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Owing to increasingly important drivers for change, such as automation, digitisation, and dynamic demand patterns, simulation models of production systems become outdated rapidly. At the same time, building simulation models often requires much time, cost, and expertise, especially when dealing with complex job shop production systems. To address these challenges, an automated simulation model generation (ASMG) framework for material flow simulation of production systems is presented. This framework contains multiple approaches to infer routeing, control and temporal aspects from event-based data. To achieve this, methods from process mining (PM) and machine learning (ML) are applied. Additionally, the suitability of Coloured Petri Nets (CPNs) to serve as conceptual and operational simulation models is examined. The inferred simulation models have high validity when compared to the real system concerning the KPIs machine utilisation, throughput, and work in process. It is shown, that most model elements can be inferred very well, in particular process routes, processing times, and resource selection rules. This proof of concept serves as a foundation for research on detection approaches inferring further model elements such as setup times accurately. [ABSTRACT FROM AUTHOR]

In automated manufacturing systems (AMSs), because of unpredictable failures, resources can lose functions such that the deadlock control methods, in existence, are invalidated. In this paper, a robust deadlock control approach is proposed for AMSs with multiple unreliable resources. The considered AMSs modelled by Petri nets (PNs) allow to acquire different types of resources at each processing stage. In order to visualise the fact that resource failures occur in AMSs, recovery subnets are designed for the modelling AMSs to depict the failures and recoveries of resources. Based on a siphon detection method performed by a set of integer linear programming formulations, a control specification is proposed. Control places (monitors) with their control variables are designed for the detected unmarked siphons at a marking to guarantee that they are always marked even if some unreliable resources break down. Iteratively, all unmarked siphons are detected and controlled. Therefore, a robust deadlock supervisor is synthesised to ensure the controlled system's liveness no matter there exist resource failures or not. The theoretical analyses and proof are given to verify the correctness of the proposed method. Finally, the comparative studies are presented to expound the proposed method's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

Summary: The frequent geographical changes of mobile nodes in Internet of Things (IoT) systems affect communication, activities, and behaviors. In such scenarios, it is crucial to establish a system model capable of evaluating quality of service (QoS) measures. However, the existing formal modeling techniques pose complexities in modeling mobility. To deal with these challenges, this study aims to propose a model that simplifies the process of modeling mobility within IoT systems. This paper presents a method for modeling mobility within IoT systems by leveraging a widely recognized extension of stochastic Petri nets known as stochastic reward nets (SRNs). The proposed method enhances the SRN model by incorporating the location concept, resulting in a novel extension called mobile SRN (MSRN). In this work, a case study utilizes the MSRN to evaluate the suggested features, examining various scenarios and investigating the impact of factors such as environmental conditions, sensor sampling rate, and the permissible distance of the node from the sink. [ABSTRACT FROM AUTHOR]

Petri nets are commonly applied in modeling biological systems. However, construction of a Petri net model for complex biological systems is often time consuming, and requires expertise in the research area, limiting their application. To address this challenge, we developed GINtoSPN, an R package that automates the conversion of multi-omics molecular interaction network extracted from the Global Integrative Network (GIN) into Petri nets in GraphML format. These GraphML files can be directly used for Signaling Petri Net (SPN) simulation. To demonstrate the utility of this tool, we built a Petri net model for neurofibromatosis type I. Simulation of NF1 gene knockout, compared to normal skin fibroblast cells, revealed persistent accumulation of Ras-GTPs as expected. Additionally, we identified several other genes substantially affected by the loss of NF1's function, exhibiting individual-specific variability. These results highlight the effectiveness of GINtoSPN in streamlining the modeling and simulation of complex biological systems. [ABSTRACT FROM AUTHOR]

