Search Results (71)

We develop a closed-form analysis of the joint distribution for cumulative shock reliability systems with phase-type inter-shock times. The analytical literature on shock-driven reliability has hitherto been split into two largely separate traditions: scalar fluctuation theory, which delivers closed-form joint distributions of pre-failure and failure-time observables but cannot accommodate matrix phase structure; and matrix-analytic methods, which handle phase-type dynamics naturally but focus on stationary indicators rather than first-passage distributions. We bridge these traditions by introducing a matrix-valued reliability functional ${\mathbf{\Phi }}_{\nu }(\xi ,u,v,\vartheta ,\theta )$ that encodes the joint distribution of the failure index, pre-failure damage and time, failure-time damage and time, and the operational phase at the moment of failure. We derive ${\mathbf{\Phi }}_{\nu }$ in closed form via Sherman–Morrison reduction of the matrix Laplace–Stieltjes transform together with the Dshalalow $\mathfrak{D}$-operator, and establish a span-reduction theorem showing that ${\mathbf{\Phi }}_{\nu }$ lies in a three-dimensional matrix subspace generated by the identity and two matrix LSTs. The functional simultaneously generalizes the scalar fluctuation functional of Dshalalow and White and the phase-tagged first excess functional of Tadj, recovering both as projections. We extract twelve closed-form reliability indices, including the reliability function, mean time to failure, mean overshoot, joint pre-failure and failure transforms, and, new to the cumulative shock literature, the phase distribution at failure and the phase-resolved failure-time distribution. Two structural identities of Wald type emerge as corollaries. The framework reduces to elementary arithmetic for rational model primitives and is verified against $2\times {10}^5$ Monte Carlo trajectories in a worked example. Full article

In this article, we numerically investigate the effects of noise and heterogeneity on a model of immune–tumor cell interactions. We focus on stochastic dynamics and simulation-based analysis of the time required for tumor elimination. We identify the existence of a bistable response, which is disrupted by the introduction of intrinsic noise into the system. In particular, we characterize noise-induced transitions using first-passage time statistics and waiting-time distributions. We discuss various scenarios of tumor elimination, including the impact of vitamin intake and chemotherapy on tumor cell count, mean elimination time, and the duration of tumor dominance. Our results show that increasing chemotherapy reduces the maximum tumor count and decreases the average tumor elimination time, while intrinsic noise promotes memoryless switching toward the tumor-free state. This behavior is explained by the emergence of a quasi-stationary distribution governing the metastable tumor-present regime, leading to exponentially distributed extinction times. Furthermore, this framework enables the decay rate $\lambda$ to be estimated from simulation data and related to treatment parameters $({\beta }_1,\gamma )$. These findings provide a theoretical and statistical justification for memoryless tumor elimination dynamics and offer quantitative insights into stochastic treatment outcomes. Full article

This paper investigates the transition behaviour and stochastic resonance phenomenon in a class of bifurcation systems with a symmetric piecewise smooth potential, induced by a control parameter, under the combined influence of multiplicative white noise, additive white noise, and a periodic force. As the control parameter increases, the symmetric piecewise smooth potential of the system evolves from tristability to bistability. To study stochastic resonance in this system, an approximate Fokker–Planck equation is first derived based on Novikov’s theorem and the Fox approximation method. Subsequently, the approximate stationary probability density of the system is obtained from the Fokker–Planck equation, revealing the occurrence of a stochastic P-bifurcation. Then, within the bistable and multistable regimes, the effects of the bifurcation parameter, multiplicative noise intensity, and additive noise intensity on the mean first passage time (MFPT) are analysed. Finally, based on the mean first passage time, the response amplitude for stochastic resonance is derived via linear response theory, and the influences of the bifurcation parameter, noise intensities, correlation time, and signal frequency on the response amplitude are examined. In the bifurcation regime, the correctness of the expressions is verified numerically. It is found that multistability reduces the mean first passage time, and stochastic resonance is further analysed using the Fokker–Planck equation. Full article

