For each virtual society, we can get a matrix of position ratio profile, denoted by (mathcal{Z}), in which rows correspond to individuals and columns correspond to positions in triadic motifs.
where the first two rows and columns of C v consist of covariance matrix of positioning error, while the last diagonal element is the covariance of power estimation error.
where x ∈ R d, t > 0, θ is the liquid temperature, u is the liquid discharge, p is the scalar pressure, k is the matrix of position-independent medium permeabilities in the different directions, respectively, divided by the viscosity, g is the acceleration due to gravity, and γ ∈ R d is the last canonical vector e d.
While the |π〉 base keeps the phenomenology of the overlap between neighboring atomic orbitals, the |π0〉 base allows the construction of diagonal matrices of position-dependent operators.
Principal components (PCs) were generated by diagonalizing the covariance matrix of Cα positions.
To this end a contact map, a correlation matrix of Cα positions and a fragment correlation matrix (Γ f) for a window of 4 adjacent Cα atoms were generated for each protein.
The symmetry observed in this geometric interpretation of steady-state metabolite vectors is identical to that found in the distance matrix of corner positions for a rectangular parallelepiped with two sides equal.
To quantify the methodological improvement provided by this approach, we compared it with a static model based on the residue contact map of the experimental structure, a model of global dynamics based on the correlation matrix of Cα positions, and a continuum model of local dynamics based on the fragment correlation matrix (Γ f).
The problem of the IDC algorithm is that there is no good way to estimate a covariance matrix of the position estimate, which prohibits an effective fusion with other position estimates of other sensors.
A close inspection of the density matrix of the position degree of freedom only, in fact, reveals the virtual absence of off-diagonal elements.
