NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Ranjha, Bilal; Zhou, Zhou; Kavehrad, Mohsen
2014-08-01
We have compared the bit error rate (BER) performance of precoding-based asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) and pulse amplitude modulated discrete multitone (PAM-DMT) optical wireless (OW) systems in additive white Gaussian noise (AWGN) and indoor multipath frequency selective channel. Simulation and analytical results show that precoding schemes such as discrete Fourier transform, discrete cosine transform, and Zadoff-Chu sequences do not affect the performance of the OW systems in the AWGN channel while they do reduce the peak-to-average power ratio (PAPR) of the OFDM output signal. However, in a multipath indoor channel, using zero forcing frequency domain equalization precoding-based systems give better BER performance than their conventional counterparts. With additional clipping to further reduce the PAPR, precoding-based systems also show better BER performance compared to nonprecoded systems when clipped relative to the peak of nonprecoded systems. Therefore, precoding-based ACO-OFDM and PAM-DMT systems offer better BER performance, zero signaling overhead, and low PAPR compared to conventional systems.
Gaussian white noise analysis and its application to Feynman path integral
NASA Astrophysics Data System (ADS)
Suryawan, Herry Pribawanto
2016-02-01
In applied science, Gaussian white noise (the time derivative of Brownian motion) is often chosen as a mathematical idealization of phenomena involving sudden and extremely large fluctuations. It is also possible to define and study Gaussian white noise in a mathematically rigorous framework. In this survey paper we review the Gaussian white noise as an object in an infinite dimensional topological vector space. A brief construction of Gaussian white noise space and Gaussian white noise distributions will be presented. Gaussian white noise analysis provides a framework which offers various generalization of concept known from finite dimensional analysis to the infinite dimensional case, among them are differential operators, Fourier transform, and distribution theory. We will also present some recent developments and results on the application of Gaussian white noise theory to Feynman's path integral approach for quantum mechanics.
NASA Astrophysics Data System (ADS)
Ganguly, Jayanta; Ghosh, Manas
2014-06-01
We investigate the profiles of diagonal components of frequency-dependent linear (αxx and αyy) optical response of repulsive impurity doped quantum dots. The dopant impurity potential chosen assumes Gaussian form. The study principally puts emphasis on investigating the role of noise on the polarizability components. In view of this we have exploited Gaussian white noise containing additive and multiplicative characteristics (in Stratonovich sense). The frequency-dependent polarizabilities are studied by exposing the doped dot to a periodically oscillating external electric field of given intensity. The oscillation frequency, confinement potentials, dopant location, and above all, the noise characteristics tune the linear polarizability components in a subtle manner. Whereas the additive noise fails to have any impact on the polarizabilities, the multiplicative noise influences them delicately and gives rise to additional interesting features.
Analysis of regularized inversion of data corrupted by white Gaussian noise
NASA Astrophysics Data System (ADS)
Kekkonen, Hanne; Lassas, Matti; Siltanen, Samuli
2014-04-01
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 \\begin{eqnarray*} m(x) = Au(x) + \\delta \\varepsilon (x), \\end{eqnarray*} where δ > 0 is the noise magnitude. If ɛ was an L2-function, Tikhonov regularization gives an estimate \\begin{eqnarray*} T_\\alpha (m) = \\mathop {{arg\\, min}}_{u\\in H^r} \\big \\lbrace \\Vert A u-m\\Vert _{L^2}^2+ \\alpha \\Vert u\\Vert _{H^r}^2 \\big \\rbrace \\end{eqnarray*} for u where α = α(δ) is the regularization parameter. Here penalization of the Sobolev norm \\Vert u\\Vert _{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 L2, but do belong to Hs 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.
NASA Astrophysics Data System (ADS)
Bera, Aindrila; Saha, Surajit; Ganguly, Jayanta; Ghosh, Manas
2016-11-01
We explore diamagnetic susceptibility (DMS) of impurity doped quantum dot (QD) in presence of Gaussian white noise. Noise has been introduced to the system additively and multiplicatively. In view of these profiles of DMS have been pursued with variations of several important quantities e.g. magnetic field strength, confinement frequency, dopant location, dopant potential, and aluminium concentration, both in presence and absence of noise. We have invariably envisaged noise-induced suppression of DMS. Moreover, the extent of suppression noticeably depends on mode of application (additive/multiplicative) of noise. The said mode of application also plays a governing role in the onset of saturation of DMS values. The present study provides a deep insight into the promising role played by noise in controlling effective confinement imposed on the system which bears significant relevance.
NASA Astrophysics Data System (ADS)
Saha, Surajit; Ghosh, Manas
2016-03-01
We perform a broad exploration of profiles of third harmonic generation (THG) susceptibility of impurity doped quantum dots (QDs) in the presence and absence of noise. We have invoked Gaussian white noise in the present study. A Gaussian impurity has been introduced into the QD. Noise has been applied to the system additively and multiplicatively. A perpendicular magnetic field emerges out as a confinement source and a static external electric field has been applied. The THG profiles have been pursued as a function of incident photon energy when several important parameters such as electric field strength, magnetic field strength, confinement energy, dopant location, Al concentration, dopant potential, relaxation time and noise strength assume different values. Moreover, the role of the pathway through which noise is applied (additive/multiplicative) on the THG profiles has also been deciphered. The THG profiles are found to be decorated with interesting observations such as shift of THG peak position and maximization/minimization of THG peak intensity. Presence of noise alters the characteristics of THG profiles and sometimes enhances the THG peak intensity. Furthermore, the mode of application of noise (additive/multiplicative) also regulates the THG profiles in a few occasions in contrasting manners. The observations highlight the possible scope of tuning the THG coefficient of doped QD systems in the presence of noise and bears tremendous technological importance.
On stochastic differential equations driven by the renormalized square of the Gaussian white noise
NASA Astrophysics Data System (ADS)
Ben Ammou, Bilel Kacem; Lanconelli, Alberto
2015-11-01
We investigate the properties of the Wick square of Gaussian white noises through a new method to perform nonlinear operations on Hida distributions. This method lays in between the Wick product interpretation and the usual definition of nonlinear functions. We prove an Itô-type formula and solve stochastic differential equations driven by the renormalized square of the Gaussian white noise. Our approach works with standard assumptions on the coefficients of the equations, global Lipschitz continuity, and produces existence and uniqueness results in the space where the noise lives. The linear case is studied in details and positivity of the solution is proved.
NASA Astrophysics Data System (ADS)
Ganguly, Jayanta; Ghosh, Manas
2015-07-01
We investigate the modulation of diagonal components of static linear (αxx, αyy) and first nonlinear (βxxx, βyyy) polarizabilities of quantum dots by Gaussian white noise. Quantum dot is doped with impurity represented by a Gaussian potential and repulsive in nature. The study reveals the importance of mode of application of noise (additive/multiplicative) on the polarizability components. The doped system is further exposed to a static external electric field of given intensity. As important observation we have found that the strength of additive noise becomes unable to influence the polarizability components. However, the multiplicative noise influences them conspicuously and gives rise to additional interesting features. Multiplicative noise even enhances the magnitude of the polarizability components immensely. The present investigation deems importance in view of the fact that noise seriously affects the optical properties of doped quantum dot devices.
NASA Astrophysics Data System (ADS)
Ganguly, Jayanta; Ghosh, Manas
2014-05-01
We investigate the profiles of diagonal components of frequency-dependent first nonlinear (βxxx and βyyy) optical response of repulsive impurity doped quantum dots. We have assumed a Gaussian function to represent the dopant impurity potential. This study primarily addresses the role of noise on the polarizability components. We have invoked Gaussian white noise consisting of additive and multiplicative characteristics (in Stratonovich sense). The doped system has been subjected to an oscillating electric field of given intensity, and the frequency-dependent first nonlinear polarizabilities are computed. The noise characteristics are manifested in an interesting way in the nonlinear polarizability components. In case of additive noise, the noise strength remains practically ineffective in influencing the optical responses. The situation completely changes with the replacement of additive noise by its multiplicative analog. The replacement enhances the nonlinear optical response dramatically and also causes their maximization at some typical value of noise strength that depends on oscillation frequency.
Ganguly, Jayanta; Ghosh, Manas
2014-05-07
We investigate the profiles of diagonal components of frequency-dependent first nonlinear (β{sub xxx} and β{sub yyy}) optical response of repulsive impurity doped quantum dots. We have assumed a Gaussian function to represent the dopant impurity potential. This study primarily addresses the role of noise on the polarizability components. We have invoked Gaussian white noise consisting of additive and multiplicative characteristics (in Stratonovich sense). The doped system has been subjected to an oscillating electric field of given intensity, and the frequency-dependent first nonlinear polarizabilities are computed. The noise characteristics are manifested in an interesting way in the nonlinear polarizability components. In case of additive noise, the noise strength remains practically ineffective in influencing the optical responses. The situation completely changes with the replacement of additive noise by its multiplicative analog. The replacement enhances the nonlinear optical response dramatically and also causes their maximization at some typical value of noise strength that depends on oscillation frequency.
NASA Technical Reports Server (NTRS)
Blasche, P. R.
1980-01-01
Specific configurations of first and second order all digital phase locked loops are analyzed for both ideal and additive white gaussian noise inputs. In addition, a design for a hardware digital phase locked loop capable of either first or second order operation is presented along with appropriate experimental data obtained from testing of the hardware loop. All parameters chosen for the analysis and the design of the digital phase locked loop are consistent with an application to an Omega navigation receiver although neither the analysis nor the design are limited to this application.
Fokker-Planck description for a linear delayed Langevin equation with additive Gaussian noise
NASA Astrophysics Data System (ADS)
Giuggioli, Luca; McKetterick, Thomas John; Kenkre, V. M.; Chase, Matthew
2016-09-01
We construct an equivalent probability description of linear multi-delay Langevin equations subject to additive Gaussian white noise. By exploiting the time-convolutionless transform and a time variable transformation we are able to write a Fokker-Planck equation (FPE) for the 1-time and for the 2-time probability distributions valid irrespective of the regime of stability of the Langevin equations. We solve exactly the derived FPEs and analyze the aging dynamics by studying analytically the conditional probability distribution. We discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non-Markov process as both preparation and observation times have bearing on its dynamics. As our analytic procedure can also be applied to linear Langevin equations with memory kernels, we compare the non-Markov dynamics of a one-delay system with that of a generalized Langevin equation with an exponential as well as a power law memory. Application to a generalization of the Green-Kubo formula is also presented.
Fokker–Planck description for a linear delayed Langevin equation with additive Gaussian noise
NASA Astrophysics Data System (ADS)
Giuggioli, Luca; McKetterick, Thomas John; Kenkre, V. M.; Chase, Matthew
2016-09-01
We construct an equivalent probability description of linear multi-delay Langevin equations subject to additive Gaussian white noise. By exploiting the time-convolutionless transform and a time variable transformation we are able to write a Fokker–Planck equation (FPE) for the 1-time and for the 2-time probability distributions valid irrespective of the regime of stability of the Langevin equations. We solve exactly the derived FPEs and analyze the aging dynamics by studying analytically the conditional probability distribution. We discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non-Markov process as both preparation and observation times have bearing on its dynamics. As our analytic procedure can also be applied to linear Langevin equations with memory kernels, we compare the non-Markov dynamics of a one-delay system with that of a generalized Langevin equation with an exponential as well as a power law memory. Application to a generalization of the Green–Kubo formula is also presented.
Ultimate capacity of linear time-invariant bosonic channels with additive Gaussian noise
NASA Astrophysics Data System (ADS)
Roy Bardhan, Bhaskar; Shapiro, Jeffrey H.
2016-03-01
Fiber-optic communications are moving to coherent detection in order to increase their spectral efficiency, i.e., their channel capacity per unit bandwidth. At power levels below the threshold for significant nonlinear effects, the channel model for such operation a linear time-invariant filter followed by additive Gaussian noise is one whose channel capacity is well known from Shannon's noisy channel coding theorem. The fiber channel, however, is really a bosonic channel, meaning that its ultimate classical information capacity must be determined from quantum-mechanical analysis, viz. from the Holevo-Schumacher-Westmoreland (HSW) theorem. Based on recent results establishing the HSW capacity of a linear (lossy or amplifying) channel with additive Gaussian noise, we provide a general continuous-time result, namely the HSW capacity of a linear time-invariant (LTI) bosonic channel with additive Gaussian noise arising from a thermal environment. In particular, we treat quasi-monochromatic communication under an average power constraint through a channel comprised of a stable LTI filter that may be attenuating at all frequencies or amplifying at some frequencies and attenuating at others. Phase-insensitive additive Gaussian noise-associated with the continuous-time Langevin noise operator needed to preserve free-field commutator brackets is included at the filter output. We compare the resulting spectral efficiencies with corresponding results for heterodyne and homodyne detection over the same channel to assess the increased spectral efficiency that might be realized with optimum quantum reception.
NASA Astrophysics Data System (ADS)
Ganguly, Jayanta; Saha, Surajit; Pal, Suvajit; Ghosh, Manas
2016-03-01
We perform a meticulous analysis of profiles of third-order nonlinear optical susceptibility (TONOS) of impurity doped quantum dots (QDs) in the presence and absence of noise. We have invoked Gaussian white noise in the present study and noise has been introduced to the system additively and multiplicatively. The QD is doped with a Gaussian impurity. A magnetic field applied perpendicularly serves as a confinement source and the doped system has been exposed to a static external electric field. The TONOS profiles have been monitored against a continuous variation of incident photon energy when several important parameters such as electric field strength, magnetic field strength, confinement energy, dopant location, Al concentration, dopant potential, relaxation time, anisotropy, and noise strength assume different values. Moreover, the influence of mode of introduction of noise (additive/multiplicative) on the TONOS profiles has also been addressed. The said profiles are found to be consisting of interesting observations such as shift of TONOS peak position and maximization/minimization of TONOS peak intensity. The presence of noise alters the features of TONOS profiles and sometimes enhances the TONOS peak intensity from that of noise-free state. Furthermore, the mode of application of noise also often tailors the TONOS profiles in diverse fashions. The observations accentuate the possibility of tuning the TONOS of doped QD systems in the presence of noise.
Additive non-Gaussian noise attacks on the scalar Costa scheme (SCS)
NASA Astrophysics Data System (ADS)
Tzschoppe, Roman; Bauml, Robert; Fischer, Robert; Huber, Johannes; Kaup, Andre
2005-03-01
The additive attack public mutual information game is explicitly solved for one of the simplest quantization based watermarking schemes, the scalar Costa scheme (SCS). It is a zero-sum game played between the embedder and the attacker, and the payoff function is the mutual information. The solution of the game, a subgame perfect nash equilibrium, is found by backward induction. Therefore, the Blahut-Arimoto algorithm is employed for numerically optimizing the mutual information over noise distributions. Although the worst case distribution is in general strongly non-Gaussian, the capacity degradation compared to a suboptimal Gaussian noise attack is quite small. The loss, if the embedder optimizes SCS for a Gaussian attack but the worst case attack is employed, is negligible.
Wassermann, D; Bloy, L; Kanterakis, E; Verma, R; Deriche, R
2010-05-15
With the increasing importance of fiber tracking in diffusion tensor images for clinical needs, there has been a growing demand for an objective mathematical framework to perform quantitative analysis of white matter fiber bundles incorporating their underlying physical significance. This article presents such a novel mathematical framework that facilitates mathematical operations between tracts using an inner product between fibres. Such inner product operation, based on Gaussian processes, spans a metric space. This metric facilitates combination of fiber tracts, rendering operations like tract membership to a bundle or bundle similarity simple. Based on this framework, we have designed an automated unsupervised atlas-based clustering method that does not require manual initialization nor an a priori knowledge of the number of clusters. Quantitative analysis can now be performed on the clustered tract volumes across subjects, thereby avoiding the need for point parameterization of these fibers, or the use of medial or envelope representations as in previous work. Experiments on synthetic data demonstrate the mathematical operations. Subsequently, the applicability of the unsupervised clustering framework has been demonstrated on a 21-subject dataset. PMID:20079439
NASA Astrophysics Data System (ADS)
Saha, Surajit; Ganguly, Jayanta; Pal, Suvajit; Ghosh, Manas
2016-08-01
We study the modulation of electro-optic effect (EOE) of impurity doped QD under the influence of geometrical anisotropy and position-dependent effective mass (PDEM) in presence of Gaussian white noise. Always a comparison has been made between fixed effective mass (FEM) and PDEM to understand the role of the latter. In addition, the role of mode of application of noise (additive/multiplicative) has also been analyzed. The EOE profiles are found to be enriched with shift of peak position and maximization of peak intensity. The observations reveal sensitive interplay between noise and anisotropy/PDEM to fine-tune the features of EOE profiles.
NASA Technical Reports Server (NTRS)
Painter, J. H.; Gupta, S. C.
1973-01-01
This paper presents the derivation of the recursive algorithms necessary for real-time digital detection of M-ary known signals that are subject to independent multiplicative and additive Gaussian noises. The motivating application is minimum probability of error detection of digital data-link messages aboard civil aircraft in the earth reflection multipath environment. For each known signal, the detector contains one Kalman filter and one probability computer. The filters estimate the multipath disturbance. The estimates and the received signal drive the probability computers. Outputs of all the computers are compared in amplitude to give the signal decision. The practicality and usefulness of the detector are extensively discussed.
NASA Astrophysics Data System (ADS)
Xiao, Yanwen; Xu, Wei; Wang, Liang
2016-03-01
This paper focuses on the study of the stochastic Van der Pol vibro-impact system with fractional derivative damping under Gaussian white noise excitation. The equations of the original system are simplified by non-smooth transformation. For the simplified equation, the stochastic averaging approach is applied to solve it. Then, the fractional derivative damping term is facilitated by a numerical scheme, therewith the fourth-order Runge-Kutta method is used to obtain the numerical results. And the numerical simulation results fit the analytical solutions. Therefore, the proposed analytical means to study this system are proved to be feasible. In this context, the effects on the response stationary probability density functions (PDFs) caused by noise excitation, restitution condition, and fractional derivative damping are considered, in addition the stochastic P-bifurcation is also explored in this paper through varying the value of the coefficient of fractional derivative damping and the restitution coefficient. These system parameters not only influence the response PDFs of this system but also can cause the stochastic P-bifurcation.
Xiao, Yanwen; Xu, Wei; Wang, Liang
2016-03-01
This paper focuses on the study of the stochastic Van der Pol vibro-impact system with fractional derivative damping under Gaussian white noise excitation. The equations of the original system are simplified by non-smooth transformation. For the simplified equation, the stochastic averaging approach is applied to solve it. Then, the fractional derivative damping term is facilitated by a numerical scheme, therewith the fourth-order Runge-Kutta method is used to obtain the numerical results. And the numerical simulation results fit the analytical solutions. Therefore, the proposed analytical means to study this system are proved to be feasible. In this context, the effects on the response stationary probability density functions (PDFs) caused by noise excitation, restitution condition, and fractional derivative damping are considered, in addition the stochastic P-bifurcation is also explored in this paper through varying the value of the coefficient of fractional derivative damping and the restitution coefficient. These system parameters not only influence the response PDFs of this system but also can cause the stochastic P-bifurcation. PMID:27036188
On estimating the phase of periodic waveform in additive Gaussian noise, part 2
NASA Astrophysics Data System (ADS)
Rauch, L. L.
1984-11-01
Motivated by advances in signal processing technology that support more complex algorithms, a new look is taken at the problem of estimating the phase and other parameters of a periodic waveform in additive Gaussian noise. The general problem was introduced and the maximum a posteriori probability criterion with signal space interpretation was used to obtain the structures of optimum and some suboptimum phase estimators for known constant frequency and unknown constant phase with an a priori distribution. Optimal algorithms are obtained for some cases where the frequency is a parameterized function of time with the unknown parameters and phase having a joint a priori distribution. In the last section, the intrinsic and extrinsic geometry of hypersurfaces is introduced to provide insight to the estimation problem for the small noise and large noise cases.
81. THREE ADDITIONAL BLACK AND WHITE VIDEO MONITORS LOCATED IMMEDIATELY ...
81. THREE ADDITIONAL BLACK AND WHITE VIDEO MONITORS LOCATED IMMEDIATELY WEST OF THOSE IN CA-133-1-A-80. COMPLEX SAFETY WARNING LIGHTS FOR SLC-3E (PAD 2) AND BLDG. 763 (LOB) LOCATED ABOVE MONITOR 3; GREEN LIGHTS ON BOTTOM OF EACH STACK ILLUMINATED. LEFT TO RIGHT BELOW MONITORS: ACCIDENT REPORTING EMERGENCY NOTIFICATION SYSTEM TELEPHONE, ATLAS H FUEL COUNTER, AND DIGITAL COUNTDOWN CLOCK. - Vandenberg Air Force Base, Space Launch Complex 3, Launch Operations Building, Napa & Alden Roads, Lompoc, Santa Barbara County, CA
NASA Astrophysics Data System (ADS)
Waubke, Holger; Kasess, Christian H.
2016-11-01
Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.
NASA Astrophysics Data System (ADS)
Yong-Ge, Yang; Wei, Xu; Ya-Hui, Sun; Xu-Dong, Gu
2016-02-01
This paper aims to investigate the stochastic response of the van der Pol (VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary. Project supported by the National Natural Science Foundation of China (Grant Nos. 11472212, 11532011, and 11502201).
Adaptive subspace detection of extended target in white Gaussian noise using sinc basis
NASA Astrophysics Data System (ADS)
Zhang, Xiao-Wei; Li, Ming; Qu, Jian-She; Yang, Hui
2016-01-01
For the high resolution radar (HRR), the problem of detecting the extended target is considered in this paper. Based on a single observation, a new two-step detection based on sparse representation (TSDSR) method is proposed to detect the extended target in the presence of Gaussian noise with unknown covariance. In the new method, the Sinc dictionary is introduced to sparsely represent the high resolution range profile (HRRP). Meanwhile, adaptive subspace pursuit (ASP) is presented to recover the HRRP embedded in the Gaussian noise and estimate the noise covariance matrix. Based on the Sinc dictionary and the estimated noise covariance matrix, one step subspace detector (OSSD) for the first-order Gaussian (FOG) model without secondary data is adopted to realise the extended target detection. Finally, the proposed TSDSR method is applied to raw HRR data. Experimental results demonstrate that HRRPs of different targets can be sparsely represented very well with the Sinc dictionary. Moreover, the new method can estimate the noise power with tiny errors and have a good detection performance.
Smolin, John A; Gambetta, Jay M; Smith, Graeme
2012-02-17
We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.
Performance of peaky template matching under additive white Gaussian noise and uniform quantization
NASA Astrophysics Data System (ADS)
Horvath, Matthew S.; Rigling, Brian D.
2015-05-01
Peaky template matching (PTM) is a special case of a general algorithm known as multinomial pattern matching originally developed for automatic target recognition of synthetic aperture radar data. The algorithm is a model- based approach that first quantizes pixel values into Nq = 2 discrete values yielding generative Beta-Bernoulli models as class-conditional templates. Here, we consider the case of classification of target chips in AWGN and develop approximations to image-to-template classification performance as a function of the noise power. We focus specifically on the case of a uniform quantization" scheme, where a fixed number of the largest pixels are quantized high as opposed to using a fixed threshold. This quantization method reduces sensitivity to the scaling of pixel intensities and quantization in general reduces sensitivity to various nuisance parameters difficult to account for a priori. Our performance expressions are verified using forward-looking infrared imagery from the Army Research Laboratory Comanche dataset.
NASA Astrophysics Data System (ADS)
Pratim Ghosh, Arghya; Mandal, Arkajit; Sarkar, Sucharita; Ghosh, Manas
2016-05-01
We examine the influence of position-dependent effective mass (PDEM) on a few nonlinear optical (NLO) properties of impurity doped quantum dots (QDs) in presence and absence of noise. The said properties include total optical absorption coefficient (TOAC), nonlinear optical rectification (NOR), second harmonic generation (SHG) and third harmonic generation (THG). The impurity potential is modeled by a Gaussian function and the noise applied being Gaussian white noise. The profiles of above NLO properties have been pursued as a function of incident photon energy for different values of PDEM. Using PDEM the said profiles exhibit considerable departure from that of fixed effective mass (FEM). Presence of noise almost invariably amplifies the NLO properties with a few exceptions. A change in the mode of application of noise also sometimes affects the above profiles. The investigation furnishes us with a detailed picture of the subtle interplay between noise and PDEM through which the said NLO properties of doped QD systems can be tailored.
Gaussian entanglement of formation
Wolf, M.M.; Giedke, G.; Krueger, O.; Werner, R. F.; Cirac, J.I.
2004-05-01
We introduce a Gaussian version of the entanglement of formation adapted to bipartite Gaussian states by considering decompositions into pure Gaussian states only. We show that this quantity is an entanglement monotone under Gaussian operations and provide a simplified computation for states of arbitrary many modes. For the case of one mode per site the remaining variational problem can be solved analytically. If the considered state is in addition symmetric with respect to interchanging the two modes, we prove additivity of the considered entanglement measure. Moreover, in this case and considering only a single copy, our entanglement measure coincides with the true entanglement of formation.
NASA Astrophysics Data System (ADS)
Kleine, Achim
Models were developed to investigate the tracking behavior of combined Costas/AFC (Automatic Frequency Control) feedback loops under Rayleigh/Rician fading conditions with additive Gaussian noise jamming. A general linearized tracking model was developed for land-mobile channels. The model can be used for the nonlinearized case with sinusoidal phase detection characteristic using a standard solution of the Fokker-Planck equation. A tracking analysis for Costas/AFC loops with coherent automatic gain control, and an accuracy analysis for interferometers equipped with Costas/AFC loops are treated as examples. The tracking model is the most inaccurate in the case of quasistationary channels.
Federal Register 2010, 2011, 2012, 2013, 2014
2011-07-21
...). The first list of such additions was published in the Federal Register on March 27, 1991 (56 FR 12818... (59 FR 17174), and on January 13, 2005 (70 FR 2423.) The list included herein contains more additions... Bureau of Indian Affairs List of Additional Lands Affected by White Earth Reservation Land Settlement...
Arif, Saqib; Ali, Tahira Mohsin; Ul Afzal, Qurat; Ahmed, Mubarik; Siddiqui, Asim Jamal; Hasnain, Abid
2014-06-01
The effects of water extractable pentosans (WEP) and water unextractable pentosans (WUP) on pasting properties in flours of eight different hard white spring wheat (HWSW) cultivars was studied. WEP and WUP isolated from a hard wheat flour were added to each of the cultivars at 1% and 2% level. The results indicated that WEP exhibited a pronounced effect on pasting properties as compared to WUP and variety. Univariate analysis of variance (ANOVA) was used to evaluate sources of variation. The variety significantly (P < 0.001) influenced all the pasting parameters. WUP caused significant (P < 0.001) variation in paste viscosities (except breakdown). WEP influenced more pronouncedly the hot paste, cold paste, breakdown and setback viscosities with F values-221.802, 214.286, 98.073 and 120.159, respectively. Variety-by-WEP interaction exhibited significant (P < 0.01) influence on pasting time, peak, hot paste and cold paste viscosities. Whereas, variety-by-WUP interaction only significantly (P < 0.001) influenced the pasting- time and -temperature. Duncan's test was used to analyze the significant difference (P < 0.05) within the variety. The results revealed that WUP did not induce significant (P < 0.05) influence on all the pasting parameters, whereas, WEP influenced significantly (P < 0.05) the paste viscosities of some of the varieties. It was also found that the addition of WEP remarkably reduced the setback, hot paste, cold paste viscosities and increased the breakdown viscosity in all cultivar flours. The effect of WEP was greater at higher level of supplementation on paste viscosities. PMID:24876638
Novel high refractive index, thermally conductive additives for high brightness white LEDs
NASA Astrophysics Data System (ADS)
Hutchison, Richard Stephen
In prior works the inclusion of nanoparticle fillers has typically been shown to increase the thermal conductivity or refractive index of polymer nanocomposites separately. High refractive index zirconia nanoparticles have already proved their merit in increasing the optical efficiency of encapsulated light emitting diodes. However, the thermal properties of zirconia-silicone nanocomposites have yet to be investigated. While phosphor-converted light emitting diodes are at the forefront of solid-state lighting technologies for producing white light, they are plagued by efficiency losses due to excessive heating at the semiconductor die and in and around the phosphor particles, as well as photon scattering losses in the phosphor layer. It would then be of great interest if the high refractive index nanoparticles were found to both be capable of increasing the refractive index, thus reducing the optical scattering, and also the thermal conductivity, channeling more heat away from the LED die and phosphors, mitigating efficiency losses from heat. Thermal conductance measurements on unfilled and nanoparticle loaded silicone samples were conducted to quantify the effect of the zirconia nanoparticle loading on silicone nanocomposite thermal conductivity. An increase in thermal conductivity from 0.27 W/mK to 0.49 W/mK from base silicone to silicone with 33.5 wt% zirconia nanoparticles was observed. This trend closely mirrored a basic rule of mixtures prediction, implying a further enhancement in thermal conductivity could be achieved at higher nanoparticle loadings. The optical properties of transparency and light extraction efficiency of these composites were also investigated. While overall the zirconia nanocomposite showed good transparency, there was a slight decrease at the shorter wavelengths with increasing zirconia content. For longer wavelength LEDs, such as green or red, this might not matter, but phosphor-converted white LEDs use a blue LED as the photon source
NASA Technical Reports Server (NTRS)
Smalheer, C. V.
1973-01-01
The chemistry of lubricant additives is discussed to show what the additives are chemically and what functions they perform in the lubrication of various kinds of equipment. Current theories regarding the mode of action of lubricant additives are presented. The additive groups discussed include the following: (1) detergents and dispersants, (2) corrosion inhibitors, (3) antioxidants, (4) viscosity index improvers, (5) pour point depressants, and (6) antifouling agents.
Dias, Tânia R; Alves, Marco G; Tomás, Gonçalo D; Socorro, Sílvia; Silva, Branca M; Oliveira, Pedro F
2014-01-22
Storage of sperm under refrigeration reduces its viability, due to oxidative unbalance. Unfermented teas present high levels of catechin derivatives, known to reduce oxidative stress. This study investigated the effect of white tea (WTEA) on epididymal spermatozoa survival at room temperature (RT), using green tea (GTEA) for comparative purposes. The chemical profiles of WTEA and GTEA aqueous extracts were evaluated by (1)H NMR. (-)-Epigallocatechin-3-gallate was the most abundant catechin, being twice as abundant in WTEA extract. The antioxidant power of storage media was evaluated. Spermatozoa antioxidant potential, lipid peroxidation, and viability were assessed. The media antioxidant potential increased the most with WTEA supplementation, which was concomitant with the highest increase in sperm antioxidant potential and lipid peroxidation decrease. WTEA supplementation restored spermatozoa viability to values similar to those obtained at collection time. These findings provide evidence that WTEA extract is an excellent media additive for RT sperm storage, to facilitate transport and avoid the deleterious effects of refrigeration.
Cambria, Maria Teresa; Ragusa, Santa; Calabrese, Vittorio; Cambria, Antonio
2011-02-01
The white rot fungus Rigidoporus lignosus produces substantial amounts of extracellular laccase, a multicopper blue oxidase which is capable of oxidizing a wide range of organic substrates. Laccase production can be greatly enhanced in liquid cultures supplemented with various aromatic and phenolic compounds. The maximum enzyme activity was reached at the 21st or 24th day of fungal cultivation after the addition of inducers. The zymograms of extracellular fluid of culture preparation in the presence of inducers, at maximum activity day, revealed two bands with enzymatic activity, called Lac1 and Lac2, having different intensities. Lac2 band shows the higher intensity which changed with the different inducers. Laccase induction can be also obtained by adding to the culture medium olive mill wastewaters, which shows a high content of phenolic compounds.
Dias, Tânia R; Alves, Marco G; Tomás, Gonçalo D; Socorro, Sílvia; Silva, Branca M; Oliveira, Pedro F
2014-01-22
Storage of sperm under refrigeration reduces its viability, due to oxidative unbalance. Unfermented teas present high levels of catechin derivatives, known to reduce oxidative stress. This study investigated the effect of white tea (WTEA) on epididymal spermatozoa survival at room temperature (RT), using green tea (GTEA) for comparative purposes. The chemical profiles of WTEA and GTEA aqueous extracts were evaluated by (1)H NMR. (-)-Epigallocatechin-3-gallate was the most abundant catechin, being twice as abundant in WTEA extract. The antioxidant power of storage media was evaluated. Spermatozoa antioxidant potential, lipid peroxidation, and viability were assessed. The media antioxidant potential increased the most with WTEA supplementation, which was concomitant with the highest increase in sperm antioxidant potential and lipid peroxidation decrease. WTEA supplementation restored spermatozoa viability to values similar to those obtained at collection time. These findings provide evidence that WTEA extract is an excellent media additive for RT sperm storage, to facilitate transport and avoid the deleterious effects of refrigeration. PMID:24372402
Erbay, Zafer; Koca, Nurcan
2015-12-01
There is an increasing demand for cheese as a food ingredient, especially as a flavoring agent. One of the most important cheese flavoring agents is cheese powder. To obtain an intense cheese flavor, ripened cheese is used as a raw material in cheese powder but this increases production costs. Moreover, use of natural cheese decreases the physical quality of powder because of its high fat content. In this study, we evaluated opportunities to use whey or maltodextrin for improving the physical quality of powders in production of white cheese powder. We produced cheese powders with 3 different formulations-control (CON), whey-added (WACP), and maltodextrin-added (MACP)-and determined the effects of formulation on cheese powder quality. Physical quality parameters such as color, densities, reconstitution properties, free fat content, particle morphology, and sensory characteristics were investigated. The different cheese powders were stored for 12 mo at 20°C and we evaluated the effect of storage on powder quality. Addition of maltodextrin to cheese powder formulations significantly improved their physical quality. The densities and reconstitution properties of cheese powder were increased and free fat content was decreased by use of maltodextrin. The MACP particles were spherical with a uniform distribution and larger particle sizes, whereas CON and WACP particles were wrinkled, irregular shaped with deep surface dents, and variable in size. Although caking was observed in scanning electron micrographs after 12 mo of storage, it was not detected by sensory panelists. The color of cheese powders changed very slowly during storage but browning was detected. The results of this study show that it is possible to use maltodextrin or whey in production of white cheese powder to reduce production costs and improve the physical quality of powders.
Prasad, Anushree; Pushpa, Shankarappa; Arunagiri, Doraiswamy; Sawhny, Asheesh; Misra, Abhinav; Sujatha, Ramamurthy
2015-01-01
Aims: This study examined the setting time, compressive strength, and pH of white mineral trioxide aggregate (MTA) mixed with various additives: Calcium chloride (CaCl2), calcium formate (CaF), disodium hydrogen orthophosphate (Na2HPO4). Materials and Methods: Group 1 (Control) was obtained by mixing MTA with distilled water. In Groups 2 and 3, MTA containing 10% CaCl2 and 20% CaF, respectively, was mixed with distilled water. In Group 4, MTA was mixed with 15% Na2HPO4. Setting time, compressive strength, and pH of each group were examined. Statistical Analysis Used: Analysis was done using Statistical Package for Social Sciences (SPSS) version 14. A P-value < 0.05 was considered statistically significant. Comparison of mean values was done using analysis of variance (ANOVA) with post-hoc Games-Howell test. Results: The setting time of test groups were significantly shorter than that of control group (P < 0.001). The compressive strengths of test groups were lower than that of control group (P < 0.001). The pH value obtained for Groups 3 and 4 were higher than that of the control group (P < 0.001). Conclusions: Study result showed that additives significantly reduced the setting time of MTA and also maintained the pH at a high value. However, there was not much improvement in the compressive strength of the material. PMID:26069412
Hong, D; Ragland, D; Adeola, O
2001-11-01
An experiment was conducted using the TMEn bioassay method to investigate the additivity and associative effects of metabolizable energy and amino acid digestibility in barley and canola meal for White Pekin ducks. Additivity was tested by comparing the difference between observed values determined in a complete diet and predicted values from measurements determined with individual ingredients (barley and canola meal). Six ducks each were assigned to diets of barley, canola meal, the complete diet, and dextrose. Dextrose-fed ducks were used for estimation of endogenous losses for calculation of true amino acid digestibility. The observed AME, TME, AMEn, and TMEn values in the complete diet were 0.065, 0.083, 0.016, and 0.023 (kcal/g), respectively, numerically higher than predicted values. Differences between observed and predicted values were not significant (P > 0.05), indicating that the AME, AMEn, TME, and TMEn in barley and canola meal were all additive. In general, observed values for apparent amino acid digestibility (AAAD) and true amino acid digestibility (TAAD) in the complete diet were higher than those predicted from individual ingredients. Observed AAAD for lysine, histidine, tryptophan, alanine, and aspartate were higher (P < 0.05) than predicted values, indicating that digestibilities of these amino acids were not additive. The mean of AAAD in canola meal (77.29%) was higher (P < 0.05) than the observed values of barley (52.2%) and complete diet (64.55%). For TAAD values, differences between observed and predicted values were significant for lysine, histidine, and tryptophan (P < 0.05). The mean of TAAD in canola meal, barley, and complete diet were 85.88, 80.87, and 81.33%, respectively. The average difference between observed and predicted values for TAAD (1.18 %) was smaller than that of AAAD (5.41%). These results indicated that ME values for barley and canola meal were additive in the complete diet but that digestibilities of some amino acids
Conditional and unconditional Gaussian quantum dynamics
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Lami, Ludovico; Serafini, Alessio
2016-07-01
This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as 'general-dyne') quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.
Gaussian Decomposition of Laser Altimeter Waveforms
NASA Technical Reports Server (NTRS)
Hofton, Michelle A.; Minster, J. Bernard; Blair, J. Bryan
1999-01-01
We develop a method to decompose a laser altimeter return waveform into its Gaussian components assuming that the position of each Gaussian within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. We estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform, and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a non-negative least-squares method. To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the "importance" of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked "important" are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians are included in the optimization procedure. The Gaussian decomposition method is demonstrated on data collected by the airborne Laser Vegetation Imaging Sensor (LVIS) in October 1997 over the Sequoia National Forest, California.
NASA Astrophysics Data System (ADS)
Basin, M.; Maldonado, J. J.; Zendejo, O.
2016-07-01
This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.
Long-distance continuous-variable quantum key distribution with a Gaussian modulation
Jouguet, Paul; Kunz-Jacques, Sebastien; Leverrier, Anthony
2011-12-15
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about 10{sup -3} bit per pulse at a distance of 120 km for reasonable physical parameters.
Chordas, Stephen W.; Hudson, Patrick L.; Chapman, Eric G.
2004-01-01
The dipteran fauna of Arkansas is generally poorly known. A previous study of the Aquatic macroinvertebrates of the White River National Wildlife Refuge, the largest refuge in Arkansas, reported only 12 diptera taxa out of 219 taxa collected (Chordas et al., 1996). Most of the dipterans from this study were identified only to the family level. The family Chironomidae is a large, diverse group and was predicted to be much more diverse in the refuge than indicated by previous studies. In this study, Chironomidae were targeted, with other aquatic or semiaquatic dipterans also retained, in collections designed to better define the dipteran fauna of the White River National Wildlife Refuge. Adult dipterans were collected from 22 sites within the refuge using sweep-nets, two types of blacklight traps, and lighted fan traps in June of 2001. Specimens from previous studies were retrieved and identified to the lowest possible taxonomic level. A total of 4,917 specimens representing 122 taxa was collected. The 122 taxa were comprised of the following: two chaoborids, 83 chironomids, 15 culicids, nine tabanids, and 13 tipulids. Of these, 46 species are new state records for Arkansas. Nine undescribed species of chironomids were collected, and eight species records represent significant range extensions.
GAUSSIAN BEAM LASER RESONATOR PROGRAM
NASA Technical Reports Server (NTRS)
Cross, P. L.
1994-01-01
In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.
Cloning of Gaussian states by linear optics
Olivares, Stefano; Paris, Matteo G. A.; Andersen, Ulrik L.
2006-06-15
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of nonunit quantum efficiency and unbalanced mode mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.
NASA Technical Reports Server (NTRS)
Mcgregor, D. N.; Tasoulis, G.; Kinal, G. V.
1980-01-01
The performance of Viterbi decoding in a non-Gaussian environment is investigated using a nonlinear quantization strategy. The channel model consists of a convolutionally encoded BPSK signal transmitted to a satellite where it is corrupted with additive white Gaussian noise and pulsed radio frequency interference (RFI). The resultant signal is then passed through a satellite nonlinearity and transmitted to a ground station where it is coherently detected. Interleaving is assumed in order to make the channel memoryless. The presence of RFI makes the channel statistics non-Gaussian, leading to a nonlinear log-likelihood function. A near optimum quantization scheme is found by maximizing a channel parameter, or by matching the quantizer to the log-likelihood function in a mean square error sense. Bit error rate performance improvement is achieved by using such nonlinear quantization.
Arocas, A; Sanz, T; Salvador, A; Varela, P; Fiszman, S M
2010-03-01
The effect of 5 types of starch (rice, potato, waxy corn, corn, and modified waxy corn) on the sensory properties of white sauces was studied. A comparative study was also made of variations resulting from freezing/thawing and effect of replacing 0.15% starch with 2 nonstarchy hydrocolloids, xanthan gum (XG), or locust bean gum (LBG) in samples to be frozen. The sensory properties were studied through descriptive analysis by a panel of 10 trained judges. Principal components analysis and cluster analysis were used to group each of the samples according to the scores for consistency, resilience, graininess, thickness, heterogeneity, creaminess, and mouth coating, the sensory attributes which were chosen to define the sauces under study. Significant differences were found between the different starches employed: the rice and modified starches presented similar behavior to each other, as did the potato starch and corn starch, while the waxy starch sauce stood apart from the rest because of its resilience. The freeze/thaw cycle had the greatest effect on the corn-starch sauce, increasing its graininess and heterogeneity values owing to retrogradation. Adding XG or LBG to the sauces subjected to a period of freezing/thawing did not have a significant effect on the sensory attributes of the reheated sauces made with rice, potato, or waxy or modified starch, but lower graininess and heterogeneity values were observed in the sauce made with corn starch.
Byrnes, Christian T.; Nurmi, Sami; Tasinato, Gianmassimo; Wands, David E-mail: s.nurmi@thphys.uni-heidelberg.de E-mail: david.wands@port.ac.uk
2012-03-01
We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f{sub NL}, measured within smaller patches of the sky. Correlators between n-point functions measured in one patch of the sky and k-point functions measured in another patch depend upon the (n+k)-point functions over the entire sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to detect or constrain higher- order correlators in local models of non-Gaussianity, as well as to distinguish between single and multiple-source scenarios for generating the primordial density perturbation, and more generally to probe the details of inflationary physics.
Gamal El-Dien, Omnia; Ratcliffe, Blaise; Klápště, Jaroslav; Porth, Ilga; Chen, Charles; El-Kassaby, Yousry A
2016-03-01
The open-pollinated (OP) family testing combines the simplest known progeny evaluation and quantitative genetics analyses as candidates' offspring are assumed to represent independent half-sib families. The accuracy of genetic parameter estimates is often questioned as the assumption of "half-sibling" in OP families may often be violated. We compared the pedigree- vs. marker-based genetic models by analysing 22-yr height and 30-yr wood density for 214 white spruce [Picea glauca (Moench) Voss] OP families represented by 1694 individuals growing on one site in Quebec, Canada. Assuming half-sibling, the pedigree-based model was limited to estimating the additive genetic variances which, in turn, were grossly overestimated as they were confounded by very minor dominance and major additive-by-additive epistatic genetic variances. In contrast, the implemented genomic pairwise realized relationship models allowed the disentanglement of additive from all nonadditive factors through genetic variance decomposition. The marker-based models produced more realistic narrow-sense heritability estimates and, for the first time, allowed estimating the dominance and epistatic genetic variances from OP testing. In addition, the genomic models showed better prediction accuracies compared to pedigree models and were able to predict individual breeding values for new individuals from untested families, which was not possible using the pedigree-based model. Clearly, the use of marker-based relationship approach is effective in estimating the quantitative genetic parameters of complex traits even under simple and shallow pedigree structure.
