Exponential Case Research Articles

Optimal Bayesian sampling plan for censored competing risks data

There is a substantial amount of literature in the area of acceptance sampling plan with censored lifetime data. However, the optimality of a Bayesian sampling plan in the presence of competing risks has not been considered so far. In this paper, first, the Bayesian sampling plans (BSP) for Type-II and Type-I hybrid censoring schemes are discussed in presence of competing risks when the lifetime distribution is exponential. The closed-form expression of the Bayes decision function is obtained analytically for a linear loss function. Then we consider the Weibull distribution with an unknown shape parameter under Type-I hybrid censoring scheme in presence of competing risks to obtain the BSP. However, the Bayes decision function cannot be obtained in closed-form for a general loss function, and in such cases, a numerical algorithm is proposed. As an illustration, in the exponential case, a quadratic loss function, and in Weibull case, a non-polynomial loss function, are considered for the application of the proposed numerical approach to obtain the optimum BSPs using the Bayes decision function.

Exponential stability and stabilization of positive T‐S fuzzy delayed systems

AbstractThe analysis of positive nonlinear delayed systems is of great importance for many real‐world applications. Such systems' stability and stabilization assessment is still an open topic, and there is limited literature on this field. Moreover, further convergence conditions should be considered for many experimental processes, such as exponential stability analysis, which is highly important. Considering the above, we deal in this study with the problem of exponential stability and stabilization of nonlinear fuzzy positive systems with delay. We establish exponential stability criteria using Lyapunov–Krasovskii functional (LKF) and a delay bi‐decomposition approach for bounded and time‐varying delayed systems. The obtained results are then extended to the exponential stabilization case. The control law is designed using Parallel distributed compensation (PDC). The proposed approach, formulated in terms of linear matrix inequalities (LMIs), allows reducing the conservativeness of the delay‐dependent conditions. A comparative study is presented to illustrate the superiority of our method. Moreover, simulation results for the two tanks process show the advantages of the proposed control design.

On a weighted elliptic equation of N-Kirchhoff type with double exponential growth

Abstract In this work, we study the weighted Kirchhoff problem − g ∫ B σ ( x ) ∣ ∇ u ∣ N d x div ( σ ( x ) ∣ ∇ u ∣ N − 2 ∇ u ) = f ( x , u ) in B , u > 0 in B , u = 0 on ∂ B , \left\{\begin{array}{ll}-g\left(\mathop{\displaystyle \int }\limits_{B}\sigma \left(x)| \nabla u\hspace{-0.25em}{| }^{N}{\rm{d}}x\right){\rm{div}}\left(\sigma \left(x)| \nabla u\hspace{-0.25em}{| }^{N-2}\nabla u)=f\left(x,u)& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}B,\\ u\gt 0& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}B,\\ u=0& \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial B,\end{array}\right. where B B is the unit ball of R N {{\mathbb{R}}}^{N} , σ ( x ) = log e ∣ x ∣ N − 1 \sigma \left(x)={\left(\log \left(\frac{e}{| x| }\right)\right)}^{N-1} , the singular logarithm weight in the Trudinger-Moser embedding, and g g is a continuous positive function on R + {{\mathbb{R}}}^{+} . The nonlinearity is critical or subcritical growth in view of Trudinger-Moser inequalities. We first obtain the existence of a solution in the subcritical exponential growth case with positive energy by using minimax techniques combined with the Trudinger-Moser inequality. In the critical case, the associated energy does not satisfy the condition of compactness. We provide a new condition for growth, and we stress its importance to check the compactness level.

Smoothness of Class $$C^2$$ of Nonautonomous Linearization Without Spectral Conditions

We prove that smoothness of nonautonomous linearization is of class \(C^2.\) Our approach admits the existence of stable and unstable manifolds determined by a family of nonautonomous hyperbolicities, including the non uniform exponential case, while for the classic exponential dichotomy we obtain the same class of differentiability except for a zero Lebesgue measure set. Moreover, our goal is reached without spectral conditions.

Discussion of an overview of some classical models and discussion of the signature‐based models of preventive maintenance

Discussion of an overview of some classical models and discussion of the signature‐based models of preventive maintenance

An in silico approach to study the role of epitope order in the multi-epitope-based peptide (MEBP) vaccine design

With different countries facing multiple waves, with some SARS-CoV-2 variants more deadly and virulent, the COVID-19 pandemic is becoming more dangerous by the day and the world is facing an even more dreadful extended pandemic with exponential positive cases and increasing death rates. There is an urgent need for more efficient and faster methods of vaccine development against SARS-CoV-2. Compared to experimental protocols, the opportunities to innovate are very high in immunoinformatics/in silico approaches, especially with the recent adoption of structural bioinformatics in peptide vaccine design. In recent times, multi-epitope-based peptide vaccine candidates (MEBPVCs) have shown extraordinarily high humoral and cellular responses to immunization. Most of the publications claim that respective reported MEBPVC(s) assembled using a set of in silico predicted epitopes, to be the computationally validated potent vaccine candidate(s) ready for experimental validation. However, in this article, for a given set of predicted epitopes, it is shown that the published MEBPVC is one among the many possible variants and there is high likelihood of finding more potent MEBPVCs than the published candidates. To test the same, a methodology is developed where novel MEBP variants are derived by changing the epitope order of the published MEBPVC. Further, to overcome the limitations of current qualitative methods of assessment of MEBPVC, to enable quantitative comparison and ranking for the discovery of more potent MEBPVCs, novel predictors, Percent Epitope Accessibility (PEA), Receptor specific MEBP vaccine potency (RMVP), MEBP vaccine potency (MVP) are introduced. The MEBP variants indeed showed varied MVP scores indicating varied immunogenicity. Further, the MEBP variants with IDs, SPVC_446 and SPVC_537, had the highest MVP scores indicating these variants to be more potent MEBPVCs than the published MEBPVC and hence should be preferred candidates for immediate experimental testing and validation. The method enables quicker selection and high throughput experimental validation of vaccine candidates. This study also opens the opportunity to develop new software tools for designing more potent MEBPVCs in less time.

Optimizing Dividends and Capital Injections Limited by Bankruptcy, and Practical Approximations for the Cramér-Lundberg Process

The recent papers Gajek and Kucinsky (Insur Math Econ 73:1–19, 2017) and Avram et al. (Mathematics 9(9):931, 2021) cost induced dichotomy for optimal dividends in the cramr-lundberg model. Avram et al. (Mathematics 9(9):931, 2021) investigated the control problem of optimizing dividends when limiting capital injections stopped upon bankruptcy. The first paper works under the spectrally negative Lévy model; the second works under the Cramér-Lundberg model with exponential jumps, where the results are considerably more explicit. The current paper has three purposes. First, it illustrates the fact that quite reasonable approximations of the general problem may be obtained using the particular exponential case studied in Avram et al. cost induced dichotomy for optimal dividends in the Cramér-Lundberg model (Avram et al. in Mathematics 9(9):931, 2021). Secondly, it extends the results to the case when a final penalty P is taken into consideration as well besides a proportional cost \(k>1\) for capital injections. This requires amending the “scale and Gerber-Shiu functions” already introduced in Gajek and Kucinsky (Insur Math Econ 73:1–19, 2017). Thirdly, in the exponential case, the results will be made even more explicit by employing the Lambert-W function. This tool has particular importance in computational aspects and can be employed in theoretical aspects such as asymptotics.

Dwell‐time‐based control synthesis of switched positive systems with all unstabilizable subsystems

AbstractThis article investigates the robust exponential stabilization of a class of switched positive systems with uncertainties by co‐designing controllers for subsystems and dwell time switching strategy. The uncertainties refer to interval uncertainties. One of the distinguishing features is that none of the forced individual subsystems is assumed to be stabilized. The other feature is that the stabilization for the unforced switched system can not be solvable by designing dwell time switching signal. First, for switched positive systems without uncertainties, a type of multiple time‐varying co‐positive Lyapunov functions is used, and the computable sufficient conditions on the state feedback controller for each subsystem are derived in the framework of dwell time strategy. Moreover, the exponential stabilization problem is solved by confining the lower and upper bounds of the dwell time, restricting the upper bound of derivative of considered Lyapunov function of the active subsystem, and decreasing the Lyapunov function values at successive switching instants of the overall switched system. Then, the results are extended to the robust exponential stabilization case for switched positive systems with uncertainties, and sufficient conditions are given in the same framework of the dwell time for that of the forced switched systems by further designing state feedback controllers. Finally, illustration examples are given to illustrate the effectiveness of the proposed methods.

