Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

This article addresses stability of fractional switched systems (FSSs) with stable and unstable subsystems. First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. Then, some stability conditions which have less conservation are also provided by utilizing average dwell time (ADT) technique and the property of Mittag-Leffler function. In addition, sufficient conditions on asymptotic stability of delayed FSSs are obtained by virtue of fractional Razumikhin technique. Finally, several examples are given to reveal that the conclusions obtained are valid.

Almost Global Stability of Nonlinear Switched System with Stable and Unstable Subsystems

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

Nanostructured inorganic electrochromic materials for light applications

Electrochromism, an emerging energy conversion technology, has attracted immense interest due to its various applications including bistable displays, optical filters, variable optical attenuators, optical switches, and energy-efficient smart windows. Currently, the major drawback for the development of electrochromism is the slow switching speed, especially in inorganic electrochromic materials. The slow switching speed is mainly attributed to slow reaction kinetics of the dense inorganic electrochromic films. As such, an efficient design of nanostructured electrochromic materials is a key strategy to attain a rapid switching speed for their real-world applications. In this review article, we summarize the classifications of electrochromic materials, including inorganic materials (e.g., transition metal oxides, Prussian blue, and polyoxometalates), organic materials (e.g., polymers, covalent organic frameworks, and viologens), inorganic-organic hybrids, and plasmonic materials. We also discuss the electrochromic properties and synthesis methods for various nanostructured inorganic electrochromic materials depending on structure/morphology engineering, doping techniques, and crystal phase design. Finally, we outline the major challenges to be solved and discuss the outlooks and our perspectives for the development of high-performance nanostructured electrochromic materials.

Switching environments, synchronous sex, and the evolution of mating types

While facultative sex is common in sexually reproducing species, for reasons of tractability most mathematical models assume that such sex is asynchronous in the population. In this paper, we develop a model of switching environments to instead capture the effect of an entire population transitioning synchronously between sexual and asexual modes of reproduction. We use this model to investigate the evolution of the number of self-incompatible mating types in finite populations, which empirically can range from two to thousands. When environmental switching is fast, we recover the results of earlier studies that implicitly assumed populations were engaged in asynchronous sexual reproduction. However when the environment switches slowly, we see deviations from previous asynchronous theory, including a lower number of mating types at equilibrium and bimodality in the stationary distribution of mating types. We provide analytic approximations for both the fast and slow switching regimes, as well as a numerical scheme based on the Kolmogorov equations for the system to quickly evaluate the model dynamics at intermediate parameters. Our approach exploits properties of integer partitions in number theory. We also demonstrate how additional biological processes such as selective sweeps can be accounted for in this switching environment framework, showing that beneficial mutations can further erode mating type diversity in synchronous facultatively sexual populations.

Bursty Expression Enhances Reliability of Messaging in Gene Networks

The promoter state of a gene and its expression levels are modulated by the amounts of transcription factors interacting with its regulatory regions. Hence, one may interpret a gene network as a communicating system in which the state of the promoter of a gene (the source) is communicated by the amounts of transcription factors that it expresses (the message) to modulate the state of the promoter and expression levels of another gene (the receptor). The reliability of the gene network dynamics can be quantified by the Shannon’s entropy of the message and the mutual information between the message and the promoter state. Here we consider a stochastic model for a binary gene and use its exact steady state solutions to calculate the entropy and mutual information. We show that a slow switching promoter having long and equally standing ON and OFF states maximizes the mutual information and reduces entropy. That is a bursty regime generating a high variance message governed by a bimodal probability distribution with peaks of the same height. Our results indicate that Shannon’s theory can be a powerful framework for understanding how bursty gene expression conciliates with the striking spatio-temporal precision exhibited in pattern formation of developing organisms.