As the current agricultural industry is facing several challenges such as climate changes and lack of qualified farmers, it is extremely necessary to ensure sustainable agriculture and food supply by smart farming (SF). The SF can assist farmers and the associated stakeholders in making correct decisions on improving the yield and quality of agricultural products. In this study, an SF system based on low‐cost Raspberry Pi and Internet of Things (IoT) technologies has been successfully implemented. Through the data items detected by sensors to deeply manage the planting process, the IoT‐enabled communication protocol under ISO standards of Message Queuing Telemetry Transport (MQTT) was used. The bar charts of real‐time environmental parameters are presented on ThingsBoard to achieve the goal of data visualization. Meanwhile, a web server is built for the customized requirements, and the historical datasets are stored in the SQLite database system. Furthermore, a Petri net (PN) model was employed to detect all possible abnormal processes and to verify the feasibility and soundness of an IoT‐enabled system by using a software tool, WoPeD. Finally, the experimental results show that the plants cultivated by the proposed IoT‐enabled system are superior to those cultivated by the existing systems in many perspectives, including the monitoring distance, power consumption, precision, deadlock detection, and running time. [ABSTRACT FROM AUTHOR]

To solve the problems of chaotic information management and difficult traceability in the manufacturing process of transformer coils, a traceability and management method oriented towards the manufacturing process of transformer coils has been proposed. This method integrates industrial internet identification resolution and extension of Petri net modeling theory. A comprehensive identification and resolution framework for coil manufacturing processes has been constructed. In this manuscript, the authors proposed an industrial data-sharing space based on the producer-consumer model with unified coding identification. This enables information sharing for all resources, including personnel, machinery, materials, methods, environment, and measurements. A method for modeling extensible identification primitives of coil manufacturing process information was proposed, which formalizes the correlation and data structure of process information. A Petri net model for the comprehensive acquisition and integration of elemental information in coil manufacturing processes, as well as a mathematical model for quality traceability, were constructed, thereby forming a complete path for quality traceability information. Finally, based on the method proposed above, a software and hardware environment for identification and traceability for coil manufacturing was established. Taking a certain type of coil as an example, validation was carried out; the results indicate a significant enhancement in the production management and information traceability capabilities of the coil production workshop. This study provides reference and guidance for the process traceability management of power equipment manufacturing. [ABSTRACT FROM AUTHOR]

In this study, we propose a model called LFSPN, which serves as an extension of stochastic Petri nets dedicated to the multi-agent systems paradigm. The main objective is to specify, verify, validate, and evaluate the flow of materials within an automated production chain. We illustrate the practicality of our model by engaging in a systematic process of modeling and simulation of a production chain involving material flow. To evaluate the performance, we employ a mobile learning agent, which has distinct characteristics, namely mobility and learning. So, the distinctive characteristics of the learning agent are manifested in two key behaviors: mobility and learning. Notably, the learning agent is equipped with a flexible learning algorithm that integrates stochastic elements based on transitions. We suggest using a MATLAB simulation to determine the firing time of each transition within a sequence, guided by three different probability laws (exponential, normal, and log-normal). This sequence is designed to optimize the production process objective while facilitating learning cycles through agent rewards, specified by a production and consumption of tokens in our evolving model. We validate the effectiveness of our model by performing a comparative analysis with similar existing works. The advantages of our LFSPN model are twofold. Firstly, it offers a representation with two levels of abstraction: a graph representing the classic components of an SPN, and an additional layer encompassing the learning and migration aspects inherent to a mobile learning agent. Secondly, our model stands out for its flexibility and simulation simplicity. [ABSTRACT FROM AUTHOR]

Oil refining is a branch of industry that delivers energy to move our vehicles. The transportation of people and goods by airplanes, ships, trains, trucks, buses, and cars is unthinkable for modern mankind without the use of refined petroleum automotive fuels. Thus, the optimal functioning of this industrial branch is vital to contemporary human society. The modeling of processes that take place during refined oil products' manufacturing, which are parallel in their essence, by generalized nets enables their activity optimization and better management. The generalized nets, which are in principle extensions of Petri nets, are applied in this research as a toolkit to model all processes from crude oil selection and delivery to a high complex refinery (Nelson index of 10.6) to the production of a great diversity of fuels, propylene, and polypropylene. The proposed article is a continuation and extension of the articles, published in Mathematics Journal in 2021 and 2023. It is the first (theoretical part) of our comprehensive study of modeling petroleum products' production processes in a refinery, and the second part will discuss the results of the software implementation of the model. [ABSTRACT FROM AUTHOR]

Self-driving cars are one of the main areas of research today, but it has to be acknowledged that the information from the sensors (the perceptron) is a huge amount of data, which is now unmanageable even when projected onto a single traffic junction. In the case of self-driving, the nodes have to be sequenced and organized according to the planned route. A self-driving car in Hungary would have to be able to interpret more than 70,000 traffic junctions to be able to drive all over the country. Besides the huge amount of data, another problem is the issue of validation and verification. For self-driving cars, this implies a level of complexity using traditional methods that calls into question the economics of the already existing system. Fuzzy Petri nets provide an alternative solution to both problems. They allow us to obtain a model that accurately describes the reliability of a node through its dynamics, which is essential in perception since the more reliable a node is, the smaller the deep learning mesh required. In this paper, we outline the analysis of a traffic node's safety using Petri nets and fuzzy analysis to gain information on the reliability of the node, which is essential for the modeling of self-driving cars, due to the deep learning model of perception. The reliability of the dynamics of the node is determined by using the modified fuzzy Petri net procedure. The need for a fuzzy extension of the Petri net was developed by knowledge of real traffic databases. [ABSTRACT FROM AUTHOR]

In order to express the energy flow, motion flow, and control flow in wireless rechargeable sensor networks accurately and intuitively, and to maximize the charging benefit of MVs (mobile vehicles), a type of MTS-HACO (Mobile Transition Sequence Hybrid Ant Colony Optimization) is proposed. Firstly, node places are grouped according to the firing time of node's energy consumption transition to ensure that in each time slot, MV places only enable charging transitions for the node places with lower remaining lifetimes. Then, the FSOMCT (Firing Sequence Optimization of Mobile Charging Transition) problem is formulated under the constraints of MV places capacity, travelling arc weight, charging arc weight, and so on. The elite strategy and the Max–Min Ant Colony system are further introduced to improve the ant colony algorithm, while the improved FWA (fireworks algorithm) optimizes the path constructed by each ant. Finally, the optimal mobile charging transition firing sequence and charging times are obtained, ensuring that MVs have sufficient energy to return to the base station. Simulation results indicate that, compared with the periodic algorithm and the PE-FWA algorithm, the proposed method can improve charging benefit by approximately 48.7% and 26.3%, respectively. [ABSTRACT FROM AUTHOR]

In recent years, manufacturers have increasingly applied automation techniques to enhance efficiency and remain competitive. Material handling is an essential activity in any production process. Its effectiveness has a significant impact on production costs. Automated guided vehicle (AGV) systems have become a strategic tool for factories and automated warehouses. They can reduce production costs and improve delivery times in a competitive business scenario. One of the main problems encountered in managing AGVs is the dispatching decision. The present paper proposes a vehicle dispatching system based on a multi-attribute cascaded fuzzy system with a state-space-based Petri net model to predict the future states of the factory. This work aims to reduce the production system's makespan and/or tardiness values. Additionally, the paper presents one simulated factory scenario to evaluate the proposed fuzzy system against five other dispatching methods. The statistical validation results of the simulations show a 97% confidence level in the hypotheses of this work. [ABSTRACT FROM AUTHOR]

Forest fires cause damage to life, biodiversity, and properties, affecting natural ecosystems, healthy and only. During the practical application of fire prevention, numerous detection techniques have been thoroughly researched to prevent devastating fires. The techniques improve early fire detection and accelerate emergency response, reducing damage and optimizing system containment operations. Wildfire detection requires a robust infrastructure for equipment, maintenance, and ongoing monitoring. Effective cooperation between components and integration of technologies is key to a consistent and comprehensive response to fires. This article proposes a fire monitoring system using drones, cameras, and edge computing technologies. We use Stochastic Petri Nets (SPN) to model the structure and evaluate the system's performance. The model is parameterizable, allowing adjustments to the components' resource capabilities and service time. Twenty-four parameters can be defined, making it possible to evaluate a wide variety of different scenarios. The results obtained in different scenarios in this work have the potential for auxiliary administrators of monitoring systems to estimate more than six analyses and plan more optimized architectures as needed. [ABSTRACT FROM AUTHOR]

In a sequence of papers, the author examined several statistical affinity measures for selecting the coarse degrees of freedom (CDOFs) or coarse nodes (Cnodes) in algebraic multigrid (AMG) for systems of elliptic partial differential equations (PDEs). These measures were applied to a set of relaxed vectors that exposes the problematic error components. Once the CDOFs are determined using any one of these measures, the interpolation operator is constructed in a bootstrap AMG (BAMG) procedure. However, in a recent paper of Kahl and Rottmann, the statistical least angle regression (LARS) method was utilized in the coarsening procedure and shown to be promising in the CDOF selection. This method is generally used in the statistics community to select the most relevant variables in constructing a parsimonious model for a very complicated and high‐dimensional model or data set (i.e., variable selection for a "reduced" model). As pointed out by Kahl and Rottmann, the LARS procedure has the ability to detect group relations between variables, which can be more useful than binary relations that are derived from strength‐of‐connection, or affinity measures, between pairs of variables. Moreover, by using an updated Cholesky factorization approach in the regression computation, the LARS procedure can be performed efficiently even when the original set of variables is large; and due to the LARS formulation itself (i.e., its l1$$ {l}_1 $$‐norm constraint), sparse interpolation operators can be generated. In this article, we extend the LARS coarsening approach to systems of PDEs. Furthermore, we incorporate some modifications to the LARS approach based on the so‐called elastic net and relaxed lasso methods, which are well known and thoroughly analyzed in the statistics community for ameliorating several major issues with LARS as a variable selection procedure. We note that the original LARS coarsening approach may have addressed some of these issues in similar or other ways but due to the limited details provided there, it is difficult to determine the extent of their similarities. Incorporating these modifications (or effecting them in similar ways) leads to improved robustness in the LARS coarsening procedure, and numerical experiments indicate that the changes lead to faster convergence in the multigrid method. Moreover, the relaxed lasso modification permits an indirect BAMG (iBAMG) extension to the interpolation operator. This iBAMG extension applied in an intra‐ or inter‐variable interpolation setting (i.e., nodal‐based coarsening), as well as in variable‐based coarsening, which will not preserve the nodal structure of a finest‐level discretization on the lower levels of the multilevel hierarchy, will be examined. For the variable‐based coarsening, because of the parsimonious feature of LARS, the performance is reasonably good when applied to systems of PDEs albeit at a substantial additional cost over a nodal‐based procedure. [ABSTRACT FROM AUTHOR]

This article is a tribute to Thomas J. Fararo, a pioneer in the field of mathematical sociology. Fararo believed that mathematical sociology should focus on the theoretical unification of different theories and frameworks. The article provides biographical details about Fararo's life and his contributions to the field. It also includes papers from three scholars who discuss Fararo's impact on sociological theory through mathematical modeling and the prospects for achieving his vision of unification. The article emphasizes the importance of communication and collaboration across research groups for successful theoretical integration. [Extracted from the article]

