For a data set of multiple monotonic sequences, each leaf monotonic sequence represents the kernel of a class, which then "grows" by absorbing nearby non-kernel points.
Here ρ, p > 0 and g represents the kernel of the memory term, with conditions to be stated later [see assumption (A1 - A3)].
The subfamily kerμ defined in (1) represents the kernel of the measure μ of noncompactness and since mu(X_{infty})=muBiggl(bigcap^{infty}_{n=1}X_{n} Biggr)leqmu(X_{n}), we see that muBiggl(bigcap^{infty}_{n=1}X_{n} Biggr)=0.
The subfamily kerβ, defined by (1∘), represents the kernel of the MNC β and since beta(X_{infty})=beta Biggl(bigcap_{n=1}^{infty}X_{n} Biggr)leqbeta(X_{n}), we see that beta Biggl(bigcap_{n=1}^{infty}X_{n} Biggr)=0.
ν is the unit normal vector pointing toward the exterior of Ω and p > 0. Here, g represents the kernel of the memory term satisfying some conditions to be specified later.
Here (a,b, sigma, rho, p, q>0), the functions (f,m,h :Gamma_{1} to R ) are essential bounded, g represents the kernel of the memory term, (mu_{0}, mu_{1} ) are real numbers with (mu_{0} >0, mu_{1} neq0, tau(t) >0 ) represents the time-varying delay and initial datum ((u_{0}, u_{1}, f_{0}, y_{0} )) belongs to a suitable space.
represents the kernel function of AISM given xt−1 and (mathcal {S}_{t}).
where σ represents the kernel function bandwidth and N is the number of training samples.
where σ represents the kernel width.
Km represents the kernel implementing the k-mer and the uridine features (see Section 2.1.1), Kd represents the kernel implementing the distance of the sequences from pericentromeric and subtelomeric regions on the chromosome (see Section 2.1.2) and Kn represents the kernel implementing the k-nearest neighbors sequences (see Section 2.1.3).
