and retrodiction with continuously monitored Gaussian states

DEFF Research Database (Denmark)

Zhang, Jinglei; Mølmer, Klaus

2017-01-01

Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property......(t)$ to Gaussian states implies that the matrix $E(t)$ is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems....

On the representation of the diffracted field of Hermite-Gaussian modes in an alien basis and the young diffraction principle

International Nuclear Information System (INIS)

Smirnov, V.N.; Strokovskii, G.A.

1994-01-01

An analytical form of expansion coefficients of a diffracted field for an arbitrary Hermite-Gaussian beam in an alien Hermite-Gaussian basis is obtained. A possible physical interpretation of the well-known Young phenomenological diffraction principle and experiments on diffraction of Hermite-Gaussian beams of the lowest types (n = 0 - 5) from half-plane are discussed. The case of nearly homogenous expansion corresponding to misalignment and mismatch of optical systems is also analyzed. 7 refs., 2 figs

Semi-Supervised Half-Quadratic Nonnegative Matrix Factorization for Face Recognition

KAUST Repository

Alghamdi, Masheal M.

2014-05-01

Face recognition is a challenging problem in computer vision. Difficulties such as slight differences between similar faces of different people, changes in facial expressions, light and illumination condition, and pose variations add extra complications to the face recognition research. Many algorithms are devoted to solving the face recognition problem, among which the family of nonnegative matrix factorization (NMF) algorithms has been widely used as a compact data representation method. Different versions of NMF have been proposed. Wang et al. proposed the graph-based semi-supervised nonnegative learning (S2N2L) algorithm that uses labeled data in constructing intrinsic and penalty graph to enforce separability of labeled data, which leads to a greater discriminating power. Moreover the geometrical structure of labeled and unlabeled data is preserved through using the smoothness assumption by creating a similarity graph that conserves the neighboring information for all labeled and unlabeled data. However, S2N2L is sensitive to light changes, illumination, and partial occlusion. In this thesis, we propose a Semi-Supervised Half-Quadratic NMF (SSHQNMF) algorithm that combines the benefits of S2N2L and the robust NMF by the half- quadratic minimization (HQNMF) algorithm.Our algorithm improves upon the S2N2L algorithm by replacing the Frobenius norm with a robust M-Estimator loss function. A multiplicative update solution for our SSHQNMF algorithmis driven using the half- 4 quadratic (HQ) theory. Extensive experiments on ORL, Yale-A and a subset of the PIE data sets for nine M-estimator loss functions for both SSHQNMF and HQNMF algorithms are investigated, and compared with several state-of-the-art supervised and unsupervised algorithms, along with the original S2N2L algorithm in the context of classification, clustering, and robustness against partial occlusion. The proposed algorithm outperformed the other algorithms. Furthermore, SSHQNMF with Maximum Correntropy

Error Rates of M-PAM and M-QAM in Generalized Fading and Generalized Gaussian Noise Environments

KAUST Repository

Soury, Hamza

2013-07-01

This letter investigates the average symbol error probability (ASEP) of pulse amplitude modulation and quadrature amplitude modulation coherent signaling over flat fading channels subject to additive white generalized Gaussian noise. The new ASEP results are derived in a generic closed-form in terms of the Fox H function and the bivariate Fox H function for the extended generalized-K fading case. The utility of this new general closed-form is that it includes some special fading distributions, like the Generalized-K, Nakagami-m, and Rayleigh fading and special noise distributions such as Gaussian and Laplacian. Some of these special cases are also treated and are shown to yield simplified results.

Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes

Energy Technology Data Exchange (ETDEWEB)

Stein, Michael [Univ. of Chicago, IL (United States)

2017-03-13

Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead to predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over the

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

Directory of Open Access Journals (Sweden)

Yong Li

2014-01-01

Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

Super-resolving random-Gaussian apodized photon sieve.

Science.gov (United States)

Sabatyan, Arash; Roshaninejad, Parisa

2012-09-10

A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.

Stable radiation pressure acceleration of ions by suppressing transverse Rayleigh-Taylor instability with multiple Gaussian pulses

Energy Technology Data Exchange (ETDEWEB)

Zhou, M. L.; Liu, B.; Hu, R. H.; Shou, Y. R.; Lin, C.; Lu, H. Y.; Lu, Y. R.; Ma, W. J., E-mail: wenjun.ma@pku.edu.cn [State Key Laboratory of Nuclear Physics and Technology, and Key Laboratory of HEDP of the Ministry of Education, CAPT, Peking University, Beijing 100871 (China); Gu, Y. Q. [Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang, Sichuan 621900 (China); Yan, X. Q., E-mail: x.yan@pku.edu.cn [State Key Laboratory of Nuclear Physics and Technology, and Key Laboratory of HEDP of the Ministry of Education, CAPT, Peking University, Beijing 100871 (China); Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006 (China)

2016-08-15

In the case of a thin plasma slab accelerated by the radiation pressure of an ultra-intense laser pulse, the development of Rayleigh-Taylor instability (RTI) will destroy the acceleration structure and terminate the acceleration process much sooner than theoretical limit. In this paper, a new scheme using multiple Gaussian pulses for ion acceleration in a radiation pressure acceleration regime is investigated with particle-in-cell simulation. We found that with multiple Gaussian pulses, the instability could be efficiently suppressed and the divergence of the ion bunch is greatly reduced, resulting in a longer acceleration time and much more collimated ion bunch with higher energy than using a single Gaussian pulse. An analytical model is developed to describe the suppression of RTI at the laser-plasma interface. The model shows that the suppression of RTI is due to the introduction of the long wavelength mode RTI by the multiple Gaussian pulses.

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

Science.gov (United States)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

NARCIS (Netherlands)

de Klerk, E.; Sotirov, R.

2007-01-01

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,

A biorthogonal decomposition for the identification and simulation of non-stationary and non-Gaussian random fields

Energy Technology Data Exchange (ETDEWEB)

Zentner, I. [IMSIA, UMR EDF-ENSTA-CNRS-CEA 9219, Université Paris-Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau Cedex (France); Ferré, G., E-mail: gregoire.ferre@ponts.org [CERMICS – Ecole des Ponts ParisTech, 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2 (France); Poirion, F. [Department of Structural Dynamics and Aeroelasticity, ONERA, BP 72, 29 avenue de la Division Leclerc, 92322 Chatillon Cedex (France); Benoit, M. [Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), UMR 7342 (CNRS, Aix-Marseille Université, Ecole Centrale Marseille), 49 rue Frédéric Joliot-Curie, BP 146, 13384 Marseille Cedex 13 (France)

2016-06-01

In this paper, a new method for the identification and simulation of non-Gaussian and non-stationary stochastic fields given a database is proposed. It is based on two successive biorthogonal decompositions aiming at representing spatio–temporal stochastic fields. The proposed double expansion allows to build the model even in the case of large-size problems by separating the time, space and random parts of the field. A Gaussian kernel estimator is used to simulate the high dimensional set of random variables appearing in the decomposition. The capability of the method to reproduce the non-stationary and non-Gaussian features of random phenomena is illustrated by applications to earthquakes (seismic ground motion) and sea states (wave heights).

