Periodic rhythms are ubiquitous phenomena that illuminate the underlying mechanism of cyclic activities in biological systems, which can be represented by cyclic attractors of the related biological network. Disorders of periodic rhythms are detrimental to the natural behaviours of living organisms. Previous studies have shown that the state transition from one to another attractor can be accomplished by regulating external signals. However, most of these studies until now have mainly focused on point attractors while ignoring cyclic ones. The aim of this study is to investigate an approach for reconciling abnormal periodic rhythms, such as diminished circadian amplitude and phase delay, to the regular rhythms of complex biological networks. For this purpose, we formulate and solve a mixed-integer nonlinear dynamic optimization problem simultaneously to identify regulation variables and to determine optimal control strategies for state transition and adjustment of periodic rhythms. Numerical experiments are implemented in three examples including a chaotic system, a mammalian circadian rhythm system and a gastric cancer gene regulatory network. The results show that regulating a small number of biochemical molecules in the network is sufficient to successfully drive the system to the target cyclic attractor by implementing an optimal control strategy.

Mechanical and waterproof properties were evaluated for hot-pressed cotton boards produced from different layers (3, 4, and 5) of cotton veneers under the same weight of cotton fibers and melamine-urea-formaldehyde adhesive. The mechanical and waterproof properties of cotton boards exceeded the specifications for particleboard and medium-density fiberboard of the China national standard requirements, and the four-layer cotton boards performed better. Scanning electron microscopy images showed that fibers were intertwined to form a dense network structure after hot-pressing with water, and thicker veneers were not conducive to the penetration of adhesives after cold-pressing. Fourier transform infrared spectra indicated that hydrogen bonding, physical, and mechanical bonding took place in the cotton veneers, and stronger absorption peaks were shown for the chemical functional groups of the five-layer and four-layer cotton boards. X-ray diffraction spectra revealed that the cellulose crystallinity of the cotton boards (3, 4, and 5 layers) increased to 74.5%, 74.4%, and 73.2%, respectively. Thermal gravity/ differential thermal gravity curves showed that the thinner cotton veneers of the cotton boards showed better thermal stability. These results showed promise for the revaluation of this textile waste to produce biomass composites and for its potential use as a raw material in the preparation of biomass composites.

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