The paper develops a coarse-grained framework for computing mean extinction times in multi-metastable systems modeled as one-step continuous-time Markov chains with an absorbing state. At the microscopic level, backward equations on finite corridors are solved to obtain closed-form series for committors, mean first-passage times, and intrawell (basin) waiting times. A renewal–reward construction then yields effective interwell transition rates written as a success probability divided by a mean cycle duration, providing an interpretable effective rate constant. These rates define a reduced Markov chain on the wells together with extinction; mean extinction times follow from a linear system, and the associated fundamental matrix quantifies pre-extinction residence times in each coarse state. This framework makes explicit how multiple escape pathways and intrawell dwell times contribute to extinction statistics in finite systems. The method is illustrated on a double-well landscape with an extinction state, using a reversible potential-to-rates mapping for the numerical example. Comparisons of alternative intrawell models and validation against exact one-step computations demonstrate accuracy at finite system sizes, including regimes where diffusion approximations are unreliable. The resulting formulas require only local rate data, remain numerically stable under strong bias, and extend directly to multiple wells and flexible boundary conditions. Full article

Background: Despite the advantages of extraperitoneal cesarean delivery (EPCD) indicated by observational studies, there is little accurate evidence supporting this technique, and the studies performed have included small numbers of participants. We aimed to examine intra- and postoperative maternal and neonatal outcomes in EPCD compared with transperitoneal CD (TPCD). Methods: Six databases restricted to English-language studies were searched from inception to August 2025. Only peer-reviewed randomized controlled trials (RCTs) directly comparing EPCD and TPCD were included. Study quality was evaluated using the Cochrane Risk of Bias tool. Primary neonatal and primary maternal outcomes were the Apgar score and postoperative pain, respectively. The protocol was prospectively registered in PROSPERO (#CRD42023420365). Results: Of the 69 reports identified, seven RCTs comprising 758 women (379 per group) were eligible. Data for 1 min Apgar scores were insufficient for analysis because standard deviations were missing for most studies. Five-minute Apgar scores were comparable between the two techniques (p = 0.91). Incidence of umbilical artery pH < 7.2 was higher in the EPCD group than in the TPCD group (7.9% vs. 2.3%, respectively; p = 0.047). Mean incision-to-delivery time was longer in the EPCD group (7.5 ± 5.0 min) compared with the TPCD group (6.2 ± 3.7 min, p = 0.017). Postoperative pain at 24 h was lower after EPCD (p < 0.001), and time to first gas passage was shorter (7.4 ± 2.7 h vs. 14.7 ± 2.7 h, p < 0.001) compared with TPCD. Other perioperative outcomes were comparable. Conclusions: The safety of EPCD for the neonate requires further investigation. Maternal postoperative pain and time to gas passage were favorable in EPCD. Full article

Computing the exact mathematical expression for a quantity defined in terms of a first-passage time random variable for a jump-diffusion process is in general very difficult. In this paper, we consider the following inverse problem: can we find a certain distribution for the size of the jumps that leads to a simple solution of the integro-differential equation satisfied by the quantity of interest, subject to the appropriate boundary conditions? Such distributions are found, in particular, for the mean of the first-passage time for important jump-diffusion processes. Full article

Diffusion in heterogeneous environments is usually governed by unusual dynamics, exhibiting sub- or superdiffusive scaling depending on the structural complexity and memory effects. In many systems, diffusing particles may alternate between periods of motion and rest, or may undergo stochastic resetting to a preferred position. While each of these mechanisms has been studied independently, their combined effect in a heterogeneous medium has been insufficiently investigated. We formulate and solve a coupled set of one dimension diffusion equations for the probability densities of moving and resting particles, accounting for space-dependent diffusivity and stochastic resetting. We obtain expressions for the probability distribution and show the behavior of the survival probability, mean-square displacement, and first-passage time. The results reveal a diverse range of behaviors with distinct diffusion regimes. One of them is obtained for small times, which can be connected to the heterogeneity present in the system, and another for intermediate times related to the intermittent process produced by the moving and pauses before the system reaches the stationary state. Full article

