Extinction Conditions Research Articles

Stochastic stability and instability of rumor model

Abstract In this study, we present a stochastic rumor model. The stability of the disease-free equilibrium state and instability of the free equilibrium E 0 {E}_{0} of stochastic epidemics model are considered with the help of Lyapunov functions. Sufficient conditions of persistence and extinction of rumor are given. Numerical simulations verify the analytical results.

Outcome devaluation as a method for identifying goal-directed behaviors in rats.

Goal-directed behaviors allow animals to act to satisfy needs and desires. The outcome devaluation task is an effective method for identifying goal-directed behaviors and distinguishing these from other types of behavior. Rats can be trained to lever-press for one or multiple distinct food rewards. During testing, the previously earned food-or a control food for comparison-is devalued by allowing the animal to freely feed on it until they are sated before testing lever-press performance under extinction conditions (no rewards are delivered). Behavior that adapts to reflect the new value of the outcome is considered goal-directed, whereas behavior that continues as in previous training despite the change in outcome value, is not. As more research groups have used this task, variability in the procedures used has increased. Here, we provide a reliable procedure for conducting the outcome devaluation task with appropriate controls. We describe the most common variants of the task and control conditions and discuss troubleshooting measures such as outcome pre-exposure, habituation to pre-feeding chambers and attention to animals' hunger levels. The method outlined can be executed in ~2 weeks including training (~8 d) and testing (1-4 d) by researchers who are familiar with performing behavioral tasks in laboratory rodents, although longer training may be considered for those who are interested in observing habitual control of behavior. This protocol should facilitate the comparison of results from different studies and laboratories, while allowing flexibility in the application of the outcome devaluation task to different research questions.

Extended Monte Carlo modeling for submicron particle size measurement under high light extinction conditions.

The light extinction method (LEM) based on Lambert Beer's law (LB) is widely used to characterize particle size distribution (PSD) in multiphase flow. However, as the optical thickness increases with concentration, the phenomenon of multiple scattering is enhanced, potentially leading to reduced accuracy and a limited application range. In this study, an extended Monte Carlo-based light extinction model (EMC) was developed, which was initially employed to calculate and evaluate the impact of multiple scattering. Subsequently, it was used to predict the extinction spectrum that incorporates multiple scattering effects under varying concentrations. To validate the modeling, a compact setup was constructed to perform a series of experiments on polystyrene and silica dioxide (SiO2) suspensions. A differential evolution algorithm was also implemented for the inversion of PSD based on spectral content, with the incorporation of an improved coefficient matrix that considers multiple scattering effects. In comparison to the linear LB model, the EMC exhibits a markedly enhanced capacity in handling higher particle concentrations and improving measurement accuracy. For a 700 nm PS suspension, the particle size inversion error of the EMC can be kept within 4% (93.86% for the LB model) compared with the nominal value, even with an optical thickness of 5.

Extinction Dynamics and Equilibrium Patterns in Stochastic Epidemic Model for Norovirus: Role of Temporal Immunity and Generalized Incidence Rates

Norovirus is a leading global cause of viral gastroenteritis, significantly affecting mortality, morbidity, and healthcare costs. This paper develops and analyzes a stochastic SEIQR epidemic model for norovirus dynamics, incorporating temporal immunity and a generalized incidence rate. The model is proven to have a unique positive global solution, with extinction conditions explored. Using Khasminskii’s method, the model’s ergodicity and equilibrium distribution are investigated, demonstrating a unique ergodic stationary distribution when R^s>1. Extinction occurs when R0E<1. Computer simulations confirm that noise level significantly influences epidemic spread.

Partial tipping in bistable ecological systems under periodic environmental variability.

Periodic environmental variability is a common source affecting ecosystems and regulating their dynamics. This paper investigates the effects of periodic variation in species growth rate on the population dynamics of three bistable ecological systems. The first is a one-dimensional insect population model with coexisting outbreak and refuge equilibrium states, the second one describes two-species predator-prey interactions with extinction and coexistence states, and the third one is a three-species food chain model where chaotic and limit cycle states may coexist. We demonstrate with numerical simulations that a periodic variation in species growth rate may cause switching between two coexisting attractors without crossing any bifurcation point. Such a switchover occurs only for a specific initial population density close to the basin boundary, leading to partial tipping if the frozen system is non-chaotic. Partial tipping may also occur for some initial points far from the basin boundary if the frozen system is chaotic. Interestingly, the probability of tipping shows a frequency response with a maximum for a specific frequency of periodic forcing, as noticed for equilibrium and non-equilibrium limit cycle systems. The findings suggest that unexpected outbreaks or abrupt declines in population density may occur due to time-dependent variations in species growth parameters. Depending on the selective frequency of the periodic environmental variation, this may lead to species extinction or help the species to survive.