The airport apron is a high-risk area for aircraft collisions due to its heavy operational load and high aircraft density. Currently, existing quantitative models for apron collision risk provide limited consideration and classification of risk areas. In response, this paper proposes a Petri net-based method for assessing aircraft collision risk. The method predicts the probability of aircraft reaching different areas at different times based on operational data, enabling the calculation of collision risks within the Petri net framework. This approach highlights areas with potential collision risks and provides a classification evaluation. Subsequently, aircraft path re-planning is carried out to reduce collision risks. The model simplifies the complex operations of the apron system, making the calculation process clearer. The results show that, during the mid-phase of aircraft taxiing, there is a significant deviation between the actual and ideal positions of aircraft. Areas with high taxiway occupancy are more prone to collision risks. On peak days, due to relatively high flight volumes, the frequency of collision risks is 14% higher than on regular days, with an average risk increase of 23.3%, and the risks are more concentrated. Therefore, reducing collision risks through path planning becomes more challenging. It is recommended to focus attention on areas with high taxiway occupancy during peak periods and carefully plan routes to ensure apron safety. [ABSTRACT FROM AUTHOR]

Interactive scientific visualization applications have been more and more used to observe, analyze and understand the complex phenomena studied in several scientific disciplines such as (nano-sciences, fluid simulations, etc.). To facilitate the coupling of the different computation, visualization and exploration codes, which are often heterogeneous and difficult to cooperate, scientists must be able to use and reuse the different parts of the applications already built in order to interchange and enrich certain parts without being experts. In this context, a middleware called FlowVR has been developed by the scientific community leading to make applications divided into set of components exchanging messages. Moreover, this middleware enables to encapsulate existing codes in components, interconnect them via data links, and deploy them on distributed computing resources. Nevertheless, FlowVR does not offer any capability to check the functional correctness of new developed component-based applications. This paper presents a framework called Model and Component-based framework for Scientific Applications (MCSA) based on a interplay of model-driven and component-based software engineering. On the one hand, we provide a domain specific language dedicated to physics/chemistry scientists in order to built their MCSA applications. This language also allows to capitalize efforts by proposing existing components that have been already developed. On the other hand, we propose a model transformation to check the correctness of instantiated models, for this, we use a new subclass of Petri net called strict Colored FIFO Nets (sCFN). Our approach has been backed by a case study relies on a molecular dynamics application. [ABSTRACT FROM AUTHOR]

Event structures have emerged as a foundational model for concurrent computation, explaining computational processes by outlining the events and the relationships that dictate their execution. They play a pivotal role in the study of key aspects of concurrent computation models, such as causality and independence, and have found applications across a broad range of languages and models, spanning realms like persistence, probabilities, and quantum computing. Recently, event structures have been extended to address reversibility, where computational processes can undo previous computations. In this context, reversible event structures provide abstract representations of processes capable of both forward and backward steps in a computation. Since their introduction, event structures have played a crucial role in bridging operational models, traditionally exemplified by Petri nets and process calculi, with denotational ones, i.e., algebraic domains. In this context, we revisit the standard connection between Petri nets and event structures under the lenses of reversibility. Specifically, we introduce a subset of contextual Petri nets, dubbed reversible causal nets, that precisely correspond to reversible prime event structures. The distinctive feature of reversible causal nets lies in deriving causality from inhibitor arcs, departing from the conventional dependence on the overlap between the postset and preset of transitions. In this way, we are able to operationally explain the full model of reversible prime event structures. [ABSTRACT FROM AUTHOR]

This paper introduces software patterns (registration, acquire-release, and cache awareness) and data structures (Petri net, finite state machine, and protocol flag array) to support the coordinated execution of software activities (also called "components" or "agents"). Moreover, it presents and tests an implementation for Petri nets that supports real-time execution in shared memory for deployment inside one individual robot and separates event firing and handling, enabling distributed deployment between multiple robots. Experimental validation of the introduced patterns and data structures is performed within the context of activities for task execution, control and perception, and decision making for an application on coordinated navigation. [ABSTRACT FROM AUTHOR]

