Sentence examples for matrices and ii from inspiring English sources

The key contributions of this paper are to obtain exact results for the cumulative distribution function (CDF) and PDF of (i) the extreme eigenvalues of the quotient ensemble comprising two Wishart matrices and (ii) mutual information for the case when it is a random variable and again depends on the quotient of two Wishart matrices.

As described earlier, the main idea can be summarized as (i) finding hidden representations for the data points by mapping them into a subspace with the help of kernel and projection matrices and (ii) performing binary classification in this shared subspace using the task-specific classification parameters.

Recently, responding to this necessity, two nongraphical strategies were proposed: (i) [ 43] suggests ranking genes by comparing the cophenetic correlation coefficients among individual protein distances matrices and (ii) [ 16] advocates ranking phylogenetic performance of genes using a topological metric, comparing individual gene topology against a reliable reference tree.

Additionally, 5-fluorouracil incorporation was investigated by two procedures: (i) entrapment into the nanoparticulate matrix and (ii) surface deposition onto already formed magnetoliposome particles.

In this context, the subject of this research work was to evaluate the rheological properties of two injectable biomaterials used in osteoarticular and dental tissue engineering: (i) a synthetic extracellular matrix and (ii) an injectable calcium phosphate suspension.

The composite microstructure is modeled as (i) random distribution of ceramic particles (voxels) in the metal matrix, and (ii) using micro-CT scans of the real microstructure transformed into a FE mesh.

The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations.

It was shown that high performance of the catalysts is caused by the ability of fiberglass materials to (i) stabilize very small Pd clusters (around 1 nm in size) in the glass matrix and (ii) absorb predominately polar and polarizable molecules, such as acetylene.

Ectomesenchymal cells give rise to (i) odontoblasts, which synthesize the dentin extracellular matrix, and (ii) dental pulp cells assuming tooth homeostasis.

Batch cultivations in bioreactor were used with 100% bdHSSL to evaluate the effects of (i) immobilization in a calcium alginate matrix and (ii) pH control in suspended and immobilized S. stipitis cultures.

The two main assumptions of our models are (i) that the phylogenetic trees are ultrametric, so that the correlation matrix is proportional to the variance-covariance matrix and (ii) that evolution can be modelled by a Brownian Motion (BM) process.