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Relevant bibliographies by topics / Gaussian correlation

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Academic literature on the topic 'Gaussian correlation'

Author: Grafiati

Published: 6 September 2023

Last updated: 7 September 2023

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Journal articles on the topic "Gaussian correlation"

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Vitale, Richard A. "Majorization and Gaussian correlation." Statistics & Probability Letters 45, no. 3 (November 1999): 247–51. http://dx.doi.org/10.1016/s0167-7152(99)00064-4.

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Liu, Liang, Jinchuan Hou, and Xiaofei Qi. "Quantum Correlation Based on Uhlmann Fidelity for Gaussian States." Entropy 21, no. 1 (December 22, 2018): 6. http://dx.doi.org/10.3390/e21010006.

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A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states.

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Nourdin, Ivan, and Fei Pu. "Gaussian fluctuation for Gaussian Wishart matrices of overall correlation." Statistics & Probability Letters 181 (February 2022): 109269. http://dx.doi.org/10.1016/j.spl.2021.109269.

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Liu, Liang, Jinchuan Hou, and Xiaofei Qi. "A Computable Gaussian Quantum Correlation for Continuous-Variable Systems." Entropy 23, no. 9 (September 9, 2021): 1190. http://dx.doi.org/10.3390/e23091190.

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Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

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Liu, Liang, Xiaofei Qi, and Jinchuan Hou. "Fidelity-based unitary operation-induced quantum correlation for continuous-variable systems." International Journal of Quantum Information 17, no. 04 (June 2019): 1950035. http://dx.doi.org/10.1142/s0219749919500357.

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We propose a measure of nonclassical correlation [Formula: see text] in terms of local Gaussian unitary operations based on square of the fidelity [Formula: see text] for bipartite continuous-variable systems. This quantity is easier to be calculated or estimated and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of [Formula: see text] for any [Formula: see text]-mode Gaussian states is presented and an estimation of [Formula: see text] for any [Formula: see text]-mode Gaussian states is given. For any [Formula: see text]-mode Gaussian states, [Formula: see text] does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing [Formula: see text] in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that [Formula: see text] is much better in detecting quantum correlations of Gaussian states.

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Xiao, M. Y., and H. P. Hong. "Unconditional and conditional simulation of nonstationary and non-Gaussian vector and field with prescribed marginal and correlation by using iteratively matched correlation." Disaster Prevention and Resilience 1, no. 1 (2022): 5. http://dx.doi.org/10.20517/dpr.2022.01.

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In many probabilistic analysis problems, the homogeneous/nonhomogeneous non-Gaussian field is represented as a mapped Gaussian field based on the Nataf translation system. We propose a new sample-based iterative procedure to estimate the underlying Gaussian correlation for homogeneous/nonhomogeneous non-Gaussian vector or field. The numerical procedure takes advantage that the range of feasible correlation coefficients for non-Gaussian random variables is bounded if the translation system is adopted. The estimated underlying Gaussian correlation is then employed for unconditional as well as conditional simulation of the non-Gaussian vector or field according to the theory of the translation process. We then present the steps for augmenting the simulated non-Gaussian field through the Karhunen-Loeve expansion for a refined discretized grid of the field. In addition, the steps to extend the procedure described in the previous section to the multi-dimensional field are highlighted. The application of the proposed algorithms is presented through numerical examples.

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Elliott, Peter, and Neepa T. Maitra. "Electron correlation via frozen Gaussian dynamics." Journal of Chemical Physics 135, no. 10 (September 14, 2011): 104110. http://dx.doi.org/10.1063/1.3630134.

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Fyfe, Colin, Gayle Leen, and Pei Ling Lai. "Gaussian processes for canonical correlation analysis." Neurocomputing 71, no. 16-18 (October 2008): 3077–88. http://dx.doi.org/10.1016/j.neucom.2008.04.037.

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Casasent, David, Gopalan Ravichandran, and Srinivas Bollapragada. "Gaussian–minimum average correlation energy filters." Applied Optics 30, no. 35 (December 10, 1991): 5176. http://dx.doi.org/10.1364/ao.30.005176.

