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Topic: Cumulant

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In the News (Mon 23 Apr 18)

  Cumulant - Wikipedia, the free encyclopedia
The nth cumulant is homogeneous of degree n, i.e.
The first cumulant is simply the expected value; the second and third cumulants are respectively the second and third central moments (the second central moment is the variance); but the higher cumulants are neither moments nor central moments, but rather more complicated polynomial functions of the moments.
The joint cumulant of just one random variable is its expected value, and that of two random variables is their covariance.
en.wikipedia.org /wiki/Cumulant   (1321 words)

 Cumulant   (Site not responding. Last check: 2007-11-07)
The cumulants of the uniform distribution on the interval [−1, 0] are κ
) indicates that the joint cumulant of the random variables whose indices are in that block of the partition.
For any sequence of scalars in a field of characteristic zero, being considered formal cumulants, there is a corresponding sequence of formal moments, given by the polynomials above.
www.worldhistory.com /wiki/C/Cumulant.htm   (1275 words)

The cumulant of a random process is obtained from cumulant generating function, which is defined as the Log of the moment generating function mentioned above.
Cumulant spectra are the Fourier transforms of cumulants.
The non-redundant region of a cumulant or bispectrum is defined as a subset of the support of the function which suffices to calculate the function in the whole region.
www.owlnet.rice.edu /~elec532/PROJECTS00/commies/intro.html   (406 words)

 Abstracts of Papers by John Kolassa
In this case, the multivariate cumulants must be adjusted by the multivariate version of Sheppard's corrections, and the series must be evaluated at the midpoints of hypercubes whose vertices are lattice points.
Calculations for the logistic distribution are presented to illustrate the case of a known but intractable cumulant generating function, and an example involving an overdispersed binomial model is presented to illustrate the case of an unavailable cumulant generating function.
This approximation is then used in conjunction with noniterative Monte Carlo methods to generate a sample from a distribution that approximates the joint distribution of the sufficient statistics associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters.
www.stat.rutgers.edu /~kolassa/abs.html   (2822 words)

 [No title]   (Site not responding. Last check: 2007-11-07)
Matching between the trace cumulant and the wavelet moment is done in a minimum mean-squared error sense under the assumption of a non-Gaussian, stationary, and statistically independent reflectivity series.
However, using a multidimensional taper to smooth the trace cumulant, we show that the method can be used even in a trace-by-trace implementation, which is very important from the point of view of stationarity and consistency.
The consistency of the results is very encouraging because the improved cumulant matching strategy we describe can be effectively used with a limited amount of data.
www.fcaglp.unlp.edu.ar /~velis/pubs/cm.html   (221 words)

 Chapter 3: Critical Temperatures of Pure Ising Spin Models
When measuring some quantity such as the Binder cumulant, it is thus necessary to ascertain first, by experiment, how long it takes for this to stabilize under the algorithm in use, for the lattice sizes and the temperatures at which one wishes to measure the quantity.
Thus, e.g., the measured value for the Binder cumulant at a given temperature is actually an average, over a range of timepoints (after equilibrium is reached), of averages of actual measurements made at those timepoints (at that temperature) over many samples.
Figure 3.4.6 shows the plots of the Binder cumulant against temperature for each lattice size for five temperatures in the range 2.65 through 2.75 (the data is given in Table 3.4.6 in Appendix 5).
www.hermetic.ch /compsci/thesis/chap3.htm   (2144 words)

 Cumulant Analysis of Charge Recombination Kinetics in Bacterial Reaction Centers Reconstituted into Lipid Vesicles -- ...
Cumulant Analysis of Charge Recombination Kinetics in Bacterial Reaction Centers Reconstituted into Lipid Vesicles -- Palazzo et al.
The fit corresponding to the numerical inversion of the Laplace transform (CONTIN) is not shown for the sake of clarity.
Koppel, D. Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulant.
www.biophysj.org /cgi/content/full/79/3/1171   (4564 words)

 [No title]
A full discussion of the theory # on which the computations are based is found in the book by # Jamie Stafford and the author of the same title.
# The file contains examples of computing moments, cumulants, # unbiased estimates of cumulants, expansions of mle's and # mean log likelihood rations and their expectations to order n^(-2).
# #Evaluate the expression for the estimate of the cumulant.
www.utstat.utoronto.ca /david/SCSI/EX.R.txt   (798 words)

 Functional Coupling of Motor Units Is Modulated During Walking in Human Subjects -- Halliday et al. 89 (2): 960 -- ...
The coherence and cumulant were calculated for muscle combinations in which overlapping EMG activity was seen.
B and C: coherence and cumulant for the 2 TA recordings (duration of overlapping segment used for the analysis: 600 ms).
The coherence and cumulant are based on analysis of segments of EMG activity in which there was overlapping activity between the different pairs of muscles during the gait cycle.
jn.physiology.org /cgi/content/full/89/2/960   (5038 words)

 The moment-cumulant connection
Although the cumulants can be obtained from the moments (or vice versa) by the above expressions, in the multivariate case it appears to be a rather difficult task.
The same procedure can be applied to yield multivariate expressions of either moments or cumulants in terms of the others.
The symbolic procedure again is quite general and can be used to express any cumulant in terms of the required moments.
www.theorie.physik.uni-goettingen.de /~morales/proto2/node8.html   (295 words)

 Biophysical Journal: Cumulant Analysis in Fluorescence Fluctuation Spectroscopy
Fluorescence cumulant analysis (FCA) exploits the factorial cumulants of the photon counts and resolves heterogeneous samples based on differences in brightness.
A simple analytical model connects the cumulants of the photon counts with the brightness [epsilon] and the number of molecules N in the optical observation volume for each fluorescent species.
We introduce a simple model that expresses cumulants as functions of the brightness [epsilon] and the number of molecules N for each fluorescent species present.
www.findarticles.com /p/articles/mi_qa3938/is_200406/ai_n9417768   (1335 words)

 USC-SIPI REPORT #125   (Site not responding. Last check: 2007-11-07)
Recursive formulas for diagonal-slice cumulant computations of a state-variable model are developed.
The connection between stationary and non-stationary cumulant computations is also considered; it depends upon the assumption of an asymptotic stable model.
Vector representations for third- and fourth-order cumulants are given and elegant recursive cumulant computation formulas are obtained.
sipi.usc.edu /reports/abstracts/usc-sipi.125.html   (126 words)

 Variational cumulant expansions for intractable distributions   (Site not responding. Last check: 2007-11-07)
Intractable distributions present a common difficulty in inference with in the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution.
In this article, we describe a perturbational approach in the form of a cumulant expansion which, to lowest order, recovers the standard Kullback-Leibler variational bound.
We demonstrate the method on a particular class of undirected graphical models, Boltzmann machines, for which our simulation results confirm improved accuracy and enhanced stability during learning.
www.nici.kun.nl /Publications/1999/13404.html   (130 words)

 [No title]
Therefore, it is % pointless to try to deal precisely with the additive noise and it % is very unlikely that the cumulant tensor can be accurately % summarized by its first n eigen-matrices.
Also, since we are % dealing with reals signals, it becomes easier to exploit the % symmetries of the cumulants to further reduce the number of % matrices to be diagonalized.
The convention is % that the first element of each row of B is positive.
www.sccn.ucsd.edu /eeglab/allfunctions/jader.m   (1203 words)