Stochastic two-strain epidemic model with saturated incidence rates driven by Lévy noise

In this paper, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model. Then, it moves to the determination of sufficient conditions of extinction and persistence in mean of the two-strain disease. In order to illustrate the theoretical findings, we give some numerical simulations.

Dynamic properties of rumor propagation model induced by Lévy noise on social networks

Abstract Social networks are inevitably subject to disruptions from the physical world, such as sudden internet outages that sever local connections and impede information flow. While Gaussian white noise, commonly used to simulate stochastic disruptions, only fluctuates within a narrow range around its mean and fails to capture large-scale variations, Lévy noise can effectively compensate for this limitation. Therefore, a susceptible–infected–removed rumor propagation model with Lévy noise is constructed on homogeneous and heterogeneous networks, respectively. Then, the existence of a global positive solution and the asymptotic path-wise of the solution are derived on heterogeneous networks, and the sufficient conditions of rumor extinction and persistence are investigated. Subsequently, theoretical results are verified through numerical calculations and the sensitivity analysis related to the threshold is conducted on the model parameters. Through simulation experiments on Watts–Strogatz (WS) and Barabási–Albert networks, it is found that the addition of noise can inhibit the spread of rumors, resulting in a stochastic resonance phenomenon, and the optimal noise intensity is obtained on the WS network. The validity of the model is verified on three real datasets by particle swarm optimization algorithm.

Involvement of Pre-limbic Cortex-Nucleus accumbens projections in Context-Induced alcohol seeking

Alcohol use disorder (AUD) remains a critical public health issue worldwide, characterized by high relapse rates often triggered by contextual cues. This research investigates the neural mechanisms behind context-induced reinstatement of alcohol-seeking behavior, focusing on the nucleus accumbens and its interactions with the prelimbic cortex, employing Male Long-Evans rats in an ABA renewal model. In our experimental setup, rats were trained to self-administer 10 % ethanol in Context A, followed by extinction of lever pressing in the presence of discrete cues in Context B. The context-induced reinstatement of ethanol-seeking was then assessed by re-exposing rats to Context A or B under extinction conditions, aiming to simulate the environmental cues’ influence on relapse behaviors. Three experiments were conducted: Experiment 1 utilized Fos-immunohistochemistry to examine neuronal activation in the nucleus accumbens; Experiment 2 applied the baclofen + muscimol inactivation technique to probe the functional importance of the nucleus accumbens core; Experiment 3 used Fos-immunofluorescence along with Retrobeads injection to investigate activation of neurons projecting from the prelimbic cortex to the nucleus accumbens core. Our findings revealed significant increases in Fos-immunoreactive nuclei within the nucleus accumbens core and shell during the reinstatement phase in Context A, underscoring the environment’s potent effect on ethanol-seeking behavior. Additionally, inactivation of the nucleus accumbens core markedly reduced reinstatement, and there was a notable activation of neurons from the prelimbic cortex to the nucleus accumbens core in the ethanol-associated context. These results highlight the critical role of the nucleus accumbens core and its corticostriatal projections in the neural circuitry underlying context-driven ethanol seeking.

Imagery rescripting and extinction: Effects on US expectancy, US revaluation, and the generalization of fear reduction

Exposure therapy consists of exposing patients to their fears and thereby diminishing their harm expectancies (i.e., extinction or expectancy learning). Although effective for many anxiety patients, its long-term success depends on the generalization of these harm expectancies to other stimuli. However, research shows that this generalization of extinction is limited. Besides decreasing harm expectancies, fear reduction may also be achieved by changing the meaning of an aversive memory representation (US revaluation). Imagery rescripting (ImRs) may be more successful in generalizing fear reduction because it allegedly works through US revaluation. The current experiment aimed to test working mechanisms for ImRs and extinction (revaluation and expectancy learning, respectively), and to examine generalization of fear reduction. In a fear conditioning paradigm, 113 healthy participants watched an aversive film clip that was used as the US. The manipulation consisted of imagining a script with a positive ending to the film clip (ImRs-only), extinction (extinction-only), or both (ImRs + extinction). Results showed enhanced US revaluation in ImRs + extinction. US expectancy decreased more strongly in the extinction conditions. Generalization of fear reduction was found in all conditions. Our results suggest different working mechanisms for ImRs and exposure. Future research should replicate this in (sub)clinical samples.

The role of posterior parietal cortex in detecting changes in feedback contingency.

Well-practiced or learned behaviors are extremely resilient. For example, it is extremely difficult for a trained typist to forget how to use a keyboard configuration that they are familiar with. While they can be trained on a new keyboard configuration, the original skill quickly comes back when the old keyboard configuration is used again. This resiliency of learned skills is both a blessing and a curse. It makes useful skills durable, but it also makes maladaptive behaviors difficult to extinguish. Crossley et al. (2013) proposed a computational model and behavioral paradigm aimed at unlearning skills using various feedback contingency manipulations during an extinction phase. They showed that partially-valid feedback during extinction removed evidence for fast reacquisition, which they interpreted as evidence for unlearning. In this article, we replicated the Crossley et al. paradigm using fMRI. Univariate analyses showed differences in BOLD signals between the different experiment phases in the frontoparietal attention network. The superior and inferior parietal lobules (SPL and IPL, respectively) showed the largest cluster differences both between experimental phases and between extinction conditions. In contrast, the prefrontal cortex only showed differences in cluster of activities between extinction conditions. Multivariate pattern analysis was also used with seeds in the SPL and IPL. The results showed that these brain areas were critical in detecting changes in experimental phases. Overall, the fMRI results found mixed evidence for the Crossley et al. model and suggest that while unlearning prevents fast reacquisition, the absence of fast reacquisition does not necessarily implies that unlearning occurred.

Hierarchical higher-order dynamic mode decomposition for clustering and feature selection

This article introduces a novel, fully data-driven method for forming reduced order models (ROMs) in complex flow databases that consist of a large number of variables. The algorithm utilizes higher order dynamic mode decomposition (HODMD), a modal decomposition method, to identify the main frequencies and associated patterns that govern the flow dynamics. By incorporating various normalization techniques into an iterative process, clusters of variables with similar dynamics are identified, allowing the classification of different instabilities and patterns present in the flow. This method, known as hierarchical HODMD (h-HODMD), has been thoroughly tested in the development of ROMs using three different databases obtained from numerical simulations of a nonpremixed coflow methane flame. The effectiveness of h-HODMD has been demonstrated as it consistently outperforms HODMD in terms of modeling and reconstructing flow dynamics using a reduced number of modes. Additionally, the clusters of variables identified by h-HODMD reveal the algorithm's ability to group chemical species whose behavior is consistent from a kinetic perspective. h-HODMD allows for the construction of inexpensive reduced dynamical models that can predict flame liftoff, identify the occurrence of local extinction and blowout conditions, and facilitate control purposes.

On a singular parabolic $ p $-Laplacian equation with logarithmic nonlinearity

<p>In this paper, we considered a singular parabolic $ p $-Laplacian equation with logarithmic nonlinearity in a bounded domain with homogeneous Dirichlet boundary conditions. We established the local solvability by the technique of cut-off combining with the method of Faedo-Galerkin approximation. Based on the potential well method and Hardy-Sobolev inequality, the global existence of solutions was derived. In addition, we obtained the results of the decay. The blow-up phenomenon of solutions with different indicator ranges was also given. Moreover, we discussed the blow-up of solutions with arbitrary initial energy and the conditions of extinction.</p>

Interactive role-playing game for elementary students to introducing Javan Langur

Indonesia is a country with a lot of biodiversity, both in the form of animals and plants, unfortunately, some of the biodiversity is classified as almost extinct, or even extinct, and the Javan Langur is included in the group of endangered animals because of its declining population, recorded at the Javan Langur Center there are only a few of Javan Langurs that have been successfully repatriated. Javan Langurs are also not widely known to people about their existence and extinction conditions, so there must be media to provide information to the wider community, especially to elementary students to form knowledge and prevention. With the rapid development of technology in the current era, there are various learning media that can be used, one of which is interactive games. This work aims to help students recognize endangered animals, including the Javan Langur, and help teaching institutions provide effective learning media for students. This research use design thinking as the research method. Questionnaires and interviews with resource persons who are elementary school students in grades 5 and 6, teachers, and parents. The result of this research is an interactive learning media in the form of a game with storytelling feature. This storytelling feature also include lesson contents and some challenge games with a character that will guide the storyline, much like a role-playing game or RPG.

Effects of radiative heat loss on extinction limits of counterflow premixed ammonia-air flames

The effect of radiative heat loss on counterflow premixed ammonia-air flames has been investigated as a function of equivalence ratio and system pressure. Non-adiabatic counterflow premixed flame simulations incorporating detailed chemistry, transport, and radiative heat transfer in the optically thin limit have been employed to elucidate important underlying physics and extinction characteristics. Similar to methane-air flame systems, non-adiabatic counterflow premixed computations show that the combined effects of positive flame stretch, sub-unity Lewis number, and radiative heat loss lead to the extension of the lean flammability limit for ammonia-air flames, revealing a C-shaped curve near the lean flammability limit that exhibits both radiation-induced and stretch-induced extinction states. The computations compare favorably with the experimentally determined extinction stretch rate values for the stretch-induced extinction states over a wide range of equivalence ratios at different pressures up to 5 atm. A novel feature sensitivity analysis has also been developed to highlight important sensitive reactions for the stretch- and radiation-induced extinction states. Furthermore, the controlling chemistry at the dual-extinction states and at varying pressures are compared and discussed.

Stationary distribution and extinction of a stochastic HIV/AIDS model with nonlinear incidence rate.

This paper studies a stochastic HIV/AIDS model with nonlinear incidence rate. In the model, the infection rate coefficient and the natural death rates are affected by white noise, and infected people are affected by an intervention strategy. We derive the conditions of extinction and permanence for the stochastic HIV/AIDS model, that is, if $ R_0^s < 1, $ HIV/AIDS will die out with probability one and the distribution of the susceptible converges weakly to a boundary distribution; if $ R_0^s > 1 $, HIV/AIDS will be persistent almost surely and there exists a unique stationary distribution. The conclusions are verified by numerical simulation.

Conditions for extinction and ergodicity of a stochastic Mycobacterium tuberculosis model with Markov switching

&lt;p&gt;This paper is concerned with a stochastic Mycobacterium tuberculosis model, which is perturbed by both white noise and colored noise. First, we prove that the stochastic model has a unique global positive solution. Second, we derive an important condition $ R_0^* $ depending on environmental noise for this stochastic model. We construct an appropriate Lyapunov function, and show that the model possesses a unique ergodic stationary distribution when $ R_0^* &amp;lt; 0 $, in other words, it indicates the long-term persistence of the disease. Finally, we investigate the related conditions of extinction.&lt;/p&gt;

Environmental Enrichment during Abstinence Reduces Oxycodone Seeking and c-Fos Expression in a Subpopulation of Medial Prefrontal Cortex Neurons

BackgroundSeveral preclinical studies have demonstrated that environmental enrichment (EE) during abstinence reduces drug seeking for psychostimulant and opioid drugs. Drug seeking is dependent on activity within the dorsomedial prefrontal cortex, and enrichment has been able to reduce drug seeking-associated increases in c-Fos in this region. In this study, we tested the hypothesis that EE during abstinence from oxycodone self-administration would reduce drug seeking and c-Fos immunoreactivity within the prefrontal cortex in a cell-type specific manner. MethodsMale rats self-administered oxycodone in two-hours sessions for three weeks, then underwent an initial drug seeking test under extinction conditions after one week of forced abstinence. Following this test, rats received either EE or remained individually housed in their home cage, then a second drug seeking test, with tissue collection immediately afterward. ResultsCompared to rats in standard housing, environmentally enriched rats had lower oxycodone seeking. In the prelimbic and infralimbic prefrontal cortices, the number of c-Fos+ cells was reduced, and this reduction was predominantly in inhibitory cells neurons, as evidenced by a reduction in the proportion of c-Fos+ cells in GAD+, but not CamKII+ cells. There was also a robust positive relationship between the number of c-Fos+ cells and persistence of oxycodone seeking in both the PrL and IL. ConclusionsThese findings further support the effectiveness of enriched environments to reduce reactivity to drug-associated stimuli and contexts and provide a potential mechanism by which this occurs.

Critical conditions for ignition of boron particles in chlorine

This paper provides an analysis of ignition and extinction conditions of boron particles (with a diameter of up to 200 μm) in a nitrogen-chlorine gas mixture. The analytical description is carried out in a dimensionless form without using the Frank-Kamenetsky distribution. This makes it possible to more correctly describe extinction conditions of particle. An analytical approach is used to analyze critical conditions, which consists in founding dependencies in the form of parametric functions. It is shown that, depending on the parameters of the gas environment (temperature and proportion of chlorine), there are hysteresis areas, areas of ignition and extinction, and areas of the crisis-free chlorination mode of boron particles.&#x0D; The obtained dependencies are compared with experimental results. Their satisfactory agreement allows us to confirm the kinetic parameters of the chlorination reaction of boron particles, namely the activation energy E = 60 kJ/mol and the pre-exponential factor k0 = 4 m/s.

On a Coupled Time-Varying Beverton–Holt Model with Two Habitats Subject to Harvesting, Repopulation, and Mixed Migratory Flows of Populations

Two time-varying Beverton–Holt models are investigated in which the population of the same species evolves jointly in two coupled habitats which can be subject to population exchanges. Both habitats can have different parameterizations concerning their intrinsic growth rates and their environment carrying capacities due to different environmental conditions. Mutual fluxes of populations in-between both habitats are possible together with harvesting actions. In one of the models harvesting acts on juvenile individuals. In the other proposed model, harvesting takes place on the adult populations after the reproduction cycle they have performed has ended. The second investigated model, contrarily to the first one, relies on an “a posteriori” harvesting action to the reproductive stage which is able to modify the stocks of population. The considered harvesting can also be negative to describe repopulation actions. The equilibrium points in steady-state and their stability properties as well as the extinction conditions and the boundedness, oscillation issues, and positivity of the solutions are also investigated.

Role of nucleus accumbens D1-type medium spiny neurons in the expression and extinction of sign-tracking

While sign-tracking, also known as autoshaping, has been studied for many decades, only recently has the tendency to show sign-tracking behavior been linked to the development and persistence of addiction. Sign-tracking is dependent upon dopamine activity in the nucleus accumbens (NAc). The NAc is comprised predominantly of medium spiny projection neurons (MSN) that can be differentiated by their D1-like or D2-like dopamine receptor expression. Here we determined how reducing activity of D1-type MSNs in the NAc affects the expression and extinction of sign-tracking. To address this, we transfected the NAc of transgenic male and female rats that selectively express Cre recombinase in D1-type MSNs with a DIO viral vector expressing hM4Di. Cre- rats were given the same viral infusion but did not express the hM4Di receptor and therefore served as controls. Rats were then conditioned to associate lever presentations with pellet delivery. After sign-tracking was established, all rats were administered clozapine-n-oxide (CNO) prior to three additional conditioning sessions to assess the effects of NAc D1-MSNs inhibition on sign-tracking in the presence of reward. CNO treatment did not alter the expression of sign-tracking in Cre+ or Cre- rats. Next rats underwent extinction training where lever presentations occurred without pellet delivery and all rats received a CNO injection prior to each extinction session. In these extinction conditions, Cre+ rats exhibited robust extinction of sign-tracking across sessions, whereas Cre- rats did not. To determine if D1-MSN inhibition merely produced a temporary cessation of sign-tracking or instead had facilitated a persistent loss of sign-tracking, we evaluated the reemergence of sign-tracking in a test for reconditioning. During testing, reintroduction of the CS-US pairing did not promote the reemergence of sign-tracking in Cre+ rats, but restored sign-tracking in Cre- rats. Thus, chemogenetic inhibition of NAc D1-MSNs promoted extinction of sign-tracking. Collectively, these data suggest that D1-MSNs play an important role in resistance to extinction that typifies sign-tracking behavior.