Turing Instability in Reaction-Diffusion Systems with a Single Diffuser: Characterization Based on Root Locus

Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic analysis of Turing instability in such reaction-diffusion systems. (i) We first introduce a unified framework to formulate the reaction-diffusion system as an interconnected multi-agent dynamical system. (ii) Then, we mathematically classify biologically plausible and implausible Turing instabilities and characterize them by the root locus of each agent's dynamics, or the local reaction dynamics. (iii) Using this characterization, we derive analytic conditions for biologically plausible Turing instability, which provide useful guidance for the design and the analysis of biological networks. These results are demonstrated on an extended Gray-Scott model with a single diffuser

Quasi L₂/L₂ Hankel Norms and L₂/L₂ Hankel Norm/Operator of Sampled-Data Systems

This article is relevant to appropriately defining the L₂/L₂ Hankel norm of sampled-data systems through setting a general time instant Θ at which past and future are to be separated and introducing the associated quasi L₂/L₂ Hankel operator/norm at Θ . We first provide a method for computing the quasi L₂/L₂ Hankel norm for each Θ , which is carried out by introducing a shifted variant of the standard lifting technique for sampled-data systems. In particular, it is shown that the quasi L₂/L₂ Hankel norm can be represented as the l₂/l₂ Hankel norm of a Θ -dependent discrete-time system. It is further shown that an equivalent discretization of the generalized plant exists, which means that the aforementioned discrete-time system can be represented as the feedback connection of the discretized plant and the same discrete-time controller as the one in the sampled-data system. It is also shown that the supremum of the quasi L₂/L₂ Hankel norms at Θ belonging to a sampling interval is actually attained as the maximum, which means that what is called a critical instant always exists and the L₂/L₂ Hankel operator is always definable (as the quasi L₂/L₂ Hankel operator at the critical instant). Finally, we illustrate those theoretical developments through a numerical example

Coordinated Spatial Pattern Formation in Biomolecular Communication Networks

This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular communication networks, bio-nanomachines, or biological cells, communicate with each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule, thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser. We first introduce a feedback model representation of the reaction-diffusion system and provide a systematic local stability/instability analysis tool using the root locus of the feedback system. The instability analysis then allows us to analytically derive the conditions for the self-organized spatial pattern formation, or Turing pattern formation, of the bionanomachines. We propose a novel synthetic biocircuit motif called activator-repressor-diffuser system and show that it is one of the minimum biomolecular circuits that admit self-organized patterns over cell population

Class Practice Research Aimed at Achieving Proactive, Interactive, and Deep Learning in the Junior High School Music Department: From the Perspective of Teaching Methods in Instrumental Ensemble

The purpose of this study was to clarify which teaching method could produce proactive, interactive, and deep learning, during an instrumental ensemble, and to assess the results of implementing such a program. We developed and presented the instrumental ensemble class plan based on the bottom up instruction method at two junior high schools. Data were collected by using a questionnaire and an M-GTA. We found that each student displayed a proactive learning attitude toward the music while maintaining an awareness of their own development areas and growth. Furthermore, the students showed an interactive learning attitude during collaborative activities by watching and listening to others while observing their performance in an effort to improve the quality of music , and learn through the class experience. In addition, we noticed an attitude that promoted deep learning whereby students attempted to solve problems and create music while utilizing what they learned from negative experiences. In addition, the bottom up instruction approach used during instrumental ensemble training was associated with originality, growth and the acceptance and awareness of others