 USC-SIPI REPORT #177   (Site not responding. Last check: 2007-11-07)
In this report, we compare the use of biased and unbiased, segmented and unsegmented estimators for both correlation and 1-D diagonal slice of the fourth-order cumulant function.
We compare correlation-based and cumulant-based methods for determining the number of harmonics when the amplitude of one harmonic decreases and when the frequency of one harmonic approaches the other for the case of two sinusoids measured in colored Gaussian noise.
Our studies: (1) provide further support for using cumulants over correlations when measurement noise is colored and Gaussian; (2) demonstrate that one should use unbiased unsegmented correlation or cumulant estimators; (3) indicate that high-resolution results are best obtained using cumulant-based MUSIC or minimum-norm algorithms; and (4) show that LS estimates of amplitudes suffice.
sipi.usc.edu /reports/abstracts/usc-sipi.177.html   (250 words)

 Output Cumulant Matching For Source Separation (ResearchIndex)   (Site not responding. Last check: 2007-11-07)
This paper investigates the optimal use of the whole set of 4th-order cumulants.
An optimal cumulant matching procedure is re-expressed in terms of the cumulants of the output of the separator.
This approach allows one to determine the optimal weights to be applied to the sample cumulants of the separated signals.
citeseer.ist.psu.edu /628012.html   (273 words)

 S Archive: Zero Cumulant Distribution   (Site not responding. Last check: 2007-11-07)
Density of the Zero Cumulant Distribution of order 6.
The first six cumulants are specified, and the others are assumed zero.
vector of length 6 holding the cumulants of the distribution.
www.statsci.org /webguide/s/dzeroc.html   (73 words)

 Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
Energy Citations Database (ECD) Document #7355243 - Cumulant methods in the theory of multiphonon absorption
Availability information may be found in the Availability, Publisher, Research Organization, Resource Relation and/or Author (affiliation information) fields and/or via the "Full-text Availability" link.
Cumulant methods in the theory of multiphonon absorption
www.osti.gov /energycitations/product.biblio.jsp?osti_id=7355243   (98 words)

 Edinburgh Research Archive : Item 1842/230   (Site not responding. Last check: 2007-11-07)
Third cumulant of the total transmission of diffuse waves
The probability distibution of the total transmission is studied for waves multiply scattered from a random, static configuration of scatterers.
A theoretical study of the second and third cumulants of this distribution is given.
hdl.handle.net /1842/230   (94 words)

 Output Cumulant Matching For Source Separation - Cardoso, Bose, Friedlander (ResearchIndex)   (Site not responding. Last check: 2007-11-07)
Output Cumulant Matching For Source Separation - Cardoso, Bose, Friedlander (ResearchIndex)
by considering optimal blind estimation of the mixing matrix from both 2nd and 4th order cumulants (ref. 5] considered only 4th order...
J.-F. Cardoso, S. Bose, and B. Friedlander, "Output cumulant matching for source separation," in Proc.
citeseer.ist.psu.edu /cardoso95output.html   (425 words)

 CAM Fellows   (Site not responding. Last check: 2007-11-07)
This first cumulant of the cost is used in Linear Quadratic Gaussian (LQG) control as a performance function.
It is not hard to see that the cumulant control problem attempts to minimize a performance index that has multiple cumulants.
Using this approach, a control law may be developed that will minimize k cumulants of a cost, while designing for some worst case disturbance.
www.nd.edu /~cam/fellows/fellows.htm   (3648 words)

 Skewness   (Site not responding. Last check: 2007-11-07)
This is analogous to the definition of kurtosis, which is expressed as the fourth cumulant divided by the fourth power of the square root of the second cumulant.
is the unique symmetric unbiased estimator of the third cumulant and
is the symmetric unbiased estimator of the second cumulant.
www.worldhistory.com /wiki/S/Skewness.htm   (350 words)

 A Carcinogenesis Model at the Nucleotide Level -- from Mathematica Information Center
This notebook elaborates on some symbolic and numeric computational aspects of a carcinogenesis model proposed recently by the author and his colleagues which describes certain mutational events at the nucleotide level.
One is the symbolic derivation of systems of ordinary differential equations which are used to solve for the joint cumulant functions.
carcinogenesis model, cancer, survival, cumulant, mutation, differential equation
library.wolfram.com /infocenter/MathSource/745   (102 words)

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