Nodal solutions for Q-Laplacian problem with exponential nonlinearities on the Heisenberg group

This paper deals with the existence of nodal solutions (sign-changing) to the following elliptic equation involving Q-Laplacian:{−ΔQu=λf(ξ,u)inΩ,u=0on∂Ω, where ΔQ(⋅):=divHn(|∇Hn(⋅)|HnQ−2∇Hn(⋅)) is the Q-Laplacian operator, Ω is an open, smooth bounded domain in the Heisenberg group Hn, Q=2n+2 is the homogeneous dimension of Hn, λ is a positive parameter, and nonlinear term f(ξ,u) behaves like exp⁡(β|s|QQ−1) as s→∞. Under suitable conditions on f, together with the constraint variational method and the quantitative deformation lemma, we obtain the existence, energy estimates and the convergence property of the least energy sign-changing solutions for the above problem in subcritical and critical exponential growth cases.

Multiple Upper Outlier Detection Procedure in Generalized Exponential Sample

Hawkins [6] defined an outlier as an observation that is significantly different from the remaining observations in a dataset so as to arouse suspicion that it was generated by different mechanism. Barnett and Lewis [2] defined an outlier as an observation that deviates significantly in the sample in which it occurs. Spatial outliers are different from outliers and many authors like Singh and Lalitha [9]. Outlier detection procedures for two parameter gamma distribution have been discussed by many authors. But one major disadvantage of the gamma distribution is that the distribution (or survival) function cannot be expressed in a closed form if the shape parameter is not an integer. Since it is in terms of an incomplete gamma function, one needs to obtain the distribution/survival function or the failure rate by numerical integration. This is a limitation in the usage of gamma distribution. It is observed that the generalized exponential distribution can be used as an alternative to the gamma distribution in many situations. Different properties like monotonicity of the hazard functions and tail behaviours of the gamma distribution and that of the generalized exponential distribution are quite similar in nature. But the latter one has a nice compact distribution (or survival) function. It is observed that for a given gamma distribution there exists a generalized exponential distribution so that the two distribution functions are almost identical. Since the gamma distribution function does not have a compact form, efficiently generating gamma random numbers is known to be problematic. It was observed that for all practical purposes it is possible to generate approximate gamma random numbers using generalized exponential distribution and the random samples thus obtained cannot be differentiated using any statistical tests. Many authors proposed a location and scale invariant test based on the test statistic Zk for testing the upper outliers in two-parameter exponential sample. Kumar et. al. [7] and Singh and Lalitha [10] have proposed test statistics for testing multiple upper outlier detection in gamma sample. Various test statistics have been proposed to detect outliers in an exponential sample. Likes [8] also proposed a new test statistics to detect outlier in the exponential case. In this paper, the test statistic proposed by Likes has been used to detect outliers in a generalized exponential sample and the critical value of the test statistics has been obtained. A simulation study is carried out to compare the theoretical developments.

‘Authorized to Depart from the Law’

The COVID-19 pandemic has posed myriad brain-wracking questions to decision-makers at all levels. Viet Nam managed to curb mortality and morbidity to praiseworthy levels in the past COVID-19 waves, however, has now had its back against the wall amidst the recent exponential infection cases and draining medical resources. For swiftly flattening the curve, the legislature authorized the Government to take bolder steps where needed, even different from the laws. This article argues that while the empowerment comes from the goodwill of the legislature for the purpose of containing the raging outbreak, there remain procedural irregularities. This should garner more attention from the state authority to ensure the rule of law and legality of all state actions during the time of public health emergency.

Drivers of the third wave of COVID-19 in Zimbabwe and challenges for control: perspectives and recommendations.

Since the beginning of June 2021, Zimbabwe entered into a harsh third wave of the COVID-19 pandemic, which saw an increase in the cumulative number of cases from approximately 38,000 to 120,000 in just two months. This exponential case rise was accompanied by an increase in the absolute number of case fatalities, with a corresponding strain on the public health sector. To effectively inform public health responses, policy and strategy to deal with the current wave and prepare for further waves, we discuss the drivers and challenges of control for this current wave and future waves, and offer practical recommendations. Vaccination will be the most important public health intervention to deal with the spread, morbidity and mortality of COVID-19, therefore, efforts to fight vaccine hesitancy and build vaccine confidence and availability will be critical. Similarly, it will be important to build public health sector capacity and resilience to adequately deal with large-scale outbreaks and absorb the shock waves associated with such. Resuscitating and building the economy is an indispensable component of protecting public health. Therefore, collaborative efforts from relevant public health stakeholders, economists, politicians and other players are required to effectively coordinate the necessary responses and formulate the right policies and strategies.

Semi-Markov model for delivery delay prediction in multi-copy opportunistic networks with heterogeneous pairwise encounter rates

This work proposes an analytical model based on absorbing semi-Markov process for predicting the expected pairwise delivery delay for single and multi-copy opportunistic forwarding schemes. The framework can be applied to any inter-meeting times distribution. For the exponential case, it only requires the number of nodes and the pairwise encounter rates, which can be completely heterogeneous. Results show that the model predictions are quite accurate, with error values being less than 1% in some cases.

Trade-off between job losses and the spread of COVID-19 in Japan

This paper quantitatively analyzes the trade-off between job losses and the spread of COVID-19 in Japan. We derive an empirical specification from the social planner’s resource constraint under the susceptible, infected, recovered, and deaths (SIRD) model and estimate how job losses and the case growth rate are related to people’s mobility using the Japanese prefecture-level panel data on confirmed cases, involuntary job losses, people’s mobility, and teleworkability. Our findings are summarized as follows. First, we find that a decrease in mobility driven by containment policies is associated with an increase in involuntary job separations, but the high teleworkability mitigates the negative effect of decreased mobility on job losses. Second, estimating how the case growth is related to people’s mobility and past cases, we find that the case growth rate is positively related to an increase in people’s mobility but negatively associated with past confirmed cases. Third, using these estimates, we provide a quantitative analysis of the trade-off between job losses and the number of confirmed cases. Taking Tokyo in July 2020 as a benchmark, we find that the cost of saving 1 job per month is 2.3 more confirmed cases per month in the short run of 1 month. When we consider a trade-off for 3 months from July to September of 2020, protecting 1 job per month requires 6.6 more confirmed cases per month. Therefore, the trade-off becomes worse substantially in the longer run of 3 months, reflecting the exponential case growth when the people’s mobility is high.

706 Sleep and Mental Health in College Students Before and During the Initial COVID-19 Shutdown

IntroductionThe COVID-19 pandemic has had an unparalleled impact on college students. Following the initial and abrupt shutdown of campuses in March 2020, several investigators assessed the immediate effects on University students. Early reports found that college students reported a higher prevalence of anxiety and depression, sedentary behavior, and sleep problems. Most were conducted outside the U.S. Data from U.S. college students are critical to identify which areas are should receive resources and interventions as the U.S. continues to experience exponential COVID cases along with continued remote learning, social restrictions and/or lockdowns.MethodsStudents enrolled in the Spring 2020 semester (18 years of age +) were invited to participate in an online survey (April – May 2020). A final sample of 491 completed the entire survey (length ~45 minutes) which asked about sleep quality, psychological stress, depression, and exercise.Paired t-tests were conducted to compare pre-COVID and during COVID data.ResultsThere were significant differences in sleep onset latency (26.44 ± 23.53 min vs 32.06 ± 26.88 min; t = -3.81, P < .001), sleep duration (7.30 ± 1.45 hours vs 7.63 ± 2.07 hours; t = -2.23, p = 0.027) and overall sleep quality (6.29 ± 3.29 vs 7.44 ± 3.86; t = -7.26, p < .001), as well as depression scores (IDS no sleep questions) (5.61 ± 4.18 vs 17.59 ± 5.45; t = -54.9, P < .001). There was no difference in perceived stress (28.03 ±5.27 vs 28.39 ±5.53, t = -1.49, p = .138). Exercise (vigorous, moderate and walking) all decreased with regards to days and time spent, (all P’s < .001), whereas minutes sitting significantly increased (426.50 ± 239.88 vs 542.26 ± 249.63, p < .001).ConclusionThese data empirically support the claim that the pandemic is having a significant negative impact on physical and mental health among college students. In the best of times, college students have irregular sleep patterns and significant depression, but these behaviors are worsened under government restrictions. These findings underscore the need to prioritize prevention and intervention of modifiable behaviors, especially if the pandemic extends into 2021.Support (if any):

On two product form modifications for finite overflow systems

Overflow mechanisms can be found in a variety of queueing models. This paper studies a simple and generic overflow system that allows the service times to be both job type and station dependent. This system does not exhibit a product form. To justify simple product form computations, two product form modifications are given, as by a so-called call packing principle and by a stop protocol. The provided proofs are self-contained and straightforward for the exponential case and of merit by itself. Next, it is numerically studied whether and when, or under which conditions, the modifications lead to a reasonable approximation of the blocking probability, if not an ordering. The numerical results indicate that call packing provides a rather accurate approximation when the overflow station is not heavily utilized. Moreover, when overflowed jobs have an equal or faster service rate, the approximation is consistently found to be pessimistic, which can be useful for practical purposes. The stop protocol, in contrast, appears to be less accurate for most natural situations. Nevertheless, for an extreme situation the order might change. In addition, for the stop protocol the product form is proven to be insensitive (i.e. to also apply for arbitrary non-exponential service times). For call packing, this numerically appears not to be the case, as of interest by itself. However, from a practical viewpoint the sensitivity seems light. The results are intriguing for both theoretical and practical further research.

The fractional energy balance equation

AbstractClassical Energy Balance Equations (EBEs) are differential equations of integer order (h = 1), here we generalize this to fractional orders: the Fractional EBE (FEBE, 0 &lt; h ≤ 1). In the FEBE, when the Earth is perturbed by a forcing, the temperature relaxes to equilibrium via a slow power‐law process: h = 1 is the exceptional (but standard) exponential case. Our FEBE derivation is phenomenological, it complements derivations based on the classical continuum mechanics heat equation (that imply h = 1/2 for the surface temperature) and of the more general Fractional Heat Equation which allows for 0 &lt; h &lt; 2. Unlike some of the earlier “scale free” models based purely on scaling, the FEBE has an extra blackbody radiation term that allows for energy balance. It therefore has two scaling regimes (not one), it has the advantage of being stable to infinitesimal step‐function perturbations and it has a finite Equilibrium Climate Sensitivity. We solve the FEBE using Green's functions, whose high‐ and low‐frequency limits are power laws with a relaxation scale transition (several years). When stochastically forced, the high‐frequency parts of the internal variability are fractional Gaussian noises that can be used for monthly and seasonal forecasts; when deterministically forced, the low‐frequency response describes the consequences of anthropogenic forcing, it has been used for climate projections. The FEBE introduces complex climate sensitivities that are convenient for handling periodic (especially annual) forcing. The FEBE obeys Newton's law of cooling, but the heat flux crossing a surface nonetheless depends on the fractional time derivative of the temperature. The FEBE's ratio of transient to equilibrium climate sensitivity is compatible with GCM estimates. A simple ramp forcing model of the industrial‐epoch warming combining deterministic (external) with stochastic (internal) forcing is statistically validated against centennial‐scale temperature series.

Inverses of Matérn covariances on grids

Summary We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, elucidating the properties of a popular approximation based on stochastic partial differential equations. While other researchers have shown that this approximation can work well for the covariance function, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid spacing goes to zero, except in the one-dimensional exponential covariance case.

Convexity, monotonicity, and positivity results for sequential fractional nabla difference operators with discrete exponential kernels

We consider positivity, monotonicity, and convexity results for discrete fractional operators with exponential kernels. Our results cover both the sequential and nonsequential cases, and we demonstrate both similarities and dissimilarities between the exponential kernel case and fractional differences with other types of kernels. This shows that the qualitative information gleaned in the exponential kernel case is not precisely the same as in other cases.

Radio-wave absorption by aluminum and its dependence on the absorption distance

The absorption of radio wave is relevant to electromagnetic interference (EMI) shielding and low observability. The effect of the absorption distance much above the calculated skin depth on the absorption of radio wave (600–2000 MHz) is studied by determining the absorption loss per unit thickness for aluminum sheets of thickness ranging from 0.528 to 2.053 mm. Aluminum is dominantly used for EMI shielding. The absorption loss SEA increases with increasing thickness, such that when the absorption distance x exceeds 1.3 mm, the increase is slight. The distance 1.3 mm corresponds to ~ 500 times the calculated skin depth for x = 0. Furthermore, when x exceeds 1.3 mm, the linear absorption coefficient α obtained from SEA/thickness decreases linearly with increasing x. At x below 1.3 mm, α decreases with increasing x in a nonlinear non-exponential manner that is not far from linearity and corresponds to much less decrease for the same x than the exponential case. The non-exponential relationship indicates that the skin effect alone cannot explain the observed relationship. The observed high α at large x, at which the electric field is low, indicates nonlinear dielectric behavior. The factor β that relates α2/α1 and x1/x2 (where α1 is the α value at x1, and α2 is the α value at x2) increases with x and levels off at ~ 1.5 when x exceeds 1.3 mm. The effect of x on α is large compared to the effect of the frequency on α.