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Liu, Youming, and Chunguang Ren. "Estimation of canonical correlation directions: From Gaussian to sub-Gaussian population." Journal of Multivariate Analysis 186 (November 2021): 104795. http://dx.doi.org/10.1016/j.jmva.2021.104795.

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Dissertations / Theses on the topic "Gaussian correlation"

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Hamdi, Walaa Ahmed. "Local Distance Correlation: An Extension of Local Gaussian Correlation." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1589239468129597.

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Ofosuhene, Patrick. "The energy goodness-of-fit test for the inverse Gaussian distribution." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1605273458669328.

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Mackenzie, Mark. "Correlation with the hermite series using artificial neural network technology." Access electronically, 2004. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20050202.122218/index.html.

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Roininen, L. (Lassi). "Discretisation-invariant and computationally efficient correlation priors for Bayesian inversion." Doctoral thesis, University of Oulu, 2015. http://urn.fi/urn:isbn:9789526207544.

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Abstract We are interested in studying Gaussian Markov random fields as correlation priors for Bayesian inversion. We construct the correlation priors to be discretisation-invariant, which means, loosely speaking, that the discrete priors converge to continuous priors at the discretisation limit. We construct the priors with stochastic partial differential equations, which guarantees computational efficiency via sparse matrix approximations. The stationary correlation priors have a clear statistical interpretation through the autocorrelation function. We also consider how to make structural model of an unknown object with anisotropic and inhomogeneous Gaussian Markov random fields. Finally we consider these fields on unstructured meshes, which are needed on complex domains. The publications in this thesis contain fundamental mathematical and computational results of correlation priors. We have considered one application in this thesis, the electrical impedance tomography. These fundamental results and application provide a platform for engineers and researchers to use correlation priors in other inverse problem applications.

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Prascher, Brian P. Wilson Angela K. "Systematic approaches to predictive computational chemistry using the correlation consistent basis sets." [Denton, Tex.] : University of North Texas, 2009. http://digital.library.unt.edu/permalink/meta-dc-9920.

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Angelchev, Shiryaev Artem, and Johan Karlsson. "Estimating Dependence Structures with Gaussian Graphical Models : A Simulation Study in R." Thesis, Umeå universitet, Statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-184925.

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Graphical models are powerful tools when estimating complex dependence structures among large sets of data. This thesis restricts the scope to undirected Gaussian graphical models. An initial predefined sparse precision matrix was specified to generate multivariate normally distributed data. Utilizing the generated data, a simulation study was conducted reviewing accuracy, sensitivity and specificity of the estimated precision matrix. The graphical LASSO was applied using four different packages available in R with seven selection criteria's for estimating the tuning parameter. The findings are mostly in line with previous research. The graphical LASSO is generally faster and feasible in high dimensions, in contrast to stepwise model selection. A portion of the selection methods for estimating the optimal tuning parameter obtained the true network structure. The results provide an estimate of how well each model obtains the true, predefined dependence structure as featured in our simulation. As the simulated data used in this thesis is merely an approximation of real-world data, one should not take the results as the only aspect of consideration when choosing a model.

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Tamburello, Philip Michael. "Iterative Memoryless Non-linear Estimators of Correlation for Complex-Valued Gaussian Processes that Exhibit Robustness to Impulsive Noise." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/64785.

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The autocorrelation function is a commonly used tool in statistical time series analysis. Under the assumption of Gaussianity, the sample autocorrelation function is the standard method used to estimate this function given a finite number of observations. Non-Gaussian, impulsive observation noise following probability density functions with thick tails, which often occurs in practice, can bias this estimator, rendering classical time series analysis methods ineffective. This work examines the robustness of two estimators of correlation based on memoryless nonlinear functions of observations, the Phase-Phase Correlator (PPC) and the Median- of-Ratios Estimator (MRE), which are applicable to complex-valued Gaussian random pro- cesses. These estimators are very fast and easy to implement in current processors. We show that these estimators are robust from a bias perspective when complex-valued Gaussian pro- cesses are contaminated with impulsive noise at the expense of statistical efficiency at the assumed Gaussian distribution. Additionally, iterative versions of these estimators named the IMRE and IPPC are developed, realizing an improved bias performance over their non- iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). An impulsive noise suppression technique is developed using basis pursuit and a priori atom weighting derived from the newly developed iterative estimators. This new technique is proposed as an alternative to the robust filter cleaner, a Kalman filter-like approach that relies on linear prediction residuals to identity and replace corrupted observations. It does not have the same initialization issues as the robust filter cleaner. Robust spectral estimation methods are developed using these new estimators and impulsive noise suppression techniques. Results are obtained for synthetic complex-valued Guassian processes and real-world digital television signals collected using a software defined radio.
Ph. D.

