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This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems.

Phytophthora infestans, a representative of phytopathogenic oomycetes, have been proven to cope with redundant sources of internal and host-derived reactive nitrogen species (RNS). To gain insight into its nitrosative stress resistance mechanisms, metabolic sensors activated in response to nitrosative challenge during both in vitro growth and colonization of the host plant were investigated. The conducted analyses of gene expression, protein accumulation, and enzyme activity reveal for the first time that P. infestans (avirulent MP946 and virulent MP977 toward potato cv. Sarpo Mira) withstands nitrosative challenge and has an efficient system of RNS elimination. The obtained data indicate that the system protecting P. infestans against nitric oxide (NO) involved the expression of the nitric oxide dioxygenase (Pi-NOD1) gene belonging to the globin family. The maintenance of RNS homeostasis was also supported by an elevated S-nitrosoglutathione reductase activity and upregulation of peroxiredoxin 2 at the transcript and protein levels; however, the virulence pattern determined the expression abundance. Based on the experiments, it can be concluded that P. infestans possesses a multifarious system of metabolic sensors controlling RNS balance via detoxification, allowing the oomycete to exist in different micro-environments flexibly.

The paper concerns the optimization of a tuned mass damper with inerter (TMDI) based on two strategies, i.e., the minimum amplitude in the resonance peak and minimum area under the frequency response curve. The optimization is based on real, accessible parameters. Both optimization procedures are presented in two steps. In the first one, two parameters of the TMDI are tuned (inertance and damping coefficient), while in the second one, three parameters (mass, inertance, and damping coefficient). We show that both strategies give the optimum sets of parameters and allow the reduction of the amplitude of the damped system.

Abstract Nitric oxide (NO) has been proven to be involved in the regulation of many physiological processes in plants. Though the contribution of NO in plant response to drought has been demonstrated in numerous studies, this phenomenon remains still not fully recognized. The research presented here was performed to decipher the role of NO metabolism in drought tolerance and the ability to recover after stress cessation in two closely related species of forage grasses, important for agriculture in European temperate regions: Festuca arundinacea and F. glaucescens. In both species, two genotypes with distinct levels of drought tolerance were selected to compare their physiological reactions to simulated water deficit and further re-watering, combined with a simultaneous application of NO scavenger, 2-phenyl-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide (PTIO). The results clearly indicated a strong relationship between scavenging of NO in leaves and physiological response of both analyzed grass species to water deficit and re-watering. It was revealed that NO generated under drought was mainly located in mesophyll cells. In plants with reduced NO level a higher photosynthetic capacity and delay in stomatal closure under drought, were observed. Moreover, NO scavenging resulted also in the increased membrane permeability and higher accumulation of ROS in cells of analyzed plants both under drought and re-watering. This phenomena indicate that lower NO level might reduce drought tolerance and the ability of F. arundinacea and F. glaucescens to recover after stress cessation.

Drought resistance in plants can be associated with four different strategies to cope with water stress. These strategies are classified as drought escape, avoidance, tolerance, and recovery. The expression of each strategy depends on plant species and its genetic potential, but also on the environmental conditions, including the stress intensity and duration. Often, prolonged drought conditions are associated with drought escape or avoidance, whereas short but severe drought periods induce drought tolerance. To analyze the components of drought resistance in forage grasses, we applied two Lolium multiflorum/Festuca arundinacea introgression forms into a comprehensive research. Obtained results clearly show that the response of plants to severe short term drought conditions with limited rhizosphere did not reflect their response to long progressive drought conditions, which did not limit root growth. The BC4-INT-40 introgression form with extensive and deep roots was characterized by a more efficient drought avoidance and regeneration mechanisms under long-term drought, whereas the BC4-INT-66 form with shorter roots revealed a lower productivity and re-growth capacity under the prolonged drought. On the other hand, this form had also a better photosynthetic performance under short and intensive drought conditions with a limited space for root development.

Rye was used here to dissect molecular mechanisms of resistance to Fusarium head blight (FHB) and to go deeper with our understanding of that process in cereals. F. culmorum-damaged kernels of two lines different in their potential of resistance to FHB were analyzed using two-dimensional gel electrophoresis and mass spectrometry to identify resistance markers. The proteome profiling was accompanied by measurements of α- and β-amylase activities and mycotoxin content. The proteomic studies indicated a total of 18 spots with clear differences in protein abundance between the more resistant and more susceptible rye lines after infection. Eight proteins were involved in carbohydrate metabolism of which six proteins showed a significantly higher abundance in the resistant line. The other proteins recognized here were involved in stress response and redox homeostasis. Three remaining proteins were associated with protease inhibition/resistance and lignin biosynthesis, revealing higher accumulation levels in the susceptible rye line. After inoculation, the activities of α- and β-amylases, higher in the susceptible line, were probably responsible for a higher level of starch decomposition after infection and a higher susceptibility to FHB. The presented results could be a good reference for further research to improve crop resistance to FHB.

The investigations of this paper revolve around the concept of stability. We would like to make several analytical distinctions which would allow us to differentiate between various concepts of stability. The background of our work is the theory of political change supported by examples of this kind presented by Plato, Polybius, James Harrington, Jean-Jacques Rousseau, and Aristotle.The paper includes some remarks on Hobbes’s and Hume’s theories of stability which, strictly speaking, can be smoothly subsumed under a modern political concept thereof. Also worthy of note is the specification of the main subject-matter of political theories in terms of the problem of stability. Finally, we propose a sketch of the map of the problem of stability.

In the present study, we provide useful data related to one of the most promising materials in thin-film solar cell technologies: Cu2ZnSnS4 (CZTS) kesterite structures. Sol-gel spin coating and chemical bath deposition methods were used to fabricate and further investigate Mo/CZTS/CdS/ZnO/AZO heterostructures. In order to examine the crystal structure of the samples, Raman scattering measurements using two excitation wavelengths (514.5 nm and 785 nm) were performed. Three Raman bands related to CZTS were found, as well as one that had its origin in CdS. By using laser ablation and performing Raman spectroscopy on these modified samples, it was shown that during the manufacturing process a MoS2 interlayer was formed between the CZTS and Mo layers. Our method proved that the CZTS layer in a multilayer device structure fabricated by solution-based methods can be decomposed, and thus a detailed analysis of the layer can be performed. Subsequently, current-voltage curves were investigated in terms of the essential electrical properties of glass/Mo/p-CZTS/n-CdS/ZnO/AZO junctions and occurring current transport mechanisms. Finally, AFM data were acquired to study the surface topography of the studied samples. The images showed that these surfaces had a uniform grain structure.

Abstract In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values.

In this paper, we study the dynamics of a two-degree freedom system consisting of the main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. We investigate different types of the non-linear characteristic of the dash-pot. We investigate devices in which damping coefficient change according to the relative displacement or the relative velocity between the damped mass and tuned mass damper. We also include in the investigation of different types of control functions. We show the two-parameter diagrams presenting the main body’s maximum amplitude versus the frequency of excitation of the damped body and different control parameter. We show how the application of a non-linear damper lets us control the main system’s oscillation amplitude.

Though winter-hardiness is a complex trait, freezing tolerance was proved to be its main component. Species from temperate regions acquire tolerance to freezing in a process of cold acclimation, which is associated with the exposure of plants to low but non-freezing temperatures. However, mechanisms of cold acclimation in Lolium-Festuca grasses, important for forage production in Europe, have not been fully recognized. Thus, two L. multiflorum/F. arundinacea introgression forms with distinct freezing tolerance were used herein as models in the comprehensive research to dissect these mechanisms in that group of plants. The work was focused on: (i) analysis of cellular membranes’ integrity; (ii) analysis of plant photosynthetic capacity (chlorophyll fluorescence; gas exchange; gene expression, protein accumulation, and activity of selected enzymes of the Calvin cycle); (iii) analysis of plant antioxidant capacity (reactive oxygen species generation; gene expression, protein accumulation, and activity of selected enzymes); and (iv) analysis of Cor14b accumulation, under cold acclimation. The more freezing tolerant introgression form revealed a higher integrity of membranes, an ability to cold acclimate its photosynthetic apparatus and higher water use efficiency after three weeks of cold acclimation, as well as a higher capacity of the antioxidant system and a lower content of reactive oxygen species in low temperature.

Lolium multiflorum/Festuca arundinacea introgression forms have been proved several times to be good models to identify key components of grass metabolism involved in the mechanisms of tolerance to water deficit. Here, for the first time, a relationship between photosynthetic and antioxidant capacities with respect to drought tolerance of these forms was analyzed in detail. Two closely related L. multiflorum/F. arundinacea introgression forms distinct in their ability to re-grow after cessation of prolonged water deficit in the field were selected and subjected to short-term drought in pots to dissect precisely mechanisms of drought tolerance in this group of plants. The studies revealed that the form with higher drought tolerance was characterized by earlier and higher accumulation of abscisic acid, more stable cellular membranes, and more balanced reactive oxygen species metabolism associated with a higher capacity of the antioxidant system under drought conditions. On the other hand, both introgression forms revealed the same levels of stomatal conductance, CO2 assimilation, and consequently, intrinsic water use efficiency under drought and recovery conditions. However, simultaneous higher adjustment of the Calvin cycle to water deficit and reduced CO2 availability, with respect to the accumulation and activity of plastid fructose-1,6-bisphosphate aldolase, were clearly visible in the form with higher drought tolerance.

Impact of photosynthetic and antioxidant capacities on drought tolerance of two closely related forage grasses, Festuca arundinacea and Festuca glaucescens, was deciphered. Within each species, two genotypes distinct in drought tolerance were subjected to a short-term drought, followed by a subsequent re-watering. The studies were focused on: (i) analysis of plant physiological performance, including: water uptake, abscisic acid (ABA) content, membrane integrity, gas exchange, and relative water content in leaf tissue; (ii) analysis of plant photosynthetic capacity (chlorophyll fluorescence; gene expression, protein accumulation, and activity of selected enzymes of the Calvin cycle); and (iii) analysis of plant antioxidant capacity (reactive oxygen species (ROS) generation; gene expression, protein accumulation and activity of selected enzymes). Though, F. arundinacea and F. glaucescens revealed different strategies in water uptake, and partially also in ABA signaling, their physiological reactions to drought and further re-watering, were similar. On the other hand, performance of the Calvin cycle and antioxidant system differed between the analyzed species under drought and re-watering periods. A stable efficiency of the Calvin cycle in F. arundinacea was crucial to maintain a balanced network of ROS/redox signaling, and consequently drought tolerance. The antioxidant capacity influenced mostly tolerance to stress in F. glaucescens.