Nerve impulses can be modelled as electromechanical density waves within the improved Heimburg–Jackson model. Including higher-order polynomial nonlinearities leads to a generalized Boussinesq equation which, by using the travelling-wave reduction, becomes a constant-coefficient Liénard equation with a fifth-order polynomial nonlinearity. Although the resulting equation fails the Painlevé test for integrability, its resonances allow local solutions to be constructed. Noncommutative factorization of the Liénard equation yields analytical travelling-wave solutions near the membrane melting transition, including asymmetric Lambert W-kink solitons. Reversing the factorization ordering generates a supersymmetric partner with generally different amplitude and width. The explicit supersymmetric pairing of these nonlinear density-wave solutions, together with the associated non-shape-invariant supersymmetric potential, constitutes the main novelty of this work. In the context of nerve-membrane dynamics, this factorization structure can be interpreted as an effective modification of the generalized Boussinesq description of nonlinear density-wave propagation. The analytical solutions are verified numerically, and their linear stability is analysed. These results provide a mathematical framework linking higher-order nonlinearities in nerve membranes with asymmetric kink propagation, supersymmetric pairing, and stability.
We address the problem of safety control for nonlinear systems with input delay within the framework of Control Barrier Functions. In contrast to what is already reported in the literature, we approach the problem under the observer-predictor scheme, which avoids the implementation of distributed terms in the controller. We lay the foundations for guaranteeing the safety of the closed-loop system when there are perturbations and the delay is known. The presented results are illustrated and discussed by numerical simulations.
Viruses are among the most prevalent pathogens threatening plants. As a defense mechanism, plants have evolved a sequence-specific antiviral strategy known as RNA silencing. After infection, some plants undergo recovery, during which newly emerging leaves become asymptomatic and resistant to further infection. To identify mechanisms that contribute to recovery in addition to RNA silencing, we studied transgenic tobacco plants expressing the complete NIa cistron of Tobacco etch virus (TEV) that recover three weeks after inoculation. Using in situ hybridization with an NIa probe, qRT-PCR targeting CP and NIa, and back-inoculation assays, we found that the NIa-hybridizing signal persisted in the stem and leaf vasculature. The probe detects both viral and transgene-derived RNA, thereby showing the spatial distribution of NIa-hybridizing RNA. The RNA silencing-associated genes DCL2 and RDR6 were upregulated in recovered leaves, whereas the endogenous silencing suppressor rgs-CaM was upregulated in stems. Callose-related genes and callose deposition at plasmodesmata were also increased in recovered leaves. Our findings indicate that recovery is compartmentalized: a marked reduction in total NIa RNA, consistent with sequence-specific RNA silencing, is associated with the loss of detectable CP RNA from recovered leaf extracts, whereas CP RNA and infectivity remain detectable in stem tissue. In recovered leaves, callose deposition at plasmodesmata is associated with this tissue-specific restriction of viral movement and may act alongside RNA silencing, suggesting that recovery may involve both sequence-specific RNA silencing and a tissue-level restriction of viral spread.
Heavy metals in urban dust, derived from anthropogenic activities and natural sources, are considered potentially toxic elements for human health. The city of Puebla, located in Central Mexico, is one of the ten largest metropolitan cities in Mexico. Near this city is the Popocat & eacute;petl volcano, which contributes heavy metals through the emission of ash. The objectives of this study were to evaluate heavy metal contamination in urban dust and volcanic ash from the city of Puebla, and to determine the associated human health risks. Heavy metals were analyzed using an XRF spectrometer. The level of contamination was established according to the contamination factor, the geoaccumulation index and the contaminant load index. Furthermore, non-carcinogenic risk indices (HIs) were calculated to evaluate the health risk. The results revealed the presence of 18 elements (Ca, Cr, Cu, Fe, K, Mn, Nb, Ni, Pb, Rb, Sb, Sn, Sr, Ti, Y, V, Zn and Zr), with the highest concentrations found for most in urban dust samples, while Rb, Ca and K showed higher concentrations in ash samples. High levels of Sb and Sn contamination were found in 90 to 100% of the dust and ash samples, while Cr, Cu, Ni, Pb and Zn showed considerable levels of contamination in 60 to 90% of the samples. According to the US EPA thresholds, the health risk assessment indicated safe levels (HI < 0.25) for Cu, Fe, Mn, Ni, Pb, Sn, V and Zn in the urban dust and volcanic ash samples, while some of the samples exceeded the safety threshold (HI > 1) for Cr and Sb with respect to the child population in the city of Puebla. These results must be taken into consideration by environmental and government authorities, and the degree of pollution should be reduced accordingly.
An extreme disturbance, i.e. a 1-day chloroform fumigation, had a strong impact on the bacterial community structure in an extreme saline alkaline soil, but how Archaea respond to such an event is largely unknown. Three alkaline saline soils with electrolytic conductivity (EC) between 139 and 157 dS m− 1 and pH 10.0–10.3 were chloroform fumigated for one day and the recovery of the archaeal community determined after 1, 5 and 10 days, while an unfumigated soil served as control. Six archaeal phyla dominated by Candidatus Halobacterota (relative abundance 96.9