In order to improve quality assurance in wafer manufacturing, there are strict process requirements. Besides the well-known residency time constraints (RTCs), a dual-arm cluster tool also requires each robot arm to execute a specific set of tasks. We call such a tool an arm task-constrained dual-arm cluster tool (ATC-DACT). To do this, one of the arms is identified as the dirty one and the other as the clean one. The dirty one can deal with raw wafers, while the clean one can deal with processed wafers. This requirement raises a new problem for scheduling a cluster tool. This paper discusses the scheduling problem of ATC-DACTs with RTCs. Due to the arm task constraints, the proven, effective swap strategy is no longer applicable to ATC-DACTs, making the scheduling problem difficult. To address this problem, we explicitly describe the robot waiting as an event and build a Petri net (PN) model. Then, we propose a hybrid task sequence (HTS) as an operation strategy by combining the swap and backward strategies. Based on the HTS, the necessary and sufficient conditions for schedulability are established; also, a linear programming model is developed. We then develop an algorithm using these results to optimally schedule the system. Industrial case studies demonstrate the application of this method. [ABSTRACT FROM AUTHOR]

This paper addresses the one-dimensional cutting stock problem, focusing on minimizing total stock usage. Most procedures that deal with this problem reside on linear programming methods, heuristics, metaheuristics, and hybridizations. These methods face drawbacks like handling only low-complexity instances or requiring extensive parameter tuning. To address these limitations we develop a Petri-net model to construct cutting patterns. Using the filtered beam search algorithm, the reachability tree of the Petri net is constructed level by level from its root node to find the best solution, pruning the nodes that worsen the solution as the search progresses through the tree. Our algorithm is compared with the Least Lost Algorithm and the Generate and Solve algorithm over five datasets of instances. These algorithms share some characteristics with ours and have proven to be effective and efficient. Experimental results demonstrate that our algorithm effectively finds optimal and near-optimalsolutions for both low and high-complexity instances. These findings confirm that Petri nets are suitable for modeling and solving the one-dimensional cutting stock problem. [ABSTRACT FROM AUTHOR]

To address issues such as inadequate fault tolerance, long computation time, and limited universality in fault location for active distribution networks, this paper proposes a fault location method that combines Petri nets with an improved particle swarm optimization (PSO) algorithm. This method enhances the efficiency of fault location in distribution networks with distributed power sources, demonstrating good applicability and convergence, especially in complex network scenarios. The results from two test functions and simulation analyses of two types of node distribution networks show that (1) in the single-point fault simulation, the improved algorithm successfully located the fault in the ninth iteration, outperforming the 14th iteration result of the standard PSO algorithm. (2) In networks with randomly interconnected distributed power sources, the algorithm accurately located both single and multiple faults. (3) Experimental verification further supports the simulation results, proving the effectiveness of this method in practical applications. [ABSTRACT FROM AUTHOR]

In business process management, business process change analysis is the key link to ensure the flexibility and adaptability of the system. The existing methods mostly focus on the change analysis of a single business process from the perspective of control flow, ignoring the influence of data changes on collaborative processes with information interaction. In order to compensate for this deficiency, this paper proposes a rule-driven consistency analysis method for data changes in collaborative processes. Firstly, it analyzes the influence of data changes on other elements (such as activities, data, roles, and guards) in collaborative processes, and gives the definition of data influence. Secondly, the optimal alignment technology is used to explore how data changes interfere with the expected behavior of deviation activities, and decision rules are integrated into the Petri net model to accurately evaluate and screen out the effective expected behavior that conforms to business logic and established rules. Finally, the initial optimal alignment is repaired according to the screened effective expected behavior, and the consistency of business processes is recalculated. The experimental results show that the introduced rule constraint mechanism can effectively avoid the misjudgment of abnormal behavior. Compared with the traditional method, the average accuracy, recall rate, and F1-score of effective expected behavior are improved by 4%, 4.7%, and 4.3%, respectively. In addition, the repaired optimal alignment significantly enhances the system's ability to respond quickly and self-adjust to data changes, providing a strong support for the intelligent and automated transformation of business process management. [ABSTRACT FROM AUTHOR]