The arrival of tracers at boundaries with defined distances from the origin of their motion in stochastically fluctuating advection processes is investigated. The advection model is a stationary one-dimensional integrated stochastic process with an arbitrary a priori known correlation and with possible mean drift. The current (direction-sensitive), the total flux (direction-insensitive) of tracers through a non-absorbing boundary, and the first-passage times of the tracers at an absorbing boundary are derived depending on the correlation function of the carrying flow velocity. While the general derivations are universal with respect to the distribution function of the advection’s increments, the current and the total flux are explicitly derived for a Gaussian distribution. The first-passage time is derived implicitly through an integral that is solved numerically in the present study. No approximations or restrictions to special cases of the advection process are used. One application is one-dimensional Gaussian turbulence, where the one-dimensional random velocity carries tracer particles through space. Finally, subdiffusive or superdiffusive behavior can temporarily be reached by such a stochastic process with an adequately designed correlation function. Full article

For human beings, accepting loss and absence is a constant effort, particularly when it comes to accepting their own finitude, which becomes apparent as time passes and people leave us. This is closely linked to nostalgia and the processes of remembrance. While there are many nuances, we can distinguish between constructive and destructive nostalgia. The former cannot accept absence or the passage of time and deludes itself into thinking that it can recover what has been lost. The latter recognizes the temptation to recover everything, but knows that this is impossible, and accepts that the past can only be preserved by transforming it into something else. Contemporary technologies that use algorithms can exacerbate the former tendency by manipulating memory processes and distorting the meaning of the virtual. The aim of this contribution is to shed light on the dynamics and implications of nostalgia as it is influenced by algorithms. To this end, it is divided into three stages. In the first stage, nostalgia is examined for its “restraining” power in relation to deterministically progressive philosophies of history, also through a reference to the original philosophical meaning of the term ‘virtual’. In the second stage, the relation to progress is thematized through a reflection on technologies and artificial intelligence, which uses algorithms and devours our data. In the third stage, it will be shown how thinking about nostalgia and artificial and algorithmic ‘intelligence(s)’ can be a valuable test case for distinguishing between the uses and abuses of nostalgia, between constructive nostalgia and destructive nostalgia. Full article

This article describes the relationship between spatial perception and temporal experience, emphasizing the limitations of linear frameworks in understanding these phenomena for contemporary students of design. Drawing on recent literature in neuroscience, the author argues for wider recognition of how our brains represent space through an awareness of non-Euclidean geometries, particularly hyperbolic models that more holistically reflect the complexity of lived experience. Through the lens of personal narratives, including reflections on living in a militarized landscape in Hawai‘i, the paper emphasizes the importance of various cultural and sensory interpretations of time—such as “Hawaiian Time” and “Turtle Time”—which offer unique perspectives on what it means to exist in these built environments. Ultimately, it advocates for a pedagogical shift in design education that encourages students to embrace and integrate more diverse temporal experiences in their work, fostering a richer awareness of their present as they engage with the conceptualization and design of built space. Three key assertions are described. First, multiple, different perceptions of time coexist in the same universe and reality, offering various sensations and registrations of existence. Second, these diverse views on the passage of time, like Island Time, emphasize a slower, more direct engagement with life’s vicissitudes, in contrast to mechanical time, for example. Lastly, by acknowledging the presence of differing states of temporal perception, design students are aided in more holistic and rational conceptualization of built space and therefore in their own movement into complex and indeterminant futures in design. Full article

In this article, I investigate the ontological status of the minor working-class character Mrs. McNab, the cleaner in “Time Passes", the middle section of Virginia Woolf’s tripartite novel To the Lighthouse. Woolf regarded this section as the connecting block between the two outer blocks, “The Window” and “The Lighthouse”, in which she aimed to depict an empty house, devoid of human presence, and to highlight the passage of time. This section has often been analysed by literary-stylistic criticism as if written from a non-anthropocentric worldview. However, the presence of a lower-class cleaner and the absence of the upper middle-class characters who predominate in the other two blocks has also raised much debate in the literary arena. Literary critics agree that this character is given a narrative voice, but how this voice functions, and whether this character is granted narrative agency in terms of the class issues and social relations in the period of transition between Victorian England and the early twentieth-century, is an issue which still remains open. Drawing upon cognitive stylistics, I suggest reading this character both as a category-based and person-based character, and as a narrative device. First, I carry out the analysis of the repetitive she-clusters and their semantic prosodies; then, through samples of the section “Time Passes", I analyse how viewpoint blending between narrator/author and character concur to grant narrative agency to Mrs. McNab and to what extent such agency may be limited by our perception of her through the social schemata of a servant, or whether such a perception may undergo a process of schema refreshment. Last, I suggest that this character may also be viewed as a narrative agent by means of which the reader can activate mental processes of TIME and SPACE blending between the three different blocks of the novel. This blending process allows for the completion of the narrative design of the novel: the journey to the lighthouse. Full article