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Yockel, Scott. "The evaluation, development, and application of the correlation consistent basis sets." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5484/.

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Employing correlation consistent basis sets coupled with electronic structure methods has enabled accurate predictions of chemical properties for second- and third-row main group and transition metal molecular species. For third-row (Ga-Kr) molecules, the performance of the correlation consistent basis sets (cc-pVnZ, n=D, T, Q, 5) for computing energetic (e.g., atomization energies, ionization energies, electron and proton affinities) and structural properties using the ab initio coupled cluster method including single, double, and quasiperturbative triple excitations [CCSD(T)] and the B3LYP density functional method was examined. The impact of relativistic corrections on these molecular properties was determined utilizing the Douglas-Kroll (cc-pVnZ-DK) and pseudopotential (cc-pVnZ-PP) forms of the correlation consistent basis sets. This work was extended to the characterization of molecular properties of novel chemically bonded krypton species, including HKrCl, FKrCF3, FKrSiF3, FKrGeF3, FKrCCF, and FKrCCKrF, and provided the first evidence of krypton bonding to germanium and the first di-krypton system. For second-row (Al-Ar) species, the construction of the core-valence correlation consistent basis sets, cc-pCVnZ was reexamined, and a revised series, cc-pCV(n+d)Z, was developed as a complement to the augmented tight-d valence series, cc-pV(n+d)Z. Benchmark calculations were performed to show the utility of these new sets for second-row species. Finally, the correlation consistent basis sets were used to study the structural and spectroscopic properties of Au(CO)Cl, providing conclusive evidence that luminescence in the solid-state can be attributed to oligomeric species rather than to the monomer.

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Mukhopadhyay, Amit Kumar. "Statistics for motion of microparticles in a plasma." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1369.

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I report experimental and numerical studies of microparticle motion in a dusty plasma. These microparticles are negatively charged and are levitated in a plasma consisting of electrons, ions and neutral gas atoms. The microparticles repel each other, and are confined by the electric fields in the plasma. The neutral gas damps the microparticle motion, and also exerts random forces on them. I investigate and characterize microparticle motion. In order to do this, I study velocity distributions of microparticles and correlations of their motion. To perform such a study, I develop new experimental and analysis techniques. My thesis consists of four separate projects. In the first project, the battle between deterministic and random motion of microparticles is investigated. Two particle velocity distributions and correlations have previously studied only in theory. I performed an experiment with a very simple one dimensional (1D) system of two microparticles in a plasma. My study of velocity correlations involves just two microparticles which is the simplest system that allows interactions. A study of such a simple system provides insight into the motions of the microparticles. It allowed for the experimental measurement of two-particle distributions and correlations. For such a system, it is shown that the motion of the microparticles is dominated by deterministic or oscillatory effects. In the second project, two experiments with just two microparticles are performed to isolate the effects of ion wakes. The two experiments differ in the alignment of the two microparticles: they are aligned either perpendicular or parallel to the ion flow. To have different alignments, the sheath is shaped differently in the two experiments. I demonstrate that microparticle motion is more correlated when they are aligned along the ion flow, rather than perpendicular to the ion flow. In the third project, I develop a model with some key assumptions to compare with the experiments in the first two projects. My model includes all significant forces: gravity, electrical forces due to curved sheath and interparticle interaction, and gas forces. The model does not agree with both the experiments. In the last project, I study the non-Gaussian statistics by analyzing data for microparticle motion from an experiment performed under microgranity conditions. Microparticle motion is studied in a very thin region of microparticles in a three dimensional dust cloud. The microparticle velocity distributions exhibit non-Gaussian characteristics.

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Han, Gang. "Modeling the output from computer experiments having quantitative and qualitative input variables and its applications." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1228326460.