Some continual integrals from gaussian forms

International Nuclear Information System (INIS)

Mazmanishvili, A.S.

1985-01-01

The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes

Staff turnover in hotels : exploring the quadratic and linear relationships.

OpenAIRE

Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

2015-01-01

The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

Current inversion induced by colored non-Gaussian noise

International Nuclear Information System (INIS)

Bag, Bidhan Chandra; Hu, Chin-Kung

2009-01-01

We study a stochastic process driven by colored non-Gaussian noises. For the flashing ratchet model we find that there is a current inversion in the variation of the current with the half-cycle period which accounts for the potential on–off operation. The current inversion almost disappears if one switches from non-Gaussian (NG) to Gaussian (G) noise. We also find that at low value of the asymmetry parameter of the potential the mobility controlled current is more negative for NG noise as compared to G noise. But at large magnitude of the parameter the diffusion controlled positive current is higher for the former than for the latter. On increasing the noise correlation time (τ), keeping the noise strength fixed, the mean velocity of a particle first increases and then decreases after passing through a maximum if the noise is non-Gaussian. For Gaussian noise, the current monotonically decreases. The current increases with the noise parameter p, 0< p<5/3, which is 1 for Gaussian noise

Passivity and practical work extraction using Gaussian operations

International Nuclear Information System (INIS)

Brown, Eric G; Huber, Marcus; Friis, Nicolai

2016-01-01

Quantum states that can yield work in a cyclical Hamiltonian process form one of the primary resources in the context of quantum thermodynamics. Conversely, states whose average energy cannot be lowered by unitary transformations are called passive. However, while work may be extracted from non-passive states using arbitrary unitaries, the latter may be hard to realize in practice. It is therefore pertinent to consider the passivity of states under restricted classes of operations that can be feasibly implemented. Here, we ask how restrictive the class of Gaussian unitaries is for the task of work extraction. We investigate the notion of Gaussian passivity, that is, we present necessary and sufficient criteria identifying all states whose energy cannot be lowered by Gaussian unitaries. For all other states we give a prescription for the Gaussian operations that extract the maximal amount of energy. Finally, we show that the gap between passivity and Gaussian passivity is maximal, i.e., Gaussian-passive states may still have a maximal amount of energy that is extractable by arbitrary unitaries, even under entropy constraints. (paper)

Tachyon mediated non-Gaussianity

International Nuclear Information System (INIS)

Dutta, Bhaskar; Leblond, Louis; Kumar, Jason

2008-01-01

We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.

Large deviations for Gaussian processes in Hoelder norm

International Nuclear Information System (INIS)

Fatalov, V R

2003-01-01

Some results are proved on the exact asymptotic representation of large deviation probabilities for Gaussian processes in the Hoeder norm. The following classes of processes are considered: the Wiener process, the Brownian bridge, fractional Brownian motion, and stationary Gaussian processes with power-law covariance function. The investigation uses the method of double sums for Gaussian fields

orthogonal and scaling transformations of quadratic functions

African Journals Online (AJOL)

Preferred Customer

functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

Science.gov (United States)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

Quadratic forms for Feynman-Kac semigroups

International Nuclear Information System (INIS)

Hibey, Joseph L.; Charalambous, Charalambos D.

2006-01-01

Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

Increasing Entanglement between Gaussian States by Coherent Photon Subtraction

DEFF Research Database (Denmark)

Ourjoumtsev, Alexei; Dantan, Aurelien Romain; Tualle Brouri, Rosa

2007-01-01

We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a nondegenerate parametric amplifier, produces delocalized states...

Generalized massive optimal data compression

Science.gov (United States)

Alsing, Justin; Wandelt, Benjamin

2018-05-01

In this paper, we provide a general procedure for optimally compressing N data down to n summary statistics, where n is equal to the number of parameters of interest. We show that compression to the score function - the gradient of the log-likelihood with respect to the parameters - yields n compressed statistics that are optimal in the sense that they preserve the Fisher information content of the data. Our method generalizes earlier work on linear Karhunen-Loéve compression for Gaussian data whilst recovering both lossless linear compression and quadratic estimation as special cases when they are optimal. We give a unified treatment that also includes the general non-Gaussian case as long as mild regularity conditions are satisfied, producing optimal non-linear summary statistics when appropriate. As a worked example, we derive explicitly the n optimal compressed statistics for Gaussian data in the general case where both the mean and covariance depend on the parameters.

New gaussian points for the solution of first order ordinary ...

African Journals Online (AJOL)

Numerical experiments carried out using the new Gaussian points revealed there efficiency on stiff differential equations. The results also reveal that methods using the new Gaussian points are more accurate than those using the standard Gaussian points on non-stiff initial value problems. Keywords: Gaussian points ...

Decay constants for pulsed monoenergetic neutron systems with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1977-06-01

The eigenvalues of the time-dependent transport equation for monoenergetic neutrons have been studied numerically for various combinations of linearly and quadratically anisotropic scattering assuming a space dependence of e β . The results, presented in the form of tables and graphs, show that quadratic anisotropy leads to a more complicated eigenvalue spectrum. However, no drastic changes occur in comparison to purely linear anistropy.(author)

Permanent vegetation quadrats on Olkiluoto island. Establishment and results from the first inventory

Energy Technology Data Exchange (ETDEWEB)

Huhta, A.P.; Korpela, L. [Finnish Forest Research Institute, Helsinki (Finland)

2006-05-15

This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m{sup 2}), each containing eight quadrats (a 1m{sup 2}), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)

Permanent vegetation quadrats on Olkiluoto island. Establishment and results from the first inventory

International Nuclear Information System (INIS)

Huhta, A.P.; Korpela, L.

2006-05-01

This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m 2 ), each containing eight quadrats (a 1m 2 ), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)

Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

Directory of Open Access Journals (Sweden)

Iacob Theodor-Felix

2015-12-01

Full Text Available We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Analysis of some methods for reduced rank Gaussian process regression

DEFF Research Database (Denmark)

Quinonero-Candela, J.; Rasmussen, Carl Edward

2005-01-01

While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent...... proliferation of a number of cost-effective approximations to GPs, both for classification and for regression. In this paper we analyze one popular approximation to GPs for regression: the reduced rank approximation. While generally GPs are equivalent to infinite linear models, we show that Reduced Rank...... Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning...

Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

International Nuclear Information System (INIS)

Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

2017-01-01

A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)

STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY

Directory of Open Access Journals (Sweden)

Damián Fernández

2014-12-01

Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.

Estimation of stature from sternum - Exploring the quadratic models.

