Approximation Procedure Research Articles

A Self-Adaptive Learning Approach for Uncertain Disassembly Planning Based on Extended Petri Net

Disassembly is the first phase to demanufacture end-of-life (EOL) products that are separated into parts/components for recovery. The quality conditions of EOL products are highly uncertain, which would result in some uncertain information during the disassembly process, e.g., the disassembly time and recovering revenue of each subassembly. It is quite challenging to determine the optimal/near-optimal disassembly solutions under uncertain information. This paper studies uncertain disassembly planning (UDP) and proposes a self-adaptive learning approach to quickly identify the near-optimal disassembly solutions. First, we model the UDP by extending Petri nets, where not only disassembly operations but also EOL options of each subassembly are represented in the extended Petri Net. Based on the UDP model, we develop the self-adaptive learning approach, which integrates an approximation procedure for estimating uncertain disassembly information, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -learning algorithm for training disassembly samples, and a heuristic method for selecting the best disassembly solution. Finally, a hybrid Li-ion battery pack of Audi A3 Sportback e-tron is selected as the case study and applied to test the proposed self-adaptive learning approach. The experimental results demonstrate that our proposed method can efficiently find a better disassembly solution than the existing disassembly solution within 200 trainings in the case study.

On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data.

The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed.

Automated control of the immune response to the causants of infectious disease

The problems that arose as a result of the rapid spread of the new coronavirus infection COVID-19 and the inability of health care institutions to provide the necessary medical care to a large number of patients in a timely manner showed the need to develop new approaches to diagnosis and the formation of an individual treatment program. Important in this direction is the development and implementation of specialized decision support systems based on the integration of expert systems for the analysis and interpretation of medical data and mathematical modeling tools. In order to form effective treatment programs, it is necessary to ensure the availability of reliable tools for predicting the dynamics of the disease in the conditions of external medical influences, various protection mechanisms, spatial effects, mixed infections etc. The purpose of this work is to generalize the basic model of viral infection to predict the complex controlled influence of adsorption and immune therapy on the development of the disease, taking into account diffusion disturbance and temperature response of the body, which is an important element of specialized decision-making systems for the formation of effective treatment programs. To find the solution of the original model singularly perturbed problem with delays, the procedure of stepwise numerical asymptotic approximation of the solutions of the corresponding specially constructed sequence of problems without delay has been modernized. Based on the obtained results of computer modeling, it was confirmed that the introduction of adsorbents during periods of intensive growth of the number of viral elements makes it possible to sufficiently effectively reduce the rate of their reproduction, and, therefore, provides an additional way of controlling the number of antigens in the body and preventing their supercritical growth. It is emphasized that taking into account the features of the action of adsorption drugs is important for making optimized decisions regarding the use of adsorption therapy

Long-term outcomes of foreskin reconstruction in distal hypospadias; a cohort study spanning twenty years

Surgical correction of hypospadias aims to achieve normal functionality and appearance. This entails foreskin reconstruction (FR) in countries where the uncircumcised penis constitutes the norm. Long-term data are however scarce. To investigate the long-term outcome of FR in cohort of patients operated for distal hypospadias combined with approximately 20 years after surgery. The hospital management system was searched for patients operated for distal hypospadias in conjunction with FR between 1997 and 2004. Prospective participants were invited to participate in an online questionnaire. Signed consent allowed for extended medical chart review, with regards to hypospadias grade, surgical procedure and complications. Response rate of 44.6%. For 113 participants, median age at primary surgery was 5.2 (1.0-15.5) years. Two-thirds had a distal meatus while the remaining, meatus was mid to distal shaft. Urethroplasties performed were mainly glanular approximation procedures and meatal based flap procedures in 85%. Foreskin fistula developed in 15% of cases. There was no significant relationship between urethroplasty procedure or meatal position and risk of foreskin complications. Three layer closure of foreskin resulted in significantly less complications than two layer closure. Twenty years on 95% of the men still had an intact foreskin, of whom 16.8% had received treatment for phimosis. Foreskin was retractable in 92.5% and 74.7% in the flaccid and erect states respectively. Ninety intact men had had their sexual debut and in those 23.3% reported foreskin related issues with intercourse. Evolution of foreskin retractability can be seen in the figure. Current results show that three layer FR in conjunction with hypospadias surgery is feasible and that short-term complication rates were comparable with what has previously been published in the literature. Long-term results indicate that FR is durable with regards to anatomical reconstruction however foreskin function especially in relation to sexual function was compromised in about 25%. Foreskin retractability after surgery predicted retractability in adulthood for the flaccid but not erect penis. Limitations of this study include the retrospective nature of data collection, and that the questionnaire used was not validated. We however achieved a decent response rate and were able to capture important long-term data. FR has an acceptable complication rate. Long-term results two decades on are remarkably durable with regards to the anatomical preservation of the prepuce, however functionality was compromised with regards to retractability and sexual function in approximately 25%.

