When both the dimension p and the sample size N tend to infinity with p/N -> y is an element of (0,1], it proves that under the assumption of Gaussian, the logarithmic likelihood ratio statistic converges in distribution to a Gaussian random variable, and the specific expressions of the...
The author describes a simplified derivation of the representation of the circular error probability (CEP) integral, which is the integral over a disk centered at the origin of a zero mean two-dimensional Gaussian random variable, as a one-dimensional integral. In addition, two series are present...
To annotate pixels with high local intensity, we convolved the original image with a sampled Gaussian kernel, with a standard deviation of three pixels and a size of seven by seven pixels. After convolving, we applied a threshold of 15 / 255 pixel brightness. Then, to filter out low ...
For analyzing error growth in our schemes it will be convenient to use the notion of subgaussian random variables and matrices. We say that a real random variable X (or its distribution) is subgaussian with parameter s if for all t∈R, the (scaled) moment-generating function satisfiesFootnot...
In particular, in order to compute this distribution, one can assume that .v is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular Awsh iac hco aroslslaerryt,s w teh avetas μtlau_be1li s dnhi~ sth(t1rewi/ b2chui)...
the mean spectral measures of random jacobi matrices related to gaussian beta ensembles. electron. commun. probab. 20 , 1–15 (2015) mathscinet math google scholar ercolani, n.m., lozano, g.: a bi-hamiltonian structure for the integrable, discrete non-linear schrödinger ...
Here is an example of defining a circular value variable with a given type: C++ CircVal<UnsignedDegRange>c1; 7. Range checking and wrapping CircVal::IsInRangestatic function is used for testing that a givenlinearvalue is within the range of aCircValclass. ...
Average and standard deviations were calculated for all data, where Gaussian distribution could be assumed. Median values were used to describe data relating to size, number, and content of eccDNA, as the underlying data distribution was unknown. ...
Then, sample one observation x (m) n+1 from a bivariate Gaussian distribution N2 · | μs(m), I and project this value onto the unit circle to obtain a sampled value, θn(m+)1, from the predictive density, noting that if more weights are required, these can be sampled as in the...
Lines represent time-averaged positions with a Gaussian weight function of 100 ps (FWHM) for 0 to 1 ns and 400 ps (FWHM) for 1 to 8 ns. The progression in time is symbolized by the dot color. Red arrows show the trajectory during the field pulse; black arrows show the direction of ...