Science.gov (United States)

Saraf, Ashish; Kanchan, Tanuj; Krishan, Kewal; Ateriya, Navneet; Setia, Puneet

2018-04-14

Identification of the dead is significant in examination of unknown, decomposed and mutilated human remains. Establishing the biological profile is the central issue in such a scenario, and stature estimation remains one of the important criteria in this regard. The present study was undertaken to estimate stature from different parts of the sternum. A sample of 100 sterna was obtained from individuals during the medicolegal autopsies. Length of the deceased and various measurements of the sternum were measured. Student's t-test was performed to find the sex differences in stature and sternal measurements included in the study. Correlation between stature and sternal measurements were analysed using Karl Pearson's correlation, and linear and quadratic regression models were derived. All the measurements were found to be significantly larger in males than females. Stature correlated best with the combined length of sternum, among males (R = 0.894), females (R = 0.859), and for the total sample (R = 0.891). The study showed that the models derived for stature estimation from combined length of sternum are likely to give the most accurate estimates of stature in forensic case work when compared to manubrium and mesosternum. Accuracy of stature estimation further increased with quadratic models derived for the mesosternum among males and combined length of sternum among males and females when compared to linear regression models. Future studies in different geographical locations and a larger sample size are proposed to confirm the study observations. Copyright © 2018 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.

Quaternion orders, quadratic forms, and Shimura curves

CERN Document Server

Alsina, Montserrat

2004-01-01

Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

Coherent states of systems with quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

2015-06-15

Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

Coherent states of systems with quadratic Hamiltonians

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

2015-01-01

Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

Gaussian entanglement distribution via satellite

Science.gov (United States)

Hosseinidehaj, Nedasadat; Malaney, Robert

2015-02-01

In this work we analyze three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme, the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the tradeoff between space-based engineering complexity and the rate of ground-station entanglement generation.

Fast, multiple optimizations of quadratic dose objective functions in IMRT

International Nuclear Information System (INIS)

Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M

2006-01-01

Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved

Non-Gaussianity in multi-sound-speed disformally coupled inflation

Energy Technology Data Exchange (ETDEWEB)

De Bruck, Carsten van; Longden, Chris [Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Koivisto, Tomi, E-mail: C.vandeBruck@sheffield.ac.uk, E-mail: tomi.koivisto@nordita.org, E-mail: cjlongden1@sheffield.ac.uk [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm (Sweden)

2017-02-01

Most, if not all, scalar-tensor theories are equivalent to General Relativity with a disformally coupled matter sector. In extra-dimensional theories such a coupling can be understood as a result of induction of the metric on a brane that matter is confined to. This article presents a first look at the non-Gaussianities in disformally coupled inflation, a simple two-field model that features a novel kinetic interaction. Cases with both canonical and Dirac-Born-Infeld (DBI) kinetic terms are taken into account, the latter motivated by the possible extra-dimensional origin of the disformality. The computations are carried out for the equilateral configuration in the slow-roll regime, wherein it is found that the non-Gaussianity is typically rather small and negative. This is despite the fact that the new kinetic interaction causes the perturbation modes to propagate with different sounds speeds, which may both significantly deviate from unity during inflation.

Gaussian limit of compact spin systems

International Nuclear Information System (INIS)

Bellissard, J.; Angelis, G.F. de

1981-01-01

It is shown that the Wilson and Wilson-Villain U(1) models reproduce, in the low coupling limit, the gaussian lattice approximation of the Euclidean electromagnetic field. By the same methods it is also possible to prove that the plane rotator and the Villain model share a common gaussian behaviour in the low temperature limit. (Auth.)

Determining the Gaussian Modulus and Edge Properties of 2D Materials: From Graphene to Lipid Bilayers

Science.gov (United States)

Zelisko, Matthew; Ahmadpoor, Fatemeh; Gao, Huajian; Sharma, Pradeep

2017-08-01

The dominant deformation behavior of two-dimensional materials (bending) is primarily governed by just two parameters: bending rigidity and the Gaussian modulus. These properties also set the energy scale for various important physical and biological processes such as pore formation, cell fission and generally, any event accompanied by a topological change. Unlike the bending rigidity, the Gaussian modulus is, however, notoriously difficult to evaluate via either experiments or atomistic simulations. In this Letter, recognizing that the Gaussian modulus and edge tension play a nontrivial role in the fluctuations of a 2D material edge, we derive closed-form expressions for edge fluctuations. Combined with atomistic simulations, we use the developed approach to extract the Gaussian modulus and edge tension at finite temperatures for both graphene and various types of lipid bilayers. Our results possibly provide the first reliable estimate of this elusive property at finite temperatures and appear to suggest that earlier estimates must be revised. In particular, we show that, if previously estimated properties are employed, the graphene-free edge will exhibit unstable behavior at room temperature. Remarkably, in the case of graphene, we show that the Gaussian modulus and edge tension even change sign at finite temperatures.

Forecasts of non-Gaussian parameter spaces using Box-Cox transformations

Science.gov (United States)

Joachimi, B.; Taylor, A. N.

2011-09-01

Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex features of posterior probability distributions. Combining the standard Fisher matrix with Box-Cox transformations, we propose a novel method that accurately predicts arbitrary posterior shapes. The Box-Cox transformations are applied to parameter space to render it approximately multivariate Gaussian, performing the Fisher matrix calculation on the transformed parameters. We demonstrate that, after the Box-Cox parameters have been determined from an initial likelihood evaluation, the method correctly predicts changes in the posterior when varying various parameters of the experimental setup and the data analysis, with marginally higher computational cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher formalism to forecast cosmological parameter constraints by future weak gravitational lensing surveys. The characteristic non-linear degeneracy between matter density parameter and normalization of matter density fluctuations is reproduced for several cases, and the capabilities of breaking this degeneracy by weak-lensing three-point statistics is investigated. Possible applications of Box-Cox transformations of posterior distributions are discussed, including the prospects for performing statistical data analysis steps in the transformed Gaussianized parameter space.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

Directory of Open Access Journals (Sweden)

David O. Smallwood

1997-01-01

Full Text Available The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general case of matching a target probability density function using a zero memory nonlinear (ZMNL function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.

Gaussian polynomials and content ideal in trivial extensions

International Nuclear Information System (INIS)

Bakkari, C.; Mahdou, N.

2006-12-01

The goal of this paper is to exhibit a class of Gaussian non-coherent rings R (with zero-divisors) such that wdim(R) = ∞ and fPdim(R) is always at most one and also exhibits a new class of rings (with zerodivisors) which are neither locally Noetherian nor locally domain where Gaussian polynomials have a locally principal content. For this purpose, we study the possible transfer of the 'Gaussian' property and the property 'the content ideal of a Gaussian polynomial is locally principal' to various trivial extension contexts. This article includes a brief discussion of the scopes and limits of our result. (author)

Quantifying entanglement in two-mode Gaussian states

Science.gov (United States)

Tserkis, Spyros; Ralph, Timothy C.

2017-12-01

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

Science.gov (United States)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

Graphical calculus for Gaussian pure states

International Nuclear Information System (INIS)

Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van

2011-01-01

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.

Gaussian Mixture Model of Heart Rate Variability

Science.gov (United States)

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386

Learning conditional Gaussian networks

DEFF Research Database (Denmark)

Bøttcher, Susanne Gammelgaard

This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... a configuration of the discrete parents. We assume parameter independence and complete data. Further, to learn the structure of the network, the network score is deduced. We then develop a local master prior procedure, for deriving parameter priors in these networks. This procedure satisfies parameter...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....

Fermionic particles with positron-dependent mass in the presence of inversely quadratic Yukawa potential and tensor interaction

International Nuclear Information System (INIS)

Bahar, M.K.; Yasuk, F.

2013-01-01

Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Two-photon optics of Bessel-Gaussian modes

CSIR Research Space (South Africa)

McLaren, M

2013-09-01

Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...

Non-Gaussianity in two-field inflation beyond the slow-roll approximation

Energy Technology Data Exchange (ETDEWEB)

Jung, Gabriel; Tent, Bartjan van, E-mail: gabriel.jung@th.u-psud.fr, E-mail: bartjan.van-tent@th.u-psud.fr [Laboratoire de Physique Théorique (UMR 8627), CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bâtiment 210, 91405 Orsay Cedex (France)

2017-05-01

We use the long-wavelength formalism to investigate the level of bispectral non-Gaussianity produced in two-field inflation models with standard kinetic terms. Even though the Planck satellite has so far not detected any primordial non-Gaussianity, it has tightened the constraints significantly, and it is important to better understand what regions of inflation model space have been ruled out, as well as prepare for the next generation of experiments that might reach the important milestone of Δ f {sub NL}{sup local}=1. We derive an alternative formulation of the previously derived integral expression for f {sub NL}, which makes it easier to physically interpret the result and see which types of potentials can produce large non-Gaussianity. We apply this to the case of a sum potential and show that it is very difficult to satisfy simultaneously the conditions for a large f {sub NL} and the observational constraints on the spectral index n {sub s} . In the case of the sum of two monomial potentials and a constant we explicitly show in which small region of parameter space this is possible, and we show how to construct such a model. Finally, the new general expression for f {sub NL} also allows us to prove that for the sum potential the explicit expressions derived within the slow-roll approximation remain valid even when the slow-roll approximation is broken during the turn of the field trajectory (as long as only the ε slow-roll parameter remains small).

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-01-01

Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

Subgroups of class groups of algebraic quadratic function fields

International Nuclear Information System (INIS)

Wang Kunpeng; Zhang Xianke

2001-09-01

Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

Science.gov (United States)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Functional Dual Adaptive Control with Recursive Gaussian Process Model

International Nuclear Information System (INIS)

Prüher, Jakub; Král, Ladislav

2015-01-01

The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)

Back to Normal! Gaussianizing posterior distributions for cosmological probes

Science.gov (United States)

Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.

2014-05-01

We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

Graphical Gaussian models with edge and vertex symmetries

DEFF Research Database (Denmark)

Højsgaard, Søren; Lauritzen, Steffen L

2008-01-01

We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where parameters that are associated with edges or vertices of the same colour are restricted to being identical. We...... study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation...

Genetic algorithm–based varying parameter linear quadratic regulator control for four-wheel independent steering vehicle

Directory of Open Access Journals (Sweden)

Linlin Gao

2015-11-01

Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.

Super-Gaussian transport theory and the field-generating thermal instability in laser–plasmas

International Nuclear Information System (INIS)

Bissell, J J; Ridgers, C P; Kingham, R J

2013-01-01

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser–plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density n e , which we associate with a novel heat-flow q n ∝∇n e . Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇T e × ∇n e field generation mechanism by ∼30% (where T e is the electron temperature), and the diffusive and Righi–Leduc heat-flows by ∼80 and ∼90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux q n are checked against kinetic simulation using the Vlasov–Fokker–Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields. (paper)

Super-Gaussian transport theory and the field-generating thermal instability in laser-plasmas

Science.gov (United States)

Bissell, J. J.; Ridgers, C. P.; Kingham, R. J.

2013-02-01

Inverse bremsstrahlung (IB) heating is known to distort the electron distribution function in laser-plasmas from a Gaussian towards a super-Gaussian, thereby modifying the equations of classical transport theory (Ridgers et al 2008 Phys. Plasmas 15 092311). Here we explore these modified equations, demonstrating that super-Gaussian effects both suppress traditional transport processes, while simultaneously introducing new effects, such as isothermal (anomalous Nernst) magnetic field advection up gradients in the electron number density ne, which we associate with a novel heat-flow qn∝∇ne. Suppression of classical phenomena is shown to be most pronounced in the limit of low Hall-parameter χ, in which case the Nernst effect is reduced by a factor of five, the ∇Te × ∇ne field generation mechanism by ˜30% (where Te is the electron temperature), and the diffusive and Righi-Leduc heat-flows by ˜80 and ˜90% respectively. The new isothermal field advection phenomenon and associated density-gradient driven heat-flux qn are checked against kinetic simulation using the Vlasov-Fokker-Planck code impact, and interpreted in relation to the underlying super-Gaussian distribution through simplified kinetic analysis. Given such strong inhibition of transport at low χ, we consider the impact of IB on the seeding and evolution of magnetic fields (in otherwise un-magnetized conditions) by examining the well-known field-generating thermal instability in the light of super-Gaussian transport theory (Tidman and Shanny 1974 Phys. Fluids 12 1207). Estimates based on conditions in an inertial confinement fusion (ICF) hohlraum suggest that super-Gaussian effects can reduce the growth-rate of the instability by ≳80%. This result may be important for ICF experiments, since by increasing the strength of IB heating it would appear possible to inhibit the spontaneous generation of large magnetic fields.

Non-Gaussian covariance of CMB B modes of polarization and parameter degradation

International Nuclear Information System (INIS)

Li Chao; Smith, Tristan L.; Cooray, Asantha

2007-01-01

The B-mode polarization lensing signal is a useful probe of the neutrino mass and to a lesser extent the dark energy equation of state as the signal depends on the integrated mass power spectrum between us and the last scattering surface. This lensing B-mode signal, however, is non-Gaussian and the resulting non-Gaussian covariance to the power spectrum could impact cosmological parameter measurements, as correlations between B-mode bins are at a level of 0.1. On the other hand, for temperature and E-mode polarization power spectra, the non-Gaussian covariance is not significant, where we find correlations at the 10 -5 level even for adjacent bins. When the power spectrum is estimated with roughly 5 uniformly spaced bins from l=5 to l=100 and 13 logarithmic uniformly spaced bins from l=100 to l=2000, the resulting degradation on neutrino mass and dark energy equation of state is about a factor of 2 to 3 when compared to the case where statistics are simply considered to be Gaussian. If we increase the total number of bins between l=5 and l=2000 to be about 100, we find that the non-Gaussianities only make a minor difference with less than a few percent correction to uncertainties of most cosmological parameters determined from the data. For Planck, the resulting constraints on the sum of the neutrino masses is σ Σm ν ∼0.2 eV and on the dark energy equation of state parameter we find that σ w ∼0.5. A post-Planck experiment can improve the neutrino mass measurement by a factor of 3 to 4

Quadratic blind linear unmixing: A graphical user interface for tissue characterization.

Science.gov (United States)

Gutierrez-Navarro, O; Campos-Delgado, D U; Arce-Santana, E R; Jo, Javier A

2016-02-01

Spectral unmixing is the process of breaking down data from a sample into its basic components and their abundances. Previous work has been focused on blind unmixing of multi-spectral fluorescence lifetime imaging microscopy (m-FLIM) datasets under a linear mixture model and quadratic approximations. This method provides a fast linear decomposition and can work without a limitation in the maximum number of components or end-members. Hence this work presents an interactive software which implements our blind end-member and abundance extraction (BEAE) and quadratic blind linear unmixing (QBLU) algorithms in Matlab. The options and capabilities of our proposed software are described in detail. When the number of components is known, our software can estimate the constitutive end-members and their abundances. When no prior knowledge is available, the software can provide a completely blind solution to estimate the number of components, the end-members and their abundances. The characterization of three case studies validates the performance of the new software: ex-vivo human coronary arteries, human breast cancer cell samples, and in-vivo hamster oral mucosa. The software is freely available in a hosted webpage by one of the developing institutions, and allows the user a quick, easy-to-use and efficient tool for multi/hyper-spectral data decomposition. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Optimal multicopy asymmetric Gaussian cloning of coherent states

International Nuclear Information System (INIS)

Fiurasek, Jaromir; Cerf, Nicolas J.

2007-01-01

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward

Optimal multicopy asymmetric Gaussian cloning of coherent states

Science.gov (United States)

Fiurášek, Jaromír; Cerf, Nicolas J.

2007-05-01

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.

Are ghost surfaces quadratic-flux-minimizing?

International Nuclear Information System (INIS)

Hudson, S.R.; Dewar, R.L.

2009-01-01

Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.

Electron laser acceleration in vacuum by a quadratically chirped laser pulse

International Nuclear Information System (INIS)

Salamin, Yousef I; Jisrawi, Najeh M

2014-01-01

Single MeV electrons in vacuum subjected to single high-intensity quadratically chirped laser pulses are shown to gain multi-GeV energies. The laser pulses are modelled by finite-duration trapezoidal and cos  2 pulse-shapes and the equations of motion are solved numerically. It is found that, typically, the maximum energy gain from interaction with a quadratic chirp is about half of what would be gained from a linear chirp. (paper)

Quadratic rational rotations of the torus and dual lattice maps

CERN Document Server

Kouptsov, K L; Vivaldi, F

2002-01-01

We develop a general formalism for computed-assisted proofs concerning the orbit structure of certain non ergodic piecewise affine maps of the torus, whose eigenvalues are roots of unity. For a specific class of maps, we prove that if the trace is a quadratic irrational (the simplest nontrivial case, comprising 8 maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of exceptional families. The proof is based on exact computations with algebraic numbers, where units play the role of scaling parameters. Exploiting a duality existing between these maps and lattice maps representing rounded-off planar rotations, we establish the global periodicity of the latter systems, for a set of orbits of full density.

Integrable Hamiltonian systems and interactions through quadratic constraints

International Nuclear Information System (INIS)

Pohlmeyer, K.

1975-08-01

Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

Boltzmann-Gaussian transition under specific noise effect

International Nuclear Information System (INIS)

Anh, Chu Thuy; Lan, Nguyen Tri; Viet, Nguyen Ai

2014-01-01

It is observed that a short time data set of market returns presents almost symmetric Boltzmann distribution whereas a long time data set tends to show a Gaussian distribution. To understand this universal phenomenon, many hypotheses which are spreading in a wide range of interdisciplinary research were proposed. In current work, the effects of background fluctuations on symmetric Boltzmann distribution is investigated. The numerical calculation is performed to show that the Gaussian noise may cause the transition from initial Boltzmann distribution to Gaussian one. The obtained results would reflect non-dynamic nature of the transition under consideration.

Non-Gaussianity at tree and one-loop levels from vector field perturbations

International Nuclear Information System (INIS)

Valenzuela-Toledo, Cesar A.; Rodriguez, Yeinzon; Lyth, David H.

2009-01-01

We study the spectrum P ζ and bispectrum B ζ of the primordial curvature perturbation ζ when the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree-level terms [both (either) in P ζ and (or) in B ζ ] and vice versa. The level of non-Gaussianity in the bispectrum, f NL , is calculated and related to the level of statistical anisotropy in the power spectrum, g ζ . For very small amounts of statistical anisotropy in the power spectrum, the level of non-Gaussianity may be very high, in some cases exceeding the current observational limit.

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

Science.gov (United States)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

Accelerating Sequential Gaussian Simulation with a constant path

Science.gov (United States)

Nussbaumer, Raphaël; Mariethoz, Grégoire; Gravey, Mathieu; Gloaguen, Erwan; Holliger, Klaus

2018-03-01

Sequential Gaussian Simulation (SGS) is a stochastic simulation technique commonly employed for generating realizations of Gaussian random fields. Arguably, the main limitation of this technique is the high computational cost associated with determining the kriging weights. This problem is compounded by the fact that often many realizations are required to allow for an adequate uncertainty assessment. A seemingly simple way to address this problem is to keep the same simulation path for all realizations. This results in identical neighbourhood configurations and hence the kriging weights only need to be determined once and can then be re-used in all subsequent realizations. This approach is generally not recommended because it is expected to result in correlation between the realizations. Here, we challenge this common preconception and make the case for the use of a constant path approach in SGS by systematically evaluating the associated benefits and limitations. We present a detailed implementation, particularly regarding parallelization and memory requirements. Extensive numerical tests demonstrate that using a constant path allows for substantial computational gains with very limited loss of simulation accuracy. This is especially the case for a constant multi-grid path. The computational savings can be used to increase the neighbourhood size, thus allowing for a better reproduction of the spatial statistics. The outcome of this study is a recommendation for an optimal implementation of SGS that maximizes accurate reproduction of the covariance structure as well as computational efficiency.

Gaussian sum rules for optical functions

International Nuclear Information System (INIS)

Kimel, I.

1981-12-01

A new (Gaussian) type of sum rules (GSR) for several optical functions, is presented. The functions considered are: dielectric permeability, refractive index, energy loss function, rotatory power and ellipticity (circular dichroism). While reducing to the usual type of sum rules in a certain limit, the GSR contain in general, a Gaussian factor that serves to improve convergence. GSR might be useful in analysing experimental data. (Author) [pt

Approximation problems with the divergence criterion for Gaussian variablesand Gaussian processes

NARCIS (Netherlands)

A.A. Stoorvogel; J.H. van Schuppen (Jan)

1996-01-01

textabstractSystem identification for stationary Gaussian processes includes an approximation problem. Currently the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a finite time series to canonical variable form followed by a truncation.