Gamal El-Dien, Omnia; Ratcliffe, Blaise; Klápště, Jaroslav; Porth, Ilga; Chen, Charles; El-Kassaby, Yousry A.
2016-01-01
The open-pollinated (OP) family testing combines the simplest known progeny evaluation and quantitative genetics analyses as candidates’ offspring are assumed to represent independent half-sib families. The accuracy of genetic parameter estimates is often questioned as the assumption of “half-sibling” in OP families may often be violated. We compared the pedigree- vs. marker-based genetic models by analysing 22-yr height and 30-yr wood density for 214 white spruce [Picea glauca (Moench) Voss] OP families represented by 1694 individuals growing on one site in Quebec, Canada. Assuming half-sibling, the pedigree-based model was limited to estimating the additive genetic variances which, in turn, were grossly overestimated as they were confounded by very minor dominance and major additive-by-additive epistatic genetic variances. In contrast, the implemented genomic pairwise realized relationship models allowed the disentanglement of additive from all nonadditive factors through genetic variance decomposition. The marker-based models produced more realistic narrow-sense heritability estimates and, for the first time, allowed estimating the dominance and epistatic genetic variances from OP testing. In addition, the genomic models showed better prediction accuracies compared to pedigree models and were able to predict individual breeding values for new individuals from untested families, which was not possible using the pedigree-based model. Clearly, the use of marker-based relationship approach is effective in estimating the quantitative genetic parameters of complex traits even under simple and shallow pedigree structure. PMID:26801647
Gamal El-Dien, Omnia; Ratcliffe, Blaise; Klápště, Jaroslav; Porth, Ilga; Chen, Charles; El-Kassaby, Yousry A
2016-03-01
The open-pollinated (OP) family testing combines the simplest known progeny evaluation and quantitative genetics analyses as candidates' offspring are assumed to represent independent half-sib families. The accuracy of genetic parameter estimates is often questioned as the assumption of "half-sibling" in OP families may often be violated. We compared the pedigree- vs. marker-based genetic models by analysing 22-yr height and 30-yr wood density for 214 white spruce [Picea glauca (Moench) Voss] OP families represented by 1694 individuals growing on one site in Quebec, Canada. Assuming half-sibling, the pedigree-based model was limited to estimating the additive genetic variances which, in turn, were grossly overestimated as they were confounded by very minor dominance and major additive-by-additive epistatic genetic variances. In contrast, the implemented genomic pairwise realized relationship models allowed the disentanglement of additive from all nonadditive factors through genetic variance decomposition. The marker-based models produced more realistic narrow-sense heritability estimates and, for the first time, allowed estimating the dominance and epistatic genetic variances from OP testing. In addition, the genomic models showed better prediction accuracies compared to pedigree models and were able to predict individual breeding values for new individuals from untested families, which was not possible using the pedigree-based model. Clearly, the use of marker-based relationship approach is effective in estimating the quantitative genetic parameters of complex traits even under simple and shallow pedigree structure. PMID:26801647
Quantum steering of Gaussian states via non-Gaussian measurements
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul
2016-07-01
Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.
Quantum steering of Gaussian states via non-Gaussian measurements
Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul
2016-01-01
Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime. PMID:27411853
Autonomous Gaussian Decomposition
NASA Astrophysics Data System (ADS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-04-01
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
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Dickey, John
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.
The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise
NASA Astrophysics Data System (ADS)
Guo, Qin; Sun, Zhongkui; Xu, Wei
2016-05-01
The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.
Gaussian discriminating strength
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Flauger, Raphael; Pajer, Enrico E-mail: ep295@cornell.edu
2011-01-01
We provide a derivation from first principles of the primordial bispectrum of scalar perturbations produced during inflation driven by a canonically normalized scalar field whose potential exhibits small sinusoidal modulations. A potential of this type has been derived in a class of string theory models of inflation based on axion monodromy. We use this model as a concrete example, but we present our derivations and results for a general slow-roll potential with superimposed modulations. We show analytically that a resonance between the oscillations of the background and the oscillations of the fluctuations is responsible for the production of an observably large non-Gaussian signal. We provide an explicit expression for the shape of this resonant non-Gaussianity. We show that there is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and we stress that resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. We hope our analytic expression will be useful to further observationally constrain this class of models.
Graphical calculus for Gaussian pure states
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-04-15
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 entanglement in the turbulent atmosphere
NASA Astrophysics Data System (ADS)
Bohmann, M.; Semenov, A. A.; Sperling, J.; Vogel, W.
2016-07-01
We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a nontrivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.
Weltz, Kay; Kock, Alison A; Winker, Henning; Attwood, Colin; Sikweyiya, Monwabisi
2013-01-01
Shark attacks on humans are high profile events which can significantly influence policies related to the coastal zone. A shark warning system in South Africa, Shark Spotters, recorded 378 white shark (Carcharodon carcharias) sightings at two popular beaches, Fish Hoek and Muizenberg, during 3690 six-hour long spotting shifts, during the months September to May 2006 to 2011. The probabilities of shark sightings were related to environmental variables using Binomial Generalized Additive Mixed Models (GAMMs). Sea surface temperature was significant, with the probability of shark sightings increasing rapidly as SST exceeded 14 °C and approached a maximum at 18 °C, whereafter it remains high. An 8 times (Muizenberg) and 5 times (Fish Hoek) greater likelihood of sighting a shark was predicted at 18 °C than at 14 °C. Lunar phase was also significant with a prediction of 1.5 times (Muizenberg) and 4 times (Fish Hoek) greater likelihood of a shark sighting at new moon than at full moon. At Fish Hoek, the probability of sighting a shark was 1.6 times higher during the afternoon shift compared to the morning shift, but no diel effect was found at Muizenberg. A significant increase in the number of shark sightings was identified over the last three years, highlighting the need for ongoing research into shark attack mitigation. These patterns will be incorporated into shark awareness and bather safety campaigns in Cape Town. PMID:23874668
Weltz, Kay; Kock, Alison A; Winker, Henning; Attwood, Colin; Sikweyiya, Monwabisi
2013-01-01
Shark attacks on humans are high profile events which can significantly influence policies related to the coastal zone. A shark warning system in South Africa, Shark Spotters, recorded 378 white shark (Carcharodon carcharias) sightings at two popular beaches, Fish Hoek and Muizenberg, during 3690 six-hour long spotting shifts, during the months September to May 2006 to 2011. The probabilities of shark sightings were related to environmental variables using Binomial Generalized Additive Mixed Models (GAMMs). Sea surface temperature was significant, with the probability of shark sightings increasing rapidly as SST exceeded 14 °C and approached a maximum at 18 °C, whereafter it remains high. An 8 times (Muizenberg) and 5 times (Fish Hoek) greater likelihood of sighting a shark was predicted at 18 °C than at 14 °C. Lunar phase was also significant with a prediction of 1.5 times (Muizenberg) and 4 times (Fish Hoek) greater likelihood of a shark sighting at new moon than at full moon. At Fish Hoek, the probability of sighting a shark was 1.6 times higher during the afternoon shift compared to the morning shift, but no diel effect was found at Muizenberg. A significant increase in the number of shark sightings was identified over the last three years, highlighting the need for ongoing research into shark attack mitigation. These patterns will be incorporated into shark awareness and bather safety campaigns in Cape Town.
Weltz, Kay; Kock, Alison A.; Winker, Henning; Attwood, Colin; Sikweyiya, Monwabisi
2013-01-01
Shark attacks on humans are high profile events which can significantly influence policies related to the coastal zone. A shark warning system in South Africa, Shark Spotters, recorded 378 white shark (Carcharodon carcharias) sightings at two popular beaches, Fish Hoek and Muizenberg, during 3690 six-hour long spotting shifts, during the months September to May 2006 to 2011. The probabilities of shark sightings were related to environmental variables using Binomial Generalized Additive Mixed Models (GAMMs). Sea surface temperature was significant, with the probability of shark sightings increasing rapidly as SST exceeded 14°C and approached a maximum at 18°C, whereafter it remains high. An 8 times (Muizenberg) and 5 times (Fish Hoek) greater likelihood of sighting a shark was predicted at 18°C than at 14°C. Lunar phase was also significant with a prediction of 1.5 times (Muizenberg) and 4 times (Fish Hoek) greater likelihood of a shark sighting at new moon than at full moon. At Fish Hoek, the probability of sighting a shark was 1.6 times higher during the afternoon shift compared to the morning shift, but no diel effect was found at Muizenberg. A significant increase in the number of shark sightings was identified over the last three years, highlighting the need for ongoing research into shark attack mitigation. These patterns will be incorporated into shark awareness and bather safety campaigns in Cape Town. PMID:23874668
Lee, E.P.
1982-11-03
The growth rate of the hose instability is derived for a beam with Gaussian radial profile, using the spread mass model of phase mix damping. It is found that the maximum growth rate of a convecting wave packet is 49% larger than that derived for a beam with the Bennett profile, and the inverse group velocity (dz/d tau) is also increased by about this amount. A general discussion of spread mass models is presented along with an explanation of the regurgitation phenomena seen in their numerical treatment.
Distillation and purification of symmetric entangled Gaussian states
Fiurasek, Jaromir
2010-10-15
We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by Browne et al. [Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy degaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences of single-photon addition and subtraction operations.
Normal form decomposition for Gaussian-to-Gaussian superoperators
De Palma, Giacomo; Mari, Andrea; Giovannetti, Vittorio; Holevo, Alexander S.
2015-05-15
In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.
Efficient entanglement criteria beyond Gaussian limits using Gaussian measurements.
Nha, Hyunchul; Lee, Su-Yong; Ji, Se-Wan; Kim, M S
2012-01-20
We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation. PMID:22400723
2011-01-01
Background Enhancement of antimicrobial plant products e.g. pomegranate extract by copper (II) sulphate is known. Such combinations have applications in various settings, including the identification of novel compositions to study, treat and control infection. Methods A combination of white tea (WT) (made allowing 10 minutes infusion time at 100°C) was combined with 4.8 mM copper (II) sulphate and tested for antimicrobial effect on the viability of Staphylococcus aureus NCTC 06571. Comparisons were made with green (GT) and black (BT) teas. A WT sub-fraction (WTF < 1000 Da) was tested with copper (II) sulphate and 4.8 mM vitamin C. pH measurements of samples were taken for controls and to observe any changes due to tea/agent interaction. Catalase was used to investigate hydrogen peroxide release. UV-vis. was used to compare WT and WTF. Results A 30 minute incubation at room temperature of copper (II) sulphate alone and combined with WT reduced the viability of S. aureus NCTC 06571 by c.a 1 log10 cfu mL-1. GT and BT with copper (II) sulphate negated activity to buffer values. Combined with copper (II) sulphate, vitamin C, WTF and, vitamin C plus WTF all reduced the viability of S. aureus NCTC 06571 by c.a. 3.5 log10 cfu mL-1. Independent experiments showed the results were not due to pH effects. Adding WT or WTF to copper (II) sulphate resulted in increased acidity. Copper (II) sulphate alone and combined with WT required c.a 300 μg mL-1 (final concentration) catalase to restore S. aureus viability, WTF with copper (II) sulphate and added vitamin C required c.a 600 μg mL-1. WT and WTF UV-visible spectra were similar. Conclusions WT showed no efficacy in the combinations tested. WTF was enhanced with copper (II) sulphate and further with vitamin C. WT and WTF increased acidity of copper (II) sulphate possibly via the formation of chemical complexes. The difference in WT/WTF absorbance possibly represented substances less concentrated or absent in WTF
Pérez Suárez, Santiago T.; Travieso González, Carlos M.; Alonso Hernández, Jesús B.
2013-01-01
This article presents a design methodology for designing an artificial neural network as an equalizer for a binary signal. Firstly, the system is modelled in floating point format using Matlab. Afterward, the design is described for a Field Programmable Gate Array (FPGA) using fixed point format. The FPGA design is based on the System Generator from Xilinx, which is a design tool over Simulink of Matlab. System Generator allows one to design in a fast and flexible way. It uses low level details of the circuits and the functionality of the system can be fully tested. System Generator can be used to check the architecture and to analyse the effect of the number of bits on the system performance. Finally the System Generator design is compiled for the Xilinx Integrated System Environment (ISE) and the system is described using a hardware description language. In ISE the circuits are managed with high level details and physical performances are obtained. In the Conclusions section, some modifications are proposed to improve the methodology and to ensure portability across FPGA manufacturers.
NASA Technical Reports Server (NTRS)
2002-01-01
(Released 19 April 2002) The Science 'White Rock' is the unofficial name for this unusual landform which was first observed during the Mariner 9 mission in the early 1970's. As later analysis of additional data sets would show, White Rock is neither white nor dense rock. Its apparent brightness arises from the fact that the material surrounding it is so dark. Images from the Mars Global Surveyor MOC camera revealed dark sand dunes surrounding White Rock and on the floor of the troughs within it. Some of these dunes are just apparent in the THEMIS image. Although there was speculation that the material composing White Rock could be salts from an ancient dry lakebed, spectral data from the MGS TES instrument did not support this claim. Instead, the White Rock deposit may be the erosional remnant of a previously more continuous occurrence of air fall sediments, either volcanic ash or windblown dust. The THEMIS image offers new evidence for the idea that the original deposit covered a larger area. Approximately 10 kilometers to the southeast of the main deposit are some tiny knobs of similarly bright material preserved on the floor of a small crater. Given that the eolian erosion of the main White Rock deposit has produced isolated knobs at its edges, it is reasonable to suspect that the more distant outliers are the remnants of a once continuous deposit that stretched at least to this location. The fact that so little remains of the larger deposit suggests that the material is very easily eroded and simply blows away. The Story Fingers of hard, white rock seem to jut out like icy daggers across a moody Martian surface, but appearances can be deceiving. These bright, jagged features are neither white, nor icy, nor even hard and rocky! So what are they, and why are they so different from the surrounding terrain? Scientists know that you can't always trust what your eyes see alone. You have to use other kinds of science instruments to measure things that our eyes can
Non-Gaussian eccentricity fluctuations
NASA Astrophysics Data System (ADS)
Grönqvist, Hanna; Blaizot, Jean-Paul; Ollitrault, Jean-Yves
2016-09-01
We study the fluctuations of the anisotropy of the energy density profile created in a high-energy collision at the LHC. We show that the anisotropy in harmonic n has generic non-Gaussian fluctuations. We argue that these non-Gaussianities have a universal character for small systems such as p+Pb collisions, but not for large systems such as Pb+Pb collisions where they depend on the underlying non-Gaussian statistics of the initial density profile. We generalize expressions for the eccentricity cumulants ɛ2{4 } and ɛ3{4 } previously obtained within the independent-source model to a general fluctuating initial density profile.
Constraint optimized weight adaptation for Gaussian mixture reduction
NASA Astrophysics Data System (ADS)
Chen, H. D.; Chang, K. C.; Smith, Chris
2010-04-01
Gaussian mixture model (GMM) has been used in many applications for dynamic state estimation such as target tracking or distributed fusion. However, the number of components in the mixture distribution tends to grow rapidly when multiple GMMs are combined. In order to keep the computational complexity bounded, it is necessary to approximate a Gaussian mixture by one with reduced number of components. Gaussian mixture reduction is traditionally conducted by recursively selecting two components that appear to be most similar to each other and merging them. Different definitions on similarity measure have been used in literature. For the case of one-dimensional Gaussian mixtures, Kmeans algorithms and some variations are recently proposed to cluster Gaussian mixture components in groups, use a center component to represent all in each group, readjust parameters in the center components, and finally perform weight optimization. In this paper, we focus on multi-dimensional Gaussian mixture models. With a variety of reduction algorithms and possible combinations, we developed a hybrid algorithm with constraint optimized weight adaptation to minimize the integrated squared error (ISE). In additions, with extensive simulations, we showed that the proposed algorithm provides an efficient and effective Gaussian mixture reduction performance in various random scenarios.
Gaussian-Based Hue Descriptors.
Mirzaei, Hamidreza; Funt, Brian
2015-12-01
A robust and accurate hue descriptor that is useful in modeling human color perception and for computer vision applications is explored. The hue descriptor is based on the peak wavelength of a Gaussian-like function (called a wraparound Gaussian) and is shown to correlate as well as CIECAM02 hue to the hue designators of papers from the Munsell and Natural Color System color atlases and to the hue names found in Moroney's Color Thesaurus. The new hue descriptor is also shown to be significantly more stable under a variety of illuminants than CIECAM02. The use of wraparound Gaussians as a hue model is similar in spirit to the use of subtractive Gaussians proposed by Mizokami et al., but overcomes many of their limitations. PMID:26539849
Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces
NASA Astrophysics Data System (ADS)
Heaps, Charles W.; Mazziotti, David A.
2016-04-01
Trajectory-based Gaussian basis sets have been tremendously successful in describing high-dimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussian-based method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O ( N ) potential energy calculations, in contrast to O ( N 2 ) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O ( N ) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant.
Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.
Heaps, Charles W; Mazziotti, David A
2016-04-28
Trajectory-based Gaussian basis sets have been tremendously successful in describing high-dimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussian-based method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O(N) potential energy calculations, in contrast to O(N(2)) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O(N) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant.
Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.
Heaps, Charles W; Mazziotti, David A
2016-04-28
Trajectory-based Gaussian basis sets have been tremendously successful in describing high-dimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussian-based method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O(N) potential energy calculations, in contrast to O(N(2)) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O(N) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant. PMID:27131532
Schäfer, Joachim; Karpov, Evgueni; Cerf, Nicolas J.
2014-12-04
We seek for a realistic implementation of multimode Gaussian entangled states that can realize the optimal encoding for quantum bosonic Gaussian channels with memory. For a Gaussian channel with classical additive Markovian correlated noise and a lossy channel with non-Markovian correlated noise, we demonstrate the usefulness using Gaussian matrix-product states (GMPS). These states can be generated sequentially, and may, in principle, approximate well any Gaussian state. We show that we can achieve up to 99.9% of the classical Gaussian capacity with GMPS requiring squeezing parameters that are reachable with current technology. This may offer a way towards an experimental realization.
Exact Results for `Bouncing' Gaussian Wave Packets
NASA Astrophysics Data System (ADS)
Belloni, M.; Doncheski, M. A.; Robinett, R. W.
2005-01-01
We consider time-dependent Gaussian wave packet solutions of the Schrödinger equation, with arbitrary initial central position, x0, and momentum, p0, for an otherwise free particle, but with an infinite wall at x = 0, so-called bouncing wave packets. We show how difference or mirror solutions of the form ψ(x,t) - ψ(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate langp2rangt explicitly which illustrates how the free-particle kinetic (and hence total energy) is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, langxrangt, and momentum, langprangt, and their relation to the impulsive force during the `collision' with the wall. Finally, the x0, p0 → 0 limit is shown to reduce a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands of the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.
Resonant non-Gaussianity with equilateral properties
Gwyn, Rhiannon; Rummel, Markus; Westphal, Alexander E-mail: markus.rummel@desy.de
2013-04-01
We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to ''Fourier synthesize'' different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of O(10) oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of resonant N-point functions give a constraint of f{sub NL}∼
Quantum correlations in Gaussian states via Gaussian channels: steering, entanglement, and discord
NASA Astrophysics Data System (ADS)
Wang, Zhong-Xiao; Wang, Shuhao; Li, Qiting; Wang, Tie-Jun; Wang, Chuan
2016-06-01
Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein-Podolsky-Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.
Design criteria for noncoherent Gaussian channels with MFSK signaling and coding
NASA Technical Reports Server (NTRS)
Butman, S. A.; Levitt, B. K.; Bar-David, I.; Lyon, R. F.; Klass, M. J.
1976-01-01
This paper presents data and criteria to assess and guide the design of modems for coded noncoherent communication systems subject to practical system constraints of power, bandwidth, noise spectral density, coherence time, and number of orthogonal signals M. Three basic receiver types are analyzed for the noncoherent multifrequency-shift keying (MFSK) additive white Gaussian noise channel: hard decision, unquantized (optimum), and quantized (soft decision). Channel capacity and computational cutoff rate are computed for each type and presented as functions of the predetection signal-to-noise ratio and the number of orthogonal signals. This relates the channel constraints of power, bandwidth, coherence time, and noise power to the optimum choice of signal duration and signal number.
Information geometry of Gaussian channels
Monras, Alex; Illuminati, Fabrizio
2010-06-15
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).
Detection methods for non-Gaussian gravitational wave stochastic backgrounds
NASA Astrophysics Data System (ADS)
Drasco, Steve; Flanagan, Éanna É.
2003-04-01
A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant hiss, and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned
Gaussian entanglement distribution via satellite
NASA Astrophysics Data System (ADS)
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.
Large-size Gaussian mode in unstable resonators using Gaussian mirrors.
McCarthy, N; Lavigne, P
1985-11-01
Gaussian modes with large sections have been experimentally produced in Cassegrain resonators using Gaussian reflectivity convex couplers. The far field of the beam, which was coupled through a Gaussian coupler, was found to be free from secondary rings. PMID:19730482
Tachyon mediated non-Gaussianity
Dutta, Bhaskar; Leblond, Louis; Kumar, Jason
2008-10-15
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.
Non-gaussianity versus nonlinearity of cosmological perturbations.
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.
Non-gaussianity versus nonlinearity of cosmological perturbations.
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. PMID:11411156
Hamzeh, Yahya; Ziabari, Kamran Pourhooshyar; Torkaman, Javad; Ashori, Alireza; Jafari, Mohammad
2013-03-15
This work assesses the effects of white rice husk ash (WRHA) as pozzolanic material, virgin kraft pulp (VKP), old corrugated container (OCC) and fibers derived from fiberboard (FFB) as reinforcing agents on some properties of blended cement composites. In the sample preparation, composites were manufactured using fiber-to-cement ratio of 25:75 by weight and 5% CaCl(2) as accelerator. Type II Portland cement was replaced by WRHA at 0%, 25% and 50% by weight of binder. A water-to-binder ratio of 0.55 was used for all blended cement paste mixes. For parametric study, compressive strength, water absorption and density of the composite samples were evaluated. Results showed that WRHA can be applied as a pozzolanic material to cement and also improved resistance to water absorption. However, increasing the replacement level of WRHA tends to reduce the compressive strength due to the low binding ability. The optimum replacement level of WRHA in mortar was 25% by weight of binder; this replacement percentage resulted in better compressive strengths and water absorption. OCC fiber is shown to be superior to VKF and FFB fibers in increasing the compressive strength, due to its superior strength properties. As expected, the increase of the WRHA content induced the reduction of bulk density of the cement composites. Statistical analysis showed that the interaction of above-mentioned variable parameters was significant on the mechanical and physical properties at 1% confidence level.
Gaussian Velocity Distributions in Avalanches
NASA Astrophysics Data System (ADS)
Shattuck, Mark
2004-03-01
Imagine a world where gravity is so strong that if an ice cube is tilted the shear forces melt the surface and water avalanches down. Further imagine that the ambient temperature is so low that the water re-freezes almost immediately. This is the world of granular flows. As a granular solid is tilted the surface undergoes a sublimation phase transition and a granular gas avalanches down the surface, but the inelastic collisions rapidly remove energy from the flow lowering the granular temperature (kinetic energy per particle) until the gas solidifies again. It is under these extreme conditions that we attempt to uncover continuum granular flow properties. Typical continuum theories like Navier-Stokes equation for fluids follow the space-time evolution of the first few moments of the velocity distribution. We study continuously avalanching flow in a rotating two-dimensional granular drum using high-speed video imaging and extract the position and velocities of the particles. We find a universal near Gaussian velocity distribution throughout the flowing regions, which are characterized by a liquid-like radial distribution function. In the remaining regions, in which the radial distribution function develops sharp crystalline peaks, the velocity distribution has a Gaussian peak but is much broader in the tails. In a companion experiment on a vibrated two-dimensional granular fluid under constant pressure, we find a clear gas-solid phase transition in which both the temperature and density change discontinuously. This suggests that a low temperature crystal and a high temperature gas can coexist in steady state. This coexistence could result in a narrower, cooler, Gaussian peak and a broader, warmer, Gaussian tail like the non-Gaussian behavior seen in the crystalline portions of the rotating drum.
Information Content in Uniformly Discretized Gaussian Noise:. Optimal Compression Rates
NASA Astrophysics Data System (ADS)
Romeo, August; Gaztañaga, Enrique; Barriga, Jose; Elizalde, Emilio
We approach the theoretical problem of compressing a signal dominated by Gaussian noise. We present expressions for the compression ratio which can be reached, under the light of Shannon's noiseless coding theorem, for a linearly quantized stochastic Gaussian signal (noise). The compression ratio decreases logarithmically with the amplitude of the frequency spectrum P(f) of the noise. Entropy values and compression rates are shown to depend on the shape of this power spectrum, given different normalizations. The cases of white noise (w.n.), fnp power-law noise (including 1/f noise), (w.n.+1/f) noise, and piecewise (w.n.+1/f | w.n.+1/f2) noise are discussed, while quantitative behaviors and useful approximations are provided.
White-light luminescence properties of Mg and Sn doped ZnO prepared by thermal oxidation
Zeng, Jun; Fan, Huiqing; Xue, Jun; Wang, Yangli
2014-02-01
Graphical abstract: The PL spectrum of MgSnZnO was measured at room temperature through multi-peak Gaussian fitting, it is found that the broad emission is composed of six peaks. - Highlights: • Mg and Sn doped ZnO are synthesized by thermal oxidation of MgSnZn alloys. • The structure is characterized by XRD and micro-Raman scattering technology. • The optical properties are characterized by photoluminescence spectrum. • The resulting Mg and Sn doped ZnO shows white photoluminescence. - Abstract: This work reports that Mg and Sn doped ZnO (MgSnZnO) are synthesized by thermal oxidation of MgSnZn alloys. The structure and optical properties are characterized by X-ray diffraction (XRD), micro-Raman scattering technology and photoluminescence spectrum. Interestingly, the resulting MgSnZnO shows white photoluminescence. Additionally, the photoluminescence spectrum of MgSnZnO shows two broad emission bands ranging from 360 to 420 nm and 420 to 630 nm, respectively. Through multi-peak Gaussian fitting, it is found that the broad emission is composed of six Gaussian peaks. The six Gaussian peaks are centrered at 383 nm, 397 nm, 455 nm, 516 nm, 560 nm and 614 nm.
Inseparability of photon-added Gaussian states
Li Hongrong; Li Fuli; Zhu Shiyao
2007-06-15
The inseparability of photon-added Gaussian states which are generated from two-mode Gaussian states by adding photons is investigated. According to the established inseparability conditions [New J. Phys. 7, 211 (2005); Phys. Rev. Lett. 96, 050503 (2006)], we find that even if a two-mode Gaussian state is separable, the photon-added Gaussian state becomes entangled when the purity of the Gaussian state is larger than a certain value. The lower bound of entanglement of symmetric photon-added Gaussian states is derived. The result shows that entanglement of the photon-added Gaussian states is involved with high-order moment correlations. We find that fidelity of teleporting coherent states cannot be raised by employing the photon-added Gaussian states as a quantum channel of teleportation.
Hierarchical similarity transformations between Gaussian mixtures.
Rigas, George; Nikou, Christophoros; Goletsis, Yorgos; Fotiadis, Dimitrios I
2013-11-01
In this paper, we propose a method to estimate the density of a data space represented by a geometric transformation of an initial Gaussian mixture model. The geometric transformation is hierarchical, and it is decomposed into two steps. At first, the initial model is assumed to undergo a global similarity transformation modeled by translation, rotation, and scaling of the model components. Then, to increase the degrees of freedom of the model and allow it to capture fine data structures, each individual mixture component may be transformed by another, local similarity transformation, whose parameters are distinct for each component of the mixture. In addition, to constrain the order of magnitude of the local transformation (LT) with respect to the global transformation (GT), zero-mean Gaussian priors are imposed onto the local parameters. The estimation of both GT and LT parameters is obtained through the expectation maximization framework. Experiments on artificial data are conducted to evaluate the proposed model, with varying data dimensionality, number of model components, and transformation parameters. In addition, the method is evaluated using real data from a speech recognition task. The obtained results show a high model accuracy and demonstrate the potential application of the proposed method to similar classification problems. PMID:24808615
Scaling Multidimensional Inference for Structured Gaussian Processes.
Gilboa, Elad; Saatçi, Yunus; Cunningham, John P
2013-09-30
Exact Gaussian process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and inputs on a lattice (both enable O(N) or O(N log N) runtime). However, these GP advances have not been well extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests three novel extensions of structured GPs to multidimensional inputs, for models with additive and multiplicative kernels. First we present a new method for inference in additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. We extend this model using two advances: a variant of projection pursuit regression, and a Laplace approximation for non-Gaussian observations. Lastly, for multiplicative kernel structure, we present a novel method for GPs with inputs on a multidimensional grid. We illustrate the power of these three advances on several datasets, achieving performance equal to or very close to the naive GP at orders of magnitude less cost.
Scaling Multidimensional Inference for Structured Gaussian Processes.
Gilboa, Elad; Saatçi, Yunus; Cunningham, John P
2015-02-01
Exact Gaussian process (GP) regression has O(N(3)) runtime for data size N, making it intractable for large N . Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and inputs on a lattice (both enable O(N) or O(N log N) runtime). However, these GP advances have not been well extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests three novel extensions of structured GPs to multidimensional inputs, for models with additive and multiplicative kernels. First we present a new method for inference in additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. We extend this model using two advances: a variant of projection pursuit regression, and a Laplace approximation for non-Gaussian observations. Lastly, for multiplicative kernel structure, we present a novel method for GPs with inputs on a multidimensional grid. We illustrate the power of these three advances on several data sets, achieving performance equal to or very close to the naive GP at orders of magnitude less cost.
Gaussian statistics for palaeomagnetic vectors
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
Non-Gaussian Photon Probability Distribution
NASA Astrophysics Data System (ADS)
Solomon, Benjamin T.
2010-01-01
This paper investigates the axiom that the photon's probability distribution is a Gaussian distribution. The Airy disc empirical evidence shows that the best fit, if not exact, distribution is a modified Gamma mΓ distribution (whose parameters are α = r, βr/√u ) in the plane orthogonal to the motion of the photon. This modified Gamma distribution is then used to reconstruct the probability distributions along the hypotenuse from the pinhole, arc from the pinhole, and a line parallel to photon motion. This reconstruction shows that the photon's probability distribution is not a Gaussian function. However, under certain conditions, the distribution can appear to be Normal, thereby accounting for the success of quantum mechanics. This modified Gamma distribution changes with the shape of objects around it and thus explains how the observer alters the observation. This property therefore places additional constraints to quantum entanglement experiments. This paper shows that photon interaction is a multi-phenomena effect consisting of the probability to interact Pi, the probabilistic function and the ability to interact Ai, the electromagnetic function. Splitting the probability function Pi from the electromagnetic function Ai enables the investigation of the photon behavior from a purely probabilistic Pi perspective. The Probabilistic Interaction Hypothesis is proposed as a consistent method for handling the two different phenomena, the probability function Pi and the ability to interact Ai, thus redefining radiation shielding, stealth or cloaking, and invisibility as different effects of a single phenomenon Pi of the photon probability distribution. Sub wavelength photon behavior is successfully modeled as a multi-phenomena behavior. The Probabilistic Interaction Hypothesis provides a good fit to Otoshi's (1972) microwave shielding, Schurig et al. (2006) microwave cloaking, and Oulton et al. (2008) sub wavelength confinement; thereby providing a strong case that
NASA Astrophysics Data System (ADS)
Rubel, Aleksey S.; Lukin, Vladimir V.; Egiazarian, Karen O.
2015-03-01
Results of denoising based on discrete cosine transform for a wide class of images corrupted by additive noise are obtained. Three types of noise are analyzed: additive white Gaussian noise and additive spatially correlated Gaussian noise with middle and high correlation levels. TID2013 image database and some additional images are taken as test images. Conventional DCT filter and BM3D are used as denoising techniques. Denoising efficiency is described by PSNR and PSNR-HVS-M metrics. Within hard-thresholding denoising mechanism, DCT-spectrum coefficient statistics are used to characterize images and, subsequently, denoising efficiency for them. Results of denoising efficiency are fitted for such statistics and efficient approximations are obtained. It is shown that the obtained approximations provide high accuracy of prediction of denoising efficiency.
Achromatic doublets for Gaussian beams
NASA Astrophysics Data System (ADS)
Biraud, F.; Daigne, G.
1991-04-01
The properties of doublets of thin lenses in the Gaussian optics approximation were investigated. Two different ways for such a doublet to give strictly achromatic images of the input beam waist were found. Both solutions may be useful in a variety of applications, one being the possibility of shaping asymmetrical beams for fan beam antennas illumination. Using modes higher than the fundamental mode will allow the design of more realistic focal systems.
Nurmi, Sami; Byrnes, Christian T.; Tasinato, Gianmassimo E-mail: ctb22@sussex.ac.uk
2013-06-01
Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f{sub NL}{sup 0}| >> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |f{sub NL}{sup obs.}|∼<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.
Purification of Gaussian maximally mixed states
NASA Astrophysics Data System (ADS)
Jeong, Kabgyun; Lim, Youngrong
2016-10-01
We find that the purifications of several Gaussian maximally mixed states (GMMSs) correspond to some Gaussian maximally entangled states (GMESs) in the continuous-variable regime. Here, we consider a two-mode squeezed vacuum (TMSV) state as a purification of the thermal state and construct a general formalism of the Gaussian purification process. Moreover, we introduce other kind of GMESs via the process. All of our purified states of the GMMSs exhibit Gaussian profiles; thus, the states show maximal quantum entanglement in the Gaussian regime.
The conditional entropy power inequality for Gaussian quantum states
Koenig, Robert
2015-02-15
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.
Hyperbranched polymer stars with Gaussian chain statistics revisited.
Polińska, P; Gillig, C; Wittmer, J P; Baschnagel, J
2014-02-01
Conformational properties of regular dendrimers and more general hyperbranched polymer stars with Gaussian statistics for the spacer chains between branching points are revisited numerically. We investigate the scaling for asymptotically long chains especially for fractal dimensions df = 3 (marginally compact) and df = 2.5 (diffusion limited aggregation). Power-law stars obtained by imposing the number of additional arms per generation are compared to truly self-similar stars. We discuss effects of weak excluded-volume interactions and sketch the regime where the Gaussian approximation should hold in dense solutions and melts for sufficiently large spacer chains. PMID:24574057
Gaussian weighted projection for visualization of cardiac calcification
NASA Astrophysics Data System (ADS)
Chen, Xiang; Li, Ke; Gilkeson, Robert; Fei, Baowei
2008-03-01
At our institution, we are using dual-energy digital radiography (DEDR) as a cost-effective screening tool for the detection of cardiac calcification. We are evaluating DEDR using CT as the gold standard. We are developing image projection methods for the generation of digitally reconstructed radiography (DRR) from CT image volumes. Traditional visualization methods include maximum intensity projection (MIP) and average-based projection (AVG) that have difficulty to show cardiac calcification. Furthermore, MIP can over estimate the calcified lesion as it displays the maximum intensity along the projection rays regardless of tissue types. For AVG projection, the calcified tissue is usually overlapped with bone, lung and mediastinum. In order to improve the visualization of calcification on DRR images, we developed a Gaussian-weighted projection method for this particular application. We assume that the CT intensity values of calcified tissues have a Gaussian distribution. We then use multiple Gaussian functions to fit the intensity histogram. Based on the mean and standard deviation parameters, we incorporate a Gaussian weighted function into the perspective projection and display the calcification exclusively. Our digital and physical phantom studies show that the new projection method can display tissues selectively. In addition, clinical images show that the Gaussian-weighted projection method better visualizes cardiac calcification than either the AVG or MIP method and can be used to evaluate DEDR as a screening tool for the detection of coronary artery diseases.
Passive interferometric symmetries of multimode Gaussian pure states
NASA Astrophysics Data System (ADS)
Gabay, Natasha; Menicucci, Nicolas C.
2016-05-01
As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful tools for their representation, while this work presents a useful tool for their analysis: passive interferometric (i.e., number-conserving) symmetries. Here we show that these symmetries of multimode Gaussian states simplify calculations in measurement-based quantum computing and provide constructive tools for engineering large-scale harmonic systems with specific physical properties, and we provide a general mathematical framework for deriving them. Such symmetries are generated by linear combinations of operators expressed in the Schwinger representation of U (2 ) , called nullifiers because the Gaussian state in question is a zero eigenstate of them. This general framework is shown to have applications in the noise analysis of continuous-various cluster states and is expected to have additional applications in future work with large-scale multimode Gaussian states.
Kochunov, Peter; Jahanshad, Neda; Sprooten, Emma; Nichols, Thomas E.; Mandl, René C.; Almasy, Laura; Booth, Tom; Brouwer, Rachel M.; Curran, Joanne E.; de Zubicaray, Greig I.; Dimitrova, Rali; Duggirala, Ravi; Fox, Peter T.; Hong, L. Elliot; Landman, Bennett A.; Lemaitre, Hervé; Lopez, Lorna; Martin, Nicholas G.; McMahon, Katie L.; Mitchell, Braxton D.; Olvera, Rene L.; Peterson, Charles P.; Starr, John M.; Sussmann, Jessika E.; Toga, Arthur W.; Wardlaw, Joanna M.; Wright, Margaret J.; Wright, Susan N.; Bastin, Mark E.; McIntosh, Andrew M.; Boomsma, Dorret I.; Kahn, René S.; den Braber, Anouk; de Geus, Eco JC; Deary, Ian J.; Hulshoff Pol, Hilleke E.; Williamson, Douglas E.; Blangero, John; van ’t Ent, Dennis; Thompson, Paul M.; Glahn, David C.
2014-01-01
Combining datasets across independent studies can boost statistical power by increasing the numbers of observations and can achieve more accurate estimates of effect sizes. This is especially important for genetic studies where a large number of observations are required to obtain sufficient power to detect and replicate genetic effects. There is a need to develop and evaluate methods for joint-analytical analyses of rich datasets collected in imaging genetics studies. The ENIGMA-DTI consortium is developing and evaluating approaches for obtaining pooled estimates of heritability through meta-and mega-genetic analytical approaches, to estimate the general additive genetic contributions to the intersubject variance in fractional anisotropy (FA) measured from diffusion tensor imaging (DTI). We used the ENIGMA-DTI data harmonization protocol for uniform processing of DTI data from multiple sites. We evaluated this protocol in five family-based cohorts providing data from a total of 2248 children and adults (ages: 9–85) collected with various imaging protocols. We used the imaging genetics analysis tool, SOLAR-Eclipse, to combine twin and family data from Dutch, Australian and Mexican-American cohorts into one large “mega-family”. We showed that heritability estimates may vary from one cohort to another. We used two meta-analytical (the sample-size and standard-error weighted) approaches and a mega-genetic analysis to calculate heritability estimates across-population. We performed leave-one-out analysis of the joint estimates of heritability, removing a different cohort each time to understand the estimate variability. Overall, meta- and mega-genetic analyses of heritability produced robust estimates of heritability. PMID:24657781
Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
NASA Astrophysics Data System (ADS)
Glicksman, Hal
1998-12-01
Green is the center of the visible spectrum and the hue to which we are most sensitive. In RGB color, green is 60 percent of white. When we look through a prism at a white square, as Goethe did, we see white between yellow and cyan, just where green appears in the spectrum of Newton. Additional arguments were published previously and appear at www.csulb.edu/-percept, along with the Percept color chart of the hue/value relationships. A new argument, derived from the perception of leaves, is presented here. The Percept color chart transformed into a color wheel is also presented.
Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
Novaes, C.P.; Wuensche, C.A.; Bernui, A.; Ferreira, I.S. E-mail: bernui@on.br E-mail: ca.wuensche@inpe.br
2014-01-01
The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two powerful statistical tools that appears to be sensitive enough to detect tiny deviations from Gaussianity in CMB maps. This estimator combines the Minkowski functionals with a Neural Network, maximizing a tool widely used to study non-Gaussian signals with a reinforcement of another tool designed to identify patterns in a data set. We test our estimator by analyzing simulated CMB maps contaminated with different amounts of local primordial non-Gaussianity quantified by the dimensionless parameter f{sub NL}. We apply it to these sets of CMB maps and find ∼> 98% of chance of positive detection, even for small intensity local non-Gaussianity like f{sub NL} = 38±18, the current limit from Planck data for large angular scales. Additionally, we test the suitability to distinguish between primary and secondary non-Gaussianities: first we train the Neural Network with two sets, one of nearly Gaussian CMB maps (|f{sub NL}| ≤ 10) but contaminated with realistic inhomogeneous Planck noise (i.e., secondary non-Gaussianity) and the other of non-Gaussian CMB maps, that is, maps endowed with weak primordial non-Gaussianity (28 ≤ f{sub NL} ≤ 48); after that we test an ensemble composed of CMB maps either with one of these non-Gaussian contaminations, and find out that our method successfully classifies ∼ 95% of the tested maps as being CMB maps containing primordial or
NASA Technical Reports Server (NTRS)
Simon, M. K.; Huth, G. K.; Polydoros, A.
1982-01-01
Bandwidth-conserving modulation techniques, which trade average power for bandwidth in a favorable exchange, have recently found widespread application in digital radio and satellite communication systems. Quadrature amplitude-shift-keying (QASK) is a particular type of the considered techniques. QASK makes use of multilevel signals to amplitude modulate the in-phase and quadrature components of a carrier. Frequency hopping (FH) is used to protect a conventional communication system from radio frequency interference (RFI) or jamming. Differentially coherent detection provides a possible solution to the effect of phase discontinuities introduced by FH. The application of such a detection technique to QASK signals is discussed. A receiver structure is proposed and its symbol error probability performance for an additive white Gaussian noise (AWGN) background is investigated.
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-01
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.
Strongly scale-dependent non-Gaussianity
Riotto, Antonio; Sloth, Martin S.
2011-02-15
We discuss models of primordial density perturbations where the non-Gaussianity is strongly scale dependent. In particular, the non-Gaussianity may have a sharp cutoff and be very suppressed on large cosmological scales, but sizable on small scales. This may have an impact on probes of non-Gaussianity in the large-scale structure and in the cosmic microwave background radiation anisotropies.
D'Amico, Guido; Kleban, Matthew
2014-08-22
We analyze primordial non-Gaussianity in single-field inflationary models when the tensor-to-scalar ratio is large. Our results show that detectable levels of non-Gaussianity f(NL) ∼ 50 are still possible in the simplest class of models described by the effective theory of inflation. However, the shape is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity. PMID:25192084
Monogamy inequality for distributed gaussian entanglement.
Hiroshima, Tohya; Adesso, Gerardo; Illuminati, Fabrizio
2007-02-01
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. PMID:17358836
Elegant Gaussian beams for enhanced optical manipulation
Alpmann, Christina Schöler, Christoph; Denz, Cornelia
2015-06-15
Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread function is relevant.
Breaking Gaussian incompatibility on continuous variable quantum systems
Heinosaari, Teiko; Kiukas, Jukka; Schultz, Jussi
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.
Non-Gaussian Photon Probability Distribution
Solomon, Benjamin T.
