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Consider a general continuous-state branching process with additional interaction, which destroys the branching property. We give precise conditions on the interaction term, in order to decide whet...

Compound jet fire extinguishing technology is an efficient technology for oil fires. The hydrophobic ultrafine dry powder is used for the solid phase in the compound jet, but it can't be supplied continuously due to the insufficient supply of compressed nitrogen. Thus, the feasibility of using the compressed air to replace the compressed nitrogen in the compound jet was explored. The key factor for the replacement, which influences the fire extinguishing efficiency, is the oxygen content in the contact point between the jet and the flame. Firstly, the oxygen content of the ultrafine powder jet driven by air or nitrogen were investigated by gas analyzer; Secondly, 150 L (liter) gas oil and 50 L water were put in a oil pan, the compared fire extinguishing experiments were conducted, the fire extinction time and the temperature drop range were investigated. In order to reveal the effect of ultrafine dry powder on oxygen content in gas jet, the experiment that spray the compressed nitrogen were conducted. The results show that there are not much differences for the two gases in extinguishing the pool fire, indicating that compressed air as the driving gas of the compound jet is feasible during fire extinguishing process.

In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions., Comment: minor corrections

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected consequences of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a collectively harmful alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the presence of non-public fitness benefits. When public good production is inexpensive, quorum sensing is a destructive alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a constructive strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

In late 2019, a novel coronavirus (COVID-19) was determined in Wuhan, China. The newly emerged epidemic has spread rapidly, with an increasing number of confirmed cases worldwide. While intelligent systems have been immensely tested and implemented across a wide range of health problems, the emergence of COVID-19 requires the need to use these systems in detecting, identifying, and preventing its outbreak. By using the bibliometric analysis approach, this research aims to provide a holistic view on the state-of-the-art research concerning intelligent systems and COVID-19 by analyzing the most used keywords, most cited articles and journals, most productive countries and institutions, most cited authors, and the role of intelligent systems during the COVID-19 outbreak. The results indicated that the existing research studies on intelligent systems during the COVID-19 outbreak have mainly concentrated on the use of machine learning algorithms in identifying and diagnosing the potential COVID-19 cases and predicting its extinction time. However, the number of articles published on the role of intelligent systems during COVID-19 pandemic is relatively few, suggesting that research in this field is still in its early stages, and more intensive research is required.

This article belongs to the Special Issue Statistical Methods for the Analysis of Infectious Diseases., We extend the classical compartmental frameworks for susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) systems to include an exposed/latent class or a chronic class of infection. Using a suite of stochastic continuous-time Markov chain models we examine the impact of latent and chronic infection on the mean time to extinction of the infection. Our findings indicate that the mean time to pathogen extinction is increased for infectious diseases which cause exposed/latent infection prior to full infection and that the extinction time is increased further if these exposed individuals are also capable of transmitting the infection. A chronic infection stage can decrease or increase the mean time to pathogen extinction and in particular this depends on whether chronically infected individuals incur disease-induced mortality and whether they are able to transmit the infection. We relate our findings to specific infectious diseases that exhibit latent and chronic infectious stages and argue that infectious diseases with these characteristics may be more difficult to manage and control., X.O. was supported by The Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training funded by the UK Engineering and Physical Sciences Research Council (grant EP/L016508/01), the Scottish Funding Council, Heriot-Watt University and the University of Edinburgh. A.W. was supported in part by a BBSRC EEID research grant BB/V00378X/1. This work is a contribution to the MCIU project CGL2017-89866 WildDriver.