Gaussian processes for machine learning.

Science.gov (United States)

Seeger, Matthias

2004-04-01

Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided.

Comparison of halo detection from noisy weak lensing convergence maps with Gaussian smoothing and MRLens treatment

International Nuclear Information System (INIS)

Jiao Yangxiu; Shan Huanyuan; Fan Zuhui

2011-01-01

Taking into account the noise from intrinsic ellipticities of source galaxies, we study the efficiency and completeness of halo detections from weak lensing convergence maps. Particularly, with numerical simulations, we compare the Gaussian filter with the so called MRLens treatment based on the modification of the Maximum Entropy Method. For a pure noise field without lensing signals, a Gaussian smoothing results in a residual noise field that is approximately Gaussian in terms of statistics if a large enough number of galaxies are included in the smoothing window. On the other hand, the noise field after the MRLens treatment is significantly non-Gaussian, resulting in complications in characterizing the noise effects. Considering weak-lensing cluster detections, although the MRLens treatment effectively deletes false peaks arising from noise, it removes the real peaks heavily due to its inability to distinguish real signals with relatively low amplitudes from noise in its restoration process. The higher the noise level is, the larger the removal effects are for the real peaks. For a survey with a source density n g ∼ 30 arcmin -2 , the number of peaks found in an area of 3 x 3 deg 2 after MRLens filtering is only ∼ 50 for the detection threshold κ = 0.02, while the number of halos with M > 5 x 10 13 M circleddot and with redshift z ≤ 2 in the same area is expected to be ∼ 530. For the Gaussian smoothing treatment, the number of detections is ∼ 260, much larger than that of the MRLens. The Gaussianity of the noise statistics in the Gaussian smoothing case adds further advantages for this method to circumvent the problem of the relatively low efficiency in weak-lensing cluster detections. Therefore, in studies aiming to construct large cluster samples from weak-lensing surveys, the Gaussian smoothing method performs significantly better than the MRLens treatment.

Palm distributions for log Gaussian Cox processes

DEFF Research Database (Denmark)

Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus

This paper reviews useful results related to Palm distributions of spatial point processes and provides a new result regarding the characterization of Palm distributions for the class of log Gaussian Cox processes. This result is used to study functional summary statistics for a log Gaussian Cox...

QUANTUM AND CLASSICAL CORRELATIONS IN GAUSSIAN OPEN QUANTUM SYSTEMS

Directory of Open Access Journals (Sweden)

Aurelian ISAR

2015-01-01

Full Text Available In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum correlations (quantum entanglement and quantum discord for a system consisting of two noninteracting bosonic modes embedded in a thermal environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement and discord in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that it decays asymptotically in time under the effect of the thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.

Making tensor factorizations robust to non-gaussian noise.

Energy Technology Data Exchange (ETDEWEB)

Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson

2011-03-01

Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).

Accurate nonlocal theory for cascaded quadratic soliton compression

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Moses, Jeffrey

2007-01-01

We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

Science.gov (United States)

Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

2017-10-01

We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

A comparison on the propagation characteristics of focused Gaussian beam and fundamental Gaussian beam in vacuum

International Nuclear Information System (INIS)

Liu Shixiong; Guo Hong; Liu Mingwei; Wu Guohua

2004-01-01

Propagation characteristics of focused Gaussian beam (FoGB) and fundamental Gaussian beam (FuGB) propagating in vacuum are investigated. Based on the Fourier transform and the angular spectral analysis, the transverse component and the second-order approximate longitudinal component of the electric field are obtained in the paraxial approximation. The electric field components, the phase velocity and the group velocity of FoGB are compared with those of FuGB. The spot size of FoGB is also discussed

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Institute of Scientific and Technical Information of China (English)

XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian

2007-01-01

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.

Calculating emittance for Gaussian and Non-Gaussian distributions by the method of correlations for slits

International Nuclear Information System (INIS)

Tan, Cheng-Yang; Fermilab

2006-01-01

One common way for measuring the emittance of an electron beam is with the slits method. The usual approach for analyzing the data is to calculate an emittance that is a subset of the parent emittance. This paper shows an alternative way by using the method of correlations which ties the parameters derived from the beamlets to the actual parameters of the parent emittance. For parent distributions that are Gaussian, this method yields exact results. For non-Gaussian beam distributions, this method yields an effective emittance that can serve as a yardstick for emittance comparisons

Non-Gaussianity in a quasiclassical electronic circuit

Science.gov (United States)

Suzuki, Takafumi J.; Hayakawa, Hisao

2017-05-01

We study the non-Gaussian dynamics of a quasiclassical electronic circuit coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the stationary probability density function (PDF) of the flux in the dissipative circuit. We incorporate weak quantum fluctuation of the dissipative LC circuit with a stochastic method and evaluate the quantum correction of the stationary PDF. Furthermore, an inverse formula to infer the statistical properties of the non-Gaussian noise from the stationary PDF is derived in the classical-quantum crossover regime. The quantum correction is indispensable to correctly estimate the microscopic transfer events in the QPC with the quasiclassical inverse formula.

A fast Gaussian filtering algorithm for three-dimensional surface roughness measurements

International Nuclear Information System (INIS)

Yuan, Y B; Piao, W Y; Xu, J B

2007-01-01

The two-dimensional (2-D) Gaussian filter can be separated into two one-dimensional (1-D) Gaussian filters. The 1-D Gaussian filter can be implemented approximately by the cascaded Butterworth filters. The approximation accuracy will be improved with the increase of the number of the cascaded filters. A recursive algorithm for Gaussian filtering requires a relatively small number of simple mathematical operations such as addition, subtraction, multiplication, or division, so that it has considerable computational efficiency and it is very useful for three-dimensional (3-D) surface roughness measurements. The zero-phase-filtering technique is used in this algorithm, so there is no phase distortion in the Gaussian filtered mean surface. High-order approximation Gaussian filters are proposed for practical use to assure high accuracy of Gaussian filtering of 3-D surface roughness measurements

A fast Gaussian filtering algorithm for three-dimensional surface roughness measurements

Science.gov (United States)

Yuan, Y. B.; Piao, W. Y.; Xu, J. B.

2007-07-01

The two-dimensional (2-D) Gaussian filter can be separated into two one-dimensional (1-D) Gaussian filters. The 1-D Gaussian filter can be implemented approximately by the cascaded Butterworth filters. The approximation accuracy will be improved with the increase of the number of the cascaded filters. A recursive algorithm for Gaussian filtering requires a relatively small number of simple mathematical operations such as addition, subtraction, multiplication, or division, so that it has considerable computational efficiency and it is very useful for three-dimensional (3-D) surface roughness measurements. The zero-phase-filtering technique is used in this algorithm, so there is no phase distortion in the Gaussian filtered mean surface. High-order approximation Gaussian filters are proposed for practical use to assure high accuracy of Gaussian filtering of 3-D surface roughness measurements.