We study approximate integration of a function f over [0,1]^s based on taking the median of 2r-1 integral estimates derived from independently randomized (t,m,s)-nets in base 2. The nets are randomized by Matousek's random linear scramble with a random digital shift. If f is analytic over [0,1]^s, then the probability that any one randomized net's estimate has an error larger than 2^{-cm^2/s} times a quantity depending on f is O(1/\sqrt {m}) for any c<3\log (2)/\pi ^2\approx 0.21. As a result, the median of the distribution of these scrambled nets has an error that is O(n^{-c\log (n)/s}) for n=2^m function evaluations. The sample median of 2r-1 independent draws attains this rate too, so long as r/m^2 is bounded away from zero as m\to \infty. We include results for finite precision estimates and some nonasymptotic comparisons to taking the mean of 2r-1 independent draws. [ABSTRACT FROM AUTHOR]

To construct a user-friendly nomogram with MRI and clinicopathological parameters for the prediction of pathological complete response (pCR) after neoadjuvant therapy (NAT) in patients with breast cancer (BC). We retrospectively enrolled consecutive female patients pathologically confirmed with breast cancer who received NAT followed by surgery between January 2018 and December 2022 as the development cohort. Additionally, we prospectively collected eligible candidates between January 2023 and December 2023 as an external validation group at our institution. Pretreatment MRI features and clinicopathological variables were collected, and the pre- and post-treatment background parenchymal enhancement (BPE) and the changes in BPE on two MRIs were compared between patients who achieved pCR and those who did not. Multivariable logistic regression analysis was used to identify independent variables associated with pCR in the development cohort. These independent variables were combined into a predictive nomogram for which performance was assessed using the area under the receiver operating characteristic curve (AUC), calibration plot, decision curve analysis, and external validation. In the development cohort, there were a total of 276 female patients with a mean age of 48.3 ± 8.7 years, while in the validation cohort, there were 87 female patients with a mean age of 49.0 ± 9.5 years. Independent prognostic factors of pCR included small tumor size, HER2(+), high Ki-67 index,high signal enhancement ratio (SER), low minimum value of apparent diffusion coefficient (ADC min), and significantly decreased BPE after NAT(change of BPE). The nomogram, which incorporates the above parameters, demonstrated excellent predictive performance in both the development and external validation cohorts, with AUC values of 0.900 and 0.850, respectively. Additionally, the nomogram showed excellent calibration capacities, as indicated by Hosmer-Lemeshow test p values of 0.508 and 0.423 in the two cohorts. Furthermore, the nomogram provided greater net benefits compared to the default simple schemes in both cohorts. A nomogram constructed using tumor size, HER2 status, Ki-67 index, SER, ADC min , and changes in pre- and post-NAT BPE demonstrated strong predictive performance, calibration ability, and greater net benefits for predicting pCR in patients with BC after NAT. This suggests that the user-friendly nomogram could be a valuable imaging biomarker for identifying suitable candidates for NAT. [ABSTRACT FROM AUTHOR]

To solve some scheduling problems of batch processes based on timed Petri net models, timed extended reachability graphs (TERGs) and approximated TERGs can be used. Such graphs abstract temporal specifications and represent parts of timed languages. By exploring the feasible trajectories in a TERG, optimal schedules can be obtained with respect to the makespans of batch processes that are modeled by timed Petri nets. Nevertheless, the rapid growth of the number of states in a TERG makes the problem intractable for large systems. In this paper, we improve the existing clustering TERG approach, and we make it suitable for large sized batch processes. We also enlarge a systematic approach to model batch processes with timed Petri nets. Finally, a comprehensive example of scheduling problem is studied for an archetypal chemical production plant in order to illustrate the efficiency of the proposed approach. • The scheduling issue of batch chemical processes is formalized with timed Petri nets. • A graph named ClusTERG approximates the state space through hierarchical clustering. • The approximation error of this ClusTERG is far less than other approximations. • Such an approach is used to obtain near-optimal schedules of a batch process. [ABSTRACT FROM AUTHOR]