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Books on the topic "Gaussian correlation"

1

Bogomolny, E. B. Random matrix theory and the Riemann zeros II: N-point correlations. Bristol [England]: Hewlett Packard, 1996.

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Electron Correlation in Molecules – ab initio Beyond Gaussian Quantum Chemistry. Elsevier, 2016. http://dx.doi.org/10.1016/s0065-3276(16)x0002-0.

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Electron Correlation in Molecules - Ab Initio Beyond Gaussian Quantum Chemistry. Elsevier Science & Technology Books, 2016.

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Hoggan, Philip E., and Telhat Ozdogan. Electron Correlation in Molecules - Ab Initio Beyond Gaussian Quantum Chemistry. Elsevier Science & Technology, 2016.

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Khoruzhenko, Boris, and Hans-Jurgen Sommers. Characteristic polynomials. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.19.

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This article considers characteristic polynomials and reviews a few useful results obtained in simple Gaussian models of random Hermitian matrices in the presence of an external matrix source. It first considers the products and ratio of characteristic polynomials before discussing the duality theorems for two different characteristic polynomials of Gaussian weights with external sources. It then describes the m-point correlation functions of the eigenvalues in the Gaussian unitary ensemble and how they are deduced from their Fourier transforms U(s1, … , sm). It also analyses the relation of the correlation function of the characteristic polynomials to the standard n-point correlation function using the replica and supersymmetric methods. Finally, it shows how the topological invariants of Riemann surfaces, such as the intersection numbers of the moduli space of curves, may be derived from averaged characteristic polynomials.

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Borodin, Alexei. Random matrix representations of critical statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.12.

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This article examines two random matrix ensembles that are useful for describing critical spectral statistics in systems with multifractal eigenfunction statistics: the Gaussian non-invariant ensemble and the invariant random matrix ensemble. It first provides an overview of non-invariant Gaussian random matrix theory (RMT) with multifractal eigenvectors and invariant random matrix theory (RMT) with log-square confinement before discussing self-unfolding and not self-unfolding in invariant RMT. It then considers a non-trivial unfolding and how it changes the form of the spectral correlations, along with the appearance of a ghost correlation dip in RMT and Hawking radiation. It also describes the correspondence between invariant and non-invariant ensembles and concludes by introducing a simple field theory in 1+1 dimensions which reproduces level statistics of both of the two random matrix models and the classical Wigner-Dyson spectral statistics in the framework of the unified formalism of Luttinger liquid.

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1948-, Farina A., and Institution of Electrical Engineers, eds. Optimised radar processors. Peregrinus, 1987.

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Akemann, Gernot. Random matrix theory and quantum chromodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0005.

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This chapter was originally presented to a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian unitary ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions, and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in quantum chromodynamics with three colors in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered, including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. This chapter also provides some open random matrix problems.

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Berber, Stevan. Discrete Communication Systems. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198860792.001.0001.

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The book present essential theory and practice of the discrete communication systems design, based on the theory of discrete time stochastic processes, and their relation to the existing theory of digital communication systems. Using the notion of stochastic linear time invariant systems, in addition to the orhogonality principles, a general structure of the discrete communication system is constructed in terms of mathematical operators. Based on this structure, the MPSK, MFSK, QAM, OFDM and CDMA systems, using discrete modulation methods, are deduced as special cases. The signals are processed in the time and frequency domain, which requires precise derivatives of their amplitude spectral density functions, correlation functions and related energy and pover spectral densities. The book is self-sufficient, because it uses the unified notation both in the main ten chapters explaining communications systems theory and nine supplementary chapters dealing with the continuous and discrete time signal processing for both the deterministic and stochastic signals. In this context, the indexing of vital signals and finctions makes obvious distinction beteween them. Having in mind the controversial nature of the continuous time white Gaussian noise process, a separate chapter is dedicated to the noise discretisation by introducing notions of noise entropy and trauncated Gaussian density function to avoid limitations in applying the Nyquist criterion. The text of the book is acompained by the solutions of problems for all chapters and a set of deign projects with the defined projects’ topics and tasks and offered solutions.

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Book chapters on the topic "Gaussian correlation"

1

Bobkov, Sergey, Gennadiy Chistyakov, and Friedrich Götze. "Moments and Correlation Conditions." In Concentration and Gaussian Approximation for Randomized Sums, 3–22. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-31149-9_1.