Climate change and intensified human activities have led to plant degradation and land desertification in desert areas, which seriously threaten ecological security. The establishment of the Caragana korshinskii plantation is considered to be one of the important means to improve the ecological environment in thealpine sandy region. This study focuses on Caragana korshinskii plantation in the alpine sandy region of the Qinghai–Tibet Plateau. Adopting a space-for-time substitution approach, six restoration chrono sequences were selected: 0 years, 5 years, 15 years, 25 years, 35 years, and 50 years. By investigating the variations in vegetation community composition and soil properties, we aim to elucidate the plant and soil system interactions under different restoration durations. The findings will clarify the stability evolution patterns of Caragana korshinskii plantation during desertification control and contribute to promoting green development strategies. The main conclusions of this study are as follows: With the passage of planting time, the plant biomass and species diversity of the Caragana korshinskii plantation community showed a trend of first increasing and then decreasing, reaching their peak in 25~35 years. Soil water content exhibited fluctuating trends, while soil organic matter showed progressive accumulation, demonstrating that Caragana korshinskii plantations effectively improved soil fertility. Community stability reaches its maximum (4.98) at 25 years. In summary, the Caragana korshinskii plantation are in an early stage of ecological secondary succession, with plant communities developing from simple to complex structures and gradually approaching, though not yet achieving a stable state. Full article

This study examines the diffusion of spherical particles in a conical widening channel, with a focus on the effects of deterministic drift and entropic forces. Through numerical simulations, we analyze the motion of particles from a reflecting boundary to an absorbing one. Properties of diffusive motion are explored by inspection of mean squared displacement and mean first passage time. The results show that the diffusion type depends on the drift strength. Without the drift, entropic forces induce effective superdiffusion; however, the increasing drift strength can counterbalance entropic forces and shift the system to standard diffusion and then effective subdiffusion. The mean squared displacement exhibits bending points for high drift values, as predicted by one-dimensional theoretical considerations. The study underscores the importance of considering deterministic and entropic forces in confined geometries. Full article

First-exit problems are studied for two-dimensional diffusion processes with jumps according to a Poisson process. The size of the jumps is distributed as an exponential random variable. We are interested in the random variable that denotes the first time that the sum of the two components of the process leaves a given interval. The function giving the probability that the process will leave the interval on its left-hand side satisfies a partial differential–integral equation. This equation is solved analytically in particular cases by making use of the method of similarity solutions. The problem of calculating the mean and the moment-generating function of the first-passage time random variable is also considered. The results obtained have applications in various fields, notably, financial mathematics and reliability theory. Full article

Even though Kemeny’s constant was first discovered in Markov chains and expressed by Kemeny in terms of mean first passage times on a graph, it can also be expressed using the pseudo-inverse of the Laplacian matrix representing the graph, which facilitates the calculation of a sharp upper bound of Kemeny’s constant. We show that for certain classes of graphs, a previously found bound is tight, which generalises previous results for bipartite and (generalised) windmill graphs. Moreover, we show numerically that for real-world networks, this bound can be used to find good numerical approximations for Kemeny’s constant. For certain graphs consisting of up to 100 K nodes, we find a speedup of a factor 30, depending on the accuracy of the approximation that can be achieved. For networks consisting of over 500 K nodes, the approximation can be used to estimate values for the Kemeny constant, where exact calculation is no longer feasible within reasonable computation time. Full article