Forensic facial approximation of an individual with achondroplasia from medieval cemetery in Central Europe

Achondroplasia (ACH, achondroplastic dwarfism) represents the most common form of skeletal dysplasia, occurring in c. 4 out of every 100,000 births. This study presents a computer-based facial approximation of the skull of a male individual living with ACH, who died at 30–45 years of age and was buried in Łekno, Poland between the 9th and 11th centuries AD. For the approximation procedure, soft tissue data from CT scans and ultrasonic measurements performed on living individuals were used. Additionally, an anatomical deformation technique was applied to arrive at the most reliable reconstruction of the achondroplastic individual's appearance. To our knowledge, this is the first facial depiction of a person with achondroplasia, and one of the few showing a head of an individual suffering from a hereditary disease, with dimensions and shape differing from the population average values.

PSXII-22 Analysis of the Upper Respiratory Tract Microbiome in Newly Received Feedlot Heifers According to Subsequent Incidence of Bovine Respiratory Disease

Abstract This study compared the relative abundance of bacteria in the upper respiratory tract (RT) of newly received feedlot heifers according to incidence of bovine respiratory disease (BRD). Angus-influenced heifers (n = 76) were transported for 1,100 km (11 h) to the feedlot (d -1). At feedlot arrival (d 0), heifers were weighed [initial shrunk body weight (BW) = 234 ± 15 kg] and a nasal swab collected for analysis of the upper RT microbiome. Heifers were ranked by arrival BW and allocated into 6 pens on d 1 where they remained until d 55. Heifers were evaluated daily for BRD signs (d 0 to 55), and a final shrunk BW was recorded on d 56 (16-h feed and water deprivation). Heifers were classified according to number of antimicrobial treatments for BRD received (0, 1, or ≥ 2), or according to time of first incidence of BRD signs [no incidence (NOBRD), early incidence (EARLY; 4.1 ± 0.1 d), or late incidence (LATE; 18.5 ± 9.6 d). All data were analyzed using heifer as the experimental unit, the PROC MIXED procedure of SAS and Satterthwaite approximation to determine the denominator degrees of freedom for tests of fixed effects. The first model statement included the number of BRD treatments received, the second model statement included the time of first incidence of BRD signs. Average daily gain decreased linearly (P = 0.04) according to number of BRD treatments and was less (P = 0.04) in LATE and tended (P = 0.08) to be less in EARLY compared with NOBRD heifers. The abundance of the phyla Tenericutes increased linearly (P &amp;lt; 0.01), while the abundance of Firmicutes, Bacteroidetes, Actinobacteria, Verrucomicrobia, Spirochaetes, Euryarchaeota, Chlorobi, and Chloroflexi decreased linearly (P ≤ 0.05) according to number of BRD treatments. Heifers classified as EARLY had greater (P = 0.01) abundance of Tenericutes and less (P = 0.03) abundance of Firmicutes compared with NOBRD, as well as less (P ≤ 0.03) abundance of Euryarchaeota and Chloroflexi compared with both NOBRD and LATE heifers. The abundance of the genera Mycoplasma increased linearly (P &amp;lt; 0.01) while the abundance of Corynebacterium, Blautia, Jeotgalicoccus, Clostridium, and Dietzia decreased linearly (P ≤ 0.03) according to number of BRD treatments. Heifers classified as NOBRD had less (P = 0.01) abundance of Mycoplasma compared with EARLY, and greater (P ≤ 0.05) abundance of Corynebacterium, Jeotgalicoccus, Dietzia, and Planomicrobium compared with EARLY and LATE heifers. Collectively, heifers that developed BRD had altered upper RT microbiome at the time of feedlot arrival compared with heifers that remained healthy, particularly increased prevalence of Tenericutes phylum and Mycoplasma genera. Such differences in upper RT microbiome were heightened in heifers that developed BRD shortly after arrival, or that required multiple antimicrobial treatments.

Jacobian-free implicit MDRK methods for stiff systems of ODEs

In this work, an approximate family of implicit multiderivative Runge-Kutta (MDRK) time integrators for stiff initial value problems is presented. The approximation procedure is based on the recent Approximate Implicit Taylor method (Baeza et al., 2020 [7]). As a Taylor method can be written in MDRK format, the novel family constitutes a multistage generalization. Two different alternatives are investigated for the computation of the higher order derivatives: either directly as part of the stage equation, or either as a separate formula for each derivative added on top of the stage equation itself. From linearizing through Newton's method, it turns out that the conditioning of the Newton matrix behaves significantly different for both cases. We show that direct computation results in a matrix with a conditioning that is highly dependent on the stiffness, increasing exponentially in the stiffness parameter with the amount of derivatives. Adding separate formulas has a more favorable behavior, the matrix conditioning being linearly dependent on the stiffness, regardless of the amount of derivatives. Despite increasing the Newton system significantly in size, through several numerical results it is demonstrated that doing so can be considerably beneficial.

Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures

This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from micro-CT images featuring intricate microstructures. The proposed method is guided by the Support Vector Machine (SVM) classification, offering an effective approach for discretizing microstructural images. An SVM soft margin training process is introduced as a classification of heterogeneous material points, and image segmentation is accomplished by identifying support vectors through a local regularized optimization problem. In addition, an Interface-Modified Reproducing Kernel Particle Method (IM-RKPM) is proposed for appropriate approximations of weak discontinuities across material interfaces. The proposed method modifies the smooth kernel functions with a regularized Heaviside function concerning the material interfaces to alleviate Gibb's oscillations. This IM-RKPM is formulated without introducing duplicated degrees of freedom associated with the interface nodes commonly needed in the conventional treatments of weak discontinuities in the meshfree methods. Moreover, IM-RKPM can be implemented with various domain integration techniques, such as Stabilized Conforming Nodal Integration (SCNI). The extension of the proposed method to 3-dimension is straightforward, and the effectiveness of the proposed method is validated through the image-based modeling of polymer-ceramic composite microstructures.

Upper bounds for the derivatives of the density associated to solutions of stochastic differential equations with jumps

In this article, we prove the existence and regularity of densities associated to stochastic differential equations driven by a jump process with infinite activity. Furthermore, we provide explicit bounds for the density and its derivatives. The main argument is based on two ideas: (1) The use of the regularity of the Brownian motion approximation of small jumps of an infinite activity process (the so-called Asmussen-Rosiński approximation); (2) The improvement of the approximation procedure using a Taylor like expansion of the law based on the so-called Levi parametrix method.

Impact of cost approximation on the efficiency of collaborative regulation resolution mechanisms

Air Traffic Flow Management (ATFM) measures are often used to alleviate capacity demand imbalances. Usually, these measures impose a departure delay on flights crossing the airspace in question, where delay is assigned on a “First Planned First Served” (FPFS) base, which minimises total delay. Since delays typically have a different impact on individual flights in terms of cost, a procedure based on cost minimisation could reduce delay-related costs. User-Driven Prioritisation Process (UDPP) is developing a set of solutions aimed at allowing airlines to rearrange their flights within their own slots assigned by the FPFS rule. Inter-airline cost reducing approaches are still missing, but several works have been launched in this direction, using either central optimisations or market-based mechanisms.We analyse the impact of cost approximations procedures, integral part of certain inter-airline mechanisms, overall likely to be used by airlines or the Network Manager (that manages ATFM measures). Using cost models and simulations to collect the true cost of delay profiles, we show that the impact of cost approximations have been severely underestimated, leaving little room for new mechanisms to improve over UDPP. Moreover, we show that the errors made by the airlines on their own costs, expected at least for some airlines, further deteriorate the situation, including UDPP. However, we find that approximation procedures create a strong resilience to these errors, showing how both UDPP and inter-airline procedures may benefit from not having the airlines communicate their detailed costs. Thus, we find that any design of new mechanisms could include a cost approximation procedure in order to increase its resilience.

Laplace based Bayesian inference for ordinary differential equation models using regularized artificial neural networks

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterised by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically intractable trajectories which result in likelihoods and posterior distributions that are similarly intractable. Bayesian inference for ODE systems via simulation methods require numerical approximations to produce inference with high accuracy at a cost of heavy computational power and slow convergence. At the same time, Artificial Neural Networks (ANN) offer tractability that can be utilized to construct an approximate but tractable likelihood and posterior distribution. In this paper we propose a hybrid approach, where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories as a function of the unknown initial values and system parameters. Suitable choices of customized loss functions are proposed to fine tune the approximated ODE trajectories and the subsequent Laplace approximation procedure. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions—the Susceptible-Infectious-Removed (SIR) model for infectious diseases—based on simulated and real-life influenza datasets. The novelty and attractiveness of our proposed approach include (i) a new development of Bayesian inference using ANN architectures for ODE based dynamical systems, and (ii) a computationally fast posterior inference by avoiding convergence issues of benchmark Markov Chain Monte Carlo methods. These two features establish the developed approach as an accurate alternative to traditional Bayesian computational methods, with improved computational cost.

Modeling the dispersion of waves on a loaded bi-elastic cylindrical tube with variable material constituents

The present study analyzes the propagation of surface waves on a strongly inhomogeneous loaded bi-elastic cylindrical tube with variable material constituents. More precisely, due to the number of related physical applications, the exerted load is considered to be in favor of the Winkler elastic foundation. Further, analytical and approximation procedures of solution are beseeched to examine the model. The revealed results by two approaches are then graphically portrayed, which are then found to possess a high level of conformity. Finally, both the external load due to Winkler foundation d, and the internal material property b are found to oppose the propagation of surface waves in the media. In fact, the opposition deteriorates when both the dimensionless parameters d and b are greater than 0.5.

Quasilinear Dirichlet systems with competing operators and convection

In this paper, we consider a quasi-linear Dirichlet system with possible competing (p,q)-Laplacians and convections. Due to the lack of ellipticity, monotonicity, and variational structure, the standard approaches to the existence of weak solutions cannot be adopted. Nevertheless, through an approximation procedure and a corollary of Brouwer's fixed point theorem we show that the problem admits a solution in a suitable sense.

A constraint programming-based iterated greedy algorithm for the open shop with sequence-dependent processing times and makespan minimization

In this paper, a novel variant of the open shop scheduling problem where the jobs have sequence-dependent processing times is addressed. The performance measure considered is the minimization of the length of the schedule (makespan). This problem arises in several real-life settings and, particularly, our work is inspired in scheduling samples in a quality control laboratory where a series of tests have to be performed in different equipment – being irrelevant the order in which these tests are performed –, and the time required to perform the tests depends on the previous sample tested. For this problem, we compare the results of a Mixed-Integer Linear Programming (MILP) model with those from a Constraint Programming (CP) model specifically proposed for the problem, showing that the latter yields better results. Given the NP-hard nature of the problem, in order to obtain good – but not necessarily optimal – solutions within reasonable computational effort, we propose a matheuristic consisting of an Iterated Greedy Algorithm hybridized with a reconstruction phase based in executing the CP model with a partial solution. The results of the computational experiments carried out on 160 instances based on established datasets show the ability of the matheuristic to solve large-sized instances, in contrast with exact (i.e. MILP and CP) models. Our proposal outperforms the most efficient approximate procedures from related problems that have been adapted to the problem under consideration. A subsequent statistical analysis is carried out to prove the statistical significance of these results.

An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents

In this work, we present a method that applies Deep Reinforcement Learning, an approximate dynamic programming procedure using deep neural networks, to the job shop scheduling problem (JSSP). The aim is to show that a greedy-like heuristic trained on a subset of problems, can effectively generalize to some extent to unseen instances, and be competitive compared to other methods. We model the JSSP as a Markov Decision Process and we exploit the efficacy of reinforcement learning to solve the problem. We adopt an actor-critic scheme based on policy gradients, specifically the Proximal Policy Gradient method, where the action taken by the agent is influenced by policy considerations on the state-value function. The procedures take into account the challenging nature of JSSP, where the state and the action space change for every instance and after each decision. To tackle this variability, we introduced a novel model based on two incident Long-Short Term Memory networks, followed by an encoding model, different in structure for both the actor and the critic. Experiments show the algorithm reaches good solutions in a short time, proving that is possible to generate new greedy heuristics just from learning-based methodologies. We compared our algorithms against several established heuristics, an adaptive method, a commercial solver based on branch and cut, and another approach based on Deep Reinforcement Learning, proving the validity of the proposed method in terms of time and makespan. The model can generalize, to some extent, to larger problems originating from a different distribution.

Intelligent computing for the double-diffusive peristaltic rheology of magneto couple stress nanomaterials

Abstract In nanofluids, the effect of convection in the presence of double diffusivity on a magneto couple stress fluid with the peristaltic flow of a model in a non-uniform channel (MCSFM) is reviewed in this article. This research discusses MCSF in a non-uniform channel by applying the Levenberg–Marquardt procedure via an artificial backpropagated neural network (LMP-ABNN). For two-dimensional and two-directional flows, mathematical formulations of double-diffusivity convection of a magneto couple stress fluid in nanofluids are developed. The partial differential equations are reduced to ordinary differential equations by using appropriate transformations. The assessment of the Hartmann number, thermophoresis parameter, Dufour parameter, Soret parameter, and magnetic Reynolds number over concentration profiles and temperature profiles is made by generating a dataset for LMP-ABNN based on the ND solve method for different variations of MSCFM. To examine the approximate solution validation, training and testing procedures are interpreted, and the performance is verified through error histogram and mean square error results. The extremely nonlinear equations are reduced by employing a long-wavelength approximation and a low but finite Reynolds number. To describe the behavior of flow quantities, graphical representations of a variety of physical characteristics of importance are shown. The impact of the Hartmann number and magnetic Reynolds number over axial magnetic field and current density is also studied. The concentration increases as the thermophoresis parameter and Dufour parameter values increase. This occurs because the concentration and both these parameters have a direct relationship. We observed opposite behavior for both the magnetic Reynolds number and the Hartman number. The behavior of current density J z increases with increasing values of R m. Both the temperature distribution and solute concentration increase. The final outcome of this study is to provide the potential for these techniques to provide new insights and solutions to challenging problems in nanofluids and other areas of fluid mechanics and to facilitate the design of more efficient and effective microfluidic devices.

Existence of constant mean curvature 2‐Spheres in Riemannian 3‐spheres

AbstractWe prove the existence of branched immersed constant mean curvature (CMC) 2‐spheres in an arbitrary Riemannian 3‐sphere for almost every prescribed mean curvature, and moreover for all prescribed mean curvatures when the 3‐sphere is positively curved. To achieve this, we develop a min‐max scheme for a weighted Dirichlet energy functional. There are three main ingredients in our approach: a bi‐harmonic approximation procedure to obtain compactness of the new functional, a derivative estimate of the min‐max values to gain energy upper bounds for min‐max sequences for almost every choice of mean curvature, and a Morse index estimate to obtain another uniform energy bound required to reach the remaining constant mean curvatures in the presence of positive curvature.

The reversibility of cancelable biometric templates based on iterative perturbation stochastic approximation strategy

Researchers have been proposing different matching frameworks for cancelable template design to improve the matching performance and security of biometric authentication systems. Despite the advantages provided by these systems, they are often vulnerable to different attacks due to their templates' invertible nature. This study utilized an iterative perturbation stochastic approximation procedure to analyze the irreversible order-based encoding approach used in cancelable biometric template transformation. The strategy begins by exploiting the scores corresponding to the encoded words, then a mixed variable-based iterative perturbation is used to generate independent random elements and consequently the corresponding template from the scores. The strategy exploits the vulnerability of three different cancelable systems it has tested, demonstrating that other techniques of similar nature fall short of the security standard for attack mitigation that cancelable biometric systems require. After analyzing the reasons that exploit the system's vulnerability, we use a parameterized thresholding non-uniform quantization as a countermeasure to boost the system's robustness while maintaining a balanced performance-security trade-off. As a result, the system can evade attacks without significantly hindering its matching performance. Finally, generality and computational complexity evaluations on different modalities and strategies validate the attack's efficacy and realism, respectively.

The Large Deviation of Semi-linear Stochastic Partial Differential Equation Driven by Brownian Sheet

We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation procedure, we obtain the existence of global solution. Then the large deviation principle is obtained via weak convergence method.

On Boussinesq's Problem for a Power-Law Graded Elastic Half-Space on Elliptical and General Contact Domains.

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson's ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is derived, based on the generalizations of Galin's theorem and Barber's extremal principle for the inhomogeneous half-space. As a special case, the elliptical Hertzian contact is revisited. Generally, elastic grading with a positive grading exponent reduces the contact eccentricity. Fabrikant's approximation for the pressure distribution under a flat punch of arbitrary planform is generalized for power-law graded elastic media and compared with rigorous numerical calculations based on the boundary element method (BEM). Very good agreement between the analytical asymptotic solution and the numerical simulation is obtained for the contact stiffness and the contact pressure distribution. A recently published approximate analytic solution for the indentation of a homogeneous half-space by a counter body, whose shape slightly deviates from axial symmetry but is otherwise arbitrary, is generalized for the power-law graded half-space. The approximate procedure for the elliptical Hertzian contact exhibits the same asymptotic behavior as the exact solution. The approximate analytic solution for the indentation by a pyramid with square planform is in very good agreement with a BEM-based numerical solution of the same problem.