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Bobkov, Sergey, Gennadiy Chistyakov, and Friedrich Götze. "Applications of the Second Order Correlation Condition." In Concentration and Gaussian Approximation for Randomized Sums, 331–54. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-31149-9_17.

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Latała, Rafał, and Dariusz Matlak. "Royen’s Proof of the Gaussian Correlation Inequality." In Lecture Notes in Mathematics, 265–75. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-45282-1_17.

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Li, Wenbo V., and Qi-Man Shao. "A Note on the Gaussian Correlation Conjecture." In High Dimensional Probability II, 163–71. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1358-1_11.

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Wegman, Edward J., and Chris Shull. "A Graphical Tool for Distribution and Correlation Analysis of Multiple Time Series." In Topics in Non-Gaussian Signal Processing, 73–86. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4613-8859-3_5.

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Roverato, A. "Partial Correlation Coefficient Comparison in Graphical Gaussian Models." In COMPSTAT, 429–34. Heidelberg: Physica-Verlag HD, 1996. http://dx.doi.org/10.1007/978-3-642-46992-3_58.

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Su, Xiangbo, Baochang Zhang, Linlin Yang, Zhigang Li, and Yun Yang. "Scale Invariant Kernelized Correlation Filter Based on Gaussian Output." In Cloud Computing and Security, 567–77. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48674-1_50.

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Chen, Junjie, Tingfa Xu, Jianan Li, Lei Wang, Ying Wang, and Xiangmin Li. "Adaptive Gaussian-Like Response Correlation Filter for UAV Tracking." In Lecture Notes in Computer Science, 596–609. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87361-5_49.

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Salahub, D. R., M. Castro, and E. I. Proynov. "Density Functional Theory, Its Gaussian Implementation and Applications to Complex Systems." In Relativistic and Electron Correlation Effects in Molecules and Solids, 411–45. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-1340-1_14.

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Xanthopoulos, Constantinos, Ke Huang, Ali Ahmadi, Nathan Kupp, John Carulli, Amit Nahar, Bob Orr, Michael Pass, and Yiorgos Makris. "Gaussian Process-Based Wafer-Level Correlation Modeling and Its Applications." In Machine Learning in VLSI Computer-Aided Design, 119–73. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04666-8_5.

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Conference papers on the topic "Gaussian correlation"

1

Augustyniak, Ireneusz, Agnieszka Popiolek-Masajada, and Jan Masajada. "Focused Gaussian beam with induced optical vortex movement." In Correlation Optics 2011, edited by Oleg V. Angelsky. SPIE, 2011. http://dx.doi.org/10.1117/12.916657.

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Koudela, Ivo, and Miroslav Miler. "Holographic diffractive elements transforming Gaussian beams into super-Gaussian beams." In International Conference on Holography and Correlation Optics, edited by Oleg V. Angelsky. SPIE, 1995. http://dx.doi.org/10.1117/12.226683.

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Fadeyeva, Tatyana A., Vladlen G. Shvedov, and Alexander V. Volyar. "Gaussian beam beyond a paraxial barrier." In International Conference on Correlation Optics, edited by Oleg V. Angelsky. SPIE, 1999. http://dx.doi.org/10.1117/12.370465.

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Reshetnikoff, Sergey A., Vladimir A. Volyar, Oleg A. Shipulin, Vladlen G. Shvedov, and Alexander V. Volyar. "Chain dislocations reaction in a nonparaxial Gaussian beam focus." In International Conference on Correlation Optics, edited by Oleg V. Angelsky. SPIE, 1999. http://dx.doi.org/10.1117/12.370393.

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Ogle, Terrence L., Ben P. Davis, W. Dale Blair, and Peter K. Willett. "Correlation of Gaussian Mixture Tracks." In 2018 21st International Conference on Information Fusion (FUSION 2018). IEEE, 2018. http://dx.doi.org/10.23919/icif.2018.8455572.

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Popov, Ivan A., Nikolay V. Sidorovsky, and Leonid M. Veselov. "Non-Gaussian intensity fluctuations in the image plane of an optical system." In International Conference on Correlation Optics, edited by Oleg V. Angelsky. SPIE, 1997. http://dx.doi.org/10.1117/12.295698.

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Khoroshun, Anna N., Aleksey Chernykh, Aleksandr Bekshaev, Aleksandr Akhmerov, and Halyna Tatarchenko. "Laguerre-Gaussian beam transformations by the double-phase-ramp converter: singular skeleton formation and its sensitivity to small misalignments." In Correlation Optics 2017, edited by Oleg V. Angelsky. SPIE, 2018. http://dx.doi.org/10.1117/12.2303901.

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Witonski, Piotr, and Pawel Szczepanski. "Gain saturation effects in hollow waveguide and slab resonator with Gaussian output mirror." In International Conference on Correlation Optics, edited by Oleg V. Angelsky. SPIE, 1997. http://dx.doi.org/10.1117/12.295693.

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Tyszka-Zawadzka, Anna, Piotr Witonski, and Pawel Szczepanski. "Statistical properties of light generated by a laser having resonator with Gaussian output mirror." In International Conference on Correlation Optics, edited by Oleg V. Angelsky. SPIE, 1997. http://dx.doi.org/10.1117/12.295682.

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Soskin, Marat S., Galina V. Bogatiryova, and Vyacheslav N. Gorshkov. "Spontaneous birth of optical vortices in a system of copropagating Gaussian beams." In Fifth International Conference on Correlation Optics, edited by Oleg V. Angelsky. SPIE, 2002. http://dx.doi.org/10.1117/12.455213.

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Reports on the topic "Gaussian correlation"

1

Michels, James H. Correlation Function Estimator Performance in Non-Gaussian Spherically Invariant Random Processes. Fort Belvoir, VA: Defense Technical Information Center, October 1993. http://dx.doi.org/10.21236/ada273498.

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Lee, Jhong S., Leonard E. Miller, Robert H. French, and Young K. Kim. Ocean Surveillance Detection Studies. Part 1. Detection in Gaussian Mixture Noise. Part 2. An Investigation of Canonical Correlation as an Automatic Detection and Beamforming Technique. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada160931.

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Derbentsev, V., A. Ganchuk, and Володимир Миколайович Соловйов. Cross correlations and multifractal properties of Ukraine stock market. Politecnico di Torino, 2006. http://dx.doi.org/10.31812/0564/1117.

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Abstract:

Recently the statistical characterizations of ﬁnancial markets based on physics concepts and methods attract considerable attentions. The correlation matrix formalism and concept of multifractality are used to study temporal aspects of the Ukraine Stock Market evolution. Random matrix theory (RMT) is carried out using daily returns of 431 stocks extracted from database time series of prices the First Stock Trade System index (www.kinto.com) for the ten-year period 1997-2006. We ﬁnd that a majority of the eigenvalues of C fall within the RMT bounds for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and ﬁnd good agreement with the results for the Gaussian orthogonal ensemble of random matrices—implying a large degree of randomness in the measured cross-correlation coeﬃcients. Further, we ﬁnd that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. We analyze the components of the deviating eigenvectors and ﬁnd that the largest eigenvalue corresponds to an inﬂuence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identiﬁed business sectors. Comparison with the Mantegna minimum spanning trees method gives a satisfactory consent. The found out the pseudoeﬀects related to the artiﬁcial unchanging areas of price series come into question We used two possible procedures of analyzing multifractal properties of a time series. The ﬁrst one uses the continuous wavelet transform and extracts scaling exponents from the wavelet transform amplitudes over all scales. The second method is the multifractal version of the detrended ﬂuctuation analysis method (MF-DFA). The multifractality of a time series we analysed by means of the diﬀerence of values singularity stregth (or Holder exponent) ®max and ®min as a suitable way to characterise multifractality. Singularity spectrum calculated from daily returns using a sliding 250 day time window in discrete steps of 1. . . 10 days. We discovered that changes in the multifractal spectrum display distinctive pattern around signiﬁcant “drawdowns”. Finally, we discuss applications to the construction of crushes precursors at the ﬁnancial markets.

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Tan, Cheng-Yang. Calculating emittance for Gaussian and Non-Gaussian distributions by the method of correlations for slits. Office of Scientific and Technical Information (OSTI), August 2006. http://dx.doi.org/10.2172/892489.

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