2010-01-28
This paper investigates the axiom that the photon's probability distribution is a Gaussian distribution. The Airy disc empirical evidence shows that the best fit, if not exact, distribution is a modified Gamma mGAMMA distribution (whose parameters are alpha = r, betar/sq root(u)) in the plane orthogonal to the motion of the photon. This modified Gamma distribution is then used to reconstruct the probability distributions along the hypotenuse from the pinhole, arc from the pinhole, and a line parallel to photon motion. This reconstruction shows that the photon's probability distribution is not a Gaussian function. However, under certain conditions, the distribution can appear to be Normal, thereby accounting for the success of quantum mechanics. This modified Gamma distribution changes with the shape of objects around it and thus explains how the observer alters the observation. This property therefore places additional constraints to quantum entanglement experiments. This paper shows that photon interaction is a multi-phenomena effect consisting of the probability to interact P{sub i}, the probabilistic function and the ability to interact A{sub i}, the electromagnetic function. Splitting the probability function P{sub i} from the electromagnetic function A{sub i} enables the investigation of the photon behavior from a purely probabilistic P{sub i} perspective. The Probabilistic Interaction Hypothesis is proposed as a consistent method for handling the two different phenomena, the probability function P{sub i} and the ability to interact A{sub i}, thus redefining radiation shielding, stealth or cloaking, and invisibility as different effects of a single phenomenon P{sub i} of the photon probability distribution. Sub wavelength photon behavior is successfully modeled as a multi-phenomena behavior. The Probabilistic Interaction Hypothesis provides a good fit to Otoshi's (1972) microwave shielding, Schurig et al.(2006) microwave cloaking, and Oulton et al.(2008) sub
Near grazing scattering from non-Gaussian ocean surfaces
NASA Technical Reports Server (NTRS)
Kim, Yunjin; Rodriguez, Ernesto
1993-01-01
We investigate the behavior of the scattered electromagnetic waves from non-Gaussian ocean surfaces at near grazing incidence. Even though the scattering mechanisms at moderate incidence angles are relatively well understood, the same is not true for near grazing rough surface scattering. However, from the experimental ocean scattering data, it has been observed that the backscattering cross section of a horizontally polarized wave can be as large as the vertical counterpart at near grazing incidence. In addition, these returns are highly intermittent in time. There have been some suggestions that these unexpected effects may come from shadowing or feature scattering. Using numerical scattering simulations, it can be shown that the horizontal backscattering cannot be larger than the vertical one for the Gaussian surfaces. Our main objective of this study is to gain a clear understanding of scattering mechanisms underlying the near grazing ocean scattering. In order to evaluate the backscattering cross section from ocean surfaces at near grazing incidence, both the hydrodynamic modeling of ocean surfaces and an accurate near grazing scattering theory are required. For the surface modeling, we generate Gaussian surfaces from the ocean surface power spectrum which is derived using several experimental data. Then, weakly nonlinear large scale ocean surfaces are generated following Longuet-Higgins. In addition, the modulation of small waves by large waves is included using the conservation of wave action. For surface scattering, we use MOM (Method of Moments) to calculate the backscattering from scattering patches with the two scale shadowing approximation. The differences between Gaussian and non-Gaussian surface scattering at near grazing incidence are presented.
Entanglement generation via non-Gaussian transfer over atmospheric fading channels
NASA Astrophysics Data System (ADS)
Hosseinidehaj, Nedasadat; Malaney, Robert
2015-12-01
In this work we probe the usefulness of non-Gaussian entangled states as a resource for quantum communication through atmospheric channels. We outline the initial conditions in which non-Gaussian state transfer leads to enhanced entanglement transfer relative to that obtainable via Gaussian state transfer. However, we conclude that in (anticipated) operational scenarios—where most of the non-Gaussian states to be transferred over the air are created just in time via photonic subtraction, addition, or replacement from incoming Gaussian states—the entanglement-generation rate between stations via non-Gaussian state transfer will be substantially less than that created by direct Gaussian state transfer. The role of postselection, distillation, and quantum memory in altering this conclusion is discussed, and comparison with entanglement rates produced via single-photon technologies is provided. Our results suggest that in the near term entangled Gaussian states, squeezed beyond some modest level, offer the most attractive proposition for the distribution of entanglement through high-loss atmospheric channels. The implications of our results for entanglement-based quantum key distribution to low-Earth orbit are presented.
Halo/galaxy bispectrum with primordial non-Gaussianity from integrated perturbation theory
NASA Astrophysics Data System (ADS)
Yokoyama, Shuichiro; Matsubara, Takahiko; Taruya, Atsushi
2014-02-01
We derive a formula for the halo/galaxy bispectrum on the basis of the integrated perturbation theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (local, equilateral, and orthogonal types), and primordial trispectrum of the local-type non-Gaussianity. We find that the equilateral- and orthogonal-type non-Gaussianities show distinct scale-dependent behaviors which can dominate the gravity-induced non-Gaussianity at very large scales. For the local-type non-Gaussianity, higher-order loop corrections are found to give a significantly large contribution to the halo/galaxy bispectrum of the squeezed shape and eventually dominate over the other contributions on large scales. A diagrammatic approach based on the iPT helps us to systematically investigate an impact of such higher-order contributions to the large-scale halo/galaxy bispectrum.
Measurement-induced disturbances and nonclassical correlations of Gaussian states
Mista, Ladislav Jr.; Tatham, Richard; Korolkova, Natalia; Girolami, Davide; Adesso, Gerardo
2011-04-15
We study quantum correlations beyond entanglement in two-mode Gaussian states of continuous-variable systems by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two-mode Gaussian states comprising pure states where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two-mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong similarity with the case of two qubits. Upper and lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We further present a comparison between Gaussian AMID and Gaussian entanglement of formation, and classify families of two-mode states in terms of their Gaussian AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings provide a further confirmation of the genuinely quantum nature of general Gaussian states, yet they reveal that non-Gaussian measurements can play a crucial role for the optimized extraction and potential exploitation of classical and nonclassical correlations in Gaussian states.
NASA Astrophysics Data System (ADS)
Troncossi, M.; Di Sante, R.; Rivola, A.
2016-10-01
In the field of vibration qualification testing, random excitations are typically imposed on the tested system in terms of a power spectral density (PSD) profile. This is the one of the most popular ways to control the shaker or slip table for durability tests. However, these excitations (and the corresponding system responses) exhibit a Gaussian probability distribution, whereas not all real-life excitations are Gaussian, causing the response to be also non-Gaussian. In order to introduce non-Gaussian peaks, a further parameter, i.e., kurtosis, has to be controlled in addition to the PSD. However, depending on the specimen behaviour and input signal characteristics, the use of non-Gaussian excitations with high kurtosis and a given PSD does not automatically imply a non-Gaussian stress response. For an experimental investigation of these coupled features, suitable measurement methods need to be developed in order to estimate the stress amplitude response at critical failure locations and consequently evaluate the input signals most representative for real-life, non-Gaussian excitations. In this paper, a simple test rig with a notched cantilevered specimen was developed to measure the response and examine the kurtosis values in the case of stationary Gaussian, stationary non-Gaussian, and burst non-Gaussian excitation signals. The laser Doppler vibrometry technique was used in this type of test for the first time, in order to estimate the specimen stress amplitude response as proportional to the differential displacement measured at the notch section ends. A method based on the use of measurements using accelerometers to correct for the occasional signal dropouts occurring during the experiment is described. The results demonstrate the ability of the test procedure to evaluate the output signal features and therefore to select the most appropriate input signal for the fatigue test.
Constraining primordial non-Gaussianity with cosmological weak lensing: shear and flexion
Fedeli, C.; Bartelmann, M.; Moscardini, L. E-mail: bartelmann@uni-heidelberg.de
2012-10-01
We examine the cosmological constraining power of future large-scale weak lensing surveys on the model of the ESA planned mission Euclid, with particular reference to primordial non-Gaussianity. Our analysis considers several different estimators of the projected matter power spectrum, based on both shear and flexion. We review the covariance and Fisher matrix for cosmic shear and evaluate those for cosmic flexion and for the cross-correlation between the two. The bounds provided by cosmic shear alone are looser than previously estimated, mainly due to the reduced sky coverage and background number density of sources for the latest Euclid specifications. New constraints for the local bispectrum shape, marginalized over σ{sub 8}, are at the level of Δf{sub NL} ∼ 100, with the precise value depending on the exact multipole range that is considered in the analysis. We consider three additional bispectrum shapes, for which the cosmic shear constraints range from Δf{sub NL} ∼ 340 (equilateral shape) up to Δf{sub NL} ∼ 500 (orthogonal shape). Also, constraints on the level of non-Gaussianity and on the amplitude of the matter power spectrum σ{sub 8} are almost perfectly anti-correlated, except for the orthogonal bispectrum shape for which they are correlated. The competitiveness of cosmic flexion constraints against cosmic shear ones depends by and large on the galaxy intrinsic flexion noise, that is still virtually unconstrained. Adopting the very high value that has been occasionally used in the literature results in the flexion contribution being basically negligible with respect to the shear one, and for realistic configurations the former does not improve significantly the constraining power of the latter. Since the shear shot noise is white, while the flexion one decreases with decreasing scale, by considering high enough multipoles the two contributions have to become comparable. Extending the analysis up to l{sub max} = 20,000 cosmic flexion, while
Experimental characterization of Gaussian quantum discord generated by four-wave mixing
NASA Astrophysics Data System (ADS)
Vogl, Ulrich; Glasser, Ryan T.; Glorieux, Quentin; Clark, Jeremy B.; Corzo, Neil V.; Lett, Paul D.
2013-01-01
We experimentally determine the Gaussian quantum discord present in two-mode squeezed vacuum generated by a four-wave mixing process in hot rubidium vapor. The frequency spectra of the discord as well as the quantum and classical mutual information are also measured. In addition, the effects of symmetric attenuation introduced into both modes of the squeezed vacuum on the Gaussian quantum discord, and the quantum mutual information and the classical correlations are examined experimentally. Finally, we show that due to the multi-spatial-mode nature of the four-wave mixing process, the Gaussian quantum discord may exhibit sub- or superadditivity depending on which spatial channels are selected.
Gaussian translation operator in a multilevel scheme
NASA Astrophysics Data System (ADS)
Hansen, Thorkild B.; Borries, Oscar
2015-08-01
A multilevel computation scheme for time-harmonic fields in three dimensions will be formulated with a new Gaussian translation operator that decays exponentially outside a circular cone centered on the line connecting the source and observation groups. This Gaussian translation operator is directional and diagonal with its sharpness determined by a beam parameter. When the beam parameter is set to zero, the Gaussian translation operator reduces to the standard fast multipole method translation operator. The directionality of the Gaussian translation operator makes it possible to reduce the number of plane waves required to achieve a given accuracy. The sampling rate can be determined straightforwardly to achieve any desired accuracy. The use of the computation scheme will be illustrated through a near-field scanning problem where the far-field pattern of a source is determined from near-field measurements with a known probe. Here the Gaussian translation operator improves the condition number of the matrix equation that determines the far-field pattern. The Gaussian translation operator can also be used when the probe pattern is known only in one hemisphere, as is common in practice. Also, the Gaussian translation operator will be used to solve the scattering problem of the perfectly conducting sphere.
Asymmetric Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
Quark and Lepton Masses from Gaussian Landscapes
Hall, Lawrence J.; Salem, Michael P.; Watari, Taizan
2008-04-11
The flavor structure of the standard model (SM) might arise from random selection on a landscape. We propose a class of simple models, 'Gaussian landscapes', where Yukawa couplings derive from overlap integrals of Gaussian wave functions on extra-dimensions. Statistics of vacua are generated by scanning the peak positions of these zero-modes, giving probability distributions for all flavor observables. Gaussian landscapes can account for all observed flavor patterns with few free parameters. Although they give broad probability distributions, the predictions are correlated and accounting for measured parameters sharpens the distributions of future neutrino measurements.
Quantum bit commitment under Gaussian constraints
NASA Astrophysics Data System (ADS)
Mandilara, Aikaterini; Cerf, Nicolas J.
2012-06-01
Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
Adesso, Gerardo; Illuminati, Fabrizio
2005-09-15
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
Gondal, Mohammed A; Chang, Xiaofeng; Al-Saadi, Abdulaziz A; Yamani, Zain H; Zhang, Jun; Ji, Guangbin
2012-01-01
BiOCl-assisted photodegradation of Rhodamine B (Rh. B) molecules was investigated by using white light and green pulsed laser as sources of irradiation in the visible region for the first time. The dependences of removal efficiencies on catalyst dosage, incident pulsed laser energy were investigated and discussed. The dissolved oxygen was found to play an important role during the photochemical reaction. In addition the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) levels of Rh. B molecular were calculated using a Gaussian 03 program. These calculations were valuable to identify the possible photo-catalytic excitation process involved in degradation of Rh.B. PMID:22506712
Sepke, Scott M; Umstadter, Donald P
2006-05-15
The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series. PMID:16642134
Bakshi, Ashish; Roy, Sourya; Mallick, Arijit; Ghosh, Kuntal
2016-03-01
The Oriented Difference of Gaussian (ODOG) filter of Blakeslee and McCourt has been successfully employed to explain several brightness perception illusions which include illusions of both brightness-contrast type, for example, Simultaneous Brightness Contrast and Grating Induction and the brightness-assimilation type, for example, the White effect and the shifted White effect. Here, we demonstrate some limitations of the ODOG filter in predicting perceived brightness by comparing the ODOG responses to various stimuli (generated by varying two parameters, namely, test patch length and spatial frequency) with experimental observations of the same.
Brain MRI segmentation and lesion detection using generalized Gaussian and Rician modeling
NASA Astrophysics Data System (ADS)
Wu, Xuqiang; Bricq, Stéphanie; Collet, Christophe
2011-03-01
In this paper we propose a mixed noise modeling so as to segment the brain and to detect lesion. Indeed, accurate segmentation of multimodal (T1, T2 and Flair) brain MR images is of great interest for many brain disorders but requires to efficiently manage multivariate correlated noise between available modalities. We addressed this problem in1 by proposing an entirely unsupervised segmentation scheme, taking into account multivariate Gaussian noise, imaging artifacts,intrinsic tissue variation and partial volume effects in a Bayesian framework. Nevertheless, tissue classification remains a challenging task especially when one addresses the lesion detection during segmentation process2 as we did. In order to improve brain segmentation into White and Gray Matter (resp. WM and GM) and cerebro-spinal fluid (CSF), we propose to fit a Rician (RC) density distribution for CSF whereas Generalized Gaussian (GG) models are used to fit the likelihood between model and data corresponding to WM and GM. In this way, we present in this paper promising results showing that in a multimodal segmentation-detection scheme, this model fits better with the data and increases lesion detection rate. One of the main challenges consists in being able to take into account various pdf (Gaussian and non- Gaussian) for correlated noise between modalities and to show that lesion-detection is then clearly improved, probably because non-Gaussian noise better fits to the physic of MRI image acquisition.
Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing
NASA Technical Reports Server (NTRS)
Choi, Benjamin B.
2002-01-01
Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.
Near-unit-fidelity entanglement distribution scheme using Gaussian communication
Praxmeyer, Ludmila; Loock, Peter van
2010-06-15
We show how to distribute with percentage success probabilities almost perfectly entangled qubit memory pairs over repeater channel segments of the order of the optical attenuation distance. In addition to some weak, dispersive light-matter interactions, only Gaussian state transmissions and measurements are needed for this scheme. Our protocol outperforms the existing coherent-state-based schemes for entanglement distribution, even those using error-free non-Gaussian measurements. This is achieved through two innovations: First, optical squeezed states are utilized instead of coherent states. Second, the amplitudes of the bright signal pulses are reamplified at each repeater station. This latter variation is a strategy reminiscent of classical repeaters and would be impossible in single-photon-based schemes.
Optimal cloning of mixed Gaussian states
Guta, Madalin; Matsumoto, Keiji
2006-09-15
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.
Why Should We Pivot in Gaussian Elimination?
ERIC Educational Resources Information Center
Rozema, Edward
1988-01-01
The article discusses the use of computers to teacher college level mathematics. In particular, the Gaussian elimination procedure for solving a system of n linear equations in n unknowns, using a computer, is examined. (PK)
Improved Gaussian Beam-Scattering Algorithm
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.
Non-Gaussianities in New Ekpyrotic Cosmology.
Buchbinder, Evgeny I; Khoury, Justin; Ovrut, Burt A
2008-05-01
The new ekpyrotic model is an alternative scenario of the early Universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of cosmic microwave background experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that can yield large non-Gaussianity, such as Dirac-Born-Infeld inflation and the simplest curvatonlike models, through the shape dependence of the correlation functions. Non-Gaussianity therefore provides a distinguishing and testable prediction of New Ekpyrotic Cosmology.
Gaussian-Beam Laser-Resonator Program
NASA Technical Reports Server (NTRS)
Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman
1989-01-01
Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).
Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics.
Towghi, N; Javidi, B
2001-08-01
We develop algorithms to detect a known pattern or a reference signal in the presence of additive, disjoint background, and multiplicative white Gaussian noise with unknown statistics. The presence of three different types of noise processes with unknown statistics presents difficulties in estimating the unknown parameters. The standard methods such as expected-maximization-type algorithms are iterative, and in the framework of hypothesis testing they are time-consuming, because corresponding to each hypothesis one must estimate a set of parameters. Other standard methods such as setting the gradient of the likelihood function with respect to the unknown parameters will lead to a nonlinear system of equations that do not have a closed-form solution and require iterative methods. We develop an approach to overcome these handicaps and derive algorithms to detect a known object. We present new methods to estimate unknown parameters within the framework of hypothesis testing. The methods that we present are direct and provide closed-form estimates of the unknown parameters. Computer simulations are used to show that for the images tested, the receivers that we have designed perform better than existing receivers. PMID:11488488
Non-stationary noise estimation using dictionary learning and Gaussian mixture models
NASA Astrophysics Data System (ADS)
Hughes, James M.; Rockmore, Daniel N.; Wang, Yang
2014-02-01
Stationarity of the noise distribution is a common assumption in image processing. This assumption greatly simplifies denoising estimators and other model parameters and consequently assuming stationarity is often a matter of convenience rather than an accurate model of noise characteristics. The problematic nature of this assumption is exacerbated in real-world contexts, where noise is often highly non-stationary and can possess time- and space-varying characteristics. Regardless of model complexity, estimating the parameters of noise dis- tributions in digital images is a difficult task, and estimates are often based on heuristic assumptions. Recently, sparse Bayesian dictionary learning methods were shown to produce accurate estimates of the level of additive white Gaussian noise in images with minimal assumptions. We show that a similar model is capable of accu- rately modeling certain kinds of non-stationary noise processes, allowing for space-varying noise in images to be estimated, detected, and removed. We apply this modeling concept to several types of non-stationary noise and demonstrate the model's effectiveness on real-world problems, including denoising and segmentation of images according to noise characteristics, which has applications in image forensics.
Multi-Compartment T2 Relaxometry Using a Spatially Constrained Multi-Gaussian Model
Raj, Ashish; Pandya, Sneha; Shen, Xiaobo; LoCastro, Eve; Nguyen, Thanh D.; Gauthier, Susan A.
2014-01-01
The brain’s myelin content can be mapped by T2-relaxometry, which resolves multiple differentially relaxing T2 pools from multi-echo MRI. Unfortunately, the conventional fitting procedure is a hard and numerically ill-posed problem. Consequently, the T2 distributions and myelin maps become very sensitive to noise and are frequently difficult to interpret diagnostically. Although regularization can improve stability, it is generally not adequate, particularly at relatively low signal to noise ratio (SNR) of around 100–200. The purpose of this study was to obtain a fitting algorithm which is able to overcome these difficulties and generate usable myelin maps from noisy acquisitions in a realistic scan time. To this end, we restrict the T2 distribution to only 3 distinct resolvable tissue compartments, modeled as Gaussians: myelin water, intra/extra-cellular water and a slow relaxing cerebrospinal fluid compartment. We also impose spatial smoothness expectation that volume fractions and T2 relaxation times of tissue compartments change smoothly within coherent brain regions. The method greatly improves robustness to noise, reduces spatial variations, improves definition of white matter fibers, and enhances detection of demyelinating lesions. Due to efficient design, the additional spatial aspect does not cause an increase in processing time. The proposed method was applied to fast spiral acquisitions on which conventional fitting gives uninterpretable results. While these fast acquisitions suffer from noise and inhomogeneity artifacts, our preliminary results indicate the potential of spatially constrained 3-pool T2 relaxometry. PMID:24896833
Eyyuboğlu, Halil T
2014-06-10
Using the random phase screen approach, we carry out a simulation analysis of the probability of error performance of Gaussian, annular Gaussian, cos Gaussian, and cosh Gaussian beams. In our scenario, these beams are intensity-modulated by the randomly generated binary symbols of an electrical message signal and then launched from the transmitter plane in equal powers. They propagate through a turbulent atmosphere modeled by a series of random phase screens. Upon arriving at the receiver plane, detection is performed in a circuitry consisting of a pin photodiode and a matched filter. The symbols detected are compared with the transmitted ones, errors are counted, and from there the probability of error is evaluated numerically. Within the range of source and propagation parameters tested, the lowest probability of error is obtained for the annular Gaussian beam. Our investigation reveals that there is hardly any difference between the aperture-averaged scintillations of the beams used, and the distinctive advantage of the annular Gaussian beam lies in the fact that the receiver aperture captures the maximum amount of power when this particular beam is launched from the transmitter plane.
2006-01-01
Statistical image reconstruction methods based on maximum a posteriori (MAP) principle have been developed for emission tomography. The prior distribution of the unknown image plays an important role in MAP reconstruction. The most commonly used prior are Gaussian priors, whose logarithm has a quadratic form. Gaussian priors are relatively easy to analyze. It has been shown that the effect of a Gaussian prior can be approximated by linear filtering a maximum likelihood (ML) reconstruction. As a result, sharp edges in reconstructed images are not preserved. To preserve sharp transitions, non-Gaussian priors have been proposed. However, their effect on clinical tasks is less obvious. In this paper, we compare MAP reconstruction with Gaussian and non-Gaussian priors for lesion detection and region of interest quantification using computer simulation. We evaluate three representative priors: Gaussian prior, Huber prior, and Geman-McClure prior. We simulate imaging a prostate tumor using positron emission tomography (PET). The detectability of a known tumor in either a fixed background or a random background is measured using a channelized Hotelling observer. The bias-variance tradeoff curves are calculated for quantification of the total tumor activity. The results show that for the detection and quantification tasks, the Gaussian prior is as effective as non-Gaussian priors. PMID:23165056
Integrated Risk Information System (IRIS)
White phosphorus ; CASRN 7723 - 14 - 0 Human health assessment information on a chemical substance is included in the IRIS database only after a comprehensive review of toxicity data , as outlined in the IRIS assessment development process . Sections I ( Health Hazard Assessments for Noncarcinogenic
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
NASA Astrophysics Data System (ADS)
Berg, J.; Mann, J.; Natarajan, A.; Patton, E. G.
2014-12-01
In wind energy applications the turbulent velocity field of the Atmospheric Boundary Layer (ABL) is often characterised by Gaussian probability density functions. When estimating the dynamical loads on wind turbines this has been the rule more than anything else. From numerous studies in the laboratory, in Direct Numerical Simulations, and from in-situ measurements of the ABL we know, however, that turbulence is not purely Gaussian: the smallest and fastest scales often exhibit extreme behaviour characterised by strong non-Gaussian statistics. In this contribution we want to investigate whether these non-Gaussian effects are important when determining wind turbine loads, and hence of utmost importance to the design criteria and lifetime of a wind turbine. We devise a method based on Principal Orthogonal Decomposition where non-Gaussian velocity fields generated by high-resolution pseudo-spectral Large-Eddy Simulation (LES) of the ABL are transformed so that they maintain the exact same second-order statistics including variations of the statistics with height, but are otherwise Gaussian. In that way we can investigate in isolation the question whether it is important for wind turbine loads to include non-Gaussian properties of atmospheric turbulence. As an illustration the Figure show both a non-Gaussian velocity field (left) from our LES, and its transformed Gaussian Counterpart (right). Whereas the horizontal velocity components (top) look close to identical, the vertical components (bottom) are not: the non-Gaussian case is much more fluid-like (like in a sketch by Michelangelo). The question is then: Does the wind turbine see this? Using the load simulation software HAWC2 with both the non-Gaussian and newly constructed Gaussian fields, respectively, we show that the Fatigue loads and most of the Extreme loads are unaltered when using non-Gaussian velocity fields. The turbine thus acts like a low-pass filter which average out the non-Gaussian behaviour on time
Numerical characteristics of the intensity distribution for a white organic light-emitting diode
NASA Astrophysics Data System (ADS)
Yang, Henglong; Li, Wei-Sheng; Huang, Pin-Jui; Hsieh, Meng-Huan
2015-09-01
A statistical distribution function capable of numerically characterizing the unique intensity distribution of a planar white organic light-emitting diodes (WOLED) was theoretically investigated by fitting our experimental data obtained by microscopic goniometer (MG) system associated with an energy analyzer to the normal distribution function with amplitude, average, and standard deviation as adjustable parameters. The WOLED is one of the upcoming lighting sources with planar device structure without additional optical components. The intensity characteristic of a lighting source is crucial for practical purpose. The procedure of an optical design usually requires proper numerical tools to satisfy specific application by adjusting parameters. Relatively uniform intensity distribution of a planar lighting source is needed for a specific lighting application such as back-lighting (BL) for liquid-crystal displays (LCD) in which Regular white LED's (WLED) and light-guide plate are assembled as a planar module. Our intensity measurement of a WOLED revealed a unique pattern in which the relative intensities near central area are higher than that near the edge of the emissive area. This unique intensity profile is similar to the feature of Gaussian distribution function. Our preliminary result of applying Gaussian distribution function to numerically characterize the intensity profile of a WOLED suggests that the unique intensity profile can be represented by single distribution function properly.
Dynamic generation of Ince-Gaussian modes with a digital micromirror device
Ren, Yu-Xuan; Fang, Zhao-Xiang; Chen, Yue; Lu, Rong-De; Gong, Lei; Huang, Kun
2015-04-07
Ince-Gaussian (IG) beam with elliptical profile, as a connection between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams, has showed unique advantages in some applications such as quantum entanglement and optical micromanipulation. However, its dynamic generation with high switching frequency is still challenging. Here, we experimentally reported the quick generation of Ince-Gaussian beam by using a digital micro-mirror device (DMD), which has the highest switching frequency of 5.2 kHz in principle. The configurable properties of DMD allow us to observe the quasi-smooth variation from LG (with ellipticity ε=0) to IG and HG (ε=∞) beam. This approach might pave a path to high-speed quantum communication in terms of IG beam. Additionally, the characterized axial plane intensity distribution exhibits a 3D mould potentially being employed for optical micromanipulation.
NASA Astrophysics Data System (ADS)
Tidhar, G. A.; Rotman, S. R.
2013-05-01
Performance of algorithms for target signal detection in Hyperspectral Imagery (HSI) is often deteriorated when the data is neither statistically homogeneous nor Gaussian or when its Joint Probability Density (JPD) does not match any presumed particular parametric model. In this paper we propose a novel detection algorithm which first attempts at dividing data domain into mostly Gaussian and mostly Non-Gaussian (NG) subspaces, and then estimates the JPD of the NG subspace with a non-parametric Graph-based estimator. It then combines commonly used detection algorithms operating on the mostly-Gaussian sub-space and an LRT calculated directly with the estimated JPD of the NG sub-space, to detect anomalies and known additive-type target signals. The algorithm performance is compared to commonly used algorithms and is found to be superior in some important cases.
Born modeling for heterogeneous media using the Gaussian beam summation based Green's function
NASA Astrophysics Data System (ADS)
Huang, Xingguo; Sun, Hui; Sun, Jianguo
2016-08-01
Born approximation is a commonly used approximation in the simulation of seismic wave propagation. Calculation of the Green's function in Born approximation integral is essential for Born modeling. We derive a new Born formula based on the Gaussian beam representations of Green's functions. This procedure can be used to mitigate the problems like the caustic, shadow region, and multivalued traveltime caused by multipathing that traditional geometric ray theory cannot deal with. However, due to the characteristic of complex traveltime in the Gaussian beam, we present a new isochronous stack method for Gaussian beam based Born modeling. Additionally, two basic issues, background velocity and integral region selection, are discussed. Numerical results demonstrate the accuracy and efficiency of the Gaussian beam based Born theory and implementation.
Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers.
Zhao, Xinyu; Gang, Tie
2009-01-01
A nonparaxial multi-Gaussian beam model is proposed in order to overcome the limitation that paraxial Gaussian beam models lose accuracy in simulating the beam steering behavior of phased array transducers. Using this nonparaxial multi-Gaussian beam model, the focusing and steering sound fields generated by an ultrasonic linear phased array transducer are calculated and compared with the corresponding results obtained by paraxial multi-Gaussian beam model and more exact Rayleigh-Sommerfeld integral model. In addition, with help of this novel nonparaxial method, an ultrasonic measurement model is provided to investigate the sensitivity of linear phased array transducers versus steering angles. Also the comparisons of model predictions with experimental results are presented to certify the accuracy of this provided measurement model.
Non-Gaussianity and large-scale structure in a two-field inflationary model
Tseliakhovich, Dmitriy; Hirata, Christopher
2010-08-15
Single-field inflationary models predict nearly Gaussian initial conditions, and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large-scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constraints on the local non-Gaussianity parameter f-tilde{sub NL} and the ratio {xi} of the amplitude of primordial perturbations due to the inflaton and curvaton using WMAP and Sloan Digital Sky Survey data.
Relativistic corrections and non-Gaussianity in radio continuum surveys
Maartens, Roy; Zhao, Gong-Bo; Bacon, David; Koyama, Kazuya; Raccanelli, Alvise E-mail: Gong-bo.Zhao@port.ac.uk E-mail: Kazuya.Koyama@port.ac.uk
2013-02-01
Forthcoming radio continuum surveys will cover large volumes of the observable Universe and will reach to high redshifts, making them potentially powerful probes of dark energy, modified gravity and non-Gaussianity. We consider the continuum surveys with LOFAR, WSRT and ASKAP, and examples of continuum surveys with the SKA. We extend recent work on these surveys by including redshift space distortions and lensing convergence in the radio source auto-correlation. In addition we compute the general relativistic (GR) corrections to the angular power spectrum. These GR corrections to the standard Newtonian analysis of the power spectrum become significant on scales near and beyond the Hubble scale at each redshift. We find that the GR corrections are at most percent-level in LOFAR, WODAN and EMU surveys, but they can produce O(10%) changes for high enough sensitivity SKA continuum surveys. The signal is however dominated by cosmic variance, and multiple-tracer techniques will be needed to overcome this problem. The GR corrections are suppressed in continuum surveys because of the integration over redshift — we expect that GR corrections will be enhanced for future SKA HI surveys in which the source redshifts will be known. We also provide predictions for the angular power spectra in the case where the primordial perturbations have local non-Gaussianity. We find that non-Gaussianity dominates over GR corrections, and rises above cosmic variance when f{sub NL}∼>5 for SKA continuum surveys.
Relativistic corrections and non-Gaussianity in radio continuum surveys
NASA Astrophysics Data System (ADS)
Maartens, Roy; Zhao, Gong-Bo; Bacon, David; Koyama, Kazuya; Raccanelli, Alvise
2013-02-01
Forthcoming radio continuum surveys will cover large volumes of the observable Universe and will reach to high redshifts, making them potentially powerful probes of dark energy, modified gravity and non-Gaussianity. We consider the continuum surveys with LOFAR, WSRT and ASKAP, and examples of continuum surveys with the SKA. We extend recent work on these surveys by including redshift space distortions and lensing convergence in the radio source auto-correlation. In addition we compute the general relativistic (GR) corrections to the angular power spectrum. These GR corrections to the standard Newtonian analysis of the power spectrum become significant on scales near and beyond the Hubble scale at each redshift. We find that the GR corrections are at most percent-level in LOFAR, WODAN and EMU surveys, but they can produce O(10%) changes for high enough sensitivity SKA continuum surveys. The signal is however dominated by cosmic variance, and multiple-tracer techniques will be needed to overcome this problem. The GR corrections are suppressed in continuum surveys because of the integration over redshift — we expect that GR corrections will be enhanced for future SKA HI surveys in which the source redshifts will be known. We also provide predictions for the angular power spectra in the case where the primordial perturbations have local non-Gaussianity. We find that non-Gaussianity dominates over GR corrections, and rises above cosmic variance when fNLgtrsim5 for SKA continuum surveys.
From particle counting to Gaussian tomography
NASA Astrophysics Data System (ADS)
Parthasarathy, K. R.; Sengupta, Ritabrata
2015-12-01
The momentum and position observables in an n-mode boson Fock space Γ(ℂn) have the whole real line ℝ as their spectrum. But the total number operator N has a discrete spectrum ℤ+ = {0, 1, 2,…}. An n-mode Gaussian state in Γ(ℂn) is completely determined by the mean values of momentum and position observables and their covariance matrix which together constitute a family of n(2n + 3) real parameters. Starting with N and its unitary conjugates by the Weyl displacement operators and operators from a representation of the symplectic group Sp(2n) in Γ(ℂn), we construct n(2n + 3) observables with spectrum ℤ+ but whose expectation values in a Gaussian state determine all its mean and covariance parameters. Thus measurements of discrete-valued observables enable the tomography of the underlying Gaussian state and it can be done by using five one-mode and four two-mode Gaussian symplectic gates in single and pair mode wires of Γ(ℂn) = Γ(ℂ)⊗n. Thus the tomography protocol admits a simple description in a language similar to circuits in quantum computation theory. Such a Gaussian tomography applied to outputs of a Gaussian channel with coherent input states permit a tomography of the channel parameters. However, in our procedure the number of counting measurements exceeds the number of channel parameters slightly. Presently, it is not clear whether a more efficient method exists for reducing this tomographic complexity. As a byproduct of our approach an elementary derivation of the probability generating function of N in a Gaussian state is given. In many cases the distribution turns out to be infinitely divisible and its underlying Lévy measure can be obtained. However, we are unable to derive the exact distribution in all cases. Whether this property of infinite divisibility holds in general is left as an open problem.
Conformal invariance, dark energy, and CMB non-gaussianity
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Mazur, Pawel O.; Mottola, Emil
2012-09-01
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 Bbb R3 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 Bbb S2 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 symmetries of de Sitter space, and in that sense, independent of specific model assumptions. Each is different from the predictions of single field slow roll inflation models, which rely on the breaking of de Sitter invariance. We propose a quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise to these non-Gaussianities without a slow roll inflaton field, and argue that conformal invariance also leads to the expectation for the relation nS-1 = nT between the spectral indices of the scalar and tensor power spectrum. Confirmation of this prediction or detection of non-Gaussian correlations in the CMB of one of the bispectral shape functions predicted by conformal invariance can be used both to establish the physical origins of primordial density fluctuations, and distinguish between different dynamical models of cosmological vacuum dark energy.
Conformal invariance, dark energy, and CMB non-gaussianity
Antoniadis, Ignatios; Mazur, Pawel O.; Mottola, Emil E-mail: mazur@physics.sc.edu
2012-09-01
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{sup 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{sup 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 symmetries of de Sitter space, and in that sense, independent of specific model assumptions. Each is different from the predictions of single field slow roll inflation models, which rely on the breaking of de Sitter invariance. We propose a quantum origin for the CMB fluctuations in the scalar gravitational sector from the conformal anomaly that could give rise to these non-Gaussianities without a slow roll inflaton field, and argue that conformal invariance also leads to the expectation for the relation n{sub S}−1 = n{sub T} between the spectral indices of the scalar and tensor power spectrum. Confirmation of this prediction or detection of non-Gaussian correlations in the CMB of one of the bispectral shape functions predicted by conformal invariance can be used both to establish the physical origins of primordial density fluctuations, and distinguish between different dynamical models of cosmological vacuum dark energy.
Error probabilities in optical PPM receivers with Gaussian mixture densities
NASA Technical Reports Server (NTRS)
Gagliardi, R. M.
1982-01-01
A Gaussian mixture density arises when a discrete variable (e.g., a photodetector count variable) is added to a continuous Gaussian variable (e.g., thermal noise). Making use of some properties of photomultiplier Gaussian mixture distributions, some approximate error probability formulas can be derived. These appear as averages of M-ary orthogonal Gaussian error probabilities. The use of a pure Gaussian assumption is considered, and when properly defined, appears as an accurate upper bound to performance.
Mechanisms of particle clustering in Gaussian and non-Gaussian synthetic turbulence.
Nilsen, Christopher; Andersson, Helge I
2014-10-01
We use synthetic turbulence simulations to study how inertial particles cluster in a turbulent flow, for a wide range of Stokes numbers. Two different types of synthetic turbulence are used: one Gaussian, where the time evolution of the velocity field is a simple phase shift, and one non-Gaussian, where convection is used to evolve the velocity field in time. In both flow types we observe significant particle clustering over a wide range of scales and Stokes numbers. The clustering found at low Stokes numbers can be attributed to the vortex centrifuge effect, where heavy particles are expelled from regions dominated by vorticity. This mechanism is much more effective in the non-Gaussian turbulence, because local flow structures are convected with the particles. The preferential sampling of regions with low vorticity is almost negligible in the Gaussian turbulence. At higher Stokes numbers, caustics are formed in a very similar manner in both Gaussian and non-Gaussian synthetic turbulence. In non-Gaussian turbulence, heavy particles cluster in regions of low fluid kinetic energy, while the opposite is true in Gaussian turbulence. Our results show that synthetic simulations cannot correctly predict how the particle clustering correlates with local fluid flow properties, without including convection.
Iterative Gaussianization: from ICA to random rotations.
Laparra, Valero; Camps-Valls, Gustavo; Malo, Jesús
2011-04-01
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this paper, we propose a solution to this problem by using a family of rotation-based iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential application of a univariate marginal Gaussianization transform followed by an orthonormal transform. The proposed procedure looks for differentiable transforms to a known PDF so that the unknown PDF can be estimated at any point of the original domain. In particular, we aim at a zero-mean unit-covariance Gaussian for convenience. RBIG is formally similar to classical iterative projection pursuit algorithms. However, we show that, unlike in PP methods, the particular class of rotations used has no special qualitative relevance in this context, since looking for interestingness is not a critical issue for PDF estimation. The key difference is that our approach focuses on the univariate part (marginal Gaussianization) of the problem rather than on the multivariate part (rotation). This difference implies that one may select the most convenient rotation suited to each practical application. The differentiability, invertibility, and convergence of RBIG are theoretically and experimentally analyzed. Relation to other methods, such as radial Gaussianization, one-class support vector domain description, and deep neural networks is also pointed out. The practical performance of RBIG is successfully illustrated in a number of multidimensional problems such as image synthesis, classification, denoising, and multi-information estimation. PMID:21349790
Propagation properties of cylindrical sinc Gaussian beam
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil T.; Bayraktar, Mert
2016-09-01
We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.
Optimal estimation of non-Gaussianity
Babich, Daniel
2005-08-15
We systematically analyze the primordial non-Gaussianity estimator used by the Wilkinson Microwave Anisotropy Probe (WMAP) science team with the basic ideas of estimation theory in order to see if the limited cosmic microwave background (CMB) data is being optimally utilized. The WMAP estimator is based on the implicit assumption that the CMB bispectrum, the harmonic transform of the three-point correlation function, contains all of the primordial non-Gaussianity information in a CMB map. We first demonstrate that the signal-to-noise (S/N) of an estimator based on CMB three-point correlation functions is significantly larger than the S/N of any estimator based on higher-order correlation functions; justifying our choice to focus on the three-point correlation function. We then conclude that the estimator based on the three-point correlation function, which was used by WMAP, is optimal, meaning it saturates the Cramer-Rao inequality when the underlying CMB map is nearly Gaussian. We quantify this restriction by demonstrating that the suboptimal character of our estimator is proportional to the square of the fiducial non-Gaussianity, which is already constrained to be extremely small, so we can consider the WMAP estimator to be optimal in practice. Our conclusions do not depend on the form of the primordial bispectrum, only on the observationally established weak levels of primordial non-Gaussianity.
Hydraulic Conductivity Fields: Gaussian or Not?
Meerschaert, Mark M.; Dogan, Mine; Van Dam, Remke L.; Hyndman, David W.; Benson, David A.
2013-01-01
Hydraulic conductivity (K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales. PMID:24415806
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NASA Astrophysics Data System (ADS)
Verpoorter, C.; Carrère, V.; Combe, J.-P.; Le Corre, L.
2009-04-01
Understanding of the uppermost layer of cohesive sediment beds provides important clues for predicting future sediment behaviours. Sediment consolidation, grain size, water content and biological slimes (EPS: extracellular polymeric substances) were found to be significant factors influencing erosion resistance. The surface spectral signatures of mudflat sediments reflect such bio-geophysical parameters. The overall shape of the spectrum, also called a continuum, is a function of grain size and moisture content. Composition translates into specific absorption features. Finally, the chlorophyll-a concentration derived from the strength of the absorption at 675 nm, is a good proxy for biofilm biomass. Bourgneuf Bay site, south of the Loire river estuary, France, was chosen to represent a range of physical and biological influences on sediment erodability. Field spectral measurements and samples of sediments were collected during various field campaigns. An ASD Fieldspec 3 spectroradiometer was used to produce sediment reflectance hyperspectra in the wavelength range 350-2500 nm. We have developed an automatic procedure based on the Modified Gaussian Model that uses, as the first step, the Spectroscopic Derivative Analysis (SDA) to extract from spectra the bio-geophysical properties on mudflat sediments (Verpoorter et al., 2007). This AMGM algorithm is a powerfull tool to deconvolve spectra into two components, first gaussian curves for the absorptions bands, and second a straight line in the wavenumber range for the continuum. We are investigating the possibility of including other approaches, as the inverse gaussian band centred on 2800 nm initially developed by Whiting et al., (2006) to estimate water content. Additionally, soils samples were analysed to determine moisture content, grain size (laser grain size analyses), organic matter content, carbonate content (calcimetry) and clay content. X-ray diffraction analysis was performed on selected non
Index Distribution of Gaussian Random Matrices
Majumdar, Satya N.; Nadal, Celine; Scardicchio, Antonello; Vivo, Pierpaolo
2009-11-27
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N{sub +}) of a random NxN matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N{sub +}/N scales, for large N, as P(c,N){approx_equal}exp[-betaN{sup 2}PHI(c)] where the rate function PHI(c), symmetric around c=1/2 and universal (independent of beta), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.
CMB non-gaussianity from vector fields
Peloso, Marco
2014-01-01
The Planck satellite has recently measured the CMB temperature anisotropies with unprecedented accuracy, and it has provided strong bounds on primordial non-gaussianity. Such bounds constrain models of inflation, and mechanisms that produce the primordial perturbations. We discuss the non-gaussian signatures from the interactions of the inflation φ with spin-1 fields. We study the two different cases in which the inflaton is (i) a pseudo-scalar field with a (φ)/(fa) F·F interaction with a vector field, and (ii) a scalar field with a f (φ)F² interaction. In the first case we obtain the strong limit f{sub a} ≥ 10¹⁶GeV on the decay constant. In the second case, specific choices of the function f (φ) can lead to a non-gaussianity with a characteristic shape not encountered in standard models of scalar field inflation, and which has also been constrained by Planck.
Majorization preservation of Gaussian bosonic channels
NASA Astrophysics Data System (ADS)
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2016-07-01
It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.
Gaussian quantum operator representation for bosons
Corney, Joel F.; Drummond, Peter D.
2003-12-01
We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.
Inflationary prediction for primordial non-gaussianity.
Lyth, David H; Rodríguez, Yeinzon
2005-09-16
We extend the deltaN formalism so that it gives all of the stochastic properties of the primordial curvature perturbation zeta if the initial field perturbations are Gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalization f(NL) of the bispectrum of zeta, which is the main signal of non-Gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained. PMID:16197063
Invariant measures on multimode quantum Gaussian states
Lupo, C.; Mancini, S.; De Pasquale, A.; Facchi, P.; Florio, G.; Pascazio, S.
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.
