arXiv subjects

Zhou Fang

Publications and source records attributed to Zhou Fang.

60 records · Page 4Linked to original sources

arXiv2018

Complex Balancing Reconstructed to the Asymptotic Stability of Mass-action Chemical Reaction Networks with Conservation Laws

Motivated by the fact that the pseudo-Helmholtz function is a valid Lyapunov function for characterizing asymptotic stability of complex balanced mass action systems (MASs), this paper develops the generalized pseudo-Helmholtz function for stability analysis for more general MASs assisted with conservation laws. The key technique is to transform the original network into two different MASs, defined by reconstruction and reverse reconstruction, with an important aspect that the dynamics of the original network for free species is equivalent to that of the reverse reconstruction. Stability analysis of the original network is then conducted based on an analysis of how stability properties are retained from the original network to the reverse reconstruction. We prove that the reverse reconstruction possesses only an equilibrium in each positive stoichiometric compatibility class if the corresponding reconstruction is complex balanced. Under this complex balanced reconstruction strategy, the asymptotic stability of the reverse reconstruction, which also applies to the original network, is thus reached by taking the generalized pseudo-Helmholtz function as the Lyapunov function. To facilitate applications, we further provide a systematic method for computing complex balanced reconstructions assisted with conservation laws. Some representative examples are presented to exhibit the validity of the complex balanced reconstruction strategy.

math.DS↗

arXiv2017

Stabilization of (state, input)-disturbed CSTRs through the port-Hamiltonian systems approach

It is a universal phenomenon that the state and input of the continuous stirred tank reactor (CSTR) systems are both disturbed. This paper proposes a (state, input)-disturbed port-Hamiltonian framework that can be used to model and further designs a stochastic passivity based controller to asymptotically stabilize in probability the (state, input)-disturbed CSTR (sidCSTR) systems. The opposite entropy function and the availability function are selected as the Hamiltonian for the model and control purposes, respectively. Furthermore, the proposed (state, input)-disturbed port-Hamiltonian model can simultaneously characterize the first law and the second law of thermodynamics when the opposite entropy function acts as the Hamiltonian. A simple CSTR example illustrates how the port-Hamiltonian method is utilized for modeling and controlling sidCSTR systems.

math.OC↗

arXiv2016

Observation of Ising spin-nematic order and its close relationship to the superconductivity in FeSe single crystals

Superconducting FeSe single crystals of (001) orientation are synthesized via a hydrothermal ion-release route. An Ising spin-nematic order is identified by our systematic measurements of in-plane angular-dependent magnetoresistance (AMR) and static magnetization. The turn-on temperature of anisotropic AMR signifies the Ising spin-nematic ordering temperature Tsn, below which a two-fold rotational symmetry is observed in the iron plane. A downward curvature appears below Tsn in the temperature dependence of static magnetization for the weak in-plane magnetic field as reported previously. Remarkably, we find a universal linear relationship between Tc and Tsn among various superconducting samples, indicating that the spin nematicity and the superconductivity in FeSe have a common microscopic origin.

cond-mat.supr-con↗

arXiv2016

Stochastic Weak Passivity Based Stabilization of Stochastic Systems with Nonvanishing Noise

For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to the loss of stochastic passivity at the desired state if a radially unbounded Lyapunov function is expected as the storage function. To characterize a certain (globally) stable behavior for such a class of systems, the stochastic asymptotic weak stability is proposed in this paper which suggests the transition measure of the state to be convergent and the ergodicity. By defining stochastic weak passivity that admits stochastic passivity only outside a ball centered around the desired state but not in the whole state space, we develop stochastic weak passivity theorems to ensure that the stochastic systems with nonvanishing noise can be globally\locally stabilized in weak sense through negative feedback law. Applications are shown to stochastic linear systems and a nonlinear process system, and some simulation are made on the latter further.

math.DS↗

arXiv2011

Sparse Group Selection Through Co-Adaptive Penalties

Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well approximated by a fit involving only a small number of covariates -- a so called sparsity assumption, which leads to the Lasso and other methods. In many situations, however, the covariates can be considered to be structured, in that the selection of some variables favours the selection of others -- with variables organised into groups entering or leaving the model simultaneously as a special case. This structure creates a different form of sparsity. In this paper, we suggest the Co-adaptive Lasso to fit models accommodating this form of `group sparsity'. The Co-adaptive Lasso is fast and simple to calculate, and we show that it holds theoretical advantages over the Lasso, performs well under a broad set of conclusions, and is very competitive in empirical simulations in comparison with previously suggested algorithms like the Group Lasso and the Adaptive Lasso.

stat.ME↗

arXiv2010

LASSO ISOtone for High Dimensional Additive Isotonic Regression

Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method for such regression called LASSO Isotone (LISO). LISO adapts ideas from sparse linear modelling to additive isotonic regression. Thus, it is viable in many situations with high dimensional predictor variables, where selection of significant versus insignificant variables are required. We suggest an algorithm involving a modification of the backfitting algorithm CPAV. We give a numerical convergence result, and finally examine some of its properties through simulations. We also suggest some possible extensions that improve performance, and allow calculation to be carried out when the direction of the monotonicity is unknown.

stat.ME↗