Sparse Gaussian Process Based On Hat Basis Functions

in 2020 International Conference on Electrical, Communication, and Computer Engineering (ICECCE) (2020, August 28)

Gaussian process is a popular non-parametric Bayesian methodology for modeling the regression problem, which is completely determined by its mean and covariance function. Nevertheless, this method still ... [more ▼]

Gaussian process is a popular non-parametric Bayesian methodology for modeling the regression problem, which is completely determined by its mean and covariance function. Nevertheless, this method still has two major disadvantages: it is difficult to handle large datasets and may not meet inequality constraints in specific problems. These two issues have been addressed by the so-called sparse Gaussian process and constrained Gaussian process in recent years. In this paper, to reduce the overall computational complexity in the exact Gaussian process, we propose a new sparse Gaussian process method to solve the unconstrained regression problem. The idea is inspired by the constrained Gaussian process method. The critical point of our method is that we introduce the hat basis function, which is mentioned in the constrained Gaussian process, and modify its definition according to the range of training or test data. It turns out that this method belongs to the spectral approximation methods. Similar to the exact Gaussian process and Gaussian process with Fully Independent Training Conditional approximation, our method obtains satisfactory approximate results on analytical functions or open-source datasets. [less ▲]

Monostability and multistability of genetic regulatory networks with different types of regulation functions

in Nonlinear Analysis: Real World Applications (2010), 11(4), 31703185

Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by ... [more ▼]

Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by applying control theory and mathematical tools. The genetic regulatory networks (GRNs) with multiple time-varying delays and different types of regulation functions are considered. By putting forward a general sector-like regulation function and utilizing up-to-date techniques, a novel Lyapunov–Krasovskii functional is introduced for achieving delay dependence to ensure less conservatism. A new condition is then proposed for the general stability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the upper and lower bounds of the delays. Our general stability conditions are applicable to several frequently used regulation functions. It is shown that the existing results for monostability of GRNs are special cases of our main results. Five examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲]

On multistability of delayed genetic regulatory networks with multivariable regulation functions

in Mathematical Biosciences (2010), 228(1), 100-109

Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and ... [more ▼]

Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov–Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲]