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This paper provides a full classification of the dynamics for continuous-time Markov chains (CTMCs) on the nonnegative integers with polynomial transition rate functions and without arbitrary large backward jumps. Such stochastic processes are abundant in applications, in particular in biology. More precisely, for CTMCs of bounded jumps, we provide necessary and sufficient conditions in terms of calculable parameters for explosivity, recurrence versus transience, positive recurrence versus null recurrence, certain absorption, and implosivity. Simple sufficient conditions for exponential ergodicity of stationary distributions and quasi-stationary distributions as well as existence and nonexistence of moments of hitting times are also obtained. Similar simple sufficient conditions for the aforementioned dynamics together with their opposite dynamics are established for CTMCs with unbounded forward jumps. Finally, we apply our results to stochastic reaction networks, an extended class of branching processes, a general bursty single-cell stochastic gene expression model, and population processes, none of which are birth–death processes. The approach is based on a mixture of Lyapunov–Foster-type results, the classical semimartingale approach, and estimates of stationary measures.

Dispersal is a central process in ecology and evolution. It strongly influences the dynamics of spatially structured populations and affects evolutionary processes by shaping patterns of gene flow. For these reasons, dispersal has received considerable attention from ecologists, evolutionary biologists, and conservationists. Although it has been studied extensively in taxa such as birds and mammals, much less is known about dispersal in vertebrates with complex life cycles such as pond-breeding amphibians. Over the past two decades, researchers have taken an ever-increasing interest in amphibian dispersal and initiated both basic and applied studies, using a broad range of experimental and observational approaches. This body of research reveals complex dispersal patterns, causations, and syndromes, with dramatic consequences for the demography and genetics of amphibian populations. In this review, our goals are to: redefine and clarify the concept of amphibian dispersal; review current knowledge about the effects of individual (i.e., condition-dependent dispersal) and environmental (i.e., context-dependent dispersal) factors during the three stages of dispersal (i.e., emigration, transience, and immigration); identify the demographic and genetic consequences of dispersal in spatially structured amphibian populations; and propose new research avenues to extend our understanding of amphibian dispersal.

Block-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In this paper we will present transient properties for two specific types of block-structured Markov chains, including M/G/1 type and GI/M/1 type. Necessary and sufficient conditions in terms of system parameters are obtained for geometric transience and algebraic transience. Possible extensions of the results to continuous-time Markov chains are also included.

Dispersal is a key ecological process that influences the dynamics of spatially and socially structured populations and consists of three stages—emigration, transience, and settlement—and each stage is influenced by different social, individual, and environmental factors. Despite our appreciation of the complexity of the process, we lack a firm empirical understanding of the mechanisms underlying the different stages. Here, using data from 65 GPS-collared dispersing female coalitions of the cooperatively breeding meerkat (Suricata suricatta), we present a comprehensive analysis of the effects of population density, mate availability, dispersing coalition size, and individual factors on each of the three stages of dispersal in a wild population. We expected a positive effect of density on dispersal due to increased kin competition at high densities. We further anticipated positive effects of mate availability, coalition size, and body condition on dispersal success. We observed increasing daily emigration and settlement probabilities at high population densities. In addition, we found that emigration and settlement probabilities also increased at low densities and were lowest at medium densities. Daily emigration and settlement probabilities increased with increasing female coalition size and in the presence of unrelated males. Furthermore, the time individuals spent in the transient stage increased with population density, whereas coalition size and presence of unrelated males decreased dispersal distance. The observed nonlinear relationship between dispersal and population density is likely due to limited benefits of cooperation at low population densities and increased kin competition at high densities. Our study provides empirical validation for the theoretical predictions that population density is an important factor driving the evolution of delayed dispersal and philopatry in cooperative breeders.

Transient technology seeks the development of materials, devices, or systems that undergo controlled degradation processes after a stable operation period, leaving behind harmless residues. To enable externally powered fully transient devices operating for longer periods compared to passive devices, transient batteries are needed. Albeit transient batteries are initially intended for biomedical applications, they represent an effective solution to circumvent the current contaminant leakage into the environment. Transient technology enables a more efficient recycling as it enhances material retrieval rates, limiting both human and environmental exposures to the hazardous pollutants present in conventional batteries. Little efforts are focused to catalog and understand the degradation characteristics of transient batteries. As the energy field is a property‐driven science, not only electrochemical performance but also their degradation behavior plays a pivotal role in defining the specific end‐use applications. The state‐of‐the‐art transient batteries are critically reviewed with special emphasis on the degradation mechanisms, transiency time, and biocompatibility of the released degradation products. The potential of transient batteries to change the current paradigm that considers batteries as harmful waste is highlighted. Overall, transient batteries are ready for takeoff and hold a promising future to be a frontrunner in the uptake of circular economy concepts. A critical discussion from the circular economy point of view about the degradation mechanisms, transiency time, and biocompatibility of transient batteries is provided.

Death, disturbing as it can be, is an inevitable phenomenon. All cultures must find the right language to explain this reality or at least provide the linguistic tools to navigate it. Among the tools cultures employ for dealing with this phenomenon are texts, the biblical text being an example. This study, using the comparative approach of African biblical hermeneutics, examines Psalm 90 as an example of a text that is used to address the concept of death. It further argues that the ideas and strategies adopted by the biblical text are comparable to those employed by African indigenous sacred texts, such as the Owuo atwedie [the ladder of death], the Adinkra textual system. Contribution: Moreover, the parallel reading of these two texts complements our understanding and facilitates our communication about a rather difficult subject in contemporary African contexts.

Changes in consumption and changes in the structure of the system always occur in each power system. One of the effects of these changes can be the instability of the system voltage. When voltage is unstable, their performance is in conditions of power fluctuations after large errors occur. Determining the voltage stability of traditional methods is time consuming and does not have the necessary efficiency for instantaneous monitoring. In this paper, an index based on the changes of two indices of frequency deviation and frequency response of inertia in the time after the occurrence of perturbation is presented, which has the ability to detect the occurrence of instability and at the same time high speed timely estimation of voltage instability in the power system. In addition, this indicator has been used to determine the appropriate time to start load removal (voltage reduction load). All simulations are performed on the IEEE 33-bus network in DIgSILENT software, the results of which indicate that the proposed index has a very low computational load. Because the proposed method for instantaneous voltage instability prediction does not depend on the network structure and load model and does not require any threshold value. Therefore, the proposed index has a very low computational load. These advantages make the proposed method an interesting option for online and practical applications.

The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite d-ary tree. We prove the model undergoes a phase transition, finding it recurrent for d = 2 and transient for d ≥ 5. Simulations suggest strong recurrence for d = 2, weak recurrence for d = 3, and transience for d ≥ 4. Additionally, we prove a 0–1 law for all d-ary trees, and we exhibit a graph on which a 0–1 law does not hold. To prove recurrence when d = 2, we construct a recursive distributional equation for the number of visits to the root in a smaller process and show the unique solution must be infinity a.s. The proof of transience when d = 5 relies on computer calculations for the transition probabilities of a large Markov chain. We also include the proof for d ≥ 6, which uses similar techniques but does not require computer assistance.

1. Dispersal is a key mechanism enabling species to adjust their geographic range to rapid global change. However, dispersal is costly and environmental modifications are likely to modify the cost–benefit balance of individual dispersal decisions, for example, by decreasing functional connectivity. 2. Dispersal costs occur during departure, transience and settlement, and are levied in terms of energy, risk, time and lost opportunity, potentially influencing individual fitness. However, to the best of our knowledge, no study has yet quantified the energetic costs of dispersal across the dispersal period by comparing dispersing and philopatric individuals in the wild. 3. Here, we employed animal‐borne biologgers on a relatively large sample (N = 105) of juvenile roe deer to estimate energy expenditure indexed using the vector of dynamic body acceleration and mobility (distance travelled) in an intensively monitored population in the south‐west of France. We predicted that energy expenditure would be higher in dispersers compared to philopatric individuals. We expected costs to be (a) particularly high during transience, (b) especially high in the more fragmented areas of the landscape and (c) concentrated during the night to avoid disturbance caused by human activity. 4. There were no differences in energy expenditure between dispersers and philopatric individuals during the pre‐dispersal phase. However, dispersers expended around 22% more energy and travelled around 63% further per day than philopatric individuals during transience. Differences in energy expenditure were much less pronounced during the settlement phase. The costs of transience were almost uniquely confined to the dawn period, when dispersers spent 23% more energy and travelled 112% further than philopatric individuals. Finally, the energetic costs of transience per unit time and the total distance travelled to locate a suitable settlement range were higher in areas of high road density. 5. Our results provide strong support for the hypothesis that natal dispersal is energetically costly and indicate that transience is the most costly part of the process, particularly in fragmented landscapes. Further work is required to link dispersal costs with fitness components so as to understand the likely outcome of further environmental modifications on the evolution of dispersal behaviour.

The article examines the concept of wabi-sabi as the foundation of Japanese aesthetics, emphasizing its role in art and everyday life. Wabi-sabi celebrates the beauty of imperfection, impermanence and natural decay, which is expressed in practices such as the tea ceremony (chanoyu). In the context of art, this aesthetic allows for reflection on the transience of existence, contrasting with the Western tradition of vanitas. The wabi-sabi aesthetic evokes an emotional response akin to Julien’s notion of dé-coïncidence – the experience of contradiction between what is enduring and what is ephemeral, a key element of the Japanese approach to impermanence. The article juxtaposes these manifestations of transience, showcasing both universal and culturally specific ways of coping with the passage of time.