Imprint of primordial non-Gaussianity on dark matter halo profiles

Energy Technology Data Exchange (ETDEWEB)

Dizgah, Azadeh Moradinezhad; Dodelson, Scott; Riotto, Antonio

2013-09-01

We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian density field. In the context of the semi-analytic model for halo profiles, currently allowed values for primordial non-Gaussianity would increase the shapes of the inner dark matter profiles, but only at the sub-percent level except in the very innermost regions.

Factorization method of quadratic template

Science.gov (United States)

Kotyrba, Martin

2017-07-01

Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

On the dependence structure of Gaussian queues

NARCIS (Netherlands)

Es-Saghouani, A.; Mandjes, M.R.H.

2009-01-01

In this article we study Gaussian queues (that is, queues fed by Gaussian processes, such as fractional Brownian motion (fBm) and the integrated Ornstein-Uhlenbeck (iOU) process), with a focus on the dependence structure of the workload process. The main question is to what extent does the workload

Shedding new light on Gaussian harmonic analysis

NARCIS (Netherlands)

Teuwen, J.J.B.

2016-01-01

This dissertation consists out of two rather disjoint parts. One part concerns some results on Gaussian harmonic analysis and the other on an optimization problem in optics. In the first part we study the Ornstein–Uhlenbeck process with respect to the Gaussian measure. We focus on two areas. One is

Design of variable-weight quadratic congruence code for optical CDMA

Science.gov (United States)

Feng, Gang; Cheng, Wen-Qing; Chen, Fu-Jun

2015-09-01

A variable-weight code family referred to as variable-weight quadratic congruence code (VWQCC) is constructed by algebraic transformation for incoherent synchronous optical code division multiple access (OCDMA) systems. Compared with quadratic congruence code (QCC), VWQCC doubles the code cardinality and provides the multiple code-sets with variable code-weight. Moreover, the bit-error rate (BER) performance of VWQCC is superior to those of conventional variable-weight codes by removing or padding pulses under the same chip power assumption. The experiment results show that VWQCC can be well applied to the OCDMA with quality of service (QoS) requirements.

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

Directory of Open Access Journals (Sweden)

Georgios C Manikis

Full Text Available The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer.Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2 at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG and non-Gaussian (MNG and BNG were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE. To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC and F-ratio.All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area.No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Mixmaster cosmological model in theories of gravity with a quadratic Lagrangian

International Nuclear Information System (INIS)

Barrow, J.D.; Sirousse-Zia, H.

1989-01-01

We use the method of matched asymptotic expansions to examine the behavior of the vacuum Bianchi type-IX mixmaster universe in a gravity theory derived from a purely quadratic gravitational Lagrangian. The chaotic behavior characteristic of the general-relativistic mixmaster model disappears and the asymptotic behavior is of the monotonic, nonchaotic form found in the exactly soluble Bianchi type-I models of the quadratic theory. The asymptotic behavior far from the singularity is also found to be of monotonic nonchaotic type

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

Science.gov (United States)

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 sciencedirect.com/science/journal/03770427>, 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.

Representation of Gaussian semimartingales with applications to the covariance function

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas

2010-01-01

stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Science.gov (United States)

Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

2012-09-01

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Fractional Gaussian noise: Prior specification and model comparison

KAUST Repository

Sørbye, Sigrunn Holbek

2017-07-07

Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.

Fractional Gaussian noise: Prior specification and model comparison

KAUST Repository

Sø rbye, Sigrunn Holbek; Rue, Haavard

2017-01-01

Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.

Geometric Methods in the Algebraic Theory of Quadratic Forms : Summer School

CERN Document Server

2004-01-01

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes - an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions; - papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension; - a contribution in French by Bruno Kahn which lays out a general fra...

Multi-fidelity Gaussian process regression for prediction of random fields

International Nuclear Information System (INIS)

Parussini, L.; Venturi, D.; Perdikaris, P.; Karniadakis, G.E.

2017-01-01

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.

Multi-fidelity Gaussian process regression for prediction of random fields

Energy Technology Data Exchange (ETDEWEB)

Parussini, L. [Department of Engineering and Architecture, University of Trieste (Italy); Venturi, D., E-mail: venturi@ucsc.edu [Department of Applied Mathematics and Statistics, University of California Santa Cruz (United States); Perdikaris, P. [Department of Mechanical Engineering, Massachusetts Institute of Technology (United States); Karniadakis, G.E. [Division of Applied Mathematics, Brown University (United States)

2017-05-01

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.

Scaled unscented transform Gaussian sum filter: Theory and application

KAUST Repository

Luo, Xiaodong

2010-05-01

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to

Efficiency of the human observer for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds.

Science.gov (United States)

Park, Subok; Gallas, Bradon D; Badano, Aldo; Petrick, Nicholas A; Myers, Kyle J

2007-04-01

A previous study [J. Opt. Soc. Am. A22, 3 (2005)] has shown that human efficiency for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds is approximately 4%. This human efficiency is much less than the reported 40% efficiency that has been documented for Gaussian-distributed lumpy backgrounds [J. Opt. Soc. Am. A16, 694 (1999) and J. Opt. Soc. Am. A18, 473 (2001)]. We conducted a psychophysical study with a number of changes, specifically in display-device calibration and data scaling, from the design of the aforementioned study. Human efficiency relative to the ideal observer was found again to be approximately 5%. Our variance analysis indicates that neither scaling nor display made a statistically significant difference in human performance for the task. We conclude that the non-Gaussian distributed lumpy background is a major factor in our low human-efficiency results.

Limit theorems for functionals of Gaussian vectors

Institute of Scientific and Technical Information of China (English)

Hongshuai DAI; Guangjun SHEN; Lingtao KONG

2017-01-01

Operator self-similar processes,as an extension of self-similar processes,have been studied extensively.In this work,we study limit theorems for functionals of Gaussian vectors.Under some conditions,we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process.

Gaussian statistics for palaeomagnetic vectors

Science.gov (United States)

Love, J.J.; Constable, C.G.

2003-01-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to

Gaussian statistics for palaeomagnetic vectors

Science.gov (United States)

Love, J. J.; Constable, C. G.

2003-03-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to

Quadratic Variation by Markov Chains

DEFF Research Database (Denmark)

Hansen, Peter Reinhard; Horel, Guillaume

We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...

Coherent states for quadratic Hamiltonians

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

2011-01-01

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

Separability of diagonal symmetric states: a quadratic conic optimization problem

Directory of Open Access Journals (Sweden)

Jordi Tura

2018-01-01

Full Text Available We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS states. First, we show that separability in the case of DS in $C^d\\otimes C^d$ (symmetric qudits can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT is sufficient and necessary for separability of DS states for $d \\leq 4$. Furthermore, for $d \\geq 5$, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on $N$-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

Consistency relations for sharp inflationary non-Gaussian features

Energy Technology Data Exchange (ETDEWEB)

Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Blanco Encalada 2008, Santiago (Chile); Soto, Alex, E-mail: sander.mooij@ing.uchile.cl, E-mail: gpalmaquilod@ing.uchile.cl, E-mail: gpanotop@ing.uchile.cl, E-mail: gatogeno@gmail.com [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago (Chile)

2016-09-01

If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming from the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.