N-body simulations with generic non-Gaussian initial conditions II: halo bias
NASA Astrophysics Data System (ADS)
Wagner, Christian; Verde, Licia
2012-03-01
We present N-body simulations for generic non-Gaussian initial conditions with the aim of exploring and modelling the scale-dependent halo bias. This effect is evident on very large scales requiring large simulation boxes. In addition, the previously available prescription to implement generic non-Gaussian initial conditions has been improved to keep under control higher-order terms which were spoiling the power spectrum on large scales. We pay particular attention to the differences between physical, inflation-motivated primordial bispectra and their factorizable templates, and to the operational definition of the non-Gaussian halo bias (which has both a scale-dependent and an approximately scale-independent contributions). We find that analytic predictions for both the non-Gaussian halo mass function and halo bias work well once a fudge factor (which was introduced before but still lacks convincing physical explanation) is calibrated on simulations. The halo bias remains therefore an extremely promising tool to probe primordial non-Gaussianity and thus to give insights into the physical mechanism that generated the primordial perturbations. The simulation outputs and tables of the analytic predictions will be made publicly available via the non-Gaussian comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html.
Karakida, Ryo; Okada, Masato; Amari, Shun-Ichi
2016-07-01
The restricted Boltzmann machine (RBM) is an essential constituent of deep learning, but it is hard to train by using maximum likelihood (ML) learning, which minimizes the Kullback-Leibler (KL) divergence. Instead, contrastive divergence (CD) learning has been developed as an approximation of ML learning and widely used in practice. To clarify the performance of CD learning, in this paper, we analytically derive the fixed points where ML and CDn learning rules converge in two types of RBMs: one with Gaussian visible and Gaussian hidden units and the other with Gaussian visible and Bernoulli hidden units. In addition, we analyze the stability of the fixed points. As a result, we find that the stable points of CDn learning rule coincide with those of ML learning rule in a Gaussian-Gaussian RBM. We also reveal that larger principal components of the input data are extracted at the stable points. Moreover, in a Gaussian-Bernoulli RBM, we find that both ML and CDn learning can extract independent components at one of stable points. Our analysis demonstrates that the same feature components as those extracted by ML learning are extracted simply by performing CD1 learning. Expanding this study should elucidate the specific solutions obtained by CD learning in other types of RBMs or in deep networks. PMID:27131468
Non-Gaussian Analysis of Turbulent Boundary Layer Fluctuating Pressure on Aircraft Skin Panels
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Steinwolf, Alexander
2005-01-01
The purpose of the study is to investigate the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the outer sidewall of a supersonic transport aircraft and to approximate these PDFs by analytical models. Experimental flight results show that the fluctuating pressure PDFs differ from the Gaussian distribution even for standard smooth surface conditions. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations in front of forward-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. There is a certain spatial pattern of the skewness and kurtosis behavior depending on the distance upstream from the step. All characteristics related to non-Gaussian behavior are highly dependent upon the distance from the step and the step height, less dependent on aircraft speed, and not dependent on the fuselage location. A Hermite polynomial transform model and a piecewise-Gaussian model fit the flight data well both for the smooth and stepped conditions. The piecewise-Gaussian approximation can be additionally regarded for convenience in usage after the model is constructed.
A Gaussian-product stochastic Gent-McWilliams parameterization
NASA Astrophysics Data System (ADS)
Grooms, Ian
2016-10-01
The locally-averaged horizontal buoyancy flux by mesoscale eddies is computed from eddy-resolving quasigeostrophic simulations of ocean-mesoscale eddy dynamics. This flux has a very non-Gaussian distribution peaked at zero, not at the mean value. This non-Gaussian flux distribution arises because the flux is a product of zero-mean random variables: the eddy velocity and buoyancy. A framework for stochastic Gent-McWilliams (GM) parameterization is presented. Gaussian random field models for subgrid-scale velocity and buoyancy are developed. The product of these Gaussian random fields is used to construct a non-Gaussian stochastic parameterization of the horizontal subgrid-scale density flux, which leads to a non-Gaussian stochastic GM parameterization. This new non-Gaussian stochastic GM parameterization is tested in an idealized box ocean model, and compared to a Gaussian approach that simply multiplies the deterministic GM parameterization by a Gaussian random field. The non-Gaussian approach has a significant impact on both the mean and variability of the simulations, more so than the Gaussian approach; for example, the non-Gaussian simulation has a much larger net kinetic energy and a stronger overturning circulation than a comparable Gaussian simulation. Future directions for development of the stochastic GM parameterization and extensions of the Gaussian-product approach are discussed.
Experimental characterization of Gaussian quantum-communication channels
Di Guglielmo, James; Hage, Boris; Franzen, Alexander; Schnabel, Roman; Fiurasek, Jaromir
2007-07-15
We present a full experimental characterization of continuous-variable quantum-communication channels established by shared entanglement together with local operations and classical communication. The resulting teleportation channel was fully characterized by measuring all elements of the covariance matrix of the shared two-mode squeezed Gaussian state. From the experimental data we determined the lower bound to the quantum channel capacity, the teleportation fidelity of coherent states, and the logarithmic negativity and purity of the shared state. Additionally, a positive secret key rate was obtained for two of the established channels.
NASA Astrophysics Data System (ADS)
Ji, Se-Wan; Kim, M. S.; Nha, Hyunchul
2015-04-01
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.
NASA Technical Reports Server (NTRS)
2008-01-01
This image was acquired by NASA's Phoenix Mars Lander's Robotic Arm Camera on the 35th Martian day of the mission, or Sol 34 (June 29, 2008), after the May 25, 2008, landing. This image shows the trench informally called 'Snow White 5.' The trench is 4-to-5 centimeters (about 1.5-to-1.9 inches) deep, 24 centimeters (about 9 inches) wide and 33 centimeters (13 inches) long.
Snow White 5 is Phoenix's current active digging area after additional trenching, grooming, and scraping by Phoenix's Robotic Arm in the last few sols to trenches informally called Snow White 1, 2, 3, and 4. Near the top center of the image is the Robotic Arm's Thermal and Electrical Conductivity Probe.
Snow White 5 is located in a patch of Martian soil near the center of a polygonal surface feature, nicknamed 'Cheshire Cat.' The digging site has been named 'Wonderland.'
This image has been enhanced to brighten shaded areas.
The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes.
Enderlein, Jörg; Pampaloni, Francesco
2004-08-01
A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field.
Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes
NASA Astrophysics Data System (ADS)
Enderlein, Jörg; Pampaloni, Francesco
2004-08-01
A unified operator approach is described for deriving Hermite-Gaussian and Laguerre-Gaussian laser beams by using as a starting point a plane-wave-spectrum representation of the electromagnetic field. We show that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution. The approach presented can be easily generalized to nonparaxial situations and to include vector effects of the electromagnetic field.
Cluster size distribution in Gaussian glasses
NASA Astrophysics Data System (ADS)
Novikov, S. V.
2011-03-01
A simple method for the estimation of the asymptotics of the cluster numbers in Gaussian glasses is described. Validity of the method was tested by the comparison with the exact analytic result for the non-correlated field and simulation data for the distribution of random energies in strongly spatially correlated dipolar glass model.
Diffusion of Super-Gaussian Profiles
ERIC Educational Resources Information Center
Rosenberg, C.-J.; Anderson, D.; Desaix, M.; Johannisson, P.; Lisak, M.
2007-01-01
The present analysis describes an analytically simple and systematic approximation procedure for modelling the free diffusive spreading of initially super-Gaussian profiles. The approach is based on a self-similar ansatz for the evolution of the diffusion profile, and the parameter functions involved in the modelling are determined by suitable…
A Reflective Gaussian Coronagraph for Extreme Adaptive Optics: Laboratory Performance
NASA Astrophysics Data System (ADS)
Park, Ryeojin; Close, Laird M.; Siegler, Nick; Nielsen, Eric L.; Stalcup, Thomas
2006-11-01
We report laboratory results of a coronagraphic test bench to assess the intensity reduction differences between a ``Gaussian'' tapered focal plane coronagraphic mask and a classical hard-edged ``top hat'' function mask at extreme adaptive optics (ExAO) Strehl ratios of ~94%. However, unlike a traditional coronagraph design, we insert a reflective focal plane mask at 45° to the optical axis. We also use an intermediate secondary mask (mask 2) before a final image in order to block additional mask-edge-diffracted light. The test bench simulates the optical train of ground-based telescopes (in particular, the 8.1 m Gemini North Telescope). It includes one spider vane, different mask radii (r = 1.9λ/D, 3.7λ/D, and 7.4λ/D), and two types of reflective focal plane masks (hard-edged top-hat and Gaussian tapered profiles). In order to investigate the relative performance of these competing coronagraphic designs with regard to extrasolar planet detection sensitivity, we utilize the simulation of realistic extrasolar planet populations (Nielsen et al.). With an appropriate translation of our laboratory results to expected telescope performance, a Gaussian tapered mask radius of 3.7λ/D with an additional mask (mask 2) performs best (highest planet detection sensitivity). For a full survey with this optimal design, the simulation predicts that ~30% more planets would be detected than with a top-hat function mask of similar size with mask 2. Using the best design, the point contrast ratio between the stellar point-spread function (PSF) peak and the coronagraphic PSF at 10λ/D (0.4" in the H band if D = 8.1 m) is ~10 times higher than a classical Lyot top-hat coronagraph. Hence, we find that a Gaussian apodized mask with an additional blocking mask is superior (~10 times higher contrast) to the use of a classical Lyot coronagraph for ExAO-like Strehl ratios.
Fractional Gaussian noise, functional MRI and Alzheimer's disease.
Maxim, Voichiţa; Sendur, Levent; Fadili, Jalal; Suckling, John; Gould, Rebecca; Howard, Rob; Bullmore, Ed
2005-03-01
Fractional Gaussian noise (fGn) provides a parsimonious model for stationary increments of a self-similar process parameterised by the Hurst exponent, H, and variance, sigma2. Fractional Gaussian noise with H < 0.5 demonstrates negatively autocorrelated or antipersistent behaviour; fGn with H > 0.5 demonstrates 1/f, long memory or persistent behaviour; and the special case of fGn with H = 0.5 corresponds to classical Gaussian white noise. We comparatively evaluate four possible estimators of fGn parameters, one method implemented in the time domain and three in the wavelet domain. We show that a wavelet-based maximum likelihood (ML) estimator yields the most efficient estimates of H and sigma2 in simulated fGn with 0 < H < 1. Applying this estimator to fMRI data acquired in the "resting" state from healthy young and older volunteers, we show empirically that fGn provides an accommodating model for diverse species of fMRI noise, assuming adequate preprocessing to correct effects of head movement, and that voxels with H > 0.5 tend to be concentrated in cortex whereas voxels with H < 0.5 are more frequently located in ventricles and sulcal CSF. The wavelet-ML estimator can be generalised to estimate the parameter vector beta for general linear modelling (GLM) of a physiological response to experimental stimulation and we demonstrate nominal type I error control in multiple testing of beta, divided by its standard error, in simulated and biological data under the null hypothesis beta = 0. We illustrate these methods principally by showing that there are significant differences between patients with early Alzheimer's disease (AD) and age-matched comparison subjects in the persistence of fGn in the medial and lateral temporal lobes, insula, dorsal cingulate/medial premotor cortex, and left pre- and postcentral gyrus: patients with AD had greater persistence of resting fMRI noise (larger H) in these regions. Comparable abnormalities in the AD patients were also identified
a Distributed Gaussian Discrete Variable Representation
NASA Astrophysics Data System (ADS)
Karabulut, Hasan
In this work a discrete variable representation (DVR) is constructed from a distributed Gaussian basis (DGB). A DGB is a finite or infinite chain of uniformly distributed Gaussians g_{n}(x) = e^{-c^2(x/d-n)^2} where n takes integer values. There are three main parts of this thesis. In the first part (Chapter III) the finite chain distributed Gaussian DVR (Finite Chain DG-DVR) is derived. In order to accomplish this, the distributed Gaussian orthogonal polynomials are introduced. The connection of these polynomials to Stieltjes-Wigert polynomials is shown. The recurrence relation for these orthogonal polynomials is derived. Tested recipes are given to calculate the quadrature points and weights and to construct the corresponding Lagrange functions which are analogs of Lagrange interpolation polynomials. The symmetries of quadrature points, weights, and Lagrange functions are derived. Limit cases ctoinfty and cto 0 are studied. In the second part (Chapter IV)the infinite chain limit DG-DVR is derived from a limit of the finite chain DG-DVR. The quadrature points and weights and the Lagrange functions are found in this limit and kinetic energy operator is constructed. It is shown that in the limit c to 0 the infinite chain DG-DVR reduces to Colbert and Miller's DVR. A discussion of ability of a distributed Gaussian basis to represent an arbitrary function is given. The results of this treatment yield a possible explanation of surprising accuracy of Colbert-Miller DVR. In the third part construction of the DG-DVR is given when one point is chosen arbitrarily. Some interesting identities and integral representations for the b _{n} and sigma_ {n} coefficients that are introduced in the second part are found.
Capacity of Pulse-Position Modulation (PPM) on Gaussian and Webb Channels
NASA Technical Reports Server (NTRS)
Dolinar, S.; Divsalar, D.; Hamkins, J.; Pollara, F.
2000-01-01
This article computes the capacity of various idealized soft-decision channels modeling an optical channel using an avalanche photodiode detector (APD) and pulse-position modulation (PPM). The capacity of this optical channel depends in a complicated way on the physical parameters of the APD and the constraints imposed by the PPM orthogonal signaling set. This article attempts to identify and separate the effects of several fundamental parameters on the capacity of the APD-detected optical PPM channel. First, an overall signal-to-noise ratio (SNR) parameter is de ned such that the capacity as a function of a bit-normalized version of this SNR drops precipitously toward zero at quasi-brick-wall limits on bit SNR that are numerically the same as the well-understood brick-wall limits for the standard additive white Gaussian noise (AWGN) channel. A second parameter is used to quantify the effects on capacity of one unique facet of the optical PPM channel (as compared with the standard AWGN channel) that causes the noise variance to be higher in signal slots than in nonsignal slots. This nonuniform noise variance yields interesting capacity effects even when the channel model is AWGN. A third parameter is used to measure the effects on capacity of the difference between an AWGN model and a non-Gaussian model proposed by Webb (see reference in [2]) for approximating the statistics of the APD-detected optical channel. Finally, a fourth parameter is used to quantify the blending of a Webb model with a pure AWGN model to account for thermal noise. Numerical results show that the capacity of M-ary orthogonal signaling on the Webb channel exhibits the same brick-wall Shannon limit, (M ln 2)=(M 1), as on the AWGN channel ( 1:59 dB for large M). Results also compare the capacity obtained by hard- and soft-output channels and indicate that soft-output channels o er a 3-dB advantage.
Symul, Thomas; Alton, Daniel J.; Lance, Andrew M.; Lam, Ping Koy; Assad, Syed M.; Weedbrook, Christian; Ralph, Timothy C.
2007-09-15
In realistic continuous-variable quantum key distribution protocols, an eavesdropper may exploit the additional Gaussian noise generated during transmission to mask her presence. We present a theoretical framework for a post-selection-based protocol which explicitly takes into account excess Gaussian noise. We derive a quantitative expression of the secret key rates based on the Levitin and Holevo bounds. We experimentally demonstrate that the post-selection-based scheme is still secure against both individual and collective Gaussian attacks in the presence of this excess noise.
A reflective Gaussian coronagraph for ExAO: laboratory performance
NASA Astrophysics Data System (ADS)
Park, Ryeojin; Close, Laird M.; Siegler, Nick; Nielsen, Eric L.; Stalcup, Thomas
2006-06-01
We report laboratory results of a coronagraphic testbed to assess the intensity reduction differences between a "Gaussian" tapered focal plane coronagraphic mask and a classical hard-edged "Top Hat" function mask at Extreme Adaptive Optics (ExAO) Strehl ratios of ~94%. However, unlike a traditional coronagraph design, we insert a reflective focal plane mask at 45 ° to the optical axis and used a "spot of Arago blocker" (axicon stop) before a final image in order to block additional mask edge-diffracted light. The testbed simulates the optical train of ground-based telescopes (in particular the 8.1m Gemini North telescope) and includes one spider vane and different mask radii (r= 1.9λ/D, 3.7λ/D, 7.4λ/D) and two types of reflective focal plane masks (hard-edged "Top Hat" and "Gaussian" tapered profiles). In order to investigate the performance of these competing coronagraphic designs with regard to extra-solar planet detection sensitivity, we utilize the simulation of realistic extra-solar planet populations (Nielsen et al. 2006). With an appropriate translation of our laboratory results to expected telescope performance, a "Gaussian" tapered mask radius of 3.7λ/D with an axicon stop performs best (highest planet detection sensitivity). For a full survey with this optimal design, the simulation predicts ~30% more planets detected compared to a similar sized "Top Hat" function mask with an axicon stop. Using the best design, the "point contrast ratio" between the stellar PSF peak and the coronagraphic PSF at 10λ/D (0.4" in H band if D = 8.1m) is 1.4 x 10 6. This is ~10 times higher than a classical Lyot "Top Hat" coronagraph.
High-energy flat-top beams for laser launching using a Gaussian mirror.
Fujiwara, Hiroki; Brown, Kathryn E; Dlott, Dana D
2010-07-01
Converting a Gaussian to a flat-top beam is useful for many applications including laser-launched thin-foil flyer plates. A flat-top beam is needed to maintain a constant launch velocity across the flyer; otherwise, the flyer can disintegrate in flight. Here we discuss and demonstrate the use of a variable reflectivity mirror (VRM) with a Gaussian reflectivity profile with an additional hard aperture and compare it to a refractive beam shaper. An ideal VRM would generate a flat-top beam with 37% efficiency. Readily available high-power Gaussian or super-Gaussian mirrors create an approximate flat-top profile, but there is a trade-off between flatness and efficiency. We show that a super-Gaussian mirror can, in principle, convert an input Gaussian beam with 30% efficiency to a flat-top beam with 3% (maximum-to-minimum) variation. With a Gaussian mirror and a high-energy pulsed Nd:YAG laser having relatively poor beam quality, we generate flat-top beams with 25% conversion efficiency having 6% variation (standard deviation sigma=4.2%). The beams are used to launch 400 microm diameter, 25 microm thick Al flyer plates, whose flight was monitored by a high-speed displacement interferometer. The plates flew across a 300 microm gap at 1.3 km/s. The distribution of arrival times at the witness plate was 5 ns, as determined by the rise time of the impact emission. Compared to a total flight time of 260 ns, the velocity spread of different parts of the flyer plate was 2%.
Chaudhari, M I; Pratt, L R; Paulaitis, M E
2015-07-23
Parallel-tempering MD results for a CH3(CH2-O-CH2)mCH3 chain in water are exploited as a database for analysis of collective structural characteristics of the PEO globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of Corexit type. The chain structure factor, relevant to neutron scattering from a deuterated chain in null water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple k → ∞ behavior, but we consider a discrete-Gaussian model that does achieve that consistency. Shifting and scaling the discrete-Gaussian model helps to identify the low-k to high-k transition near k ≈ 2π/0.6 nm when an empirically matched number of Gaussian links is about one-third of the total number of effective atom sites. This short distance-scale boundary of 0.6 nm is directly verified with the r space distributions, and this distance is thus identified with a natural size for coarsened monomers. The probability distribution of Rg(2) is compared with the classic predictions for both the Gaussian model and freely jointed chains. ⟨Rg(2)(j)⟩, the contribution of the jth chain segment to ⟨Rg(2)⟩, depends on the contour index about as expected for Gaussian chains despite significant quantitative discrepancies that express the swelling of these chains in water. Monomers central to the chain contour occupy the center of the chain globule. The density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due to the close proximity of central elements to the globule center. However, that density structuring washes out for longer chains where many chain elements additively contribute to the density profiles. Gaussian chain models thus become more satisfactory for the density profiles for longer chains. PMID:25121580
Large non-gaussianity in axion inflation.
Barnaby, Neil; Peloso, Marco
2011-05-01
The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields cΦFF, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, δΦ. For c≥10(2)M(p)(-1), these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.
Quantum Fidelity for Arbitrary Gaussian States
NASA Astrophysics Data System (ADS)
Banchi, Leonardo; Braunstein, Samuel L.; Pirandola, Stefano
2015-12-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Fock expansion of multimode pure Gaussian states
Cariolaro, Gianfranco; Pierobon, Gianfranco
2015-12-15
The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
A Fast Incremental Gaussian Mixture Model
Pinto, Rafael Coimbra; Engel, Paulo Martins
2015-01-01
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets. PMID:26444880
Gaussian quadrature for multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Coussement, Jonathan; van Assche, Walter
2005-06-01
We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.
Quantum Fidelity for Arbitrary Gaussian States.
Banchi, Leonardo; Braunstein, Samuel L; Pirandola, Stefano
2015-12-31
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources. PMID:26764978
Edge Detection By Differences Of Gaussians
NASA Astrophysics Data System (ADS)
Marthon, Ph.; Thiesse, B.; Bruel, A.
1986-06-01
The Differences of Gaussians (DOGs) are of fundamental importance in edge detection. They belong to the human vision system as shown by Enroth-Cugell and Robson [ENR66]. The zero-crossings of their outputs mark the loci of the intensity changes. The set of descriptions from different operator sizes forms the input for later visual processes, such as stereopsis and motion analysis. We show that DOGs uniformly converge to the Laplacian of a Gaussian (ΔG2,σ) when both the inhibitory and excitatory variables converge to σ. Spatial and spectral properties of DOGs and ΔGs are compared: width and height of their central positive regions, bandiwidths... Finally, DOGs' responses to some features such as ideal edge, right angle corner, general corner..., are presented and magnitudes of error on edge position are given.
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.
Microwave Realization of the Gaussian Symplectic Ensemble
NASA Astrophysics Data System (ADS)
Rehemanjiang, A.; Allgaier, M.; Joyner, C. H.; Müller, S.; Sieber, M.; Kuhl, U.; Stöckmann, H.-J.
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T2=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry.
Consistency relations for non-Gaussianity
NASA Astrophysics Data System (ADS)
Li, Miao; Wang, Yi
2008-09-01
We investigate consistency relations for non-Gaussianity. We provide a model-independent dynamical proof for the consistency relation for three-point correlation functions from the Hamiltonian and field redefinition. This relation can be applied to single-field inflation, multi-field inflation and the curvaton scenario. This relation can also be generalized to n-point correlation functions up to arbitrary order in perturbation theory and with arbitrary number of loops.
Computational aspects of Gaussian beam migration
Hale, D.
1992-01-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Computational aspects of Gaussian beam migration
Hale, D.
1992-08-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Entropic Fluctuations in Gaussian Dynamical Systems
NASA Astrophysics Data System (ADS)
Jakšić, V.; Pillet, C.-A.; Shirikyan, A.
2016-06-01
We study nonequilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state and the nonequilibrium steady state. The entropy production observable of this model is an unbounded function on the phase space, and its large deviation functionals have a surprisingly rich structure. We explore this structure in some detail.
Gaussian Confinement in a Jkj Decay Model
NASA Astrophysics Data System (ADS)
da Silva, Mario L. L.; Hadjimichef, Dimiter; Vasconcellos, Cesar A. Z.
In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.
Non-Markovianity of Gaussian Channels.
Torre, G; Roga, W; Illuminati, F
2015-08-14
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states. PMID:26317700
Extended Decentralized Linear-Quadratic-Gaussian Control
NASA Technical Reports Server (NTRS)
Carpenter, J. Russell
2000-01-01
A straightforward extension of a solution to the decentralized linear-Quadratic-Gaussian problem is proposed that allows its use for commonly encountered classes of problems that are currently solved with the extended Kalman filter. This extension allows the system to be partitioned in such a way as to exclude the nonlinearities from the essential algebraic relationships that allow the estimation and control to be optimally decentralized.
Microwave Realization of the Gaussian Symplectic Ensemble.
Rehemanjiang, A; Allgaier, M; Joyner, C H; Müller, S; Sieber, M; Kuhl, U; Stöckmann, H-J
2016-08-01
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T^{2}=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry. PMID:27541466
Non-Gaussianity from axionic curvaton
Kawasaki, Masahiro; Kobayashi, Takeshi; Takahashi, Fuminobu E-mail: takeshi@cita.utoronto.ca
2013-03-01
We study non-Gaussianity of density perturbations generated by an axionic curvaton, focusing on the case that the curvaton sits near the hilltop of the potential during inflation. Such hilltop curvatons can generate a red-tilted density perturbation spectrum without invoking large-field inflation. We show that, even when the curvaton dominates the Universe, the non-Gaussianity parameter f{sub NL} is positive and mildly increases towards the hilltop of the curvaton potential, and that f{sub NL} = O(10) is a general and robust prediction of such hilltop axionic curvatons. In particular, we find that the non-Gaussianity parameter is bounded as f{sub NL}∼<30–40 for a range of the scalar spectral index, n{sub s} = 0.94–0.99, and that f{sub NL} = 20–40 is realized for the curvaton mass m{sub σ} = 10–10{sup 6} GeV and the decay constant f = 10{sup 12}–10{sup 17} GeV. One of the plausible candidates for the axionic curvaton is an imaginary component of a modulus field with mass of order 10–100 TeV and decay constant of 10{sup 16–17}GeV. We also discuss extreme cases where the curvaton drives a second inflation and find that f{sub NL} is typically smaller compared to non-inflating cases.
Unitarily localizable entanglement of Gaussian states
Serafini, Alessio; Adesso, Gerardo; Illuminati, Fabrizio
2005-03-01
We consider generic (mxn)-mode bipartitions of continuous-variable systems, and study the associated bisymmetric multimode Gaussian states. They are defined as (m+n)-mode Gaussian states invariant under local mode permutations on the m-mode and n-mode subsystems. We prove that such states are equivalent, under local unitary transformations, to the tensor product of a two-mode state and of m+n-2 uncorrelated single-mode states. The entanglement between the m-mode and the n-mode blocks can then be completely concentrated on a single pair of modes by means of local unitary operations alone. This result allows us to prove that the PPT (positivity of the partial transpose) condition is necessary and sufficient for the separability of (m+n)-mode bisymmetric Gaussian states. We determine exactly their negativity and identify a subset of bisymmetric states whose multimode entanglement of formation can be computed analytically. We consider explicit examples of pure and mixed bisymmetric states and study their entanglement scaling with the number of modes.
Control charts for non-Gaussian distributions
NASA Astrophysics Data System (ADS)
Babus, Florina; Kobi, Abdessamad; Tiplica, Th.; Bacivarov, Ioan; Bacivarov, Angelica
2007-05-01
Traditional statistical process control (SPC) techniques applied in the industrial processes field consider often that the distribution ofdata is Gaussian. The estimation ofparameters, the detection ofthe out oforder situations and the control of the followed characteristics are easy to achieve for the normal populations. In reality, whatever the origin of a characteristic (large series productions for components, mechanical parts of OE communication systems, etc. ) the curve of distributions of the measured values is generally far from being normal. The simple approximation to the Gauss distribution and the use of the classical control methods sometimes induces serious errors. In this paper, a study on the statistical control of non Gaussian populations is presented. Particularly we discuss the Rayleigh and the Weibull distribution as being representatives in (SPC for some category of data. The X control charts with variable limits are tested. Experimental simulations are presented for different parameters of the two distributions. The results confirm the methodology and encourage the research in the field of non Gaussian processes.
Local Gaussian operations can enhance continuous-variable entanglement distillation
Zhang Shengli; Loock, Peter van
2011-12-15
Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.
Experimental Studies with Spatial Gaussian-Cut Laser for the LCLS Photocathode Gun
Zhou, F.; Brachmann, A.; Emma, P.; Gilevich, S.; Huang, Z.; /SLAC
2011-12-13
To simplify the LCLS operation and further enhance the injector performances, we are evaluating the various parameters including the photocathode drive laser system. Extensive simulations show that both the projected and time-sliced emittances with spatial Gaussian profiles having reasonable tail-cut are better than those with uniform one. The simulated results are also supported by theoretical analyses. In the LCLS, the spatial uniform or Gaussian-cut laser profiles are conveniently obtained by adjusting the optics of the telescope upstream of an iris, used to define laser size on the cathode. Preliminary beam studies at the LCLS injector show that both the projected and time-sliced emittances with spatial Gaussian-cut laser are almost as good as, although not better than, those with uniform one. In addition, the laser transmission through the iris with the Gaussian-cut profile is twice with uniform one, which can significantly ease LCLS copper cathode/laser operations and thus improve the LCLS operation efficiency. More beam studies are planned to measure FEL performances with the Gaussian-cut in comparison with the uniform one. All simulations and measurements are presented in the paper.
Numerical fitting of molecular properties to Hermite Gaussians.
Cisneros, G Andrés; Elking, Dennis; Piquemal, Jean-Philip; Darden, Thomas A
2007-11-29
A procedure is presented to fit gridded molecular properties to auxiliary basis sets (ABSs) of Hermite Gaussians, analogous to the density fitting (DF) method (Dunlap; et al. J. Chem. Phys. 1979, 71, 4993). In this procedure, the ab initio calculated properties (density, electrostatic potential, and/or electric field) are fitted via a linear- or nonlinear-least-squares procedure to auxiliary basis sets (ABS). The calculated fitting coefficients from the numerical grids are shown to be more robust than analytic density fitting due to the neglect of the core contributions. The fitting coefficients are tested by calculating intermolecular Coulomb and exchange interactions for a set of dimers. It is shown that the numerical instabilities observed in DF are caused by the attempt of the ABS to fit the core contributions. In addition, this new approach allows us to reduce the number of functions required to obtain an accurate fit. This results in decreased computational cost, which is shown by calculating the Coulomb energy of a 4096 water box in periodic boundary conditions. Using atom centered Hermite Gaussians, this calculation is only 1 order of magnitude slower than conventional atom-centered point charges.
Tridiagonal realization of the antisymmetric Gaussian {beta}-ensemble
Dumitriu, Ioana; Forrester, Peter J.
2010-09-15
The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter {beta}, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of (q{sub i}), the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and (q{sub i}). The third proof maps matrices from the antisymmetric Gaussian {beta}-ensemble to those realizing particular examples of the Laguerre {beta}-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pruefer phases of the random matrices.
Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering
NASA Astrophysics Data System (ADS)
Kondorskiy, Alexey D.; Nanbu, Shinkoh
2015-09-01
We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully's models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories. We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio "on-the-fly" simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.
Self-measuring Similarity for Multi-task Gaussian Process
NASA Astrophysics Data System (ADS)
Hayashi, Kohei; Takenouchi, Takashi; Tomioka, Ryota; Kashima, Hisashi
Multi-task learning aims at transferring knowledge between similar tasks. The multi-task Gaussian process framework of Bonilla et al. models (incomplete) responses of C data points for R tasks (e.g., the responses are given by R × C matrix) by a Gaussian process; the covariance function is defined as the product of a covariance function on input-dependent features and the inter-task covariance matrix (which is empirically estimated as a model parameter). We extend this framework by incorporating a novel similarity measurement, which allows for the representation of much more complex data structures. The proposed framework also enables us to exploit additional information (e.g., the input-dependent features) by constructing the covariance matrices with combining them on the covariance function. We also derive an efficient learning algorithm to make prediction by using an iterative method. Finally, we apply our model to a real data set of recommender systems and show that the proposed method achieves the best prediction accuracy on the data set.
Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering
Kondorskiy, Alexey D.; Nanbu, Shinkoh
2015-09-21
We present an approach, which allows to employ the adiabatic wave packet propagation technique and semiclassical theory to treat the nonadiabatic processes by using trajectory hopping. The approach developed generates a bunch of hopping trajectories and gives all additional information to incorporate the effect of nonadiabatic coupling into the wave packet dynamics. This provides an interface between a general adiabatic frozen Gaussian wave packet propagation method and the trajectory surface hopping technique. The basic idea suggested in [A. D. Kondorskiy and H. Nakamura, J. Chem. Phys. 120, 8937 (2004)] is revisited and complemented in the present work by the elaboration of efficient numerical algorithms. We combine our approach with the adiabatic Herman-Kluk frozen Gaussian approximation. The efficiency and accuracy of the resulting method is demonstrated by applying it to popular benchmark model systems including three Tully’s models and 24D model of pyrazine. It is shown that photoabsorption spectrum is successfully reproduced by using a few hundreds of trajectories. We employ the compact finite difference Hessian update scheme to consider feasibility of the ab initio “on-the-fly” simulations. It is found that this technique allows us to obtain the reliable final results using several Hessian matrix calculations per trajectory.
Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field
NASA Astrophysics Data System (ADS)
Tang, Xu-Bing; Gao, Fang; Wang, Yao-Xiong; Kuang, Sen; Shuang, Feng
2015-03-01
Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations (namely subtracting and adding a single photon), we propose a scheme to generate non-Gaussian quantum states named single-photon-added and -subtracted coherent (SPASC) superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of non-Gaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states (DCSS). The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203061 and 61074052), the Outstanding Young Talent Foundation of Anhui Province, China (Grant No. 2012SQRL040), and the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012Z035).
Stochastic geometry and topology of non-Gaussian fields
Beuman, Thomas H.; Turner, Ari M.; Vitelli, Vincenzo
2012-01-01
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher-order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion. PMID:23169625
Optimizing Electromagnetically Induced Transparency Signals with Laguerre-Gaussian Beams
NASA Astrophysics Data System (ADS)
Holtfrerich, Matthew; Akin, Tom; Krzyzewski, Sean; Marino, Alberto; Abraham, Eric
2016-05-01
We have performed electromagnetically induced transparency in ultracold Rubidium atoms using a Laguerre-Gaussian laser mode as the control beam. Laguerre-Gaussian modes are characterized by a ring type transverse intensity profile and carry intrinsic orbital angular momentum. This angular momentum carried by the control beam can be utilized in optical computing applications which is unavailable to the more common Gaussian laser field. Specifically, we use a Laguerre-Gaussian control beam with a Gaussian probe to show that the linewidth of the transmission spectrum can be narrowed when compared to a Gaussian control beam that has the same peak intensity. We present data extending this work to compare control fields in both the Gaussian and Laguerre-Gaussian modes with constant total power. We have made efforts to find the optical overlap that best minimizes the transmission linewidth while also maintaining signal contrast. This was done by changing the waist size of the control beam with respect to the probe. The best results were obtained when the waist of a Laguerre-Gaussian control beam is equal to the waist of the Gaussian probe resulting in narrow linewidth features.
Monthly streamflow forecasting using Gaussian Process Regression
NASA Astrophysics Data System (ADS)
Sun, Alexander Y.; Wang, Dingbao; Xu, Xianli
2014-04-01
Streamflow forecasting plays a critical role in nearly all aspects of water resources planning and management. In this work, Gaussian Process Regression (GPR), an effective kernel-based machine learning algorithm, is applied to probabilistic streamflow forecasting. GPR is built on Gaussian process, which is a stochastic process that generalizes multivariate Gaussian distribution to infinite-dimensional space such that distributions over function values can be defined. The GPR algorithm provides a tractable and flexible hierarchical Bayesian framework for inferring the posterior distribution of streamflows. The prediction skill of the algorithm is tested for one-month-ahead prediction using the MOPEX database, which includes long-term hydrometeorological time series collected from 438 basins across the U.S. from 1948 to 2003. Comparisons with linear regression and artificial neural network models indicate that GPR outperforms both regression methods in most cases. The GPR prediction of MOPEX basins is further examined using the Budyko framework, which helps to reveal the close relationships among water-energy partitions, hydrologic similarity, and predictability. Flow regime modification and the resulting loss of predictability have been a major concern in recent years because of climate change and anthropogenic activities. The persistence of streamflow predictability is thus examined by extending the original MOPEX data records to 2012. Results indicate relatively strong persistence of streamflow predictability in the extended period, although the low-predictability basins tend to show more variations. Because many low-predictability basins are located in regions experiencing fast growth of human activities, the significance of sustainable development and water resources management can be even greater for those regions.
Boson sampling from a Gaussian state.
Lund, A P; Laing, A; Rahimi-Keshari, S; Rudolph, T; O'Brien, J L; Ralph, T C
2014-09-01
We pose a randomized boson-sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of bosons. We describe a quantum optical processor that can solve this problem efficiently based on a Gaussian input state, a linear optical network, and nonadaptive photon counting measurements. All the elements required to build such a processor currently exist. The demonstration of such a device would provide empirical evidence that quantum computers can, indeed, outperform classical computers and could lead to applications. PMID:25238340
Non-gaussianity from broken symmetries
Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto; /Chicago U. /Fermilab
2005-11-01
Recently we studied inflation models in which the inflation potential is characterized by an underlying approximate global symmetry. In the first work we pointed out that in such a model curvature perturbations are generated after the end of the slow-roll phase of inflation. In this work we develop further the observational implications of the model and compute the degree of non-Gaussianity predicted in the scenario. We find that the corresponding nonlinearity parameter, F{sub NL}, can be as large as 10{sup 2}.
A Gaussian measure of quantum phase noise
NASA Technical Reports Server (NTRS)
Schleich, Wolfgang P.; Dowling, Jonathan P.
1992-01-01
We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.
Negative Gaussian curvature from induced metric changes
NASA Astrophysics Data System (ADS)
Modes, Carl D.; Warner, Mark
2015-07-01
We revisit the light or heat-induced changes in topography of initially flat sheets of a solid that elongate or contract along patterned in-plane director fields. For radial or azimuthal directors, negative Gaussian curvature is generated—so-called "anticones." We show that azimuthal material displacements are required for the distorted state to be stretch free and bend minimizing. The resultant shapes are smooth and asterlike and can become reentrant in the azimuthal coordinate for large deformations. We show that care is needed when considering elastomers rather than glasses, although the former offer huge deformations.
Video compressive sensing using Gaussian mixture models.
Yang, Jianbo; Yuan, Xin; Liao, Xuejun; Llull, Patrick; Brady, David J; Sapiro, Guillermo; Carin, Lawrence
2014-11-01
A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.
Lifting primordial non-Gaussianity above the noise
NASA Astrophysics Data System (ADS)
Welling, Yvette; van der Woude, Drian; Pajer, Enrico
2016-08-01
Primordial non-Gaussianity (PNG) in Large Scale Structures is obfuscated by the many additional sources of non-linearity. Within the Effective Field Theory approach to Standard Perturbation Theory, we show that matter non-linearities in the bispectrum can be modeled sufficiently well to strengthen current bounds with near future surveys, such as Euclid. We find that the EFT corrections are crucial to this improvement in sensitivity. Yet, our understanding of non-linearities is still insufficient to reach important theoretical benchmarks for equilateral PNG, while, for local PNG, our forecast is more optimistic. We consistently account for the theoretical error intrinsic to the perturbative approach and discuss the details of its implementation in Fisher forecasts.
Detection of Gaussian signals in Poisson-modulated interference.
Streit, R L
2000-10-01
Passive broadband detection of target signals by an array of hydrophones in the presence of multiple discrete interferers is analyzed under Gaussian statistics and low signal-to-noise ratio conditions. A nonhomogeneous Poisson-modulated interference process is used to model the ensemble of possible arrival directions of the discrete interferers. Closed-form expressions are derived for the recognition differential of the passive-sonar equation in the presence of Poisson-modulated interference. The interference-compensated recognition differential differs from the classical recognition differential by an additive positive term that depend on the interference-to-noise ratio, the directionality of the Poisson-modulated interference, and the array beam pattern.
Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing
NASA Astrophysics Data System (ADS)
Bárdossy, András.; Hörning, Sebastian
2016-06-01
This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
Depolarizing differential Mueller matrix of homogeneous media under Gaussian fluctuation hypothesis.
Devlaminck, Vincent
2015-10-01
In this paper, we address the issue of the existence of a solution of depolarizing differential Mueller matrix for a homogeneous medium. Such a medium is characterized by linear changes of its differential optical properties with z the thickness of the medium. We show that, under a short correlation distance assumption, it is possible to derive such linear solution, and we clarify this solution in the particular case where the random fluctuation processes associated to the optical properties are Gaussian white noise-like. A solution to the problem of noncommutativity of a previously proposed model [J. Opt. Soc. Am.30, 2196 (2013)JOSAAH0030-394110.1364/JOSAA.30.002196] is given by assuming a random permutation of the order of the layers and by averaging all the differential matrices resulting from these permutations. It is shown that the underlying assumption in this case is exactly the Gaussian white noise assumption. Finally, a recently proposed approach [Opt. Lett.39, 4470 (2014)OPLEDP0146-959210.1364/OL.39.004470] for analysis of the statistical properties related to changes in optical properties is revisited, and the experimental conditions of application of these results are specified. PMID:26479926
Depolarizing differential Mueller matrix of homogeneous media under Gaussian fluctuation hypothesis.
Devlaminck, Vincent
2015-10-01
In this paper, we address the issue of the existence of a solution of depolarizing differential Mueller matrix for a homogeneous medium. Such a medium is characterized by linear changes of its differential optical properties with z the thickness of the medium. We show that, under a short correlation distance assumption, it is possible to derive such linear solution, and we clarify this solution in the particular case where the random fluctuation processes associated to the optical properties are Gaussian white noise-like. A solution to the problem of noncommutativity of a previously proposed model [J. Opt. Soc. Am.30, 2196 (2013)JOSAAH0030-394110.1364/JOSAA.30.002196] is given by assuming a random permutation of the order of the layers and by averaging all the differential matrices resulting from these permutations. It is shown that the underlying assumption in this case is exactly the Gaussian white noise assumption. Finally, a recently proposed approach [Opt. Lett.39, 4470 (2014)OPLEDP0146-959210.1364/OL.39.004470] for analysis of the statistical properties related to changes in optical properties is revisited, and the experimental conditions of application of these results are specified.
Spencer, Michael
1974-01-01
Food additives are discussed from the food technology point of view. The reasons for their use are summarized: (1) to protect food from chemical and microbiological attack; (2) to even out seasonal supplies; (3) to improve their eating quality; (4) to improve their nutritional value. The various types of food additives are considered, e.g. colours, flavours, emulsifiers, bread and flour additives, preservatives, and nutritional additives. The paper concludes with consideration of those circumstances in which the use of additives is (a) justified and (b) unjustified. PMID:4467857
Bourlier, Christophe
2005-07-10
The emissivity of two-dimensional anisotropic rough sea surfaces with non-Gaussian statistics is investigated. The emissivity derivation is of importance for retrieval of the sea-surface temperature or equivalent temperature of a rough sea surface by infrared thermal imaging. The well-known Cox-Munk slope probability-density function, considered non-Gaussian, is used for the emissivity derivation, in which the skewness and the kurtosis (related to the third- and fourth-order statistics, respectively) are included. The shadowing effect, which is significant for grazing angles, is also taken into account. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In addition, multiple reflections are ignored. Numerical results of the emissivity are presented for Gaussian and non-Gaussian statistics, for moderate wind speeds, for near-infrared wavelengths, for emission angles ranging from 0 degrees (nadir) to 90 degrees (horizon), and according to the wind direction. In addition, the emissivity is compared with both measurements and a Monte Carlo ray-tracing method.
Bourlier, Christophe
2005-07-10
The emissivity of two-dimensional anisotropic rough sea surfaces with non-Gaussian statistics is investigated. The emissivity derivation is of importance for retrieval of the sea-surface temperature or equivalent temperature of a rough sea surface by infrared thermal imaging. The well-known Cox-Munk slope probability-density function, considered non-Gaussian, is used for the emissivity derivation, in which the skewness and the kurtosis (related to the third- and fourth-order statistics, respectively) are included. The shadowing effect, which is significant for grazing angles, is also taken into account. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In addition, multiple reflections are ignored. Numerical results of the emissivity are presented for Gaussian and non-Gaussian statistics, for moderate wind speeds, for near-infrared wavelengths, for emission angles ranging from 0 degrees (nadir) to 90 degrees (horizon), and according to the wind direction. In addition, the emissivity is compared with both measurements and a Monte Carlo ray-tracing method. PMID:16045222
Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise.
Khan, Ali Fahim; Younis, Muhammad Shahzad; Bajwa, Khalid Bashir
2015-01-01
Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF. PMID:25691911
Nonlinear Bayesian Estimation of BOLD Signal under Non-Gaussian Noise
Khan, Ali Fahim; Younis, Muhammad Shahzad; Bajwa, Khalid Bashir
2015-01-01
Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF. PMID:25691911
Rogue Waves in Near Gaussian Sea States
NASA Astrophysics Data System (ADS)
Osborne, Alfred R.
2015-04-01
The field of nonlinear waves often emphasizes the importance of small amplitude modulations in the nonlinear Schroedinger equation (NLS). The Akhmediev and Peregrine breather trains are examples which manifest themselves from the usual linear instability analyses of NLS. In reality, however, oceanic sea states generated by wind waves are very nearly Gaussian processes and so the modulus of the Hilbert transform envelope is approximately Rayleigh distributed (with of course the possibility of a large amplitude tail) and is therefore never a small amplitude modulation. How can we then reconcile our usual perceptions with this fact? What are indeed the solutions of the nonlinear Schroedinger equation non Gaussianity have on the actual types of solutions that are likely to occur in the real ocean? I discuss how finite gap theory for NLS allows us to answer these and many more questions about rogue sea states. I analyze data from various laboratory and oceanic experiments to illustrate the method. Finally, I discuss whether breather trains such as Akhmediev, Peregrine and Ma-Kuznetsov can actually occur in ocean wave data.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : {mathbb{Z}^2tomathbb{Z}}} a probability proportional to {exp(-β mathcal{H}(η))}, where {β} is the inverse-temperature and {mathcal{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Lloglog L}}. The key is a large deviation estimate for the height at the origin in {mathbb{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
Relaxation oscillations in a laser with a Gaussian mirror.
Mossakowska-Wyszyńska, Agnieszka; Witoński, Piotr; Szczepański, Paweł
2002-03-20
We present an analysis of the relaxation oscillations in a laser with a Gaussian mirror by taking into account the three-dimensional spatial field distribution of the laser modes and the spatial hole burning effect. In particular, we discuss the influence of the Gaussian mirror peak reflectivity and a Gaussian parameter on the damping rate and frequency of the relaxation oscillation for two different laser structures, i.e., with a classically unstable resonator and a classically stable resonator. PMID:11921794
Quantum reading of digital memory with non-Gaussian entangled light
NASA Astrophysics Data System (ADS)
Tej, J. Prabhu; Devi, A. R. Usha; Rajagopal, A. K.
2013-05-01
It has been shown recently S. Pirandola [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.090504 106, 090504 (2011)] that entangled light with Einstein-Podolsky-Rosen correlations retrieves information from digital memory better than any classical light. In identifying this, a model of digital memory with each cell consisting of a reflecting medium with two reflectivities (each memory cell encoding the binary numbers 0 or 1) is employed. The readout of binary memory essentially corresponds to discrimination of two bosonic attenuator channels characterized by different reflectivities. The model requires an entire mathematical paraphernalia of a continuous variable Gaussian setting for its analysis when arbitrary values of reflectivities 0≤r0,r1≤1 are considered. Here we restrict ourselves to a basic quantum readout mechanism with two different families of non-Gaussian entangled states of light, in which the binary channels to be discriminated are (i) ideal memory characterized by reflectivity r1=1 (identity channel) and (ii) a thermal noise channel—where the signal light illuminating the memory location gets completely lost (r0=0) and only a white thermal noise hitting the upper side of the memory reaches the decoder. We compare the quantum reading efficiency of two families of non-Gaussian entangled light [(m,m') family of path-entangled photon states and entangled state obtained by mixing a single photon with coherent light in a 50:50 beam splitter] with any classical source of light in this model. We identify that the classes of non-Gaussian entangled transmitters studied here offer significantly better reading performance than any classical transmitters of light in the regime of low signal intensity. We also demonstrate that the (m,m') family of entangled light exhibits better reading performance than NOON states.
Diagnosis and impacts of non-Gaussianity of innovations in data assimilation
NASA Astrophysics Data System (ADS)
Pires, Carlos A.; Talagrand, Olivier; Bocquet, Marc
2010-09-01
Most of the atmospheric and oceanic data assimilation (DA) schemes rely on the Best Linear Unbiased Estimator (BLUE), which is sub-optimal if errors of assimilated data are non-Gaussian, thus calling for a full Bayesian data assimilation. This paper contributes to the study of the non-Gaussianity of errors in the observational space. Possible sources of non-Gaussianity range from the inherent statistical skewness and positiveness of some physical observables (e.g. moisture, chemical species), the nonlinearity, both of the data assimilation models and of the observation operators among others. Deviations from Gaussianity can be justified from a priori hypotheses or inferred from statistical diagnostics of innovations (observation minus background), leading to consistency relationships between the error statistics. From samples of observations and backgrounds as well as their specified error variances, we evaluate some measures of the innovation non-Gaussianity, such as the skewness, kurtosis and negentropy. Under the assumption of additive errors and by relating statistical moments from both data errors and innovations, we identify potential sources of the innovation non-Gaussianity. These sources range from: (1) univariate error non-Gaussianity, (2), nonlinear correlations between errors, (3) spatio-temporal variability of error variances (heteroscedasticity) and (4) multiplicative noise. Observational and background errors are often assumed independent. This leads to variance-dependent bounds for the skewness and the kurtosis of errors. From innovation statistics, we assess the potential DA impact of some scenarios of non-Gaussian errors. This impact is measured through the mean square difference between the BLUE and the Minimum Variance Unbiased Estimator (MVUE), obtained with univariate observations and background estimates. In order to accomplish this, we compute maximum entropy probability density functions (pdfs) of the errors, constrained by the first four
Gaussianity versus intermittency in solar system plasma turbulence
NASA Astrophysics Data System (ADS)
Echim, M.
2014-12-01
Statistical properties of plasma and magnetic field fluctuations exhibit features linked with the dynamics of the targeted system and sometimes with the physical processes that are at the origin of these fluctuations. Intermittency is sometimes discussed in terms of non-Gaussianity of the Probability Distribution Functions (PDFs) of fluctuations for ranges of spatio/temporal scales. Some examples of self-similarity have been however shown for PDFs whose wings are not Gaussian. In this study we discuss intermittency in terms of non-Gaussianity as well as scale dependence of the higher order moments of PDFs, in particular the flatness. We use magnetic field and plasma data from several space missions, in the solar wind (Ulysses, Cluster, and Venus Express), and in the planetary magnetosheaths (Cluster and Venus Express). We analyze Ulysses data that satisfy a consolidated set of selection criteria able to identify "pure" fast and slow wind. We investigate Venus Express data close to the orbital apogee, in the solar wind, at 0.72 AU, and in the Venus magnetosheath. We study Cluster data in the solar wind (for time intervals not affected by planetary ions effects), and the magnetosheath. We organize our results in three solar wind data bases (one for the solar maximum, 1999-2001, two for the solar minimum, 1997-1998 and respectively, 2007-2008), and two planetary databases (one for the solar maximum, 2000-2001, that includes PDFs obtained in the terrestrial magnetosphere, and one for the solar minimum, 2007-2008, that includes PDFs obtained in the terrestrial and Venus magnetospheres and magnetosheaths). In addition to investigating the statistical properties of fluctuations for the minimum and maximum of the solar cycle we also analyze the similarities and differences between fast and slow wind. We emphasize the importance of our data survey and analysis in the context of understanding the solar wind turbulence and complexity, and the exploitation of data bases and as
Distributed static linear Gaussian models using consensus.
Belanovic, Pavle; Valcarcel Macua, Sergio; Zazo, Santiago
2012-10-01
Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance trade-off.
Bimetric structure formation: Non-Gaussian predictions
Magueijo, Joao; Noller, Johannes; Piazza, Federico
2010-08-15
The minimal bimetric theory employing a disformal transformation between matter and gravity metrics is known to produce exactly scale-invariant fluctuations. It has a purely equilateral non-Gaussian signal, with an amplitude smaller than that of Dirac Born Infeld inflation (with opposite sign) but larger than standard inflation. We consider nonminimal bimetric models, where the coupling B appearing in the disformal transformation g-circumflex{sub {mu}{nu}}=g{sub {mu}{nu}}-B{partial_derivative}{sub {mu}{phi}{partial_derivative}{nu}{phi}} can run with {phi}. For power-law B({phi}) these models predict tilted spectra. For each value of the spectral index, a distinctive distortion to the equilateral property can be found. The constraint between this distortion and the spectral index can be seen as a 'consistency relation' for nonminimal bimetric models.
Bimetric structure formation: Non-Gaussian predictions
NASA Astrophysics Data System (ADS)
Magueijo, João; Noller, Johannes; Piazza, Federico
2010-08-01
The minimal bimetric theory employing a disformal transformation between matter and gravity metrics is known to produce exactly scale-invariant fluctuations. It has a purely equilateral non-Gaussian signal, with an amplitude smaller than that of Dirac Born Infeld inflation (with opposite sign) but larger than standard inflation. We consider nonminimal bimetric models, where the coupling B appearing in the disformal transformation g^μν=gμν-B∂μϕ∂νϕ can run with ϕ. For power-law B(ϕ) these models predict tilted spectra. For each value of the spectral index, a distinctive distortion to the equilateral property can be found. The constraint between this distortion and the spectral index can be seen as a “consistency relation” for nonminimal bimetric models.
IBS for non-gaussian distributions
Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.
2010-09-27
In many situations distribution can significantly deviate from Gaussian which requires accurate treatment of IBS. Our original interest in this problem was motivated by the need to have an accurate description of beam evolution due to IBS while distribution is strongly affected by the external electron cooling force. A variety of models with various degrees of approximation were developed and implemented in BETACOOL in the past to address this topic. A more complete treatment based on the friction coefficient and full 3-D diffusion tensor was introduced in BETACOOL at the end of 2007 under the name 'local IBS model'. Such a model allowed us calculation of IBS for an arbitrary beam distribution. The numerical benchmarking of this local IBS algorithm and its comparison with other models was reported before. In this paper, after briefly describing the model and its limitations, they present its comparison with available experimental data.
Non-Gaussian Berkson errors in bioassay.
Althubaiti, Alaa; Donev, Alexander
2016-02-01
The experimental design plays an important role in every experimental study. However, if errors in the settings of the studied factors cannot be avoided, i.e. Berkson errors occur, the estimates of the model parameters may be biased and the variability in the study increased. Correction methods for the effect of Berkson errors are compared. The emphasis is on the study of correlated Berkson errors which follow non-Gaussian distribution as this appears to have been a neglected, yet important, area. It is shown that the regression calibration approach bias correction methods are useful when the Berkson errors are independent. However, when these errors are dependent, the newly proposed method B-SIMEX clearly outperforms the other methods.
Absolute instability of the Gaussian wake profile
NASA Technical Reports Server (NTRS)
Hultgren, Lennart S.; Aggarwal, Arun K.
1987-01-01
Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.
Exploring scalar field dynamics with Gaussian processes
Nair, Remya; Jhingan, Sanjay; Jain, Deepak E-mail: sanjay.jhingan@gmail.com
2014-01-01
The origin of the accelerated expansion of the Universe remains an unsolved mystery in Cosmology. In this work we consider a spatially flat Friedmann-Robertson-Walker (FRW) Universe with non-relativistic matter and a single scalar field contributing to the energy density of the Universe. Properties of this scalar field, like potential, kinetic energy, equation of state etc. are reconstructed from Supernovae and BAO data using Gaussian processes. We also reconstruct energy conditions and kinematic variables of expansion, such as the jerk and the slow roll parameter. We find that the reconstructed scalar field variables and the kinematic quantities are consistent with a flat ΛCDM Universe. Further, we find that the null energy condition is satisfied for the redshift range of the Supernovae data considered in the paper, but the strong energy condition is violated.
Scintillations of partially coherent Laguerre Gaussian beams
NASA Astrophysics Data System (ADS)
Yüceer, M.; Eyyuboğlu, H. T.; Lukin, I. P.
2010-12-01
Scintillations of Laguerre-Gaussian (LG) beams for weak atmospheric turbulence conditions are derived for on-axis receiver positions by using Huygens-Fresnel (HF) method in semi-analytic fashion. Numerical evaluations indicate that at the fully coherent limit, higher values of radial mode numbers will give rise to more scintillations, at medium and low partial coherence levels, particularly at longer propagation distances, scintillations will fall against rises in radial mode numbers. At small source sizes, the scintillations of LG beams having full coherence will initially rise, reaching saturation at large source sizes. For LG beams with low partial coherence levels, a steady fall toward the larger source sizes is observed. Partially coherent beams of medium levels generally exhibit a rising trend toward the large source sizes, also changing the respective positions of the related curves. Beams of low coherence levels will be less affected by the variations in the refractive index structure constant.
Gaussian polarizable-ion tight binding
NASA Astrophysics Data System (ADS)
Boleininger, Max; Guilbert, Anne AY; Horsfield, Andrew P.
2016-10-01
To interpret ultrafast dynamics experiments on large molecules, computer simulation is required due to the complex response to the laser field. We present a method capable of efficiently computing the static electronic response of large systems to external electric fields. This is achieved by extending the density-functional tight binding method to include larger basis sets and by multipole expansion of the charge density into electrostatically interacting Gaussian distributions. Polarizabilities for a range of hydrocarbon molecules are computed for a multipole expansion up to quadrupole order, giving excellent agreement with experimental values, with average errors similar to those from density functional theory, but at a small fraction of the cost. We apply the model in conjunction with the polarizable-point-dipoles model to estimate the internal fields in amorphous poly(3-hexylthiophene-2,5-diyl).
Turbo Equalization Using Partial Gaussian Approximation
NASA Astrophysics Data System (ADS)
Zhang, Chuanzong; Wang, Zhongyong; Manchon, Carles Navarro; Sun, Peng; Guo, Qinghua; Fleury, Bernard Henri
2016-09-01
This paper deals with turbo-equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation-propagation rule to convert messages passed from the demodulator-decoder to the equalizer and computes messages returned by the equalizer by using a partial Gaussian approximation (PGA). Results from Monte Carlo simulations show that this approach leads to a significant performance improvement compared to state-of-the-art turbo-equalizers and allows for trading performance with complexity. We exploit the specific structure of the ISI channel model to significantly reduce the complexity of the PGA compared to that considered in the initial paper proposing the method.
Semiconductor band gap localization via Gaussian function
NASA Astrophysics Data System (ADS)
Ullrich, B.; Brown, G. J.; Xi, H.
2012-10-01
To determine the band gap of bulk semiconductors with transmission spectroscopy alone is considered as an extremely difficult task because in the higher energy range, approaching and exceeding the band gap energy, the material is opaque yielding no useful data to be recorded. In this paper, by investigating the transmission of industrial GaSb wafers with a thickness of 500 µm, we demonstrate how these obstacles of transmission spectroscopy can be overcome. The key is the transmission spectrums’ derivative, which coincides with the Gaussian function. This understanding can be used to transfer Beers’ law in an integral form opening the pathway of band gap determinations based on mathematical parameters only. The work also emphasizes the correlation between the thermal band gap variation and Debye temperature.
Occupancy mapping and surface reconstruction using local Gaussian processes with Kinect sensors.
Kim, Soohwan; Kim, Jonghyuk
2013-10-01
Although RGB-D sensors have been successfully applied to visual SLAM and surface reconstruction, most of the applications aim at visualization. In this paper, we propose a noble method of building continuous occupancy maps and reconstructing surfaces in a single framework for both navigation and visualization. Particularly, we apply a Bayesian nonparametric approach, Gaussian process classification, to occupancy mapping. However, it suffers from high-computational complexity of O(n(3))+O(n(2)m), where n and m are the numbers of training and test data, respectively, limiting its use for large-scale mapping with huge training data, which is common with high-resolution RGB-D sensors. Therefore, we partition both training and test data with a coarse-to-fine clustering method and apply Gaussian processes to each local clusters. In addition, we consider Gaussian processes as implicit functions, and thus extract iso-surfaces from the scalar fields, continuous occupancy maps, using marching cubes. By doing that, we are able to build two types of map representations within a single framework of Gaussian processes. Experimental results with 2-D simulated data show that the accuracy of our approximated method is comparable to previous work, while the computational time is dramatically reduced. We also demonstrate our method with 3-D real data to show its feasibility in large-scale environments. PMID:23893758
Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
Monras, Alex; Illuminati, Fabrizio
2011-01-15
We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within d-dimensional cutoff subspaces (d{<=}6) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones.
A novel Gaussian-Sinc mixed basis set for electronic structure calculations
NASA Astrophysics Data System (ADS)
Jerke, Jonathan L.; Lee, Young; Tymczak, C. J.
2015-08-01
A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the "delocalized" regions and the atom-centered Gaussian functions are used to represent the "localized" regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree-Fock energies for atoms up to neon, the diatomic systems H2, O2, and N2, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.
A novel Gaussian-Sinc mixed basis set for electronic structure calculations
Jerke, Jonathan L.; Lee, Young; Tymczak, C. J.
2015-08-14
A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.
A novel Gaussian-Sinc mixed basis set for electronic structure calculations.
Jerke, Jonathan L; Lee, Young; Tymczak, C J
2015-08-14
A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a new basis methodology-a lattice of orthonormal sinc functions is used to represent the "delocalized" regions and the atom-centered Gaussian functions are used to represent the "localized" regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree-Fock energies for atoms up to neon, the diatomic systems H2, O2, and N2, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species. PMID:26277128
ERIC Educational Resources Information Center
Swalwell, Katy
2012-01-01
Even as the United States becomes more diverse, a new era of "white flight" is unfolding. Whether they live in urban, suburban or rural communities, white students are likely to attend schools that reinforce their perceptions of cultural dominance. The average white student attends a school where 77 percent of the student body is of their race.…
Optimality of Gaussian attacks in continuous-variable quantum cryptography.
Navascués, Miguel; Grosshans, Frédéric; Acín, Antonio
2006-11-10
We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
Degeneracy of energy levels of pseudo-Gaussian oscillators
Iacob, Theodor-Felix; Iacob, Felix; Lute, Marina
2015-12-07
We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.
A Paper-and-Pencil gcd Algorithm for Gaussian Integers
ERIC Educational Resources Information Center
Szabo, Sandor
2005-01-01
As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.
A note on the wide-band Gaussian broadcast channel
NASA Technical Reports Server (NTRS)
Mceliece, Robert J.; Swanson, Laif
1987-01-01
The observations of Posner (1983) that on a wideband Gaussian broadcast channel ordinary time-shared coding performs almost as well as broadcast coding are investigated. A quantitative version of Posner's results is derived. A numerical example comparing the performance of broadcast coding and time-shared coding for a Gaussian broadcast channel model is presented.
Limitations of quantum computing with Gaussian cluster states
Ohliger, M.; Kieling, K.; Eisert, J.
2010-10-15
We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian-projected entangled pair states, we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information are not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states and points toward the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.
Weakly anomalous diffusion with non-Gaussian propagators
NASA Astrophysics Data System (ADS)
Cressoni, J. C.; Viswanathan, G. M.; Ferreira, A. S.; da Silva, M. A. A.
2012-08-01
A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H≈1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H=1/2 but with a non-Gaussian propagator.
Excitotoxic damage to white matter
Matute, Carlos; Alberdi, Elena; Domercq, María; Sánchez-Gómez, María-Victoria; Pérez-Samartín, Alberto; Rodríguez-Antigüedad, Alfredo; Pérez-Cerdá, Fernando
2007-01-01
Glutamate kills neurons by excitotoxicity, which is caused by sustained activation of glutamate receptors. In recent years, it has been shown that glutamate can also be toxic to white matter oligodendrocytes and to myelin by this mechanism. In particular, glutamate receptor-mediated injury to these cells can be triggered by activation of alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid, kainate and N-methyl-d-aspartate glutamate receptor types. Thus, these receptor classes, and the intermediaries of the signal cascades they activate, are potential targets for drug development to treat white matter damage in acute and chronic diseases. In addition, alterations of glutamate homeostasis in white matter can determine glutamate injury to oligodendrocytes and myelin. Astrocytes are responsible for most glutamate uptake in synaptic and non-synaptic areas and consequently are the major regulators of glutamate homeostasis. Activated microglia in turn may secrete cytokines and generate radical oxygen species, which impair glutamate uptake and reduce the expression of glutamate transporters. Finally, oligodendrocytes also contribute to glutamate homeostasis. This review aims at summarizing the current knowledge about the mechanisms leading to oligodendrocyte cell death and demyelination as a consequence of alterations in glutamate signalling, and their clinical relevance to disease. In addition, we show evidence that oligodendrocytes can also be killed by ATP acting at P2X receptors. A thorough understanding of how oligodendrocytes and myelin are damaged by excitotoxicity will generate knowledge that can lead to improved therapeutic strategies to protect white matter. PMID:17504270
Gaussian cloning of coherent states with known phases
Alexanian, Moorad
2006-04-15
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.
Non-ideal boson system in the Gaussian approximation
Tommasini, P.R.; de Toledo Piza, A.F.
1997-01-01
We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent Gaussian mean-field approximation which consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. Finite temperature results are obtained in a grand canonical framework. Contact is made with the results of Lee, Yang, and Huang in terms of particular truncations of the Gaussian approximation. The full Gaussian approximation supports a free phase or a thermodynamically unstable phase when contact forces and a standard renormalization scheme are used. When applied to a Hamiltonian with zero range forces interpreted as an effective theory with a high momentum cutoff, the full Gaussian approximation generates a quasi-particle spectrum having an energy gap, in conflict with perturbation theory results. {copyright} 1997 Academic Press, Inc.
REJUVENATING POWER SPECTRA. II. THE GAUSSIANIZED GALAXY DENSITY FIELD
Neyrinck, Mark C.; Szalay, Alexander S.; Szapudi, Istvan
2011-04-20
We find that, even in the presence of discreteness noise, a Gaussianizing transform (producing a more Gaussian one-point distribution) reduces nonlinearities in the power spectra of cosmological matter and galaxy density fields, in many cases drastically. Although Gaussianization does increase the effective shot noise, it also increases the power spectrum's fidelity to the linear power spectrum on scales where the shot noise is negligible. Gaussianizing also increases the Fisher information in the power spectrum in all cases and resolutions, although the gains are smaller in redshift space than in real space. We also find that the gain in cumulative Fisher information from Gaussianizing peaks at a particular grid resolution depends on the sampling level.
Power deposited by a Gaussian beam on a decentered circular aperture
NASA Astrophysics Data System (ADS)
Barbeau, Nicolas R.
1995-10-01
An expression for the energy or power deposited by a Gaussian beam on a decentered circular aperture is derived. It represents a generalization of the classic laser-beam truncation problem, with applications in the areas of laser scanning, detection theory, lidar, free-space communications, and so on. In addition, it can be used to quantify the effect of alignment errors on laser systems.
A utilitarian approach to modeling non-Gaussian characteristics of a topographic field
NASA Astrophysics Data System (ADS)
Goff, John A.
1993-11-01
This paper develops a general framework for the analysis of the moments greater than 2 of a topographic field. This framework uses 'iterated' expectation to reduce a statistical moment function to component parts involving the vertical (disjoint) moment of the same order, lower moments, and two-point conditional expectations. In this way it is possible to isolate the unique informational contribution of each moment. Use of this framework necessitates a 'bootstrap' or perturbation method, where lower moments are modeled first and then are used as constraints in the modeling of higher moments. Functional modeling of any moment is thus reducible to characterization of the disjoint moment (e.g., skewness, kurtosis) and the two-point conditional expectation. In this paper, I demonstrate how it is possible to 'design' a statistical model most sensitive to specific non-Gaussian topographic characteristics by solving for the two-point conditional expectation under an invertable mapping between Gaussian and non-Gaussian fields of interest. Mapping of this sort are useful both for the fact that they can be intuitive descriptions of non-Gaussian characteristics and for their utility in generating non-Gaussian synthetic topography. The primary intent of this methodology is to forge a link between physical topography characteristics, the information we want to know, and statistical moments, our tool for quantitatively measuring topographic fields. In addition, mapping models can be used to calculate the skewness and kurtosis (or higher moments) of topographic slopes directly. The applicability of these methods is demonstrated for mapping models which create vertical and lateral asymmetry and peakiness in a topographic field.
Effects of non-Gaussian copula-based hydraulic conductivity fields on macrodispersion
NASA Astrophysics Data System (ADS)
Haslauer, C. P.; Guthke, P.; BáRdossy, A.; Sudicky, E. A.
2012-07-01
This is an application of a spatial copula model that is fitted to a real world data set. The copula model allows modeling of pure spatial dependence independently of the marginal distribution. Using non-Gaussian copula models it is demonstrated that the spatial dependence structure of the Borden aquifer is significantly non-Gaussian—despite the fact that the Borden aquifer is commonly thought of as a relatively homogeneous porous medium with a small variance of hydraulic conductivity. In addition to evaluating the spatial dependence structure of the Borden hydraulic conductivity data set using copulas, goal of this study is to explore if the structure of the hydraulic conductivity field influences a physical property, such as plume evolution as evaluated by second spatial central moments of concentration fields. For this comparison, two types of hydraulic conductivity fields were fitted to the Borden hydraulic conductivity data set: one with a Gaussian and the other with a non-Gaussian type of dependence. These two types of hydraulic conductivity fields were constructed such that their second-order spatial moments are identical, and hence they cannot be distinguished by semivariogram-based geostatistics. This paper illustrates that the spatial dependence structure of the Borden hydraulic conductivity data set is significantly non-Gaussian. Despite the fact that Borden is a relatively homogeneous porous medium, and despite the fact that both types of spatial fields are not distinguishable by their variograms, the solute transport characteristics based on these two types of isotropic fields differ significantly in two-dimensional settings. The difference is less pronounced in three-dimensions with anisotropy. It is postulated that non-Gaussian spatial dependence of hydraulic conductivity and a more skewed marginal distribution of hydraulic conductivity will have significant implications in the other more heterogeneous aquifers.
Harrup, Mason K; Rollins, Harry W
2013-11-26
An additive comprising a phosphazene compound that has at least two reactive functional groups and at least one capping functional group bonded to phosphorus atoms of the phosphazene compound. One of the at least two reactive functional groups is configured to react with cellulose and the other of the at least two reactive functional groups is configured to react with a resin, such as an amine resin of a polycarboxylic acid resin. The at least one capping functional group is selected from the group consisting of a short chain ether group, an alkoxy group, or an aryloxy group. Also disclosed are an additive-resin admixture, a method of treating a wood product, and a wood product.
Rudolf Keller
2004-08-10
In this project, a concept to improve the performance of aluminum production cells by introducing potlining additives was examined and tested. Boron oxide was added to cathode blocks, and titanium was dissolved in the metal pool; this resulted in the formation of titanium diboride and caused the molten aluminum to wet the carbonaceous cathode surface. Such wetting reportedly leads to operational improvements and extended cell life. In addition, boron oxide suppresses cyanide formation. This final report presents and discusses the results of this project. Substantial economic benefits for the practical implementation of the technology are projected, especially for modern cells with graphitized blocks. For example, with an energy savings of about 5% and an increase in pot life from 1500 to 2500 days, a cost savings of $ 0.023 per pound of aluminum produced is projected for a 200 kA pot.
[Optimizing Color Rendering for Mixed-Color White Light LED].
Yu, Chun-yu; Jin, Peng; Zhou, Qi-feng
2015-05-01
To optimize color rendering of mixed-color LEDs, the Gaussian model was used to analyze the color-mixed LED's spectrum power distribution. The peak wavelength "λm", spectral half width "Δλ" and amplitude "A" were basic parameters for optimizing color rendering R9, which is very important for objects to be colorful and vivid under the white light LED's'illuminating. The typical methods for color mixing were used to get white light LEDs. Result was that to get the satisfied color rendering index, one of the color primaries should be certain and then other color primaries would be analyzed through changing three basic parameters step by step. It was concluded that the analysis in this paper would be referential to optimize the color-mixed white LED's color rendering. PMID:26415452
[Optimizing Color Rendering for Mixed-Color White Light LED].
Yu, Chun-yu; Jin, Peng; Zhou, Qi-feng
2015-05-01
To optimize color rendering of mixed-color LEDs, the Gaussian model was used to analyze the color-mixed LED's spectrum power distribution. The peak wavelength "λm", spectral half width "Δλ" and amplitude "A" were basic parameters for optimizing color rendering R9, which is very important for objects to be colorful and vivid under the white light LED's'illuminating. The typical methods for color mixing were used to get white light LEDs. Result was that to get the satisfied color rendering index, one of the color primaries should be certain and then other color primaries would be analyzed through changing three basic parameters step by step. It was concluded that the analysis in this paper would be referential to optimize the color-mixed white LED's color rendering.
Axial acoustic radiation force on a sphere in Gaussian field
Wu, Rongrong; Liu, Xiaozhou Gong, Xiufen
2015-10-28
Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated. Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.
Probing Non-Gaussianity in Confined Diffusion of Nanoparticles.
Xue, Chundong; Zheng, Xu; Chen, Kaikai; Tian, Yu; Hu, Guoqing
2016-02-01
Confined diffusion is ubiquitous in nature. Ever since the "anomalous yet Brownian" motion was observed, the non-Gaussianity in confined diffusion has been unveiled as an important issue. In this Letter, we experimentally investigate the characteristics and source of non-Gaussian behavior in confined diffusion of nanoparticles suspended in polymer solutions. A time-varied and size-dependent non-Gaussianity is reported based on the non-Gaussian parameter and displacement probability distribution, especially when the nanoparticle's size is smaller than the typical polymer mesh size. This non-Gaussianity does not vanish even at the long-time Brownian stage. By inspecting the displacement autocorrelation, we observe that the nanoparticle-structure interaction, indicated by the anticorrelation, is limited in the short-time stage and makes little contribution to the non-Gaussianity in the long-time stage. The main source of the non-Gaussianity can therefore be attributed to hopping diffusion that results in an exponential probability distribution with the large displacements, which may also explain certain processes dominated by rare events in the biological environment. PMID:26784864
Recovering dark-matter clustering from galaxies with Gaussianization
NASA Astrophysics Data System (ADS)
McCullagh, Nuala; Neyrinck, Mark; Norberg, Peder; Cole, Shaun
2016-04-01
The Gaussianization transform has been proposed as a method to remove the issues of scale-dependent galaxy bias and non-linearity from galaxy clustering statistics, but these benefits have yet to be thoroughly tested for realistic galaxy samples. In this paper, we test the effectiveness of the Gaussianization transform for different galaxy types by applying it to realistic simulated blue and red galaxy samples. We show that in real space, the shapes of the Gaussianized power spectra of both red and blue galaxies agree with that of the underlying dark matter, with the initial power spectrum, and with each other to smaller scales than do the statistics of the usual (untransformed) density field. However, we find that the agreement in the Gaussianized statistics breaks down in redshift space. We attribute this to the fact that red and blue galaxies exhibit very different fingers of god in redshift space. After applying a finger-of-god compression, the agreement on small scales between the Gaussianized power spectra is restored. We also compare the Gaussianization transform to the clipped galaxy density field and find that while both methods are effective in real space, they have more complicated behaviour in redshift space. Overall, we find that Gaussianization can be useful in recovering the shape of the underlying dark-matter power spectrum to k ˜ 0.5 h Mpc-1 and of the initial power spectrum to k ˜ 0.4 h Mpc-1 in certain cases at z = 0.
Spatial entanglement of nonvacuum Gaussian states
NASA Astrophysics Data System (ADS)
Kiałka, Filip; Ahmadi, Mehdi; Dragan, Andrzej
2016-06-01
The vacuum state of a relativistic quantum field contains entanglement between regions separated by spacelike intervals. Such spatial entanglement can be revealed using an operational method introduced in [M. Rodriguez-Vazquez, M. del Rey, H. Westman, and J. Leon, Ann. Phys. (N.Y.) 351, 112 (2014), E. G. Brown, M. del Rey, H. Westman, J. Leon, and A. Dragan, Phys. Rev. D 91, 016005 (2015)]. In this approach, a cavity is instantaneously divided into halves by an introduction of an extra perfect mirror. Causal separation of the two regions of the cavity reveals nonlocal spatial correlations present in the field, which can be quantified by measuring particles generated in the process. We use this method to study spatial entanglement properties of nonvacuum Gaussian field states. In particular, we show how to enhance the amount of harvested spatial entanglement by an appropriate choice of the initial state of the field in the cavity. We find a counterintuitive influence of the initial entanglement between cavity modes on the spatial entanglement which is revealed by dividing the cavity in half.
Anomalous dimensions and non-gaussianity
Green, Daniel; Lewandowski, Matthew; Senatore, Leonardo; Silverstein, Eva; Zaldarriaga, Matias
2013-10-01
We analyze the signatures of inflationary models that are coupled to interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to ~ 103 times the inflationary Hubble scale.
Probabilistic stellar rotation periods with Gaussian processes
NASA Astrophysics Data System (ADS)
Angus, Ruth; Aigrain, Suzanne; Foreman-Mackey, Daniel
2015-08-01
Stellar rotation has many applications in the field of exoplanets. High-precision photometry from space-based missions like Kepler and K2 allows us to measure stellar rotation periods directly from light curves. Stellar variability produced by rotation is usually not sinusoidal or perfectly periodic, therefore sine-fitting periodograms are not well suited to rotation period measurement. Autocorrelation functions are often used to extract periodic information from light curves, however uncertainties on rotation periods measured by autocorrelation are difficult to define. A ‘by eye’ check, or a set of heuristic criteria are used to validate measurements and rotation periods are only reported for stars that pass this vetting process. A probabilistic rotation period measurement method, with a suitable generative model bypasses the need for a validation stage and can produce realistic uncertainties. The physics driving the production of variability in stellar light curves is still poorly understood and difficult to model. We therefore use an effective model for stellar variability: a Gaussian process with a quasi-periodic covariance function. By injecting fake signals into Kepler light curves we show that the GP model is well suited to quasi-periodic, non-sinusoidal signals, is capable of modelling noise and physical signals simultaneously and provides probabilistic rotation period measurements with realistic uncertainties.
Bayesian nonparametric adaptive control using Gaussian processes.
Chowdhary, Girish; Kingravi, Hassan A; How, Jonathan P; Vela, Patricio A
2015-03-01
Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.
Sufficient condition for Gaussian departure in turbulence.
Tordella, Daniela; Iovieno, Michele; Bailey, Peter Roger
2008-01-01
The interaction of two isotropic turbulent fields of equal integral scale but different kinetic energy generates the simplest kind of inhomogeneous turbulent field. In this paper we present a numerical experiment where two time decaying isotropic fields of kinetic energies E1 and E2 initially match over a narrow region. Within this region the kinetic energy varies as a hyperbolic tangent. The following temporal evolution produces a shearless mixing. The anisotropy and intermittency of velocity and velocity derivative statistics is observed. In particular the asymptotic behavior in time and as a function of the energy ratio E_{1}E_{2}-->infinity is discussed. This limit corresponds to the maximum observable turbulent energy gradient for a given E1 and is obtained through the limit E_{2}-->0 . A field with E_{1}E_{2}-->infinity represents a mixing which could be observed near a surface subject to a very small velocity gradient separating two turbulent fields, one of which is nearly quiescent. In this condition the turbulent penetration is maximum and reaches a value equal to 1.2 times the nominal mixing layer width. The experiment shows that the presence of a turbulent energy gradient is sufficient for the appearance of intermittency and that during the mixing process the pressure transport is not negligible with respect to the turbulent velocity transport. These findings may open the way to the hypothesis that the presence of a gradient of turbulent energy is the minimal requirement for Gaussian departure in turbulence.
Castle, Toen; Sussman, Daniel M.; Tanis, Michael; Kamien, Randall D.
2016-01-01
Kirigami uses bending, folding, cutting, and pasting to create complex three-dimensional (3D) structures from a flat sheet. In the case of lattice kirigami, this cutting and rejoining introduces defects into an underlying 2D lattice in the form of points of nonzero Gaussian curvature. A set of simple rules was previously used to generate a wide variety of stepped structures; we now pare back these rules to their minimum. This allows us to describe a set of techniques that unify a wide variety of cut-and-paste actions under the rubric of lattice kirigami, including adding new material and rejoining material across arbitrary cuts in the sheet. We also explore the use of more complex lattices and the different structures that consequently arise. Regardless of the choice of lattice, creating complex structures may require multiple overlapping kirigami cuts, where subsequent cuts are not performed on a locally flat lattice. Our additive kirigami method describes such cuts, providing a simple methodology and a set of techniques to build a huge variety of complex 3D shapes. PMID:27679822
Castle, Toen; Sussman, Daniel M.; Tanis, Michael; Kamien, Randall D.
2016-01-01
Kirigami uses bending, folding, cutting, and pasting to create complex three-dimensional (3D) structures from a flat sheet. In the case of lattice kirigami, this cutting and rejoining introduces defects into an underlying 2D lattice in the form of points of nonzero Gaussian curvature. A set of simple rules was previously used to generate a wide variety of stepped structures; we now pare back these rules to their minimum. This allows us to describe a set of techniques that unify a wide variety of cut-and-paste actions under the rubric of lattice kirigami, including adding new material and rejoining material across arbitrary cuts in the sheet. We also explore the use of more complex lattices and the different structures that consequently arise. Regardless of the choice of lattice, creating complex structures may require multiple overlapping kirigami cuts, where subsequent cuts are not performed on a locally flat lattice. Our additive kirigami method describes such cuts, providing a simple methodology and a set of techniques to build a huge variety of complex 3D shapes.
Gauge-invariant temperature anisotropies and primordial non-Gaussianity.
Bartolo, Nicola; Matarrese, Sabino; Riotto, Antonio
2004-12-01
We provide the gauge-invariant expression for large-scale cosmic microwave background temperature fluctuations at second-order perturbation theory. This enables us to define unambiguously the nonlinearity parameter f(NL), which is used by experimental collaborations to pin down the level of non-Gaussianity in the temperature fluctuations. Furthermore, it contains a primordial term encoding all the information about the non-Gaussianity generated at primordial epochs and about the mechanism which gave rise to cosmological perturbations, thus neatly disentangling the primordial contribution to non-Gaussianity from the one caused by the postinflationary evolution.
Non-Gaussian extrema counts for CMB maps
Pogosyan, Dmitri; Pichon, Christophe; Gay, Christophe
2011-10-15
In the context of the geometrical analysis of weakly non-Gaussian cosmic microwave background maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient, and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non-Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian Planck data.
Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.
Observations on the formulation of paraxial and Gaussian optics
NASA Astrophysics Data System (ADS)
Greivenkamp, John E.
2014-12-01
In several of the standard derivations of first-order optics, the actual approximations used are unclear or overstated. Some derivations are also incomplete. Several of the fundamental derivations of paraxial and Gaussian optics have been reformulated to provide a clearer explanation and better understanding of the key concepts of basic image formation for our students. The paraxial refraction raytrace equation, the power of a general Gaussian system and the relationship between the numerical aperture and the F-number are examined. The paraxial refraction equation is shown to be a bridge between paraxial optics and Gaussian optics that defines the power of an optical system.
Noncommutative geometry modified non-Gaussianities of cosmological perturbation
Fang Kejie; Xue Wei; Chen Bin
2008-03-15
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. In particular, the dominant modification of the non-Gaussianity estimator f{sub NL} could reach O(1) in Dirac-Born-Infeld (DBI) inflation and K-inflation. The corrections are sensitive to the speed of sound and the choice of string length scale. Moreover the shapes of the corrected non-Gaussianities are distinct from that of ordinary ones.
Generalised Hermite-Gaussian beams and mode transformations
NASA Astrophysics Data System (ADS)
Wang, Yi; Chen, Yujie; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-05-01
Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function α, which can be used to unite conventional HG modes and Laguerre-Gaussian modes (LG modes). An infinite number of normalised orthogonal modes can thus be obtained by modulation of the function α. The gHG mode notion provides a useful tool in analysis of the deformation and transformation phenomena occurring in propagation of HG and LG modes with astigmatic perturbation.
Controllable gaussian-qubit interface for extremal quantum state engineering.
Adesso, Gerardo; Campbell, Steve; Illuminati, Fabrizio; Paternostro, Mauro
2010-06-18
We study state engineering through bilinear interactions between two remote qubits and two-mode gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios. PMID:20867288
Canales-Rodríguez, Erick J; Daducci, Alessandro; Sotiropoulos, Stamatios N; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data.
Canales-Rodríguez, Erick J.; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M.; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024
Canales-Rodríguez, Erick J; Daducci, Alessandro; Sotiropoulos, Stamatios N; Caruyer, Emmanuel; Aja-Fernández, Santiago; Radua, Joaquim; Yurramendi Mendizabal, Jesús M; Iturria-Medina, Yasser; Melie-García, Lester; Alemán-Gómez, Yasser; Thiran, Jean-Philippe; Sarró, Salvador; Pomarol-Clotet, Edith; Salvador, Raymond
2015-01-01
Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data. PMID:26470024
NASA Astrophysics Data System (ADS)
Labbé, R.; Bustamante, G.
2012-10-01
Extreme value statistics, or extreme statistics for short, refers to the statistics that characterizes rare events of either unusually high or low intensity: climate disasters like floods following extremely intense rains are among the principal examples. Extreme statistics is also found in fluctuations of global magnitudes in systems in thermal equilibrium, as well as in systems far from equilibrium. A remarkable example in this last class is fluctuations of injected power in confined turbulence. Here we report results in a confined von Kármán swirling flow, produced by two counter-rotating stirrers, in which quantities derived from the same global magnitude—the rotation rate of the stirrers—can display both, extreme and Gaussian statistics. On the one hand, we find that underlying the extreme statistics displayed by the global shear of the flow, there is a nearly Gaussian process resembling a white noise, corresponding to the action of the normal stresses exerted by the turbulent flow, integrated on the flow-driving surfaces of the stirrers. On the other hand, the magnitude displaying Gaussian statistics is the global rotation rate of the fluid, which happens to be a realization of a 1D diffusion where the variance of the angular speed increments ΩR(t + Δt) - ΩR(t) scales as Δtν, while the power spectral density of the angular speed follows a 1/fα scaling law. These scaling exponents are found to be α ≈ 0.37 and ν ≈ 1.36, which implies that this process can be described as a 1D superdiffusion.
Chen, Yunjie; Zhan, Tianming; Zhang, Ji
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms. PMID:27648448
Chen, Yunjie; Zhan, Tianming; Zhang, Ji; Wang, Hongyuan
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms. PMID:27648448
Evolution of the Magnetic Field Line Diffusion Coefficient and Non-Gaussian Statistics
NASA Astrophysics Data System (ADS)
Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.
2016-08-01
The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with these underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.
NASA Astrophysics Data System (ADS)
Xiang, NingJing; Wu, ZhenSen; Wang, MingJun
2014-10-01
The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function (MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.
Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence.
Xu, Hua-Feng; Zhang, Zhou; Qu, Jun; Huang, Wei
2014-09-22
Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov's power spectrum on the propagation factor are also analyzed in detailed.
Large-scale 3D galaxy correlation function and non-Gaussianity
Raccanelli, Alvise; Doré, Olivier; Bertacca, Daniele; Maartens, Roy E-mail: daniele.bertacca@gmail.com E-mail: roy.maartens@gmail.com
2014-08-01
We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects --- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the gravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f{sub NL} is small), so that a relativistic approach is needed. Furthermore, we look at how large-scale corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.
Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization.
Sumaya-Martinez, J; Mata-Mendez, O; Chavez-Rivas, F
2003-05-01
A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions. PMID:12747430
Non-Gaussianity and gravitational waves from a quadratic and self-interacting curvaton
Fonseca, Jose; Wands, David
2011-03-15
In this paper we consider how non-Gaussianity of the primordial density perturbation and the amplitude of gravitational waves from inflation can be used to determine parameters of the curvaton scenario for the origin of structure. We show that in the simplest quadratic model, where the curvaton evolves as a free scalar field, measurement of the bispectrum relative to the power spectrum, f{sub NL}, and the tensor-to-scalar ratio can determine both the expectation value of the curvaton field during inflation and its dimensionless decay rate relative to the curvaton mass. We show how these predictions are altered by the introduction of self-interactions, in models where higher-order corrections are determined by a characteristic mass scale and discuss how additional information about primordial non-Gaussianity and scale dependence may constrain curvaton interactions.
On the robustness of the q-Gaussian family
NASA Astrophysics Data System (ADS)
Sicuro, Gabriele; Tempesta, Piergiulio; Rodríguez, Antonio; Tsallis, Constantino
2015-12-01
We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family.
Optimal multicopy asymmetric Gaussian cloning of coherent states
Fiurasek, Jaromir; Cerf, Nicolas J.
2007-05-15
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.
Transmission loss between single-mode Gaussian antennas.
Perlot, Nicolas; Rohde, Michael
2016-08-22
We analytically derive a set of formulas for the transmission loss in vacuum between antennas that send and receive single-mode Gaussian beams. We relate our results to standard far-field link budget parameters. PMID:27557226
Transmission loss between single-mode Gaussian antennas.
Perlot, Nicolas; Rohde, Michael
2016-08-22
We analytically derive a set of formulas for the transmission loss in vacuum between antennas that send and receive single-mode Gaussian beams. We relate our results to standard far-field link budget parameters.
Evolution of massive haloes in non-Gaussian scenarios
NASA Astrophysics Data System (ADS)
Grossi, M.; Dolag, K.; Branchini, E.; Matarrese, S.; Moscardini, L.
2007-12-01
We have performed high-resolution cosmological N-body simulations of a concordance ΛCDM model to study the evolution of virialized, dark matter haloes in the presence of primordial non-Gaussianity. Following a standard procedure, departures from Gaussianity are modelled through a quadratic Gaussian term in the primordial gravitational potential, characterized by a dimensionless non-linearity strength parameter fNL. We find that the halo mass function and its redshift evolution closely follow the analytic predictions of Matarrese, Verde & Jimenez. The existence of precise analytic predictions makes the observation of rare, massive objects at large redshift an even more attractive test to detect primordial non-Gaussian features in the large-scale structure of the Universe.
Gaussian mixture models as flux prediction method for central receivers
NASA Astrophysics Data System (ADS)
Grobler, Annemarie; Gauché, Paul; Smit, Willie
2016-05-01
Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.
Primordial non-Gaussianities after Planck 2015: An introductory review
NASA Astrophysics Data System (ADS)
Renaux-Petel, Sébastien
2015-12-01
Deviations from Gaussian statistics of the cosmological density fluctuations, so-called primordial non-Gaussianities (NG), are one of the most informative fingerprints of the origin of structures in the universe. Indeed, they can probe physics at energy scales inaccessible to laboratory experiments, and are sensitive to the interactions of the field(s) that generated the primordial fluctuations, contrary to the Gaussian linear theory. As a result, they can discriminate between inflationary models that are otherwise almost indistinguishable. In this short review, we explain how to compute the non-Gaussian properties in any inflationary scenario. We review the theoretical predictions of several important classes of models. We then describe the ways NG can be probed observationally, and we highlight the recent constraints from the Planck mission, as well as their implications. We finally identify well motivated theoretical targets for future experiments and discuss observational prospects. xml:lang="fr"
Minimal disturbance measurement for coherent states is non-Gaussian
Mista, Ladislav Jr.
2006-03-15
In standard coherent state teleportation with a shared two-mode squeezed vacuum (TMSV) state there is a trade-off between the teleportation fidelity and the fidelity of estimation of the teleported state from the results of the Bell measurement. Within the class of Gaussian operations this trade-off is optimal, i.e., there is not a Gaussian operation that would give a larger estimation fidelity for a given output fidelity. We show that this trade-off can be improved by up to 2.77% if we use a suitable non-Gaussian operation. This operation can be implemented by the standard teleportation protocol in which the shared TMSV state is replaced with a suitable non-Gaussian entangled state. We also demonstrate that this operation can be used to enhance the transmission fidelity of a certain noisy channel.
Making tensor factorizations robust to non-gaussian noise.
Chi, Eric C.; 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).
A comparative study of Gaussian geostatistical models and Gaussian Markov random field models1
Song, Hae-Ryoung; Fuentes, Montserrat; Ghosh, Sujit
2008-01-01
Gaussian geostatistical models (GGMs) and Gaussian Markov random fields (GM-RFs) are two distinct approaches commonly used in spatial models for modeling point referenced and areal data, respectively. In this paper, the relations between GGMs and GMRFs are explored based on approximations of GMRFs by GGMs, and approximations of GGMs by GMRFs. Two new metrics of approximation are proposed: (i) the Kullback-Leibler discrepancy of spectral densities and (ii) the chi-squared distance between spectral densities. The distances between the spectral density functions of GGMs and GMRFs measured by these metrics are minimized to obtain the approximations of GGMs and GMRFs. The proposed methodologies are validated through several empirical studies. We compare the performance of our approach to other methods based on covariance functions, in terms of the average mean squared prediction error and also the computational time. A spatial analysis of a dataset on PM2.5 collected in California is presented to illustrate the proposed method. PMID:19337581
Gaussian Process Regression Plus Method for Localization Reliability Improvement.
Liu, Kehan; Meng, Zhaopeng; Own, Chung-Ming
2016-01-01
Location data are among the most widely used context data in context-aware and ubiquitous computing applications. Many systems with distinct deployment costs and positioning accuracies have been developed over the past decade for indoor positioning. The most useful method is focused on the received signal strength and provides a set of signal transmission access points. However, compiling a manual measuring Received Signal Strength (RSS) fingerprint database involves high costs and thus is impractical in an online prediction environment. The system used in this study relied on the Gaussian process method, which is a nonparametric model that can be characterized completely by using the mean function and the covariance matrix. In addition, the Naive Bayes method was used to verify and simplify the computation of precise predictions. The authors conducted several experiments on simulated and real environments at Tianjin University. The experiments examined distinct data size, different kernels, and accuracy. The results showed that the proposed method not only can retain positioning accuracy but also can save computation time in location predictions.
Unsupervised learning of binary vectors: A Gaussian scenario
NASA Astrophysics Data System (ADS)
Copelli, Mauro; van den Broeck, Christian
2000-06-01
We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry-breaking binary direction B∈\\{-1,+1\\}N, onto which the projections have a Gaussian distribution. We show that a candidate vector J undergoing Gibbs learning in this discrete space, approaches the perfect match J=B exponentially. In addition to the second-order ``retarded learning'' phase transition for unbiased distributions, we show that first-order transitions can also occur. Extending the known result that the center of mass of the Gibbs ensemble has Bayes-optimal performance, we show that taking the sign of the components of this vector (clipping) leads to the vector with optimal performance in the binary space. These upper bounds are shown generally not to be saturated with the technique of transforming the components of a special continuous vector, except in asymptotic limits and in a special linear case. Simulations are presented which are in excellent agreement with the theoretical results.
Gaussian Process Regression Plus Method for Localization Reliability Improvement.
Liu, Kehan; Meng, Zhaopeng; Own, Chung-Ming
2016-01-01
Location data are among the most widely used context data in context-aware and ubiquitous computing applications. Many systems with distinct deployment costs and positioning accuracies have been developed over the past decade for indoor positioning. The most useful method is focused on the received signal strength and provides a set of signal transmission access points. However, compiling a manual measuring Received Signal Strength (RSS) fingerprint database involves high costs and thus is impractical in an online prediction environment. The system used in this study relied on the Gaussian process method, which is a nonparametric model that can be characterized completely by using the mean function and the covariance matrix. In addition, the Naive Bayes method was used to verify and simplify the computation of precise predictions. The authors conducted several experiments on simulated and real environments at Tianjin University. The experiments examined distinct data size, different kernels, and accuracy. The results showed that the proposed method not only can retain positioning accuracy but also can save computation time in location predictions. PMID:27483276
Gaussian Process Regression Plus Method for Localization Reliability Improvement
Liu, Kehan; Meng, Zhaopeng; Own, Chung-Ming
2016-01-01
Location data are among the most widely used context data in context-aware and ubiquitous computing applications. Many systems with distinct deployment costs and positioning accuracies have been developed over the past decade for indoor positioning. The most useful method is focused on the received signal strength and provides a set of signal transmission access points. However, compiling a manual measuring Received Signal Strength (RSS) fingerprint database involves high costs and thus is impractical in an online prediction environment. The system used in this study relied on the Gaussian process method, which is a nonparametric model that can be characterized completely by using the mean function and the covariance matrix. In addition, the Naive Bayes method was used to verify and simplify the computation of precise predictions. The authors conducted several experiments on simulated and real environments at Tianjin University. The experiments examined distinct data size, different kernels, and accuracy. The results showed that the proposed method not only can retain positioning accuracy but also can save computation time in location predictions. PMID:27483276
Strong no-go theorem for Gaussian quantum bit commitment
Magnin, Loieck; Magniez, Frederic; Leverrier, Anthony
2010-01-15
Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.
Compact surfaces of constant Gaussian curvature in Randers manifolds
NASA Astrophysics Data System (ADS)
Cui, Ningwei
2016-08-01
The flag curvature of a Finsler surface is called the Gaussian curvature in Finsler geometry. In this paper, we characterize the surfaces of constant Gaussian curvature (CGC) in the Randers 3-manifold. Then we give a classification of the orientable closed CGC surfaces in two Randers space forms, which are the non-Euclidean Minkowski-Randers 3-space (K = 0) and the Bao-Shen sphere (K = 1).
GAUSSIAN 76: An ab initio Molecular Orbital Program
DOE R&D Accomplishments Database
Binkley, J. S.; Whiteside, R.; Hariharan, P. C.; Seeger, R.; Hehre, W. J.; Lathan, W. A.; Newton, M. D.; Ditchfield, R.; Pople, J. A.
1978-01-01
Gaussian 76 is a general-purpose computer program for ab initio Hartree-Fock molecular orbital calculations. It can handle basis sets involving s, p and d-type Gaussian functions. Certain standard sets (STO-3G, 4-31G, 6-31G*, etc.) are stored internally for easy use. Closed shell (RHF) or unrestricted open shell (UHF) wave functions can be obtained. Facilities are provided for geometry optimization to potential minima and for limited potential surface scans.
Simulations of Gaussian electron guns for RHIC electron lens
Pikin, A.
2014-02-28
Simulations of two versions of the electron gun for RHIC electron lens are presented. The electron guns have to generate an electron beam with Gaussian radial profile of the electron beam density. To achieve the Gaussian electron emission profile on the cathode we used a combination of the gun electrodes and shaping of the cathode surface. Dependence of electron gun performance parameters on the geometry of electrodes and the margins for electrodes positioning are presented.
Gauge invariance and non-Gaussianity in inflation
NASA Astrophysics Data System (ADS)
Rigopoulos, Gerasimos
2011-07-01
We clarify the role of gauge invariance for the computation of quantum non-Gaussian correlators in inflation. A gauge invariant generating functional for n-point functions is given and the special status of the spatially flat gauge is pointed out. We also comment on the relation between gauge transformations, field redefinitions, the choice of t=const hypersurfaces and the use of boundary terms in computations of non-Gaussianity.
Unstable laser resonators with super-Gaussian mirrors
De Silvestri, S.; Laporta, P.; Magni, V.; Svelto, O.; Majocchi, B.
1988-03-01
A new class of tapered reflectivity mirrors with a super-Gaussian profile R atmI exp(-kr/sup n/) is introduced, and a geometrical-optics approach for analysis and design of unstable resonators made with these mirrors is presented. A super-Gaussian mirror, built by a special evaporation technique, has been tested in an unstable resonator of a pulsed Nd:YAG laser, demonstrating its effectiveness in generating diffraction-limited beams.
Unstable laser resonators with super-Gaussian mirrors.
De Silvestri, S; Laporta, P; Magni, V; Svelto, O; Majocchi, B
1988-03-01
A new class of tapered reflectivity mirrors with a super-Gaussian profile R infinity exp(-kr(n)) is introduced, and a geometrical-optics approach for analysis and design of unstable resonators made with these mirrors is presented. A super-Gaussian mirror, built by a special evaporation technique, has been tested in an unstable resonator of a pulsed Nd:YAG laser, demonstrating its effectiveness in generating diffraction-limited beams. PMID:19742027
Nonclassicality of a photon-subtracted Gaussian field
Kim, M.S.; Park, E.; Knight, P.L.; Jeong, H.
2005-04-01
We investigate the nonclassicality of a photon-subtracted Gaussian field, which was produced in a recent experiment, using negativity of the Wigner function and the nonexistence of well-behaved positive P function. We obtain the condition to see negativity of the Wigner function for the case including the mixed Gaussian incoming field, the threshold photodetection and the inefficient homodyne measurement. We show how similar the photon-subtracted state is to a superposition of coherent states.
A note on the wideband Gaussian broadcast channel
NASA Technical Reports Server (NTRS)
Mceliece, R. J.; Posner, E. C.; Swanson, L.
1986-01-01
It is well known that for the Gaussian broadcast channel, timeshared coding is not as efficient as more sophisticated broadcast coding strategies. However, the relative advantage of broadcast coding over timeshared coding is shown to be small if the signal-to-noise ratios of both receivers are small. One surprising consequence of this is that for the wideband Gaussian broadcast channel, which is defined, broadcast coding offers no advantage over timeshared coding at all, and so timeshared coding is optimal.
Propagation of a Gaussian beam in a nonhomogeneous plasma
Mazzucato, E.
1989-06-01
The asymptotic theory of Choudhary and Felsen on the propagation of scalar inhomogeneous waves in two-dimensional isotropic media is extended to the case of three-dimensional vector fields. The theory is applied to the propagation of Gaussian beams in nonhomogeneous media. The wave trajectory equations are then reformulated for anisotropic media and used for tracking a Gaussian beam in a tokamak plasma. 14 refs., 5 figs.
Unstable laser resonators with super-Gaussian mirrors.
De Silvestri, S; Laporta, P; Magni, V; Svelto, O; Majocchi, B
1988-03-01
A new class of tapered reflectivity mirrors with a super-Gaussian profile R infinity exp(-kr(n)) is introduced, and a geometrical-optics approach for analysis and design of unstable resonators made with these mirrors is presented. A super-Gaussian mirror, built by a special evaporation technique, has been tested in an unstable resonator of a pulsed Nd:YAG laser, demonstrating its effectiveness in generating diffraction-limited beams.
Non-Gaussianity and Excursion Set Theory: Halo Bias
Adshead, Peter; Baxter, Eric J.; Dodelson, Scott; Lidz, Adam
2012-09-01
We study the impact of primordial non-Gaussianity generated during inflation on the bias of halos using excursion set theory. We recapture the familiar result that the bias scales as $k^{-2}$ on large scales for local type non-Gaussianity but explicitly identify the approximations that go into this conclusion and the corrections to it. We solve the more complicated problem of non-spherical halos, for which the collapse threshold is scale dependent.
Characterizing Accreting White Dwarf Pulsators
NASA Astrophysics Data System (ADS)
Szkody, Paula; Mukadam, Anjum
2014-02-01
Understanding the population, mass distribution, and evolution of accreting white dwarfs impacts the entire realm of binary interaction, including the creation of Type Ia supernovae. We are concentrating on accreting white dwarf pulsators, as the pulsation properties allow us a view of how the accretion affects the interior of the star. Our ground- based photometry on 11 accreting pulsators with corresponding temperatures from HST UV spectra suggest a broad instability strip in the range of 10500 to 16000K. Additionally, tracking a post-outburst heated white dwarf as it cools and crosses the blue edge and resumes pulsation provides an independent method to locate the empirical instability strip. Determining a post-outburst cooling curve yields an estimate of the amount of heating and the accreted mass during the outburst. We request additional photometry of 2 objects that present unique properties: GW Lib which has not yet returned to its pre-outburst pulsation spectrum after 6 yrs, and EQ Lyn which returned to its pre- outburst pulsation after 3 yrs but is now turning on and off without ongoing outbursts. Following the pulsation spectrum changes over stretches of several nights in a row will provide specific knowledge of the stability of the observed modes.
Gaussian Analytic Centroiding method of star image of star tracker
NASA Astrophysics Data System (ADS)
Wang, Haiyong; Xu, Ershuai; Li, Zhifeng; Li, Jingjin; Qin, Tianmu
2015-11-01
The energy distribution of an actual star image coincides with the Gaussian law statistically in most cases, so the optimized processing algorithm about star image centroiding should be constructed also by following Gaussian law. For a star image spot covering a certain number of pixels, the marginal distribution of the gray accumulation on rows and columns are shown and analyzed, based on which the formulas of Gaussian Analytic Centroiding method (GAC) are deduced, and the robustness is also promoted due to the inherited filtering effect of gray accumulation. Ideal reference star images are simulated by the PSF (point spread function) with integral form. Precision and speed tests for the Gaussian Analytic formulas are conducted under three scenarios of Gaussian radius (0.5, 0.671, 0.8 pixel), The simulation results show that the precision of GAC method is better than that of the other given algorithms when the Gaussian radius is not bigger than 5 × 5 pixel window, a widely used parameter. Above all, the algorithm which consumes the least time is still the novel GAC method. GAC method helps to promote the comprehensive performance in the attitude determination of a star tracker.
Gaussian reference fluid and interpretation of quantum geometrodynamics
Kuchar, K.V. ); Torre, C.G. )
1991-01-15
The Wheeler-DeWitt equation of vacuum geometrodynamics is turned into a Schroedinger equation by imposing the normal Gaussian coordinate conditions with Lagrange multipliers and then restoring the coordinate invariance of the action by parametrization. This procedure corresponds to coupling the gravitational field to a reference fluid. The source appearing in the Einstein law of gravitation has the structure of a heat-conducting dust. When one imposes only the Gaussian time condition but not the Gaussian frame conditions, the heat flow vanishes and the dust becomes incoherent. The canonical description of the fluid uses the Gaussian coordinates and their conjugate momenta as the fluid variables. The energy density and the momentum density of the fluid turn out to be homogeneous linear functions of such momenta. This feature guarantees that the Dirac constraint quantization of the gravitational field coupled to the Gaussian reference fluid leads to a functional Schroedinger equation in Gaussian time. Such an equation possesses the standard positive-definite conserved norm.
Characterization of non-Gaussianity in gravitational wave detector noise
NASA Astrophysics Data System (ADS)
Yamamoto, Takahiro; Hayama, Kazuhiro; Mano, Shuhei; Itoh, Yousuke; Kanda, Nobuyuki
2016-04-01
The first detection of a gravitational wave (GW) has been achieved by two detectors of the advanced LIGO. Routine detections of GW events from various GW sources are expected in the coming decades. Although the first signal was statistically significant, we expect to see numerous low signal-to-noise ratio (SNR) events with which we may be able to learn various aspects of the Universe that have yet to be unveiled. On the other hand, instrumental glitches due to nonstationarity and/or a non-Gaussian tail of detector noise distribution prevent us from confidently identifying true but low SNR GW signals out of instrumental noise. Thus, to make the best use of data from GW detectors, it is important to establish a method to safely distinguish true GW signals from false signals due to instrumental noises. For this purpose, we urgently need to understand characteristics of detector noises, since the nonstationarity and non-Gaussianity inherent in detector outputs are known to increase false detections of signals. Focusing on identifying the non-Gaussian noise components, this paper introduces a new measure for characterizing the non-Gaussian noise components using the parameter ν which characterizes the weight of tail in a Student-t distribution. A confidence interval is reported on the extent to which detector noise deviates from Gaussianity. Our method revealed stationary and transient deterioration of Gaussianity in LIGO S5 data.
Ballistic diffusion induced by non-Gaussian noise
NASA Astrophysics Data System (ADS)
Qin, Li; Li, Qiang
2013-03-01
In this letter, we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources. We discuss two time correlation functions C(t) of the non-Gaussian stochastic process, and find that they depend on the parameter q, indicating the departure of the non-Gaussian noise from Gaussian behavior: for q <= 1, C(t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the long-time limit, whereas for q > 1, C(t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant. Due to the properties of C(t), the particle exhibits a normal diffusion for q <= 1, while for q > 1 the non-Gaussian noise induces a ballistic diffusion, i.e., the long-time mean square displacement of the free particle reads <[x(t) -
NASA Technical Reports Server (NTRS)
1999-01-01
Mainstream Engineering Corporation was awarded Phase I and Phase II contracts from Goddard Space Flight Center's Small Business Innovation Research (SBIR) program in early 1990. With support from the SBIR program, Mainstream Engineering Corporation has developed a unique low cost additive, QwikBoost (TM), that increases the performance of air conditioners, heat pumps, refrigerators, and freezers. Because of the energy and environmental benefits of QwikBoost, Mainstream received the Tibbetts Award at a White House Ceremony on October 16, 1997. QwikBoost was introduced at the 1998 International Air Conditioning, Heating, and Refrigeration Exposition. QwikBoost is packaged in a handy 3-ounce can (pressurized with R-134a) and will be available for automotive air conditioning systems in summer 1998.
ERIC Educational Resources Information Center
Segall, Avner; Garrett, James
2013-01-01
In light of the increasing racial diversity in American schools and the consistently homogenous teacher workforce in the United States, understanding the ways white teachers consider and attend to racial issues is of crucial importance to the educational landscape. This paper, based on a qualitative study, explores five white American…
NASA Technical Reports Server (NTRS)
2004-01-01
This is a composite red-green-blue image of the rock called White Boat. It is the first rock target that Spirit drove to after finishing a series of investigations on the rock Adirondack. White Boat stood out to scientists due to its light color and more tabular shape compared to the dark, rounded rocks that surround it.
Whites in Desegregated Schools.
ERIC Educational Resources Information Center
Northwestern Univ., Evanston, IL. Center for Equal Education.
In 1972, over 1.3 million white children attended schools in which they were a minority. This document consists of articles addressing this little studied phenomenon. In Gretchen Schafft's article, an anthropological method is employed to study the role of white children in a predominantly black junior high school in Washington, D.C. Jean Le…
PREFACE: 16th European White Dwarfs Workshop
NASA Astrophysics Data System (ADS)
Garcia-Berro, Enrique; Hernanz, Margarita; Isern, Jordi; Torres, Santiago
2009-07-01
The 16th European Workshop on White Dwarfs was held in Barcelona, Spain, from 30 June to 4 July 2008 at the premises of the UPC. Almost 120 participants from Europe (France, Germany, United Kingdom, Italy, and several others), America (USA, Canada, Argentina, Brazil, and Chile), and other continents (Australia, South Africa, . . . ) attended the workshop. Among these participants were the most relevant specialists in the field. The topics covered by the conference were: White dwarf structure and evolution Progenitors and Planetary Nebulae White dwarfs in binaries: cataclysmic variables, double degenerates and other binaries White dwarfs, dust disks and planetary systems Atmospheres, chemical composition, magnetic fields Variable white dwarfs White dwarfs in stellar clusters and the halo White Dwarfs as SNIa progenitors The programme included 54 talks, and 45 posters. The oral presentations were distributed into the following sessions: Luminosity function, mass function and populations White dwarf structure and evolution White dwarf ages White dwarf catalogs and surveys Central stars of planetary nebulae Supernovae progenitors White dwarfs in novae and CVs Physical processes in white dwarfs and magnetic white dwarfs Disks, dust and planets around white dwarfs Pulsating white dwarfs Additionally we had a special open session about Spitzer and white dwarfs. The Proceedings of the 16th European Workshop on White Dwarfs are representative of the current state-of-the-art of the research field and include new and exciting results. We acknowledge the very positive attitude of the attendants to the workshop, which stimulated very fruitful discussions that took place in all the sessions and after the official schedule. Also, the meeting allowed new collaborations tp start that will undoubtedly result in significant advances in the research field. We also acknowledge the willingness of the participants to deliver their contributions before the final deadline. We sincerely
Elevation from east. White Holly in foreground, with White Sage ...
Elevation from east. White Holly in foreground, with White Sage behind. - U.S. Coast Guard Cutter WHITE HOLLY, U.S. Coast Guard 8th District Base, 4640 Urquhart Street, New Orleans, Orleans Parish, LA
Working decks for buoy maintenance. White Sage on left, White ...
Working decks for buoy maintenance. White Sage on left, White Holly on right. - U.S. Coast Guard Cutter WHITE HOLLY, U.S. Coast Guard 8th District Base, 4640 Urquhart Street, New Orleans, Orleans Parish, LA
Physicochemical and nutritional characteristics of preserved duck egg white.
Zhao, Yan; Tu, Yonggang; Xu, Mingsheng; Li, Jianke; Du, Huaying
2014-12-01
In this paper, the physicochemical and nutritional characteristics of preserved duck egg white were analyzed and compared with fresh egg and hard-cooked egg white (n = 3). The data obtained showed that the preserved egg white was rich in essential amino acids and minerals, such as Ca, Mg, Fe, Zn, Cu, K, and Na. After fresh duck eggs were processed into preserved eggs, contents of moisture, CP, amino acid, and water-soluble vitamin of egg white significantly decreased (P < 0.05); however, pH, free amino acid content, and most inorganic elemental contents of egg white significantly increased (P < 0.05). The preserved egg white had higher a* (redness/greenness) and b* values (yellowness/blueness; P < 0.05) and lower L* value (lightness; P < 0.05) than hard-cooked egg white. The gel hardness of preserved egg white was approximately 50% of hard-cooked egg white; however, its springiness and cohesiveness were approximately 1.5 times of hard-cooked egg white. The results indicated that pickling with alkaline and other additives can significantly change physical properties and chemical composition of duck egg white, which make preserved egg white with characteristics of rich elements, brown color, and high springiness, but low vitamin. PMID:25332139
ERIC Educational Resources Information Center
Hines, Mack T., III
2016-01-01
This study analyzes the prevalence of white fragility within the six white, pre-service principals' online responses to readings about white privilege. Six white, pre-service principals were asked to provide commentary to class readings on the relevance of white privilege to their preparation for future positions as principals. The findings showed…
NASA Astrophysics Data System (ADS)
Baker, C. R.; Chao, I. F.
1990-10-01
The additive infinite-dimensional Gaussian channel subject to jamming is modeled as a two-person zero-sum game with mutual information as the payoff function. The jammer's noise is added to the ambient Gaussian noise. The coder's signal energy is subject to a constraint is necessary in order that the capacity without feedback be finite. It is shown that use of this same RKHS constraint on the jammer's process is too strong; the jammer would then not be able to reduce capacity, regardless of the amount of jamming energy available. The constraint on the jammer is thus on the total jamming energy, without regard to its distribution relative to that of the ambient noise energy. The existence of a saddle value for the problem does not follow from the von Neuman minimax theorem in the original problem formulation. However, a solution is shown to exist. A saddle point, saddle value, and the jammer's minimax strategy are determined. The solution is a function of the problem parameters: the constraint on the coder, the constraint on the jammer, and the covariance of the ambient Gaussian noise.
Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes.
Soh, Harold; Demiris, Yiannis
2015-03-01
Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair. PMID:25720008
Probabilistic inference using linear Gaussian importance sampling for hybrid Bayesian networks
NASA Astrophysics Data System (ADS)
Sun, Wei; Chang, K. C.
2005-05-01
Probabilistic inference for Bayesian networks is in general NP-hard using either exact algorithms or approximate methods. However, for very complex networks, only the approximate methods such as stochastic sampling could be used to provide a solution given any time constraint. There are several simulation methods currently available. They include logic sampling (the first proposed stochastic method for Bayesian networks, the likelihood weighting algorithm) the most commonly used simulation method because of its simplicity and efficiency, the Markov blanket scoring method, and the importance sampling algorithm. In this paper, we first briefly review and compare these available simulation methods, then we propose an improved importance sampling algorithm called linear Gaussian importance sampling algorithm for general hybrid model (LGIS). LGIS is aimed for hybrid Bayesian networks consisting of both discrete and continuous random variables with arbitrary distributions. It uses linear function and Gaussian additive noise to approximate the true conditional probability distribution for continuous variable given both its parents and evidence in a Bayesian network. One of the most important features of the newly developed method is that it can adaptively learn the optimal important function from the previous samples. We test the inference performance of LGIS using a 16-node linear Gaussian model and a 6-node general hybrid model. The performance comparison with other well-known methods such as Junction tree (JT) and likelihood weighting (LW) shows that LGIS-GHM is very promising.
The Non-Gaussian Nature of Prostate Motion Based on Real-Time Intrafraction Tracking
Lin, Yuting; Liu, Tian; Yang, Wells; Yang, Xiaofeng; Khan, Mohammad K.
2013-10-01
Purpose: The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Methods and Materials: Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including all fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. Results: There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Conclusions: Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to
Capacity and optimal collusion attack channels for Gaussian fingerprinting games
NASA Astrophysics Data System (ADS)
Wang, Ying; Moulin, Pierre
2007-02-01
In content fingerprinting, the same media covertext - image, video, audio, or text - is distributed to many users. A fingerprint, a mark unique to each user, is embedded into each copy of the distributed covertext. In a collusion attack, two or more users may combine their copies in an attempt to "remove" their fingerprints and forge a pirated copy. To trace the forgery back to members of the coalition, we need fingerprinting codes that can reliably identify the fingerprints of those members. Researchers have been focusing on designing or testing fingerprints for Gaussian host signals and the mean square error (MSE) distortion under some classes of collusion attacks, in terms of the detector's error probability in detecting collusion members. For example, under the assumptions of Gaussian fingerprints and Gaussian attacks (the fingerprinted signals are averaged and then the result is passed through a Gaussian test channel), Moulin and Briassouli1 derived optimal strategies in a game-theoretic framework that uses the detector's error probability as the performance measure for a binary decision problem (whether a user participates in the collusion attack or not); Stone2 and Zhao et al. 3 studied average and other non-linear collusion attacks for Gaussian-like fingerprints; Wang et al. 4 stated that the average collusion attack is the most efficient one for orthogonal fingerprints; Kiyavash and Moulin 5 derived a mathematical proof of the optimality of the average collusion attack under some assumptions. In this paper, we also consider Gaussian cover signals, the MSE distortion, and memoryless collusion attacks. We do not make any assumption about the fingerprinting codes used other than an embedding distortion constraint. Also, our only assumptions about the attack channel are an expected distortion constraint, a memoryless constraint, and a fairness constraint. That is, the colluders are allowed to use any arbitrary nonlinear strategy subject to the above
NASA Astrophysics Data System (ADS)
Ye, Chuyang; Bazin, Pierre-Louis; Bogovic, John A.; Ying, Sarah H.; Prince, Jerry L.
2012-02-01
The cerebellar peduncles are white matter tracts that play an important role in the communication of the cerebellum with other regions of the brain. They can be grouped into three fiber bundles: inferior cerebellar peduncle middle cerebellar peduncle, and superior cerebellar peduncle. Their automatic segmentation on diffusion tensor images would enable a better understanding of the cerebellum and would be less time-consuming and more reproducible than manual delineation. This paper presents a method that automatically labels the three fiber bundles based on the segmentatin results from the diffusion oriented tract segmentation (DOTS) algorithm, which achieves volume segmentation of white matter tracts using a Markov random field (MRF) framework. We use the DOTS labeling result as a guide to determine the classification of fibers produced by wild bootstrap probabilistic tractography. Mean distances from each fiber to each DOTS volume label are defined and then used as features that contribute to classification. A supervised Gaussian classifier is employed to label the fibers. Manually delineated cerebellar peduncles serve as training data to determine the parameters of class probabilities for each label. Fibers are labeled ad the class that has the highest posterior probability. An outlier detection ste[ re,pves fober tracts that belong to noise of that are not modeled by DOTS. Experiments show a successful classification of the cerebellar peduncles. We have also compared results between successive scans to demonstrate the reproducibility of the proposed method.
Blakeslee, Barbara; Cope, Davis; McCourt, Mark E
2016-03-01
The Oriented Difference of Gaussians (ODOG) model of brightness (perceived intensity) by Blakeslee and McCourt (Vision Research 39:4361-4377, 1999), which is based on linear spatial filtering by oriented receptive fields followed by contrast normalization, has proven highly successful in parsimoniously predicting the perceived intensity (brightness) of regions in complex visual stimuli such as White's effect, which had been believed to defy filter-based explanations. Unlike competing explanations such as anchoring theory, filling-in, edge-integration, or layer decomposition, the spatial filtering approach embodied by the ODOG model readily accounts for the often overlooked but ubiquitous gradient structure of induction which, while most striking in grating induction, also occurs within the test fields of classical simultaneous brightness contrast and the White stimulus. Also, because the ODOG model does not require defined regions of interest, it is generalizable to any stimulus, including natural images. The ODOG model has motivated other researchers to develop modified versions (LODOG and FLODOG), and has served as an important counterweight and proof of concept to constrain high-level theories which rely on less well understood or justified mechanisms such as unconscious inference, transparency, perceptual grouping, and layer decomposition. Here we provide a brief but comprehensive description of the ODOG model as it has been implemented since 1999, as well as working Mathematica (Wolfram, Inc.) notebooks which users can employ to generate ODOG model predictions for their own stimuli.
Gaussianization for fast and accurate inference from cosmological data
NASA Astrophysics Data System (ADS)
Schuhmann, Robert L.; Joachimi, Benjamin; Peiris, Hiranya V.
2016-06-01
We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box-Cox transformations and generalizations thereof. This permits an analytical reconstruction of the posterior from a point sample, like a Markov chain, and simplifies the subsequent joint analysis with other experiments. This way, a multivariate posterior density can be reported efficiently, by compressing the information contained in Markov Chain Monte Carlo samples. Further, the model evidence integral (i.e. the marginal likelihood) can be computed analytically. This method is analogous to the search for normal parameters in the cosmic microwave background, but is more general. The search for the optimally Gaussianizing transformation is performed computationally through a maximum-likelihood formalism; its quality can be judged by how well the credible regions of the posterior are reproduced. We demonstrate that our method outperforms kernel density estimates in this objective. Further, we select marginal posterior samples from Planck data with several distinct strongly non-Gaussian features, and verify the reproduction of the marginal contours. To demonstrate evidence computation, we Gaussianize the joint distribution of data from weak lensing and baryon acoustic oscillations, for different cosmological models, and find a preference for flat Λcold dark matter. Comparing to values computed with the Savage-Dickey density ratio, and Population Monte Carlo, we find good agreement of our method within the spread of the other two.
Kurtosis, skewness, and non-Gaussian cosmological density perturbations
NASA Technical Reports Server (NTRS)
Luo, Xiaochun; Schramm, David N.
1993-01-01
Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
Consistency relations for sharp inflationary non-Gaussian features
NASA Astrophysics Data System (ADS)
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex
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.
Reactive power in the full Gaussian light wave.
Seshadri, S R
2009-11-01
The electric current sources that are required for the excitation of the fundamental Gaussian beam and the corresponding full Gaussian light wave are determined. The current sources are situated on the secondary source plane that forms the boundary between the two half-spaces in which the waves are launched. The electromagnetic fields and the complex power generated by the current sources are evaluated. For the fundamental Gaussian beam, the reactive power vanishes, and the normalization is chosen such that the real power is 2 W. The various full Gaussian waves are identified by the length parameter b(t) that lies in the range 0 < or = b(t) < or = b, where b is the Rayleigh distance. The other parameters are the wavenumber k, the free-space wavelength lambda, and the beam waist w0 at the input plane. The dependence of the real power of the full Gaussian light wave on b(t)/b and w0/lambda is examined. For a specified w0/lambda, the reactive power, which can be positive or negative, increases as b(t)/b is increased from 0 to 1 and becomes infinite for b(t)/b=1. For a specified b(t)/b, the reactive power approaches zero as kw0 is increased and reaches the limiting value of zero of the paraxial beam.
Large Non-Gaussianity from Multi-Brid Inflation
NASA Astrophysics Data System (ADS)
Naruko, A.; Sasaki, M.
2009-01-01
A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.
The Gaussian CLs method for searches of new physics
NASA Astrophysics Data System (ADS)
Qian, X.; Tan, A.; Ling, J. J.; Nakajima, Y.; Zhang, C.
2016-08-01
We describe a method based on the CLs approach to present results in searches of new physics, under the condition that the relevant parameter space is continuous. Our method relies on a class of test statistics developed for non-nested hypotheses testing problems, denoted by ΔT, which has a Gaussian approximation to its parent distribution when the sample size is large. This leads to a simple procedure of forming exclusion sets for the parameters of interest, which we call the Gaussian CLs method. Our work provides a self-contained mathematical proof for the Gaussian CLs method that explicitly outlines the required conditions. These conditions are milder than that required by Wilks' theorem to set confidence intervals (CIs). We illustrate the Gaussian CLs method in an example of searching for a sterile neutrino, where the CLs approach was rarely used before. We also compare data analysis results produced by the Gaussian CLs method and various CI methods to showcase their differences.
Non-gaussian mode coupling and the statistical cosmological principle
LoVerde, Marilena; Nelson, Elliot; Shandera, Sarah E-mail: eln121@psu.edu
2013-06-01
Local-type primordial non-Gaussianity couples statistics of the curvature perturbation ζ on vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of ζ in our Hubble volume may not be representative of those in the larger universe — that is, they may be biased. The bias depends on the local background value of ζ, which includes contributions from all modes with wavelength k∼
Non-Gaussian error distribution of 7Li abundance measurements
NASA Astrophysics Data System (ADS)
Crandall, Sara; Houston, Stephen; Ratra, Bharat
2015-07-01
We construct the error distribution of 7Li abundance measurements for 66 observations (with error bars) used by Spite et al. (2012) that give A(Li) = 2.21 ± 0.065 (median and 1σ symmetrized error). This error distribution is somewhat non-Gaussian, with larger probability in the tails than is predicted by a Gaussian distribution. The 95.4% confidence limits are 3.0σ in terms of the quoted errors. We fit the data to four commonly used distributions: Gaussian, Cauchy, Student’s t and double exponential with the center of the distribution found with both weighted mean and median statistics. It is reasonably well described by a widened n = 8 Student’s t distribution. Assuming Gaussianity, the observed A(Li) is 6.5σ away from that expected from standard Big Bang Nucleosynthesis (BBN) given the Planck observations. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to 4.9σ, which is still significant.
NASA Technical Reports Server (NTRS)
2008-01-01
This image of White Rock in Pollack crater was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) on February 3, 2007 at 1750 UTC (12:50 p.m. EST), near 8 degrees south latitude, 25 degrees east longitude. The CRISM image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 40 meters (132 feet) across. The region covered is roughly 20 kilometers (12 miles) long and 10 kilometers (6 miles) wide at its narrowest point.
First imaged by the Mariner 9 spacecraft in 1972, the enigmatic group of wind-eroded ridges known as White Rock has been the subject of many subsequent investigations. White Rock is located on the floor of Pollack Crater in the Sinus Sabaeus region of Mars. It measures some 15 by 18 kilometers (9 by 11 miles) and was named for its light-colored appearance. In contrast-enhanced images, the feature's higher albedo or reflectivity compared with the darker material on the floor of the crater makes it appear white. In reality, White Rock has a dull, reddish color more akin to Martian dust. This higher albedo as well as its location in a topographic low suggested to some researchers that White Rock may be an eroded remnant of an ancient lake deposit. As water in a desert lake on Earth evaporates, it leaves behind white-colored salts that it leached or dissolved out of the surrounding terrain. These salt deposits may include carbonates, sulfates, and chlorides.
In 2001, the Thermal Emission Spectrometer (TES) on NASA's Mars Global Surveyor measured White Rock and found no obvious signature of carbonates or sulfates, or any other indication that White Rock holds evaporite minerals. Instead, it found Martian dust.
CRISM's challenge was to obtain greater detail of White Rock's mineralogical composition and how it formed. The instrument operates at a different wavelength range than TES, giving it greater sensitivity to carbonate, sulfate and phyllosilicate (clay-like) minerals. It also
NASA Astrophysics Data System (ADS)
Hawley, Wendy Phyllis
2012-01-01
3D models of white dwarf collisions are used to assess the likelihood of double-degenerate mergers as progenitors for Type Ia supernovae (henceforth SNIa) and to identify observational signatures of double-degenerate collisions. Observations of individual SNIa, SNIa rates in different galaxy types, and double white dwarf binary systems suggest that mergers or collisions between two white dwarfs play a role in the overall SNIa population. Given the possibility of two progenitor systems (single-degenerate and double-degenerate), the sample of SNIa used in cosmological calcula- tions needs to be carefully examined. To improve calculations of cosmological parameters, the development of calibrated diagnostics for double-degenerate progenitor SNIa is essential. Head-on white dwarf collision simulations are used to provide an upper limit on the 56Ni production in white dwarf collisions. In chapter II, I explore zero impact parameter collisions of white dwarfs using the Eulerian grid code FLASH. The initial 1D white dwarf profiles are created assuming hydrostatic equilibrium and a uniform composition of 50% 12C and 50% 16O. The masses range from 0.64 to 0.81 solar masses and have an isothermal temperature of 107 K. I map these 1D models onto a 3D grid, where the dimensions of the grid are each eight times the white dwarf radius, and the dwarfs are initially placed four white dwarf radii apart (center to center). To provide insight into a larger range of physical possibilities, I also model non-zero impact parameter white dwarf collisions (Chapter III). Although head-on white dwarf collisions provide an upper limit on 56Ni production, non-zero impact parameter collisions provide insight into a wider range of physical scenarios. The initial conditions (box size, initial separation, composition, and initial temperature) are identical to those used for the head-on collisions (Chapter II) for the same range of masses. For each mass pair- ing, collision simulations are carried
White Racial Identity Statuses as Predictors of White Privilege Awareness
ERIC Educational Resources Information Center
Hays, Danica G.; Chang, Catherine Y.; Havice, Pamela
2008-01-01
This study explored the relationship between White privilege awareness and White racial identity development for 197 counseling trainees. Results indicated that 3 of J. E. Helms's (1984, 1990, 1995) White racial identity statuses (i.e., Contact, Reintegration, and Immersion/Emersian) significantly predicted White privilege awareness. Implications…
ERIC Educational Resources Information Center
Comer, James P.
Black and white conflict is a by-product of a more basic problem: the failure of this society to develop a social system that enables all people to meet their basic human needs at a reasonable level. Until this is done, we will not be able to move beyond black and white. The underlying problem is related to a sudden acceleration of human history…
Stochastic model updating utilizing Bayesian approach and Gaussian process model
NASA Astrophysics Data System (ADS)
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
A sparse Gaussian process framework for photometric redshift estimation
NASA Astrophysics Data System (ADS)
Almosallam, Ibrahim A.; Lindsay, Sam N.; Jarvis, Matt J.; Roberts, Stephen J.
2016-01-01
Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Synthetic data set simulating the Euclid survey and real data from SDSS DR12 are used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms use the minimization of the sum of squared errors as the objective function. For redshift inference, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper, we directly minimize the target metric Δz = (zs - zp)/(1 + zs) and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as artificial neural networks (ANN), Gaussian processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute Δz = 0.0026(1 + zs), over the redshift range of 0 ≤ zs ≤ 2 on the simulated data, and Δz = 0.0178(1 + zs) over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNz used in the literature. We also investigate how the relative size of the training sample affects the photometric redshift accuracy. We find that a training sample of >30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNz in the sparse data regime for the simulated data set.
Scattering of polarized Gaussian light by a spheroidal particle
NASA Astrophysics Data System (ADS)
Sun, Xianming; Xiao, Sai; Ma, Lixiu; Su, Baochen
2015-02-01
Light scattering by a small particle can produce light with polarization characteristics different from those of the incident beam. In this article, we studied the polarized Gaussian beam scattered by a spheroidal particle within the generalized Lorenz-Mie theory framework. A theoretical procedure is given to expand an incident Gaussian beam in terms of spheroidal vector wave functions. We studied the single scattering properties of a single spheroidal particle with varying aspect ratios and size parameters. Exact analytic solutions are obtained for computing the amplitude matrix and single scattering Muller matrix for a single spheroid with normal illumination. The Muller scattering matrix elements of a single spheroid are compared between plane wave and Gaussian light beam as incident light source.
Best approximation of Gaussian neural networks with nodes uniformly spaced.
Mulero-Martinez, J I
2008-02-01
This paper is aimed at exposing the reader to certain aspects in the design of the best approximants with Gaussian radial basis functions (RBFs). The class of functions to which this approach applies consists of those compactly supported in frequency. The approximative properties of uniqueness and existence are restricted to this class. Functions which are smooth enough can be expanded in Gaussian series converging uniformly to the objective function. The uniqueness of these series is demonstrated by the context of the orthonormal basis in a Hilbert space. Furthermore, the best approximation to a given band-limited function from a truncated Gaussian series is analyzed by an energy-based argument. This analysis not only gives a theoretical proof concerned with the existence of best approximations but addresses the problems of architectural selection. Specifically, guidance for selecting the variance and the oversampling parameters is provided for practitioners. PMID:18269959
Effects of non-Gaussian noise near supercritical Hopf bifurcation
NASA Astrophysics Data System (ADS)
Zhang, Ruiting; Hou, Zhonghuai; Xin, Houwen
2011-01-01
We have studied the effects of non-Gaussian colored noise in a chemical oscillation system, the well-known Brusselator model, in the parameter region close to the supercritical Hopf bifurcation. With the variation of the parameter q, which quantifies the deviation from Gaussian character, the signal-to-noise ratio of noise induced oscillation exhibits a bell-shaped change, indicating the presence of resonant activity. The cooperative effects of q and the correlation time τ on the performance of noise induced oscillation are also investigated. Interestingly, resonance-like behavior can be induced by either q or τ when the other parameter is properly fixed. Stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced. This work provides us comprehensive understanding of how non-Gaussian noise influences the dynamics in chemical oscillation systems.
Quantum Entanglement and Quantum Discord in Gaussian Open Systems
Isar, Aurelian
2011-10-03
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 entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. 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 quantum discord decays asymptotically in time under the effect of the thermal bath.
Non-Gaussian isocurvature perturbations in dark radiation
Kawakami, Etsuko; Kawasaki, Masahiro; Miyamoto, Koichi; Nakayama, Kazunori; Sekiguchi, Toyokazu E-mail: kawasaki@icrr.u-tokyo.ac.jp E-mail: kazunori@hep-th.phys.s.u-tokyo.ac.jp
2012-07-01
We study non-Gaussian properties of the isocurvature perturbations in the dark radiation, which consists of the active neutrinos and extra light species, if exist. We first derive expressions for the bispectra of primordial perturbations which are mixtures of curvature and dark radiation isocurvature perturbations. We also discuss CMB bispectra produced in our model and forecast CMB constraints on the non-linearity parameters based on the Fisher matrix analysis. Some concrete particle physics motivated models are presented in which large isocurvature perturbations in extra light species and/or the neutrino density isocurvature perturbations as well as their non-Gaussianities may be generated. Thus detections of non-Gaussianity in the dark radiation isocurvature perturbation will give us an opportunity to identify the origin of extra light species and lepton asymmetry.
Continuous-variable quantum teleportation with non-Gaussian resources
Dell'Anno, F.; De Siena, S.; Albano, L.; Illuminati, F.
2007-08-15
We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity.
Controllably accelerating and decelerating Airy–Bessel–Gaussian wave packets
NASA Astrophysics Data System (ADS)
Deng, Fu; Yu, Weihao; Deng, Dongmei
2016-11-01
By solving the (3 + 1)D free-space Schrödinger equation in polar coordinates analytically, we have investigated the propagation of 3D controllably accelerating and decelerating Airy–Bessel–Gaussian (CAiBG) wave packets, even CAiBG wave packets, odd CAiBG wave packets and the superposition of several CAiBG wave packets in free space. The CAiBG wave packets are constructed with the Airy pulses with initial velocity in temporal domain and the Bessel–Gaussian beams in space domain. Due to the initial velocity on Airy pulses, we can obtain decelerating and accelerating Airy–Bessel–Gaussian wave packets by selecting different initial velocities. Moreover, by superposing several CAiBG wave packets, we can obtain the rotating wave packets.
Recurrence plots of discrete-time Gaussian stochastic processes
NASA Astrophysics Data System (ADS)
Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick
2016-09-01
We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.
Neutrino mixing and mass hierarchy in Gaussian landscapes
Hall, Lawrence J.; Salem, Michael P.; Watari, Taizan
2009-01-15
The flavor structure of the standard model may arise from random selection on a landscape. In a class of simple models, called ''Gaussian landscapes,'' Yukawa couplings derive from overlap integrals of Gaussian zero-mode wave functions on an extra-dimensional space. Statistics of vacua are generated by scanning the peak positions of these wave functions, giving probability distributions for all flavor observables. Gaussian landscapes can account for all of the major features of flavor, including both the small electroweak mixing in the quark sector and the large mixing observed in the lepton sector. We find that large lepton mixing stems directly from lepton doublets having broad wave functions on the internal manifold. Assuming the seesaw mechanism, we find the mass hierarchy among neutrinos is sensitive to the number of right-handed neutrinos and can provide a good fit to neutrino oscillation measurements.
Renormalized Newtonian cosmic evolution with primordial non-Gaussianity
Izumi, Keisuke; Soda, Jiro
2007-10-15
We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affects the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wave number. On the other hand, the negative skewness gives the opposite result.
Gaussian geometric discord in terms of Hellinger distance
Suciu, Serban Isar, Aurelian
2015-12-07
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.
Qubit Noise Spectroscopy for Non-Gaussian Dephasing Environments.
Norris, Leigh M; Paz-Silva, Gerardo A; Viola, Lorenza
2016-04-15
We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.
Non-Gaussianity from tachyonic preheating in hybrid inflation
Barnaby, Neil; Cline, James M.
2007-04-15
In a previous work we showed that large non-Gaussianities and nonscale-invariant distortions in the cosmic microwave background power spectrum can be generated in hybrid inflation models, due to the contributions of the tachyon (waterfall) field to the second order curvature perturbation. Here we clarify, correct, and extend those results. We show that large non-Gaussianity occurs only when the tachyon remains light throughout inflation, whereas n=4 contamination to the spectrum is the dominant effect when the tachyon is heavy. We find constraints on the parameters of warped-throat brane-antibrane inflation from non-Gaussianity. For F-term and D-term inflation models from supergravity, we obtain nontrivial constraints from the spectral distortion effect. We also establish that our analysis applies to complex tachyon fields.
Local non-Gaussianity from rapidly varying sound speeds
Emery, Jon; Tasinato, Gianmassimo; Wands, David E-mail: gianmassimo.tasinato@port.ac.uk
2012-08-01
We study the effect of non-trivial sound speeds on local-type non-Gaussianity during multiple-field inflation. To this end, we consider a multiple-DBI model and use the δN formalism to track the super-horizon evolution of perturbations. By adopting a sum separable Hubble parameter we derive analytic expressions for the relevant quantities in the two-field case, valid beyond slow variation. We find that non-trivial sound speeds can, in principle, curve the trajectory in such a way that significant local-type non-Gaussianity is produced. Deviations from slow variation, such as rapidly varying sound speeds, enhance this effect. To illustrate our results we consider two-field inflation in the tip regions of two warped throats and find large local-type non-Gaussianity produced towards the end of the inflationary process.
Anomalous structure and dynamics of the Gaussian-core fluid.
Krekelberg, William P; Kumar, Tanuj; Mittal, Jeetain; Errington, Jeffrey R; Truskett, Thomas M
2009-03-01
It is known that there are thermodynamic states for which the Gaussian-core fluid displays anomalous properties such as expansion upon isobaric cooling (density anomaly) and increased single-particle mobility upon isothermal compression (self-diffusivity anomaly). Here, we investigate how temperature and density affect its short-range translational structural order, as characterized by the two-body excess entropy. We find that there is a wide range of conditions for which the short-range translational order of the Gaussian-core fluid decreases upon isothermal compression (structural order anomaly). As we show, the origin of the structural anomaly is qualitatively similar to that of other anomalous fluids (e.g., water or colloids with short-range attractions) and is connected to how compression affects static correlations at different length scales. Interestingly, we find that the self-diffusivity of the Gaussian-core fluid obeys a scaling relationship with the two-body excess entropy that is very similar to the one observed for a variety of simple liquids. One consequence of this relationship is that the state points for which structural, self-diffusivity, and density anomalies of the Gaussian-core fluid occur appear as cascading regions on the temperature-density plane; a phenomenon observed earlier for models of waterlike fluids. There are, however, key differences between the anomalies of Gaussian-core and waterlike fluids, and we discuss how those can be qualitatively understood by considering the respective interparticle potentials of these models. Finally, we note that the self-diffusivity of the Gaussian-core fluid obeys different scaling laws depending on whether the two-body or total excess entropy is considered. This finding, which deserves more comprehensive future study, appears to underscore the significance of higher-body correlations for the behavior of fluids with bounded interactions. PMID:19391927
Economical Gaussian cloning of coherent states with known phase
Dong Yuli; Zou Xubo; Guo Guangcan; Li Shangbin
2007-07-15
We investigate the economical Gaussian cloning of coherent states with the known phase, which produces M copies from N input replica and can be implemented with degenerate parametric amplifiers and beam splitters.The achievable fidelity of single copy is given by 2M{radical}(N)/[{radical}(N)(M-1)+{radical}((1+N)(M{sup 2}+N))], which is bigger than the optimal fidelity of the universal Gaussian cloning. The cloning machine presented here works without ancillary optical modes and can be regarded as the continuous variable generalization of the economical cloning machine for qudits.
Improving entanglement concentration of Gaussian states by local displacements
Fiurasek, Jaromir
2011-07-15
We investigate entanglement concentration of continuous-variable Gaussian states by local single-photon subtractions combined with local Gaussian operations. We first analyze the local squeezing-enhanced entanglement-concentration protocol proposed very recently by Zhang and van Loock [arXiv:1103.4500] and discuss the mechanism by which local squeezing before photon subtraction helps to increase the entanglement of the output state of the protocol. We next show that a similar entanglement improvement can be achieved by using local coherent displacements instead of single-mode squeezing.
Moving target detection algorithm based on Gaussian mixture model
NASA Astrophysics Data System (ADS)
Wang, Zhihua; Kai, Du; Zhang, Xiandong
2013-07-01
In real-time video surveillance system, background noise and disturbance for the detection of moving objects will have a significant impact. The traditional Gaussian mixture model;GMM&;has strong adaptive various complex background ability, but slow convergence speed and vulnerable to illumination change influence. the paper proposes an improved moving target detection algorithm based on Gaussian mixture model which increase the convergence rate of foreground to the background model transformation and introducing the concept of the changing factors, through the three frame differential method solved light mutation problem. The results show that this algorithm can improve the accuracy of the moving object detection, and has good stability and real-time.
Trans-Planckian enhancements of the primordial non-Gaussianities
Collins, Hael; Holman, R.
2009-08-15
This article examines how breaking a Lorentz-invariant description of nature at tiny space-time intervals would affect the non-Gaussian character of the pattern of primordial perturbations left by inflation. We specifically study a set of irrelevant operators that preserve the spatial symmetries of the usual inflationary background. The non-Gaussian component in the primordial fluctuations can be much larger than the usual, small, inflationary prediction and can thus lead to much stronger constraints on the role of 'trans-Planckian' physics in inflation than those from the measurements of the primordial power spectrum.
A new method for generating a hollow Gaussian beam
NASA Astrophysics Data System (ADS)
Wei, Cun; Lu, Xingyuan; Wu, Gaofeng; Wang, Fei; Cai, Yangjian
2014-04-01
Hollow Gaussian beam (HGB) was introduced 10 years ago (Cai et al. in Opt Lett 28:1084, 2003). In this paper, we introduce a new method for generating a HGB through transforming a Laguerre-Gaussian beam with radial index 0 and azimuthal index l into a HGB with mode n = l/2. Furthermore, we report experimental generation of a HGB based on the proposed method, and we carry out experimental study of the focusing properties of the generated HGB. Our experimental results agree well with the theoretical predictions.
Fractionalization of optical beams: II. Elegant Laguerre Gaussian modes
NASA Astrophysics Data System (ADS)
Gutiérrez-Vega, Julio C.
2007-05-01
We apply the tools of fractional calculus to introduce new fractional-order solutions of the paraxial wave equation that smoothly connect the elegant Laguerre-Gaussian beams of integral-order. The solutions are characterized in general by two fractional indices and are obtained by fractionalizing the creation operators used to create elegant Laguerre-Gauss beams from the fundamental Gaussian beam. The physical and mathematical properties of the circular fractional beams are discussed in detail. The orbital angular momentum carried by the fractional beam is a continuous function of the angular mode index and it is not restricted to take only discrete values.
Statistical naturalness and non-gaussianity in a finite universe.
Nelson, Elliot; Shandera, Sarah
2013-03-29
We study the behavior of n-point functions of the primordial curvature perturbations, assuming our observed Universe is only a subset of a larger space with statistically homogeneous and isotropic perturbations. If the larger space has arbitrary n-point functions in a family of local type non-gaussian statistics, sufficiently biased smaller volumes will have statistics from a "natural" version of that family with moments that are weakly non-gaussian and ordered, regardless of the statistics of the original field. We also describe the effect of this bias on the shape of the bispectrum.
Nonclassicality Invariant of General Two-Mode Gaussian States
NASA Astrophysics Data System (ADS)
Arkhipov, Ievgen I.; Peřina, Jan, Jr.; Svozilík, Jiří; Miranowicz, Adam
2016-05-01
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
NASA Astrophysics Data System (ADS)
Kotlyar, V. V.; Kovalev, A. A.; Porfirev, A. P.
2016-07-01
We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.
Nonclassicality Invariant of General Two-Mode Gaussian States
Arkhipov, Ievgen I.; Peřina Jr., Jan; Svozilík, Jiří; Miranowicz, Adam
2016-01-01
We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given. PMID:27210547
Non-Gaussianities from the Standard Model Higgs
Simone, Andrea De; Perrier, Hideki; Riotto, Antonio E-mail: hideki.perrier@unige.ch
2013-01-01
We have recently proposed that the Standard Model Higgs might be responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In this paper we study the level of non-Gaussianity in the cosmological perturbations which are inevitably generated due to the non-linearities of the Standard Model Higgs potential. In particular, for the current central value of the top mass, we find that a future detection of non-Gaussianity would exclude the detection of tensor modes by the PLANCK satellite.
Non-gaussian statistics of pencil beam surveys
NASA Technical Reports Server (NTRS)
Amendola, Luca
1994-01-01
We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.
Gaussian beam scattering by a gyrotropic anisotropic object
NASA Astrophysics Data System (ADS)
Chen, Zhenzhen; Zhang, Huayong; Wu, Xianliang; Huang, Zhixiang
2016-09-01
An exact semi-analytical solution is presented to the scattering of an on-axis Gaussian beam incident on a gyrotropic anisotropic object. The on-axis incident Gaussian beam, scattered fields as well as internal fields are expanded in terms of appropriate spherical vector wave functions, and the unknown expansion coefficients of the scattered fields are determined by virtue of Schelkunoff's equivalence theorem and electromagnetic boundary conditions. Numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.
Local features with large spiky non-Gaussianities during inflation
Abolhasani, Ali Akbar; Firouzjahi, Hassan; Khosravi, Shahram; Sasaki, Misao E-mail: firouz@mail.ipm.ir E-mail: misao@yukawa.kyoto-u.ac.jp
2012-11-01
We provide a dynamical mechanism to generate localized features during inflation. The local feature is due to a sharp waterfall phase transition which is coupled to the inflaton field. The key effect is the contributions of waterfall quantum fluctuations which induce a sharp peak on the curvature perturbation which can be as large as the background curvature perturbation from inflaton field. Due to non-Gaussian nature of waterfall quantum fluctuations a large spike non-Gaussianity is produced which is narrowly peaked at modes which leave the Hubble radius at the time of phase transition. The large localized peaks in power spectrum and bispectrum can have interesting consequences on CMB anisotropies.
Mock LISA data challenge for the Galactic white dwarf binaries
Blaut, Arkadiusz; Babak, Stanislav; Krolak, Andrzej
2010-03-15
We present data analysis methods used in the detection and estimation of parameters of gravitational-wave signals from the white dwarf binaries in the mock LISA data challenge. Our main focus is on the analysis of challenge 3.1, where the gravitational-wave signals from more than 6x10{sup 7} Galactic binaries were added to the simulated Gaussian instrumental noise. The majority of the signals at low frequencies are not resolved individually. The confusion between the signals is strongly reduced at frequencies above 5 mHz. Our basic data analysis procedure is the maximum likelihood detection method. We filter the data through the template bank at the first step of the search, then we refine parameters using the Nelder-Mead algorithm, we remove the strongest signal found and we repeat the procedure. We detect reliably and estimate parameters accurately of more than ten thousand signals from white dwarf binaries.
White matter injury detection in neonatal MRI
NASA Astrophysics Data System (ADS)
Cheng, Irene; Hajari, Nasim; Firouzmanesh, Amirhossein; Shen, Rui; Miller, Steven; Poskitt, Ken; Basu, Anup
2013-02-01
Early detection of white matter injury in premature newborns can facilitate timely clinical treatments reducing the potential risk of later developmental deficits. It was reported that there were more than 5% premature newborns in British Columbia, Canada, among which 5-10% exhibited major motor deficits and 25-50% exhibited significant developmental and visual deficits. With the advancement of computer assisted detection systems, it is possible to automatically identify white matter injuries, which are found inside the grey matter region of the brain. Atlas registration has been suggested in the literature to distinguish grey matter from the soft tissues inside the skull. However, our subjects are premature newborns delivered at 24 to 32 weeks of gestation. During this period, the grey matter undergoes rapid changes and differs significantly from one to another. Besides, not all detected white spots represent injuries. Additional neighborhood information and expert input are required for verification. In this paper, we propose a white matter feature identification system for premature newborns, which is composed of several steps: (1) Candidate white matter segmentation; (2) Feature extraction from candidates; (3) Validation with data obtained at a later stage on the children; and (4) Feature confirmation for automated detection. The main challenge of this work lies in segmenting white matter injuries from noisy and low resolution data. Our approach integrates image fusion and contrast enhancement together with a fuzzy segmentation technique to achieve promising results. Other applications, such as brain tumor and intra-ventricular haemorrhage detection can also benefit from our approach.
Optimal search in interacting populations: Gaussian jumps versus Lévy flights
NASA Astrophysics Data System (ADS)
Martínez-García, Ricardo; Calabrese, Justin M.; López, Cristóbal
2014-03-01
We investigated the relationships between search efficiency, movement strategy, and nonlocal communication in the biological context of animal foraging. We considered situations where the members of a population of foragers perform either Gaussian jumps or Lévy flights, and show that the search time is minimized when communication among individuals occurs at intermediate ranges, independently of the type of movement. Additionally, while Brownian strategies are more strongly influenced by the communication mechanism, Lévy flights still result in shorter overall search durations.
NASA Astrophysics Data System (ADS)
Li, Xinzhong; Tai, Yuping; Nie, Zhaogang; Wang, Hui; Li, Hehe; Wang, Jingge; Tang, Jie; Wang, Yishan
2015-12-01
We investigate the Fraunhofer diffraction of a Laguerre-Gaussian (LG) beam incident on a dynamic superposed dual-triangular aperture. The evolution of the diffraction pattern from this aperture is analyzed experimentally and theoretically. A special aperture, called the hex-star triangular aperture, demonstrates interesting diffraction patterns. Further, the diffraction properties of integer, half-integer, and fractional orders of topological charges at the Fraunhofer zone are studied by using the hex-star triangular aperture. This study can provide additional information to enhance the understanding of the diffraction properties of the LG beam transmitted through a complex aperture.
The Total Gaussian Class of Quasiprobabilities and its Relation to Squeezed-State Excitations
NASA Technical Reports Server (NTRS)
Wuensche, Alfred
1996-01-01
The class of quasiprobabilities obtainable from the Wigner quasiprobability by convolutions with the general class of Gaussian functions is investigated. It can be described by a three-dimensional, in general, complex vector parameter with the property of additivity when composing convolutions. The diagonal representation of this class of quasiprobabilities is connected with a generalization of the displaced Fock states in direction of squeezing. The subclass with real vector parameter is considered more in detail. It is related to the most important kinds of boson operator ordering. The properties of a specific set of discrete excitations of squeezed coherent states are given.
Application of Gaussian moment method to a gene autoregulation model of rational vector field
NASA Astrophysics Data System (ADS)
Kang, Yan-Mei; Chen, Xi
2016-07-01
We take a lambda expression autoregulation model driven by multiplicative and additive noises as example to extend the Gaussian moment method from nonlinear stochastic systems of polynomial vector field to noisy biochemical systems of rational polynomial vector field. As a direct application of the extended method, we also disclose the phenomenon of stochastic resonance. It is found that the transcription rate can inhibit the stochastic resonant effect, but the degradation rate may enhance the phenomenon. These observations should be helpful in understanding the functional role of noise in gene autoregulation.
Application of Gaussian Process Modeling to Analysis of Functional Unreliability
R. Youngblood
2014-06-01
This paper applies Gaussian Process (GP) modeling to analysis of the functional unreliability of a “passive system.” GPs have been used widely in many ways [1]. The present application uses a GP for emulation of a system simulation code. Such an emulator can be applied in several distinct ways, discussed below. All applications illustrated in this paper have precedents in the literature; the present paper is an application of GP technology to a problem that was originally analyzed [2] using neural networks (NN), and later [3, 4] by a method called “Alternating Conditional Expectations” (ACE). This exercise enables a multifaceted comparison of both the processes and the results. Given knowledge of the range of possible values of key system variables, one could, in principle, quantify functional unreliability by sampling from their joint probability distribution, and performing a system simulation for each sample to determine whether the function succeeded for that particular setting of the variables. Using previously available system simulation codes, such an approach is generally impractical for a plant-scale problem. It has long been recognized, however, that a well-trained code emulator or surrogate could be used in a sampling process to quantify certain performance metrics, even for plant-scale problems. “Response surfaces” were used for this many years ago. But response surfaces are at their best for smoothly varying functions; in regions of parameter space where key system performance metrics may behave in complex ways, or even exhibit discontinuities, response surfaces are not the best available tool. This consideration was one of several that drove the work in [2]. In the present paper, (1) the original quantification of functional unreliability using NN [2], and later ACE [3], is reprised using GP; (2) additional information provided by the GP about uncertainty in the limit surface, generally unavailable in other representations, is discussed
A neural-network based estimator to search for primordial non-Gaussianity in Planck CMB maps
NASA Astrophysics Data System (ADS)
Novaes, C. P.; Bernui, A.; Ferreira, I. S.; Wuensche, C. A.
2015-09-01
We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the SMICA map we found fNL = 33 ± 23, at 1σ confidence level, in excellent agreement with the WMAP-9yr and Planck results. In addition, for the other three Planck maps we obtain similar constraints with values in the interval fNL in [33, 41], concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixel's noise intensities.
A new way of setting the phases for cosmological multiscale Gaussian initial conditions
NASA Astrophysics Data System (ADS)
Jenkins, Adrian
2013-09-01
We describe how to define an extremely large discrete realization of a Gaussian white noise field that has a hierarchical structure and the property that the value of any part of the field can be computed quickly. Tiny subregions of such a field can be used to set the phase information for Gaussian initial conditions for individual cosmological simulations of structure formation. This approach has several attractive features: (i) the hierarchical structure based on an octree is particularly well suited for generating follow-up resimulation or zoom initial conditions; (ii) the phases are defined for all relevant physical scales in advance so that resimulation initial conditions are, by construction, consistent both with their parent simulation and with each other; (iii) the field can easily be made public by releasing a code to compute it - once public, phase information can be shared or published by specifying a spatial location within the realization. In this paper, we describe the principles behind creating such realizations. We define an example called Panphasia and in a companion paper by Jenkins and Booth (2013) make public a code to compute it. With 50 octree levels Panphasia spans a factor of more than 1015 in linear scale - a range that significantly exceeds the ratio of the current Hubble radius to the putative cold dark matter free-streaming scale. We show how to modify a code used for making cosmological and resimulation initial conditions so that it can take the phase information from Panphasia and, using this code, we demonstrate that it is possible to make good quality resimulation initial conditions. We define a convention for publishing phase information from Panphasia and publish the initial phases for several of the Virgo Consortium's most recent cosmological simulations including the 303 billion particle MXXL simulation. Finally, for reference, we give the locations and properties of several dark matter haloes that can be resimulated within these
Probing the cosmological viability of non-gaussian statistics
NASA Astrophysics Data System (ADS)
Nunes, Rafael C.; Barboza, Edésio M., Jr.; Abreu, Everton M. C.; Ananias Neto, Jorge
2016-08-01
Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. The effect of these non-gaussian statistics in the cosmological context is to change the strength of the gravitational constant. In this paper, we consider the wCDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modification with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we will use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data. We show that Tsallis' statistics is favored at 1σ confidence level.
Bayesian Gaussian Copula Factor Models for Mixed Data
Murray, Jared S.; Dunson, David B.; Carin, Lawrence; Lucas, Joseph E.
2013-01-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.1 PMID:23990691
Pseudo-Hermitian ensemble of random Gaussian matrices.
Marinello, G; Pato, M P
2016-07-01
It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate. PMID:27575116
Non-Gaussian microwave background fluctuations from nonlinear gravitational effects
NASA Technical Reports Server (NTRS)
Salopek, D. S.; Kunstatter, G. (Editor)
1991-01-01
Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.
STATISTICS OF TURBULENT FIELD VARIATIONS, NON-GAUSSIANITY AND INTERMITTENCY
Ragot, B. R
2009-05-10
Statistics of magnetic field and velocity variations are important to the study of turbulence. Their departure from Gaussianity on the short separation scales has long been recognized and ascribed to intermittency. Non-Gaussian log-normal statistics of field-line separations are now predicted, however, from simple nonfluctuating turbulence Fourier spectra that do not model any intermittency, and one may wonder how this result may impact our interpretation of the statistics of field variations. It is shown in this paper how the intermittency of the turbulence can be taken into account to estimate the distributions of field-line separations and of field variations from the simple Fourier-spectra calculations. The first accurate theory/modeling predictions for the observed in situ distributions of turbulent field variations are thereby made, free of parameter adjustment. Magnetic field data from Helios 2 and Wind are used for the validation. Because the field variations are measured between points of constant separation and not between real field lines, intermittency remains the main cause for the observed non-Gaussianity of the statistics of field variations on the short scales, even if spatial limitations and/or short-scale phase correlations could also contribute to the deviations from Gaussianity.
Bayesian Gaussian Copula Factor Models for Mixed Data.
Murray, Jared S; Dunson, David B; Carin, Lawrence; Lucas, Joseph E
2013-06-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.
Maneuver tracking using an adaptive Gaussian sum technique
NASA Astrophysics Data System (ADS)
Stubberud, Stephen C.; Kramer, Kathleen A.
2005-03-01
The best method to track through a maneuver is to know the motion model of the maneuvering target. Unfortunately, a priori knowledge of the maneuver is not usually known. If the motion model of the maneuver can be estimated quickly from the measurements then the resulting track estimate will be better than the a priori static model. An adaptive function approximation technique to improve the motion model while tracking is analyzed for its potential to track through various maneuvers. The basic function approximation technique is that of a Gaussian sum. The Gaussian sum approximates the function which represents the error between the initial static model and the actual model of the maneuver. The parameters of the Gaussian sum are identified on-line using a Kalman filter identification scheme. This scheme, used in conjunction with a Kalman filter tracker, creates a coupled technique that can improve the motion model quickly. This adaptive Gaussian sum approach to maneuver tracking has its performance analyzed for three maneuvers. These maneuvers include a maneuvering ballistic target, a target going through an s-curve, and real target with a multiple racetrack flight path. The results of these test cases demonstrate the capabilities of this approach to track maneuvering targets.
Gaussian quantum steering and its asymmetry in curved spacetime
NASA Astrophysics Data System (ADS)
Wang, Jieci; Cao, Haixin; Jing, Jiliang; Fan, Heng
2016-06-01
We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a "sudden death" and the steering from anti-Bob to Bob experiences a "sudden birth" with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln 2 , which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) s =arccosh cosh/2r 1 -sinh2r is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.
Extreme value statistics of smooth Gaussian random fields
NASA Astrophysics Data System (ADS)
Colombi, Stéphane; Davis, Olaf; Devriendt, Julien; Prunet, Simon; Silk, Joe
2011-07-01
We consider the Gumbel or extreme value statistics describing the distribution function pG(νmax) of the maximum values of a random field ν within patches of fixed size. We present, for smooth Gaussian random fields in two and three dimensions, an analytical estimate of pG which is expected to hold in a regime where local maxima of the field are moderately high and weakly clustered. When the patch size becomes sufficiently large, the negative of the logarithm of the cumulative extreme value distribution is simply equal to the average of the Euler characteristic of the field in the excursion ν≥νmax inside the patches. The Gumbel statistics therefore represents an interesting alternative probe of the genus as a test of non-Gaussianity, e.g. in cosmic microwave background temperature maps or in 3D galaxy catalogues. It can be approximated, except in the remote positive tail, by a negative Weibull-type form, converging slowly to the expected Gumbel-type form for infinitely large patch size. Convergence is facilitated when large-scale correlations are weaker. We compare the analytic predictions to numerical experiments for the case of a scale-free Gaussian field in two dimensions, achieving impressive agreement between approximate theory and measurements. We also discuss the generalization of our formalism to non-Gaussian fields.
Non Gaussian Minkowski functionals and extrema counts for CMB maps
NASA Astrophysics Data System (ADS)
Pogosyan, Dmitri; Codis, Sandrine; Pichon, Christophe
2016-10-01
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating the effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.
Mixed non-Gaussianity in multiple-DBI inflation
Emery, Jon; Tasinato, Gianmassimo; Wands, David E-mail: gianmassimo.tasinato@port.ac.uk
2013-05-01
We study a model of multiple-field DBI inflation leading to mixed form of primordial non-Gaussianity, including equilateral and local bispectrum shapes. We present a general formalism based on the Hamilton-Jacobi approach, allowing us to go beyond slow-roll, combining the three-point function for the fields at Hubble-exit with the non-linear evolution of super-Hubble scales. We are able to obtain analytic results by taking a separable Ansatz for the Hubble rate. We find general expressions for both the equilateral and local type non-Gaussianity parameter f{sub NL}. The equilateral non-Gaussianity includes the usual enhancement for small sound speeds, but multiplied by an analytic factor which can lead to a suppression. We illustrate our results with two scenarios. In the first model, previously found to have detectable local non-Gaussianity, we find that the equilateral signal is not sufficiently suppressed to evade current observational bounds. In our second scenario we construct a model which exhibits both a detectable equilateral f{sub NL} and a negative local f{sub NL}.
Stochastic Schroedinger equations with general complex Gaussian noises
Bassi, Angelo
2003-06-01
Within the framework of non-Markovian stochastic Schroedinger equations, we generalize the results of [W. T. Strunz, Phys. Lett. A 224, 25 (1996)] to the case of general complex Gaussian noises; we analyze the two important cases of purely real and purely imaginary stochastic processes.
Two-Gaussian excitations model for the glass transition
NASA Astrophysics Data System (ADS)
Matyushov, Dmitry V.; Angell, C. A.
2005-07-01
We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two-state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant-volume heat capacity found by recent simulations for binary mixed Lennard-Jones and soft-sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited-state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of first-order phase transitions for fragile liquids. The analysis of laboratory data for toluene and o-terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a first-order transition from supercooled liquid to ideal-glass state at a temperature between Tg and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuation-dissipation theorem, in analyzing the liquid thermodynamics.
Renormalization of the frozen Gaussian approximation to the quantum propagator
Tatchen, Joerg; Pollak, Eli; Tao Guohua; Miller, William H.
2011-04-07
The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining 'on the fly' quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to 'on the fly' computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable 'on the fly'; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.
Triangular Numbers, Gaussian Integers, and KenKen
ERIC Educational Resources Information Center
Watkins, John J.
2012-01-01
Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…
Effect of Gaussian intensity profiles on difference-frequency generation
NASA Astrophysics Data System (ADS)
Rustagi, K. C.; Gupta, P. K.
1980-04-01
The effect of a Gaussian intensity profile on the efficiency of difference-frequency generation in the near-field limit is evaluated. The effect of a nonuniform intensity profile in the incident beams are significant qualitatively as well as quantitatively. These effects become more important when the incident pump intensity is much larger than the incident idler intensity.
Generating Nice Linear Systems for Matrix Gaussian Elimination
ERIC Educational Resources Information Center
Homewood, L. James
2004-01-01
In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…
Large Non-Gaussianity from Multi-Brid Inflation
NASA Astrophysics Data System (ADS)
Naruko, Atsushi; Sasaki, Misao
A model of multi-component hybrid inflation, dubbed multi-brid inflation, which may yield a large non-Gaussian paramter fNL, was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories. In this talk, in order to see if this result is a general feature of multi-brid inflation, we consider a model with a potential with an exponent quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation. Focusing on the case of two-brid inflation, we find that large non-Gaussianity is also possible in the present model. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.
X-ray optics simulation using Gaussian superposition technique
Idir, M.; Cywiak, M.; Morales, A. and Modi, M.H.
2011-09-15
We present an efficient method to perform x-ray optics simulation with high or partially coherent x-ray sources using Gaussian superposition technique. In a previous paper, we have demonstrated that full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, x-rays, acoustic waves, etc. We describe the technique and include some computer simulations as illustrative examples for x-ray optical component. We show also that this method can be used to study partial or total coherence illumination problem.
Tables Of Gaussian-Type Orbital Basis Functions
NASA Technical Reports Server (NTRS)
Partridge, Harry
1992-01-01
NASA technical memorandum contains tables of estimated Hartree-Fock wave functions for atoms lithium through neon and potassium through krypton. Sets contain optimized Gaussian-type orbital exponents and coefficients, and near Hartree-Fock quality. Orbital exponents optimized by minimizing restricted Hartree-Fock energy via scaled Newton-Raphson scheme in which Hessian evaluated numerically by use of analytically determined gradients.
Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels.
Jayasumana, Sadeep; Hartley, Richard; Salzmann, Mathieu; Li, Hongdong; Harandi, Mehrtash
2015-12-01
In this paper, we develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These kernels make it possible to utilize algorithms developed for linear spaces on nonlinear manifold-valued data. Since the Gaussian RBF defined with any given metric is not always positive definite, we present a unified framework for analyzing the positive definiteness of the Gaussian RBF on a generic metric space. We then use the proposed framework to identify positive definite kernels on two specific manifolds commonly encountered in computer vision: the Riemannian manifold of symmetric positive definite matrices and the Grassmann manifold, i.e., the Riemannian manifold of linear subspaces of a Euclidean space. We show that many popular algorithms designed for Euclidean spaces, such as support vector machines, discriminant analysis and principal component analysis can be generalized to Riemannian manifolds with the help of such positive definite Gaussian kernels. PMID:26539851
Optimization of Gaussian beam widths in acoustic propagation
NASA Astrophysics Data System (ADS)
Gordon, D. F.
1989-10-01
The use of Gaussian beams to compute wave propagation phenomena is a field of current interest and activity. Porter and Bucker (1987) supply an extensive list of references. More recent references can be found in Benites and Aki (1989). Gaussian beams can be traced as rays in range-dependent media providing not only propagation loss, but travel times, multipath structure, and frequency dependence. The well-known ray theory problems of caustics and shadow zones are treated automatically. A beam width minimization technique applied to a Gaussian beam model developed by Dr. H. P. Bucker, is outlined. Porter and Bucker (1987) gives the formulation upon which the techniques is built. A free parameter E is usually determined in a heuristic manner. Here, it is shown that the minimization of beam width assigns a precise value to E. Examples are given showing that the minimized beams give good propagation losses in some cases. A case also shown in the standard Gaussian beams give poor results and the minimized beams give even worse results. The problem appears to arise in beams that pass near boundaries. This problem will have to be corrected before a final judgment can be made on the validity of minimum-width beams.
Anodic Oxidative Modification of Egg White for Heat Treatment.
Takahashi, Masahito; Handa, Akihiro; Yamaguchi, Yusuke; Kodama, Risa; Chiba, Kazuhiro
2016-08-31
A new functionalization of egg white was achieved by an electrochemical reaction. The method involves electron transfer from thiol groups of egg white protein to form disulfide bonds. The oxidized egg white produced less hydrogen sulfide during heat treatment; with sufficient application of electricity, almost no hydrogen sulfide was produced. In addition, gels formed by heating electrochemically oxidized egg white exhibited unique properties, such as a lower gelation temperature and a softened texture, presumably due to protein aggregation and electrochemically mediated intramolecular disulfide bond formation. PMID:27518910
NASA Astrophysics Data System (ADS)
Gu, Yimin; Narendran, Nadarajah; Freyssinier, Jean Paul
2004-10-01
Two life tests were conducted to compare the effects of drive current and ambient temperature on the degradation rate of 5 mm and high-flux white LEDs. Tests of 5 mm white LED arrays showed that junction temperature increases produced by drive current had a greater effect on the rate of light output degradation than junction temperature increases from ambient heat. A preliminary test of high-flux white LEDs showed the opposite effect, with junction temperature increases from ambient heat leading to a faster depreciation. However, a second life test is necessary to verify this finding. The dissimilarity in temperature effect among 5 mm and high-flux LEDs is likely caused by packaging differences between the two device types.
NASA Astrophysics Data System (ADS)
Baur, J.; Schlotter, P.; Schneider, J.
Using blue-emitting GaN LEDs on SiC substrate chips as primary light sources, we have fabricated green, yellow, red and white light emitting diodes (LUCOLEDs). The generation of mixed colors, as turquoise and magenta, is also demonstrated. The underlying physical principle is that of luminescence downconversion (Stokes shift), as typical for organic dye molecules and many inorganic phosphors. For white light generation via the LUCOLED principle, the phosphor Y3Al5O12:Ce3+(4f1) is ideally suited. The optical characteristics of Ce3+(4f1) in Y3Al5O12(YAG) are discussed in detail. Possibilities to "tune" the white color by various substitutions in the garnet lattice are shortly outlined.
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
NASA Technical Reports Server (NTRS)
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
Bimodal and Gaussian Ising spin glasses in dimension two
NASA Astrophysics Data System (ADS)
Lundow, P. H.; Campbell, I. A.
2016-02-01
An analysis is given of numerical simulation data to size L =128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J ) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η ≡0 , and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T*(L ) there is a regime of effectively continuous energy levels; below T*(L ) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T*(L ) tends to zero at very large L , leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t =T and with a scaling variable τb=T2/(1 +T2) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ (τb,L ) and second moment correlation length ξ (τb,L ) in the thermodynamic limit regime are extrapolated to the τb=0 critical limit. The Gaussian critical exponent estimates from the simulations, η =0 and ν =3.55 (5 ) , are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η =0.20 (2 ) and ν =4.8 (3 ) , distinctly different from the Gaussian critical exponents.
Bimodal and Gaussian Ising spin glasses in dimension two.
Lundow, P H; Campbell, I A
2016-02-01
An analysis is given of numerical simulation data to size L=128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η≡0, and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T(*)(L) there is a regime of effectively continuous energy levels; below T(*)(L) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T(*)(L) tends to zero at very large L, leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t=T and with a scaling variable τ(b)=T(2)/(1+T(2)) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ(τ(b),L) and second moment correlation length ξ(τ(b),L) in the thermodynamic limit regime are extrapolated to the τ(b)=0 critical limit. The Gaussian critical exponent estimates from the simulations, η=0 and ν=3.55(5), are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η=0.20(2) and ν=4.8(3), distinctly different from the Gaussian critical exponents. PMID:26986300
Non-Gaussianity and CMB aberration and Doppler
Catena, Riccardo; Liguori, Michele; Renzi, Alessandro; Notari, Alessio E-mail: michele.liguori@pd.infn.it E-mail: arenzi@pd.infn.it
2013-09-01
The peculiar motion of an observer with respect to the CMB rest frame induces a deflection in the arrival direction of the observed photons (also known as CMB aberration) and a Doppler shift in the measured photon frequencies. As a consequence, aberration and Doppler effects induce non trivial correlations between the harmonic coefficients of the observed CMB temperature maps. In this paper we investigate whether these correlations generate a bias on non-Gaussianity estimators f{sub NL}. We perform this analysis simulating a large number of temperature maps with Planck-like resolution (lmax = 2000) as different realizations of the same cosmological fiducial model (WMAP7yr). We then add to these maps aberration and Doppler effects employing a modified version of the HEALPix code. We finally evaluate a generalization of the Komatsu, Spergel and Wandelt non-Gaussianity estimator for all the simulated maps, both when peculiar velocity effects have been considered and when these phenomena have been neglected. Using the value v/c = 1.23 × 10{sup −3} for our peculiar velocity, we found that the aberration/Doppler induced non-Gaussian signal is at most of about half of the cosmic variance σ for f{sub NL} both in a full-sky and in a cut-sky experimental configuration, for local, equilateral and orthogonal estimators. We conclude therefore that when estimating f{sub NL} it is safe to ignore aberration and Doppler effects if the primordial map is already Gaussian. More work is necessary however to assess whether a map which contains non-Gaussianity can be significantly distorted by a peculiar velocity.
White cell design considerations
NASA Technical Reports Server (NTRS)
Hannan, Paul
1989-01-01
The White cell is a unit-magnification image relay system consisting of three noncoaxial spherical mirrors of equal curvature. The cell is used to provide a long optical path in a relatively small physical space. Multiple reflections are used, in a manner similar to a unstable laser resonator. A particular application is an optical delay line on the input of a streak camera to allow for the finite triggering time of the sweep start. This paper addresses the first- and third-order properties of the White cell. A displacement sensitivity analysis is included.
White light velocity interferometer
Erskine, David J.
1999-01-01
The invention is a technique that allows the use of broadband and incoherent illumination. Although denoted white light velocimetry, this principle can be applied to any wave phenomenon. For the first time, powerful, compact or inexpensive sources can be used for remote target velocimetry. These include flash and arc lamps, light from detonations, pulsed lasers, chirped frequency lasers, and lasers operating simultaneously in several wavelengths. The technique is demonstrated with white light from an incandescent source to measure a target moving at 16 m/s.
White light velocity interferometer
Erskine, D.J.
1997-06-24
The invention is a technique that allows the use of broadband and incoherent illumination. Although denoted white light velocimetry, this principle can be applied to any wave phenomenon. For the first time, powerful, compact or inexpensive sources can be used for remote target velocimetry. These include flash and arc lamps, light from detonations, pulsed lasers, chirped frequency lasers, and lasers operating simultaneously in several wavelengths. The technique is demonstrated with white light from an incandescent source to measure a target moving at 16 m/s. 41 figs.
White light velocity interferometer
Erskine, David J.
1997-01-01
The invention is a technique that allows the use of broadband and incoherent illumination. Although denoted white light velocimetry, this principle can be applied to any wave phenomenon. For the first time, powerful, compact or inexpensive sources can be used for remote target velocimetry. These include flash and arc lamps, light from detonations, pulsed lasers, chirped frequency lasers, and lasers operating simultaneously in several wavelengths. The technique is demonstrated with white light from an incandescent source to measure a target moving at 16 m/s.
White light velocity interferometer
Erskine, D.J.
1999-06-08
The invention is a technique that allows the use of broadband and incoherent illumination. Although denoted white light velocimetry, this principle can be applied to any wave phenomenon. For the first time, powerful, compact or inexpensive sources can be used for remote target velocimetry. These include flash and arc lamps, light from detonations, pulsed lasers, chirped frequency lasers, and lasers operating simultaneously in several wavelengths. The technique is demonstrated with white light from an incandescent source to measure a target moving at 16 m/s. 41 figs.
Pohle, H.
1989-03-15
We investigate lambdaphi/sup 4/ theory within the Gaussian approximation in spatially flat Robertson-Walker space in 3+1 dimensions. After having performed an adiabatic expansion for one of the ansatz functions, we find that the renormalization of the energy-momentum tensor provides two additional constraints which have to be satisfied by the bare couplings. These conditions force the theory to be trivial after renormalization.
NASA Astrophysics Data System (ADS)
Genovese, Mariangela; Napoli, Ettore; Petra, Nicola
2014-04-01
Background identification is a fundamental task in many video processing systems. The Gaussian Mixture Model is a background identification algorithm that models the pixel luminance with a mixture of K Gaussian distributions. The number of Gaussian distributions determines the accuracy of the background model and the computational complexity of the algorithm. This paper compares two hardware implementations of the Gaussian Mixture Model that use three and five Gaussians per pixel. A trade off analysis is carried out by evaluating the quality of the processed video sequences and the hardware performances. The circuits are implemented on FPGA by exploiting state of the art, hardware oriented, formulation of the Gaussian Mixture Model equations and by using truncated binary multipliers. The results suggest that the circuit that uses three Gaussian distributions provides video with good accuracy while requiring significant less resources than the option that uses five Gaussian distributions per pixel.
Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.
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. PMID:25504231
Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.
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.
Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko
2010-06-01
We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.
Probing primordial non-Gaussianity via iSW measurements with SKA continuum surveys
Raccanelli, Alvise; Doré, Olivier E-mail: olivier.dore@caltech.edu; Bacon, David J.; Maartens, Roy E-mail: roy.maartens@gmail.com; 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
ERIC Educational Resources Information Center
Widmar, Marge
1985-01-01
A secondary teacher describes how she has her students use liquid white enamel. With the enameling process, students can create lasting, exciting artwork. They can exercise an understanding of design and color while learning the value of careful, sustained craft skills. (RM)
NASA Technical Reports Server (NTRS)
2002-01-01
At bottom center of this true-color Moderate Resolution Imaging Spectroradiometer (MODIS) image from April 13, 2001, the White Sea in western Russia is becoming free of ice in its southern extent. Meanwhile, the blue-green waters along the coast of the peninsula jutting out into the Barents Sea to the northeast could be due to a phytoplankton bloom.
Improved performance white LED
NASA Astrophysics Data System (ADS)
Narendran, Nadarajah
2005-09-01
This paper describes work leading to the development of a new packaging method for white LEDs, called scattered photon extraction (SPE). Previous work by our group showed that the traditional placement of the phosphor close to the die negatively affects the overall luminous efficacy and lumen maintenance of phosphor-converted white LEDs. The new SPE method enables higher luminous efficacy by placing the phosphor at a remote location from the die and by shaping the lens surrounding the die to extract a significant portion of the back-transferred light before it is absorbed by packaging components. Although the remote phosphor concept is not new, SPE is the first method to demonstrate efficient extraction of back-transferred light and show over 60 percent improvement in light output and efficacy compared to similar commercial white LEDs. At low currents, the prototype white LEDs based on the SPE technique showed over 80 lumens per watt. The SPE concept was tried on two types of commercial packages and both showed similar improvements.
ERIC Educational Resources Information Center
Gundy, Jan
1978-01-01
Presented as a fairy tale with the characters of Snow White and the seven dwarves, this paper points out some of the professional, emotional, and health characteristics and problems of individual teachers, and ways an administrator might deal with them. (SJL)
NASA Technical Reports Server (NTRS)
2002-01-01
Editor's Note: The caption below, published on May 10, 2001, is incorrect. According to Masha Vorontsova, director of the International Fund for Animal Welfare in Moscow, the situation with the seal pups in the White Sea is normal. There is no disaster and there never was. For more details, refer to the article entitled 'No Danger' on the New Scientist home page. The Earth Observatory regrets the earlier errant report. Original Caption According to the Russian Polar Research Institute for Fisheries and Oceanography, between 250,000 and 300,000 Greenland seal pups face death by starvation over the next two months due to a cruel trick by mother nature. The seals, most of them less than two months old, are trapped on ice sheets that remain locked in the White Sea, located near Archangel in Northern Russia. Typically, during the spring thaw the ice sheets break up and flow with the currents northward into the Barents Sea, the seals' spring feeding grounds. The seal pups hitch a ride on the ice floes, living on their own individual stores of fat until they arrive in the Barents Sea. Their mothers departed for the Barents Sea weeks ago. In a normal year, the seal pups' trip from the White Sea out to the Barents takes about six weeks and the seals have adapted to rely upon this mechanism of mother nature. During their yearly migration, the mother seals usually stay with their pups and feed them until their pelts turn from white to grey--a sign that the pups are mature enough to swim and feed themselves. Unfortunately, this year unusually strong northerly winds created a bottleneck of ice near the mouth of the white sea, thus blocking the flow of ice and trapping the pups. These true-color images of the White Sea were acquired by the Moderate-resolution Imaging Spectroradiometer (MODIS), flying aboard NASA's Terra spacecraft. This image, taken May 2, 2000 that there is usually much less ice in the White Sea this time of year as most of it is typically en route to the
NASA Astrophysics Data System (ADS)
Kepler, S. O.
2014-10-01
White dwarfs are the evolutionary endpoint for nearly 95% of all stars born in our Galaxy, the final stages of evolution of all low- and intermediate mass stars, i.e., main sequence stars with masses below (8.5± 1.5) M_{odot}, depending on metallicity of the progenitor, mass loss and core overshoot. Massive white dwarfs are intrinsically rare objects, tand produce a gap in the determination of the initial vs. final mass relation at the high mass end (e.g. Weidemann 2000 A&A, 363, 647; Kalirai et al. 2008, ApJ, 676, 594; Williams, Bolte & Koester 2009, ApJ, 693, 355). Main sequences stars with higher masses will explode as SNII (Smartt S. 2009 ARA&A, 47, 63), but the limit does depend on the metallicity of the progenitor. Massive white dwarfs are probably SNIa progenitors through accretion or merger. They are rare, being the final product of massive stars (less common) and have smaller radius (less luminous). Kepler et al. 2007 (MNRAS, 375, 1315), Kleinman et al. 2013 (ApJS, 204, 5) estimate only 1-2% white dwarfs have masses above 1 M_{odot}. The final stages of evolution after helium burning are a race between core growth and loss of the H-rich envelope in a stellar wind. When the burning shell is exposed, the star rapidly cools and burning ceases, leaving a white dwarf. As they cool down, the magnetic field freezes in, ranging from a few kilogauss to a gigagauss. Peculiar type Ia SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg suggest progenitors in the range 2.4-2.8 M_{odot}, and Das U. & Mukhopadhyay B. (2012, Phys. Rev. D, 86, 042001) estimate that the Chandrasekhar limit increases to 2.3-2.6 M_{odot} for extremely high magnetic field stars, but differential rotation induced by accretion could also increase it, according to Hachisu I. et al. 2012 (ApJ, 744, 69). García-Berro et al. 2012, ApJ, 749, 25, for example, proposes double degenerate mergers are the progenitors of high-field magnetic white dwarfs. We propose magnetic fields enhance the line broadening in
NASA Astrophysics Data System (ADS)
Kang-Kang, Wang; Xian-Bin, Liu; Yu, Zhou
2015-08-01
In this paper, the stability and stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal for a metapopulation system driven by the additive Gaussian noise, multiplicative non-Gaussian noise and noise correlation time is investigated. By using the fast descent method, unified colored noise approximation and McNamara and Wiesenfeld’s SR theory, the analytical expressions of the stationary probability distribution function and signal-to-noise ratio (SNR) are derived in the adiabatic limit. Via numerical calculations, each effect of the addictive noise intensity, the multiplicative noise intensity and the correlation time upon the steady state probability distribution function and the SNR is discussed, respectively. It is shown that multiplicative, additive noises and the departure parameter from the Gaussian noise can all destroy the stability of the population system. However, the noise correlation time can consolidate the stability of the system. On the other hand, the correlation time always plays an important role in motivating the SR and enhancing the SNR. Under different parameter conditions of the system, the multiplicative, additive noises and the departure parameter can not only excite SR phenomenon, but also restrain the SR phenomenon, which demonstrates the complexity of different noises upon the nonlinear system.
Recombination energy in double white dwarf formation
NASA Astrophysics Data System (ADS)
Nandez, J. L. A.; Ivanova, N.; Lombardi, J. C.
2015-06-01
In this Letter, we investigate the role of recombination energy during a common envelope event. We confirm that taking this energy into account helps to avoid the formation of the circumbinary envelope commonly found in previous studies. For the first time, we can model a complete common envelope event, with a clean compact double white dwarf binary system formed at the end. The resulting binary orbit is almost perfectly circular. In addition to considering recombination energy, we also show that between 1/4 and 1/2 of the released orbital energy is taken away by the ejected material. We apply this new method to the case of the double white dwarf system WD 1101+364, and we find that the progenitor system at the start of the common envelope event consisted of an ˜1.5 M⊙ red giant star in an ˜30 d orbit with a white dwarf companion.
Bosten, J. M.; Beer, R. D.; MacLeod, D. I. A.
2015-01-01
To shed light on the perceptual basis of the color white, we measured settings of unique white in a dark surround. We find that settings reliably show more variability in an oblique (blue-yellow) direction in color space than along the cardinal axes of the cone-opponent mechanisms. This is against the idea that white perception arises at the null point of the cone-opponent mechanisms, but one alternative possibility is that it occurs through calibration to the visual environment. We found that the locus of maximum variability in settings lies close to the locus of natural daylights, suggesting that variability may result from uncertainty about the color of the illuminant. We tested this by manipulating uncertainty. First, we altered the extent to which the task was absolute (requiring knowledge of the illumination) or relative. We found no clear effect of this factor on the reduction in sensitivity in the blue-yellow direction. Second, we provided a white surround as a cue to the illumination or left the surround dark. Sensitivity was selectively worse in the blue-yellow direction when the surround was black than when it was white. Our results can be functionally related to the statistics of natural images, where a greater blue-yellow dispersion is characteristic of both reflectances (where anisotropy is weak) and illuminants (where it is very pronounced). Mechanistically, the results could suggest a neural signal responsive to deviations from the blue-yellow locus or an adaptively matched range of contrast response functions for signals that encode different directions in color space. PMID:26641948
X-ray cluster constraints on non-Gaussianity
Shandera, Sarah; Mantz, Adam; Rapetti, David; Allen, Steven W. E-mail: amantz@kicp.uchicago.edu E-mail: swa@stanford.edu
2013-08-01
We report constraints on primordial non-Gaussianity from the abundance of X-ray detected clusters. Our analytic prescription for adding non-Gaussianity to the cluster mass function takes into account moments beyond the skewness, and we demonstrate that those moments should not be ignored in most analyses of cluster data. We constrain the amplitude of the skewness for two scenarios that have different overall levels of non-Gaussianity, characterized by how amplitudes of higher cumulants scale with the skewness. We find that current data can constrain these one-parameter non-Gaussian models at a useful level, but are not sensitive to adding further details of the corresponding inflation scenarios. Combining cluster data with Cosmic Microwave Background constraints on the cosmology and power spectrum amplitude, we find the dimensionless skewness to be 10{sup 3}M{sub 3} = −1{sub −28}{sup +24} for one of our scaling scenarios, and 10{sup 3}M{sub 3} = −4±7 for the other. These are the first constraints on non-Gaussianity from Large Scale Structure that can be usefully applied to any model of primordial non-Gaussianity. The former constraint, when applied to the standard local ansatz (where the n-th cumulant scales as M{sub n}∝M{sub 3}{sup n−2}), corresponds to f{sub NL}{sup local} = −3{sub −91}{sup +78}. When applied to a model with a local-shape bispectrum but higher cumulants that scale as M{sub n}∝M{sub 3}{sup n/3} (the second scaling scenario), the amplitude of the local-shape bispectrum is constrained to be f{sub NL}{sup local*} = −14{sub −21}{sup +22}. For this second scaling (which occurs in various well-motivated models of inflation), we also obtain strong constraints on the equilateral and orthogonal shapes of the bispectrum, f{sub NL}{sup equil} = −52{sub −79}{sup +85} and f{sub NL}{sup orth} = 63{sub −104}{sup +97}. This sensitivity implies that cluster counts could be used to distinguish qualitatively different models for the
White Students Reflecting on Whiteness: Understanding Emotional Responses.
Todd, Nathan R; Spanierman, Lisa B; Aber, Mark S
2010-06-01
In the present investigation, the authors explored potential predictors of White students' general emotional responses after they reflected on their Whiteness in a semi-structured interview (n = 88) or written reflection (n = 187). Specifically, the authors examined how color-blindness (i.e., awareness of White privilege) and racial affect (i.e., White empathy, White guilt, and White fear), assessed before the interview or written reflection, may predict positive and negative emotional responses, assessed immediately following the interview or written reflection. Furthermore, the authors considered whether affective costs of racism to Whites moderated the association between racial color-blindness and general positive and negative emotional responses of White students. Findings indicated that affective costs of racism moderated associations between racial color-blindness and general emotional responses. Specifically, White fear moderated associations for the written reflection group whereas White empathy moderated an association in the interview. White guilt did not moderate, but instead directly predicted a negative emotional response in the written reflection group. Findings suggest that the interaction between racial color-blindness and racial affect is important when predicting students' emotional responses to reflecting on their Whiteness. Implications for educators and administrators are discussed.
White Students Reflecting on Whiteness: Understanding Emotional Responses
Todd, Nathan R.; Spanierman, Lisa B.; Aber, Mark S.
2010-01-01
In the present investigation, the authors explored potential predictors of White students’ general emotional responses after they reflected on their Whiteness in a semi-structured interview (n = 88) or written reflection (n = 187). Specifically, the authors examined how color-blindness (i.e., awareness of White privilege) and racial affect (i.e., White empathy, White guilt, and White fear), assessed before the interview or written reflection, may predict positive and negative emotional responses, assessed immediately following the interview or written reflection. Furthermore, the authors considered whether affective costs of racism to Whites moderated the association between racial color-blindness and general positive and negative emotional responses of White students. Findings indicated that affective costs of racism moderated associations between racial color-blindness and general emotional responses. Specifically, White fear moderated associations for the written reflection group whereas White empathy moderated an association in the interview. White guilt did not moderate, but instead directly predicted a negative emotional response in the written reflection group. Findings suggest that the interaction between racial color-blindness and racial affect is important when predicting students’ emotional responses to reflecting on their Whiteness. Implications for educators and administrators are discussed. PMID:20657811
Exploring Whiteness: A Study of Self Labels for White Americans.
ERIC Educational Resources Information Center
Martin, Judith N.; Krizek, Robert L.; Nakayama, Thomas K.; Bradford, Lisa
1996-01-01
Examines the preferences and meanings of labels for White Americans as discursively defined expressions of identity, after preliminary revelations of resistance by Whites to self-labeling was seen. Surveys 371 White undergraduate students, rating seven labels regarding preference and discussing feelings about self-labeling. Reveals that the most…
White Institutional Presence: The Impact of Whiteness on Campus Climate
ERIC Educational Resources Information Center
Gusa, Diane Lynn
2010-01-01
In this conceptual paper, Diane Gusa highlights the salience of race by scrutinizing the culture of Whiteness within predominately White institutions of higher education. Using existing research in higher education retention literature, Gusa examines embedded White cultural ideology in the cultural practices, traditions, and perceptions of…
White dwarf stars with carbon atmospheres.
Dufour, P; Liebert, J; Fontaine, G; Behara, N
2007-11-22
White dwarfs represent the endpoint of stellar evolution for stars with initial masses between approximately 0.07 and 8-10, where is the mass of the Sun (more massive stars end their life as either black holes or neutron stars). The theory of stellar evolution predicts that the majority of white dwarfs have a core made of carbon and oxygen, which itself is surrounded by a helium layer and, for approximately 80 per cent of known white dwarfs, by an additional hydrogen layer. All white dwarfs therefore have been traditionally found to belong to one of two categories: those with a hydrogen-rich atmosphere (the DA spectral type) and those with a helium-rich atmosphere (the non-DAs). Here we report the discovery of several white dwarfs with atmospheres primarily composed of carbon, with little or no trace of hydrogen or helium. Our analysis shows that the atmospheric parameters found for these stars do not fit satisfactorily in any of the currently known theories of post-asymptotic giant branch evolution, although these objects might be the cooler counterpart of the unique and extensively studied PG 1159 star H1504+65 (refs 4-7). These stars, together with H1504+65, might accordingly form a new evolutionary sequence that follows the asymptotic giant branch. PMID:18033290
White dwarf stars with carbon atmospheres.
Dufour, P; Liebert, J; Fontaine, G; Behara, N
2007-11-22
White dwarfs represent the endpoint of stellar evolution for stars with initial masses between approximately 0.07 and 8-10, where is the mass of the Sun (more massive stars end their life as either black holes or neutron stars). The theory of stellar evolution predicts that the majority of white dwarfs have a core made of carbon and oxygen, which itself is surrounded by a helium layer and, for approximately 80 per cent of known white dwarfs, by an additional hydrogen layer. All white dwarfs therefore have been traditionally found to belong to one of two categories: those with a hydrogen-rich atmosphere (the DA spectral type) and those with a helium-rich atmosphere (the non-DAs). Here we report the discovery of several white dwarfs with atmospheres primarily composed of carbon, with little or no trace of hydrogen or helium. Our analysis shows that the atmospheric parameters found for these stars do not fit satisfactorily in any of the currently known theories of post-asymptotic giant branch evolution, although these objects might be the cooler counterpart of the unique and extensively studied PG 1159 star H1504+65 (refs 4-7). These stars, together with H1504+65, might accordingly form a new evolutionary sequence that follows the asymptotic giant branch.
Efficient White SSL Component for General Illumination
Sean Evans
2011-01-31
Cree has developed a new, high-efficiency, low-cost, light emitting diode (LED) module that should be capable of replacing standard, halogen, fluorescent and metal halide lamps based on the total cost of ownership. White LEDs are produced by combining one or more saturated color LEDs with a phosphor or other light down-converting media to achieve white broad-band illumination. This two year project addressed LED chip, package and phosphor efficiency improvements to establish a technology platform suitable for low-cost, high-efficiency commercial luminaires. New phosphor materials with improved quantum efficiency at 'real-life' operating conditions were developed along with new package technology to improve the efficiency of warm white LED modules compared to the baseline technology. Specifically, Cree has successfully demonstrated warm white LED modules providing 540 lumens at a correlated color temperature (CCT) of 3000 K. The LED module had an efficacy of 102.8 lumens per watt (LPW) using 1 mm2 chips biased at 350 mA - a 27% improvement over the technology at project start (81 LPW at 3000K). The white modules also delivered an efficacy of 88 LPW at elevated junction temperatures of 125 C. In addition, a proof-of-concept 4-inch downlight luminaire produced a flux of 1183 lumens at a CCT of 2827 K and a color rendering index (CRI) of 80 using this project's phosphor developments.
Gravitational Interactions of White Dwarf Double Stars
NASA Astrophysics Data System (ADS)
McKeough, James; Robinson, Chloe; Ortiz, Bridget; Hira, Ajit
2016-03-01
In the light of the possible role of White Dwarf stars as progenitors of Type Ia supernovas, we present computational simulations of some astrophysical phenomena associated with a study of gravitationally-bound binary stars, composed of at least one white dwarf star. Of particular interest to astrophysicists are the conditions inside a white dwarf star in the time frame leading up to its explosive end as a Type Ia supernova, for an understanding of the massive stellar explosions. In addition, the studies of the evolution of white dwarfs could serve as promising probes of theories of gravitation. We developed FORTRAN computer programs to implement our models for white dwarfs and other stars. These codes allow for different sizes and masses of stars. Simulations were done in the mass interval from 0.1 to 2.5 solar masses. Our goal was to obtain both atmospheric and orbital parameters. The computational results thus obtained are compared with relevant observational data. The data are further analyzed to identify trends in terms of sizes and masses of stars. We will extend our computational studies to blue giant and red giant stars in the future. Funding from National Science Foundation.
Broad-band Gaussian noise is most effective in improving motor performance and is most pleasant
Trenado, Carlos; Mikulić, Areh; Manjarrez, Elias; Mendez-Balbuena, Ignacio; Schulte-Mönting, Jürgen; Huethe, Frank; Hepp-Reymond, Marie-Claude; Kristeva, Rumyana
2014-01-01
Modern attempts to improve human performance focus on stochastic resonance (SR). SR is a phenomenon in non-linear systems characterized by a response increase of the system induced by a particular level of input noise. Recently, we reported that an optimum level of 0–15 Hz Gaussian noise applied to the human index finger improved static isometric force compensation. A possible explanation was a better sensorimotor integration caused by increase in sensitivity of peripheral receptors and/or of internal SR. The present study in 10 subjects compares SR effects in the performance of the same motor task and on pleasantness, by applying three Gaussian noises chosen on the sensitivity of the fingertip receptors (0–15 Hz mostly for Merkel receptors, 250–300 Hz for Pacini corpuscles and 0–300 Hz for all). We document that only the 0–300 Hz noise induced SR effect during the transitory phase of the task. In contrast, the motor performance was improved during the stationary phase for all three noise frequency bandwidths. This improvement was stronger for 0–300 Hz and 250–300 Hz than for 0–15 Hz noise. Further, we found higher degree of pleasantness for 0–300 Hz and 250–300 Hz noise bandwidths than for 0–15 Hz. Thus, we show that the most appropriate Gaussian noise that could be used in haptic gloves is the 0–300 Hz, as it improved motor performance during both stationary and transitory phases. In addition, this noise had the highest degree of pleasantness and thus reveals that the glabrous skin can also forward pleasant sensations. PMID:24550806
Broad-band Gaussian noise is most effective in improving motor performance and is most pleasant.
Trenado, Carlos; Mikulić, Areh; Manjarrez, Elias; Mendez-Balbuena, Ignacio; Schulte-Mönting, Jürgen; Huethe, Frank; Hepp-Reymond, Marie-Claude; Kristeva, Rumyana
2014-01-01
Modern attempts to improve human performance focus on stochastic resonance (SR). SR is a phenomenon in non-linear systems characterized by a response increase of the system induced by a particular level of input noise. Recently, we reported that an optimum level of 0-15 Hz Gaussian noise applied to the human index finger improved static isometric force compensation. A possible explanation was a better sensorimotor integration caused by increase in sensitivity of peripheral receptors and/or of internal SR. The present study in 10 subjects compares SR effects in the performance of the same motor task and on pleasantness, by applying three Gaussian noises chosen on the sensitivity of the fingertip receptors (0-15 Hz mostly for Merkel receptors, 250-300 Hz for Pacini corpuscles and 0-300 Hz for all). We document that only the 0-300 Hz noise induced SR effect during the transitory phase of the task. In contrast, the motor performance was improved during the stationary phase for all three noise frequency bandwidths. This improvement was stronger for 0-300 Hz and 250-300 Hz than for 0-15 Hz noise. Further, we found higher degree of pleasantness for 0-300 Hz and 250-300 Hz noise bandwidths than for 0-15 Hz. Thus, we show that the most appropriate Gaussian noise that could be used in haptic gloves is the 0-300 Hz, as it improved motor performance during both stationary and transitory phases. In addition, this noise had the highest degree of pleasantness and thus reveals that the glabrous skin can also forward pleasant sensations.
Dorn, Sebastian; Enßlin, Torsten A.; Ramirez, Erandy; Kunze, Kerstin E.
2014-06-01
We present a generic inference method for inflation models from observational data by the usage of higher-order statistics of the curvature perturbation on uniform density hypersurfaces. This method is based on the calculation of the posterior for the primordial non-Gaussianity parameters f{sub NL} and g{sub NL}, which in general depend on specific parameters of inflation and reheating models, and enables to discriminate among the still viable inflation models. To keep analyticity as far as possible to dispense with numerically expensive sampling techniques a saddle-point approximation is introduced, whose precision is validated for a numerical toy example. The mathematical formulation is done in a generic way so that the approach remains applicable to cosmic microwave background data as well as to large scale structure data. Additionally, we review a few currently interesting inflation models and present numerical toy examples thereof in two and three dimensions to demonstrate the efficiency of the higher-order statistics method. A second quantity of interest is the primordial power spectrum. Here, we present two Bayesian methods to infer it from observational data, the so called critical filter and an extension thereof with smoothness prior, both allowing for a non-parametric spectrum reconstruction. These methods are able to reconstruct the spectra of the observed perturbations and the primordial ones of curvature perturbation even in case of non-Gaussianity and partial sky coverage. We argue that observables like T- and B-modes permit to measure both spectra. This also allows to infer the level of non-Gaussianity generated since inflation.
Rust, Pete; Wakkinen, Virginia
2005-06-01
The objective of this research was to determine the environmental requirements for successful spawning and recruitment of the Kootenai River white sturgeon Acipenser transmontanus population. Annual tasks include monitoring and evaluating the various life stages of Kootenai River white sturgeon. Sampling for adult Kootenai River white sturgeon in 2003 began in March and continued through April. Eighty-one adult white sturgeon were captured with 3,576 hours of angling and set-lining effort in the Kootenai River. Discharge from Libby Dam and river stage at Bonners Ferry in 2003 peaked in May and early June. Flows remained above 500 m{sup 3}/s throughout June, decreased rapidly through mid July, and increased back to near 500 m{sup 3}/s after mid July and through mid August. By late August, flows had decreased to below 400 m{sup 3}/s. We monitored the movements of 24 adult sturgeon in Kootenay Lake, British Columbia (BC) and the Kootenai River from March 15, 2003 to August 31, 2003. Some of the fish were radio or sonic tagged in previous years. Twelve adult white sturgeon were moved upstream to the Hemlock Bar reach (rkm 260.0) and released as part of the Set and Jet Program. Transmitters were attached to seven of these fish, and their movements were monitored from the time of release until they moved downstream of Bonners Ferry. Eight additional radio-tagged white sturgeon adults were located in the traditional spawning reach (rkm 228-240) during May and June. Sampling with artificial substrate mats began May 21, 2003 and ended June 30, 2003. We sampled 717 mat d (a mat d is one 24 h set) during white sturgeon spawning. Three white sturgeon eggs were collected near Shortys Island on June 3, 2003, and five eggs were collected from the Hemlock Bar reach on June 5, 2003. Prejuvenile sampling began June 17, 2003 and continued until July 31, 2003. Sampling occurred primarily at Ambush Rock (rkm 244.0) in an attempt to document any recruitment that might have occurred from
White matter is found in the deeper tissues of the brain (subcortical). It contains nerve fibers (axons), which are ... or covering called myelin. Myelin gives the white matter its color. It also protects the nerve fibers ...
Revisiting Additivity Violation of Quantum Channels
NASA Astrophysics Data System (ADS)
Fukuda, Motohisa
2014-12-01
We prove additivity violation of minimum output entropy of quantum channels by straightforward application of -net argument and Lévy's lemma. The additivity conjecture was disproved initially by Hastings. Later, a proof via asymptotic geometric analysis was presented by Aubrun, Szarek and Werner, which uses Dudley's bound on Gaussian process (or Dvoretzky's theorem with Schechtman's improvement). In this paper, we develop another proof along Dvoretzky's theorem in Milman's view, showing additivity violation in broader regimes than the existing proofs. Importantly,Dvoretzky's theorem works well with norms to give strong statements, but these techniques can be extended to functions which have norm-like structures-positive homogeneity and triangle inequality. Then, a connection between Hastings' method and ours is also discussed. In addition, we make some comments on relations between regularized minimum output entropy and classical capacity of quantum channels.
Building an Unusual White-Dwarf Duo
NASA Astrophysics Data System (ADS)
Kohler, Susanna
2016-09-01
A new study has examined how the puzzling wide binary system HS 2220+2146 which consists of two white dwarfs orbiting each other might have formed. This system may be an example of a new evolutionary pathway for wide white-dwarf binaries.Evolution of a BinaryMore than 100 stellar systems have been discovered consisting of two white dwarfs in a wide orbit around each other. How do these binaries form? In the traditional picture, the system begins as a binary consisting of two main-sequence stars. Due to the large separation between the stars, the stars evolve independently, each passing through the main-sequence and giant branches and ending their lives as white dwarfs.An illustration of a hierarchical triple star system, in which two stars orbit each other, and a third star orbits the pair. [NASA/JPL-Caltech]Because more massive stars evolve more quickly, the most massive of the two stars in a binary pair should be the first to evolve into a white dwarf. Consequently, when we observe a double-white-dwarf binary, its usually a safe bet that the more massive of the two white dwarfs will also be the older and cooler of the pair, since it should have formed first.But in the case of the double-white-dwarf binary HS 2220+2146, the opposite is true: the more massive of the two white dwarfs appears to be the younger and hotter of the pair. If it wasnt created in the traditional way, then how did this system form?Two From Three?Led by Jeff Andrews (Foundation for Research and Technology-Hellas, Greece and Columbia University), a team of scientists recently examined this system more carefully, analyzing its spectra to confirm our understanding of the white dwarfs temperatures and masses.Based on their observations, Andrews and collaborators determined that there are no hidden additional companions that could have caused the unusual evolution of this system. Instead, the team proposed that this unusual binary might be an example of an evolutionary channel that involves three
Selective cloning of Gaussian states by linear optics
Olivares, Stefano
2007-08-15
We investigate the performance of a selective cloning machine based on linear optical elements and Gaussian measurements, which allows one to clone at will one of the two incoming input states. This machine is a complete generalization of a 1{yields}2 cloning scheme demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is studied for a generic Gaussian input state, and the effect of nonunit quantum efficiency is also taken into account. We show that, if the states to be cloned are squeezed states with known squeezing parameter, then the fidelity can be enhanced using a third suitable squeezed state during the final stage of the cloning process. A binary communication protocol based on the selective cloning machine is also discussed.
Designing Multi-target Compound Libraries with Gaussian Process Models.
Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert
2016-05-01
We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design.
Fluctuation theory of Rashba Fermi gases: Gaussian and beyond
NASA Astrophysics Data System (ADS)
Shenoy, Vijay B.; Vyasanakere, Jayantha P.
Fermi gases with generalized Rashba spin orbit coupling induced by a synthetic gauge field have the potential of realizing many interesting states such as rashbon condensates and topological phases. Here we address the key open problem of the fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture finite temperature physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature (Tc) of a weakly attracting superfluid to the order of Fermi temperature, paving a pathway towards high Tc superfluids. Work supported by CSIR, DST, DAE and IUSSTF.
Scattering of Gaussian beams by disordered particulate media
NASA Astrophysics Data System (ADS)
Mishchenko, Michael I.; Dlugach, Janna M.
2016-11-01
A frequently observed characteristic of electromagnetic scattering by a disordered particulate medium is the absence of pronounced speckles in angular patterns of the scattered light. It is known that such diffuse speckle-free scattering patterns can be caused by averaging over randomly changing particle positions and/or over a finite spectral range. To get further insight into the possible physical causes of the absence of speckles, we use the numerically exact superposition T-matrix solver of the Maxwell equations and analyze the scattering of plane-wave and Gaussian beams by representative multi-sphere groups. We show that phase and amplitude variations across an incident Gaussian beam do not serve to extinguish the pronounced speckle pattern typical of plane-wave illumination of a fixed multi-particle group. Averaging over random particle positions and/or over a finite spectral range is still required to generate the classical diffuse speckle-free regime.
Weighted Feature Gaussian Kernel SVM for Emotion Recognition
Jia, Qingxuan
2016-01-01
Emotion recognition with weighted feature based on facial expression is a challenging research topic and has attracted great attention in the past few years. This paper presents a novel method, utilizing subregion recognition rate to weight kernel function. First, we divide the facial expression image into some uniform subregions and calculate corresponding recognition rate and weight. Then, we get a weighted feature Gaussian kernel function and construct a classifier based on Support Vector Machine (SVM). At last, the experimental results suggest that the approach based on weighted feature Gaussian kernel function has good performance on the correct rate in emotion recognition. The experiments on the extended Cohn-Kanade (CK+) dataset show that our method has achieved encouraging recognition results compared to the state-of-the-art methods. PMID:27807443
Adaptive Sampling for Learning Gaussian Processes Using Mobile Sensor Networks
Xu, Yunfei; Choi, Jongeun
2011-01-01
This paper presents a novel class of self-organizing sensing agents that adaptively learn an anisotropic, spatio-temporal Gaussian process using noisy measurements and move in order to improve the quality of the estimated covariance function. This approach is based on a class of anisotropic covariance functions of Gaussian processes introduced to model a broad range of spatio-temporal physical phenomena. The covariance function is assumed to be unknown a priori. Hence, it is estimated by the maximum a posteriori probability (MAP) estimator. The prediction of the field of interest is then obtained based on the MAP estimate of the covariance function. An optimal sampling strategy is proposed to minimize the information-theoretic cost function of the Fisher Information Matrix. Simulation results demonstrate the effectiveness and the adaptability of the proposed scheme. PMID:22163785
Differential Evolution with Gaussian Mutation for Economic Dispatch
NASA Astrophysics Data System (ADS)
Basu, Mousumi; Jena, Chitralekha; Panigrahi, Chinmoy Kumar
2015-05-01
This paper presents differential evolution with Gaussian mutation (DEGM) to solve economic dispatch problem of thermal generating units with non-smooth/non-convex cost functions due to valve-point loading, taking into account transmission losses and nonlinear generator constraints such as prohibited operating zones. Differential evolution (DE) is a simple yet powerful global optimization technique. It exploits the differences of randomly sampled pairs of objective vectors for its mutation process. This mutation process is not suitable for complex multimodal optimization. This paper proposes Gaussian mutation in DE which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the simplicity of the structure of DE. The effectiveness of the proposed method has been verified on three different test systems. From the comparison with other evolutionary methods, it is found that DEGM based approach is able to provide better solution.
Robust image reconstruction enhancement based on Gaussian mixture model estimation
NASA Astrophysics Data System (ADS)
Zhao, Fan; Zhao, Jian; Han, Xizhen; Wang, He; Liu, Bochao
2016-03-01
The low quality of an image is often characterized by low contrast and blurred edge details. Gradients have a direct relationship with image edge details. More specifically, the larger the gradients, the clearer the image details become. Robust image reconstruction enhancement based on Gaussian mixture model estimation is proposed here. First, image is transformed to its gradient domain, obtaining the gradient histogram. Second, the gradient histogram is estimated and extended using a Gaussian mixture model, and the predetermined function is constructed. Then, using histogram specification technology, the gradient field is enhanced with the constraint of the predetermined function. Finally, a matrix sine transform-based method is applied to reconstruct the enhanced image from the enhanced gradient field. Experimental results show that the proposed algorithm can effectively enhance different types of images such as medical image, aerial image, and visible image, providing high-quality image information for high-level processing.
A non-Gaussian approach to risk measures
NASA Astrophysics Data System (ADS)
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.
Asymmetric Gaussian steering: When Alice and Bob disagree
Midgley, S. L. W.; Ferris, A. J.; Olsen, M. K.
2010-02-15
Asymmetric steering is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. This phenomenon is possible because of an asymmetry in the definition of the original Einstein-Podolsky-Rosen paradox and in this article we show theoretically that it may be demonstrated, at least in the case where Alice and Bob can only make Gaussian measurements, using the intracavity nonlinear coupler.
Propagation of Airy Gaussian vortex beams in uniaxial crystals
NASA Astrophysics Data System (ADS)
Weihao, Yu; Ruihuang, Zhao; Fu, Deng; Jiayao, Huang; Chidao, Chen; Xiangbo, Yang; Yanping, Zhao; Dongmei, Deng
2016-04-01
The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108, 11374107, 10904041, and 11547212), the Foundation of Cultivating Outstanding Young Scholars of Guangdong Province, China, the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 2015093), and the Science and Technology Projects of Guangdong Province, China (Grant No. 2013B031800011).
Optimal focusing conditions of lenses using Gaussian beams
NASA Astrophysics Data System (ADS)
Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; Mourad, Idir
2016-07-01
By using the analytical equations of the propagation of Gaussian beams in which truncation exhibits negligible consequences, we describe a method that uses the value of the focal length of a focusing lens to classify its focusing performance. We show that for different distances between a laser and a focusing lens there are different planes where best focusing conditions can be obtained and we demonstrate how the value of the focal length impacts the lens focusing properties. To perform the classification we introduce the term delimiting focal length. As the value of the focal length used in wave propagation theory is nominal and difficult to measure accurately, we describe an experimental approach to calculate its value matching our analytical description. Finally, we describe possible applications of the results for characterizing Gaussian sources, for measuring focal lengths and/or alternatively for characterizing piston-like movements.
Classifying gamma-ray bursts with Gaussian Mixture Model
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Bin; Yang, En-Bo; Choi, Chul-Sung; Chang, Heon-Young
2016-11-01
Using Gaussian Mixture Model (GMM) and expectation-maximization algorithm, we perform an analysis of time duration (T90) for Compton Gamma Ray Observatory (CGRO)/BATSE, Swift/BAT and Fermi/GBM gamma-ray bursts (GRBs). The T90 distributions of 298 redshift-known Swift/BAT GRBs have also been studied in both observer and rest frames. Bayesian information criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the CGRO/BATSE and Fermi/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the Swift/BAT bursts in the rest frame, which is consistent with some previous results. However, Swift GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of Swift/BAT.
Model for non-Gaussian intraday stock returns
NASA Astrophysics Data System (ADS)
Gerig, Austin; Vicente, Javier; Fuentes, Miguel A.
2009-12-01
Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.
Non-Gaussianities of single field inflation with nonminimal coupling
Qiu, Taotao; Yang, Kwei-Chou
2011-04-15
We investigate the non-Gaussianities of inflation driven by a single scalar field coupling nonminimally to the Einstein Gravity. We assume that the form of the scalar field is very general with an arbitrary sound speed. For convenience, we take the subclass that the nonminimal coupling term is linear to the Ricci scalar R. We define a parameter {mu}{identical_to}{epsilon}{sub h}/{epsilon}{sub {theta}}, where {epsilon}{sub h} and {epsilon}{sub {theta}} are two kinds of slow-roll parameters, and obtain the dependence of the shape of the 3-point correlation function on {mu}. We also show the estimator F{sub NL} in the equilateral limit. Finally, based on numerical calculations, we present the non-Gaussianities of nonminimal coupling chaotic inflation as an explicit example.
Designing Multi-target Compound Libraries with Gaussian Process Models.
Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert
2016-05-01
We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design. PMID:27492085
Diffraction of Gaussian beams on intracavity Bragg gratings
NASA Astrophysics Data System (ADS)
Bitauld, David; Menez, Ludivine; Zaquine, Isabelle; Maruani, Alain; Frey, Robert
2005-06-01
The diffraction of Gaussian beams on intracavity Bragg gratings is analyzed theoretically. For reasonable waists the associated beam divergence does not significantly influence the diffraction efficiency of such devices. Nevertheless, the tilt angle of the incident beam, imposed by the Bragg resonance condition, strongly reduces the diffraction efficiency at short grating periods. However, the angular selectivity can be maintained if the Fabry-Perot cavity is tuned to the incident beam direction, which allows the use of small-volume holograms together with a dense angular multiplex. This theoretical analysis can be applied to the optimization of the diffraction properties of Gaussian beams on any intracavity Bragg grating, which could then be used for free-space parallel signal processing.
Propagation of Airy Gaussian vortex beams in uniaxial crystals
NASA Astrophysics Data System (ADS)
Weihao, Yu; Ruihuang, Zhao; Fu, Deng; Jiayao, Huang; Chidao, Chen; Xiangbo, Yang; Yanping, Zhao; Dongmei, Deng
2016-04-01
The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108, 11374107, 10904041, and 11547212), the Foundation of Cultivating Outstanding Young Scholars of Guangdong Province, China, the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 2015093), and the Science and Technology Projects of Guangdong Province, China (Grant No. 2013B031800011).
Interpretation of Extinction in Gaussian-Beam Scattering
NASA Technical Reports Server (NTRS)
Lock, James A.
1995-01-01
The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.
Nonlinear evolutions and non-Gaussianity in generalized gravity
NASA Astrophysics Data System (ADS)
Koh, Seoktae; Kim, Sang Pyo; Song, Doo Jong
2005-06-01
We use the Hamilton-Jacobi theory to study the nonlinear evolutions of inhomogeneous spacetimes during inflation in generalized gravity. We find the exact solutions to the lowest order Hamilton-Jacobi equation for special scalar potentials and introduce an approximation method for general potentials. The conserved quantity invariant under a change of timelike hypersurfaces proves useful in dealing with gravitational perturbations. In the long-wavelength approximation, we find a conserved quantity related to the new canonical variable that makes the Hamiltonian density vanish, and calculate the non-Gaussianity in generalized gravity. The slow-roll inflation models with a single scalar field in generalized gravity predict too small non-Gaussianity to be detected by future CMB experiments.
Large non-Gaussianity from two-component hybrid inflation
NASA Astrophysics Data System (ADS)
Byrnes, Christian T.; Choi, Ki-Young; Hall, Lisa M. H.
2009-02-01
We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll inflation which is generally characterised by a large fNL, τNL and a small gNL. For certain parameter values we can satisfy τNL >> fNL2. The bispectrum is of the local type but may have a significant scale dependence. We show that the loop corrections to the power spectrum and bispectrum are suppressed during inflation, if one assume that the fields follow a classical background trajectory. We also include the effect of the waterfall field, which can lead to a significant change in the observables after the waterfall field is destabilised, depending on the couplings between the waterfall and inflaton fields.
Applications of the Gaussian kinematic formula to CMB data analysis
NASA Astrophysics Data System (ADS)
Fantaye, Yabebal; Marinucci, Domenico; Hansen, Frode; Maino, Davide
2015-03-01
The Gaussian kinematic formula (GKF) [R. J. Adler and J. E. Taylor, Random Fields and Geometry (Springer, New York, 2007).] is an extremely powerful tool allowing for explicit analytic predictions of expected values of Minkowski functionals under realistic experimental conditions for cosmological data collections. In this paper, we implement Minkowski functionals on multipoles and needlet components of CMB fields, thus allowing a better control of cosmic variance and extraction of information on both harmonic and real domains; we then exploit the GKF to provide their expected values on spherical maps, in the presence of arbitrary sky masks, and under non-Gaussian circumstances. All our results are validated by numerical experiments, which show a perfect agreement between theoretical predictions and Monte Carlo simulations.
Mean-field fluid behavior of the Gaussian core model
NASA Astrophysics Data System (ADS)
Louis, A. A.; Bolhuis, P. G.; Hansen, J. P.
2000-12-01
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated ``mean-field fluid'' over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
Large non-Gaussianity from two-component hybrid inflation
Byrnes, Christian T.; Choi, Ki-Young; Hall, Lisa M.H. E-mail: kiyoung.choi@uam.es
2009-02-15
We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll inflation which is generally characterised by a large f{sub NL}, {tau}{sub NL} and a small g{sub NL}. For certain parameter values we can satisfy {tau}{sub NL} >> f{sub NL}{sup 2}. The bispectrum is of the local type but may have a significant scale dependence. We show that the loop corrections to the power spectrum and bispectrum are suppressed during inflation, if one assume that the fields follow a classical background trajectory. We also include the effect of the waterfall field, which can lead to a significant change in the observables after the waterfall field is destabilised, depending on the couplings between the waterfall and inflaton fields.