Integrable deformations of Lotka-Volterra systems

The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found.Comment: 10 pages, revised version. The paper has been shortened and some comments and references have been adde

Ultra-low noise PEDOT:PSS electrodes on bacterial cellulose: A sensor to access bioelectrical signals in non-electrogenic cells

This study is focused on the particular advantages of organic-based devices to measure cells that do not generate action potentials, also known as non-electrogenic cells. While there is a vast literature about the application of organic conductors to measure neurons, cardiomyocytes and brain tissues, electrical measurements of non-electrogenic cells are rare. This is because non-electrogenic cells generate weak signals with frequencies below 1 Hz. Designing low noise devices in a millihertz frequency range is extremely challenging due to the intrinsic thermal and 1/f type noise generated by the sensing electrode. Here, we demonstrate that the coating of cellulose nanofibers with conducting PEDOT:PSS ink allows the fabrication of a nanostructured surface that establishes a low electrical double-layer resistance with liquid solutions. The low interfacial resistance combined with the large effective sensing area of PEDOT:PSS electrodes minimizes the thermal noise and lowers the amplitude detection limit of the sensor. The electrode noise decreases with frequency from 548 nV r.m.s at 0.1 Hz to a minimum of 6 nV r.m.s for frequencies higher than 100 Hz. This low noise makes it possible to measure low frequency bioelectrical communication signals, typical of non-electrogenic cells, that have until now been difficult to explore using metallic-based microelectrode arrays. The performance of the PEDOT:PSS-based electrodes is demonstrated by recording signals generated by populations of glioma cells with a signal-to-noise ratio as high as 140.Portuguese Foundation for Science and Technology (FCT/MCTES)Portuguese Foundation for Science and TechnologyFEDER under the PT 2020 Partnership Agreement"Implantable organic devices for advanced therapies", INNOVATE [PTDC/EEIAUT/5442/2014]Instituto de Telecomunicacoes, IT [UIDB/EEA/50008/2020]Centro de Ciencias do Mar, CCMar [UIDB/Multi/04326/2020]CICECO -Aveiro Institute of Materials [UIDB/50011/2020, UIDP/50011/2020]FCT, under the "Norma Transit.oria" project CT0020 [DL57/2016/CP1361]FCTPortuguese Foundation for Science and TechnologyEuropean Commission [SFRH/BD/148688/2019]info:eu-repo/semantics/publishedVersio