Consistency relations for sharp inflationary non-Gaussian features

International Nuclear Information System (INIS)

Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex

2016-01-01

If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming from the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.

Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources

International Nuclear Information System (INIS)

Guerrero, Mariana; Carlone, Marco

2010-01-01

Purpose: In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. Methods: The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. Results: In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter β. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusions: The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

Multi-brid inflation and non-gaussianity

International Nuclear Information System (INIS)

Sasaki, Misao

2008-01-01

We consider a class of multi-component hybrid inflation models whose evolution may be analytically solved under the slow-roll approximation. We call it multi-brid inflation (or n-brid inflation where n stands for the number of inflaton fields). As an explicit example, we consider a two-brid inflation model, in which the inflaton potentials are of exponential type and a waterfall field that terminates inflation has the standard quartic potential with two minima. Using the δN formalism, we derive an expression for the curvature perturbation valid to full nonlinear order. Then we give an explicit expression for the curvature perturbation to second order in the inflaton perturbation. We find that the final from of the curvature perturbation depends crucially on how the inflation ends. Using this expression, we present closed analytical expressions for the spectrum of the curvature perturbation Ps(k), the spectral index n s , the tensor to scalar ratio r, and the non-Gaussian parameter f NL local , in terms of the model parameters. We find that a wide range of the parameter space (n s , r, f NL local ) can be covered by varying the model parameters within a physically reasonable range. In particular, for plausible values of the model parameters, we may have a large non-Gaussianity f NL local ∼10-100. This is in sharp contrast to the case of single-field hybrid inflation in which these parameters are tightly constrained. (author)

Comparing Fixed and Variable-Width Gaussian Networks

Czech Academy of Sciences Publication Activity Database

Kůrková, Věra; Kainen, P.C.

2014-01-01

Roč. 57, September (2014), s. 23-28 ISSN 0893-6080 R&D Projects: GA MŠk(CZ) LD13002 Institutional support: RVO:67985807 Keywords : Gaussian radial and kernel networks * Functionally equivalent networks * Universal approximators * Stabilizers defined by Gaussian kernels * Argminima of error functionals Subject RIV: IN - Informatics, Computer Science Impact factor: 2.708, year: 2014

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

Directory of Open Access Journals (Sweden)

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

Quadratic mass relations in topological bootstrap theory

International Nuclear Information System (INIS)

Jones, C.E.; Uschersohn, J.

1980-01-01

From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed

A new formalism for modelling parameters α and β of the linear-quadratic model of cell survival for hadron therapy

Science.gov (United States)

Vassiliev, Oleg N.; Grosshans, David R.; Mohan, Radhe

2017-10-01

We propose a new formalism for calculating parameters α and β of the linear-quadratic model of cell survival. This formalism, primarily intended for calculating relative biological effectiveness (RBE) for treatment planning in hadron therapy, is based on a recently proposed microdosimetric revision of the single-target multi-hit model. The main advantage of our formalism is that it reliably produces α and β that have correct general properties with respect to their dependence on physical properties of the beam, including the asymptotic behavior for very low and high linear energy transfer (LET) beams. For example, in the case of monoenergetic beams, our formalism predicts that, as a function of LET, (a) α has a maximum and (b) the α/β ratio increases monotonically with increasing LET. No prior models reviewed in this study predict both properties (a) and (b) correctly, and therefore, these prior models are valid only within a limited LET range. We first present our formalism in a general form, for polyenergetic beams. A significant new result in this general case is that parameter β is represented as an average over the joint distribution of energies E 1 and E 2 of two particles in the beam. This result is consistent with the role of the quadratic term in the linear-quadratic model. It accounts for the two-track mechanism of cell kill, in which two particles, one after another, damage the same site in the cell nucleus. We then present simplified versions of the formalism, and discuss predicted properties of α and β. Finally, to demonstrate consistency of our formalism with experimental data, we apply it to fit two sets of experimental data: (1) α for heavy ions, covering a broad range of LETs, and (2) β for protons. In both cases, good agreement is achieved.

Covariance-Based Measurement Selection Criterion for Gaussian-Based Algorithms

Directory of Open Access Journals (Sweden)

Fernando A. Auat Cheein

2013-01-01

Full Text Available Process modeling by means of Gaussian-based algorithms often suffers from redundant information which usually increases the estimation computational complexity without significantly improving the estimation performance. In this article, a non-arbitrary measurement selection criterion for Gaussian-based algorithms is proposed. The measurement selection criterion is based on the determination of the most significant measurement from both an estimation convergence perspective and the covariance matrix associated with the measurement. The selection criterion is independent from the nature of the measured variable. This criterion is used in conjunction with three Gaussian-based algorithms: the EIF (Extended Information Filter, the EKF (Extended Kalman Filter and the UKF (Unscented Kalman Filter. Nevertheless, the measurement selection criterion shown herein can also be applied to other Gaussian-based algorithms. Although this work is focused on environment modeling, the results shown herein can be applied to other Gaussian-based algorithm implementations. Mathematical descriptions and implementation results that validate the proposal are also included in this work.

Walking solitons in quadratic nonlinear media

OpenAIRE

Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru

1996-01-01

We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed

Stochastic Linear Quadratic Optimal Control Problems

International Nuclear Information System (INIS)

Chen, S.; Yong, J.

2001-01-01

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

On misclassication probabilities of linear and quadratic classiers ...

African Journals Online (AJOL)

We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...

Entropy of level-cut random Gaussian structures at different volume fractions.

Science.gov (United States)

Marčelja, Stjepan

2017-10-01

Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.

Entropy of level-cut random Gaussian structures at different volume fractions

Science.gov (United States)

Marčelja, Stjepan

2017-10-01

Cutting random Gaussian fields at a given level can create a variety of morphologically different two- or several-phase structures that have often been used to describe physical systems. The entropy of such structures depends on the covariance function of the generating Gaussian random field, which in turn depends on its spectral density. But the entropy of level-cut structures also depends on the volume fractions of different phases, which is determined by the selection of the cutting level. This dependence has been neglected in earlier work. We evaluate the entropy of several lattice models to show that, even in the cases of strongly coupled systems, the dependence of the entropy of level-cut structures on molar fractions of the constituents scales with the simple ideal noninteracting system formula. In the last section, we discuss the application of the results to binary or ternary fluids and microemulsions.

Two-dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions. II. Gaussian-Markovian case

NARCIS (Netherlands)

Tanimura, Y; Steffen, T

2000-01-01

The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus