Nguyen, Ngoc Minh; Corff, Sylvain Le; Moulines, Éric
2017-12-01
This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter/smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state space models using the generalized two-filter formula together with Kalman filters/smoothers. More recently, a forward-backward decomposition of smoothing distributions mimicking the Rauch-Tung-Striebel smoother for the regimes combined with backward Kalman updates has been introduced. This paper investigates the benefit of introducing additional rejuvenation steps in all these algorithms to sample at each time instant new regimes conditional on the forward and backward particles. This defines particle-based approximations of the smoothing distributions whose support is not restricted to the set of particles sampled in the forward or backward filter. These procedures are applied to commodity markets which are described using a two-factor model based on the spot price and a convenience yield for crude oil data.
Mader, Angelika H.; Dertien, Edwin Christian; Reidsma, Dennis
2011-01-01
We live in a world of continuous information overflow, but the quality of information and communication is suffering. Single value devices contribute to the information and communication quality by fo- cussing on one explicit, relevant piece of information. The information is decoupled from a
Mader, Angelika H.; Dertien, Edwin Christian; Reidsma, Dennis; Camurri, Antonio; Costa, Cristina
We live in a world of continuous information overflow, but the quality of information and communication is suffering. Single value devices contribute to information and communication quality by focussing on one explicit, relevant piece of information. The information is decoupled from a computer and
Mader, Angelika H.; Reidsma, Dennis; Dertien, Edwin Christian; Volpe, G; Kolkmeier, Jan; Camurri, A.; Kolkmeier, Jan; Nijholt, Antinus
2015-01-01
We live in a world of continuous information overflow, but the quality of information and communication is suffering. Single value devices contribute to the information and communication quality by focussing on one explicit, relevant piece of information. The information is decoupled from a computer
Uniform Single Valued Neutrosophic Graphs
Directory of Open Access Journals (Sweden)
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Broumi, Said; Talea, Mohamed; Bakali, Assia; Smarandache, Florentin
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
An Adaptive Smoother for Counting Measurements
International Nuclear Information System (INIS)
Kondrasovs Vladimir; Coulon Romain; Normand Stephane
2013-06-01
Counting measurements associated with nuclear instruments are tricky to carry out due to the stochastic process of the radioactivity. Indeed events counting have to be processed and filtered in order to display a stable count rate value and to allow variations monitoring in the measured activity. Smoothers (as the moving average) are adjusted by a time constant defined as a compromise between stability and response time. A new approach has been developed and consists in improving the response time while maintaining count rate stability. It uses the combination of a smoother together with a detection filter. A memory of counting data is processed to calculate several count rate estimates using several integration times. These estimates are then sorted into the memory from short to long integration times. A measurement position, in terms of integration time, is then chosen into this memory after a detection test. An inhomogeneity into the Poisson counting process is detected by comparison between current position estimate and the other estimates contained into the memory in respect with the associated statistical variance calculated with homogeneous assumption. The measurement position (historical time) and the ability to forget an obsolete data or to keep in memory a useful data are managed using the detection test result. The proposed smoother is then an adaptive and a learning algorithm allowing an optimization of the response time while maintaining measurement counting stability and converging efficiently to the best counting estimate after an effective change in activity. This algorithm has also the specificity to be low recursive and thus easily embedded into DSP electronics based on FPGA or micro-controllers meeting 'real life' time requirements. (authors)
Tradeoff between smoother and sooner ''little rip''
International Nuclear Information System (INIS)
Bouhmadi-Lopez, Mariam; Chen, Pisin; Liu, Yen-Wei
2013-01-01
There exist dark-energy models that predict the occurrence of a ''little rip''. At the point of a little rip the Hubble rate and its cosmic time derivative approach infinity, which is quite similar to the big rip singularity except that the former happens at infinite future and the latter at a finite cosmic time; both events happen in the future and at high energies. In the case of the big rip, a combination of ultra-violet and infra-red effects can smooth its doomsday. We therefore wonder if the little rip can also be smoothed in a similar way. We address the ultra-violet and infra-red effects in general relativity through a brane-world model with a Gauss-Bonnet term in the bulk and an induced gravity term on the brane. We find that the little rip is transformed in this case into a sudden singularity, or a ''big brake''. Even though the big brake is smoother than the little rip in that the Hubble rate is finite at the event, the trade-off is that it takes place sooner, at a finite cosmic time. In our estimate, the big brake would happen at roughly 1300 Gyr. (orig.)
LUM Smoother with Smooth Control for Noisy Image Sequences
Directory of Open Access Journals (Sweden)
Lukàč Rastislav
2001-01-01
Full Text Available This paper focuses on adaptive structure of LUM (lower-upper-middle smoothers for noisy image sequences. For the balance between noise suppression and signal-detail preservation, the LUM smoothers are widely used in smoothing applications. The amount of smoothing done by LUM smoothers is controlled by tuning parameter. However, the smoothing level is fixed for whole image. Thus, the excessive or insufficient smoothing can be performed. This problem is solved by a new method based on the adaptive controlled level of smoothing. A new method has excellent performance of the noise reduction in the environments corrupted by the impulse noise. In addition, minimal signal-detail and motion blurring can be observed. The performance of proposed method is evaluated through objective criteria and compared with traditional temporal, spatial, and spatiotemporal LUM smoothers.
Knowledge fusion: Comparison of fuzzy curve smoothers to statistically motivated curve smoothers
International Nuclear Information System (INIS)
Burr, T.; Strittmatter, R.B.
1996-03-01
This report describes work during FY 95 that was sponsored by the Department of Energy, Office of Nonproliferation and National Security (NN) Knowledge Fusion (KF) Project. The project team selected satellite sensor data to use as the one main example to which its analysis algorithms would be applied. The specific sensor-fusion problem has many generic features, which make it a worthwhile problem to attempt to solve in a general way. The generic problem is to recognize events of interest from multiple time series that define a possibly noisy background. By implementing a suite of time series modeling and forecasting methods and using well-chosen alarm criteria, we reduce the number of false alarms. We then further reduce the number of false alarms by analyzing all suspicious sections of data, as judged by the alarm criteria, with pattern recognition methods. This report gives a detailed comparison of two of the forecasting methods (fuzzy forecaster and statistically motivated curve smoothers as forecasters). The two methods are compared on five simulated and five real data sets. One of the five real data sets is satellite sensor data. The conclusion is the statistically motivated curve smoother is superior on simulated data of the type we studied. The statistically motivated method is also superior on most real data. In defense of the fuzzy-logic motivated methods, we point out that fuzzy-logic methods were never intended to compete with statistical methods on numeric data. Fuzzy logic was developed to handle real-world situations where either real data was not available or was supplemented with either ''expert opinion'' or some sort of linguistic information
On an iterative ensemble smoother and its application to a reservoir facies estimation problem
Luo, Xiaodong; Chen, Yan; Valestrand, Randi; Stordal, Andreas; Lorentzen, Rolf; Nævdal, Geir
2014-05-01
For data assimilation problems there are different ways in utilizing the available observations. While certain data assimilation algorithms, for instance, the ensemble Kalman filter (EnKF, see, for examples, Aanonsen et al., 2009; Evensen, 2006) assimilate the observations sequentially in time, other data assimilation algorithms may instead collect the observations at different time instants and assimilate them simultaneously. In general such algorithms can be classified as smoothers. In this aspect, the ensemble smoother (ES, see, for example, Evensen and van Leeuwen, 2000) can be considered as an smoother counterpart of the EnKF. The EnKF has been widely used for reservoir data assimilation (history matching) problems since its introduction to the community of petroleum engineering (Nævdal et al., 2002). The applications of the ES to reservoir data assimilation problems are also investigated recently (see, for example, Skjervheim and Evensen, 2011). Compared to the EnKF, the ES has certain technical advantages, including, for instance, avoiding the restarts associated with each update step in the EnKF and also having fewer variables to update, which may result in a significant reduction in simulation time, while providing similar assimilation results to those obtained by the EnKF (Skjervheim and Evensen, 2011). To further improve the performance of the ES, some iterative ensemble smoothers are suggested in the literature, in which the iterations are carried out in the forms of certain iterative optimization algorithms, e.g., the Gaussian-Newton (Chen and Oliver, 2012) or the Levenberg-Marquardt method (Chen and Oliver, 2013; Emerick and Reynolds, 2012), or in the context of adaptive Gaussian mixture (AGM, see Stordal and Lorentzen, 2013). In Emerick and Reynolds (2012) the iteration formula is derived based on the idea that, for linear observations, the final results of the iterative ES should be equal to the estimate of the EnKF. In Chen and Oliver (2013), the
Recursive bias estimation for high dimensional regression smoothers
Energy Technology Data Exchange (ETDEWEB)
Hengartner, Nicolas W [Los Alamos National Laboratory; Cornillon, Pierre - Andre [AGROSUP, FRANCE; Matzner - Lober, Eric [UNIV OF RENNES, FRANCE
2009-01-01
In multivariate nonparametric analysis, sparseness of the covariates also called curse of dimensionality, forces one to use large smoothing parameters. This leads to biased smoother. Instead of focusing on optimally selecting the smoothing parameter, we fix it to some reasonably large value to ensure an over-smoothing of the data. The resulting smoother has a small variance but a substantial bias. In this paper, we propose to iteratively correct of the bias initial estimator by an estimate of the latter obtained by smoothing the residuals. We examine in details the convergence of the iterated procedure for classical smoothers and relate our procedure to L{sub 2}-Boosting, For multivariate thin plate spline smoother, we proved that our procedure adapts to the correct and unknown order of smoothness for estimating an unknown function m belonging to H({nu}) (Sobolev space where m should be bigger than d/2). We apply our method to simulated and real data and show that our method compares favorably with existing procedures.
Directory of Open Access Journals (Sweden)
E. Crestani
2013-04-01
Full Text Available Estimating the spatial variability of hydraulic conductivity K in natural aquifers is important for predicting the transport of dissolved compounds. Especially in the nonreactive case, the plume evolution is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman-filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF and the ensemble smoother (ES capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalman-filter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf and since this condition may not be met by some of the flow and transport state variables, issues related to the non-Gaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.
Extended Kalman smoother with differential evolution technique for denoising of ECG signal.
Panigrahy, D; Sahu, P K
2016-09-01
Electrocardiogram (ECG) signal gives a lot of information on the physiology of heart. In reality, noise from various sources interfere with the ECG signal. To get the correct information on physiology of the heart, noise cancellation of the ECG signal is required. In this paper, the effectiveness of extended Kalman smoother (EKS) with the differential evolution (DE) technique for noise cancellation of the ECG signal is investigated. DE is used as an automatic parameter selection method for the selection of ten optimized components of the ECG signal, and those are used to create the ECG signal according to the real ECG signal. These parameters are used by the EKS for the development of the state equation and also for initialization of the parameters of EKS. EKS framework is used for denoising the ECG signal from the single channel. The effectiveness of proposed noise cancellation technique has been evaluated by adding white, colored Gaussian noise and real muscle artifact noise at different SNR to some visually clean ECG signals from the MIT-BIH arrhythmia database. The proposed noise cancellation technique of ECG signal shows better signal to noise ratio (SNR) improvement, lesser mean square error (MSE) and percent of distortion (PRD) compared to other well-known methods.
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J. [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K.S. [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B.J. [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M. [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)
1999-03-01
The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)
A Fixed-Lag Kalman Smoother to Filter Power Line Interference in Electrocardiogram Recordings.
Warmerdam, G J J; Vullings, R; Schmitt, L; Van Laar, J O E H; Bergmans, J W M
2017-08-01
Filtering power line interference (PLI) from electrocardiogram (ECG) recordings can lead to significant distortions of the ECG and mask clinically relevant features in ECG waveform morphology. The objective of this study is to filter PLI from ECG recordings with minimal distortion of the ECG waveform. In this paper, we propose a fixed-lag Kalman smoother with adaptive noise estimation. The performance of this Kalman smoother in filtering PLI is compared to that of a fixed-bandwidth notch filter and several adaptive PLI filters that have been proposed in the literature. To evaluate the performance, we corrupted clean neonatal ECG recordings with various simulated PLI. Furthermore, examples are shown of filtering real PLI from an adult and a fetal ECG recording. The fixed-lag Kalman smoother outperforms other PLI filters in terms of step response settling time (improvements that range from 0.1 to 1 s) and signal-to-noise ratio (improvements that range from 17 to 23 dB). Our fixed-lag Kalman smoother can be used for semi real-time applications with a limited delay of 0.4 s. The fixed-lag Kalman smoother presented in this study outperforms other methods for filtering PLI and leads to minimal distortion of the ECG waveform.
Han, S. C.; Tangdamrongsub, N.; Yeo, I. Y.; Dong, J.
2017-12-01
Soil moisture and groundwater storage are important information for comprehensive understanding of the climate system and accurate assessment of the regional/global water resources. It is possible to derive the water storage from land surface models but the outputs are commonly biased by inaccurate forcing data, inefficacious model physics, and improper model parameter calibration. To mitigate the model uncertainty, the observation (e.g., from remote sensing as well as ground in-situ data) are often integrated into the models via data assimilation (DA). This study aims to improve the estimation of soil moisture and groundwater storage by simultaneously assimilating satellite observations from the Gravity Recovery And Climate Experiment (GRACE), the Soil Moisture Ocean Salinity (SMOS), and the Soil Moisture Active Passive (SMAP) into the Community Atmosphere Biosphere Land Exchange (CABLE) land surface model using the ensemble Kalman batch smoother (EnBS) and particle batch smoother (PBS) frameworks. The uncertainty of GRACE observation is obtained rigorously from the full error variance-covariance matrix of the GRACE data product. This method demonstrates the use of a realistic representative of GRACE uncertainty, which is spatially correlated in nature, leads to a higher accuracy of water storage computation. Additionally, the comparison between EnBS and PBS results is discussed to understand the filter's performance, limitation, and suitability. The joint DA is demonstrated in the Goulburn catchment, South-East Australia, where diverse ground observations (surface soil moisture, root-zone soil moisture, and groundwater level) are available for evaluation of our DA results. Preliminary results show that both smoothers provide significant improvement of surface soil moisture and groundwater storage estimates. Importantly, our developed DA scheme disaggregates the catchment-scale GRACE information into finer vertical and spatial scales ( 25 km). We present an
Directory of Open Access Journals (Sweden)
Malinowski Marcin
2015-02-01
Full Text Available In navigation practice, there are various navigational architecture and integration strategies of measuring instruments that affect the choice of the Kalman filtering algorithm. The analysis of different methods of Kalman filtration and associated smoothers applied in object tracing was made on the grounds of simulation tests of algorithms designed and presented in this paper. EKF (Extended Kalman Filter filter based on approximation with (jacobians partial derivations and derivative-free filters like UKF (Unscented Kalman Filter and CDKF (Central Difference Kalman Filter were implemented in comparison. For each method of filtration, appropriate smoothers EKS (Extended Kalman Smoother, UKS (Unscented Kalman Smoother and CDKS (Central Difference Kalman Smoother were presented as well. Algorithms performance is discussed on the theoretical base and simulation results of two cases are presented.
Dynamic Inverse Problem Solution Using a Kalman Filter Smoother for Neuronal Activity Estimation
Directory of Open Access Journals (Sweden)
Eduardo Giraldo-Suárez
2011-12-01
Full Text Available This article presents an estimation method of neuronal activity into the brain using a Kalman smoother approach that takes into account in the solution of the inverse problem the dynamic variability of the time series. This method is applied over a realistic head model calculated with the boundary element method. A comparative analysis for the dynamic estimation methods is made up from simulated EEG signals for several noise conditions. The solution of the inverse problem is achieved by using high performance computing techniques and an evaluation of the computational cost is performed for each method. As a result, the Kalman smoother approach presents better performance in the estimation task than the regularized static solution, and the direct Kalman filter.
Lam, D. T.; Kerrou, J.; Benabderrahmane, H.; Perrochet, P.
2017-12-01
The calibration of groundwater flow models in transient state can be motivated by the expected improved characterization of the aquifer hydraulic properties, especially when supported by a rich transient dataset. In the prospect of setting up a calibration strategy for a variably-saturated transient groundwater flow model of the area around the ANDRA's Bure Underground Research Laboratory, we wish to take advantage of the long hydraulic head and flowrate time series collected near and at the access shafts in order to help inform the model hydraulic parameters. A promising inverse approach for such high-dimensional nonlinear model, and which applicability has been illustrated more extensively in other scientific fields, could be an iterative ensemble smoother algorithm initially developed for a reservoir engineering problem. Furthermore, the ensemble-based stochastic framework will allow to address to some extent the uncertainty of the calibration for a subsequent analysis of a flow process dependent prediction. By assimilating the available data in one single step, this method iteratively updates each member of an initial ensemble of stochastic realizations of parameters until the minimization of an objective function. However, as it is well known for ensemble-based Kalman methods, this correction computed from approximations of covariance matrices is most efficient when the ensemble realizations are multi-Gaussian. As shown by the comparison of the updated ensemble mean obtained for our simplified synthetic model of 2D vertical flow by using either multi-Gaussian or multipoint simulations of parameters, the ensemble smoother fails to preserve the initial connectivity of the facies and the parameter bimodal distribution. Given the geological structures depicted by the multi-layered geological model built for the real case, our goal is to find how to still best leverage the performance of the ensemble smoother while using an initial ensemble of conditional multi-Gaussian
Gaussian and Non-Gaussian operations on non-Gaussian state: engineering non-Gaussianity
Directory of Open Access Journals (Sweden)
Olivares Stefano
2014-03-01
Full Text Available Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive Glauber-Sudarshan Prepresentation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully characterized by direct detection of photon numbers. In particular, the non-Gaussianity of the state is a characteristics that must be assessed by phase-sensitive measurements. We also show that the non-Gaussianity of conditional states can be manipulated by choosing suitable conditioning values and composition of phase-averaged states.
CSIR Research Space (South Africa)
Roux, FS
2009-01-01
Full Text Available , t0)} = P(du, dv) {FR{g(u, v, t0)}} Replacement: u→ du = t− t0 i2 ∂ ∂u′ v → dv = t− t0 i2 ∂ ∂v′ CSIR National Laser Centre – p.13/30 Differentiation i.s.o integration Evaluate the integral over the Gaussian beam (once and for all). Then, instead... . Gaussian beams with vortex dipoles CSIR National Laser Centre – p.2/30 Gaussian beam notation Gaussian beam in normalised coordinates: g(u, v, t) = exp ( −u 2 + v2 1− it ) u = xω0 v = yω0 t = zρ ρ = piω20 λ ω0 — 1/e2 beam waist radius; ρ— Rayleigh range ω ω...
Gaussian operations and privacy
International Nuclear Information System (INIS)
Navascues, Miguel; Acin, Antonio
2005-01-01
We consider the possibilities offered by Gaussian states and operations for two honest parties, Alice and Bob, to obtain privacy against a third eavesdropping party, Eve. We first extend the security analysis of the protocol proposed in [Navascues et al. Phys. Rev. Lett. 94, 010502 (2005)]. Then, we prove that a generalized version of this protocol does not allow one to distill a secret key out of bound entangled Gaussian states
Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Directory of Open Access Journals (Sweden)
Yangyang Wang
2018-04-01
Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
Byrnes, Christian T; Tasinato, Gianmassimo; Wands, David
2012-01-01
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_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.
Learning conditional Gaussian networks
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given...... a configuration of the discrete parents. We assume parameter independence and complete data. Further, to learn the structure of the network, the network score is deduced. We then develop a local master prior procedure, for deriving parameter priors in these networks. This procedure satisfies parameter...... independence, parameter modularity and likelihood equivalence. Bayes factors to be used in model search are introduced. Finally the methods derived are illustrated by a simple example....
AUTONOMOUS GAUSSIAN DECOMPOSITION
International Nuclear Information System (INIS)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John
2015-01-01
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...
AUTONOMOUS GAUSSIAN DECOMPOSITION
Energy Technology Data Exchange (ETDEWEB)
Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)
2015-04-15
We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.
Directory of Open Access Journals (Sweden)
Mathias Hauan Arbo
2017-01-01
Full Text Available Visual Odometry (VO is increasingly a useful tool for robotic navigation in a variety of applications, including weed removal for agricultural robotics. The methods of evaluating VO are often computationally expensive and can cause the VO measurements to be significantly delayed with respect to a compass, wheel odometry, and GPS measurements. In this paper we present a Bayesian formulation of fusing delayed displacement measurements. We implement solutions to this problem based on the unscented Kalman filter (UKF, leading to what we term an unscented multi-point smoother. The proposed methods are tested in simulations of an agricultural robot. The simulations show improvements in the localization RMS error when including the VO measurements with a variety of latencies.
On the convergence of (ensemble) Kalman filters and smoothers onto the unstable subspace
Bocquet, Marc
2016-04-01
The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters and smoothers. In particular, as emphasised in the seminal work of Anna Trevisan and co-authors, the error covariance matrix is asymptotically supported by the unstable and neutral subspace only, i.e. it is span by the backward Lyapunov vectors with non-negative exponents. This behaviour is at the heart of algorithms known as Assimilation in the Unstable Subspace, although its formal proof was still missing. This convergence property, its analytic proof, meaning and implications for the design of efficient reduced-order data assimilation algorithms are the topics of this talk. The structure of the talk is as follows. Firstly, we provide the analytic proof of the convergence on the unstable and neutral subspace in the linear dynamics and linear observation operator case, along with rigorous results giving the rate of such convergence. The derivation is based on an expression that relates explicitly the covariance matrix at an arbitrary time with the initial error covariance. Numerical results are also shown to illustrate and support the mathematical claims. Secondly, we discuss how this neat picture is modified when the dynamics become nonlinear and chaotic and when it is not possible to derive analytic formulas. In this case an ensemble Kalman filter (EnKF) is used and the connection between the convergence properties on the unstable-neutral subspace and the EnKF covariance inflation is discussed. We also explain why, in the perfect model setting, the iterative ensemble Kalman smoother (IEnKS), as an efficient filtering and smoothing technique, has an error covariance matrix whose projection is more focused on the unstable-neutral subspace than that of the EnKF. This contribution results from collaborations with A. Carrassi, K. S. Gurumoorthy, A. Apte, C. Grudzien, and C. K. R. T. Jones.
Precipitation Ensembles from Single-Value Forecasts for Hydrological Ensemble Forecasting
Demargne, J.; Schaake, J.; Wu, L.; Welles, E.; Herr, H.; Seo, D.
2005-05-01
An ensemble pre-processor was developed to produce short-term precipitation ensembles using operational single-value forecasts. The methodology attempts to quantify the uncertainty in the single-value forecast and to capture the skill therein. These precipitation ensemble forecasts could be then ingested in the NOAA/National Weather Service (NWS) Ensemble Streamflow Prediction (ESP) system to produce probabilistic hydrological forecasts that reflect the uncertainty in forecast precipitation. The procedure constructs the joint distribution of forecast and observed precipitation from historical pairs of forecast and observed values. The probability distribution function of the future events that may occur given a particular single-value forecast is then the conditional distribution of observed precipitation given the forecast. To generate individual ensemble members for each lead time and each location, the historical observed values are replaced with values sampled from the conditional distribution given the single-value forecast. The replacement procedure matches the ranks of historical and rescaled values to preserve the space-time properties of observed precipitation in the ensemble traces. Currently, the ensemble pre-processor is being tested and evaluated at four NOAA/NWS River Forecast Centers (RFCs) in the U.S.A. In this contribution, we present the results thus far from the field and retrospective evaluations, and key science issues that must be addressed toward national operational implementation.
Interconversion of pure Gaussian states requiring non-Gaussian operations
Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.
2015-01-01
We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.
Yurinsky, Vadim Vladimirovich
1995-01-01
Surveys the methods currently applied to study sums of infinite-dimensional independent random vectors in situations where their distributions resemble Gaussian laws. Covers probabilities of large deviations, Chebyshev-type inequalities for seminorms of sums, a method of constructing Edgeworth-type expansions, estimates of characteristic functions for random vectors obtained by smooth mappings of infinite-dimensional sums to Euclidean spaces. A self-contained exposition of the modern research apparatus around CLT, the book is accessible to new graduate students, and can be a useful reference for researchers and teachers of the subject.
Ye, Jun
2013-05-01
The paper presents the correlation and correlation coefficient of single-valued neutrosophic sets (SVNSs) based on the extension of the correlation of intuitionistic fuzzy sets and demonstrates that the cosine similarity measure is a special case of the correlation coefficient in SVNS. Then a decision-making method is proposed by the use of the weighted correlation coefficient or the weighted cosine similarity measure of SVNSs, in which the evaluation information for alternatives with respect to criteria is carried out by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree under single-valued neutrosophic environment. We utilize the weighted correlation coefficient or the weighted cosine similarity measure between each alternative and the ideal alternative to rank the alternatives and to determine the best one(s). Finally, an illustrative example demonstrates the application of the proposed decision-making method.
Rotating quantum Gaussian packets
International Nuclear Information System (INIS)
Dodonov, V V
2015-01-01
We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the ‘external’ momentum related to the motion of the packet center and the ‘internal’ momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for ‘co-rotating’ external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of ‘co-rotating’ and ‘anti-rotating’ packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of ‘focusing’ and ‘de-focusing’ in the orthogonal directions. (paper)
Medical Diagnosis Using Distance-Based Similarity Measures of Single Valued Neutrosophic Multisets
Directory of Open Access Journals (Sweden)
Shan Ye
2015-01-01
Full Text Available This paper proposes a generalized distance measure and its similarity measures between single valued neutrosophic multisets (SVNMs. Then, the similarity measures are applied to a medical diagnosis problem with incomplete, indeterminate and inconsistent information. This diagnosis method can deal with the diagnosis problem with indeterminate and inconsistent information which cannot be handled by the diagnosis method based on intuitionistic fuzzy multisets (IFMs.
Langer, Stefan
2014-11-01
For unstructured finite volume methods an agglomeration multigrid with an implicit multistage Runge-Kutta method as a smoother is developed for solving the compressible Reynolds averaged Navier-Stokes (RANS) equations. The implicit Runge-Kutta method is interpreted as a preconditioned explicit Runge-Kutta method. The construction of the preconditioner is based on an approximate derivative. The linear systems are solved approximately with a symmetric Gauss-Seidel method. To significantly improve this solution method grid anisotropy is treated within the Gauss-Seidel iteration in such a way that the strong couplings in the linear system are resolved by tridiagonal systems constructed along these directions of strong coupling. The agglomeration strategy is adapted to this procedure by taking into account exactly these anisotropies in such a way that a directional coarsening is applied along these directions of strong coupling. Turbulence effects are included by a Spalart-Allmaras model, and the additional transport-type equation is approximately solved in a loosely coupled manner with the same method. For two-dimensional and three-dimensional numerical examples and a variety of differently generated meshes we show the wide range of applicability of the solution method. Finally, we exploit the GMRES method to determine approximate spectral information of the linearized RANS equations. This approximate spectral information is used to discuss and compare characteristics of multistage Runge-Kutta methods.
CONVEX BODIES AND GAUSSIAN PROCESSES
Directory of Open Access Journals (Sweden)
Richard A Vitale
2011-05-01
Full Text Available For several decades, the topics of the title have had a fruitful interaction. This survey will describe some of these connections, including the GB/GC classification of convex bodies, Ito-Nisio singularities from a geometric viewpoint, Gaussian representation of intrinsic volumes, theWills functional in a Gaussian context, and inequalities.
Spectral representation of Gaussian semimartingales
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2009-01-01
The aim of the present paper is to characterize the spectral representation of Gaussian semimartingales. That is, we provide necessary and sufficient conditions on the kernel K for X t =∫ K t (s) dN s to be a semimartingale. Here, N denotes an independently scattered Gaussian random measure...
Directory of Open Access Journals (Sweden)
Shan Ye
2014-12-01
Full Text Available This paper introduces the concept of a single valued neutrosophic multiset (SVNM as a generalization of an intuitionistic fuzzy multiset (IFM and some basic operational relations of SVNMs, and then proposes the Dice similarity measure and the weighted Dice similarity measure for SVNMs and investigates their properties. Fi nally, the Dice similarity measure is applied to a medical diagnosis problem with SVNM information. This diagnosis method can deal with the medical diagnosis problem with indeterminate and inconsistent information which cannot be handled by the diagnosis method based on IFMs.
Directory of Open Access Journals (Sweden)
Rui Wang
2018-01-01
Full Text Available Single-valued neutrosophic hesitant fuzzy set (SVNHFS is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM process. This paper investigates the MCDM problems in which the criteria under SVNHF environment are in different priority levels. First, the generalized single-valued neutrosophic hesitant fuzzy prioritized weighted average operator and generalized single-valued neutrosophic hesitant fuzzy prioritized weighted geometric operator are developed based on the prioritized average operator. Second, some desirable properties and special cases of the proposed operators are discussed in detail. Third, an approach combined with the proposed operators and the score function of single-valued neutrosophic hesitant fuzzy element is constructed to solve MCDM problems. Finally, an example of investment selection is provided to illustrate the validity and rationality of the proposed method.
Malinowski Marcin; Kwiecień Janusz
2015-01-01
In navigation practice, there are various navigational architecture and integration strategies of measuring instruments that affect the choice of the Kalman filtering algorithm. The analysis of different methods of Kalman filtration and associated smoothers applied in object tracing was made on the grounds of simulation tests of algorithms designed and presented in this paper. EKF (Extended Kalman Filter) filter based on approximation with (jacobians) partial derivations and derivative-free f...
Equi-Gaussian curvature folding
Indian Academy of Sciences (India)
curvature kf (p) i.e., kp = kf (p). In this case f will map curves to curves with equal equi-. Gaussian curvature at corresponding points. It will also map area with sectional curvature k(σ, p) into areas with the same sectional curvature, and so on. The set of all equi-Gaussian curvature foldings of M into N will be denoted by.
Directory of Open Access Journals (Sweden)
Zhu Xiao
2016-05-01
Full Text Available In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS, is proposed, which enables vehicle state estimation (VSE with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.
Directory of Open Access Journals (Sweden)
Jun Ye
2017-04-01
Full Text Available Based on dynamic information collected from different time intervals in some real situations, this paper firstly proposes a dynamic single valued neutrosophic multiset (DSVNM to express dynamic information and operational relations of DSVNMs. Then, a correlation coefficient between DSVNMs and a weighted correlation coefficient between DSVNMs are presented to measure the correlation degrees between DSVNMs, and their properties are investigated. Based on the weighted correlation coefficient of DSVNMs, a multiple attribute decision-making method is established under a DSVNM environment, in which the evaluation values of alternatives with respect to attributes are collected from different time intervals and are represented by the form of DSVNMs. The ranking order of alternatives is performed through the weighted correlation coefficient between an alternative and the ideal alternative, which is considered by the attribute weights and the time weights, and thus the best one(s can also be determined. Finally, a practical example shows the application of the proposed method.
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus Plenge
2017-01-01
This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new...
Directory of Open Access Journals (Sweden)
Fei-Bin Hsiao
2011-03-01
Full Text Available This paper presents a complete procedure for sensor compatibility correction of a fixed-wing Unmanned Air Vehicle (UAV. The sensors consist of a differential air pressure transducer for airspeed measurement, two airdata vanes installed on an airdata probe for angle of attack (AoA and angle of sideslip (AoS measurement, and an Attitude and Heading Reference System (AHRS that provides attitude angles, angular rates, and acceleration. The procedure is mainly based on a two pass algorithm called the Rauch-Tung-Striebel (RTS smoother, which consists of a forward pass Extended Kalman Filter (EKF and a backward recursion smoother. On top of that, this paper proposes the implementation of the Wiener Type Filter prior to the RTS in order to avoid the complicated process noise covariance matrix estimation. Furthermore, an easy to implement airdata measurement noise variance estimation method is introduced. The method estimates the airdata and subsequently the noise variances using the ground speed and ascent rate provided by the Global Positioning System (GPS. It incorporates the idea of data regionality by assuming that some sort of statistical relation exists between nearby data points. Root mean square deviation (RMSD is being employed to justify the sensor compatibility. The result shows that the presented procedure is easy to implement and it improves the UAV sensor data compatibility significantly.
Directory of Open Access Journals (Sweden)
Zhiming Zhang
2014-04-01
Full Text Available A single-valued neutrosophic set (SVNS and an interval neutrosophic set (INS are two instances of a neutrosophic set, which can efficiently deal with uncertain, imprecise, incomplete, and inconsistent information. In this paper, we develop a novel method for solving singlevalued neutrosophic multi-criteria decision making with incomplete weight information, in which the criterion values are given in the form of single-valued neutrosophic sets (SVNSs, and the information about criterion weights is incompletely known or completely unknown. The developed method consists of two stages. The first stage is to use the maximizing deviation method to establish an optimization model, which derives the optimal weights of criteria under single-valued neutrosophic environments. After obtaining the weights of criteria through the above stage, the second stage is to develop a single-valued neutrosophic TOPSIS (SVNTOPSIS method to determine a solution with the shortest distance to the single-valued neutrosophic positive ideal solution (SVNPIS and the greatest distance from the singlevalued neutrosophic negative ideal solution (SVNNIS. Moreover, a best global supplier selection problem is used to demonstrate the validity and applicability of the developed method. Finally, the extended results in interval neutrosophic situations are pointed out and a comparison analysis with the other methods is given to illustrate the advantages of the developed methods.
The Multivariate Gaussian Probability Distribution
DEFF Research Database (Denmark)
Ahrendt, Peter
2005-01-01
This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical...
On Gaussian conditional independence structures
Czech Academy of Sciences Publication Activity Database
Lněnička, Radim; Matúš, František
2007-01-01
Roč. 43, č. 3 (2007), s. 327-342 ISSN 0023-5954 R&D Projects: GA AV ČR IAA100750603 Institutional research plan: CEZ:AV0Z10750506 Keywords : multivariate Gaussian distribution * positive definite matrices * determinants * gaussoids * covariance selection models * Markov perfectness Subject RIV: BA - General Mathematics Impact factor: 0.552, year: 2007
Gaussian processes for machine learning.
Seeger, Matthias
2004-04-01
Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided.
Laguerre Gaussian beam multiplexing through turbulence
CSIR Research Space (South Africa)
Trichili, A
2014-08-17
Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...
Stable and Efficient Gaussian Process Calculations
National Aeronautics and Space Administration — The use of Gaussian processes can be an effective approach to prediction in a supervised learning environment. For large data sets, the standard Gaussian process...
Gaussian process regression analysis for functional data
Shi, Jian Qing
2011-01-01
Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime
Analytic matrix elements with shifted correlated Gaussians
DEFF Research Database (Denmark)
Fedorov, D. V.
2017-01-01
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.......Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics....
Directory of Open Access Journals (Sweden)
Johannes Broedel
2017-02-01
Full Text Available We investigate single-valued polylogarithms in two complex variables, which are relevant for the seven-point remainder function in N=4 super-Yang–Mills theory in the multi-Regge regime. After constructing these two-dimensional polylogarithms, we determine the leading logarithmic approximation of the seven-point remainder function up to and including five loops.
General Galilei Covariant Gaussian Maps
Gasbarri, Giulio; Toroš, Marko; Bassi, Angelo
2017-09-01
We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)].
Equi-Gaussian curvature folding
Indian Academy of Sciences (India)
have the same equi-Gaussian curvature 1/a2, where a is the radius of the sphere. Now let f : S2 → Pn be a cellular folding. Then we have the following possibilities: Firstly, there are no cellular foldings f : S2 → Pn, for any n > 3 [2]. Secondly, any cellular folding f : S2 → P3 for which Gf forms a regular graph is equivalent to ...
Gaussian Embeddings for Collaborative Filtering
Dos Santos , Ludovic; Piwowarski , Benjamin; Gallinari , Patrick
2017-01-01
International audience; Most collaborative ltering systems, such as matrix factorization, use vector representations for items and users. Those representations are deterministic, and do not allow modeling the uncertainty of the learned representation, which can be useful when a user has a small number of rated items (cold start), or when there is connict-ing information about the behavior of a user or the ratings of an item. In this paper, we leverage recent works in learning Gaussian embeddi...
Detecting periodicities with Gaussian processes
Directory of Open Access Journals (Sweden)
Nicolas Durrande
2016-04-01
Full Text Available We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in the arabidopsis genome.
Directory of Open Access Journals (Sweden)
Hassana Maigary Georges
2015-01-01
Full Text Available Among the inertial navigation system (INS devices used in land vehicle navigation (LVN, low-cost microelectromechanical systems (MEMS inertial sensors have received more interest for bridging global navigation satellites systems (GNSS signal failures because of their price and portability. Kalman filter (KF based GNSS/INS integration has been widely used to provide a robust solution to the navigation. However, its prediction model cannot give satisfactory results in the presence of colored and variational noise. In order to achieve reliable and accurate positional solution for LVN in urban areas surrounded by skyscrapers or under dense foliage and tunnels, a novel model combining variational Bayesian adaptive Kalman smoother (VB-ACKS as an alternative of KF and ensemble regularized extreme learning machine (ERELM for bridging global positioning systems outages is proposed. The ERELM is applied to reduce the fluctuating performance of GNSS during an outage. We show that a well-organized collection of predictors using ensemble learning yields a more accurate positional result when compared with conventional artificial neural network (ANN predictors. Experimental results show that the performance of VB-ACKS is more robust compared with KF solution, and the prediction of ERELM contains the smallest error compared with other ANN solutions.
Directory of Open Access Journals (Sweden)
Suyan Tian
2016-01-01
Full Text Available In order to test if two chemically or pharmaceutically equivalent products have the same efficacy and/or toxicity, a bioequivalence (BE study is conducted. The 80%/125% rule is the most commonly used criteria for BE and states that BE cannot be claimed unless the 90% CIs for the ratio of selected pharmacokinetics (PK parameters of the tested to the reference drug are within 0.8 to 1.25. Considering that estimates of these PK parameters are derived from the concentration-versus-time curves, a direct comparison between these curves motivates an alternative and more flexible approach to test BE. Here, we propose to frame the BE test in terms of an equivalence of concentration-versus-time curves which are constructed using local polynomial smoother (LPS. A metric is presented to quantify the distance between the curves and its 90% CIs are calculated via bootstrapping. Then, we applied the proposed procedures to data from an animal study and found that BE between a generic drug and its brand name cannot be concluded, which was consistent with the results by applying the 80%/125% rule. However, the proposed procedure has the advantage of testing only on a single metric, instead of all PK parameters.
Breaking Gaussian incompatibility on continuous variable quantum systems
Energy Technology Data Exchange (ETDEWEB)
Heinosaari, Teiko, E-mail: teiko.heinosaari@utu.fi [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Kiukas, Jukka, E-mail: jukka.kiukas@aber.ac.uk [Department of Mathematics, Aberystwyth University, Penglais, Aberystwyth, SY23 3BZ (United Kingdom); Schultz, Jussi, E-mail: jussi.schultz@gmail.com [Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turku (Finland); Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)
2015-08-15
We characterise Gaussian quantum channels that are Gaussian incompatibility breaking, that is, transform every set of Gaussian measurements into a set obtainable from a joint Gaussian observable via Gaussian postprocessing. Such channels represent local noise which renders measurements useless for Gaussian EPR-steering, providing the appropriate generalisation of entanglement breaking channels for this scenario. Understanding the structure of Gaussian incompatibility breaking channels contributes to the resource theory of noisy continuous variable quantum information protocols.
Stochastic Resonance with a Joint Woods-Saxon and Gaussian Potential for Bearing Fault Diagnosis
Directory of Open Access Journals (Sweden)
Haibin Zhang
2014-01-01
Full Text Available This work aims for a new stochastic resonance (SR model which performs well in bearing fault diagnosis. Different from the traditional bistable SR system, we realize the SR based on the joint of Woods-Saxon potential (WSP and Gaussian potential (GP instead of a reflection-symmetric quartic potential. With this potential model, all the parameters in the Woods-Saxon and Gaussian SR (WSGSR system are not coupled when compared to the traditional one, so the output signal-to-noise ratio (SNR can be optimized much more easily by tuning the system parameters. Besides, a smoother potential bottom and steeper potential wall lead to a stable particle motion within each potential well and avoid the unexpected noise. Different from the SR with only WSP which is a monostable system, we improve it into a bistable one as a general form offering a higher SNR and a wider bandwidth. Finally, the proposed model is verified to be outstanding in weak signal detection for bearing fault diagnosis and the strategy offers us a more effective and feasible diagnosis conclusion.
Gaussian queues in light and heavy traffic
Dębicki, K.; Kosiński, K.M.; Mandjes, M.
2012-01-01
In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. Let $Q^{(c)}_{X}\\equiv\\{Q^{(c)}_{X}(t):t\\ge0\\}$ denote a stationary buffer content process for a fluid queue fed by the centered Gaussian process X≡{X(t):t∈ℝ} with stationary increments, X(0)=0,
How Gaussian can our Universe be?
Cabass, Giovanni; Pajer, Enrico; Schmidt, Fabian
Gravity is a non-linear theory, and hence, barring cancellations, the initial super-horizon perturbations produced by inflation must contain some minimum amount of mode coupling, or primordial non-Gaussianity. In single-field slow-roll models, where this lower bound is saturated, non-Gaussianity is
Palm distributions for log Gaussian Cox processes
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper; Waagepetersen, Rasmus
This paper reviews useful results related to Palm distributions of spatial point processes and provides a new result regarding the characterization of Palm distributions for the class of log Gaussian Cox processes. This result is used to study functional summary statistics for a log Gaussian Cox...
Conditional and unconditional Gaussian quantum dynamics
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.
Panigrahy, D; Sahu, P K
2017-03-01
This paper proposes a five-stage based methodology to extract the fetal electrocardiogram (FECG) from the single channel abdominal ECG using differential evolution (DE) algorithm, extended Kalman smoother (EKS) and adaptive neuro fuzzy inference system (ANFIS) framework. The heart rate of the fetus can easily be detected after estimation of the fetal ECG signal. The abdominal ECG signal contains fetal ECG signal, maternal ECG component, and noise. To estimate the fetal ECG signal from the abdominal ECG signal, removal of the noise and the maternal ECG component presented in it is necessary. The pre-processing stage is used to remove the noise from the abdominal ECG signal. The EKS framework is used to estimate the maternal ECG signal from the abdominal ECG signal. The optimized parameters of the maternal ECG components are required to develop the state and measurement equation of the EKS framework. These optimized maternal ECG parameters are selected by the differential evolution algorithm. The relationship between the maternal ECG signal and the available maternal ECG component in the abdominal ECG signal is nonlinear. To estimate the actual maternal ECG component present in the abdominal ECG signal and also to recognize this nonlinear relationship the ANFIS is used. Inputs to the ANFIS framework are the output of EKS and the pre-processed abdominal ECG signal. The fetal ECG signal is computed by subtracting the output of ANFIS from the pre-processed abdominal ECG signal. Non-invasive fetal ECG database and set A of 2013 physionet/computing in cardiology challenge database (PCDB) are used for validation of the proposed methodology. The proposed methodology shows a sensitivity of 94.21%, accuracy of 90.66%, and positive predictive value of 96.05% from the non-invasive fetal ECG database. The proposed methodology also shows a sensitivity of 91.47%, accuracy of 84.89%, and positive predictive value of 92.18% from the set A of PCDB.
Gaussian vs non-Gaussian turbulence: impact on wind turbine loads
DEFF Research Database (Denmark)
Berg, Jacob; Natarajan, Anand; Mann, Jakob
2016-01-01
taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...
Representation of Gaussian semimartingales with applications to the covariance function
DEFF Research Database (Denmark)
Basse-O'Connor, Andreas
2010-01-01
stationary Gaussian semimartingales and their canonical decomposition. Thirdly, we give a new characterization of the covariance function of Gaussian semimartingales, which enable us to characterize the class of martingales and the processes of bounded variation among the Gaussian semimartingales. We...
Lu, Yang; Dong, Jianzhi; Steele-Dunne, Susan; van de Giesen, Nick
2016-04-01
This study is focused on estimating surface sensible and latent heat fluxes from land surface temperature (LST) time series and soil moisture observations. Surface turbulent heat fluxes interact with the overlying atmosphere and play a crucial role in meteorology, hydrology and other climate-related fields, but in-situ measurements are costly and difficult. It has been demonstrated that the time series of LST contains information of energy partitioning and that surface turbulent heat fluxes can be determined from assimilation of LST. These studies are mainly based on two assumptions: (1) a monthly value of bulk heat transfer coefficient under neutral conditions (CHN) which scales the sum of the fluxes, and (2) an evaporation fraction (EF) which stays constant during the near-peak hours of the day. Previous studies have applied variational and ensemble approaches to this problem. Here the newly developed particle batch smoother (PBS) algorithm is adopted to test its capability in this application. The PBS can be seen as an extension of the standard particle filter (PF) in which the states and parameters within a fix window are updated in a batch using all observations in the window. The aim of this study is two-fold. First, the PBS is used to assimilate only LST time series into the force-restore model to estimate fluxes. Second, a simple soil water transfer scheme is introduced to evaluate the benefit of assimilating soil moisture observations simultaneously. The experiments are implemented using the First ISLSCP (International Satellite Land Surface Climatology Project) (FIFE) data. It is shown that the restored LST time series using PBS agrees very well with observations, and that assimilating LST significantly improved the flux estimation at both daily and half-hourly time scales. When soil moisture is introduced to further constrain EF, the accuracy of estimated EF is greatly improved. Furthermore, the RMSEs of retrieved fluxes are effectively reduced at both
Non-Gaussian signatures of tachyacoustic cosmology
Energy Technology Data Exchange (ETDEWEB)
Bessada, Dennis, E-mail: dennis.bessada@unifesp.br [UNIFESP — Universidade Federal de São Paulo, Laboratório de Física Teórica e Computação Científica, Rua São Nicolau, 210, 09913-030, Diadema, SP (Brazil)
2012-09-01
I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a noninflationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude A, its size f{sub NL}, and corresponding shapes for a red-tilted spectrum of primordial scalar perturbations. Specifically, for cuscuton-like models I show that f{sub NL} ∼ O(1), and the shape of its non-Gaussian amplitude peaks for both equilateral and local configurations, the latter being dominant. These results, albeit similar, are quantitatively distinct from the corresponding ones obtained by Magueijo et al. in the context of superluminal bimetric models.
Gaussian mixture model of heart rate variability.
Directory of Open Access Journals (Sweden)
Tommaso Costa
Full Text Available Heart rate variability (HRV is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters.
Loop corrections to primordial non-Gaussianity
Boran, Sibel; Kahya, E. O.
2018-02-01
We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.
Some continual integrals from gaussian forms
International Nuclear Information System (INIS)
Mazmanishvili, A.S.
1985-01-01
The result summary of continual integration of gaussian functional type is given. The summary contains 124 continual integrals which are the mathematical expectation of the corresponding gaussian form by the continuum of random trajectories of four types: real-valued Ornstein-Uhlenbeck process, Wiener process, complex-valued Ornstein-Uhlenbeck process and the stochastic harmonic one. The summary includes both the known continual integrals and the unpublished before integrals. Mathematical results of the continual integration carried in the work may be applied in the problem of the theory of stochastic process, approaching to the finding of mean from gaussian forms by measures generated by the pointed stochastic processes
Integration of non-Gaussian fields
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Mohr, Gunnar; Hoffmeyer, Pernille
1996-01-01
The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are empirically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian distribution is fast...... enough to justify that it is sufficiently accurate for the applications to shortcut the problem and just assume that the distribution of the relevant stochastic integral is Gaussian. An earlier published example exhibiting this problem concerns silo pressure fields. [Ditlevsen, O., Christensen, C......, 1994](1) The numerical technique applied to obtain approximate information about the distribution of the integral is based on a recursive application of Winterstein approximations (moment fitted linear combinations of Hermite polynomials of standard Gaussian variables). The method uses the very long...
Gravitational Lensing Mass Mapping with Gaussian Processes
Schneider, Michael; Ng, Karen; Dawson, William; Marshall, Phil; Meyers, Joshua; Bard, Deborah
2018-01-01
We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a Gaussian Process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed cosmological lensing shear maps and a reconstruction of the mass distribution of the merging galaxy cluster Abell 781 using galaxy ellipticities measured with the Deep Lens Survey. Given interim posterior samples of lensing shear or convergence fields on the sky, we describe an algorithm to infer cosmological parameters via lens field marginalization. In the most general formulation of our algorithm we make no assumptions about weak shear orGaussian-distributed shape noise or shears. Because we require solutions and matrix determinants of a linear system of dimension that scales with the number of galaxies, we present computational performance metrics with approximate algorithms that introduce sparsity in the Gaussian Process kernel.
A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families
Dutta, Subhajit
2014-07-28
Several fascinating examples of non-Gaussian bivariate distributions which have marginal distribution functions to be Gaussian have been proposed in the literature. These examples often clarify several properties associated with the normal distribution. In this paper, we generalize this result in the sense that we construct a pp-dimensional distribution for which any proper subset of its components has the Gaussian distribution. However, the jointpp-dimensional distribution is inconsistent with the distribution of these subsets because it is not Gaussian. We study the probabilistic properties of this non-Gaussian multivariate distribution in detail. Interestingly, several popular tests of multivariate normality fail to identify this pp-dimensional distribution as non-Gaussian. We further extend our construction to a class of elliptically contoured distributions as well as skewed distributions arising from selections, for instance the multivariate skew-normal distribution.
Bipartite and Multipartite Entanglement of Gaussian States
Adesso, Gerardo; Illuminati, Fabrizio
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three-mode Gaussian states, at variance with their discrete-variable counterparts, allow a promiscuous sharing of quantum correlations, exhibiting both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. Finally, we investigate the connection between multipartite entanglement and the optimal fidelity in a continuous-variable quantum teleportation network. We show how the fidelity can be maximized in terms of the best preparation of the shared entangled resources and, viceversa, that this optimal fidelity provides a clearcut operational interpretation of several measures of bipartite and multipartite entanglement, including the entanglement of formation, the localizable entanglement, and the continuous-variable tangle.
Non-Gaussian halo assembly bias
International Nuclear Information System (INIS)
Reid, Beth A.; Verde, Licia; Dolag, Klaus; Matarrese, Sabino; Moscardini, Lauro
2010-01-01
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f NL , offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ∼ 23% and ∼ 48% for galaxies at z = 1 selected by stellar mass and star formation rate, respectively
Honda, Hiroaki; Yamaki, Takayoshi; Obara, Shigeru
2002-07-01
General recurrence formulas for evaluating molecular integrals over contracted Cartesian Gaussian functions are derived by introducing auxiliary contracted hyper-Gaussian (ACH) functions. By using a contracted Gaussian function, this ACH represents an extension of the Gaussian function named derivative of Fourier-kernel multiplied Gaussian [J. Chem. Phys. 94, 3790 (1991)]. The ACH is reducible to contracted Cartesian Gaussian functions, contracted modified Hermite Gaussian functions, and to contracted Gaussian functions multiplied by phase factors, or the so-called GIAO, and is also reducible to various spatial operators necessary for ab initio molecular orbital calculations. In our formulation, all molecular integrals are expressed in terms of ACH. Therefore, the formulations have wide applicability for calculating various kinds of molecular integrals in ab initio calculations. Recursive calculations based on our formulation do not depend on the number of contraction terms, because the contraction step is completed at the evaluation of the initial integrals. Therefore, we expect that more efficient recursive calculations will be accomplished by using our formulas for evaluating molecular integrals over contracted Gaussian functions.
Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.
Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel
2009-11-01
A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.
International Nuclear Information System (INIS)
Park, Suhyung; Park, Jaeseok
2015-01-01
Accelerated dynamic MRI, which exploits spatiotemporal redundancies in k − t space and coil dimension, has been widely used to reduce the number of signal encoding and thus increase imaging efficiency with minimal loss of image quality. Nonetheless, particularly in cardiac MRI it still suffers from artifacts and amplified noise in the presence of time-drifting coil sensitivity due to relative motion between coil and subject (e.g. free breathing). Furthermore, a substantial number of additional calibrating signals is to be acquired to warrant accurate calibration of coil sensitivity. In this work, we propose a novel, accelerated dynamic cardiac MRI with sparse-Kalman-smoother self-calibration and reconstruction (k − t SPARKS), which is robust to time-varying coil sensitivity even with a small number of calibrating signals. The proposed k − t SPARKS incorporates Kalman-smoother self-calibration in k − t space and sparse signal recovery in x − f space into a single optimization problem, leading to iterative, joint estimation of time-varying convolution kernels and missing signals in k − t space. In the Kalman-smoother calibration, motion-induced uncertainties over the entire time frames were included in modeling state transition while a coil-dependent noise statistic in describing measurement process. The sparse signal recovery iteratively alternates with the self-calibration to tackle the ill-conditioning problem potentially resulting from insufficient calibrating signals. Simulations and experiments were performed using both the proposed and conventional methods for comparison, revealing that the proposed k − t SPARKS yields higher signal-to-error ratio and superior temporal fidelity in both breath-hold and free-breathing cardiac applications over all reduction factors. (paper)
DEFF Research Database (Denmark)
Bennedsen, Mikkel
Using theory on (conditionally) Gaussian processes with stationary increments developed in Barndorff-Nielsen et al. (2009, 2011), this paper presents a general semiparametric approach to conducting inference on the fractal index, α, of a time series. Our setup encompasses a large class of Gaussian...
Approximate reversal of quantum Gaussian dynamics
Lami, Ludovico; Das, Siddhartha; Wilde, Mark M.
2018-03-01
Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed that the quantum relative entropy between two quantum states stays the same after the action of a quantum channel if and only if there is a reversal channel that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the Petz recovery map. Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state σ and a bosonic Gaussian channel N is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of the state σ and the Gaussian specification of the channel N .
Polar Functions for Anisotropic Gaussian Random Fields
Directory of Open Access Journals (Sweden)
Zhenlong Chen
2014-01-01
Full Text Available Let X be an (N, d-anisotropic Gaussian random field. Under some general conditions on X, we establish a relationship between a class of continuous functions satisfying the Lipschitz condition and a class of polar functions of X. We prove upper and lower bounds for the intersection probability for a nonpolar function and X in terms of Hausdorff measure and capacity, respectively. We also determine the Hausdorff and packing dimensions of the times set for a nonpolar function intersecting X. The class of Gaussian random fields that satisfy our conditions includes not only fractional Brownian motion and the Brownian sheet, but also such anisotropic fields as fractional Brownian sheets, solutions to stochastic heat equation driven by space-time white noise, and the operator-scaling Gaussian random field with stationary increments.
HE11 radiation patterns and gaussian approximations
International Nuclear Information System (INIS)
Rebuffi, L.; Crenn, J.P.
1986-12-01
The possibility of approximating the HE11 radiation pattern with a Gaussian distribution is presented. A numerical comparison between HE11 far-field theoretical patterns and Abrams and Crenn approximations permits an evaluation of the validity of these two approximations. A new numerically optimized HE11 Gaussian approximation for the far-field, extended to great part of the near field, has been found. In particular, the value given for the beam radius at the waist, has been demonstrated to give the best HE11 Gaussian approximation in the far-field. The Crenn approximation is found to be very close to this optimal approximation, while the Abrams approximation is shown to be less precise. Universal curves for intensity, amplitude and power distribution are given for the HE11 radiated mode. These results are of interest for laser waveguide applications and for plasma ECRH transmission systems
Semisupervised Gaussian Process for Automated Enzyme Search.
Mellor, Joseph; Grigoras, Ioana; Carbonell, Pablo; Faulon, Jean-Loup
2016-06-17
Synthetic biology is today harnessing the design of novel and greener biosynthesis routes for the production of added-value chemicals and natural products. The design of novel pathways often requires a detailed selection of enzyme sequences to import into the chassis at each of the reaction steps. To address such design requirements in an automated way, we present here a tool for exploring the space of enzymatic reactions. Given a reaction and an enzyme the tool provides a probability estimate that the enzyme catalyzes the reaction. Our tool first considers the similarity of a reaction to known biochemical reactions with respect to signatures around their reaction centers. Signatures are defined based on chemical transformation rules by using extended connectivity fingerprint descriptors. A semisupervised Gaussian process model associated with the similar known reactions then provides the probability estimate. The Gaussian process model uses information about both the reaction and the enzyme in providing the estimate. These estimates were validated experimentally by the application of the Gaussian process model to a newly identified metabolite in Escherichia coli in order to search for the enzymes catalyzing its associated reactions. Furthermore, we show with several pathway design examples how such ability to assign probability estimates to enzymatic reactions provides the potential to assist in bioengineering applications, providing experimental validation to our proposed approach. To the best of our knowledge, the proposed approach is the first application of Gaussian processes dealing with biological sequences and chemicals, the use of a semisupervised Gaussian process framework is also novel in the context of machine learning applied to bioinformatics. However, the ability of an enzyme to catalyze a reaction depends on the affinity between the substrates of the reaction and the enzyme. This affinity is generally quantified by the Michaelis constant KM
Construction of Capacity Achieving Lattice Gaussian Codes
Alghamdi, Wael
2016-04-01
We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].
Model selection for Gaussian kernel PCA denoising
DEFF Research Database (Denmark)
Jørgensen, Kasper Winther; Hansen, Lars Kai
2012-01-01
We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...
Gaussian processes and constructive scalar field theory
International Nuclear Information System (INIS)
Benfatto, G.; Nicolo, F.
1981-01-01
The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)
Statistically tuned Gaussian background subtraction technique for ...
Indian Academy of Sciences (India)
ground, small objects, moving background and multiple objects are considered for evaluation. The technique is statistically compared with frame differencing technique, temporal median method and mixture of Gaussian model and performance evaluation is done to check the effectiveness of the proposed technique after ...
Log Gaussian Cox processes on the sphere
DEFF Research Database (Denmark)
Pacheco, Francisco Andrés Cuevas; Møller, Jesper
We define and study the existence of log Gaussian Cox processes (LGCPs) for the description of inhomogeneous and aggregated/clustered point patterns on the d-dimensional sphere, with d = 2 of primary interest. Useful theoretical properties of LGCPs are studied and applied for the description of sky...
Open problems in Gaussian fluid queueing theory
Dȩbicki, K.; Mandjes, M.
2011-01-01
We present three challenging open problems that originate from the analysis of the asymptotic behavior of Gaussian fluid queueing models. In particular, we address the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to
Fourth Power Diophantine Equations in Gaussian Integers
Indian Academy of Sciences (India)
25
Fourth Power Diophantine Equations in Gaussian Integers. 7. 7. U. Schneiders and H.G. Zimmer, The rank of elliptic curves upon quadratic extensions,. Computational Number Theory (A. Petho, H.C. Williams,H.G. Zimmer, eds.), de Gruyter,. 239-260, Berlin, (1991). 8. Y. Suzuki, On the Diophantine Equation 2aX4 + 2bY 4 ...
Statistically tuned Gaussian background subtraction technique for ...
Indian Academy of Sciences (India)
The non-parametric background modelling approach proposed by Martin Hofmann et al (2012) involves modelling of foreground by the history of recently ... background subtraction system with mixture of Gaussians, deviation scaling factor and max– min background model for outdoor environment. Selection of detection ...
Gaussian vector fields on triangulated surfaces
DEFF Research Database (Denmark)
Ipsen, John H
2016-01-01
proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method...
The Wehrl entropy has Gaussian optimizers
DEFF Research Database (Denmark)
De Palma, Giacomo
2018-01-01
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...
Gaussian curvature on hyperelliptic Riemann surfaces
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.
Bregman Cost for Non-Gaussian Noise
DEFF Research Database (Denmark)
Burger, Martin; Dong, Yiqiu; Sciacchitano, Federica
estimator for the Bregman cost if the image is corrupted by Gaussian noise. In this work we extend this result to other noise models with log-concave likelihood density, by introducing two related Bregman cost functions for which the CM and the MAP estimates are proper Bayes estima-tors. Moreover, we also...
Non-Gaussianity effects in petrophysical quantities
Koohi Lai, Z.; Jafari, G. R.
2013-10-01
It has been proved that there are many indicators (petrophysical quantities) for the estimation of petroleum reservoirs. The value of information contained in each indicator is yet to be addressed. In this work, the most famous and applicable petrophysical quantities for a reservoir, which are the gamma emission (GR), sonic transient time (DT), neutron porosity (NPHI), bulk density (RHOB), and deep induced resistivity (ILD), have been analyzed in order to characterize a reservoir. The implemented technique is the well-logging method. Based on the log-normal model defined in random multiplicative processes, the probability distribution function (PDF) for the data sets is described. The shape of the PDF depends on the parameter λ2 which determines the efficiency of non-Gaussianity. When non-Gaussianity appears, it is a sign of uncertainty and phase transition in the critical regime. The large value and scale-invariant behavior of the non-Gaussian parameter λ2 is an indication of a new phase which proves adequate for the existence of petroleum reservoirs. Our results show that one of the indicators (GR) is more non-Gaussian than the other indicators, scale wise. This means that GR is a continuously critical indicator. But by moving windows with various scales, the estimated λ2 shows that the most appropriate indicator for distinguishing the critical regime is ILD, which shows an increase at the end of the measured region of the well.
The Gaussian entropy of fermionic systems
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav, E-mail: T.Prokopec@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands); Schmidt, Michael G., E-mail: M.G.Schmidt@thphys.uni-heidelberg.de [Institut fuer Theoretische Physik, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany); Weenink, Jan, E-mail: J.G.Weenink@uu.nl [Institute for Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht (Netherlands)
2012-12-15
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence and classicalization. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields. - Highlights: Black-Right-Pointing-Pointer We construct the Gaussian density operator for relativistic fermionic systems. Black-Right-Pointing-Pointer The Gaussian entropy of relativistic fermionic systems is described in terms of 2-point correlators. Black-Right-Pointing-Pointer We explicitly show the growth of entropy for fermionic fields mixing with a thermal fermionic environment.
Fourth Power Diophantine Equations in Gaussian Integers
Indian Academy of Sciences (India)
25
Fourth Power Diophantine Equations in Gaussian. Integers. Farzali Izadi · Rasool Naghdali. Forooshani · Amaneh Amiryousefi. Varnousfaderani . Received: date / Accepted: date. Abstract In this paper we examine a class of fourth power Diophantine equa- tions of the form x4 + kx2y2 + y4 = z2 and ax4 + by4 = cz2, in the ...
Gaussian shaping filter for nuclear spectrometry
International Nuclear Information System (INIS)
Menezes, A.S.C. de.
1980-01-01
A theorical study of a gaussian shaping filter, using Pade approximation, for using in gamma spectroscopy is presented. This approximation has proved superior to the classical cascade RC integrators approximation in therms of signal-to-noise ratio and pulse simmetry. An experimental filter was designed, simulated in computer, constructed, and tested in the laboratory. (author) [pt
Gaussian processes for prediction in intensive care
Guiza Grandas, Fabian; Ramon, Jan; Blockeel, Hendrik
2006-01-01
In this paper we present the use of Gaussian Processes for regression in the application of prediction in Intensive Care. We propose a preliminary solution to predicting the evolution of a patient's state during his stay in intensive care by means of defined patient specific characteristics.
Survival Exponents for Some Gaussian Processes
Directory of Open Access Journals (Sweden)
G. Molchan
2012-01-01
Full Text Available The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional Brownian motion (FBM in , and the integrated FBM in , .
Estimators for local non-Gaussianities
International Nuclear Information System (INIS)
Creminelli, P.; Senatore, L.; Zaldarriaga, M.
2006-05-01
We study the Likelihood function of data given f NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f NL and show that for small values of f NL the 3- point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f NL , the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f NL only decrease as 1/ln N pix rather than N pix -1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non- Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as N pix -1/2 even for large f NL , asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f NL . In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f NL . (author)
Gaussian-input Gaussian mixture model for representing density maps and atomic models.
Kawabata, Takeshi
2018-03-06
A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.
MCEM algorithm for the log-Gaussian Cox process
Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis
2014-01-01
Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...
Directory of Open Access Journals (Sweden)
Shih-Sen Chang
1994-01-01
Full Text Available In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.
Linking network usage patterns to traffic Gaussianity fit
de Oliveira Schmidt, R.; Sadre, R.; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko
Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001,
On Alternate Relaying with Improper Gaussian Signaling
Gaafar, Mohamed
2016-06-06
In this letter, we investigate the potential benefits of adopting improper Gaussian signaling (IGS) in a two-hop alternate relaying (AR) system. Given the known benefits of using IGS in interference-limited networks, we propose to use IGS to relieve the inter-relay interference (IRI) impact on the AR system assuming no channel state information is available at the source. In this regard, we assume that the two relays use IGS and the source uses proper Gaussian signaling (PGS). Then, we optimize the degree of impropriety of the relays signal, measured by the circularity coefficient, to maximize the total achievable rate. Simulation results show that using IGS yields a significant performance improvement over PGS, especially when the first hop is a bottleneck due to weak source-relay channel gains and/or strong IRI.
Interweave Cognitive Radio with Improper Gaussian Signaling
Hedhly, Wafa
2018-01-15
Improper Gaussian signaling (IGS) has proven its ability in improving the performance of underlay and overlay cognitive radio paradigms. In this paper, the interweave cognitive radio paradigm is studied when the cognitive user employs IGS. The instantaneous achievable rate performance of both the primary and secondary users are analyzed for specific secondary user sensing and detection capabilities. Next, the IGS scheme is optimized to maximize the achievable rate secondary user while satisfying a target minimum rate requirement for the primary user. Proper Gaussian signaling (PGS) scheme design is also derived to be used as benchmark of the IGS scheme design. Finally, different numerical results are introduced to show the gain reaped from adopting IGS over PGS under different system parameters. The main advantage of employing IGS is observed at low sensing and detection capabilities of the SU, lower PU direct link and higher SU interference on the PU side.
Geometrical approach to gaussian beam propagation.
Laures, P
1967-04-01
The curvature of the wavefront and the spot size of a propagating Gaussian beam may be determined from simple geometrical transformations of the lateral foci. The analysis starts from the construction of the lateral foci in the case of a spherical Fabry-Perot. Then the cases of Gaussian beam propagation through media with different refractive indices, lenses, and simple optical systems are treated. Constructions show how propagation in the image space is readily determined in each case. This analysis is the generalization of the technique outlined by Deschamps and Mast. The geometrical constructions developed for simple cases are applied to the design of some special cases of interest in laser optics: cavities by a lens, laser zoom telescope, and ring cavity.
Extended Linear Models with Gaussian Priors
DEFF Research Database (Denmark)
Quinonero, Joaquin
2002-01-01
In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....
Environmental Modeling Framework using Stacked Gaussian Processes
Abdelfatah, Kareem; Bao, Junshu; Terejanu, Gabriel
2016-01-01
A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest through a cascade of intermediate predictions, and to propagate uncertainties through emulated dynamical systems driven by uncertain forcing variables. By using analytical first an...
Adaptive multiple importance sampling for Gaussian processes
Czech Academy of Sciences Publication Activity Database
Xiong, X.; Šmídl, Václav; Filippone, M.
2017-01-01
Roč. 87, č. 8 (2017), s. 1644-1665 ISSN 0094-9655 R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Gaussian Process * Bayesian estimation * Adaptive importance sampling Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.757, year: 2016 http://library.utia.cas.cz/separaty/2017/AS/smidl-0469804.pdf
Dimensionality Reduction by Local Discriminative Gaussians
Parrish, Nathan; Gupta, Maya
2012-01-01
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training point in order to find a mapping where similar data can be discriminated from dissimilar data. While other state-of-the-art linear dimensionality reduction methods require gradien...
Recognition of Images Degraded by Gaussian Blur
Czech Academy of Sciences Publication Activity Database
Flusser, Jan; Farokhi, Sajad; Höschl, Cyril; Suk, Tomáš; Zitová, Barbara; Pedone, M.
2016-01-01
Roč. 25, č. 2 (2016), s. 790-806 ISSN 1057-7149 R&D Projects: GA ČR(CZ) GA15-16928S Institutional support: RVO:67985556 Keywords : Blurred image * object recognition * blur invariant comparison * Gaussian blur * projection operators * image moments * moment invariants Subject RIV: JD - Computer Applications, Robotics Impact factor: 4.828, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/flusser-0454335.pdf
Stochastic Energetics for Non-Gaussian Processes
Kanazawa, Kiyoshi; Sagawa, Takahiro; Hayakawa, Hisao
2012-05-01
By introducing a new stochastic integral, we investigate the energetics of classical stochastic systems driven by non-Gaussian white noises. In particular, we introduce a decomposition of the total energy difference into the work and the heat for each trajectory, and derive a formula to calculate the heat from experimental data on the dynamics. We apply our formulation and results to a Langevin system driven by a Poisson noise.
A Gaussian IV estimator of cointegrating relations
DEFF Research Database (Denmark)
Bårdsen, Gunnar; Haldrup, Niels
2006-01-01
-nonparametricestimators. Theoretically ideal instruments can be defined to ensure a limitingGaussian distribution of IV estimators, but unfortunately such instruments areunlikely to be found in real data. In the present paper we suggest an IV estimatorwhere the Hodrick-Prescott filtered trends are used as instruments forthe regressors...... in cointegrating regressions. These instruments are almost idealand simulations show that the IV estimator using such instruments alleviatethe endogeneity problem extremely well in both finite and large samples....
Modeling text with generalizable Gaussian mixtures
DEFF Research Database (Denmark)
Hansen, Lars Kai; Sigurdsson, Sigurdur; Kolenda, Thomas
2000-01-01
We apply and discuss generalizable Gaussian mixture (GGM) models for text mining. The model automatically adapts model complexity for a given text representation. We show that the generalizability of these models depends on the dimensionality of the representation and the sample size. We discuss ...... the relation between supervised and unsupervised learning in the test data. Finally, we implement a novelty detector based on the density model....
Gaussian Process-Mixture Conditional Heteroscedasticity.
Platanios, Emmanouil A; Chatzis, Sotirios P
2014-05-01
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a Gaussian process-mixture conditional heteroscedasticity (GPMCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula-based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.
Resonant non-Gaussianity with equilateral properties
International Nuclear Information System (INIS)
Gwyn, Rhiannon; Rummel, Markus
2012-11-01
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 the resonant N-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of f NL ∝O(5) will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.
Neutron inverse kinetics via Gaussian Processes
International Nuclear Information System (INIS)
Picca, Paolo; Furfaro, Roberto
2012-01-01
Highlights: ► A novel technique for the interpretation of experiments in ADS is presented. ► The technique is based on Bayesian regression, implemented via Gaussian Processes. ► GPs overcome the limits of classical methods, based on PK approximation. ► Results compares GPs and ANN performance, underlining similarities and differences. - Abstract: The paper introduces the application of Gaussian Processes (GPs) to determine the subcriticality level in accelerator-driven systems (ADSs) through the interpretation of pulsed experiment data. ADSs have peculiar kinetic properties due to their special core design. For this reason, classical – inversion techniques based on point kinetic (PK) generally fail to generate an accurate estimate of reactor subcriticality. Similarly to Artificial Neural Networks (ANNs), Gaussian Processes can be successfully trained to learn the underlying inverse neutron kinetic model and, as such, they are not limited to the model choice. Importantly, GPs are strongly rooted into the Bayes’ theorem which makes them a powerful tool for statistical inference. Here, GPs have been designed and trained on a set of kinetics models (e.g. point kinetics and multi-point kinetics) for homogeneous and heterogeneous settings. The results presented in the paper show that GPs are very efficient and accurate in predicting the reactivity for ADS-like systems. The variance computed via GPs may provide an indication on how to generate additional data as function of the desired accuracy.
Single field inflation and non-Gaussianity
International Nuclear Information System (INIS)
Gangui, Alejandro; Martin, Jerome; Sakellariadou, Mairi
2002-01-01
We study non-Gaussian signatures on the cosmic microwave background (CMB) radiation predicted within inflationary models with non-vacuum initial states for cosmological perturbations. The model incorporates a privileged scale, which implies the existence of a feature in the primordial power spectrum. This broken-scale-invariant model predicts a vanishing three-point correlation function for the CMB temperature anisotropies (or any other odd-numbered-point correlation function) whilst an intrinsic non-Gaussian signature arises for any even-numbered-point correlation function. We thus focus on the first non-vanishing moment, the CMB four-point function at zero lag, namely the kurtosis, and compute its expected value for different locations of the primordial feature in the spectrum, as suggested in the literature to conform with observations of large scale structure. The excess kurtosis is found to be negative and the signal to noise ratio for the dimensionless excess kurtosis parameter is equal to |S/N|≅4x10 -4 , almost independently of the free parameters of the model. This signature turns out to be undetectable. We conclude that, subject to current tests, Gaussianity is a generic property of single field inflationary models. The only uncertainty concerning this prediction is that the effect of back reaction has not yet been properly incorporated. The implications for the trans-Planckian problem of inflation are also briefly discussed
Resonant non-Gaussianity with equilateral properties
Energy Technology Data Exchange (ETDEWEB)
Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-11-15
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 the resonant N-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of f{sub NL} {proportional_to}O(5) will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.
Gaussian Hypothesis Testing and Quantum Illumination.
Wilde, Mark M; Tomamichel, Marco; Lloyd, Seth; Berta, Mario
2017-09-22
Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.
Perturbative Gaussianizing transforms for cosmological fields
Hall, Alex; Mead, Alexander
2018-01-01
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.
Persistent homology and non-Gaussianity
Cole, Alex; Shiu, Gary
2018-03-01
In this paper, we introduce the topological persistence diagram as a statistic for Cosmic Microwave Background (CMB) temperature anisotropy maps. A central concept in 'Topological Data Analysis' (TDA), the idea of persistence is to represent a data set by a family of topological spaces. One then examines how long topological features 'persist' as the family of spaces is traversed. We compute persistence diagrams for simulated CMB temperature anisotropy maps featuring various levels of primordial non-Gaussianity of local type. Postponing the analysis of observational effects, we show that persistence diagrams are more sensitive to local non-Gaussianity than previous topological statistics including the genus and Betti number curves, and can constrain Δ fNLloc= 35.8 at the 68% confidence level on the simulation set, compared to Δ fNLloc= 60.6 for the Betti number curves. Given the resolution of our simulations, we expect applying persistence diagrams to observational data will give constraints competitive with those of the Minkowski Functionals. This is the first in a series of papers where we plan to apply TDA to different shapes of non-Gaussianity in the CMB and Large Scale Structure.
Fixing convergence of Gaussian belief propagation
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jason K [Los Alamos National Laboratory; Bickson, Danny [IBM RESEARCH LAB; Dolev, Danny [HEBREW UNIV
2009-01-01
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.
Production and propagation of Hermite-sinusoidal-Gaussian laser beams.
Tovar, A A; Casperson, L W
1998-09-01
Hermite-sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the limit of large Hermite-Gaussian beam size, the sinusoidal factors are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar Hermite-Gaussian form. The propagation of these beams is examined in detail, and resonators are designed that will produce them. As an example, a special resonator is designed to produce hyperbolic-sine-Gaussian beams. This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. The beam mode has finite energy and is perturbation stable.
High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.
Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei
2017-07-01
Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.
International Nuclear Information System (INIS)
Tan, Cheng-Yang; Fermilab
2006-01-01
One common way for measuring the emittance of an electron beam is with the slits method. The usual approach for analyzing the data is to calculate an emittance that is a subset of the parent emittance. This paper shows an alternative way by using the method of correlations which ties the parameters derived from the beamlets to the actual parameters of the parent emittance. For parent distributions that are Gaussian, this method yields exact results. For non-Gaussian beam distributions, this method yields an effective emittance that can serve as a yardstick for emittance comparisons
Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review
Falsone, G.
2018-03-01
In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable with many difficulties. Here all the principal approaches solving the SDEs are reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible.
Polynomials of Gaussians and vortex-Gaussian beams as complete, transversely confined bases.
Gutiérrez-Cuevas, Rodrigo; Alonso, Miguel A
2017-06-01
A novel type of discrete basis for paraxial beams is proposed, consisting of monomial vortices times polynomials of Gaussians in the radial variable. These bases have the distinctive property that the effective size of their elements is roughly independent of element order, meaning that the optimal scaling for expanding a localized field does not depend significantly on truncation order. This behavior contrasts with that of bases composed of polynomials times Gaussians, such as Hermite-Gauss and Laguerre-Gauss modes, where the scaling changes roughly as the inverse square root of the truncation order.
Humanoid environmental perception with Gaussian process regression
Directory of Open Access Journals (Sweden)
Dingsheng Luo
2016-11-01
Full Text Available Nowadays, humanoids are increasingly expected acting in the real world to complete some high-level tasks humanly and intelligently. However, this is a hard issue due to that the real world is always extremely complicated and full of miscellaneous variations. As a consequence, for a real-world-acting robot, precisely perceiving the environmental changes might be an essential premise. Unlike human being, humanoid robot usually turns out to be with much less sensors to get enough information from the real world, which further leads the environmental perception problem to be more challenging. Although it can be tackled by establishing direct sensory mappings or adopting probabilistic filtering methods, the nonlinearity and uncertainty caused by both the complexity of the environment and the high degree of freedom of the robots will result in tough modeling difficulties. In our study, with the Gaussian process regression framework, an alternative learning approach to address such a modeling problem is proposed and discussed. Meanwhile, to debase the influence derived from limited sensors, the idea of fusing multiple sensory information is also involved. To evaluate the effectiveness, with two representative environment changing tasks, that is, suffering unknown external pushing and suddenly encountering sloped terrains, the proposed approach is applied to a humanoid, which is only equipped with a three-axis gyroscope and a three-axis accelerometer. Experimental results reveal that the proposed Gaussian process regression-based approach is effective in coping with the nonlinearity and uncertainty of the humanoid environmental perception problem. Further, a humanoid balancing controller is developed, which takes the output of the Gaussian process regression-based environmental perception as the seed to activate the corresponding balancing strategy. Both simulated and hardware experiments consistently show that our approach is valuable and leads to a
Entanglement rate for Gaussian continuous variable beams
Jiao Deng, Zhi; Habraken, Steven J. M.; Marquardt, Florian
2016-06-01
We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators. This expression is especially useful for situations where the source emits an arbitrary frequency spectrum, e.g. when cavities are involved. To exemplify its meaning and potential, we apply it to a four-mode optomechanical setup that enables the simultaneous up- and down-conversion of photons from a drive laser into entangled photon pairs. This setup is efficient in that both the drive and the optomechanical up- and down-conversion can be fully resonant.
Non-Gaussianity from Broken Symmetries
Kolb, Edward W; Vallinotto, A; Kolb, Edward W.; Riotto, Antonio; Vallinotto, Alberto
2006-01-01
Recently we studied inflation models in which the inflaton 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, $f_{NL}$, can be as large as 10^2.
Ripple Tank Demonstration of Gaussian Beam Propagation
Jude, Kathy J.; Wilson, Thomas E.
1997-10-01
We have reproduced a ripple tank experimentfootnote 'Ripple Tank Studies of Wave Motion' by W. Llowarch (Oxford University Press, 1961) in order to illustrate the effects of focusing and diffraction of a capillary planewave by a bi-convex carbon tetrachloride 'lens'. We compare the experimental results, captured by a video camera, to the theoretical results obtained using the ABCD matrix method for the gaussian beam propagation through this paraxial 'optical' systemfootnote 'Lasers' by Anthony Siegman (University Science Book, Mill Valley, CA, 1986). The diffraction-limited focusing of the propagating wave is clearly visible; this is a feature not easily demonstrable in optics.
Return probability: Exponential versus Gaussian decay
Energy Technology Data Exchange (ETDEWEB)
Izrailev, F.M. [Instituto de Fisica, BUAP, Apdo. Postal J-48, 72570 Puebla (Mexico)]. E-mail: izrailev@sirio.ifuap.buap.mx; Castaneda-Mendoza, A. [Instituto de Fisica, BUAP, Apdo. Postal J-48, 72570 Puebla (Mexico)
2006-02-13
We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the Gaussian decay of the return probability, and another one is the well-known regime of the exponential decay. Our analytical estimates are confirmed by the numerical data obtained for two models with random interaction. In view of these results, we also briefly discuss the dynamical model which was recently proposed for the implementation of a quantum computation.
CMB constraints on running non-Gaussianity
Oppizzi, Filippo; Liguori, Michele; Renzi, Alessandro; Arroja, Frederico; Bartolo, Nicola
2017-01-01
We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the $f_{\\rm NL}$ running spectral index, $n_{\\rm NG}$, using WMAP 9-year data. Our final bounds (68\\% C.L.) read $-0.3< n_{\\rm NG}
Optical trapping with Super-Gaussian beams
CSIR Research Space (South Africa)
Mc
2013-04-01
Full Text Available stream_source_info McLaren1_2013.pdf.txt stream_content_type text/plain stream_size 2236 Content-Encoding UTF-8 stream_name McLaren1_2013.pdf.txt Content-Type text/plain; charset=UTF-8 JT2A.34.pdf Optics in the Life... Sciences Congress Technical Digest © 2013 The Optical Society (OSA) Optical trapping with Super-Gaussian beams Melanie McLaren, Thulile Khanyile, Patience Mthunzi and Andrew Forbes* National Laser Centre, Council for Scientific and Industrial Research...
Approximation problems with the divergence criterion for Gaussian variablesand Gaussian processes
A.A. Stoorvogel; J.H. van Schuppen (Jan)
1996-01-01
textabstractSystem identification for stationary Gaussian processes includes an approximation problem. Currently the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a finite time series to canonical variable form followed by a truncation.
DEFF Research Database (Denmark)
Møller, Jesper; Jacobsen, Robert Dahl
We introduce a promising alternative to the usual hidden Markov tree model for Gaussian wavelet coefficients, where their variances are specified by the hidden states and take values in a finite set. In our new model, the hidden states have a similar dependence structure but they are jointly Gaus...... detection problems in two-dimensional images....
DEFF Research Database (Denmark)
Jacobsen, Christian Robert Dahl; Møller, Jesper
2017-01-01
We introduce new estimation methods for a subclass of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli and Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection...... problems in two-dimensional images....
On the structure of Gaussian pricing models and Gaussian Markov functional models
C.D.D. Neumann
2002-01-01
textabstractThis article investigates the structure of Gaussian pricing models (that is, models in which future returns are normally distributed). Although much is already known about such models, this article differs in that it is based on a formulation of the theory of derivative pricing in which
Multimodal Similarity Gaussian Process Latent Variable Model.
Song, Guoli; Wang, Shuhui; Huang, Qingming; Tian, Qi
2017-09-01
Data from real applications involve multiple modalities representing content with the same semantics from complementary aspects. However, relations among heterogeneous modalities are simply treated as observation-to-fit by existing work, and the parameterized modality specific mapping functions lack flexibility in directly adapting to the content divergence and semantic complicacy in multimodal data. In this paper, we build our work based on the Gaussian process latent variable model (GPLVM) to learn the non-parametric mapping functions and transform heterogeneous modalities into a shared latent space. We propose multimodal Similarity Gaussian Process latent variable model (m-SimGP), which learns the mapping functions between the intra-modal similarities and latent representation. We further propose multimodal distance-preserved similarity GPLVM (m-DSimGP) to preserve the intra-modal global similarity structure, and multimodal regularized similarity GPLVM (m-RSimGP) by encouraging similar/dissimilar points to be similar/dissimilar in the latent space. We propose m-DRSimGP, which combines the distance preservation in m-DSimGP and semantic preservation in m-RSimGP to learn the latent representation. The overall objective functions of the four models are solved by simple and scalable gradient decent techniques. They can be applied to various tasks to discover the nonlinear correlations and to obtain the comparable low-dimensional representation for heterogeneous modalities. On five widely used real-world data sets, our approaches outperform existing models on cross-modal content retrieval and multimodal classification.
Overlay Spectrum Sharing using Improper Gaussian Signaling
Amin, Osama
2016-11-30
Improper Gaussian signaling (IGS) scheme has been recently shown to provide performance improvements in interference limited networks as opposed to the conventional proper Gaussian signaling (PGS) scheme. In this paper, we implement the IGS scheme in overlay cognitive radio system, where the secondary transmitter broadcasts a mixture of two different signals. The first signal is selected from the PGS scheme to match the primary message transmission. On the other hand, the second signal is chosen to be from the IGS scheme in order to reduce the interference effect on the primary receiver. We then optimally design the overlay cognitive radio to maximize the secondary link achievable rate while satisfying the primary network quality of service requirements. In particular, we consider full and partial channel knowledge scenarios and derive the feasibility conditions of operating the overlay cognitive radio systems. Moreover, we derive the superiority conditions of the IGS schemes over the PGS schemes supported with closed form expressions for the corresponding power distribution and the circularity coefficient and parameters. Simulation results are provided to support our theoretical derivations.
An innovation approach to non-Gaussian time series analysis
Ozaki, Tohru; Iino, Mitsunori
2001-01-01
The paper shows that the use of both types of random noise, white noise and Poisson noise, can be justified when using an innovations approach. The historical background for this is sketched, and then several methods of whitening dependent time series are outlined, including a mixture of Gaussian white noise and a compound Poisson process: this appears as a natural extension of the Gaussian white noise model for the prediction errors of a non-Gaussian time series. A stati...
Prediction and retrodiction with continuously monitored Gaussian states
DEFF Research Database (Denmark)
Zhang, Jinglei; Mølmer, Klaus
2017-01-01
Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property......(t)$ to Gaussian states implies that the matrix $E(t)$ is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems....
Gaussian polynomials and content ideal in trivial extensions
International Nuclear Information System (INIS)
Bakkari, C.; Mahdou, N.
2006-12-01
The goal of this paper is to exhibit a class of Gaussian non-coherent rings R (with zero-divisors) such that wdim(R) = ∞ and fPdim(R) is always at most one and also exhibits a new class of rings (with zerodivisors) which are neither locally Noetherian nor locally domain where Gaussian polynomials have a locally principal content. For this purpose, we study the possible transfer of the 'Gaussian' property and the property 'the content ideal of a Gaussian polynomial is locally principal' to various trivial extension contexts. This article includes a brief discussion of the scopes and limits of our result. (author)
BEAM-BEAM SIMULATIONS FOR DOUBLE-GAUSSIAN BEAMS.
Energy Technology Data Exchange (ETDEWEB)
MONTAG, C.; MALITSKY, N.; BEN-ZVI, I.; LITVINENKO, V.
2005-05-16
Electron cooling together with intra-beam scattering results in a transverse distribution that can best be described by a sum of two gaussians, one for the high-density core and one for the tails of the distribution. Simulation studies are being performed to understand the beam-beam interaction of these double-gaussian beams. Here we report the effect of low-frequency random tune modulations on diffusion in double-gaussian beams and compare the effects to those in beam-beam interactions with regular gaussian beams and identical tune shift parameters.
BEAM-BEAM SIMULATIONS FOR DOUBLE-GAUSSIAN BEAMS
International Nuclear Information System (INIS)
MONTAG, C.; MALITSKY, N.; BEN-ZVI, I.; LITVINENKO, V.
2005-01-01
Electron cooling together with intra-beam scattering results in a transverse distribution that can best be described by a sum of two gaussians, one for the high-density core and one for the tails of the distribution. Simulation studies are being performed to understand the beam-beam interaction of these double-gaussian beams. Here we report the effect of loW--frequency random tune modulations on diffusion in double-gaussian beams and compare the effects to those in beam-beam interactions with regular gaussian beams and identical tune shift parameters
Beam-Beam Simulations for Double-Gaussian Beams
Montag, Christoph; Litvinenko, Vladimir N; Malitsky, Nikolay
2005-01-01
Electron cooling together with intra-beam scattering results in a transverse distribution that can best be described by a sum of two Gaussians, one for the high-density core and one for the tails of the distribution. Simulation studies are being performed to understand the beam-beam interaction of these double-Gaussian beams. Here we report the effect of low-frequency random tune modulations on diffusion in double-Gaussian beams and compare the effects to those in beam-beam interactions with regular Gaussian beams and identical tuneshift parameters.
Kalman smoother applied to LACE
Thorngren, Frank R.
1991-01-01
Approved for public release; distribution is unlimited The ability to determine the structural dynamics of space-based platforms from ground-based radar resolved Doppler measurements will aid in the study of control/structure interaction. The Naval Research Laboratory and Lincoln Laboratory conducted an experiment to determine the feasibility of this method. To accomplish this experiment the LACE satellite was equipped with retroreflectors and the ground-based Firepond laser radar facili...
Yan, Yuan
2017-07-13
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
Gaussian process regression for geometry optimization
Denzel, Alexander; Kästner, Johannes
2018-03-01
We implemented a geometry optimizer based on Gaussian process regression (GPR) to find minimum structures on potential energy surfaces. We tested both a two times differentiable form of the Matérn kernel and the squared exponential kernel. The Matérn kernel performs much better. We give a detailed description of the optimization procedures. These include overshooting the step resulting from GPR in order to obtain a higher degree of interpolation vs. extrapolation. In a benchmark against the Limited-memory Broyden-Fletcher-Goldfarb-Shanno optimizer of the DL-FIND library on 26 test systems, we found the new optimizer to generally reduce the number of required optimization steps.
IBS for non-gaussian distributions
International Nuclear Information System (INIS)
Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.
2010-01-01
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.
Image reconstruction under non-Gaussian noise
DEFF Research Database (Denmark)
Sciacchitano, Federica
During acquisition and transmission, images are often blurred and corrupted by noise. One of the fundamental tasks of image processing is to reconstruct the clean image from a degraded version. The process of recovering the original image from the data is an example of inverse problem. Due...... that the CM estimate outperforms the MAP estimate, when the error depends on Bregman distances. This PhD project can have many applications in the modern society, in fact the reconstruction of high quality images with less noise and more details enhances the image processing operations, such as edge detection......D thesis intends to solve some of the many open questions for image restoration under non-Gaussian noise. The two main kinds of noise studied in this PhD project are the impulse noise and the Cauchy noise. Impulse noise is due to for instance the malfunctioning pixel elements in the camera sensors, errors...
Bayesian multitask classification with Gaussian process priors.
Skolidis, Grigorios; Sanguinetti, Guido
2011-12-01
We present a novel approach to multitask learning in classification problems based on Gaussian process (GP) classification. The method extends previous work on multitask GP regression, constraining the overall covariance (across tasks and data points) to factorize as a Kronecker product. Fully Bayesian inference is possible but time consuming using sampling techniques. We propose approximations based on the popular variational Bayes and expectation propagation frameworks, showing that they both achieve excellent accuracy when compared to Gibbs sampling, in a fraction of time. We present results on a toy dataset and two real datasets, showing improved performance against the baseline results obtained by learning each task independently. We also compare with a recently proposed state-of-the-art approach based on support vector machines, obtaining comparable or better results.
Large Deviations for Gaussian Diffusions with Delay
Azencott, Robert; Geiger, Brett; Ott, William
2018-01-01
Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed points. Near such fixed points, one can approximate nonlinear delay SDEs by linear delay SDEs. Here, we develop a fully explicit large deviations framework for (necessarily Gaussian) processes X_t driven by linear delay SDEs with small diffusion coefficients. Our approach enables fast numerical computation of the action functional controlling rare events for X_t and of the most likely paths transiting from X_0 = p to X_T=q. Via linear noise local approximations, we can then compute most likely routes of escape from metastable states for nonlinear delay SDEs. We apply our methodology to the detailed dynamics of a genetic regulatory circuit, namely the co-repressive toggle switch, which may be described by a nonlinear chemical Langevin SDE with delay.
Gaussian process regression for tool wear prediction
Kong, Dongdong; Chen, Yongjie; Li, Ning
2018-05-01
To realize and accelerate the pace of intelligent manufacturing, this paper presents a novel tool wear assessment technique based on the integrated radial basis function based kernel principal component analysis (KPCA_IRBF) and Gaussian process regression (GPR) for real-timely and accurately monitoring the in-process tool wear parameters (flank wear width). The KPCA_IRBF is a kind of new nonlinear dimension-increment technique and firstly proposed for feature fusion. The tool wear predictive value and the corresponding confidence interval are both provided by utilizing the GPR model. Besides, GPR performs better than artificial neural networks (ANN) and support vector machines (SVM) in prediction accuracy since the Gaussian noises can be modeled quantitatively in the GPR model. However, the existence of noises will affect the stability of the confidence interval seriously. In this work, the proposed KPCA_IRBF technique helps to remove the noises and weaken its negative effects so as to make the confidence interval compressed greatly and more smoothed, which is conducive for monitoring the tool wear accurately. Moreover, the selection of kernel parameter in KPCA_IRBF can be easily carried out in a much larger selectable region in comparison with the conventional KPCA_RBF technique, which helps to improve the efficiency of model construction. Ten sets of cutting tests are conducted to validate the effectiveness of the presented tool wear assessment technique. The experimental results show that the in-process flank wear width of tool inserts can be monitored accurately by utilizing the presented tool wear assessment technique which is robust under a variety of cutting conditions. This study lays the foundation for tool wear monitoring in real industrial settings.
Zhang, Qiuzhao; Yang, Wei; Zhang, Shubi; Liu, Xin
2018-01-12
Global Navigation Satellite System (GNSS) carrier phase measurement for short baseline meets the requirements of deformation monitoring of large structures. However, the carrier phase multipath effect is the main error source with double difference (DD) processing. There are lots of methods to deal with the multipath errors of Global Position System (GPS) carrier phase data. The BeiDou navigation satellite System (BDS) multipath mitigation is still a research hotspot because the unique constellation design of BDS makes it different to mitigate multipath effects compared to GPS. Multipath error periodically repeats for its strong correlation to geometry of satellites, reflective surface and antenna which is also repetitive. We analyzed the characteristics of orbital periods of BDS satellites which are consistent with multipath repeat periods of corresponding satellites. The results show that the orbital periods and multipath periods for BDS geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites are about one day but the periods of MEO satellites are about seven days. The Kalman filter (KF) and Rauch-Tung-Striebel Smoother (RTSS) was introduced to extract the multipath models from single difference (SD) residuals with traditional sidereal filter (SF). Wavelet filter and Empirical mode decomposition (EMD) were also used to mitigate multipath effects. The experimental results show that the three filters methods all have obvious effect on improvement of baseline accuracy and the performance of KT-RTSS method is slightly better than that of wavelet filter and EMD filter. The baseline vector accuracy on east, north and up (E, N, U) components with KF-RTSS method were improved by 62.8%, 63.6%, 62.5% on day of year 280 and 57.3%, 53.4%, 55.9% on day of year 281, respectively.
Directory of Open Access Journals (Sweden)
Qiuzhao Zhang
2018-01-01
Full Text Available Global Navigation Satellite System (GNSS carrier phase measurement for short baseline meets the requirements of deformation monitoring of large structures. However, the carrier phase multipath effect is the main error source with double difference (DD processing. There are lots of methods to deal with the multipath errors of Global Position System (GPS carrier phase data. The BeiDou navigation satellite System (BDS multipath mitigation is still a research hotspot because the unique constellation design of BDS makes it different to mitigate multipath effects compared to GPS. Multipath error periodically repeats for its strong correlation to geometry of satellites, reflective surface and antenna which is also repetitive. We analyzed the characteristics of orbital periods of BDS satellites which are consistent with multipath repeat periods of corresponding satellites. The results show that the orbital periods and multipath periods for BDS geostationary earth orbit (GEO and inclined geosynchronous orbit (IGSO satellites are about one day but the periods of MEO satellites are about seven days. The Kalman filter (KF and Rauch-Tung-Striebel Smoother (RTSS was introduced to extract the multipath models from single difference (SD residuals with traditional sidereal filter (SF. Wavelet filter and Empirical mode decomposition (EMD were also used to mitigate multipath effects. The experimental results show that the three filters methods all have obvious effect on improvement of baseline accuracy and the performance of KT-RTSS method is slightly better than that of wavelet filter and EMD filter. The baseline vector accuracy on east, north and up (E, N, U components with KF-RTSS method were improved by 62.8%, 63.6%, 62.5% on day of year 280 and 57.3%, 53.4%, 55.9% on day of year 281, respectively.
Application Of Shared Gamma And Inverse-Gaussian Frailty Models ...
African Journals Online (AJOL)
Shared Gamma and Inverse-Gaussian Frailty models are used to analyze the survival times of patients who are clustered according to cancer/tumor types under Parametric Proportional Hazard framework. The result of the ... However, no evidence is strong enough for preference of either Gamma or Inverse Gaussian Frailty.
Understanding the spreading of a Gaussian wave packet using the ...
Indian Academy of Sciences (India)
Ex- ploiting the machinery of the Bohmian model of quantum mechanics, the way the wave packet spreads is re-examined. Keywords. Bohmian model; Gaussian wave packet; turning point. PACS No. 03.65.Ta. 1. Introduction and motivation. The time evolution of a Gaussian wave packet is an undergraduate textbook issue.
Non-negative matrix factorization with Gaussian process priors
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Laurberg, Hans
2008-01-01
We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance...
Comparing Fixed and Variable-Width Gaussian Networks
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Kainen, P.C.
2014-01-01
Roč. 57, September (2014), s. 23-28 ISSN 0893-6080 R&D Projects: GA MŠk(CZ) LD13002 Institutional support: RVO:67985807 Keywords : Gaussian radial and kernel networks * Functionally equivalent networks * Universal approximators * Stabilizers defined by Gaussian kernels * Argminima of error functionals Subject RIV: IN - Informatics, Computer Science Impact factor: 2.708, year: 2014
Using Mixture of Gaussians to Compare Approaches to Signal Separation
DEFF Research Database (Denmark)
Petersen, Kaare Brandt
2004-01-01
is an example of how such different approaches to separation can be compared using Mixtures of Gaussians as a prior distribution. This not only illuminates some interesting properties of Maximum Likelihood and Energy Based Models, but is also an example of how Mixtures of Gaussians can serve as a both flexible...
Higher-order Gaussian kernel in bootstrap boosting algorithm ...
African Journals Online (AJOL)
The bootstrap boosting algorithm is a bias reduction scheme. The adoption of higher-order Gaussian kernel in a bootstrap boosting algorithm in kernel density estimation was investigated. The algorithm used the higher-order. Gaussian kernel instead of the regular fixed kernels. A comparison of the scheme with existing ...
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.
New gaussian points for the solution of first order ordinary ...
African Journals Online (AJOL)
New gaussian points for the solution of first order ordinary differential equations. ... Science World Journal ... In this paper, a new set of Gaussian points has been proposed and used as collocation points for the construction of block numerical methods for the solution of first order IVP through transformation within the step ...
Convergence of posteriors for discretized log Gaussian Cox processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....
Higher-Order Hybrid Gaussian Kernel in Meshsize Boosting Algorithm
African Journals Online (AJOL)
In this paper, we shall use higher-order hybrid Gaussian kernel in a meshsize boosting algorithm in kernel density estimation. Bias reduction is guaranteed in this scheme like other existing schemes but uses the higher-order hybrid Gaussian kernel instead of the regular fixed kernels. A numerical verification of this scheme ...
A complete conformal metric of preassigned negative Gaussian ...
Indian Academy of Sciences (India)
Let ℎ be a complete metric of Gaussian curvature 0 on a punctured Riemann surface of genus ≥ 1 (or the sphere with at least three punctures). Given a smooth negative function with =0 in neighbourhoods of the punctures we prove that there exists a metric conformal to ℎ which attains this function as its Gaussian ...
Angle-domain common-image gathers from anisotropic Gaussian ...
Indian Academy of Sciences (India)
An approach for extracting angle-domain common-image gathers (ADCIGs) from anisotropic Gaussian beam prestack depth migration (GB-PSDM) is presented in this paper. The propagation angle is calcu- lated in the process of migration using the real-value traveltime information of Gaussian beam. Based on the above ...
Ultrawide Bandwidth Receiver Based on a Multivariate Generalized Gaussian Distribution
Ahmed, Qasim Zeeshan
2015-04-01
Multivariate generalized Gaussian density (MGGD) is used to approximate the multiple access interference (MAI) and additive white Gaussian noise in pulse-based ultrawide bandwidth (UWB) system. The MGGD probability density function (pdf) is shown to be a better approximation of a UWB system as compared to multivariate Gaussian, multivariate Laplacian and multivariate Gaussian-Laplacian mixture (GLM). The similarity between the simulated and the approximated pdf is measured with the help of modified Kullback-Leibler distance (KLD). It is also shown that MGGD has the smallest KLD as compared to Gaussian, Laplacian and GLM densities. A receiver based on the principles of minimum bit error rate is designed for the MGGD pdf. As the requirement is stringent, the adaptive implementation of the receiver is also carried out in this paper. Training sequence of the desired user is the only requirement when implementing the detector adaptively. © 2002-2012 IEEE.
Gaussian cloning of coherent states with known phases
International Nuclear Information System (INIS)
Alexanian, Moorad
2006-01-01
The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier
Axial acoustic radiation force on a sphere in Gaussian field
Energy Technology Data Exchange (ETDEWEB)
Wu, Rongrong; Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Gong, Xiufen [Key Laboratory of Modern Acoustics, Institute of Acoustics and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China)
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.
Recovering dark-matter clustering from galaxies with Gaussianization
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.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...... and covariance considered above correspond to, respectively, the one- and two-dimensional Cauchy (or Stieltjes) transform of the ....... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean...
Interpolation of intermolecular potentials using Gaussian processes
Uteva, Elena; Graham, Richard S.; Wilkinson, Richard D.; Wheatley, Richard J.
2017-10-01
A procedure is proposed to produce intermolecular potential energy surfaces from limited data. The procedure involves generation of geometrical configurations using a Latin hypercube design, with a maximin criterion, based on inverse internuclear distances. Gaussian processes are used to interpolate the data, using over-specified inverse molecular distances as covariates, greatly improving the interpolation. Symmetric covariance functions are specified so that the interpolation surface obeys all relevant symmetries, reducing prediction errors. The interpolation scheme can be applied to many important molecular interactions with trivial modifications. Results are presented for three systems involving CO2, a system with a deep energy minimum (HF-HF), and a system with 48 symmetries (CH4-N2). In each case, the procedure accurately predicts an independent test set. Training this method with high-precision ab initio evaluations of the CO2-CO interaction enables a parameter-free, first-principles prediction of the CO2-CO cross virial coefficient that agrees very well with experiments.
Primordial non-Gaussianity from LAMOST surveys
International Nuclear Information System (INIS)
Gong Yan; Wang Xin; Chen Xuelei; Zheng Zheng
2010-01-01
The primordial non-Gaussianity (PNG) in the matter density perturbation is a very powerful probe of the physics of the very early Universe. The local PNG can induce a distinct scale-dependent bias on the large scale structure distribution of galaxies and quasars, which could be used for constraining it. We study the detection limits of PNG from the surveys of the LAMOST telescope. The cases of the main galaxy survey, the luminous red galaxy (LRG) survey, and the quasar survey of different magnitude limits are considered. We find that the Main1 sample (i.e. the main galaxy survey which is one magnitude deeper than the SDSS main galaxy survey, or r NL are |f NL | NL | NL | is between 50 and 103, depending on the magnitude limit of the survey. With Planck-like priors on cosmological parameters, the quasar survey with g NL | < 43 (2σ). We also discuss the possibility of further tightening the constraint by using the relative bias method proposed by Seljak.
A Decentralized Receiver in Gaussian Interference
Directory of Open Access Journals (Sweden)
Christian D. Chapman
2018-04-01
Full Text Available Bounds are developed on the maximum communications rate between a transmitter and a fusion node aided by a cluster of distributed receivers with limited resources for cooperation, all in the presence of an additive Gaussian interferer. The receivers cannot communicate with one another and can only convey processed versions of their observations to the fusion center through a Local Array Network (LAN with limited total throughput. The effectiveness of each bound’s approach for mitigating a strong interferer is assessed over a wide range of channels. It is seen that, if resources are shared effectively, even a simple quantize-and-forward strategy can mitigate an interferer 20 dB stronger than the signal in a diverse range of spatially Ricean channels. Monte-Carlo experiments for the bounds reveal that, while achievable rates are stable when varying the receiver’s observed scattered-path to line-of-sight signal power, the receivers must adapt how they share resources in response to this change. The bounds analyzed are proven to be achievable and are seen to be tight with capacity when LAN resources are either ample or limited.
Link Prediction via Sparse Gaussian Graphical Model
Directory of Open Access Journals (Sweden)
Liangliang Zhang
2016-01-01
Full Text Available Link prediction is an important task in complex network analysis. Traditional link prediction methods are limited by network topology and lack of node property information, which makes predicting links challenging. In this study, we address link prediction using a sparse Gaussian graphical model and demonstrate its theoretical and practical effectiveness. In theory, link prediction is executed by estimating the inverse covariance matrix of samples to overcome information limits. The proposed method was evaluated with four small and four large real-world datasets. The experimental results show that the area under the curve (AUC value obtained by the proposed method improved by an average of 3% and 12.5% compared to 13 mainstream similarity methods, respectively. This method outperforms the baseline method, and the prediction accuracy is superior to mainstream methods when using only 80% of the training set. The method also provides significantly higher AUC values when using only 60% in Dolphin and Taro datasets. Furthermore, the error rate of the proposed method demonstrates superior performance with all datasets compared to mainstream methods.
A Gaussian Mixture Model for Nulling Pulsars
Kaplan, D. L.; Swiggum, J. K.; Fichtenbauer, T. D. J.; Vallisneri, M.
2018-03-01
The phenomenon of pulsar nulling—where pulsars occasionally turn off for one or more pulses—provides insight into pulsar-emission mechanisms and the processes by which pulsars turn off when they cross the “death line.” However, while ever more pulsars are found that exhibit nulling behavior, the statistical techniques used to measure nulling are biased, with limited utility and precision. In this paper, we introduce an improved algorithm, based on Gaussian mixture models, for measuring pulsar nulling behavior. We demonstrate this algorithm on a number of pulsars observed as part of a larger sample of nulling pulsars, and show that it performs considerably better than existing techniques, yielding better precision and no bias. We further validate our algorithm on simulated data. Our algorithm is widely applicable to a large number of pulsars even if they do not show obvious nulls. Moreover, it can be used to derive nulling probabilities of nulling for individual pulses, which can be used for in-depth studies.
Anomalous dimensions and non-gaussianity
Energy Technology Data Exchange (ETDEWEB)
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.
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.
Option pricing for non-Gaussian price fluctuations
Kleinert, Hagen
2004-07-01
From the path integral description of price fluctuations with non-Gaussian distributions we derive a stochastic calculus which replaces Itô's calculus for harmonic fluctuations. We set up a natural martingale for option pricing from the wealth balance of options, stocks, and bonds, and evaluate the resulting formula for truncated Lévy distributions. After this, an alternative formula is derived for a model of multivariant Gaussian price fluctuations which leads to non-Gaussian return distributions fitting Dow Jones data excellently from long to short time scales with a tail behavior e - x/ x3/2.
Higher moments of weighted integrals of non-Gaussian fields
DEFF Research Database (Denmark)
Mohr, Gunnar
1999-01-01
In general, the exact probability distribution of a definite integral of a given non-Gaussian random field is not known. Some information about this unknown distribution can be obtained from the 3rd and 4th moment of the integral. Approximations to these moments can be calculated by discretizing...... the integral and replacing the integrand by third-degree polynomials of correlated Gaussian Variables which reproduce the first four moments and the correlation function of the field correctly. The method described (see Ditlevsen O, Mohr G, Hoffmeyer P. Integration of non-Gaussian fields. Probabilistic...
Generalised Hermite–Gaussian beams and mode transformations
International Nuclear Information System (INIS)
Wang, Yi; Chen, Yujie; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-01-01
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. (paper)
International Nuclear Information System (INIS)
Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.
2013-01-01
Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability
Making tensor factorizations robust to non-gaussian noise.
Energy Technology Data Exchange (ETDEWEB)
Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson
2011-03-01
Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).
Optimal multicopy asymmetric Gaussian cloning of coherent states
Fiurášek, Jaromír; Cerf, Nicolas J.
2007-05-01
We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.
Optimal multicopy asymmetric Gaussian cloning of coherent states
International Nuclear Information System (INIS)
Fiurasek, Jaromir; Cerf, Nicolas J.
2007-01-01
We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward
Quantifying entanglement in two-mode Gaussian states
Tserkis, Spyros; Ralph, Timothy C.
2017-12-01
Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.
Scalable Gaussian Processes and the search for exoplanets
CERN. Geneva
2015-01-01
Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.
ARC Code TI: Block-GP: Scalable Gaussian Process Regression
National Aeronautics and Space Administration — Block GP is a Gaussian Process regression framework for multimodal data, that can be an order of magnitude more scalable than existing state-of-the-art nonlinear...
Schweiner, Frank; Laturner, Jeanine; Main, Jörg; Wunner, Günter
2017-11-01
Until now only for specific crossovers between Poissonian statistics (P), the statistics of a Gaussian orthogonal ensemble (GOE), or the statistics of a Gaussian unitary ensemble (GUE) have analytical formulas for the level spacing distribution function been derived within random matrix theory. We investigate arbitrary crossovers in the triangle between all three statistics. To this aim we propose an according formula for the level spacing distribution function depending on two parameters. Comparing the behavior of our formula for the special cases of P→GUE, P→GOE, and GOE→GUE with the results from random matrix theory, we prove that these crossovers are described reasonably. Recent investigations by F. Schweiner et al. [Phys. Rev. E 95, 062205 (2017)2470-004510.1103/PhysRevE.95.062205] have shown that the Hamiltonian of magnetoexcitons in cubic semiconductors can exhibit all three statistics in dependence on the system parameters. Evaluating the numerical results for magnetoexcitons in dependence on the excitation energy and on a parameter connected with the cubic valence band structure and comparing the results with the formula proposed allows us to distinguish between regular and chaotic behavior as well as between existent or broken antiunitary symmetries. Increasing one of the two parameters, transitions between different crossovers, e.g., from the P→GOE to the P→GUE crossover, are observed and discussed.
International Nuclear Information System (INIS)
Kenfack, Lionel Tenemeza; Tchoffo, Martin; Fai, Lukong Cornelius; Fouokeng, Georges Collince
2017-01-01
We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.
Energy Technology Data Exchange (ETDEWEB)
Kenfack, Lionel Tenemeza, E-mail: kenfacklionel300@gmail.com [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Tchoffo, Martin; Fai, Lukong Cornelius [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Fouokeng, Georges Collince [Mesoscopic and Multilayer Structure Laboratory, Department of Physics, Faculty of Science, University of Dschang, PO Box: 67 Dschang (Cameroon); Laboratoire de Génie des Matériaux, Pôle Recherche-Innovation-Entrepreneuriat (PRIE), Institut Universitaire de la Côte, BP 3001 Douala (Cameroon)
2017-04-15
We address the entanglement dynamics of a three-qubit system interacting with a classical fluctuating environment described either by a Gaussian or non-Gaussian noise in three different configurations namely: common, independent and mixed environments. Specifically, we focus on the Ornstein-Uhlenbeck (OU) noise and the random telegraph noise (RTN). The qubits are prepared in a state composed of a Greenberger-Horne-Zeilinger (GHZ) and a W state. With the help of the tripartite negativity, we show that the entanglement evolution is not only affected by the type of system-environment coupling but also by the kind and the memory properties of the considered noise. We also compared the dynamics induced by the two kinds of noise and we find that even if both noises have a Lorentzian spectrum, the effects of the OU noise cannot be in a simple way deduced from those of the RTN and vice-versa. In addition, we show that the entanglement can be indefinitely preserved when the qubits are coupled to the environmental noise in a common environment (CE). Finally, the presence or absence of peculiar phenomena such as entanglement revivals (ER) and entanglement sudden death (ESD) is observed.
Identification and estimation of non-Gaussian structural vector autoregressions
DEFF Research Database (Denmark)
Lanne, Markku; Meitz, Mika; Saikkonen, Pentti
Conventional structural vector autoregressive (SVAR) models with Gaussian errors are not identified, and additional identifying restrictions are typically imposed in applied work. We show that the Gaussian case is an exception in that a SVAR model whose error vector consists of independent non......, additional economic identifying restrictions can be tested. In an empirical application, we find a negative impact of a contractionary monetary policy shock on financial markets, and clearly reject the commonly employed recursive identifying restrictions....
Properties of Orthogonal Gaussian-Hermite Moments and Their Applications
Directory of Open Access Journals (Sweden)
Jun Shen
2005-03-01
Full Text Available Moments are widely used in pattern recognition, image processing, and computer vision and multiresolution analysis. In this paper, we first point out some properties of the orthogonal Gaussian-Hermite moments, and propose a new method to detect the moving objects by using the orthogonal Gaussian-Hermite moments. The experiment results are reported, which show the good performance of our method.
Gaussian Filtering with Tapered Liquid Crystal Photonic Bandgap Fibers
DEFF Research Database (Denmark)
Scolari, Lara; Alkeskjold, Thomas Tanggaard; Bjarklev, Anders Overgaard
2006-01-01
We present a device based on a tapered Liquid Crystal Photonic Bandgap Fiber that allows active all-in-fiber filtering. The resulting Photonic Bandgap Fiber device provides a Gaussian filter covering the wavelength range 1200-1600 nm......We present a device based on a tapered Liquid Crystal Photonic Bandgap Fiber that allows active all-in-fiber filtering. The resulting Photonic Bandgap Fiber device provides a Gaussian filter covering the wavelength range 1200-1600 nm...
Non-Gaussianity and Excursion Set Theory: Halo Bias
Energy Technology Data Exchange (ETDEWEB)
Adshead, Peter [Enrico Fermi Institute, Univ. of Chicago, IL (United States); Baxter, Eric J. [Univ. of Chicago, Chicago, IL (United States); Dodelson, Scott [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Lidz, Adam [Univ. of Pennsylvania, Philadelphia, PA (United States)
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.
Non-Gaussianity from inflation: theory and observations
Bartolo, N.; Komatsu, E.; Matarrese, S.; Riotto, A.
2004-11-01
This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.
Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin
2018-02-01
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.
Automatic image equalization and contrast enhancement using Gaussian mixture modeling.
Celik, Turgay; Tjahjadi, Tardi
2012-01-01
In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types.
Current inversion induced by colored non-Gaussian noise
International Nuclear Information System (INIS)
Bag, Bidhan Chandra; Hu, Chin-Kung
2009-01-01
We study a stochastic process driven by colored non-Gaussian noises. For the flashing ratchet model we find that there is a current inversion in the variation of the current with the half-cycle period which accounts for the potential on–off operation. The current inversion almost disappears if one switches from non-Gaussian (NG) to Gaussian (G) noise. We also find that at low value of the asymmetry parameter of the potential the mobility controlled current is more negative for NG noise as compared to G noise. But at large magnitude of the parameter the diffusion controlled positive current is higher for the former than for the latter. On increasing the noise correlation time (τ), keeping the noise strength fixed, the mean velocity of a particle first increases and then decreases after passing through a maximum if the noise is non-Gaussian. For Gaussian noise, the current monotonically decreases. The current increases with the noise parameter p, 0< p<5/3, which is 1 for Gaussian noise
Scaled unscented transform Gaussian sum filter: Theory and application
Luo, Xiaodong
2010-05-01
In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]). In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel. As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to
Maneuvering Target Detection Based on JRC System in Gaussian and Non-Gaussian Clutter
Directory of Open Access Journals (Sweden)
Yu Yao
2015-01-01
Full Text Available Aimed at the problem of detecting maneuvering targets in the Gaussian and sea clutter environments and based on the established motion state model, this paper proposed a new scheme that uses a joint radar-communication (JRC system with Kalman filter to accurately detect the target with the generalized likelihood ratio test (GLRT theory and a constant false alarm rate (CFAR based threshold. Also, the theoretical threshold and probability function of GLRT target detection based on CFAR were given. Moreover, target detection probability of the new JRC system in Weibull and K distribution clutter is deduced. In addition to theoretical considerations, simulations and measurement results of the new JRC systems demonstrate excellent detection performance for maneuvering targets in the Weibull and K distribution channel.
Directory of Open Access Journals (Sweden)
Edmundas Kazimieras Zavadskas
2015-12-01
Full Text Available The principles of sustainability have become particularly important in the construction, real estate maintenance sector, and all areas of life in recent years. The one of the major problem of urban territories that domestic and construction waste of generated products cannot be removed automatically. The above necessity induces the demand of systems and technologies for waste life cycle and proper disposal development. Siting of the waste incineration plant is a complex process, which includes all factors of sustainability principles. The selection of the construction area is a complex problem due to the existence of different tangible and intangible factors and the multiple alternatives available. Multicriteria decision-making methods (MCDM present powerful and flexible techniques for the solution of many sustainability problems. In this paper, we propose a new extension of WASPAS method, namely WASPAS-SVNS. This extension is realized in the framework of the single-valued neutrosophic set that enables to represent and model the indeterminacy explicitly and the functions of the truth-membership, the indeterminacy-membership and the falsity-membership are not related to each other. The paper deals with the solution of the waste incineration plant siting problem due to the requirements of sustainability factors.
Compensation of Gaussian curvature in developable cones is local
Wang, Jin W.; Witten, Thomas A.
2009-10-01
We use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, Comput. Aided Geom. Des. 20, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, Nature (London) 401, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, Phys. Rev. E 73, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a way to confirm the curvature cancellation phenomenon.
Gaussianization for fast and accurate inference from cosmological data
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.
Generation of Quasi-Gaussian Pulses Based on Correlation Techniques
Directory of Open Access Journals (Sweden)
POHOATA, S.
2012-02-01
Full Text Available The Gaussian pulses have been mostly used within communications, where some applications can be emphasized: mobile telephony (GSM, where GMSK signals are used, as well as the UWB communications, where short-period pulses based on Gaussian waveform are generated. Since the Gaussian function signifies a theoretical concept, which cannot be accomplished from the physical point of view, this should be expressed by using various functions, able to determine physical implementations. New techniques of generating the Gaussian pulse responses of good precision are approached, proposed and researched in this paper. The second and third order derivatives with regard to the Gaussian pulse response are accurately generated. The third order derivates is composed of four individual rectangular pulses of fixed amplitudes, being easily to be generated by standard techniques. In order to generate pulses able to satisfy the spectral mask requirements, an adequate filter is necessary to be applied. This paper emphasizes a comparative analysis based on the relative error and the energy spectra of the proposed pulses.
Are Gaussian spectra a viable perceptual assumption in color appearance?
Mizokami, Yoko; Webster, Michael A
2012-02-01
Natural illuminant and reflectance spectra can be roughly approximated by a linear model with as few as three basis functions, and this has suggested that the visual system might construct a linear representation of the spectra by estimating the weights of these functions. However, such models do not accommodate nonlinearities in color appearance, such as the Abney effect. Previously, we found that these nonlinearities are qualitatively consistent with a perceptual inference that stimulus spectra are instead roughly Gaussian, with the hue tied to the inferred centroid of the spectrum [J. Vision 6(9), 12 (2006)]. Here, we examined to what extent a Gaussian inference provides a sufficient approximation of natural color signals. Reflectance and illuminant spectra from a wide set of databases were analyzed to test how well the curves could be fit by either a simple Gaussian with three parameters (amplitude, peak wavelength, and standard deviation) versus the first three principal component analysis components of standard linear models. The resulting Gaussian fits were comparable to linear models with the same degrees of freedom, suggesting that the Gaussian model could provide a plausible perceptual assumption about stimulus spectra for a trichromatic visual system. © 2012 Optical Society of America
Maximal trace distance between isoenergetic bosonic Gaussian states
Volkoff, T. J.
2017-12-01
We locate the set of pairs (ρ1, ρ2) of Gaussian states of a single mode electromagnetic field that exhibit maximal trace distance subject to the energy constraint ⟨a†a⟩ ρ1=⟨a†a⟩ ρ2=E . Any such pair allows to achieve the minimum possible error in the task of binary distinguishability of two single mode, isoenergetic Gaussian quantum signals. In particular, we show that the logarithm of the minimal error probability for distinguishing two maximally trace distant, isoenergetic Gaussian states scales as -E2, less than the achievable scaling of the minimal error probability for distinguishing, e.g., a pair of isoenergetic Heisenberg-Weyl coherent states with energy E or a pair of isoenergetic quadrature squeezed states with energy E. For the case of a field consisting of M > 1 modes, we locate the set of pairs of maximally trace distant isoenergetic, isocovariant Gaussian states. These results have basic applications in the theory of continuous variable quantum communications with Gaussian states of light.
Consistency relations for sharp inflationary non-Gaussian features
International Nuclear Information System (INIS)
Mooij, Sander; Palma, Gonzalo A.; Panotopoulos, Grigoris; Soto, Alex
2016-01-01
If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we show that sharp features may be analyzed using only data coming from the three point correlation function parametrizing primordial non-Gaussianity. More precisely, we show that if features appear in a particular non-Gaussian triangle configuration (e.g. equilateral, folded, squeezed), these must reappear in every other configuration according to a specific relation allowing us to correlate features across the non-Gaussian bispectrum. As a result, we offer a method to study scale-dependent features generated during inflation that depends only on data coming from measurements of non-Gaussianity, allowing us to omit data from the power spectrum.
Gaussian geometric discord in terms of Hellinger distance
Suciu, Serban; Isar, Aurelian
2015-12-01
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.
Continuous-variable quantum teleportation with non-Gaussian resources
International Nuclear Information System (INIS)
Dell'Anno, F.; De Siena, S.; Albano, L.; Illuminati, F.
2007-01-01
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
Learning with Uncertainty - Gaussian Processes and Relevance Vector Machines
DEFF Research Database (Denmark)
Candela, Joaquin Quinonero
2004-01-01
This thesis is concerned with Gaussian Processes (GPs) and Relevance Vector Machines (RVMs), both of which are particular instances of probabilistic linear models. We look at both models from a Bayesian perspective, and are forced to adopt an approximate Bayesian treatment to learning for two....... Computational efficiency is obtained through sparseness: sparse linear models have a significant number of their weights set to zero. For the RVM, which we treat in Chap. 2, we show that it is precisely the particular choice of Bayesian approximation that enforces sparseness. Probabilistic models have...... family of approximations to Gaussian Processes, Reduced Rank Gaussian Processes (RRGPs), which take the form of nite extended linear models; we show that GPs are in general equivalent to in nite extended linear models. We also show that RRGPs result in degenerate GPs, which suffer, like RVMs...
Outage performance of cognitive radio systems with Improper Gaussian signaling
Amin, Osama
2015-06-14
Improper Gaussian signaling has proved its ability to improve the achievable rate of the systems that suffer from interference compared with proper Gaussian signaling. In this paper, we first study impact of improper Gaussian signaling on the performance of the cognitive radio system by analyzing the outage probability of both the primary user (PU) and the secondary user (SU). We derive exact expression of the SU outage probability and upper and lower bounds for the PU outage probability. Then, we design the SU signal by adjusting its transmitted power and the circularity coefficient to minimize the SU outage probability while maintaining a certain PU quality-of-service. Finally, we evaluate the proposed bounds and adaptive algorithms by numerical results.
Contracted auxiliary Gaussian basis integral and derivative evaluation
Giese, Timothy J.; York, Darrin M.
2008-02-01
The rapid evaluation of two-center Coulomb and overlap integrals between contracted auxiliary solid harmonic Gaussian functions is examined. Integral expressions are derived from the application of Hobson's theorem and Dunlap's product and differentiation rules of the spherical tensor gradient operator. It is shown that inclusion of the primitive normalization constants greatly simplifies the calculation of contracted functions corresponding to a Gaussian multipole expansion of a diffuse charge density. Derivative expressions are presented and it is shown that chain rules are avoided by expressing the derivatives as a linear combination of auxiliary integrals involving no more than five terms. Calculation of integrals and derivatives requires the contraction of a single vector corresponding to the monopolar result and its scalar derivatives. Implementation of the method is discussed and comparison is made with a Cartesian Gaussian-based method. The current method is superior for the evaluation of both integrals and derivatives using either primitive or contracted functions.
Can an ensemble give anything more than Gaussian probabilities?
Directory of Open Access Journals (Sweden)
J. C. W. Denholm-Price
2003-01-01
Full Text Available Can a relatively small numerical weather prediction ensemble produce any more forecast information than can be reproduced by a Gaussian probability density function (PDF? This question is examined using site-specific probability forecasts from the UK Met Office. These forecasts are based on the 51-member Ensemble Prediction System of the European Centre for Medium-range Weather Forecasts. Verification using Brier skill scores suggests that there can be statistically-significant skill in the ensemble forecast PDF compared with a Gaussian fit to the ensemble. The most significant increases in skill were achieved from bias-corrected, calibrated forecasts and for probability forecasts of thresholds that are located well inside the climatological limits at the examined sites. Forecast probabilities for more climatologically-extreme thresholds, where the verification more often lies within the tails or outside of the PDF, showed little difference in skill between the forecast PDF and the Gaussian forecast.
Standard sirens and dark sector with Gaussian process
Cai, Rong-Gen; Yang, Tao
2018-01-01
The gravitational waves from compact binary systems are viewed as a standard siren to probe the evolution of the universe. This paper summarizes the potential and ability to use the gravitational waves to constrain the cosmological parameters and the dark sector interaction in the Gaussian process methodology. After briefly introducing the method to reconstruct the dark sector interaction by the Gaussian process, the concept of standard sirens and the analysis of reconstructing the dark sector interaction with LISA are outlined. Furthermore, we estimate the constraint ability of the gravitational waves on cosmological parameters with ET. The numerical methods we use are Gaussian process and the Markov-Chain Monte-Carlo. Finally, we also forecast the improvements of the abilities to constrain the cosmological parameters with ET and LISA combined with the Planck.
How Gaussian competition leads to lumpy or uniform species distributions
DEFF Research Database (Denmark)
Pigolotti, Simone; Lopez, Cristóbal; Hernandez-Garcia, Emilio
2010-01-01
A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource...... spectrum, or their distribution is “lumped” (or “clumped”), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern...... of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either...
Folded resonant non-Gaussianity in general single field inflation
International Nuclear Information System (INIS)
Chen, Xingang
2010-01-01
We compute a novel type of large non-Gaussianity due to small periodic features in general single field inflationary models. We show that the non-Bunch-Davies vacuum component generated by features, although has a very small amplitude, can have significant impact on the non-Gaussianity. Three mechanisms are turned on simultaneously in such models, namely the resonant effect, non-Bunch-Davies vacuum and higher derivative kinetic terms, resulting in a bispectrum with distinctive shapes and running. The size can be equal to or larger than that previously found in each single mechanism. Our full results, including the resonant and folded resonant non-Gaussianities, give the leading order bispectra due to general periodic features in general single field inflation
Differential detection of Gaussian MSK in a mobile radio environment
Simon, M. K.; Wang, C. C.
1984-01-01
Minimum shift keying with Gaussian shaped transmit pulses is a strong candidate for a modulation technique that satisfies the stringent out-of-band radiated power requirements of the mobil radio application. Numerous studies and field experiments have been conducted by the Japanese on urban and suburban mobile radio channels with systems employing Gaussian minimum-shift keying (GMSK) transmission and differentially coherent reception. A comprehensive analytical treatment is presented of the performance of such systems emphasizing the important trade-offs among the various system design parameters such as transmit and receiver filter bandwidths and detection threshold level. It is shown that two-bit differential detection of GMSK is capable of offering far superior performance to the more conventional one-bit detection method both in the presence of an additive Gaussian noise background and Rician fading.
Gaussian white noise as a resource for work extraction.
Dechant, Andreas; Baule, Adrian; Sasa, Shin-Ichi
2017-03-01
We show that uncorrelated Gaussian noise can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a nonequilibrium steady state and causes a finite current if the potential is spatially asymmetric. The model thus operates as a Brownian ratchet, whose current we calculate explicitly in three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially perform work against an external load. By comparing the extracted power to the energy injection due to the noise, we discuss the efficiency of such a ratchet.
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Primordial black holes from inflation and non-Gaussianity
Franciolini, G.; Kehagias, A.; Matarrese, S.; Riotto, A.
2018-03-01
Primordial black holes may owe their origin to the small-scale enhancement of the comoving curvature perturbation generated during inflation. Their mass fraction at formation is markedly sensitive to possible non-Gaussianities in such large, but rare fluctuations. We discuss a path-integral formulation which provides the exact mass fraction of primordial black holes at formation in the presence of non-Gaussianity. Through a couple of classes of models, one based on single-field inflation and the other on spectator fields, we show that restricting to a Gaussian statistics may lead to severe inaccuracies in the estimate of the mass fraction as well as on the clustering properties of the primordial black holes.
Standard sirens and dark sector with Gaussian process*
Directory of Open Access Journals (Sweden)
Cai Rong-Gen
2018-01-01
Full Text Available The gravitational waves from compact binary systems are viewed as a standard siren to probe the evolution of the universe. This paper summarizes the potential and ability to use the gravitational waves to constrain the cosmological parameters and the dark sector interaction in the Gaussian process methodology. After briefly introducing the method to reconstruct the dark sector interaction by the Gaussian process, the concept of standard sirens and the analysis of reconstructing the dark sector interaction with LISA are outlined. Furthermore, we estimate the constraint ability of the gravitational waves on cosmological parameters with ET. The numerical methods we use are Gaussian process and the Markov-Chain Monte-Carlo. Finally, we also forecast the improvements of the abilities to constrain the cosmological parameters with ET and LISA combined with the Planck.
Self-similar Gaussian processes for modeling anomalous diffusion
Lim, S. C.; Muniandy, S. V.
2002-08-01
We study some Gaussian models for anomalous diffusion, which include the time-rescaled Brownian motion, two types of fractional Brownian motion, and models associated with fractional Brownian motion based on the generalized Langevin equation. Gaussian processes associated with these models satisfy the anomalous diffusion relation which requires the mean-square displacement to vary with tα, 0Brownian motion and time-rescaled Brownian motion all have the same probability distribution function, the Slepian theorem can be used to compare their first passage time distributions, which are different. Finally, in order to model anomalous diffusion with a variable exponent α(t) it is necessary to consider the multifractional extensions of these Gaussian processes.
Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.
García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G
2017-08-01
The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.
Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels
DEFF Research Database (Denmark)
Khorunzhina, Natalia; Richard, Jean-Francois
The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each step using a distance measure that approxima......The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each step using a distance measure...... that approximates the corresponding importance sampling variance. All functions of interest are evaluated under Gaussian quadrature rules. Examples include a sequential (filtering) evaluation of the likelihood function of a stochastic volatility model where all relevant densities (filtering, predictive...
Non-Gaussianity in a quasiclassical electronic circuit
Suzuki, Takafumi J.; Hayakawa, Hisao
2017-05-01
We study the non-Gaussian dynamics of a quasiclassical electronic circuit coupled to a mesoscopic conductor. Non-Gaussian noise accompanying the nonequilibrium transport through the conductor significantly modifies the stationary probability density function (PDF) of the flux in the dissipative circuit. We incorporate weak quantum fluctuation of the dissipative LC circuit with a stochastic method and evaluate the quantum correction of the stationary PDF. Furthermore, an inverse formula to infer the statistical properties of the non-Gaussian noise from the stationary PDF is derived in the classical-quantum crossover regime. The quantum correction is indispensable to correctly estimate the microscopic transfer events in the QPC with the quasiclassical inverse formula.
Hellinger distance as a measure of Gaussian discord
Marian, Paulina; Marian, Tudor A.
2015-03-01
Especially investigated in recent years, the Gaussian discord can tentatively be quantified by a distance between a given two-mode Gaussian state (GS) and the set of all the zero-discord two-mode GSs. However, as this set consists only of product states, such a distance captures all the correlations (quantum and classical) between modes. Therefore it is merely an upper bound for the geometric discord, no matter which is the employed distance. In this work we choose for this purpose the Hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour. In general, this metric is determined by affinity, a relative of the Uhlmann fidelity with which it shares many important features. As a first step of our work, the affinity of a pair of n-mode GSs is written. Then, in the two-mode case, we succeeded in determining exactly the closest Gaussian product state and computed the Gaussian discord accordingly. The obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two-mode GSs. We then analyse in detail two special classes of two-mode GSs of theoretical and experimental interest as well: the squeezed thermal states and the mode-mixed thermal ones. The former are separable under a well-known threshold of squeezing, while the latter are always separable. It is worth stressing that for symmetric states belonging to either of these classes, we find consistency between their geometric Hellinger discord and the originally defined discord in the Gaussian approach. At the same time, the Gaussian Hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations.
Bayesian analysis of log Gaussian Cox processes for disease mapping
DEFF Research Database (Denmark)
Benes, Viktor; Bodlák, Karel; Møller, Jesper
We consider a data set of locations where people in Central Bohemia have been infected by tick-borne encephalitis, and where population census data and covariates concerning vegetation and altitude are available. The aims are to estimate the risk map of the disease and to study the dependence...... of the risk on the covariates. Instead of using the common area level approaches we consider a Bayesian analysis for a log Gaussian Cox point process with covariates. Posterior characteristics for a discretized version of the log Gaussian Cox process are computed using markov chain Monte Carlo methods...
Neural pulse frequency modulation of an exponentially correlated Gaussian process
Hutchinson, C. E.; Chon, Y.-T.
1976-01-01
The effect of NPFM (Neural Pulse Frequency Modulation) on a stationary Gaussian input, namely an exponentially correlated Gaussian input, is investigated with special emphasis on the determination of the average number of pulses in unit time, known also as the average frequency of pulse occurrence. For some classes of stationary input processes where the formulation of the appropriate multidimensional Markov diffusion model of the input-plus-NPFM system is possible, the average impulse frequency may be obtained by a generalization of the approach adopted. The results are approximate and numerical, but are in close agreement with Monte Carlo computer simulation results.
Gaussian translation operator for Multi-Level Fast Multipole Method
DEFF Research Database (Denmark)
Borries, Oscar Peter; Hansen, Per Christian; Sorensen, Stig B.
2014-01-01
Results using a new translation operator for the Multi-Level Fast Multipole Method are presented. Based on Gaussian beams, the translation operator allows a significant portion of the plane-wave directions to be neglected, resulting in a much faster translation step.......Results using a new translation operator for the Multi-Level Fast Multipole Method are presented. Based on Gaussian beams, the translation operator allows a significant portion of the plane-wave directions to be neglected, resulting in a much faster translation step....
Propagation of Gaussian Beams through Active GRIN Materials
Energy Technology Data Exchange (ETDEWEB)
Gomez-Varela, A I; Flores-Arias, M T; Bao-Varela, C; Gomez-Reino, C [Grupo de ' Microoptica y Optica GRIN' , Unidad asociada al Instituto de Ciencias de Materiales de Aragon, ICMA/CSIC, Zaragoza, Espana y Escuela de Optica y OptometrIa, Campus Sur s/n, Universidade de Santiago, E15782 Santiago de Compostela (Spain); De la Fuente, X, E-mail: maite.flores@usc.es [Instituto de Ciencia de Materiales de Aragon (Universidad de Zaragoza-CSIC), Maria de Luna 3, E50018 Zaragoza (Spain)
2011-01-01
We discussed light propagation through an active GRIN material that exhibits loss or gain. Effects of gain or loss in GRIN materials can be phenomenologically taken into account by using a complex refractive index in the wave equation. This work examines the implication of using a complex refractive index on light propagation in an active GRIN material illuminated by a non-uniform monochromatic wave described by a Gaussian beam. We analyze how a Gaussian beam is propagated through the active material in order to characterize it by the beam parameters and the transverse irradiance distribution.
Permutation entropy of fractional Brownian motion and fractional Gaussian noise
International Nuclear Information System (INIS)
Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.
2008-01-01
We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays
Polarization coupling of vector Bessel–Gaussian beams
International Nuclear Information System (INIS)
Takeuchi, Ryushi; Kozawa, Yuichi; Sato, Shunichi
2013-01-01
We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)
Gaussian-state entanglement in a quantum beat laser
International Nuclear Information System (INIS)
Tahira, Rabia; Ikram, Manzoor; Nha, Hyunchul; Zubairy, M. Suhail
2011-01-01
Recently quantum beat lasers have been considered as a source of entangled radiation [S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, Phys. Rev. A 77, 062308 (2008)]. We investigate and quantify the entanglement of this system when the initial cavity modes are prepared in a Gaussian two-mode state, one being a nonclassical state and the other a thermal state. It is investigated how the output entanglement varies with the nonclassicality of the input Gaussian state, thermal noise, and the strength of the driving field.
Modulation depth of Michelson interferometer with Gaussian beam.
Välikylä, Tuomas; Kauppinen, Jyrki
2011-12-20
Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Bipower variation for Gaussian processes with stationary increments
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Corcuera, José Manuel; Podolskij, Mark
2009-01-01
Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing...
GPflow: A Gaussian process library using TensorFlow
Matthews, Alexander G. de G.; van der Wilk, Mark; Nickson, Tom; Fujii, Keisuke; Boukouvalas, Alexis; León-Villagrá, Pablo; Ghahramani, Zoubin; Hensman, James
2016-01-01
GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end. The distinguishing features of GPflow are that it uses variational inference as the primary approximation method, provides concise code through the use of automatic differentiation, has been engineered with a particular emphasis on software testing and is able to exploit GPU hardware.
Determination of signal intensity affected by Gaussian noise
International Nuclear Information System (INIS)
Blostein, Jeronimo J.; Bennun, Leonardo
1999-01-01
A methodology based on maximum likelihood criteria, to identify and quantify an arbitrary signal affected by Gaussian noise is shown. To use this methodology it is necessary to know the position in the spectrum where the signal of interest should appear, and the shape of the signal when the background is null or unappreciable. (author)
Triangular Numbers, Gaussian Integers, and KenKen
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…
Sparse Gaussian graphical mixture model | Lotsi | Afrika Statistika
African Journals Online (AJOL)
Abstract. This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables coupled with the degenerate nature of the likelihood. We propose as ...
Improved Gaussian Mixture Models for Adaptive Foreground Segmentation
DEFF Research Database (Denmark)
Katsarakis, Nikolaos; Pnevmatikakis, Aristodemos; Tan, Zheng-Hua
2016-01-01
Adaptive foreground segmentation is traditionally performed using Stauffer & Grimson’s algorithm that models every pixel of the frame by a mixture of Gaussian distributions with continuously adapted parameters. In this paper we provide an enhancement of the algorithm by adding two important dynamic...
Optical trapping of spermatozoa using Laguerre-Gaussian laser modes
Dasgupta, Raktim; Ahlawat, Sunita; Verma, Ravi Shanker; Shukla, Sunita; Gupta, Pradeep Kumar
2010-11-01
We report results of a study on the use of Laguerre-Gaussian (LG) modes for optical trapping of spermatozoa. The results show that for a given trap beam power the first-order LG mode (LG01) leads to lower photodamage to the cells without compromising the trapping efficiency.
Prediction and retrodiction with continuously monitored Gaussian states
Zhang, Jinglei; Mølmer, Klaus
2017-12-01
Gaussian states of quantum oscillators are fully characterized by the mean values and the covariance matrix of their quadrature observables. We consider the dynamics of a system of oscillators subject to interactions, damping, and continuous probing which maintain their Gaussian state property. Such dynamics is found in many physical systems that can therefore be efficiently described by the ensuing effective representation of the density matrix ρ (t ) . Our probabilistic knowledge about the outcome of measurements on a quantum system at time t is not only governed by ρ (t ) conditioned on the evolution and measurement outcomes obtained until time t but is also modified by any information acquired after t . It was shown [S. Gammelmark, B. Julsgaard, and K. Mølmer, Phys. Rev. Lett. 111, 160401 (2013), 10.1103/PhysRevLett.111.160401] that this information is represented by a supplementary matrix, E (t ) . We show here that the restriction of the dynamics of ρ (t ) to Gaussian states implies that the matrix E (t ) is also fully characterized by a vector of mean values and a covariance matrix. We derive the dynamical equations for these quantities and we illustrate their use in the retrodiction of measurements on Gaussian systems.
On the minimization of Hamiltonians over pure Gaussian states
DEFF Research Database (Denmark)
Derezinski, Jan; Napiorkowski, Marcin; Solovej, Jan Philip
2013-01-01
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihillation operators adapted to the minimizing state. It is shown that this proce...
Lifting Primordial Non-Gaussianity Above the Noise
Welling, Yvette; Woude, Drian van der; Pajer, Enrico
2016-01-01
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
Vortex beam characterization in terms of Hypergeometric- Gaussian modes
CSIR Research Space (South Africa)
Sephton, Bereneice C
2016-10-01
Full Text Available Q-plates are commonly used for uncomplicated generation of polarization controlled vortex beams. Here we show experimentally that the output is not a pure vortex but rather a Hypergeometric-Gaussian mode. Results are in good agreement with theory....
Evaluation of Distance Measures Between Gaussian Mixture Models of MFCCs
DEFF Research Database (Denmark)
Jensen, Jesper Højvang; Ellis, Dan P. W.; Christensen, Mads Græsbøll
2007-01-01
In music similarity and in the related task of genre classification, a distance measure between Gaussian mixture models is frequently needed. We present a comparison of the Kullback-Leibler distance, the earth movers distance and the normalized L2 distance for this application. Although...
A complete conformal metric of preassigned negative Gaussian ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. Let h be a complete metric of Gaussian curvature K0 on a punctured Riemann surface of genus g ≥ 1 (or the sphere with at least three punctures). Given a smooth negative function K with K = K0 in neighbourhoods of the punctures we prove that there exists a metric conformal to h which attains this function as its ...
Exploration vs Exploitation with Partially Observable Gaussian Autoregressive Arms
Kuhn, J.; Mandjes, M.; Nazarathy, Y.
2015-01-01
We consider a restless bandit problem with Gaussian autoregressive arms, where the state of an arm is only observed when it is played and the state-dependent reward is collected. Since arms are only partially observable, a good decision policy needs to account for the fact that information about the
Representation and properties of a class of conditionally Gaussian processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Pedersen, Jan
2009-01-01
It is shown that the class of conditionally Gaussian processes with independent increments is stable under marginalisation and conditioning. Moreover, in general such processes can be represented as integrals of a time changed Brownian motion where the time change and the integrand are jointly in...
Higher Moments of Weighted Integrals of Non-Gaussian Fields
DEFF Research Database (Denmark)
Mohr, Gunnar
1996-01-01
In general , the exact probability distribution of a definite non-Gaussian random field is not known. Some information about this unknown distribution can be obtained from the 3rd and 4th moment of the integral. Approximations to these moments are calculated by a numerical technique based...
Leveraging Gaussian process approximations for rapid image overlay production
CSIR Research Space (South Africa)
Burke, Michael
2017-10-01
Full Text Available of similar quality,despite requiring significantly fewer model evaluations. This process is illustrated using a user-driven saliency generation problem. Here,pairwise image interest comparisons are used to infer underlying image interest and a Gaussian...
A note on moving average models for Gaussian random fields
DEFF Research Database (Denmark)
Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.
basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result...
Gaussian Mixture Reduction for Tracking Multiple Maneuvering Targets in Clutter
2003-03-01
the Poisson exponential term e−λV and the factorial 2-44 of the number of measurements Nm!: c ′ = cNm! e−λV The volume of the combined validation...nonswapped tracks, often other local optima exist for track swap possibilities. The approach of centering a Gaussian optimally (in the MMSE sense) between
inverse gaussian model for small area estimation via gibbs sampling
African Journals Online (AJOL)
ADMIN
(1994) extended the work by Fries and. Bhattacharyya (1983) to include the maximum likelihood analysis of the two-factor inverse. Gaussian model for the unbalanced and interaction case for the estimation of small area parameters in finite populations. The object of this article is to develop a Bayesian approach for small ...
Inverse Gaussian model for small area estimation via Gibbs sampling
African Journals Online (AJOL)
We present a Bayesian method for estimating small area parameters under an inverse Gaussian model. The method is extended to estimate small area parameters for finite populations. The Gibbs sampler is proposed as a mechanism for implementing the Bayesian paradigm. We illustrate the method by application to ...
Generating Nice Linear Systems for Matrix Gaussian Elimination
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…
Mixed non-Gaussianity in multiple-DBI inflation
Energy Technology Data Exchange (ETDEWEB)
Emery, Jon; Tasinato, Gianmassimo; Wands, David, E-mail: jon.emery@port.ac.uk, E-mail: gianmassimo.tasinato@port.ac.uk, E-mail: david.wands@port.ac.uk [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX (United Kingdom)
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}.
Some fractional and multifractional Gaussian processes: A brief introduction
Lim, S. C.; Eab, C. H.
2015-01-01
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifractional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.
Invariance principle, multifractional Gaussian processes and long-range dependence
Cohen, Serge; Marty, Renaud
2008-01-01
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.
Predictive Active Set Selection Methods for Gaussian Processes
DEFF Research Database (Denmark)
Henao, Ricardo; Winther, Ole
2012-01-01
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists of a two step alternating procedure of active set update rules and hyperparameter optimization based upon marginal l...
Stable Lévy motion with inverse Gaussian subordinator
Kumar, A.; Wyłomańska, A.; Gajda, J.
2017-09-01
In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.
Paint stripping with high power flattened Gaussian beams
CSIR Research Space (South Africa)
Forbes, A
2009-08-01
Full Text Available In this paper the researchers present results on improved paint stripping performance with an intra-cavity generated Flattened Gaussian Beam (FGB). A resonator with suitable diffractive optical elements was designed in order to produce a single mode...
Determination of gaussian peaks in gamma spectra by iterative regression
International Nuclear Information System (INIS)
Nordemann, D.J.R.
1987-05-01
The parameters of the peaks in gamma-ray spectra are determined by a simple iterative regression method. For each peak, the parameters are associated with a gaussian curve (3 parameters) located above a linear continuum (2 parameters). This method may produces the complete result of the calculation of statistical uncertainties and an accuracy higher than others methods. (author) [pt
Continuous variable entanglement distillation of non-Gaussian states
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Dong, Ruifang; Heersink, Joel
2009-01-01
We experimentally demonstrate distillation of continuous variable entangled light that has undergone non-Gaussian attenuation loss. The continuous variable entanglement is generated with optical fibers and sent through a lossy channel, where the transmission is varying in time. By employing simple...
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 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.
Baura, Alendu; Sen, Monoj Kumar; Goswami, Gurupada; Bag, Bidhan Chandra
2011-01-28
In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual gaussian distribution but the external noise may be gaussian or non-gaussian in characteristic. The calculated rate is valid for low noise strength of non-gaussian noise such that an effective gaussian approximation of non-gaussian noise wherein the higher order even cumulants of order "4" and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-gaussian to gaussian character of the external noise.
Feasibility study on the least square method for fitting non-Gaussian noise data
Xu, Wei; Chen, Wen; Liang, Yingjie
2018-02-01
This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.
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.
Guadagnini, A.; Riva, M.; Neuman, S. P.
2016-12-01
Environmental quantities such as log hydraulic conductivity (or transmissivity), Y(x) = ln K(x), and their spatial (or temporal) increments, ΔY, are known to be generally non-Gaussian. Documented evidence of such behavior includes symmetry of increment distributions at all separation scales (or lags) between incremental values of Y with sharp peaks and heavy tails that decay asymptotically as lag increases. This statistical scaling occurs in porous as well as fractured media characterized by either one or a hierarchy of spatial correlation scales. In hierarchical media one observes a range of additional statistical ΔY scaling phenomena, all of which are captured comprehensibly by a novel generalized sub-Gaussian (GSG) model. In this model Y forms a mixture Y(x) = U(x) G(x) of single- or multi-scale Gaussian processes G having random variances, U being a non-negative subordinator independent of G. Elsewhere we developed ways to generate unconditional and conditional random realizations of isotropic or anisotropic GSG fields which can be embedded in numerical Monte Carlo flow and transport simulations. Here we present and discuss expressions for probability distribution functions of Y and ΔY as well as their lead statistical moments. We then focus on a simple flow setting of mean uniform steady state flow in an unbounded, two-dimensional domain, exploring ways in which non-Gaussian heterogeneity affects stochastic flow and transport descriptions. Our expressions represent (a) lead order autocovariance and cross-covariance functions of hydraulic head, velocity and advective particle displacement as well as (b) analogues of preasymptotic and asymptotic Fickian dispersion coefficients. We compare them with corresponding expressions developed in the literature for Gaussian Y.
Sound Event Detection for Music Signals Using Gaussian Processes
Directory of Open Access Journals (Sweden)
Pablo A. Alvarado-Durán
2013-11-01
Full Text Available In this paper we present a new methodology for detecting sound events in music signals using Gaussian Processes. Our method firstly takes a time-frequency representation, i.e. the spectrogram, of the input audio signal. Secondly the spectrogram dimension is reduced translating the linear Hertz frequency scale into the logarithmic Mel frequency scale using a triangular filter bank. Finally every short-time spectrum, i.e. every Mel spectrogram column, is classified as “Event” or “Not Event” by a Gaussian Processes Classifier. We compare our method with other event detection techniques widely used. To do so, we use MATLAB® to program each technique and test them using two datasets of music with different levels of complexity. Results show that the new methodology outperforms the standard approaches, getting an improvement by about 1.66 % on the dataset one and 0.45 % on the dataset two in terms of F-measure.
Two-mode Gaussian density matrices and squeezing of photons
International Nuclear Information System (INIS)
Tucci, R.R.
1992-01-01
In this paper, the authors generalize to 2-mode states the 1-mode state results obtained in a previous paper. The authors study 2-mode Gaussian density matrices. The authors find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows the authors to express the density matrix as a product of two 1-mode density matrices. The authors find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. The authors discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered
Generation of Quantum Correlations in Bipartite Gaussian Open Quantum Systems
Isar, Aurelian
2018-02-01
We describe the generation of quantum correlations (entanglement, discord and steering) in a system composed of two coupled non-resonant bosonic modes immersed in a common thermal reservoir, in the framework of the theory of open systems. We show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and strength of interaction between the two bosonic modes. We also show that for initial uni-modal squeezed states Gaussian discord can be generated for all non-zero values of the strength of interaction between the modes. Likewise, for an initial separable state, a generation of Gaussian steering may take place temporarily, for definite values of the parameters characterizing the initial state and the thermal environment, and the strength of coupling between the two modes.
Analysis of some methods for reduced rank Gaussian process regression
DEFF Research Database (Denmark)
Quinonero-Candela, J.; Rasmussen, Carl Edward
2005-01-01
proliferation of a number of cost-effective approximations to GPs, both for classification and for regression. In this paper we analyze one popular approximation to GPs for regression: the reduced rank approximation. While generally GPs are equivalent to infinite linear models, we show that Reduced Rank......While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent...... Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning...
A Note on Functional Averages over Gaussian Ensembles
Directory of Open Access Journals (Sweden)
Gabriel H. Tucci
2013-01-01
Full Text Available We find a new formula for matrix averages over the Gaussian ensemble. Let H be an n×n Gaussian random matrix with complex, independent, and identically distributed entries of zero mean and unit variance. Given an n×n positive definite matrix A and a continuous function f:ℝ+→ℝ such that ∫0∞e-αt|f(t|2dt0, we find a new formula for the expectation [Tr(f(HAH*]. Taking f(x=log(1+x gives another formula for the capacity of the MIMO communication channel, and taking f(x=(1+x-1 gives the MMSE achieved by a linear receiver.
Prediction of Geological Subsurfaces Based on Gaussian Random Field Models
Energy Technology Data Exchange (ETDEWEB)
Abrahamsen, Petter
1997-12-31
During the sixties, random functions became practical tools for predicting ore reserves with associated precision measures in the mining industry. This was the start of the geostatistical methods called kriging. These methods are used, for example, in petroleum exploration. This thesis reviews the possibilities for using Gaussian random functions in modelling of geological subsurfaces. It develops methods for including many sources of information and observations for precise prediction of the depth of geological subsurfaces. The simple properties of Gaussian distributions make it possible to calculate optimal predictors in the mean square sense. This is done in a discussion of kriging predictors. These predictors are then extended to deal with several subsurfaces simultaneously. It is shown how additional velocity observations can be used to improve predictions. The use of gradient data and even higher order derivatives are also considered and gradient data are used in an example. 130 refs., 44 figs., 12 tabs.
A model of non-Gaussian diffusion in heterogeneous media
Lanoiselée, Yann; Grebenkov, Denis S.
2018-04-01
Recent progress in single-particle tracking has shown evidence of the non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. Similar behavior has also been observed in granular materials, turbulent flows, gels and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior and discuss some implications and extensions.
THE CPA QUALIFICATION METHOD BASED ON THE GAUSSIAN CURVE FITTING
Directory of Open Access Journals (Sweden)
M.T. Adithia
2015-01-01
Full Text Available The Correlation Power Analysis (CPA attack is an attack on cryptographic devices, especially smart cards. The results of the attack are correlation traces. Based on the correlation traces, an evaluation is done to observe whether significant peaks appear in the traces or not. The evaluation is done manually, by experts. If significant peaks appear then the smart card is not considered secure since it is assumed that the secret key is revealed. We develop a method that objectively detects peaks and decides which peak is significant. We conclude that using the Gaussian curve fitting method, the subjective qualification of the peak significance can be objectified. Thus, better decisions can be taken by security experts. We also conclude that the Gaussian curve fitting method is able to show the influence of peak sizes, especially the width and height, to a significance of a particular peak.
Propagation of truncated modified Laguerre-Gaussian beams
Deng, D.; Li, J.; Guo, Q.
2010-01-01
By expanding the circ function into a finite sum of complex Gaussian functions and applying the Collins formula, the propagation of hard-edge diffracted modified Laguerre-Gaussian beams (MLGBs) through a paraxial ABCD system is studied, and the approximate closed-form propagation expression of hard-edge diffracted MLGBs is obtained. The transverse intensity distribution of the MLGB carrying finite power can be characterized by a single bright and symmetric ring during propagation when the aperture radius is very large. Starting from the definition of the generalized truncated second-order moments, the beam quality factor of MLGBs through a hard-edged circular aperture is investigated in a cylindrical coordinate system, which turns out to be dependent on the truncated radius and the beam orders.
Quantum Information Protocols with Gaussian States of Light
DEFF Research Database (Denmark)
Jacobsen, Christian Scheffmann
Quantum cryptography is widely regarded as the most mature field within the context of quantum information in the sense that its application and development has produced companies that base their products on genuine quantum mechanical principles. Examples include quantum random number generators...... of Gaussian states. A quantum information protocol is essentially a sequence of state exchanges between some number of parties and a certain ordering of quantum mechanical unitary operators performed by these parties. An example of this is the famous BB84 protocol for secret key generation, where photons...... with Gaussian states is a promising avenue for the development of practical quantum key distribution with a relay network structure in environments where the distances are relatively short and there is a high number of users, such as an urban environment. In addition to this we consider various point...
Representing Global Reactive Potential Energy Surfaces Using Gaussian Processes.
Kolb, Brian; Marshall, Paul; Zhao, Bin; Jiang, Bin; Guo, Hua
2017-04-06
Representation of multidimensional global potential energy surfaces suitable for spectral and dynamical calculations from high-level ab initio calculations remains a challenge. Here, we present a detailed study on constructing potential energy surfaces using a machine learning method, namely, Gaussian process regression. Tests for the 3 A″ state of SH 2 , which facilitates the SH + H ↔ S( 3 P) + H 2 abstraction reaction and the SH + H' ↔ SH' + H exchange reaction, suggest that the Gaussian process is capable of providing a reasonable potential energy surface with a small number (∼1 × 10 2 ) of ab initio points, but it needs substantially more points (∼1 × 10 3 ) to converge reaction probabilities. The implications of these observations for construction of potential energy surfaces are discussed.
Detecting Clusters in Atom Probe Data with Gaussian Mixture Models.
Zelenty, Jennifer; Dahl, Andrew; Hyde, Jonathan; Smith, George D W; Moody, Michael P
2017-04-01
Accurately identifying and extracting clusters from atom probe tomography (APT) reconstructions is extremely challenging, yet critical to many applications. Currently, the most prevalent approach to detect clusters is the maximum separation method, a heuristic that relies heavily upon parameters manually chosen by the user. In this work, a new clustering algorithm, Gaussian mixture model Expectation Maximization Algorithm (GEMA), was developed. GEMA utilizes a Gaussian mixture model to probabilistically distinguish clusters from random fluctuations in the matrix. This machine learning approach maximizes the data likelihood via expectation maximization: given atomic positions, the algorithm learns the position, size, and width of each cluster. A key advantage of GEMA is that atoms are probabilistically assigned to clusters, thus reflecting scientifically meaningful uncertainty regarding atoms located near precipitate/matrix interfaces. GEMA outperforms the maximum separation method in cluster detection accuracy when applied to several realistically simulated data sets. Lastly, GEMA was successfully applied to real APT data.
Supervised Gaussian process latent variable model for dimensionality reduction.
Gao, Xinbo; Wang, Xiumei; Tao, Dacheng; Li, Xuelong
2011-04-01
The Gaussian process latent variable model (GP-LVM) has been identified to be an effective probabilistic approach for dimensionality reduction because it can obtain a low-dimensional manifold of a data set in an unsupervised fashion. Consequently, the GP-LVM is insufficient for supervised learning tasks (e.g., classification and regression) because it ignores the class label information for dimensionality reduction. In this paper, a supervised GP-LVM is developed for supervised learning tasks, and the maximum a posteriori algorithm is introduced to estimate positions of all samples in the latent variable space. We present experimental evidences suggesting that the supervised GP-LVM is able to use the class label information effectively, and thus, it outperforms the GP-LVM and the discriminative extension of the GP-LVM consistently. The comparison with some supervised classification methods, such as Gaussian process classification and support vector machines, is also given to illustrate the advantage of the proposed method.
On the construction of capacity-achieving lattice Gaussian codes
Alghamdi, Wael Mohammed Abdullah
2016-08-15
In this paper, we propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3]. © 2016 IEEE.
Color Texture Segmentation by Decomposition of Gaussian Mixture Model
Czech Academy of Sciences Publication Activity Database
Grim, Jiří; Somol, Petr; Haindl, Michal; Pudil, Pavel
2006-01-01
Roč. 19, č. 4225 (2006), s. 287-296 ISSN 0302-9743. [Iberoamerican Congress on Pattern Recognition. CIARP 2006 /11./. Cancun, 14.11.2006-17.11.2006] R&D Projects: GA AV ČR 1ET400750407; GA MŠk 1M0572; GA MŠk 2C06019 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : texture segmentation * gaussian mixture model * EM algorithm Subject RIV: IN - Informatics, Computer Science Impact factor: 0.402, year: 2005 http://library.utia.cas.cz/separaty/historie/grim-color texture segmentation by decomposition of gaussian mixture model.pdf
Time-frequency analysis and harmonic Gaussian functions
International Nuclear Information System (INIS)
Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.
2013-01-01
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted Τ n , which associate to a function ψ, of the time variable t, a set of functions Ψ n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations Τ n and the functions Ψ n are given. It is proved in particular that the square of the modulus of each function Ψ n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ n .
Scattering of Gaussian Beams by Disordered Particulate Media
Mishchenko, Michael I.; Dlugach, Janna M.
2016-01-01
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.
Differential Evolution with Gaussian Mutation for Economic Dispatch
Basu, Mousumi; Jena, Chitralekha; Panigrahi, Chinmoy Kumar
2016-12-01
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.
Impact of Improper Gaussian Signaling on Hardware Impaired Systems
Javed, Sidrah
2016-12-18
In this paper, we accurately model the hardware impairments (HWI) as improper Gaussian signaling (IGS) which can characterize the asymmetric characteristics of different HWI sources. The proposed model encourages us to adopt IGS scheme for transmitted signal that represents a general study compared with the conventional scheme, proper Gaussian signaling (PGS). First, we express the achievable rate of HWI systems when both PGS and IGS schemes are used when the aggregate effect of HWI is modeled as IGS. Moreover, we tune the IGS statistical characteristics to maximize the achievable rate. Then, we analyze the outage probability for both schemes and derive closed form expressions. Finally, we validate the analytic expressions through numerical and simulation results. In addition, we quantify through the numerical results the performance degradation in the absence of ideal transceivers and the gain reaped from adopting IGS scheme compared with PGS scheme.
Weighted Feature Gaussian Kernel SVM for Emotion Recognition.
Wei, Wei; 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.
Weighted Feature Gaussian Kernel SVM for Emotion Recognition
Directory of Open Access Journals (Sweden)
Wei Wei
2016-01-01
Full Text Available 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.
The semantic Stroop effect: An ex-Gaussian analysis.
White, Darcy; Risko, Evan F; Besner, Derek
2016-10-01
Previous analyses of the standard Stroop effect (which typically uses color words that form part of the response set) have documented effects on mean reaction times in hundreds of experiments in the literature. Less well known is the fact that ex-Gaussian analyses reveal that such effects are seen in (a) the mean of the normal distribution (mu), as well as in (b) the standard deviation of the normal distribution (sigma) and (c) the tail (tau). No ex-Gaussian analysis exists in the literature with respect to the semantically based Stroop effect (which contrasts incongruent color-associated words with, e.g., neutral controls). In the present experiments, we investigated whether the semantically based Stroop effect is also seen in the three ex-Gaussian parameters. Replicating previous reports, color naming was slower when the color was carried by an irrelevant (but incongruent) color-associated word (e.g., sky, tomato) than when the control items consisted of neutral words (e.g., keg, palace) in each of four experiments. An ex-Gaussian analysis revealed that this semantically based Stroop effect was restricted to the arithmetic mean and mu; no semantic Stroop effect was observed in tau. These data are consistent with the views (1) that there is a clear difference in the source of the semantic Stroop effect, as compared to the standard Stroop effect (evidenced by the presence vs. absence of an effect on tau), and (2) that interference associated with response competition on incongruent trials in tau is absent in the semantic Stroop effect.
A complete conformal metric of preassigned negative Gaussian ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
be a punctured hyperbolic Riemann surface, namely a Riemann surface of genus g ≥ 1 with at least one ... that for a compact Riemann surface of genus g > 1 any negative function K is attained as the Gaussian curvature of a .... since K is negative, ∂νσn|∂M = 0 and where we define g = ∂¯zK/|K|. Let M = n1 ∪ n2 ∪ n3, ...
Continuous-variable quantum key distribution with Gaussian source noise
International Nuclear Information System (INIS)
Shen Yujie; Peng Xiang; Yang Jian; Guo Hong
2011-01-01
Source noise affects the security of continuous-variable quantum key distribution (CV QKD) and is difficult to analyze. We propose a model to characterize Gaussian source noise through introducing a neutral party (Fred) who induces the noise with a general unitary transformation. Without knowing Fred's exact state, we derive the security bounds for both reverse and direct reconciliations and show that the bound for reverse reconciliation is tight.
Gaussian beam shooting algorithm based on iterative frame decomposition
Ghannoum, Ihssan; Letrou, Christine; Beauquet, Gilles
2010-01-01
International audience; Adaptive beam re-shooting is proposed as a solution to overcome essential limitations of the Gaussian Beam Shooting technique. The proposed algorithm is based on iterative frame decompositions of beam fields in situations where usual paraxial formulas fail to give accurate enough results, such as interactions with finite obstacle edges. Collimated beam fields are successively re-expanded on narrow and wide window frames, allowing for re-shooting and further propagation...
A statistical theory on the turbulent diffusion of Gaussian puffs
International Nuclear Information System (INIS)
Mikkelsen, T.; Larsen, S.E.; Pecseli, H.L.
1982-12-01
The relative diffusion of a one-dimensional Gaussian cloud of particles is related to a two-particle covariance function in a homogeneous and stationary field of turbulence. A simple working approximation is suggested for the determination of this covariance function in terms of entirely Eulerian fields. Simple expressions are derived for the growth of the puff's standard deviation for diffusion times that are small compared to the integral time scale of the turbulence. (Auth.)
Integrals for fully correlated Gaussians in relative coordinates
Harris, Frank E.; Monkhorst, Hendrik J.
This article considers the integrals needed in energy computations on Coulombic systems using many-particle basis functions that are products of Gaussians in all the relative coordinates rij. The formulas presented are applicable to systems with arbitrary numbers of particles and with wave functions containing arbitrary nonnegative powers of all the r 2ij. Recursive procedures for evaluating the integrals are also given, and graph-theoretic representations are provided for multinomials entering the formulation.
Array processors based on Gaussian fraction-free method
Energy Technology Data Exchange (ETDEWEB)
Peng, S.; Sedukhin, S. [Aizu Univ., Aizuwakamatsu, Fukushima (Japan); Sedukhin, I.
1998-03-01
The design of algorithmic array processors for solving linear systems of equations using fraction-free Gaussian elimination method is presented. The design is based on a formal approach which constructs a family of planar array processors systematically. These array processors are synthesized and analyzed. It is shown that some array processors are optimal in the framework of linear allocation of computations and in terms of number of processing elements and computing time. (author)
Applications exponential approximation by integer shifts of Gaussian functions
Directory of Open Access Journals (Sweden)
S. M. Sitnik
2013-01-01
Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
On the likelihood function of Gaussian max-stable processes
Genton, M. G.
2011-05-24
We derive a closed form expression for the likelihood function of a Gaussian max-stable process indexed by ℝd at p≤d+1 sites, d≥1. We demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p=2 to p=3 sites in ℝ2 by means of a Monte Carlo simulation study. © 2011 Biometrika Trust.
Stochastic systems with cross-correlated Gaussian white noises
International Nuclear Information System (INIS)
Wang Cheng-Yu; Song Yu-Min; Zhou Peng; Yang Hai; Gao Yun
2010-01-01
This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises. Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the cross-correlated noises are studied. The stationary solutions of the Fokker—Planck equation for three specific examples are analysed. It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions
ECE from MAST - Gaussian beams and antenna aiming problem
Czech Academy of Sciences Publication Activity Database
Preinhaelter, Josef; Urban, Jakub; Pavlo, Pavol; Shevchenko, V.; Valovic, M.; Vahala, L.; Vahala, G.
2004-01-01
Roč. 54, suppl.C (2004), C116-C122 ISSN 0011-4626. [Symposium on Plasma Physics and Technology /21./. Praha, 14.06.2004-17.06.2004] R&D Projects: GA ČR GA202/04/0360 Institutional research plan: CEZ:AV0Z2043910 Keywords : ECEemission, Gaussian beams Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.292, year: 2004
Complexity of Gaussian-Radial-Basis Networks Approximating Smooth Functions
Czech Academy of Sciences Publication Activity Database
Kainen, P.C.; Kůrková, Věra; Sanguineti, M.
2009-01-01
Roč. 25, č. 1 (2009), s. 63-74 ISSN 0885-064X R&D Projects: GA ČR GA201/08/1744 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gaussian-radial-basis-function networks * rates of approximation * model complexity * variation norms * Bessel and Sobolev norms * tractability of approximation Subject RIV: IN - Informatics, Computer Science Impact factor: 1.227, year: 2009
Some Fractional and Multifractional Gaussian Processes: A Brief Introduction
Lim, S. C.; Eab, C. H.
2014-01-01
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifrac- tional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.
Parameter estimation of sub-Gaussian stable distributions
Czech Academy of Sciences Publication Activity Database
Omelchenko, Vadym
2014-01-01
Roč. 50, č. 6 (2014), s. 929-949 ISSN 0023-5954 R&D Projects: GA ČR GA13-14445S Institutional support: RVO:67985556 Keywords : stable distribution * sub-Gaussian distribution * maximum likelihood Subject RIV: AH - Economics Impact factor: 0.541, year: 2014 http://library.utia.cas.cz/separaty/2014/E/omelchenko-0439707.pdf
Discretisation Schemes for Level Sets of Planar Gaussian Fields
Beliaev, D.; Muirhead, S.
2018-01-01
Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic compact manifolds. Our work is motivated by questions about the geometry of such random functions, in particular relating to the structure of their nodal and level sets. We study four discretisation schemes that extract information about level sets of planar Gaussian fields. Each scheme recovers information up to a different level of precision, and each requires a maximum mesh-size in order to be valid with high probability. The first two schemes are generalisations and enhancements of similar schemes that have appeared in the literature (Beffara and Gayet in Publ Math IHES, 2017. https://doi.org/10.1007/s10240-017-0093-0; Mischaikow and Wanner in Ann Appl Probab 17:980-1018, 2007); these give complete topological information about the level sets on either a local or global scale. As an application, we improve the results in Beffara and Gayet (2017) on Russo-Seymour-Welsh estimates for the nodal set of positively-correlated planar Gaussian fields. The third and fourth schemes are, to the best of our knowledge, completely new. The third scheme is specific to the nodal set of the random plane wave, and provides global topological information about the nodal set up to `visible ambiguities'. The fourth scheme gives a way to approximate the mean number of excursion domains of planar Gaussian fields.
An approximate fractional Gaussian noise model with computational cost
Sørbye, Sigrunn H.
2017-09-18
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
Multipoint propagators for non-Gaussian initial conditions
International Nuclear Information System (INIS)
Bernardeau, Francis; Sefusatti, Emiliano; Crocce, Martin
2010-01-01
We show here how renormalized perturbation theory calculations applied to the quasilinear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce, and Scoccimarro [Phys. Rev. D 78, 103521 (2008)] is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher-order spectra and is based on a reorganization of the contributing terms into the sum of products of multipoint propagators. In case of PNG, new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multipoint propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespective of statistical properties of the initial field. We furthermore show that the high-momentum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multipoint propagators for Gaussian initial conditions. Numerical forms of the cutoff are shown for the so-called local model of PNG.
Blind signal processing algorithms under DC biased Gaussian noise
Kim, Namyong; Byun, Hyung-Gi; Lim, Jeong-Ok
2013-05-01
Distortions caused by the DC-biased laser input can be modeled as DC biased Gaussian noise and removing DC bias is important in the demodulation process of the electrical signal in most optical communications. In this paper, a new performance criterion and a related algorithm for unsupervised equalization are proposed for communication systems in the environment of channel distortions and DC biased Gaussian noise. The proposed criterion utilizes the Euclidean distance between the Dirac-delta function located at zero on the error axis and a probability density function of biased constant modulus errors, where constant modulus error is defined by the difference between the system out and a constant modulus calculated from the transmitted symbol points. From the results obtained from the simulation under channel models with fading and DC bias noise abruptly added to background Gaussian noise, the proposed algorithm converges rapidly even after the interruption of DC bias proving that the proposed criterion can be effectively applied to optical communication systems corrupted by channel distortions and DC bias noise.
Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
Ade, P.A.R.; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartlett, J.G.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R.C.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, L.Y.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Delouis, J.M.; Desert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Dore, O.; Douspis, M.; Ducout, A.; Dunkley, J.; Dupac, X.; Efstathiou, G.; Elsner, F.; Ensslin, T.A.; Eriksen, H.K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Franceschi, E.; Galeotta, S.; Ganga, K.; Giard, M.; Giraud-Heraud, Y.; Gonzalez-Nuevo, J.; Gorski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Hansen, F.K.; Hanson, D.; Harrison, D.; Heavens, A.; Henrot-Versille, S.; Hernandez-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Jaffe, T.R.; Jaffe, A.H.; Jones, W.C.; Juvela, M.; Keihanen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Knox, L.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lahteenmaki, A.; Lamarre, J.M.; Lasenby, A.; Laureijs, R.J.; Lawrence, C.R.; Leahy, J.P.; Leonardi, R.; Lesgourgues, J.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vornle, M.; Lopez-Caniego, M.; Lubin, P.M.; Macias-Perez, J.F.; Maffei, B.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Marshall, D.J.; Martin, P.G.; Martinez-Gonzalez, E.; Masi, S.; Matarrese, S.; Matthai, F.; Mazzotta, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschenes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Naselsky, P.; Natoli, P.; Netterfield, C.B.; Norgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Osborne, S.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Ponthieu, N.; Popa, L.; Poutanen, T.; Pratt, G.W.; Prezeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Racine, B.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ricciardi, S.; Riller, T.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Roudier, G.; Rubino-Martin, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Smith, K.; Spencer, L.D.; Starck, J.L.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sureau, F.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Tavagnacco, D.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Varis, J.; Vielva, P.; Villa, F.; Vittorio, N.; Wade, L.A.; Wandelt, B.D.; White, M.; White, S.D.M.; Yvon, D.; Zacchei, A.; Zonca, A.
2014-01-01
The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+\\-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional...
Productive interactions: heavy particles and non-Gaussianity
International Nuclear Information System (INIS)
Flauger, Raphael; Mirbabayi, Mehrdad; Senatore, Leonardo; Silverstein, Eva
2017-01-01
We analyze the shape and amplitude of oscillatory features in the primordial power spectrum and non-Gaussianity induced by periodic production of heavy degrees of freedom coupled to the inflaton φ. We find that non-adiabatic production of particles can contribute effects which are detectable or constrainable using cosmological data even if their time-dependent masses are always heavier than the scale φ̇ 1/2 , much larger than the Hubble scale. This provides a new role for UV completion, consistent with the criteria from effective field theory for when heavy fields cannot be integrated out. This analysis is motivated in part by the structure of axion monodromy, and leads to an additional oscillatory signature in a subset of its parameter space. At the level of a quantum field theory model that we analyze in detail, the effect arises consistently with radiative stability for an interesting window of couplings up to of order ∼< 1. The amplitude of the bispectrum and higher-point functions can be larger than that for Resonant Non-Gaussianity, and its signal/noise may be comparable to that of the corresponding oscillations in the power spectrum (and even somewhat larger within a controlled regime of parameters). Its shape is distinct from previously analyzed templates, but was partly motivated by the oscillatory equilateral searches performed recently by the Planck collaboration. We also make some general comments about the challenges involved in making a systematic study of primordial non-Gaussianity.
s -wave scattering length of a Gaussian potential
Jeszenszki, Peter; Cherny, Alexander Yu.; Brand, Joachim
2018-04-01
We provide accurate expressions for the s -wave scattering length for a Gaussian potential well in one, two, and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold-atomic gases, where the s -wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the s -wave scattering length from the parameters of the Gaussian, but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the s -wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.
Generation of correlated finite alphabet waveforms using gaussian random variables
Jardak, Seifallah
2014-09-01
Correlated waveforms have a number of applications in different fields, such as radar and communication. It is very easy to generate correlated waveforms using infinite alphabets, but for some of the applications, it is very challenging to use them in practice. Moreover, to generate infinite alphabet constant envelope correlated waveforms, the available research uses iterative algorithms, which are computationally very expensive. In this work, we propose simple novel methods to generate correlated waveforms using finite alphabet constant and non-constant-envelope symbols. To generate finite alphabet waveforms, the proposed method map the Gaussian random variables onto the phase-shift-keying, pulse-amplitude, and quadrature-amplitude modulation schemes. For such mapping, the probability-density-function of Gaussian random variables is divided into M regions, where M is the number of alphabets in the corresponding modulation scheme. By exploiting the mapping function, the relationship between the cross-correlation of Gaussian and finite alphabet symbols is derived. To generate equiprobable symbols, the area of each region is kept same. If the requirement is to have each symbol with its own unique probability, the proposed scheme allows us that as well. Although, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beampatterns. © 2014 IEEE.
QUANTUM AND CLASSICAL CORRELATIONS IN GAUSSIAN OPEN QUANTUM SYSTEMS
Directory of Open Access Journals (Sweden)
Aurelian ISAR
2015-01-01
Full Text Available In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum correlations (quantum entanglement and quantum discord for a system consisting of two noninteracting bosonic modes embedded in a thermal environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement and discord in terms of the covariance matrix for Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that it decays asymptotically in time under the effect of the thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.
Scattering of Gaussian beams by disordered particulate media
International Nuclear Information System (INIS)
Mishchenko, Michael I.; Dlugach, Janna M.
2016-01-01
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. - Highlights: • Electromagnetic scattering by a disordered particulate medium is studied. • The superposition T-matrix solver of the Maxwell equations is used. • Finite width of an incident Gaussian beam does not extinguish interference speckles. • Ensemble or spectral averaging is required to generate diffuse speckle-free patterns.
Guo, Yong-Feng; Xi, Bei; Wei, Fang; Tan, Jian-Guo
2017-12-01
In this paper, the phenomenon of stochastic resonance in FitzHugh-Nagumo (FHN) neural system driven by correlated non-Gaussian noise and Gaussian white noise is investigated. First, the analytical expression of the stationary probability distribution is derived by using the path integral approach and the unified colored noise approximation. Then, we obtain the expression of signal-to-noise ratio (SNR) by applying the theory of two-state model. The results show that the phenomena of stochastic resonance and multiple stochastic resonance appear in FHN neural system under different values of parameters. The effects of the multiplicative noise intensity D and the additive noise intensity Q on the SNR are entirely different. In addition, the discharge behavior of FHN neural system is restrained when the value of Q is smaller. But, it is conducive to enhance signal response of FHN neural system when the values of Q and D are relatively larger.
Evaluation of Gaussian approximations for data assimilation in reservoir models
Iglesias, Marco A.
2013-07-14
The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our
Operator-sum representation for bosonic Gaussian channels
International Nuclear Information System (INIS)
Ivan, J. Solomon; Sabapathy, Krishna Kumar; Simon, R.
2011-01-01
Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted D(κ) in the Holevo classification. The matrix transposition channels D(κ), D(κ -1 ) turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor κ and the beam-splitter channel with attenuation factor κ -1 turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank 1 Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of
On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration
Directory of Open Access Journals (Sweden)
Fei Xu
2016-01-01
Full Text Available Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF. A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD, probability density function (PDF, and loading cycle distribution (LCD as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS and the extreme response spectrum (ERS and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.
GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.
Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi
2017-05-24
As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.
Sasaki, Misao; Wands, David
2010-06-01
In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.
A wavelet-based Gaussian method for energy dispersive X-ray fluorescence spectrum
Directory of Open Access Journals (Sweden)
Pan Liu
2017-05-01
Full Text Available This paper presents a wavelet-based Gaussian method (WGM for the peak intensity estimation of energy dispersive X-ray fluorescence (EDXRF. The relationship between the parameters of Gaussian curve and the wavelet coefficients of Gaussian peak point is firstly established based on the Mexican hat wavelet. It is found that the Gaussian parameters can be accurately calculated by any two wavelet coefficients at the peak point which has to be known. This fact leads to a local Gaussian estimation method for spectral peaks, which estimates the Gaussian parameters based on the detail wavelet coefficients of Gaussian peak point. The proposed method is tested via simulated and measured spectra from an energy X-ray spectrometer, and compared with some existing methods. The results prove that the proposed method can directly estimate the peak intensity of EDXRF free from the background information, and also effectively distinguish overlap peaks in EDXRF spectrum.
Characterisation of non-Gaussian fluctuations in multiplicative log-normal models
Kiyono, Ken; Struzik, Zbigniew R.; Yamamoto, Yoshiharu
2007-07-01
Within the general framework of multiplicative log-normal models, we propose methods to characterise non-Gaussian and intermittent fluctuations, and study basic characteristics of non-Gaussian stochastic processes displaying slow convergence to a Gaussian with an increasing coarse-grained level of the time series. Here the multiplicative log-normal model stands for a stochastic process described by the multiplication of Gaussian and log-normally distributed variables. In other words, using two Gaussian variables, ξ and ω, the time series {xi} of this process can be described as xi = ξi expωi. Depending on the variance of ω, λ2, the probability density function (PDF) of x exhibits a non-Gaussian shape. As the non-Gaussianity parameter λ2 increases, the non-Gaussian tails become fatter. On the other hand, when λ2 → 0, the PDF converges to a Gaussian distribution. For the purpose of estimating the non-Gaussianity parameter λ2 from the observed time series, we evaluate a novel method based on analytical expressions of the absolute moments for the multiplicative log-normal models.
Gaussian random bridges and a geometric model for information equilibrium
Mengütürk, Levent Ali
2018-03-01
The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.
Analytic Treatment of Deep Neural Networks Under Additive Gaussian Noise
Alfadly, Modar M.
2018-04-12
Despite the impressive performance of deep neural networks (DNNs) on numerous vision tasks, they still exhibit yet-to-understand uncouth behaviours. One puzzling behaviour is the reaction of DNNs to various noise attacks, where it has been shown that there exist small adversarial noise that can result in a severe degradation in the performance of DNNs. To rigorously treat this, we derive exact analytic expressions for the first and second moments (mean and variance) of a small piecewise linear (PL) network with a single rectified linear unit (ReLU) layer subject to general Gaussian input. We experimentally show that these expressions are tight under simple linearizations of deeper PL-DNNs, especially popular architectures in the literature (e.g. LeNet and AlexNet). Extensive experiments on image classification show that these expressions can be used to study the behaviour of the output mean of the logits for each class, the inter-class confusion and the pixel-level spatial noise sensitivity of the network. Moreover, we show how these expressions can be used to systematically construct targeted and non-targeted adversarial attacks. Then, we proposed a special estimator DNN, named mixture of linearizations (MoL), and derived the analytic expressions for its output mean and variance, as well. We employed these expressions to train the model to be particularly robust against Gaussian attacks without the need for data augmentation. Upon training this network on a loss that is consolidated with the derived output probabilistic moments, the network is not only robust under very high variance Gaussian attacks but is also as robust as networks that are trained with 20 fold data augmentation.
On the Response of a Nonlinear Structure to High Kurtosis Non-Gaussian Random Loadings
Rizzi, Stephen A.; Przekop, Adam; Turner, Travis L.
2011-01-01
This paper is a follow-on to recent work by the authors in which the response and high-cycle fatigue of a nonlinear structure subject to non-Gaussian loadings was found to vary markedly depending on the nature of the loading. There it was found that a non-Gaussian loading having a steady rate of short-duration, high-excursion peaks produced essentially the same response as would have been incurred by a Gaussian loading. In contrast, a non-Gaussian loading having the same kurtosis, but with bursts of high-excursion peaks was found to elicit a much greater response. This work is meant to answer the question of when consideration of a loading probability distribution other than Gaussian is important. The approach entailed nonlinear numerical simulation of a beam structure under Gaussian and non-Gaussian random excitations. Whether the structure responded in a Gaussian or non-Gaussian manner was determined by adherence to, or violations of, the Central Limit Theorem. Over a practical range of damping, it was found that the linear response to a non-Gaussian loading was Gaussian when the period of the system impulse response is much greater than the rate of peaks in the loading. Lower damping reduced the kurtosis, but only when the linear response was non-Gaussian. In the nonlinear regime, the response was found to be non-Gaussian for all loadings. The effect of a spring-hardening type of nonlinearity was found to limit extreme values and thereby lower the kurtosis relative to the linear response regime. In this case, lower damping gave rise to greater nonlinearity, resulting in lower kurtosis than a higher level of damping.
Fault Tolerant Control Using Gaussian Processes and Model Predictive Control
Directory of Open Access Journals (Sweden)
Yang Xiaoke
2015-03-01
Full Text Available Essential ingredients for fault-tolerant control are the ability to represent system behaviour following the occurrence of a fault, and the ability to exploit this representation for deciding control actions. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. We therefore propose to use the two together to obtain fault-tolerant control functionality. Our proposal is illustrated by several reasonably realistic examples drawn from flight control.
Gaussian free turbulence: structures and relaxation in plasma models
International Nuclear Information System (INIS)
Gruzinov, A.V.
1993-01-01
Free-turbulent relaxation in two-dimensional MHD, the degenerate Hasegawa-Mima equation and a two-dimensional microtearing model are studied. The Gibbs distributions of these three systems can be completely analyzed, due to the special structure of their invariants and due to the existence of ultraviolet catastrophe. The free-turbulent field is seen to be a sum of a certain coherent structure (statistical attractor) and Gaussian random noise. Two-dimensional current layers are shown to be statistical attractors in 2D MHD. (author)
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
orders, corrections of increasing polynomial complexity can be applied to the approximation. The second order provides a correction in quadratic time, which we apply to an array of Gaussian process and Ising models. The corrections generalize to arbitrarily complex approximating families, which we...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Fluctuation relations with intermittent non-Gaussian variables.
Budini, Adrián A
2011-12-01
Nonequilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FRs). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a thermodynamiclike change of measure. Taking one of them as a modulated Poisson process, it is demonstrated that intermittence and FRs are compatible properties that may coexist naturally. Strong non-Gaussian features characterize the probability distribution and its generating function. Their associated large deviation functions develop a "kink" at the origin and a plateau regime respectively. Application of this model in different stationary nonequilibrium situations is discussed.
Design of a secondary lens using gaussian function
Anh, Nguyen Doan Quoc; Long, Nguyen Ngoc; Van Phuoc, Nguyen; Voznak, Miroslav; Zdralek, Jaroslav
2018-04-01
In the article, it is recognized that the high-intensity discharge (HID) fishing lamp becomes obsolete, so we designed a free secondary lens for an LED fishing/working lamp (LFWL) to serve the lighting needs of fishing and the on-board activities on fishing boats through gaussian decomposition for taking the place it. The results proved that it is really useful to the board, sea-surface, and underwater. Moreover, the lighting efficiency of 91 % with the power consumption reducing more than 3 times could be achieved when the proposed LED fishing/working lamps are used instead of the HID fishing lamps.
Gaussian beam diffraction in weakly anisotropic inhomogeneous media
Energy Technology Data Exchange (ETDEWEB)
Kravtsov, Yu.A., E-mail: kravtsov@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland); Space Research Institute, Russian Academy of Science, Moscow 117 997 (Russian Federation); Berczynski, P., E-mail: pawel.berczynski@ps.p [Institute of Physics, West Pomeranian University of Technology, Szczecin 70-310 (Poland); Bieg, B., E-mail: b.bieg@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland)
2009-08-10
Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.
Solving Dynamic Traveling Salesman Problem Using Dynamic Gaussian Process Regression
Directory of Open Access Journals (Sweden)
Stephen M. Akandwanaho
2014-01-01
Full Text Available This paper solves the dynamic traveling salesman problem (DTSP using dynamic Gaussian Process Regression (DGPR method. The problem of varying correlation tour is alleviated by the nonstationary covariance function interleaved with DGPR to generate a predictive distribution for DTSP tour. This approach is conjoined with Nearest Neighbor (NN method and the iterated local search to track dynamic optima. Experimental results were obtained on DTSP instances. The comparisons were performed with Genetic Algorithm and Simulated Annealing. The proposed approach demonstrates superiority in finding good traveling salesman problem (TSP tour and less computational time in nonstationary conditions.
Detection of local non-Gaussianity with future observations
International Nuclear Information System (INIS)
Li Hong; Liu Jie
2012-01-01
In this Letter we estimate the primordial non-Gaussianity (PNG) by simulating future observations. We use the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) as an example and focus on the cross correlation signal between the galaxies and the Integrate Sachs-Wolfe (ISW) effect of CMB. Our result is optimistical. It shows the potential of LAMOST, particularly its quasar survey, in probing for the PNG by ISW - galaxy cross correlation. This study is particularly relevant because LAMOST is almost parallel to the timetable of the upcoming high precision Planck satellite.
Case studies in Gaussian process modelling of computer codes
International Nuclear Information System (INIS)
Kennedy, Marc C.; Anderson, Clive W.; Conti, Stefano; O'Hagan, Anthony
2006-01-01
In this paper we present a number of recent applications in which an emulator of a computer code is created using a Gaussian process model. Tools are then applied to the emulator to perform sensitivity analysis and uncertainty analysis. Sensitivity analysis is used both as an aid to model improvement and as a guide to how much the output uncertainty might be reduced by learning about specific inputs. Uncertainty analysis allows us to reflect output uncertainty due to unknown input parameters, when the finished code is used for prediction. The computer codes themselves are currently being developed within the UK Centre for Terrestrial Carbon Dynamics
Divisor problem in special sets of Gaussian integers
Directory of Open Access Journals (Sweden)
O. V. Savastru
2016-12-01
Full Text Available Let $A_{1}$ and $A_{2}$ be fixed sets of gaussian integers. We denote by $\\tau_{A_{1}, A_{2}}(\\omega$ the number of representations of $\\omega$ in form $\\omega=\\alpha\\beta$, where $\\alpha \\in A_{1}, \\beta \\in A_{2}$. We construct the asymptotical formula for summatory function $\\tau_{A_{1}, A_{2}}(\\omega$ in case, when $\\omega$ lie in the arithmetic progression, $A_{1}$ is a fixed sector of complex plane, $A_{2}=\\mathbb{Z}[i]$.
Quantum entanglement with a hermite-gaussian pump; poster
CSIR Research Space (South Africa)
McLaren, M
2013-07-01
Full Text Available quantum states. Figure 3 shows our experimental setup. A mode-locked UV laser at 355 nm was used to pump a 3 mm, type-I barium borate (BBO) crystal to produce pairs of collinear, degenerate entangled photons. A cover slip, placed on a tip-tilt mount... following the selection rule in Eq. (1), we expect high coincidences when the sum of and is 1, as shown in Fig. 4(a). We expect two diagonals symmetric about the main diagonal, in contrast to SPDC with a fundamental Gaussian pump (see Fig. 4(c...
Quasi-single field inflation and non-Gaussianities
International Nuclear Information System (INIS)
Chen, Xingang; Wang, Yi
2010-01-01
In quasi-single field inflation models, massive isocurvature modes, that are coupled to the inflaton and have mass of order the Hubble parameter, can have nontrivial impacts on density perturbations, especially non-Gaussianities. We study a simple example of quasi-single field inflation in terms of turning inflaton trajectory. Large bispectra with a one-parameter family of novel shapes arise, lying between the well-known local and equilateral shape. The trispectra can also be very large and its magnitude t NL can be much larger than f NL 2
Theory of non-Gaussianity in warm inflation
Energy Technology Data Exchange (ETDEWEB)
Bastero-Gil, Mar [Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada-18071 (Spain); Berera, Arjun [SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3JZ (United Kingdom); Moss, Ian G. [School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU (United Kingdom); Ramos, Rudnei O., E-mail: mbg@ugr.es, E-mail: ab@ph.ed.ac.uk, E-mail: ian.moss@ncl.ac.uk, E-mail: rudnei@uerj.br [Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, 20550-013 Rio de Janeiro, RJ (Brazil)
2014-12-01
The theory and methodology is developed to compute the bispectrum in warm inflation, leading to results for the non-linearity parameter and the shape of the bispectrum. Particular attention is paid to the study of the bispectrum in the regime of weak dissipation and how stochastic fluctuations affect the bispectrum. It is shown that, in contrast to the strong dissipative regime, the amplitude of non-Gaussianity is strongly dependent on the parameters governing the microscopic physics in the intermediate and weak dissipation warm inflation regimes. The most important results concern the shape of the bispectrum, which has two different, but distinct, forms in the weak and strong dissipative regimes.
Graphical Gaussian models with edge and vertex symmetries
DEFF Research Database (Denmark)
Højsgaard, Søren; Lauritzen, Steffen L
2008-01-01
We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where parameters that are associated with edges or vertices of the same colour are restricted to being identical. We...... study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation...
Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables
Barnett, Lionel; Barrett, Adam B.; Seth, Anil K.
2009-12-01
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.
Gaussian Filtering with Tapered Oil-Filled Photonic Bandgap Fibers
DEFF Research Database (Denmark)
Brunetti, Anna Chiara; Scolari, Lara; Weirich, Johannes
2008-01-01
A tunable Gaussian filter based on a tapered oil-filled photonic crystal fiber is demonstrated. The filter is centered at X=1364nm with a bandwidth (FWHM) of 237nm. Tunability is achieved by changing the temperature of the filter. A shift of 210nm of the central wavelength has been observed by in...... by increasing the temperature from 25°C to 100°C. The measurements are compared to a simulated spectrum obtained by means of a vectorial Beam Propagation Method model....
Response of MDOF strongly nonlinear systems to fractional Gaussian noises
Energy Technology Data Exchange (ETDEWEB)
Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)
2016-08-15
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.
Terrain Mapping and Obstacle Detection Using Gaussian Processes
DEFF Research Database (Denmark)
Kjærgaard, Morten; Massaro, Alessandro Salvatore; Bayramoglu, Enis
2011-01-01
In this paper we consider a probabilistic method for extracting terrain maps from a scene and use the information to detect potential navigation obstacles within it. The method uses Gaussian process regression (GPR) to predict an estimate function and its relative uncertainty. To test the new...... methods, we have arranged two setups: an artificial flat surface with an object in front of the sensors and an outdoor unstructured terrain. Two sensor types have been used to determine the point cloud fed to the system: a 3D laser scanner and a stereo camera pair. The results from both sensor systems...
Performance of monitoring networks estimated from a Gaussian plume model
International Nuclear Information System (INIS)
Seebregts, A.J.; Hienen, J.F.A.
1990-10-01
In support of the ECN study on monitoring strategies after nuclear accidents, the present report describes the analysis of the performance of a monitoring network in a square grid. This network is used to estimate the distribution of the deposition pattern after a release of radioactivity into the atmosphere. The analysis is based upon a single release, a constant wind direction and an atmospheric dispersion according to a simplified Gaussian plume model. A technique is introduced to estimate the parameters in this Gaussian model based upon measurements at specific monitoring locations and linear regression, although this model is intrinsically non-linear. With these estimated parameters and the Gaussian model the distribution of the contamination due to deposition can be estimated. To investigate the relation between the network and the accuracy of the estimates for the deposition, deposition data have been generated by the Gaussian model, including a measurement error by a Monte Carlo simulation and this procedure has been repeated for several grid sizes, dispersion conditions, number of measurements per location, and errors per single measurement. The present technique has also been applied for the mesh sizes of two networks in the Netherlands, viz. the Landelijk Meetnet Radioaciviteit (National Measurement Network on Radioactivity, mesh size approx. 35 km) and the proposed Landelijk Meetnet Nucleaire Incidenten (National Measurement Network on Nuclear Incidents, mesh size approx. 15 km). The results show accuracies of 11 and 7 percent, respectively, if monitoring locations are used more than 10 km away from the postulated accident site. These figures are based upon 3 measurements per location and a dispersion during neutral weather with a wind velocity of 4 m/s. For stable weather conditions and low wind velocities, i.e. a small plume, the calculated accuracies are at least a factor 1.5 worse.The present type of analysis makes a cost-benefit approach to the
Machine learning of linear differential equations using Gaussian processes
Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
2017-11-01
This work leverages recent advances in probabilistic machine learning to discover governing equations expressed by parametric linear operators. Such equations involve, but are not limited to, ordinary and partial differential, integro-differential, and fractional order operators. Here, Gaussian process priors are modified according to the particular form of such operators and are employed to infer parameters of the linear equations from scarce and possibly noisy observations. Such observations may come from experiments or "black-box" computer simulations, as demonstrated in several synthetic examples and a realistic application in functional genomics.
Gaussian Process Regression Model in Spatial Logistic Regression
Sofro, A.; Oktaviarina, A.
2018-01-01
Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.
Information Geometric Complexity of a Trivariate Gaussian Statistical Model
Directory of Open Access Journals (Sweden)
Domenico Felice
2014-05-01
Full Text Available We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult it is to make macroscopic predictions about systems in the presence of limited information. Specifically, we observe that the complexity of such entropic inferences not only depends on the amount of available pieces of information but also on the manner in which such pieces are correlated. Finally, we uncover that, for certain correlational structures, the impossibility of reaching the most favorable configuration from an entropic inference viewpoint seems to lead to an information geometric analog of the well-known frustration effect that occurs in statistical physics.
PASS-GP: Predictive active set selection for Gaussian processes
DEFF Research Database (Denmark)
Henao, Ricardo; Winther, Ole
2010-01-01
We propose a new approximation method for Gaussian process (GP) learning for large data sets that combines inline active set selection with hyperparameter optimization. The predictive probability of the label is used for ranking the data points. We use the leave-one-out predictive probability...... to the active set selection strategy and marginal likelihood optimization on the active set. We make extensive tests on the USPS and MNIST digit classification databases with and without incorporating invariances, demonstrating that we can get state-of-the-art results (e.g.0.86% error on MNIST) with reasonable...
Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis
Directory of Open Access Journals (Sweden)
Zhanyu Ma
2014-06-01
Full Text Available As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance.
Audio analysis of statistically instantaneous signals with mixed Gaussian probability distributions
Naik, Ganesh R.; Wang, Wenwu
2012-10-01
In this article, a novel method is proposed to measure the separation qualities of statistically instantaneous audio signals with mixed Gaussian probability distributions. This study evaluates the impact of the Probability Distribution Function (PDF) of the mixed signals on the outcomes of both sub- and super-Gaussian distributions. Different Gaussian measures are evaluated by using various spectral-distortion measures. It aims to compare the different audio mixtures from both super-Gaussian and sub-Gaussian perspectives. Extensive computer simulation confirms that the separated sources always have super-Gaussian characteristics irrespective of the PDF of the signals or mixtures. The result based on the objective measures demonstrates the effectiveness of source separation in improving the quality of the separated audio sources.
Imprint of primordial non-Gaussianity on dark matter halo profiles
Energy Technology Data Exchange (ETDEWEB)
Dizgah, Azadeh Moradinezhad; Dodelson, Scott; Riotto, Antonio
2013-09-01
We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian density field. In the context of the semi-analytic model for halo profiles, currently allowed values for primordial non-Gaussianity would increase the shapes of the inner dark matter profiles, but only at the sub-percent level except in the very innermost regions.
Transport phenomena in intracellular calcium dynamics driven by non-Gaussian noises
Lin, Ling; Duan, Wei-Long
2018-02-01
The role of non-Gaussian noises on transport characteristic of Ca2+ in intracellular calcium oscillation system driven by non-Gaussian noises is studied by means of second-order stochastic Runge-Kutta type algorithm. The statistical properties of velocity of cytosolic and calcium store's Ca2+ concentration are simulated. The results exhibit, as parameter p(which is used to control the degree of the departure from the non-Gaussian noise and Gaussian noise.)increases, calcium in cytosol shows positive, zero, and negative transport, but in calcium store always hold positive value. As non-Gaussian noises increase, calcium in cytosol appears negative and zero transport, and in calcium store appears positive transport. As correlation time of non-Gaussian noises varies, calcium in both cytosol and calcium store occur negative, zero, and positive transport.
Holographic non-Gaussianities in general single-field inflation
International Nuclear Information System (INIS)
Isono, Hiroshi; Noumi, Toshifumi; Shiu, Gary; Wong, Sam S.C.; Zhou, Siyi
2016-01-01
We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as (∂ μ ϕ∂ μ ϕ) m , which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We compute the full inflationary bispectra from the deformed CFT correlators. We also discuss the squeezed limit of the bispectra from the viewpoint of operator product expansions. As is generic in the holographic description of inflation, our power spectrum is blue tilted in the UV region. We extend our bispectrum computation to the IR region by resumming the conformal perturbations to all orders. We provide a self-consistent setup which reproduces a red tilted power spectrum, as well as all possible bispectrum shapes in the slow-roll regime.
A Gaussian graphical model approach to climate networks
Energy Technology Data Exchange (ETDEWEB)
Zerenner, Tanja, E-mail: tanjaz@uni-bonn.de [Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn (Germany); Friederichs, Petra; Hense, Andreas [Meteorological Institute, University of Bonn, Auf dem Hügel 20, 53121 Bonn (Germany); Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn (Germany); Lehnertz, Klaus [Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn (Germany); Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn (Germany); Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53119 Bonn (Germany)
2014-06-15
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
A Gaussian graphical model approach to climate networks
International Nuclear Information System (INIS)
Zerenner, Tanja; Friederichs, Petra; Hense, Andreas; Lehnertz, Klaus
2014-01-01
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately
Pseudo inputs for pairwise learning with Gaussian processes
DEFF Research Database (Denmark)
Nielsen, Jens Brehm; Jensen, Bjørn Sand; Larsen, Jan
2012-01-01
We consider learning and prediction of pairwise comparisons between instances. The problem is motivated from a perceptual view point, where pairwise comparisons serve as an effective and extensively used paradigm. A state-of-the-art method for modeling pairwise data in high dimensional domains is...... to other similar approximations that have been applied in standard Gaussian process regression and classification problems such as FI(T)C and PI(T)C....... is based on a classical pairwise probit likelihood imposed with a Gaussian process prior. While extremely flexible, this non-parametric method struggles with an inconvenient O(n3) scaling in terms of the n input instances which limits the method only to smaller problems. To overcome this, we derive...... a specific sparse extension of the classical pairwise likelihood using the pseudo-input formulation. The behavior of the proposed extension is demonstrated on a toy example and on two real-world data sets which outlines the potential gain and pitfalls of the approach. Finally, we discuss the relation...
A Gaussian Approximation Approach for Value of Information Analysis.
Jalal, Hawre; Alarid-Escudero, Fernando
2018-02-01
Most decisions are associated with uncertainty. Value of information (VOI) analysis quantifies the opportunity loss associated with choosing a suboptimal intervention based on current imperfect information. VOI can inform the value of collecting additional information, resource allocation, research prioritization, and future research designs. However, in practice, VOI remains underused due to many conceptual and computational challenges associated with its application. Expected value of sample information (EVSI) is rooted in Bayesian statistical decision theory and measures the value of information from a finite sample. The past few years have witnessed a dramatic growth in computationally efficient methods to calculate EVSI, including metamodeling. However, little research has been done to simplify the experimental data collection step inherent to all EVSI computations, especially for correlated model parameters. This article proposes a general Gaussian approximation (GA) of the traditional Bayesian updating approach based on the original work by Raiffa and Schlaifer to compute EVSI. The proposed approach uses a single probabilistic sensitivity analysis (PSA) data set and involves 2 steps: 1) a linear metamodel step to compute the EVSI on the preposterior distributions and 2) a GA step to compute the preposterior distribution of the parameters of interest. The proposed approach is efficient and can be applied for a wide range of data collection designs involving multiple non-Gaussian parameters and unbalanced study designs. Our approach is particularly useful when the parameters of an economic evaluation are correlated or interact.
Multi-fidelity Gaussian process regression for computer experiments
International Nuclear Information System (INIS)
Le-Gratiet, Loic
2013-01-01
This work is on Gaussian-process based approximation of a code which can be run at different levels of accuracy. The goal is to improve the predictions of a surrogate model of a complex computer code using fast approximations of it. A new formulation of a co-kriging based method has been proposed. In particular this formulation allows for fast implementation and for closed-form expressions for the predictive mean and variance for universal co-kriging in the multi-fidelity framework, which is a breakthrough as it really allows for the practical application of such a method in real cases. Furthermore, fast cross validation, sequential experimental design and sensitivity analysis methods have been extended to the multi-fidelity co-kriging framework. This thesis also deals with a conjecture about the dependence of the learning curve (i.e. the decay rate of the mean square error) with respect to the smoothness of the underlying function. A proof in a fairly general situation (which includes the classical models of Gaussian-process based meta-models with stationary covariance functions) has been obtained while the previous proofs hold only for degenerate kernels (i.e. when the process is in fact finite- dimensional). This result allows for addressing rigorously practical questions such as the optimal allocation of the budget between different levels of codes in the multi-fidelity framework. (author) [fr
Recovering Galaxy Properties Using Gaussian Process SED Fitting
Iyer, Kartheik; Awan, Humna
2018-01-01
Information about physical quantities like the stellar mass, star formation rates, and ages for distant galaxies is contained in their spectral energy distributions (SEDs), obtained through photometric surveys like SDSS, CANDELS, LSST etc. However, noise in the photometric observations often is a problem, and using naive machine learning methods to estimate physical quantities can result in overfitting the noise, or converging on solutions that lie outside the physical regime of parameter space.We use Gaussian Process regression trained on a sample of SEDs corresponding to galaxies from a Semi-Analytic model (Somerville+15a) to estimate their stellar masses, and compare its performance to a variety of different methods, including simple linear regression, Random Forests, and k-Nearest Neighbours. We find that the Gaussian Process method is robust to noise and predicts not only stellar masses but also their uncertainties. The method is also robust in the cases where the distribution of the training data is not identical to the target data, which can be extremely useful when generalized to more subtle galaxy properties.
Tridiagonal realization of the antisymmetric Gaussian β-ensemble
International Nuclear Information System (INIS)
Dumitriu, Ioana; Forrester, Peter J.
2010-01-01
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 β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of (q 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 i ). The third proof maps matrices from the antisymmetric Gaussian β-ensemble to those realizing particular examples of the Laguerre β-ensemble. In addition to these proofs, we note some simple properties of the shooting eigenvector and associated Pruefer phases of the random matrices.
Inferring probabilistic stellar rotation periods using Gaussian processes
Angus, Ruth; Morton, Timothy; Aigrain, Suzanne; Foreman-Mackey, Daniel; Rajpaul, Vinesh
2018-02-01
Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic - spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalizing over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these and many more, altogether 1102 Kepler objects of interest, and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterizing star-planet interactions. The code used to implement this method is available online.
Fractional Gaussian noise: Prior specification and model comparison
Sørbye, Sigrunn Holbek
2017-07-07
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Remote Sensing Image Classification With Large-Scale Gaussian Processes
Morales-Alvarez, Pablo; Perez-Suay, Adrian; Molina, Rafael; Camps-Valls, Gustau
2018-02-01
Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification difficult. Machine learning classifiers can help at this, and many methods are currently available. A popular kernel classifier is the Gaussian process classifier (GPC), since it approaches the classification problem with a solid probabilistic treatment, thus yielding confidence intervals for the predictions as well as very competitive results to state-of-the-art neural networks and support vector machines. However, its computational cost is prohibitive for large scale applications, and constitutes the main obstacle precluding wide adoption. This paper tackles this problem by introducing two novel efficient methodologies for Gaussian Process (GP) classification. We first include the standard random Fourier features approximation into GPC, which largely decreases its computational cost and permits large scale remote sensing image classification. In addition, we propose a model which avoids randomly sampling a number of Fourier frequencies, and alternatively learns the optimal ones within a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery and infrared sounding data. Excellent empirical results support the proposal in both computational cost and accuracy.
Nudged elastic band calculations accelerated with Gaussian process regression.
Koistinen, Olli-Pekka; Dagbjartsdóttir, Freyja B; Ásgeirsson, Vilhjálmur; Vehtari, Aki; Jónsson, Hannes
2017-10-21
Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The computational effort can be large, especially when ab initio or electron density functional calculations are used to evaluate the energy and atomic forces. Here, we show how the number of such evaluations can be reduced by an order of magnitude using a Gaussian process regression approach where an approximate energy surface is generated and refined in each iteration. When the goal is to evaluate the transition rate within harmonic transition state theory, the evaluation of the Hessian matrix at the initial and final state minima can be carried out beforehand and used as input in the minimum energy path calculation, thereby improving stability and reducing the number of iterations needed for convergence. A Gaussian process model also provides an uncertainty estimate for the approximate energy surface, and this can be used to focus the calculations on the lesser-known part of the path, thereby reducing the number of needed energy and force evaluations to a half in the present calculations. The methodology is illustrated using the two-dimensional Müller-Brown potential surface and performance assessed on an established benchmark involving 13 rearrangement transitions of a heptamer island on a solid surface.
Gaussian theory for spatially distributed self-propelled particles
Seyed-Allaei, Hamid; Schimansky-Geier, Lutz; Ejtehadi, Mohammad Reza
2016-12-01
Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.
On full duplex Gaussian relay channels with self-interference
Behboodi, Arash
2016-08-15
Self interference (SI) in full duplex (FD) systems is the interference caused by the transmission stream on the reception stream. Being one of the main restrictive factors for performance of practical full duplex systems, however, not too much is known about its effect on the fundamental limits of relaying systems. In this work, we consider the full duplex three-node relay channel with SI where SI is modeled as an additive Gaussian noise whose variance is dependent on instantaneous input power. The classical achievable rates and upper bounds for the single three-node relay channel no longer apply due to the structure of SI. Achievable rates for Decode-and-Forward (DF) and Compress-and-Forward (CF) and upper bounds on the capacity are derived assuming Gaussian inputs and SI. The deterministic model is also introduced and its capacity is characterized. The optimal joint source-relay distributions is discussed. Numerical results are provided comparing the achievable rates and upper bound. © 2016 IEEE.
Holographic non-Gaussianities in general single-field inflation
Energy Technology Data Exchange (ETDEWEB)
Isono, Hiroshi [Department of Physics, Faculty of Science,Chulalongkorn University, Bangkok 10330 (Thailand); Noumi, Toshifumi [Department of Physics and Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology (Hong Kong); Department of Physics,Kobe University, Kobe 657-8501 (Japan); Shiu, Gary [Department of Physics and Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology (Hong Kong); Department of Physics, University of Wisconsin-Madison,Madison, WI 53706 (United States); Wong, Sam S.C.; Zhou, Siyi [Department of Physics and Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology (Hong Kong)
2016-12-07
We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as (∂{sub μ}ϕ∂{sup μ}ϕ){sup m}, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We compute the full inflationary bispectra from the deformed CFT correlators. We also discuss the squeezed limit of the bispectra from the viewpoint of operator product expansions. As is generic in the holographic description of inflation, our power spectrum is blue tilted in the UV region. We extend our bispectrum computation to the IR region by resumming the conformal perturbations to all orders. We provide a self-consistent setup which reproduces a red tilted power spectrum, as well as all possible bispectrum shapes in the slow-roll regime.
Noise Estimation and Quality Assessment of Gaussian Noise Corrupted Images
Kamble, V. M.; Bhurchandi, K.
2018-03-01
Evaluating the exact quantity of noise present in an image and quality of an image in the absence of reference image is a challenging task. We propose a near perfect noise estimation method and a no reference image quality assessment method for images corrupted by Gaussian noise. The proposed methods obtain initial estimate of noise standard deviation present in an image using the median of wavelet transform coefficients and then obtains a near to exact estimate using curve fitting. The proposed noise estimation method provides the estimate of noise within average error of +/-4%. For quality assessment, this noise estimate is mapped to fit the Differential Mean Opinion Score (DMOS) using a nonlinear function. The proposed methods require minimum training and yields the noise estimate and image quality score. Images from Laboratory for image and Video Processing (LIVE) database and Computational Perception and Image Quality (CSIQ) database are used for validation of the proposed quality assessment method. Experimental results show that the performance of proposed quality assessment method is at par with the existing no reference image quality assessment metric for Gaussian noise corrupted images.
Fast uncertainty reduction strategies relying on Gaussian process models
International Nuclear Information System (INIS)
Chevalier, Clement
2013-01-01
This work deals with sequential and batch-sequential evaluation strategies of real-valued functions under limited evaluation budget, using Gaussian process models. Optimal Stepwise Uncertainty Reduction (SUR) strategies are investigated for two different problems, motivated by real test cases in nuclear safety. First we consider the problem of identifying the excursion set above a given threshold T of a real-valued function f. Then we study the question of finding the set of 'safe controlled configurations', i.e. the set of controlled inputs where the function remains below T, whatever the value of some others non-controlled inputs. New SUR strategies are presented, together with efficient procedures and formulas to compute and use them in real world applications. The use of fast formulas to recalculate quickly the posterior mean or covariance function of a Gaussian process (referred to as the 'kriging update formulas') does not only provide substantial computational savings. It is also one of the key tools to derive closed form formulas enabling a practical use of computationally-intensive sampling strategies. A contribution in batch-sequential optimization (with the multi-points Expected Improvement) is also presented. (author)
International Nuclear Information System (INIS)
Hu Li; Cai Yangjian
2006-01-01
Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a misaligned paraxial ABCD optical system in the cylindrical coordinate system, analytical formula for a circular flattened Gaussian beam propagating through such optical system is derived. Furthermore, an approximate analytical formula is derived for a circular flattened Gaussian beam propagating through an apertured misaligned ABCD optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Numerical examples are given
Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
Energy Technology Data Exchange (ETDEWEB)
Novaes, C.P.; Wuensche, C.A. [Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais, Av. dos Astronautas 1758, São José dos Campos 12227-010, SP (Brazil); Bernui, A. [Observatório Nacional, Rua General José Cristino 77, São Cristóvão, 20921-400, Rio de Janeiro, RJ (Brazil); Ferreira, I.S., E-mail: camilapnovaes@gmail.com, E-mail: bernui@on.br, E-mail: ivan@fis.unb.br, E-mail: ca.wuensche@inpe.br [Instituto de Física, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte, 70919-970, Brasília, DF (Brazil)
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
Gaussian random-matrix process and universal parametric correlations in complex systems
International Nuclear Information System (INIS)
Attias, H.; Alhassid, Y.
1995-01-01
We introduce the framework of the Gaussian random-matrix process as an extension of Dyson's Gaussian ensembles and use it to discuss the statistical properties of complex quantum systems that depend on an external parameter. We classify the Gaussian processes according to the short-distance diffusive behavior of their energy levels and demonstrate that all parametric correlation functions become universal upon the appropriate scaling of the parameter. The class of differentiable Gaussian processes is identified as the relevant one for most physical systems. We reproduce the known spectral correlators and compute eigenfunction correlators in their universal form. Numerical evidence from both a chaotic model and weakly disordered model confirms our predictions
A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam
F, Khannous; A, A. A. Ebrahim; A, Belafhal
2016-04-01
Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.
Thermally activated switching in the presence of non-Gaussian noise
Billings, Lora; Dykman, Mark I.; Schwartz, Ira B.
2008-11-01
We study the effect of a non-Gaussian noise on interstate switching activated primarily by Gaussian noise. Even weak non-Gaussian noise can strongly change the switching rate. The effect is determined by all moments of the noise distribution. It is expressed in a closed form in terms of the noise characteristic functional. The analytical results are compared with the results of simulations for an overdamped system driven by white Gaussian noise and a Poisson noise. Switching induced by a purely Poisson noise is also discussed.
International Nuclear Information System (INIS)
Overcamp, T.J.; Fjeld, R.A.
1987-01-01
A simple approximation for estimating the centerline gamma absorbed dose rates due to a continuous Gaussian plume was developed. To simplify the integration of the dose integral, this approach makes use of the Gaussian cloud concentration distribution. The solution is expressed in terms of the I1 and I2 integrals which were developed for estimating long-term dose due to a sector-averaged Gaussian plume. Estimates of tissue absorbed dose rates for the new approach and for the uniform cloud model were compared to numerical integration of the dose integral over a Gaussian plume distribution
SCALABLE TIME SERIES CHANGE DETECTION FOR BIOMASS MONITORING USING GAUSSIAN PROCESS
National Aeronautics and Space Administration — SCALABLE TIME SERIES CHANGE DETECTION FOR BIOMASS MONITORING USING GAUSSIAN PROCESS VARUN CHANDOLA AND RANGA RAJU VATSAVAI Abstract. Biomass monitoring,...
Alan Turing and the origins of modern Gaussian elimination
Directory of Open Access Journals (Sweden)
Dopico, Froilán M.
2013-12-01
Full Text Available The solution of a system of linear equations is by far the most important problem in Applied Mathematics. It is important both in itself and because it is an intermediate step in many other important problems. Gaussian elimination is nowadays the standard method for solving this problem numerically on a computer and it was the first numerical algorithm to be subjected to rounding error analysis. In 1948, Alan Turing published a remarkable paper on this topic: “Rounding-off errors in matrix processes” (Quart. J. Mech. Appl. Math. 1, pp. 287-308. In this paper, Turing formulated Gaussian elimination as the matrix LU factorization and introduced the “condition number of a matrix”, both of them fundamental notions of modern Numerical Analysis. In addition, Turing presented an error analysis of Gaussian elimination for general matrices that deeply influenced the spirit of the definitive analysis developed by James Wilkinson in 1961. Alan Turing’s work on Gaussian elimination appears in a fascinating period for modern Numerical Analysis. Other giants of Mathematics, as John von Neumann, Herman Goldstine, and Harold Hotelling were also working in the mid-1940s on Gaussian elimination. The goal of these researchers was to find an efficient and reliable method for solving systems of linear equations in modern “automatic computers”. At that time, it was not clear at all whether Gaussian elimination was a right choice or not. The purpose of this paper is to revise, at an introductory level, the contributions of Alan Turing and other authors to the error analysis of Gaussian elimination, the historical context of these contributions, and their influence on modern Numerical Analysis.La resolución de sistemas de ecuaciones lineales es sin duda el problema más importante en Matemática Aplicada. Es importante en sí mismo y también porque es un paso intermedio en la resolución de muchos otros problemas de gran relevancia. La eliminaci
Efficient speaker verification using Gaussian mixture model component clustering.
Energy Technology Data Exchange (ETDEWEB)
De Leon, Phillip L. (New Mexico State University, Las Cruces, NM); McClanahan, Richard D.
2012-04-01
In speaker verification (SV) systems that employ a support vector machine (SVM) classifier to make decisions on a supervector derived from Gaussian mixture model (GMM) component mean vectors, a significant portion of the computational load is involved in the calculation of the a posteriori probability of the feature vectors of the speaker under test with respect to the individual component densities of the universal background model (UBM). Further, the calculation of the sufficient statistics for the weight, mean, and covariance parameters derived from these same feature vectors also contribute a substantial amount of processing load to the SV system. In this paper, we propose a method that utilizes clusters of GMM-UBM mixture component densities in order to reduce the computational load required. In the adaptation step we score the feature vectors against the clusters and calculate the a posteriori probabilities and update the statistics exclusively for mixture components belonging to appropriate clusters. Each cluster is a grouping of multivariate normal distributions and is modeled by a single multivariate distribution. As such, the set of multivariate normal distributions representing the different clusters also form a GMM. This GMM is referred to as a hash GMM which can be considered to a lower resolution representation of the GMM-UBM. The mapping that associates the components of the hash GMM with components of the original GMM-UBM is referred to as a shortlist. This research investigates various methods of clustering the components of the GMM-UBM and forming hash GMMs. Of five different methods that are presented one method, Gaussian mixture reduction as proposed by Runnall's, easily outperformed the other methods. This method of Gaussian reduction iteratively reduces the size of a GMM by successively merging pairs of component densities. Pairs are selected for merger by using a Kullback-Leibler based metric. Using Runnal's method of reduction, we
Modelling and control of dynamic systems using gaussian process models
Kocijan, Juš
2016-01-01
This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior know...
Elasto-plastic frame under horizontal and vertical Gaussian excitation
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob; Randrup-Thomsen, S.
1999-01-01
Taking geometric non-linearity into account anoscillator of the form as aportal frame with a rigid traverse and with ideal-elastic ideal-plasticclamped-in columns behaves under horizontalexcitation as an ideal-elastic hardening / softening-plastic oscilator given that the columns carry atension....../compression axial force. Assuming that the horizontal excitationof the traverse is Gaussian white noise, statistics related to the plastic displacement response are determinedby use of simulation based on the Slepian modelprocess method combined with envelope excursion properties. Besidesgiving physical insight...... the method givesgood approximations to results obtained by slow direct simulation of thetotal response. Moreover, the influence of a randomly varying axial column force isinvestigated by direct response simulation. This case corresponds to parametric excitation as generated by the vertical acceleration...
Modification of Gaussian Elimination to the Complex Seismic Data
International Nuclear Information System (INIS)
Smaglichenko, Tatyana A.
2011-01-01
A method for solution of large and sparse systems with complex seismic observations has been developed by revising of the classical Gaussian elimination. The observation matrix is divided into a set of smaller cells that can be determined based on clusters of a seismic activity. Reliable inversion solutions with minimum error rating are selected within each cell, then solutions that are non-stable with respect to the same unknown are rejected After the final sifting the found unknowns are eliminated from the initial system with subsequent decreasing of its size. A numerical example is provided to demonstrate how the method can be applied to a real data set (a case study of the Nagano fault area, Central Japan). Results of processing of a huge volume of data and their importance for the Earthquake Early Warning (EEW) system are briefly discussed.
Primordial perturbations and non-Gaussianities from modulated trapping
International Nuclear Information System (INIS)
Langlois, David; Sorbo, Lorenzo
2009-01-01
We propose a new mechanism to generate primordial curvature perturbations, based on the resonant production of particles during inflation. It is known that this phenomenon can trap the inflaton for a fraction of e-fold. This effect is governed by the mass of the produced particles and by their coupling to the inflaton, parameters which can depend on the expectation value of other fields. If one of such additional fields—a modulaton—is light, then its fluctuations, acquired during the earlier stages of inflation, will induce a spatial modulation of the trapping, and thus of the end of inflation, corresponding to a curvature perturbation. We calculate the power spectrum, bispectrum and trispectrum of the curvature perturbations generated by this mechanism, taking into account the perturbations due to the inflaton fluctuations as well. We find that modulated trapping could provide the main contribution to the observed power spectrum and lead to detectable primordial non-gaussianities
Absorbed dose from traversing spherically symmetric, Gaussian radioactive clouds
International Nuclear Information System (INIS)
Thompson, J.M.; Poston, J.W.
1999-01-01
If a large radioactive cloud is produced, sampling may require that an airplane traverse the cloud. A method to predict the absorbed dose to the aircrew from penetrating the radioactive cloud is needed. Dose rates throughout spherically symmetric Gaussian clouds of various sizes, and the absorbed doses from traversing the clouds, were calculated. Cloud size is a dominant parameter causing dose to vary by orders of magnitude for a given dose rate measured at some distance. A method to determine cloud size, based on dose rate readings at two or more distances from the cloud center, was developed. This method, however, failed to resolve the smallest cloud sizes from measurements made at 1,000 m to 2,000 m from the cloud center
Gaussian Mixture Model and Rjmcmc Based RS Image Segmentation
Shi, X.; Zhao, Q. H.
2017-09-01
For the image segmentation method based on Gaussian Mixture Model (GMM), there are some problems: 1) The number of component was usually a fixed number, i.e., fixed class and 2) GMM is sensitive to image noise. This paper proposed a RS image segmentation method that combining GMM with reversible jump Markov Chain Monte Carlo (RJMCMC). In proposed algorithm, GMM was designed to model the distribution of pixel intensity in RS image. Assume that the number of component was a random variable. Respectively build the prior distribution of each parameter. In order to improve noise resistance, used Gibbs function to model the prior distribution of GMM weight coefficient. According to Bayes' theorem, build posterior distribution. RJMCMC was used to simulate the posterior distribution and estimate its parameters. Finally, an optimal segmentation is obtained on RS image. Experimental results show that the proposed algorithm can converge to the optimal number of class and get an ideal segmentation results.
Spatial pattern formation induced by Gaussian white noise.
Scarsoglio, Stefania; Laio, Francesco; D'Odorico, Paolo; Ridolfi, Luca
2011-02-01
The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable environmental disturbances, and (iii) a linear spatial coupling component, which provides spatial coherence and takes into account diffusion mechanisms. We investigate these dynamics using analytical tools, such as mean-field theory, linear stability analysis and structure function analysis, and use numerical simulations to confirm these analytical results. Copyright © 2010 Elsevier Inc. All rights reserved.
The Gaussian radial basis function method for plasma kinetic theory
Energy Technology Data Exchange (ETDEWEB)
Hirvijoki, E., E-mail: eero.hirvijoki@chalmers.se [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden); Candy, J.; Belli, E. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Embréus, O. [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden)
2015-10-30
Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas. - Highlights: • A radically new method to address the velocity space discretization of the non-linear kinetic equation of plasmas. • Elegant and physically intuitive, flexible and mesh-free. • Demonstration of numerical solution of both 2-D and 3-D non-linear Fokker–Planck relaxation problem.
Wormholes from cosmological reconstruction based on Gaussian processes
Wang, Deng; Meng, Xin-He
2017-06-01
We study the model-independent traversable wormholes from cosmological reconstruction based on Gaussian processes (GP). Using a combination of Union 2.1 SNe Ia data, the latest observational Hubble parameter data and recent Planck's shift parameter, we find that our GP method can give a tighter constraint on the normalized comoving distance, its derivatives and the dark energy equation of state than the previous work (Seikel et al., 2012). Subsequently, two specific traversable wormhole solutions are obtained, i.e., the cases of a constant redshift function and a linear shape function. We find that, with decreasing cosmic acceleration, the traversal velocity v of the former case increases and the amounts of exotic matter IV of the latter case decreases.
Lifting primordial non-Gaussianity above the noise
International Nuclear Information System (INIS)
Welling, Yvette; Woude, Drian van der; Pajer, Enrico
2016-01-01
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 random signals in dependent Gaussian noise
Gualtierotti, Antonio F
2015-01-01
The book presents the necessary mathematical basis to obtain and rigorously use likelihoods for detection problems with Gaussian noise. To facilitate comprehension the text is divided into three broad areas – reproducing kernel Hilbert spaces, Cramér-Hida representations and stochastic calculus – for which a somewhat different approach was used than in their usual stand-alone context. One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis. The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text...
Non-Gaussianity and the Cosmic Microwave Background Anisotropies
Bartolo, N; Riotto, A
2010-01-01
We review in a pedagogical way the present status of the impact of non-Gaussianity (NG) on the Cosmic Microwave Background (CMB) anisotropies. We first show how to set the initial conditions at second-order for the (gauge invariant) CMB anisotropies when some primordial NG is present. However, there are many sources of NG in CMB anisotropies, beyond the primordial one, which can contaminate the primordial signal. We mainly focus on the NG generated from the post-inflationary evolution of the CMB anisotropies at second-order in perturbation theory at large and small angular scales, such as the ones generated at the recombination epoch. We show how to derive the equations to study the second-order CMB anisotropies and provide analytical computations to evaluate their contamination to primordial NG (complemented with numerical examples). We also offer a brief summary of other secondary effects. This review requires basic knowledge of the theory of cosmological perturbations at the linear level.
Optimization of Vehicular Trajectories under Gaussian Noise Disturbances
Directory of Open Access Journals (Sweden)
Joan Garcia-Haro
2012-12-01
Full Text Available Nowadays, research on Vehicular Technology aims at automating every single mechanical element of vehicles, in order to increase passengers’ safety, reduce human driving intervention and provide entertainment services on board. Automatic trajectory tracing for vehicles under especially risky circumstances is a field of research that is currently gaining enormous attention. In this paper, we show some results on how to develop useful policies to execute maneuvers by a vehicle at high speeds with the mathematical optimization of some already established mobility conditions of the car. We also study how the presence of Gaussian noise on measurement sensors while maneuvering can disturb motion and affect the final trajectories. Different performance criteria for the optimization of such maneuvers are presented, and an analysis is shown on how path deviations can be minimized by using trajectory smoothing techniques like the Kalman Filter. We finalize the paper with a discussion on how communications can be used to implement these schemes.
Stochastic cluster algorithms for discrete Gaussian (SOS) models
International Nuclear Information System (INIS)
Evertz, H.G.; Hamburg Univ.; Hasenbusch, M.; Marcu, M.; Tel Aviv Univ.; Pinn, K.; Muenster Univ.; Solomon, S.
1990-10-01
We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete Gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z. Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm. (orig.)
Multistatic adaptive CFAR detection in non-Gaussian clutter
Palamà, Riccardo; Greco, Maria; Gini, Fulvio
2016-12-01
This work addresses the problem of target detection for multistatic radars. We propose an algorithm that is able to keep constant the false alarm rate, when the disturbance samples associated with each receiver-transmitter pair are distributed according to a compound Gaussian model. The performance of the proposed detection algorithm are analysed to assess the impact of clutter diversity on detection performance. The results show that clutter statistical diversity has a strong impact on detection performance. The performance of both single-channel and multichannel detection schemes are evaluated by processing real sea clutter data collected by the NetRAD nodes, in order to evaluate which of the two channels, i.e. the bistatic and monostatic channels, is more favourable for target detection. Furthermore, the gain achieved by using a multistatic detection algorithm is also analysed.
Analytic functions of optical choppers for Gaussian laser beams
Pop, Nicolina; Cira, Octavian; Duma, Virgil-Florin
2017-06-01
The paper presents a report on our current work on obtaining the analytic functions of the laser impulses generated by optical choppers with disks in their classical configuration - with windows that have linear margins. With regard to our previous researches, focused on choppers working with top-hat (i.e., with constant intensity) laser beams, in the present work Gaussian laser beam distributions of the light beams to be chopped have been considered, for the most common case, of a light bundle of a sufficient small diameter in the plane of the disk; this type of section can therefore be completely obscured and uncovered by the chopper wings and windows, respectively. The functions of the transmitted light flux of the device are approached. This allows for the designing calculus of choppers for different applications, taking into account their specific requirements. A comparison between analytical results obtained in this work and results from our previous numerical modeling is pointed out.
Detecting damped Ly α absorbers with Gaussian processes
Garnett, Roman; Ho, Shirley; Bird, Simeon; Schneider, Jeff
2017-12-01
We develop an automated technique for detecting damped Ly α absorbers (DLAs) along spectroscopic lines of sight to quasi-stellar objects (QSOs or quasars). The detection of DLAs in large-scale spectroscopic surveys such as SDSS III sheds light on galaxy formation at high redshift, showing the nucleation of galaxies from diffuse gas. We use nearly 50 000 QSO spectra to learn a novel tailored Gaussian process model for quasar emission spectra, which we apply to the DLA detection problem via Bayesian model selection. We propose models for identifying an arbitrary number of DLAs along a given line of sight. We demonstrate our method's effectiveness using a large-scale validation experiment, with excellent performance. We also provide a catalogue of our results applied to 162 858 spectra from SDSS-III data release 12.
Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media
Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai
2018-01-01
Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.
Gaussian Multiscale Aggregation Applied to Segmentation in Hand Biometrics
Directory of Open Access Journals (Sweden)
Gonzalo Bailador del Pozo
2011-11-01
Full Text Available This paper presents an image segmentation algorithm based on Gaussian multiscale aggregation oriented to hand biometric applications. The method is able to isolate the hand from a wide variety of background textures such as carpets, fabric, glass, grass, soil or stones. The evaluation was carried out by using a publicly available synthetic database with 408,000 hand images in different backgrounds, comparing the performance in terms of accuracy and computational cost to two competitive segmentation methods existing in literature, namely Lossy Data Compression (LDC and Normalized Cuts (NCuts. The results highlight that the proposed method outperforms current competitive segmentation methods with regard to computational cost, time performance, accuracy and memory usage.
Generation and application of high power flattened Gaussian beams
CSIR Research Space (South Africa)
Forbes, A
2009-07-01
Full Text Available power Flattened Gaussian Beams A. Forbes1,2,3, N. du Preez4, I.A, Litvin1,3 and L.R. Botha1,3 1 CSIR National Laser Centre 2 School of Physics, University of KwaZulu-Natal 3 School of Physics, University of Stellenbosch 4 SDILasers (Pty) Ltd...C wzpinwrLpC wzpwrwzpRkrkzwzpiUzrU 2 1)1()( ),,(2exp)/(2)( )),,(/()),,(2/),,((exp),( 0 0 2 2 00 2 00 ∑ ∑ = = −= Φ−× −−−Φ−= 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0...
GAUSSIAN MIXTURE MODEL AND RJMCMC BASED RS IMAGE SEGMENTATION
Directory of Open Access Journals (Sweden)
X. Shi
2017-09-01
Full Text Available For the image segmentation method based on Gaussian Mixture Model (GMM, there are some problems: 1 The number of component was usually a fixed number, i.e., fixed class and 2 GMM is sensitive to image noise. This paper proposed a RS image segmentation method that combining GMM with reversible jump Markov Chain Monte Carlo (RJMCMC. In proposed algorithm, GMM was designed to model the distribution of pixel intensity in RS image. Assume that the number of component was a random variable. Respectively build the prior distribution of each parameter. In order to improve noise resistance, used Gibbs function to model the prior distribution of GMM weight coefficient. According to Bayes' theorem, build posterior distribution. RJMCMC was used to simulate the posterior distribution and estimate its parameters. Finally, an optimal segmentation is obtained on RS image. Experimental results show that the proposed algorithm can converge to the optimal number of class and get an ideal segmentation results.
Laser-driven acceleration with Bessel and Gaussian beams
International Nuclear Information System (INIS)
Hafizi, B.; Esarey, E.; Sprangle, P.
1997-01-01
The possibility of enhancing the energy gain in laser-driven accelerators by using Bessel laser beams is examined. Scaling laws are derived for the propagation length, acceleration gradient, and energy gain in various accelerators for both Gaussian and Bessel beam drivers. For equal beam powers, the energy gain can be increased by a factor of N 1/2 by utilizing a Bessel beam with N lobes, provided that the acceleration gradient is linearly proportional to the laser field. This is the case in the inverse free electron laser and the inverse Cherenkov accelerators. If the acceleration gradient is proportional to the square of the laser field (e.g., the laser wakefield, plasma beat wave, and vacuum beat wave accelerators), the energy gain is comparable with either beam profile. copyright 1997 American Institute of Physics
Generating Correlated QPSK Waveforms By Exploiting Real Gaussian Random Variables
Jardak, Seifallah
2012-11-01
The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar, one of them is the desired transmit beampattern design. In this work, an algorithm is proposed to generate quadrature phase shift- keying (QPSK) waveforms with required cross-correlation properties using real Gaussian random-variables (RV’s). This work can be considered as the extension of what was presented in [1] to generate BPSK waveforms. This work will be extended for the generation of correlated higher-order phase shift-keying (PSK) and quadrature amplitude modulation (QAM) schemes that can better approximate the desired beampattern.
SNR Estimation in Linear Systems with Gaussian Matrices
Suliman, Mohamed Abdalla Elhag
2017-09-27
This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.
Out-of-equilibrium dynamics in a Gaussian trap model
International Nuclear Information System (INIS)
Diezemann, Gregor
2007-01-01
The violations of the fluctuation-dissipation theorem are analysed for a trap model with a Gaussian density of states. In this model, the system reaches thermal equilibrium for long times after a quench to any finite temperature and therefore all ageing effect are of a transient nature. For not too long times after the quench it is found that the so-called fluctuation-dissipation ratio tends to a non-trivial limit, thus indicating the possibility for the definition of a timescale-dependent effective temperature. However, different definitions of the effective temperature yield distinct results. In particular, plots of the integrated response versus the correlation function strongly depend on the way they are constructed. Also the definition of effective temperatures in the frequency domain is not unique for the model considered. This may have some implications for the interpretation of results from computer simulations and experimental determinations of effective temperatures
First constraints on the running of non-Gaussianity.
Becker, Adam; Huterer, Dragan
2012-09-21
We use data from the Wilkinson Microwave Anisotropy probe temperature maps to constrain a scale-dependent generalization of the popular "local" model for primordial non-Gaussianity. In the model where the parameter f(NL) is allowed to run with scale k, f(NL)(k) = f*(NL) (k/k(piv))(n)(fNL), we constrain the running to be n(f)(NL) = 0.30(-1.2)(+1.9) at 95% confidence, marginalized over the amplitude f*(NL). The constraints depend somewhat on the prior probabilities assigned to the two parameters. In the near future, constraints from a combination of Planck and large-scale structure surveys are expected to improve this limit by about an order of magnitude and usefully constrain classes of inflationary models.
A Non-Gaussian Spatial Generalized Linear Latent Variable Model
Irincheeva, Irina
2012-08-03
We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.
Solution of the RHIC HBT puzzle with Gaussian initial conditions
Florkowski, W.; Broniowski, W.; Chojnacki, M.; Kisiel, A.
2009-06-01
It is argued that the consistent description of the transverse-momentum spectra, elliptic flow and the HBT radii in the relativistic heavy-ion collisions studied at the RHIC may be obtained within the hydrodynamic model if one uses the Gaussian profile for the initial energy density in the transverse plane. Moreover, we show that the results obtained in the scenario with an early start of hydrodynamics (at the proper time τ0 = 0.25 fm) are practically equivalent to the results obtained in the model where the hydrodynamics is preceded by the free-streaming stage of partons (in the proper time interval 0.25 fm Education, grants N202 153 32/4247 and N202 034 32/0918, and by the US NSF grant no PHY-0653432.
Iterative Mixture Component Pruning Algorithm for Gaussian Mixture PHD Filter
Directory of Open Access Journals (Sweden)
Xiaoxi Yan
2014-01-01
Full Text Available As far as the increasing number of mixture components in the Gaussian mixture PHD filter is concerned, an iterative mixture component pruning algorithm is proposed. The pruning algorithm is based on maximizing the posterior probability density of the mixture weights. The entropy distribution of the mixture weights is adopted as the prior distribution of mixture component parameters. The iterative update formulations of the mixture weights are derived by Lagrange multiplier and Lambert W function. Mixture components, whose weights become negative during iterative procedure, are pruned by setting corresponding mixture weights to zeros. In addition, multiple mixture components with similar parameters describing the same PHD peak can be merged into one mixture component in the algorithm. Simulation results show that the proposed iterative mixture component pruning algorithm is superior to the typical pruning algorithm based on thresholds.
Orbit-product representation and correction of Gaussian belief propagation
Energy Technology Data Exchange (ETDEWEB)
Johnson, Jason K [Los Alamos National Laboratory; Chertkov, Michael [Los Alamos National Laboratory; Chernyak, Vladimir [WAYNE STATE UNIV
2009-01-01
We present a new interpretation of Gaussian belief propagation (GaBP) based on the 'zeta function' representation of the determinant as a product over orbits of a graph. We show that GaBP captures back-tracking orbits of the graph and consider how to correct this estimate by accounting for non-backtracking orbits. We show that the product over non-backtracking orbits may be interpreted as the determinant of the non-backtracking adjacency matrix of the graph with edge weights based on the solution of GaBP. An efficient method is proposed to compute a truncated correction factor including all non-backtracking orbits up to a specified length.
Automatic fitting of Gaussian peaks using abductive machine learning
Abdel-Aal, R. E.
1998-02-01
Analytical techniques have been used for many years for fitting Gaussian peaks in nuclear spectroscopy. However, the complexity of the approach warrants looking for machine-learning alternatives where intensive computations are required only once (during training), while actual analysis on individual spectra is greatly simplified and quickened. This should allow the use of simple portable systems for fast and automated analysis of large numbers of spectra, particularly in situations where accuracy may be traded for speed and simplicity. This paper proposes the use of abductive networks machine learning for this purpose. The Abductory Induction Mechanism (AIM) tool was used to build models for analyzing both single and double Gaussian peaks in the presence of noise depicting statistical uncertainties in collected spectra. AIM networks were synthesized by training on 1000 representative simulated spectra and evaluated on 500 new spectra. A classifier network determines the multiplicity of single/double peaks with an accuracy of 5.8%. With statistical uncertainties corresponding to a peak count of 100, average percentage absolute errors for the height, position, and width of single peaks are 4.9, 2.9, and 4.2%, respectively. For double peaks, these average errors are within 7.0, 3.1, and 5.9%, respectively. Models have been developed which account for the effect of a linear background on a single peak. Performance is compared with a neural network application and with an analytical curve-fitting routine, and the new technique is applied to actual data of an alpha spectrum.
Modulated reheating and large non-gaussianity in string cosmology
Energy Technology Data Exchange (ETDEWEB)
Cicoli, M.; Quevedo, F. [Abdus Salam ICTP, Strada Costiera 11, Trieste 34014 (Italy); Tasinato, G. [Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX (United Kingdom); Zavala, I. [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Burgess, C.P., E-mail: michele.cicoli@desy.de, E-mail: gianmassimo.tasinato@port.ac.uk, E-mail: e.i.zavala@rug.nl, E-mail: cburgess@perimeterinstitute.ca, E-mail: F.Quevedo@damtp.cam.ac.uk [Department of Physics and Astronomy, McMaster University, Hamilton ON (Canada)
2012-05-01
A generic feature of the known string inflationary models is that the same physics that makes the inflaton lighter than the Hubble scale during inflation often also makes other scalars this light. These scalars can acquire isocurvature fluctuations during inflation, and given that their VEVs determine the mass spectrum and the coupling constants of the effective low-energy field theory, these fluctuations give rise to couplings and masses that are modulated from one Hubble patch to another. These seem just what is required to obtain primordial adiabatic fluctuations through conversion into density perturbations through the 'modulation mechanism', wherein reheating takes place with different efficiency in different regions of our Universe. Fluctuations generated in this way can generically produce non-gaussianity larger than obtained in single-field slow-roll inflation; potentially observable in the near future. We provide here the first explicit example of the modulation mechanism at work in string cosmology, within the framework of LARGE Volume Type-IIB string flux compactifications. The inflationary dynamics involves two light Kähler moduli: a fibre divisor plays the rôle of the inflaton whose decay rate to visible sector degrees of freedom is modulated by the primordial fluctuations of a blow-up mode (which is made light by the use of poly-instanton corrections). We find the challenges of embedding the mechanism into a concrete UV completion constrains the properties of the non-gaussianity that is found, since for generic values of the underlying parameters, the model predicts a local bi-spectrum with f{sub NL} of order 'a few'. However, a moderate tuning of the parameters gives also rise to explicit examples with f{sub NL} ∼ O(20) potentially observable by the Planck satellite.
Uncertainty in perception and the Hierarchical Gaussian Filter
Directory of Open Access Journals (Sweden)
Christoph Daniel Mathys
2014-11-01
Full Text Available In its full sense, perception rests on an agent’s model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the hierarchical Gaussian filter (HGF offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (instability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF’s hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient - but at the same time intuitive - framework for the resolution of perceptual uncertainty in behaving agents.
Occupational Hearing Loss from Non-Gaussian Noise.
Suter, Alice H
2017-08-01
Noise levels are truly continuous in relatively few occupations, with some degree of intermittency the most common condition. The sound levels of intermittent noise are often referred to as non-Gaussian in that they are not normally distributed in the time domain. In some conditions, intermittent noise affects the ear differently from continuous noise, and it is this assumption that underlies the selection of the 5-dB exchange rate (ER). The scientific and professional communities have debated this assumption over recent decades. This monograph explores the effect of non-Gaussian noise on the auditory system. It begins by summarizing an earlier report by the same author concentrating on the subject of the ER. The conclusions of the earlier report supported the more conservative 3-dB ER with possible adjustments to the permissible exposure limit for certain working conditions. The current document has expanded on the earlier report in light of the relevant research accomplished in the intervening decades. Although some of the animal research has supported the mitigating effect of intermittency, a closer look at many of these studies reveals certain weaknesses, along with the fact that these noise exposures were not usually representative of the conditions under which people actually work. The more recent animal research on complex noise shows that intermittencies do not protect the cochlea and that many of the previous assumptions about the ameliorative effect of intermittencies are no longer valid, lending further support to the 3-dB ER. The neurologic effects of noise on hearing have gained increasing attention in recent years because of improvements in microscopy and immunostaining techniques. Animal experiments showing damage to auditory synapses from noise exposures previously considered harmless may signify the need for a more conservative approach to the assessment of noise-induced hearing loss and consequently the practice of hearing conservation programs.
Efficient Kernel-Based Ensemble Gaussian Mixture Filtering
Liu, Bo
2015-11-11
We consider the Bayesian filtering problem for data assimilation following the kernel-based ensemble Gaussian-mixture filtering (EnGMF) approach introduced by Anderson and Anderson (1999). In this approach, the posterior distribution of the system state is propagated with the model using the ensemble Monte Carlo method, providing a forecast ensemble that is then used to construct a prior Gaussian-mixture (GM) based on the kernel density estimator. This results in two update steps: a Kalman filter (KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, we analyze the influence of the bandwidth parameter of the kernel function on the covariance of the posterior distribution. We then focus on two aspects: i) the efficient implementation of EnGMF with (relatively) small ensembles, where we propose a new deterministic resampling strategy preserving the first two moments of the posterior GM to limit the sampling error; and ii) the analysis of the effect of the bandwidth parameter on contributions of KF and PF updates and on the weights variance. Numerical results using the Lorenz-96 model are presented to assess the behavior of EnGMF with deterministic resampling, study its sensitivity to different parameters and settings, and evaluate its performance against ensemble KFs. The proposed EnGMF approach with deterministic resampling suggests improved estimates in all tested scenarios, and is shown to require less localization and to be less sensitive to the choice of filtering parameters.
Automatic fitting of Gaussian peaks using abductive machine learning
International Nuclear Information System (INIS)
Abdel-Aal, R.E.
1998-01-01
Analytical techniques have been used for many years for fitting Gaussian peaks in nuclear spectroscopy. However, the complexity of the approach warrants looking for machine-learning alternatives where intensive computations are required only once (during training), while actual analysis on individual spectra is greatly simplified and quickened. This should allow the use of simple portable systems for fast and automated analysis of large numbers of spectra, particularly in situations where accuracy may be traded for speed and simplicity. This paper proposes the use of abductive networks machine learning for this purpose. The Abductory Induction Mechanism (AIM) tool was used to build models for analyzing both single and double Gaussian peaks in the presence of noise depicting statistical uncertainties in collected spectra. AIM networks were synthesized by training on 1,000 representative simulated spectra and evaluated on 500 new spectra. A classifier network determines the multiplicity of single/double peaks with an accuracy of 98%. With statistical uncertainties corresponding to a peak count of 100, average percentage absolute errors for the height, position, and width of single peaks are 4.9, 2.9, and 4.2%, respectively. For double peaks, these average errors are within 7.0, 3.1, and 5.9%, respectively. Models have been developed which account for the effect of a linear background on a single peak. Performance is compared with a neural network application and with an analytical curve-fitting routine, and the new technique is applied to actual data of an alpha spectrum
International Nuclear Information System (INIS)
Lock, James A.
2013-01-01
The vector wave equation for electromagnetic waves, when subject to a number of constraints corresponding to propagation of a monochromatic beam, reduces to a pair of inhomogeneous differential equations describing the transverse electric and transverse magnetic polarized beam components. These differential equations are solved analytically to obtain the most general focused Gaussian beam to order s 4 , where s is the beam confinement parameter, and various properties of the most general Gaussian beam are then discussed. The radial fields of the most general Gaussian beam are integrated to obtain the on-axis beam shape coefficients of the generalized Lorenz–Mie theory formalism of light scattering. The beam shape coefficients are then compared with those of the localized Gaussian beam model and the Davis–Barton fifth-order symmetrized beam. -- Highlights: ► Derive the differential equation for the most general Gaussian beam. ► Solve the differential equation for the most general Gaussian beam. ► Determine the properties of the most general Gaussian beam. ► Determine the beam shape coefficients of the most general Gaussian beam
Core temperature in super-Gaussian pumped air-clad photonic ...
Indian Academy of Sciences (India)
In this paper we investigate the core temperature of air-clad photonic crystal fiber (PCF) lasers pumped by a super-Gaussian (SG) source of order four. The results are compared with conventional double-clad fiber (DCF) lasers pumped by the same super-Gaussian and by top-hat pump profiles.
Monte Carlo estimation for nonlinear non-Gaussian state space models
Jungbacker, B.M.J.P.; Koopman, S.J.
2007-01-01
We develop a proposal or importance density for state space models with a nonlinear non-Gaussian observation vector y ∼ p(yθ) and an unobserved linear Gaussian signal vector θ ∼ p(θ). The proposal density is obtained from the Laplace approximation of the smoothing density p(θy). We present efficient
Generation of Laguerre-Gaussian Beams Using a Diode Pumped Solid-State Digital Laser
CSIR Research Space (South Africa)
Bell, Teboho
2015-10-01
Full Text Available The solid state digital laser was used in generation of Laguerre-Gaussian modes, LGpl, of different orders. This work demonstrates that we can generate high-order Laguerre-Gaussian modes with high purity using a digital laser....
International Nuclear Information System (INIS)
Deng Dongmei; Guo Hong; Han Dingan; Liu Mingwei; Li Changfu
2005-01-01
Taking into account the dispersion and the longitudinal chromatic aberration (LCA) of the material of the lens, focusing of isodiffracting pulsed Gaussian light beam through single lens is analyzed. The smaller the cycle number of the isodiffracting pulsed Gaussian light beam is, the higher the order of the material dispersion should be considered
Estimator of a non-Gaussian parameter in multiplicative log-normal models
Kiyono, Ken; Struzik, Zbigniew R.; Yamamoto, Yoshiharu
2007-10-01
We study non-Gaussian probability density functions (PDF’s) of multiplicative log-normal models in which the multiplication of Gaussian and log-normally distributed random variables is considered. To describe the PDF of the velocity difference between two points in fully developed turbulent flows, the non-Gaussian PDF model was originally introduced by Castaing [Physica D 46, 177 (1990)]. In practical applications, an experimental PDF is approximated with Castaing’s model by tuning a single non-Gaussian parameter, which corresponds to the logarithmic variance of the log-normally distributed variable in the model. In this paper, we propose an estimator of the non-Gaussian parameter based on the q th order absolute moments. To test the estimator, we introduce two types of stochastic processes within the framework of the multiplicative log-normal model. One is a sequence of independent and identically distributed random variables. The other is a log-normal cascade-type multiplicative process. By analyzing the numerically generated time series, we demonstrate that the estimator can reliably determine the theoretical value of the non-Gaussian parameter. Scale dependence of the non-Gaussian parameter in multiplicative log-normal models is also studied, both analytically and numerically. As an application of the estimator, we demonstrate that non-Gaussian PDF’s observed in the S&P500 index fluctuations are well described by the multiplicative log-normal model.
Conditional Mean Values of Slightly Non-Gaussian processes with Application to design Wave-Loads
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
1996-01-01
Recently, conditional mean wave kinematics have been derived for slightly non-Gaussian waves. The result includes cumulants up to third order and thus the lowest order of the non-Gaussian contribution. This is consistent with application of second order Stokes waves. Here theanalysis is extended...
Liu, Peng; Wang, Yanfei
2018-04-01
We study problems associated with seismic data decomposition and migration imaging. We first represent the seismic data utilizing Gaussian beam basis functions, which have nonzero curvature, and then consider the sparse decomposition technique. The sparse decomposition problem is an l0-norm constrained minimization problem. In solving the l0-norm minimization, a polynomial Radon transform is performed to achieve sparsity, and a fast gradient descent method is used to calculate the waveform functions. The waveform functions can subsequently be used for sparse Gaussian beam migration. Compared with traditional sparse Gaussian beam methods, the seismic data can be properly reconstructed employing fewer Gaussian beams with nonzero initial curvature. The migration approach described in this paper is more efficient than the traditional sparse Gaussian beam migration.
Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.
Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.
Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance
International Nuclear Information System (INIS)
Han Yinxia; Li Jinghui; Chen Shigang
2005-01-01
The phenomenon of stochastic resonance (SR) in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio (SNR) is calculated according to the generalized two-state theory (shown in [H.S. Wio and S. Bouzat, Brazilian J. Phys. 29 (1999) 136]). We find that the SNR increases with the proximity of a to zero. In addition, the correlation time τ between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time τ between the Gaussian additive colored noise is, the higher of the peak value of SNR.
A Scalable Gaussian Process Analysis Algorithm for Biomass Monitoring
Energy Technology Data Exchange (ETDEWEB)
Chandola, Varun [ORNL; Vatsavai, Raju [ORNL
2011-01-01
Biomass monitoring is vital for studying the carbon cycle of earth's ecosystem and has several significant implications, especially in the context of understanding climate change and its impacts. Recently, several change detection methods have been proposed to identify land cover changes in temporal profiles (time series) of vegetation collected using remote sensing instruments, but do not satisfy one or both of the two requirements of the biomass monitoring problem, i.e., {\\em operating in online mode} and {\\em handling periodic time series}. In this paper, we adapt Gaussian process regression to detect changes in such time series in an online fashion. While Gaussian process (GP) have been widely used as a kernel based learning method for regression and classification, their applicability to massive spatio-temporal data sets, such as remote sensing data, has been limited owing to the high computational costs involved. We focus on addressing the scalability issues associated with the proposed GP based change detection algorithm. This paper makes several significant contributions. First, we propose a GP based online time series change detection algorithm and demonstrate its effectiveness in detecting different types of changes in {\\em Normalized Difference Vegetation Index} (NDVI) data obtained from a study area in Iowa, USA. Second, we propose an efficient Toeplitz matrix based solution which significantly improves the computational complexity and memory requirements of the proposed GP based method. Specifically, the proposed solution can analyze a time series of length $t$ in $O(t^2)$ time while maintaining a $O(t)$ memory footprint, compared to the $O(t^3)$ time and $O(t^2)$ memory requirement of standard matrix manipulation based methods. Third, we describe a parallel version of the proposed solution which can be used to simultaneously analyze a large number of time series. We study three different parallel implementations: using threads, MPI, and a
Some Metric Properties of Planar Gaussian Free Field
Goswami, Subhajit
In this thesis we study the properties of some metrics arising from two-dimensional Gaussian free field (GFF), namely the Liouville first-passage percolation (Liouville FPP), the Liouville graph distance and an effective resistance metric. In Chapter 1, we define these metrics as well as discuss the motivations for studying them. Roughly speaking, Liouville FPP is the shortest path metric in a planar domain D where the length of a path P is given by ∫Pe gammah(z)|dz| where h is the GFF on D and gamma > 0. In Chapter 2, we present an upper bound on the expected Liouville FPP distance between two typical points for small values of gamma (the near-Euclidean regime). A similar upper bound is derived in Chapter 3 for the Liouville graph distance which is, roughly, the minimal number of Euclidean balls with comparable Liouville quantum gravity (LQG) measure whose union contains a continuous path between two endpoints. Our bounds seem to be in disagreement with Watabiki's prediction (1993) on the random metric of Liouville quantum gravity in this regime. The contents of these two chapters are based on a joint work with Jian Ding. In Chapter 4, we derive some asymptotic estimates for effective resistances on a random network which is defined as follows. Given any gamma > 0 and for eta = {etav}v∈Z2 denoting a sample of the two-dimensional discrete Gaussian free field on Z2 pinned at the origin, we equip the edge ( u, v) with conductance egamma(etau + eta v). The metric structure of effective resistance plays a crucial role in our proof of the main result in Chapter 4. The primary motivation behind this metric is to understand the random walk on Z 2 where the edge (u, v) has weight egamma(etau + etav). Using the estimates from Chapter 4 we show in Chapter 5 that for almost every eta, this random walk is recurrent and that, with probability tending to 1 as T → infinity, the return probability at time 2T decays as T-1+o(1). In addition, we prove a version of subdiffusive
Gaussian copula as a likelihood function for environmental models
Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.
2017-12-01
Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an
Xiang, Yu; Xu, Buqing; Mišta, Ladislav; Tufarelli, Tommaso; He, Qiongyi; Adesso, Gerardo
2017-10-01
Einstein-Podolsky-Rosen (EPR) steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited as a resource for quantum communication with one untrusted party. In particular, steering of continuous-variable Gaussian states has been extensively studied theoretically and experimentally, as a fundamental manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by suitable non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density-matrix elements of two-mode squeezed thermal Gaussian states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a simple nonlinear criterion, based on second moments of the correlation matrix constructed from pseudospin operators. This analysis reveals previously unexplored regimes where non-Gaussian measurements are shown to be more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed more compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than conventional Gaussian observables for steering detection. Finally, we investigate continuous-variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian
A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems
Energy Technology Data Exchange (ETDEWEB)
Weerakkody, Sean [Carnegie Mellon Univ., Pittsburgh, PA (United States); Ozel, Omur [Carnegie Mellon Univ., Pittsburgh, PA (United States); Sinopoli, Bruno [Carnegie Mellon Univ., Pittsburgh, PA (United States)
2017-11-02
We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the other hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.
Sellentin, Elena; Heavens, Alan F.
2018-01-01
We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a data set, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of data points that depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnosis, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation functions are significant. With a simple exclusion of the most contaminated data points, the posterior for s8 is shifted without broadening, but we find no significant reduction in the tension with s8 derived from Planck cosmic microwave background data. However, we also show that the one-point distributions of the correlation statistics are noticeably skewed, such that sound weak-lensing data sets are intrinsically likely to lead to a systematically low lensing amplitude being inferred. The detected non-Gaussianities get larger with increasing angular scale such that for future wide-angle surveys such as Euclid or LSST, with their very small statistical errors, the large-scale modes are expected to be increasingly affected. The shifts in posteriors may then not be negligible and we recommend that these diagnostic tests be run as part of future analyses.
Non-Gaussian noise-weakened stability in a foraging colony system with time delay
Dong, Xiaohui; Zeng, Chunhua; Yang, Fengzao; Guan, Lin; Xie, Qingshuang; Duan, Weilong
2018-02-01
In this paper, the dynamical properties in a foraging colony system with time delay and non-Gaussian noise were investigated. Using delay Fokker-Planck approach, the stationary probability distribution (SPD), the associated relaxation time (ART) and normalization correlation function (NCF) are obtained, respectively. The results show that: (i) the time delay and non-Gaussian noise can induce transition from a single peak to double peaks in the SPD, i.e., a type of bistability occurring in a foraging colony system where time delay and non-Gaussian noise not only cause transitions between stable states, but also construct the states themselves. Numerical simulations are presented and are in good agreement with the approximate theoretical results; (ii) there exists a maximum in the ART as a function of the noise intensity, this maximum for ART is identified as the characteristic of the non-Gaussian noise-weakened stability of the foraging colonies in the steady state; (iii) the ART as a function of the noise correlation time exhibits a maximum and a minimum, where the minimum for ART is identified as the signature of the non-Gaussian noise-enhanced stability of the foraging colonies; and (iv) the time delay can enhance the stability of the foraging colonies in the steady state, while the departure from Gaussian noise can weaken it, namely, the time delay and departure from Gaussian noise play opposite roles in ART or NCF.
Huh, Joonsuk; Yung, Man-Hong
2017-08-07
Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.
Non-Gaussian signatures arising from warm inflation driven by geometric tachyon
International Nuclear Information System (INIS)
Bhattacharjee, Anindita; Deshamukhya, Atri
2014-01-01
In a warm inflationary scenario, the initial seeds of density perturbation arise from thermal fluctuations of the inflaton field. These fluctuations in principle have Gaussian distribution. In a Gaussian distribution the density perturbation can be expressed as the two point correlation function. Thus if in an inflationary model the density perturbation is expressed as correlation function of order higher than two, these fluctuations are non-Gaussian in nature. A simple inflationary model containing single scalar field, slow roll, canonical kinetic term and vacuum initial state can produce a tiny amount of non-Gaussianity which are very small to be detected by any experiment. Non-Gaussianity can also arise in inflationary models containing multiple scalar fields. For an inflationary scenario with single scalar field, non-Gaussianity can be expressed in terms of bi-spectrum however for multi field Inflation, it is expressed in terms of trispectrum etc. In this piece of work, the warm inflationary scenario, driven by a D3 brane due to the presence of a stack of k coincident NS 5 branes is considered and the non-Gaussian effects in such an inflationary scenario has been analysed by measuring the bispectrum of the gravitational field fluctuations generated during the warm inflation in strong dissipative regime. The bi-spectrum of the Inflation is expressed in terms of the parameter f NL and it is seen that the value of f NL parameter lies well within the limit observed by WMAP7
Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures
Directory of Open Access Journals (Sweden)
Nishchal K. Verma
2012-01-01
Full Text Available This paper presents a novel computational approach for estimating fuzzy measures directly from Gaussian mixtures model (GMM. The mixture components of GMM provide the membership functions for the input-output fuzzy sets. By treating consequent part as a function of fuzzy measures, we derived its coefficients from the covariance matrices found directly from GMM and the defuzzified output constructed from both the premise and consequent parts of the nonadditive fuzzy rules that takes the form of Choquet integral. The computational burden involved with the solution of λ-measure is minimized using Q-measure. The fuzzy model whose fuzzy measures were computed using covariance matrices found in GMM has been successfully applied on two benchmark problems and one real-time electric load data of Indian utility. The performance of the resulting model for many experimental studies including the above-mentioned application is found to be better and comparable to recent available fuzzy models. The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.
Gaussian Process Domain Experts for Modeling of Facial Affect.
Eleftheriadis, Stefanos; Rudovic, Ognjen; Deisenroth, Marc Peter; Pantic, Maja
2017-10-01
Most of existing models for facial behavior analysis rely on generic classifiers, which fail to generalize well to previously unseen data. This is because of inherent differences in source (training) and target (test) data, mainly caused by variation in subjects' facial morphology, camera views, and so on. All of these account for different contexts in which target and source data are recorded, and thus, may adversely affect the performance of the models learned solely from source data. In this paper, we exploit the notion of domain adaptation and propose a data efficient approach to adapt already learned classifiers to new unseen contexts. Specifically, we build upon the probabilistic framework of Gaussian processes (GPs), and introduce domain-specific GP experts (e.g., for each subject). The model adaptation is facilitated in a probabilistic fashion, by conditioning the target expert on the predictions from multiple source experts. We further exploit the predictive variance of each expert to define an optimal weighting during inference. We evaluate the proposed model on three publicly available data sets for multi-class (MultiPIE) and multi-label (DISFA, FERA2015) facial expression analysis by performing adaptation of two contextual factors: "where" (view) and "who" (subject). In our experiments, the proposed approach consistently outperforms: 1) both source and target classifiers, while using a small number of target examples during the adaptation and 2) related state-of-the-art approaches for supervised domain adaptation.
Gaussian Process Regression Plus Method for Localization Reliability Improvement.
Liu, Kehan; Meng, Zhaopeng; Own, Chung-Ming
2016-07-29
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.
Hamiltonian formulation of surfaces with constant Gaussian curvature
Energy Technology Data Exchange (ETDEWEB)
Trejo, Miguel; Amar, Martine Ben; Mueller, Martin Michael [Laboratoire de Physique Statistique de l' Ecole Normale Superieure (UMR 8550), associe aux Universites Paris 6 et Paris 7 et au CNRS, 24, rue Lhomond, 75005 Paris (France)
2009-10-23
Dirac's method for constrained Hamiltonian systems is used to describe surfaces of constant Gaussian curvature. A geometrical free energy, for which these surfaces are equilibrium states, is introduced and interpreted as an action. An equilibrium surface can then be generated by the evolution of a closed space curve. Since the underlying action depends on second derivatives, the velocity of the curve and its conjugate momentum must be included in the set of phase-space variables. Furthermore, the action is linear in the acceleration of the curve and possesses a local symmetry-reparametrization invariance-which implies primary constraints in the canonical formalism. These constraints are incorporated into the Hamiltonian through Lagrange multiplier functions that are identified as the components of the acceleration of the curve. The formulation leads to four first-order partial differential equations, one for each canonical variable. With the appropriate choice of parametrization, only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve. To illustrate the formalism, several evolutions of pseudospherical surfaces are discussed.
Accuracy of dynamical-decoupling-based spectroscopy of Gaussian noise
Szańkowski, Piotr; Cywiński, Łukasz
2018-03-01
The fundamental assumption of dynamical-decoupling-based noise spectroscopy is that the coherence decay rate of qubit (or qubits) driven with a sequence of many pulses, is well approximated by the environmental noise spectrum spanned on frequency comb defined by the sequence. Here we investigate the precise conditions under which this commonly used spectroscopic approach is quantitatively correct. To this end we focus on two representative examples of spectral densities: the long-tailed Lorentzian, and finite-ranged Gaussian—both expected to be encountered when using the qubit for nanoscale nuclear resonance imaging. We have found that, in contrast to Lorentz spectrum, for which the corrections to the standard spectroscopic formulas can easily be made negligible, the spectra with finite range are more challenging to reconstruct accurately. For Gaussian line shape of environmental spectral density, direct application of the standard dynamical-decoupling-based spectroscopy leads to erroneous attribution of long-tail behavior to the reconstructed spectrum. Fortunately, artifacts such as this, can be completely avoided with the simple extension to standard reconstruction method.
New entropic inequalities for qubit and unimodal Gaussian states
López-Saldívar, J. A.; Castaños, O.; Man'ko, M. A.; Man'ko, V. I.
2018-02-01
The Tsallis relative entropy Sq(ρ ˆ , σ ˆ) measures the distance between two arbitrary density matrices ρ ˆ and σ ˆ . In this work the approximation to this quantity when q = 1 + δ (δ ≪ 1) is obtained. It is shown that the resulting series is equal to the von Neumann relative entropy when δ = 0. Analyzing the von Neumann relative entropy for an arbitrary ρ ˆ and a thermal equilibrium state σ ˆ =e - β H ˆ / Tr(e - β H ˆ) is possible to define a new inequality relating the energy, the entropy, and the partition function of the system. From this inequality, a parameter that measures the distance between the two states is defined. This distance is calculated for a general qubit system and for an arbitrary unimodal Gaussian state. In the qubit case, the dependence on the purity of the system is studied for T ≥ 0 and also for T thermal light state as a thermal equilibrium state of the parametric amplifier is presented.
Libcint: An efficient general integral library for Gaussian basis functions.
Sun, Qiming
2015-08-15
An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library is able to evaluate arbitrary integral expressions on top of p, r and σ operators with one-electron overlap and nuclear attraction, two-electron Coulomb and Gaunt operators for segmented contracted and/or generated contracted basis in Cartesian, spherical or spinor form. Using a symbolic algebra tool, new integrals are derived and translated to C code programmatically. The generated integrals can be used in various types of molecular properties. To demonstrate the capability of the integral library, we computed the analytical gradients and NMR shielding constants at both nonrelativistic and 4-component relativistic Hartree-Fock level in this work. Due to the use of kinetically balanced basis and gauge including atomic orbitals, the relativistic analytical gradients and shielding constants requires the integral library to handle the fifth-order electron repulsion integral derivatives. The generality of the integral library is achieved without losing efficiency. On the modern multi-CPU platform, Libcint can easily reach the overall throughput being many times of the I/O bandwidth. On a 20-core node, we are able to achieve an average output 8.3 GB/s for C60 molecule with cc-pVTZ basis. © 2015 Wiley Periodicals, Inc.
Gaussian Processes: the Next Step in Exoplanet Data Analysis
Aigrain, Suzanne; Gibson, N.; Roberts, S.; Evans, T.; McQuillan, A.; Reece, S.; Osborne, M.
2011-09-01
When searching for or characterising exoplanets, we typically need to isolate a deterministic signal from stochastic processes - astrophysical or instrumental "noise" - in time-series data. Gaussian processes (GPs) enable us to construct distributions over random functions, and to infer the properties of "signal" and "noise" in a way that is both flexible and robust. I will give a brief overview of the principles of GPs and show two example applications which are both interesting in their own right, and highlight some specific strengths of the technique. The first is a new re-analysis of the controversial HST/NICMOS transmission spectrum of HD189733b. The second is the measurement of stellar rotation periods from light curves, when the spot distribution evolves over the duration of the dataset. NB: I could also present another topic: stellar variability studies in Kepler data, based on a new systematics correction which preserves stellar variability. I opted for the GPs because I think it's important to alert the exoplanet community to the potential of this technique, but I'm happy to talk about either.
Gaussian-Charge Polarizable and Nonpolarizable Models for CO2.
Jiang, Hao; Moultos, Othonas A; Economou, Ioannis G; Panagiotopoulos, Athanassios Z
2016-02-11
A polarizable intermolecular potential model using three classical Drude oscillators on the atomic sites has been developed for CO2. The model is rigid with bond lengths and molecular geometries set to their experimental values. Electrostatic interactions are represented by three Gaussian charges connected to the molecular frame by harmonic springs. Nonelectrostatic interactions are represented by the Buckingham exponential-6 potential, with potential parameters optimized to vapor-liquid equilibria (VLE) data. A nonpolarizable CO2 model that shares the other ingredients of the polarizable model was also developed and optimized to VLE data. Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to evaluate the two models with respect to a variety of thermodynamic and transport properties, including the enthalpy of vaporization, second virial coefficient, density in the one-phase fluid region, isobaric and isochoric heat capacities, radial distribution functions, self-diffusion coefficient, and shear viscosity. Excellent agreement between model predictions and experimental data was found for all properties studied. The polarizable and nonpolarizable models provide a similar representation of CO2 properties, which indicates that the properties of pure CO2 fluid are not strongly affected by polarization. The polarizable model, which has an order of magnitude higher computational cost than the nonpolarizable model, will likely be useful for the study of a mixture of CO2 and polar components for which polarization is important.
Sequencing batch-reactor control using Gaussian-process models.
Kocijan, Juš; Hvala, Nadja
2013-06-01
This paper presents a Gaussian-process (GP) model for the design of sequencing batch-reactor (SBR) control for wastewater treatment. The GP model is a probabilistic, nonparametric model with uncertainty predictions. In the case of SBR control, it is used for the on-line optimisation of the batch-phases duration. The control algorithm follows the course of the indirect process variables (pH, redox potential and dissolved oxygen concentration) and recognises the characteristic patterns in their time profile. The control algorithm uses GP-based regression to smooth the signals and GP-based classification for the pattern recognition. When tested on the signals from an SBR laboratory pilot plant, the control algorithm provided a satisfactory agreement between the proposed completion times and the actual termination times of the biodegradation processes. In a set of tested batches the final ammonia and nitrate concentrations were below 1 and 0.5 mg L(-1), respectively, while the aeration time was shortened considerably. Copyright © 2013 Elsevier Ltd. All rights reserved.
Bayesian Travel Time Inversion adopting Gaussian Process Regression
Mauerberger, S.; Holschneider, M.
2017-12-01
A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.
Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties
Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong
2018-03-01
This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.
Multiple Response Regression for Gaussian Mixture Models with Known Labels.
Lee, Wonyul; Du, Ying; Sun, Wei; Hayes, D Neil; Liu, Yufeng
2012-12-01
Multiple response regression is a useful regression technique to model multiple response variables using the same set of predictor variables. Most existing methods for multiple response regression are designed for modeling homogeneous data. In many applications, however, one may have heterogeneous data where the samples are divided into multiple groups. Our motivating example is a cancer dataset where the samples belong to multiple cancer subtypes. In this paper, we consider modeling the data coming from a mixture of several Gaussian distributions with known group labels. A naive approach is to split the data into several groups according to the labels and model each group separately. Although it is simple, this approach ignores potential common structures across different groups. We propose new penalized methods to model all groups jointly in which the common and unique structures can be identified. The proposed methods estimate the regression coefficient matrix, as well as the conditional inverse covariance matrix of response variables. Asymptotic properties of the proposed methods are explored. Through numerical examples, we demonstrate that both estimation and prediction can be improved by modeling all groups jointly using the proposed methods. An application to a glioblastoma cancer dataset reveals some interesting common and unique gene relationships across different cancer subtypes.
Gaussian process regression for sensor networks under localization uncertainty
Jadaliha, M.; Xu, Yunfei; Choi, Jongeun; Johnson, N.S.; Li, Weiming
2013-01-01
In this paper, we formulate Gaussian process regression with observations under the localization uncertainty due to the resource-constrained sensor networks. In our formulation, effects of observations, measurement noise, localization uncertainty, and prior distributions are all correctly incorporated in the posterior predictive statistics. The analytically intractable posterior predictive statistics are proposed to be approximated by two techniques, viz., Monte Carlo sampling and Laplace's method. Such approximation techniques have been carefully tailored to our problems and their approximation error and complexity are analyzed. Simulation study demonstrates that the proposed approaches perform much better than approaches without considering the localization uncertainty properly. Finally, we have applied the proposed approaches on the experimentally collected real data from a dye concentration field over a section of a river and a temperature field of an outdoor swimming pool to provide proof of concept tests and evaluate the proposed schemes in real situations. In both simulation and experimental results, the proposed methods outperform the quick-and-dirty solutions often used in practice.
Stellar atmospheric parameter estimation using Gaussian process regression
Bu, Yude; Pan, Jingchang
2015-02-01
As is well known, it is necessary to derive stellar parameters from massive amounts of spectral data automatically and efficiently. However, in traditional automatic methods such as artificial neural networks (ANNs) and kernel regression (KR), it is often difficult to optimize the algorithm structure and determine the optimal algorithm parameters. Gaussian process regression (GPR) is a recently developed method that has been proven to be capable of overcoming these difficulties. Here we apply GPR to derive stellar atmospheric parameters from spectra. Through evaluating the performance of GPR on Sloan Digital Sky Survey (SDSS) spectra, Medium resolution Isaac Newton Telescope Library of Empirical Spectra (MILES) spectra, ELODIE spectra and the spectra of member stars of galactic globular clusters, we conclude that GPR can derive stellar parameters accurately and precisely, especially when we use data preprocessed with principal component analysis (PCA). We then compare the performance of GPR with that of several widely used regression methods (ANNs, support-vector regression and KR) and find that with GPR it is easier to optimize structures and parameters and more efficient and accurate to extract atmospheric parameters.
GAUSSIAN RANDOM FIELD: PHYSICAL ORIGIN OF SERSIC PROFILES
International Nuclear Information System (INIS)
Cen, Renyue
2014-01-01
While the Sersic profile family provides adequate fits for the surface brightness profiles of observed galaxies, its physical origin is unknown. We show that if the cosmological density field is seeded by random Gaussian fluctuations, as in the standard cold dark matter model, galaxies with steep central profiles have simultaneously extended envelopes of shallow profiles in the outskirts, whereas galaxies with shallow central profiles are accompanied by steep density profiles in the outskirts. These properties are in accord with those of the Sersic profile family. Moreover, galaxies with steep central profiles form their central regions in smaller denser subunits that possibly merge subsequently, which naturally leads to the formation of bulges. In contrast, galaxies with shallow central profiles form their central regions in a coherent fashion without significant substructure, a necessary condition for disk galaxy formation. Thus, the scenario is self-consistent with respect to the correlation between observed galaxy morphology and the Sersic index. We further predict that clusters of galaxies should display a similar trend, which should be verifiable observationally
Gaussian graphical modeling reveals specific lipid correlations in glioblastoma cells
Mueller, Nikola S.; Krumsiek, Jan; Theis, Fabian J.; Böhm, Christian; Meyer-Bäse, Anke
2011-06-01
Advances in high-throughput measurements of biological specimens necessitate the development of biologically driven computational techniques. To understand the molecular level of many human diseases, such as cancer, lipid quantifications have been shown to offer an excellent opportunity to reveal disease-specific regulations. The data analysis of the cell lipidome, however, remains a challenging task and cannot be accomplished solely based on intuitive reasoning. We have developed a method to identify a lipid correlation network which is entirely disease-specific. A powerful method to correlate experimentally measured lipid levels across the various samples is a Gaussian Graphical Model (GGM), which is based on partial correlation coefficients. In contrast to regular Pearson correlations, partial correlations aim to identify only direct correlations while eliminating indirect associations. Conventional GGM calculations on the entire dataset can, however, not provide information on whether a correlation is truly disease-specific with respect to the disease samples and not a correlation of control samples. Thus, we implemented a novel differential GGM approach unraveling only the disease-specific correlations, and applied it to the lipidome of immortal Glioblastoma tumor cells. A large set of lipid species were measured by mass spectrometry in order to evaluate lipid remodeling as a result to a combination of perturbation of cells inducing programmed cell death, while the other perturbations served solely as biological controls. With the differential GGM, we were able to reveal Glioblastoma-specific lipid correlations to advance biomedical research on novel gene therapies.
Processing tree point clouds using Gaussian Mixture Models
Directory of Open Access Journals (Sweden)
D. Belton
2013-10-01
Full Text Available While traditionally used for surveying and photogrammetric fields, laser scanning is increasingly being used for a wider range of more general applications. In addition to the issues typically associated with processing point data, such applications raise a number of new complications, such as the complexity of the scenes scanned, along with the sheer volume of data. Consequently, automated procedures are required for processing, and analysing such data. This paper introduces a method for modelling multi-modal, geometrically complex objects in terrestrial laser scanning point data; specifically, the modelling of trees. The model method comprises a number of geometric features in conjunction with a multi-modal machine learning technique. The model can then be used for contextually dependent region growing through separating the tree into its component part at the point level. Subsequently object analysis can be performed, for example, performing volumetric analysis of a tree by removing points associated with leaves. The workflow for this process is as follows: isolate individual trees within the scanned scene, train a Gaussian mixture model (GMM, separate clusters within the mixture model according to exemplar points determined by the GMM, grow the structure of the tree, and then perform volumetric analysis on the structure.
Non-Gaussianity from Self-Ordering Scalar Fields
Figueroa, Daniel G; Kamionkowski, Marc
2010-01-01
The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges $k_1\\simeq 2 k_2 \\simeq 2 k_3$) as opposed to the local-model bispectrum, which peaks for squeezed triangles ($k_1\\simeq k_2 \\gg k_3$), and the equilateral bispectrum, which peaks at $k_1\\simeq k_2 \\simeq k_3$. We estimate that this non-...
EDPUFF- a Gaussian dispersion code for consequence analysis
International Nuclear Information System (INIS)
Oza, R.B.; Bapat, V.N.; Nair, R.N.; Hukkoo, R.K.; Krishnamoorthy, T.M.
1995-01-01
EDPUFF- Equi Distance Puff is a Gaussian dispersion code in FORTRAN language to model atmospheric dispersion of instantaneous or continuous point source releases. It is designed to incorporate the effect of changing meteorological conditions and source release rates on the spatial distribution profiles and its consequences. Effects of variation of parameters like puff spacing, puff packing, averaging schemes are discussed and the choice of the best values for minimum errors and minimum computer CPU time are identified. The code calculates the doses to individual receptors as well as average doses for population zones from internal and external routes over the area of interest. Internal dose computations are made for inhalation and ingestion pathways while the doses from external route consists of cloud doses and doses from surface deposited activity. It computes inhalation and ingestion dose (milk route only) for critical group (1 yr old child). In case of population zones it finds out maximum possible doses in a given area along with the average doses discussed above. Report gives the doses from various pathways for unit release of fixed duration. (author). 7 refs., figs., 7 appendixes
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
Ade, P.A.R.; Arnaud, M.; Arroja, F.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; De Rosa, A.; De Zotti, G.; Delabrouille, J.; Désert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Ghosh, T.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hamann, J.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Heavens, A.; Helou, G.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kim, J.; Kisner, T.S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lacasa, F.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Marinucci, D.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Münchmeyer, M.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Racine, B.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Shiraishi, M.; Smith, K.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutter, P.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Troja, A.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; van Tent, B.; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.; Zonca, A.
2016-01-01
The Planck full mission cosmic microwave background(CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity(NG). Using three classes of optimal bispectrum estimators - separable template-fitting (KSW), binned, and modal - we obtain consistent values for the local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone fNL^local=2.5+\\-5.7, fNL^equil=-16+\\-70 and fNL^ortho=-34+\\-33(68%CL). Combining temperature and polarization data we obtain fNL^local=0.8+\\-5.0, fNL^equil=-4+\\-43 and fNL^ortho=-26+\\-21 (68%CL). The results are based on cross-validation of these estimators on simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with Minkowski functionals based measurements. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization da...
Multistep Wind Speed Forecasting Based on Wavelet and Gaussian Processes
Directory of Open Access Journals (Sweden)
Niya Chen
2013-01-01
Full Text Available Accurate wind speed forecasts are necessary for the safety and economy of the renewable energy utilization. The wind speed forecasts can be obtained by statistical model based on historical data. In this paper, a novel W-GP model (wavelet decomposition based Gaussian process learning paradigm is proposed for short-term wind speed forecasting. The nonstationary and nonlinear original wind speed series is first decomposed into a set of better-behaved constitutive subseries by wavelet decomposition. Then these sub-series are forecasted respectively by GP method, and the forecast results are summed to formulate an ensemble forecast for original wind speed series. Therefore, the previous process which obtains wind speed forecast result is named W-GP model. Finally, the proposed model is applied to short-term forecasting of the mean hourly and daily wind speed for a wind farm located in southern China. The prediction results indicate that the proposed W-GP model, which achieves a mean 13.34% improvement in RMSE (Root Mean Square Error compared to persistence method for mean hourly data and a mean 7.71% improvement for mean daily wind speed data, shows the best forecasting accuracy among several forecasting models.
Computed tomography perfusion imaging denoising using Gaussian process regression
International Nuclear Information System (INIS)
Zhu Fan; Gonzalez, David Rodriguez; Atkinson, Malcolm; Carpenter, Trevor; Wardlaw, Joanna
2012-01-01
Brain perfusion weighted images acquired using dynamic contrast studies have an important clinical role in acute stroke diagnosis and treatment decisions. However, computed tomography (CT) images suffer from low contrast-to-noise ratios (CNR) as a consequence of the limitation of the exposure to radiation of the patient. As a consequence, the developments of methods for improving the CNR are valuable. The majority of existing approaches for denoising CT images are optimized for 3D (spatial) information, including spatial decimation (spatially weighted mean filters) and techniques based on wavelet and curvelet transforms. However, perfusion imaging data is 4D as it also contains temporal information. Our approach using Gaussian process regression (GPR), which takes advantage of the temporal information, to reduce the noise level. Over the entire image, GPR gains a 99% CNR improvement over the raw images and also improves the quality of haemodynamic maps allowing a better identification of edges and detailed information. At the level of individual voxel, GPR provides a stable baseline, helps us to identify key parameters from tissue time-concentration curves and reduces the oscillations in the curve. GPR is superior to the comparable techniques used in this study. (note)
ESTIMASI NILAI CONDITIONAL VALUE AT RISK MENGGUNAKAN FUNGSI GAUSSIAN COPULA
Directory of Open Access Journals (Sweden)
HERLINA HIDAYATI
2015-11-01
Full Text Available Copula is already widely used in financial assets, especially in risk management. It is due to the ability of copula, to capture the nonlinear dependence structure on multivariate assets. In addition, using copula function doesn’t require the assumption of normal distribution. There fore it is suitable to be applied to financial data. To manage a risk the necessary measurement tools can help mitigate the risks. One measure that can be used to measure risk is Value at Risk (VaR. Although VaR is very popular, it has several weaknesses. To overcome the weakness in VaR, an alternative risk measure called CVaR can be used. The porpose of this study is to estimate CVaR using Gaussian copula. The data we used are the closing price of Facebook and Twitter stocks. The results from the calculation using 90% confidence level showed that the risk that may be experienced is at 4,7%, for 95% confidence level it is at 6,1%, and for 99% confidence level it is at 10,6%.
Confronting passive and active sensors with non-Gaussian statistics.
Rodríguez-Gonzálvez, Pablo; Garcia-Gago, Jesús; Gomez-Lahoz, Javier; González-Aguilera, Diego
2014-07-30
This paper has two motivations: firstly, to compare the Digital Surface Models (DSM) derived by passive (digital camera) and by active (terrestrial laser scanner) remote sensing systems when applied to specific architectural objects, and secondly, to test how well the Gaussian classic statistics, with its Least Squares principle, adapts to data sets where asymmetrical gross errors may appear and whether this approach should be changed for a non-parametric one. The field of geomatic technology automation is immersed in a high demanding competition in which any innovation by one of the contenders immediately challenges the opponents to propose a better improvement. Nowadays, we seem to be witnessing an improvement of terrestrial photogrammetry and its integration with computer vision to overcome the performance limitations of laser scanning methods. Through this contribution some of the issues of this "technological race" are examined from the point of view of photogrammetry. A new software is introduced and an experimental test is designed, performed and assessed to try to cast some light on this thrilling match. For the case considered in this study, the results show good agreement between both sensors, despite considerable asymmetry. This asymmetry suggests that the standard Normal parameters are not adequate to assess this type of data, especially when accuracy is of importance. In this case, standard deviation fails to provide a good estimation of the results, whereas the results obtained for the Median Absolute Deviation and for the Biweight Midvariance are more appropriate measures.
Bayesian site selection for fast Gaussian process regression
Pourhabib, Arash
2014-02-05
Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.
Mutual information of optical communication in phase-conjugating Gaussian channels
Schäfermeier, Clemens; Andersen, Ulrik L.
2018-03-01
In all practical communication channels, the code word consists of Gaussian states and the measurement strategy is often a Gaussian detector such as homodyning or heterodyning. We investigate the communication performance using a phase-conjugated alphabet and joint Gaussian detection in a phase-insensitive amplifying channel. We find that a communication scheme consisting of a phase-conjugating alphabet of coherent states and a joint detection strategy significantly outperforms a standard coherent-state strategy based in individual detection. Moreover, we show that the performance can be further enhanced by using entanglement and that the performance is completely independent of the gain of the phase-insensitively amplifying channel.
Directory of Open Access Journals (Sweden)
Chao Gao
2016-01-01
Full Text Available This paper investigates the modulation transfer function of a Gaussian beam propagating through a horizontal path in weak-fluctuation non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized modified atmospheric spectrum, which includes the spectral power law value of non-Kolmogorov turbulence, the finite inner and outer scales of turbulence, and other optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the inner scale of turbulence. Additionally, the increased outer scale of turbulence makes a Gaussian beam influenced more seriously by the atmospheric turbulence.
Extension of filament propagation in water with Bessel-Gaussian beams
International Nuclear Information System (INIS)
Kaya, G.; Sayrac, M.; Boran, Y.; Kolomenskii, A. A.; Kaya, N.; Schuessler, H. A.; Strohaber, J.; Amani, M.
2016-01-01
We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.
International Nuclear Information System (INIS)
Schlegel, H.B.; Binkley, J.S.; Pople, J.A.
1984-01-01
Formulas are developed for the first and second derivatives of two electron integrals over Cartesian Gaussians. Integrals and integral derivatives are evaluated by the Rys polynomial method. Higher angular momentum functions are not used to calculate the integral derivatives; instead the integral formulas are differentiated directly to produce compact and efficient expressions for the integral derivatives. The use of this algorithm in the ab initio molecular orbital programs gaussIan 80 and gaussIan 82 is discussed. Representative timings for some small molecules with several basis sets are presented. This method is compared with previously published algorithms and its computational merits are discussed
Using Gaussian Processes to Construct Flexible Models of Stellar Spectra
Czekala, Ian
2018-01-01
The use of spectra is fundamental to astrophysical fields ranging from exoplanets to stars to galaxies. In spite of this ubiquity, or perhaps because of it, there are a plethora of use cases that do not yet have physics-based forward models that can fit high signal-to-noise data to within the observational noise. These inadequacies result in subtle but systematic residuals not captured by any model, which complicates and biases parameter inference. Fortunately, the now-prevalent collection and archiving of large spectral datasets also provides an opening for empirical, data-driven approaches. We introduce one example of a time-series dataset of high-resolution stellar spectra, as is commonly delivered by planet-search radial velocity instruments like TRES, HIRES, and HARPS. Measurements of radial velocity variations of stars and their companions are essential for stellar and exoplanetary study; these measurements provide access to the fundamental physical properties that dictate all phases of stellar evolution and facilitate the quantitative study of planetary systems. In observations of a (spatially unresolved) spectroscopic binary star, one only ever records the composite sum of the spectra from the primary and secondary stars, complicating photospheric analysis of each individual star. Our technique “disentangles” the composite spectra by treating each underlying stellar spectrum as a Gaussian process, whose posterior predictive distribution is inferred simultaneously with the orbital parameters. To demonstrate the potential of this technique, we deploy it on red-optical time-series spectra of the mid-M-dwarf eclipsing binary LP661-13, which was recently discovered by the MEarth project. We successfully reconstruct the primary and secondary stellar spectra and report orbital parameters with improved precision compared to traditional radial velocity analysis techniques.
Cosmological tests with strong gravitational lenses using Gaussian processes
Yennapureddy, Manoj K.; Melia, Fulvio
2018-03-01
Strong gravitational lenses provide source/lens distance ratios D_{obs} useful in cosmological tests. Previously, a catalog of 69 such systems was used in a one-on-one comparison between the standard model, Λ CDM, and the Rh=ct universe, which has thus far been favored by the application of model selection tools to many other kinds of data. But in that work, the use of model parametric fits to the observations could not easily distinguish between these two cosmologies, in part due to the limited measurement precision. Here, we instead use recently developed methods based on Gaussian Processes (GP), in which D_{obs} may be reconstructed directly from the data without assuming any parametric form. This approach not only smooths out the reconstructed function representing the data, but also reduces the size of the 1σ confidence regions, thereby providing greater power to discern between different models. With the current sample size, we show that analyzing strong lenses with a GP approach can definitely improve the model comparisons, producing probability differences in the range ˜ 10-30%. These results are still marginal, however, given the relatively small sample. Nonetheless, we conclude that the probability of Rh=ct being the correct cosmology is somewhat higher than that of Λ CDM, with a degree of significance that grows with the number of sources in the subsamples we consider. Future surveys will significantly grow the catalog of strong lenses and will therefore benefit considerably from the GP method we describe here. In addition, we point out that if the Rh=ct universe is eventually shown to be the correct cosmology, the lack of free parameters in the study of strong lenses should provide a remarkably powerful tool for uncovering the mass structure in lensing galaxies.
Dynamics of generalized Gaussian polymeric structures in random layered flows.
Katyal, Divya; Kant, Rama
2015-04-01
We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α. Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α, the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.
Global adiabaticity and non-Gaussianity consistency condition
Directory of Open Access Journals (Sweden)
Antonio Enea Romano
2016-10-01
Full Text Available In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, Rc, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of Rc holds only after the perturbation has reached the adiabatic limit where the constant mode of Rc dominates over the other (usually decaying mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, δPnad≡δP−cw2δρ where cw2=P˙/ρ˙, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of Rc on super-horizon scales. In this paper, we consider models that satisfy δPnad=0 on all scales, which we call global adiabaticity (GA, which is guaranteed if cw2=cs2, where cs is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll (USR inflation in which cw2=cs2=1. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with cw2=cs2, which allows Rc to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.
Vegetation Monitoring with Gaussian Processes and Latent Force Models
Camps-Valls, Gustau; Svendsen, Daniel; Martino, Luca; Campos, Manuel; Luengo, David
2017-04-01
Monitoring vegetation by biophysical parameter retrieval from Earth observation data is a challenging problem, where machine learning is currently a key player. Neural networks, kernel methods, and Gaussian Process (GP) regression have excelled in parameter retrieval tasks at both local and global scales. GP regression is based on solid Bayesian statistics, yield efficient and accurate parameter estimates, and provides interesting advantages over competing machine learning approaches such as confidence intervals. However, GP models are hampered by lack of interpretability, that prevented the widespread adoption by a larger community. In this presentation we will summarize some of our latest developments to address this issue. We will review the main characteristics of GPs and their advantages in vegetation monitoring standard applications. Then, three advanced GP models will be introduced. First, we will derive sensitivity maps for the GP predictive function that allows us to obtain feature ranking from the model and to assess the influence of examples in the solution. Second, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated radiative transfer data in a single GP model. The JGP regression provides more sensible confidence intervals for the predictions, respects the physics of the underlying processes, and allows for transferability across time and space. Finally, a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system is presented. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Empirical evidence of the performance of these models will be presented through illustrative examples.
Investigation of non-Gaussian effects in the Brazilian option market
Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.
2018-04-01
An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.
Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States
Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas
2017-11-01
Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.
Binary naive Bayesian classifiers for correlated Gaussian features: a theoretical analysis
CSIR Research Space (South Africa)
Van Dyk, E
2008-11-01
Full Text Available We investigate the use of Naive Bayesian classifiers for correlated Gaussian feature spaces and derive error estimates for these classifiers. The error analysis is done by developing an exact expression for the error performance of a binary...
Kozachenko, Yuriy; Troshki, Viktor
2015-01-01
We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\\mathbb {T}),\\,p\\geq1$, is constructed.
CSIR Research Space (South Africa)
Kok, S
2012-07-01
Full Text Available This study reports on the asymptotic behavior of the maximum likelihood function, encountered when constructing Kriging approximations using the Gaussian correlation function. Of specific interest is a maximum likelihood function that decreases...
Bootstrapping realized volatility and realized beta under a local Gaussianity assumption
DEFF Research Database (Denmark)
Hounyo, Ulrich
The main contribution of this paper is to propose a new bootstrap method for statistics based on high frequency returns. The new method exploits the local Gaussianity and the local constancy of volatility of high frequency returns, two assumptions that can simplify inference in the high frequency...... context, as recently explained by Mykland and Zhang (2009). Our main contributions are as follows. First, we show that the local Gaussian bootstrap is firstorder consistent when used to estimate the distributions of realized volatility and ealized betas. Second, we show that the local Gaussian bootstrap...... matches accurately the first four cumulants of realized volatility, implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able...
Microwave heating of the ceramic materials by the Gaussian laser beam
International Nuclear Information System (INIS)
Rajaei, L.; Shokri, B.
2010-01-01
Complete text of publication follows. The ceramic which has a complex permittivity can absorb electromagnetic energy easily and be heated quickly. In this work, the heating of a ceramic cylinder by the Gaussian electromagnetic beam in two dimensions is investigated and the heat equation is solved. It is shown that this electromagnetic beam with Gaussian profile can heat ceramic sample better than the plane electromagnetic wave. Moreover, the effects of some important physical factors such as the permittivity of ceramic, the incident wave intensity and the spot size of the Gaussian beam on the heat transfer within the sample are studied. Also, comparing the effect of Gaussian electromagnetic beam on ceramics Al 2 O 3 and, it is shown that Al 2 O 3 ceramic is heated more intensively than ZnO ceramic.
Reconstruction of electrons with the Gaussian-Sum filter in the ATLAS inner detector
Atkinson, T
2006-01-01
The ATLAS detector's ability to reconstruct and identify electrons with high precision is critical both for the calibration of the detector and for the analysis of many physics processes. High energy electrons traversing matter loose energy predominantly by bremsstrahlung. A well known model for bremsstrahlung is the Bethe- Heitler distribution, which is highly non-Gaussian. Linear fitters, such as the Kaiman filter (KF), model energy losses as Gaussian distributions and thus are not optimal for the reconstruction of electrons. The Gaussian-Sum filter (GSF) is a non-linear generalisation of the KF. This algorithm has been implemented for the reconstruction of electrons within ATLAS. The GSF models the Bethe- Heitler distribution by a weighted sum of Gaussian distributions. A comparison between the reconstruction performance of the GSF and the KF is presented using simulated events generated using the geometry of the 2004 ATLAS test-beam.
NLOS mitigation in indoor localization by marginalized Monte Carlo Gaussian smoothing
Vilà-Valls, Jordi; Closas, Pau
2017-12-01
One of the main challenges in indoor time-of-arrival (TOA)-based wireless localization systems is to mitigate non-line-of-sight (NLOS) propagation conditions, which degrade the overall positioning performance. The positive skewed non-Gaussian nature of TOA observations under LOS/NLOS conditions can be modeled as a heavy-tailed skew t-distributed measurement noise. The main goal of this article is to provide a robust Bayesian inference framework to deal with target localization under NLOS conditions. A key point is to take advantage of the conditionally Gaussian formulation of the skew t-distribution, thus being able to use computationally light Gaussian filtering and smoothing methods as the core of the new approach. The unknown non-Gaussian noise latent variables are marginalized using Monte Carlo sampling. Numerical results are provided to show the performance improvement of the proposed approach.
Dynamic generation of Ince-Gaussian modes with a digital micromirror device
Energy Technology Data Exchange (ETDEWEB)
Ren, Yu-Xuan, E-mail: yxren@ustc.edu.cn [National Center for Protein Sciences Shanghai, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Shanghai 200031 (China); Fang, Zhao-Xiang; Chen, Yue; Lu, Rong-De, E-mail: lrd@ustc.edu.cn [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Gong, Lei [Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei 230026 (China); Huang, Kun [Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576 (Singapore)
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.
SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS
National Aeronautics and Space Administration — SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS GOO JUN * AND JOYDEEP GHOSH* Abstract. A semi-supervised learning...
A Novel Method for Generating Non-Stationary Gaussian Processes for Use in Digital Radar Simulators
National Research Council Canada - National Science Library
Boehm, James A; Debroux, Patrick S
2007-01-01
This report presents a novel and simple way to determine the transient response of the output of any linear system, described in the s-domain by an nth order polynomial, subjected to white Gaussian noise...
Khan, Tariq Mahmood; Bailey, Donald G; Khan, Mohammad A U; Kong, Yinan
2017-05-01
A real-time image filtering technique is proposed which could result in faster implementation for fingerprint image enhancement. One major hurdle associated with fingerprint filtering techniques is the expensive nature of their hardware implementations. To circumvent this, a modified anisotropic Gaussian filter is efficiently adopted in hardware by decomposing the filter into two orthogonal Gaussians and an oriented line Gaussian. An architecture is developed for dynamically controlling the orientation of the line Gaussian filter. To further improve the performance of the filter, the input image is homogenized by a local image normalization. In the proposed structure, for a middle-range reconfigurable FPGA, both parallel compute-intensive and real-time demands were achieved. We manage to efficiently speed up the image-processing time and improve the resource utilization of the FPGA. Test results show an improved speed for its hardware architecture while maintaining reasonable enhancement benchmarks.
Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In the given article mean intensity of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is studied. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian beam of optical radiation. Distributions of mean intensity of a fundamental Bessel- Gaussian beam optical beam in longitudinal and transverse to a direction of propagation of optical radiation are investigated in detail. Influence of atmospheric turbulence on change of radius of the central part of a Bessel optical beam is estimated. Values of parameters at which it is possible to generate in turbulent atmosphere a nondiffracting pseudo-Bessel optical beam by means of a fundamental Bessel-Gaussian optical beam are established.
The Use of Spectral Method for Fatigue Life Assessment for Non-Gaussian Random Loads
Directory of Open Access Journals (Sweden)
Niesłony Adam
2016-06-01
Full Text Available The well-known problem with the fatigue lifetime assessment of non-Gaussian loading signals with the use of spectral method has been presented in the paper. A correction factors that transform the non-Gaussian signal into an equivalent Gaussian signal proposed by Bracessi et al. (2009 has been used for the purpose of lifetime calculations together with Palmgren-Miner Hypothesis. The calculations have been performed for the 10HNAP steel under random non-Gaussian load with four dominating frequencies. The signal has been generated on the test stand SHM250 for random tension-compression tests. The results with zero and non-zero mean stresses have been used to calculate the fatigue life with the frequency domain method based on Dirlik’s model and with a time domain method with the use of the rainflow cycle counting algorithm. The obtained calculation results have been compared with experimental results.