Remarks on a population-level model of chemotaxis: advection-diffusion approximation and simulations

This note works out an advection-diffusion approximation to the density of a population of E. coli bacteria undergoing chemotaxis in a one-dimensional space. Simulations show the high quality of predictions under a shallow-gradient regime

Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach

Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with neuronal spiking dynamics, we show that our new sufficient condition is tighter than those found in previous analyses which used nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex oscillatory systems

Phytochemical, Antibacterial, Antifungal and Antioxidant Properties of Agastache foeniculum Essential Oil

Phytochemicals are good sources of natural antioxidants and have beneficial effects on human health. Many of phenolic phytochemicals have shown antimicrobial and antifungal activity. Anise hyssop (Agastache foeniculum [Pursh] Kuntze) is a perennial aromatic plant of the Lamiaceae family with antimicrobial and antifungal properties and useful for gastrointestinal problems. In this investigation, the antioxidant activity of extracts, their antimicrobial activity against Staphylococcus aureus, Listeria monocytogenes, Bacillus cereus, B. subtilis, Salmonella thyphimurium, S. enteritidis, Escherichia coli strains and their antifungal activity against Aspergillus niger and A. flavus was evaluated. Seven components were identified, representing 95.4% of the oils including methyl chavicol (83.1%), limonene (3.4%), spathulenol (3.1%) and caryophyllene oxide (3.1%). Agar disk diffusion and broth micro-well dilution assays showed that B. subtilis was the most resistant strain against both of the EOs and E. coli was the most sensitive bacteria. Results of both disc diffusion and MIC showed that the EO was more effective against A. flavus than A. niger. Antioxidant activity of A. foeniculum by DPPH and ABTS assays revealed remarkable antioxidant activities of this EO comparing with BHT. Results of current study indicated that A. foeniculum EOs can be used as a food preservative in having antibacterial, antifungal and antioxidant activity for the control of food deterioration