Attalea nucífera is an acaulescent palm native of Colombia that is in risk of extinction. Between 2016-2017 we evaluated the structure and density of populations in six localities of the Magdalena river valley, and studied the population dynamic in the locality of Guaduas, Cundinamarca (VC). Although the population structure differs among locations (X2 = 1819; gl = 25; P < 0.05), populations tend to group according to the degree of habitat perturbation. In four localities an inverted J population structure was observed. A matrix population model showed a finite growth rate (λ) of 0.979 (CI95 % = 0.9620.997). The demographic processes of the permanence of seedlings, sub-adults and young adults show more elasticity. A transient dynamic simulation projected to 30 years shows that under the scenarios of paddock and cattle lopping the population size decrease drastically. The extinction threshold calculated for the population in the locality VC is of 145 years, but paddock and cattle lopping activities can reduce it to less than 40 years. Although Attalea nucífera persists in very disturbing locations in the Middle Magdalena Basin, the results of population dynamics in the locality VC suggest that it could be less tolerant of environmental disturbances. Thus, it is necessary to increase our knowledge of its population dynamics, as well as seed germination and seedling establishment in different disturbance conditions. RESUMEN Attalea nucífera es una palma nativa de Colombia que está en riesgo de extinción. Entre 2016-2017 se evaluó la estructura y densidad de las poblaciones en seis localidades del valle del río Magdalena, y se estudió su dinámica poblacional en una localidad de Guaduas, Cundinamarca (VC). Si bien la estructura poblacional difiere entre localidades (X2 = 1819; gl = 25; P < 0,05), las poblaciones tienden a agruparse de acuerdo al grado de perturbación del hábitat. En cuatro localidades se observó una estructura poblacional en forma de J invertida. El modelo matricial muestra una tasa finita de crecimiento poblacional (λ) de 0,979 (IC95 % = 0,962-0,997). El proceso demográfico de permanencia de las plántulas, de subadultos y de adultos jóvenes tuvo la mayor elasticidad. La dinámica transitoria proyectada a 30 años muestra que bajo los escenarios de potrerización y ramoneo del ganado el tamaño de la población disminuye drásticamente. El umbral de extinción calculado para esta población (VC) es de 145 años, pero las actividades de potrerización y ramoneo del ganado pueden reducirlo a menos de 40 años. Aunque Attalea nucífera persiste en localidades muy alteradas del Valle del Magdalena Medio, los resultados de la dinámica poblacional en la localidad VC sugieren que podría tener baja tolerancia a disturbios ambientales. Por lo cual es necesario incrementar nuestro conocimiento de la dinámica poblacional, así como la germinación de semillas y el establecimiento de plántulas en diferentes condiciones de disturbio.

The scarcity of local plant extinctions following recent climate change has been explained by demographic inertia and lags in the displacement of resident species by novel species, generating an ‘extinction debt’. We established a transplant experiment to disentangle the contribution of these processes to the local extinction risk of four alpine plants in the Swiss Alps. Projected population growth (λ) derived from integral projection models was reduced by 0.07/°C of warming on average, whereas novel species additionally decreased λ by 0.15 across warming levels. Effects of novel species on predicted extinction time were greatest at warming

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can only survive if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime., Comment: 36 pages, 18 figures

Water mist technologies have the potential either to replace and overcome problems where traditional technologies have not been as effective as desired. Thus the present work aims to describe the suitability of a low pressure water mist system in suppression class (B) (PMMA) fire. The present experimental work examine and evaluate the performance of the proposed system design configurations against the conventional sprinkler system. The evaluation is performed by analyzing both visual, temperature behavior, fire extinction time and water flow rate. The experimental program includes several tests which are conducted with four different types of nozzles include the conventional one. The results of the present work showed that low pressure water mist system have notables shorter time of flame knock-down, ghost flame, suppression and extinction is with noticeable low water flux density than the conventional system.

Let $$g=(g_{ij})$$ be a complete Riemmanian metric on $${\mathbb {R}}^2$$ with finite total area and let $$I_g$$ be the infimum of the quotient of the length of any closed simple curve $$\gamma $$ in $${\mathbb {R}}^2$$ and the sum of the reciprocal of the areas of the regions inside and outside $$\gamma $$ respectively with respect to the metric g. Under some mild growth conditions on g we prove the existence of a minimizer for $$I_g$$ . As a corollary we obtain a proof for the existence of a minimizer for $$I_{g(t)}$$ for any $$00$$ is the extinction time of the solution. This existence of minimizer result is assumed and used without proof by Daskalopoulos and Hamilton (2004).

Optimal extinction rates near the extinction time are derived for non-negative solutions to a fast diffusion equation with strong absorption, the power of the absorption exceeding that of the diffusion.

In order to improve the fire resistance of lithium battery and to study the effect of water mist containing surfactant on gas explosion in lithium battery fire, a fire extinguishing test system and an explosion test system were used to evaluate the fire extinguishing efficiency and the anti-blast performance of the lithium battery. The fire extinguishing tests show that the fire extinction time is greatly shortened after adding a certain proportion of the surface active agent to the pure water. The active agent could rapidly reduce the temperature of the combustion, wet and penetrate the surface of the combustibles and finally achieve rapid and safe fire extinguishing effect. The experimental results show that the addition of surfactant water mist reduces the temperature generated during the explosion in a short time, slows down the explosion flame propagation speed and weakens the intensity of the explosion. Through the analysis of the results of fire and explosion suppression, it is shown that the fire can be efficiently extinguished and the explosion can be significantly suppressed by adding no more than 5% surfactant.

Although antiretroviral therapies (ARTs) reduce viral load to undetectable levels, HIV can persist within a small pool of long-lived resting memory CD4+ T cells. In concert with ART, different latency reversal agents (LRAs) are under development to activate latent reservoirs thus reducing viral persistence. Based on a stochastic Markov branching process with HIV reservoirs dynamics in isolation, simulations suggest that 10 folds increase in the activation rate from latently to actively infected could reduce the extinction time for all reservoirs to 50 months. However, when viral dynamics and new infection cycles are incorporated in a more realistic scenario, stochastic simulations point out that LRAs would require at least 30 fold increase in the activation rate to induce concomitant eradication of the different sub-reservoirs.

The ignition and combustion behaviors of single particles of Zhundong lignite were experimentally investigated. Single particles of Zhundong lignite with a diameter varying from 2 to 3 mm were suspended on a SiC fiber, and their burning in air in a horizontal tube furnace operating at 1023, 1073, 1123, 1173, and 1223 K was observed, aided with a charge-coupled device camera at 25 fps. By analysis of the captured images, the ignition delay time, flame displacement, volatile flame duration, volatile extinction time, total burnout time, and ignition mechanism were determined. The typical ignition and combustion processes of Zhundong lignite consisted of four sequential but overlapping stages: (1) pre-ignition stage involving drying, devolatilization, and oxidation at the particle surface, (2) heterogeneous ignition and combustion, (3) ignition and combustion of volatile matter in the gas phase, and (4) combustion of the remaining char residue. Surprisingly, the ignition of Zhundong lignite followed a joint h...

This work is concerned with the extinction and positivity properties of solutions to the discrete p-Laplacian parabolic equation u t = Δ p , ω u − f ( u ) , p > 1 with a nonlinear absorption on a weighted graph. We provide a complete characterization for f to see when we have an extinctive solution or a positive solution. In addition, the extinction time is estimated for the extinctive solutions, and the decay rate is given to the positive solutions. Finally, we give several numerical examples which illustrate the main results.

We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness. Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed. The meanexplosion time and the total mean life time of the processes are also investigated and resolved.

In the present work, the extinguishing parameters influencing the dry chemical powder system performance were analyzed and optimized using Taguchi design for minimizing the extinction time of small-scale vertical and horizontal gaseous fires. The system-related parameters include the release pressure (0.2 MPa, 0.3 MPa, and 0.4 MPa), the suppression angle (horizontal, diagonal, and vertical), and the release distance (50 cm, 75 cm, and 100 cm). The extinguishing tests were carried out in a lab-scale local application system. In this study, the magnesium hydroxide powder (Mg(OH)2) was used as an extinguishing agent. The analysis of experimental results showed that the optimum extinguishing conditions for small vertical and horizontal fires were at the release pressure (0.4 MPa), the suppression angle (vertical), and the release distance (50 cm). The analysis of variance indicated that the percentage contribution of extinguishing parameters on vertical fire extinction time was in the following order: suppression angle (44.69%) > the release distance (39.04%) > the release pressure (2.63%). While the order in case of the horizontal fire was as follows: the release distance (66.00%) > the release pressure (17.65%) > suppression angle (12.34%). The confirmatory tests showed that the extinction time at optimal parameters was lower than that achieved in all other experimental tests.

The coexistence of many species within ecological communities poses a long-standing theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this phenomenon by examining the chance of a species population growing from rarity in the presence of all other species. The mean growth rate when rare, 𝔼[r], is used in MCT as a metric that measures persistence properties (like invasibility or time to extinction) of a population. Here we critique this reliance on 𝔼[r] and show that it fails to capture the effect of random abundance variations on persistence properties. The problem becomes particularly severe when an increase in the amplitude of stochastic temporal environmental variations leads to an increase in 𝔼[r], since at the same time it enhances random abundance fluctuations and the two effects are inherently intertwined. In this case, the chance of invasion and the mean extinction time of a population may even go down as 𝔼[r] increases.

Cyclic dominance between species may yield spiral waves that are known to provide a mechanism enabling persistent species coexistence. This observation holds true even in presence of spatial heterogeneity in the form of quenched disorder. In this work we study the effects on spatio-temporal patterns and species coexistence of structured spatial heterogeneity in the form of habitats that locally provide one of the species with an advantage. Performing extensive numerical simulations of systems with three and six species we show that these structured habitats destabilize spiral waves. Analyzing extinction events, we find that species extinction probabilities display a succession of maxima as function of time, that indicate a periodically enhanced probability for species extinction. Analysis of the mean extinction time reveals that as a function of the parameter governing the advantage of one of the species a transition between stable coexistence and unstable coexistence takes place. We also investigate how efficiency as a predator or a prey affects species coexistence., Comment: 21 pages, 9 figures, accepted for publication in Journal of Theoretical Biology

Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations the stochastic effects become more relevant. Here we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of the bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in the population growth rates on dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.

We study a version of the Hermitian curvature flow on compact homogeneous complex manifolds. We prove that the solution has a finite extinction time $$T>0$$ and we analyze its behavior when $$t\rightarrow T$$ . We also determine the invariant static metrics and we study the convergence of the normalized flow to one of them.

Worldwide, predators and humans are in conflict for resources such as game species or livestock, especially in the case of wild canids. One non-lethal method to reduce predation is conditioned food aversion (CFA), in which animals learn to avoid a food due to the illness after ingestion, caused by the addition of an undetected chemical compound. CFA can be enhanced by adding an artificial odour cue, in a process known as taste-potentiated odour aversion (TPOA). We tested CFA and TPOA with three experimental groups of penned dogs. Food was offered with a combination of microencapsulated levamisole + vanilla odour (ODO), microencapsulated levamisole (LEV), or plain food as a control. The aims were (a) to test whether dogs detected the microencapsulated levamisole, (b) to analyse the strength and extinction time of CFA induced by microencapsulated levamisole, and (c) to analyse the strength and extinction time of TPOA. Two-choice tests were carried out during 11 post-conditioning months, and two reinforcements with microencapsulated levamisole were performed during the first post-conditioning month. In the first post-conditioning test, ODO and LEV groups ate significantly less untreated food than control group. After reinforcement, the dogs in LEV group resumed eating the food. Three of four dogs in ODO group showed long-lasting CFA until the 11th month. These results show that TPOA could be used to induce odour aversion on canids and that the odour cue overshadows the slight bitter taste of microencapsulated levamisole. These results show TPOA as a promising tool to reduce predation by wild canids., This study is a result of CGL2013–40975-R project, from I + D + I National Plan funded by the Spanish Ministry of Economy and Competitiveness. Jorge Tobajas benefitted from a FPI PhD scholarship (BES-2014-068987) funded by the Spanish Ministry of Economy and Competitiveness.

Currently, China's timber industry is in high demand with the development of real estate. However, there is a certain fire hazard in the production process of wood manufacturing. Once a fire occurs, the fire is violent and the spread is rapid. Therefore, to improve the safety of its production process, ammonium dihydrogen phosphate and magnesium hydroxide were selected to prepare a new composite superfine dry powder, which was denoted as the NH4H2PO4/Mg(OH)2 composite. Furthermore, to figure out dry powders' extinction effect on Class A fire, the wood-crib fire suppression effect of the NH4H2PO4/Mg(OH)2 composite was test, and then compared with that of ultrafine dry powder (UDP) and commercial ABC dry powder (C-ABC) in a 1 m³ chamber. Three parameters of the fire extinguishing process, namely flame extinction time, powder consumption and temperature drop were adopted to measure the fire suppression performance. The results demonstrated that UDP and C-ABC both had a larger flame extinction time and powder consumption than the NH4H2PO4/Mg(OH)2 composite. Besides, a fire (wood cribs) can be extinguished by the NH4H2PO4/Mg(OH)2 composite with the fastest temperature drop and a much-improved toxic gas suppression ability. In short, the NH4H2PO4/Mg(OH)2 composite can better guarantee the safety of the wood processing production process. Moreover, the reasons for performance advantages of the NH4H2PO4/Mg(OH)2 composite were discussed.

We considered a chain-binomial epidemic model not conferring immunity after infection. Mean field dynamics of the model has been analyzed and conditions for the existence of a stable endemic equilibrium are determined. The behavior of the chain-binomial process is probabilistically linked to the mean field equation. As a result of this link, we were able to show that the mean extinction time of the epidemic increases at least exponentially as the population size grows. We also present simulation results for the process to validate our analytical findings.

In this paper we study the asymptotic behaviour near extinction of (sub-)critical continuous-state branching processes. In particular, we establish an analogue of Khintchine's law of the iterated logarithm near extinction time for a continuous-state branching process whose branching mechanism satisfies a given condition.

We study inhomogeneous host–pathogen dynamics to model the global amphibian population extinction in a lake basin system. The lake basin system is modeled as quenched disorder. In this model we show that once the pathogen arrives at the lake basin it spreads from one lake to another, eventually spreading to the entire lake basin system in a wave like pattern. The extinction time has been found to depend on the steady state host population and pathogen growth rate. Linear estimate of the extinction time is computed. The steady state host population shows a threshold behavior in the interaction strength for a given growth rate.