This note investigates the stability of switched Boolean networks (SBNs) under arbitrary switching signal by using the tool of semi-tensor product of matrices. First, an algebraic expression is given ...for the SBN via the semi-tensor product. Based on it, a necessary and sufficient condition is presented for the switching point reachability of the system. Second, using the switching point reachability, the pointwise stabilizability is studied, and a necessary and sufficient condition is obtained. Finally, the global stability of SBNs under arbitrary switching signal is investigated, and an easily verifiable necessary and sufficient condition is presented. Two illustrative examples are presented to show that the main results are effective in analyzing the stability of SBNs.
Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of evolutionary networked games with “myopic best response adjustment” ...rule, and presents a number of new results. First, the dynamics of the evolutionary networked game is converted to an algebraic form via the semi-tensor product, and an algorithm is established to construct the algebraic formulation for the game. Second, based on the algebraic form, the dynamical behavior of evolutionary networked games is discussed, and some interesting results are presented. Finally, the strategy optimization problem is considered by adding a pseudo-player to the game, and a free-type control sequence is designed to maximize the average payoff of the pseudo-player. The study of an illustrative example shows that the new results obtained in this paper work very well.
Using the semi-tensor product of matrices, this paper investigates the maximum (weight) stable set and vertex coloring problems of graphs with application to the group consensus of multi-agent ...systems, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for the internally stable set problem, based on which a new algorithm to find all the internally stable sets is established for any graph. Secondly, the maximum (weight) stable set problem is considered, and a necessary and sufficient condition is presented, by which an algorithm to find all the maximum (weight) stable sets is obtained. Thirdly, the vertex coloring problem is studied by using the semi-tensor product method, and two necessary and sufficient conditions are proposed for the colorability, based on which a new algorithm to find all the k-coloring schemes and minimum coloring partitions is put forward. Finally, the obtained results are applied to multi-agent systems, and a new protocol design procedure is presented for the group consensus problem. The study of illustrative examples shows that the results/algorithms presented in this paper are very effective.
This paper addresses the disturbance decoupling problem (DDP) of mix-valued logical networks by using both the semi-tensor product of matrices and the matrix expression of logical functions, and ...presents a number of new results on the DDP. First, in order to solve the DDP, a new algorithm is proposed to construct a kind of Y-friendly subspace for the state space of mix-valued logical networks. Second, based on the constructed Y-friendly subspace, several necessary and sufficient conditions are obtained for the existence of decoupling controllers, and a new control design procedure is established to deal with the DDP. Finally, an illustrative example is studied by the new method proposed in this paper, and two kinds of decoupling controllers are designed. The study of the illustrative example shows that the new method is effective in dealing with the DDP of mix-valued logical networks.
This technical note studies the control design problem for a class of affine nonlinear descriptor systems with actuator saturation, and presents several new results. A stabilization controller design ...method is first proposed by state feedback and compensation, and a robust H ∞ controller and a robust adaptive H ∞ controller are respectively designed for the discussed system when external disturbances and/or parametric perturbations are taken into account. Simulation results on a nonlinear descriptor circuit system illustrate the efficiency of the controllers presented in this technical note.
Objective To evaluate the efficacy and safety of cilostazol, pentoxifylline, beraprost for intermittent claudication due to lower extremity arterial occlusive disease. Methods Randomized controlled ...clinical trials were identified from PubMed, Scopus, EMbase, Cochrane Library, Web of Science, China National Knowledge Infrastructure, SinoMed, Wanfang and Chongqing VIP databases, from the database inception to 31/12/2021. The outcome measures were walking distance measured by treadmill (maximum and pain-free walking distance), ankle-brachial index and adverse events. The quality of included studies was assessed by the Cochrane bias risk assessment tool. A network meta-analysis was carried out with Stata 16.0 software. Results There were 29 RCTs included in the study, covering total 5352 patients. Cilostazol was ranked first for both maximum and pain-free walking distance, followed by beraprost and pentoxifylline. For cilostazol, pentoxifylline and beraprost, maximum walking distance increased by 62.93 95%CI(44.06, 81.79), 32.72 95%CI(13.51, 55.79) and 43.90 95%CI(2.10, 85.71) meters, respectively relative to placebo, and pain-free walking distance increased by 23.92 95%CI(11.24, 36.61), 15.16 95%CI(2.33, 27.99) and 19.78 95%CI(-3.07, 42.62) meters. For cilostazol, pentoxifylline, beraprost and cilostazol combined with beraprost, ankle-brachial index increased by 0.06 95%CI(0.04, 0.07), -0.01 95%CI(-0.08, 0.05), 0.18 95%CI(0.12, 0.23) and 0.23 95%CI(0.18, 0.27), respectively relative to placebo. The pentoxifylline and cilostazol was associated with a lower ratio of adverse events than beraprost and cilostazol combined with beraprost. Conclusion Cilostazol, pentoxifylline and beraprost were all effective treatments for intermittent claudication; cilostazol with good tolerance was likely to be the most effective in walking distance, while beraprost and cilostazol combined with beraprost were more prominent in the ankle-brachial index.
This paper studies the state feedback based output tracking control of probabilistic Boolean control networks (PBCNs) by using the semi-tensor product of matrices. A series of reachable sets (with ...probability 1) is defined inductively for PBCNs, and some useful properties are obtained for the reachable sets. Based on the properties of the reachable sets, a necessary and sufficient condition is presented for the state feedback based output tracking control of PBCNs. Meanwhile, a constructive procedure is proposed to design state feedback laws for PBCNs to track a constant reference signal. The study of two illustrative examples shows that the obtained new results are very effective.
This note investigates the logical matrix factorization with application to the topological structure analysis of Boolean networks. First, the concepts of both factorization and rank are defined for ...logical matrices, and two factorization problems are then studied. Using nonsingular logical matrix transformations, several necessary and sufficient conditions for the factorization of a given logical matrix are presented. Second, the logical matrix factorization is applied to the topological structure analysis of a given Boolean network, and a size-reduced structure-equivalent logical network is constructed for the given system. It is shown that the topological structure (including all the fixed points and cycles) of the resulting size-reduced logical network is the same as that of the original Boolean network. The study of an illustrative example shows that the new results presented in this note are effective in analyzing the topological structure of Boolean networks.
This paper investigates the consistent stabilizability of switched Boolean networks (SBNs) by using the semi-tensor product method, and presents a number of new results. First, an algebraic ...expression of SBNs is obtained by the semi-tensor product, based on which the consistent stabilizability is then studied for SBNs and some necessary and sufficient conditions are presented for the design of free-form and state-feedback switching signals, respectively. Finally, the consistent stabilizability of SBNs with state constraints is considered and some necessary and sufficient conditions are proposed. The study of illustrative examples shows that the new results obtained in this paper are very effective in designing switching signals for the consistent stabilizability of SBNs.
By the replacement of halogen anion, three new multifunctional organic-inorganic hybrid perovskites (thiomorpholinium)PbX3 (X = Cl, Br, I) were successfully synthesized and underwent reversible ...structural transformation above room temperature, accompanied by the anomalous change of dielectric constant. With the adjustment of the halogen anion from Cl to I in the inorganic skeleton, the space group is transformed from centrosymmetric space group P21/c ((thiomorpholinium)PbCl3) to chiral one P212121 ((thiomorpholinium)PbBr3, (thiomorpholinium)PbI3) at room temperature. The ordered-disordered transition of organic cations and the change of hydrogen bonds with the increase of temperature lead to above-room-temperature phase transitions. Ultraviolet absorption and second-harmonic generation (SHG) measurements confirmed that both the band gap and SHG activity of (thiomorpholinium)PbX3 (X = Cl, Br, I) crystals were tunable. The band gaps reveal a broadening trend with 3.532 eV, 3.410 eV and 3.175 eV along the Cl → Br → I series. This work provides an effective molecular design for multifunctional organic-inorganic perovskites.
Tunable phase transition, band gap and SHG properties by halogen replacement of hybrid perovskites (thiomorpholinium)PbX3, X = Cl, Br, I
. By the replacement of the halogen anions, we synthesized new one-dimensional ABX3-type perovskites, (thiomorpholinium)PbX3, X = Cl, Br, I which underwent reversible phase transitions. And the band gap and SHG activity of (thiomorpholinium)PbX3 (X = Cl, Br, I) crystals were tunable. Display omitted
