Rank of the matrix is an important concept to reflect the inherent properties of a matrix, and the inequality application of matrix rank is the key that solves the rank-related problems in the post-graduate exam. The paper makes use of the block matrix, the theory of rank, linear space ...
matrix rank minimization problem is widely applied in many fields such as control, signal processing and system identification. However, the problem is NP-hard in general and is computationally hard to directly solve in practice. In this paper, we provide a new approximation function of the...
The matrix rank minimization problem is widely applied in many fields such as control, signal processing and system identification. However, the problem is NP-hard in general and is computationally hard to directly solve in practice. In this paper, we provide a new approximation function of the ...
divisor and the smallest common multiple of matrices.It not only induces the corresponding results in the present litertures but also make a further research on the solution to the inverse of matrix polynomial.Meanwhile,it also give a uniform and simply method deal with rank identity of matrix....
A three-way array X (or three-dimensional matrix) is an array of numbers xijk subscripted by three indices. A triad is a multiplicative array, xijk = aibjck. Analogous to the rank and the row rank of a matrix, we define rank (X) to be the minimum number of triads whose sum is ...
(n = 11 independent biological pairs were imaged and this shows one matched pair of normal skin and scar from a single individual). Data are shown for each matched pair of normal skin and scar samples. Subsequent statistical analysis was performed using Wilcoxon matched-pairs signed rank ...
Now, let us consider the general case ofpvariants in the region. The use of an external LD panel (which is typically smaller in sample size than a GWAS) usually leads to a lower rank of the LD matrix and thus produces an underestimation of the variance (Eq.10with lowerp). However, a...
According to the utility theory (Yang & Xu, 2013), we can get the upper and lower bounds of the utility of alternative xi, and then rank the alternatives:(8)uximax=∑n=1NuHnpnxi+uHNpΩxiuximin=∑n=1NuHnpnxi+uH1pΩxi(9)uximin=∑n=1NuHnpnxi+uH1pΩxi(10)uxi=uximax+uximin/...
Fig. 2: Heatmap of regional rankings according to the three calculation boundaries. The PB, CB and CBk ranks between the 49 regions are given in columns 1, 2 and 3 respectively. The numbers between parenthesis after the rank number correspond to the carbon footprint in tCO2eq per capita. ...
Numerous extracellular proteins, growth factors, chemokines, cytokines, enzymes, lipoproteins, involved in a variety of biological processes, interact with heparin and/or heparan sulfate at the cell surface and in the extracellular matrix (ECM). The goal of this study is to investigate the relationsh...