Decentralized supply chain operation in India adds to inefficiency in management and control difficulties for perishable product supply chain (PPSC). One of the important categories of factors that underly the problem in supply chain is the establishment of processing units that results in end – product distribution. This paper presents an optimal establishment of processing unit around production area for apple supply chain as a case study of India. This study proposed amalgamation of mixed integer linear programming (MILP) and colored petri nets (CPN) to model the PPSC. The mathematical model was set up in regard with capacity of processing unit and transportation cost with continuation in partner selection using MILP approach. The simulation model directs the maximization of system performance by running in CPN environment. The values of the results are subjected to transportation cost and production area with estimate of 25% loss during post harvesting such as transportation and environmental variation. The results corresponding to the case study provided an optimal establishment of processing units. Further, the specific partner associated with the facility and transportation cost. Decision-makers can identify the set of partners from the set of facilities dependent upon the transportation cost for further supply of product using a threshold values. Thereby, the model can be used as a decision-making system for processing companies to result in efficient PPSC management. The developed model was tested and validated on case study to demonstrate our approach's applicability. [ABSTRACT FROM AUTHOR]

Petri nets are a graphical notation for describing a class of discrete event dynamic systems whose behaviours are characterised by concurrency, synchronisation, mutual exclusion and conflict. They have been used over the years for the modelling of various distributed systems applications. With the advent of pervasive systems and the Internet of Things, the Calculus of Context-aware Ambients (CCA) has emerged as a suitable formal notation for analysing the behaviours of these systems. In this paper, we are interested in comparing the expressive power of Petri nets to that of CCA. That is, can the class of systems represented by Petri nets be modelled in CCA? To answer this question, an algorithm is proposed that maps any Petri net onto a CCA process. We prove that a Petri net and its corresponding CCA process are behavioural equivalent. It follows that CCA is at least as expressive as Petri nets, i.e., any system that can be specified in Petri nets can also be specified in CCA. Moreover, tools developed for CCA can also be used to analyse the behaviours of Petri nets. [ABSTRACT FROM AUTHOR]

In this study, we analyzed the evolution of online public opinion on emergencies using a new Stochastic Petri Net modeling approach. First, an intuitive description of the emergency online public opinion development process was conceptualized from the life cycle evolution law perspective. Then, based on Petri net theory, a Stochastic Petri Net isomorphic Markov chain model was constructed to simulate the evolution of online public opinion on emergencies. Finally, four real-life cases were selected to validate and analyze the model, demonstrating that the evolutionary leaps, complexity, critical nodes, evolutionary rate, and execution time differ across different online public opinions on emergencies. The study results indicate that this modeling approach has certain advantages in examining the evolution based on multi-factor coupling and quantifying the evolution law in online public opinion on emergencies. [ABSTRACT FROM AUTHOR]

This survey paper explores Petri Net tools relevant to concurrent, non-deterministic, stochastic, and parallel systems. It begins with a brief introduction to Petri Nets, discussing their formalism, properties, and variants. The paper then examines several Petri Net tools, including the Oris Tool, Tapaal Tool, and Color Petri Net (CPN) Tool, detailing their modeling capabilities and presenting the results obtained from the problems addressed. [ABSTRACT FROM AUTHOR]

This paper is devoted to Petri net (PN)-based models of automated manufacturing systems (AMSs) with resources in order to prevent deadlocks in them. Their sustainability can be seen as the result of their deadlock freeness, leading to correct and fluent production, because AMSs with deadlocks work neither correctly nor fluently, need reconstruction and cause downtime in production. The paradigm of such PN models, S3PRs (systems of simple sequential processes with resources), is well known from the deadlock prevention point of view. Here, an extended S3PR (ES3PR) will be explored, with respect to its modelling and deadlock prevention. While in the case of S3PRs, ordinary Petri nets (OPNs) are used for these aims, here, for ES3PRs, generalized Petri nets (GPNs) are used. The reason for such a procedure is the possible presence of multiplex-directed arcs in the structure of PN models of AMSs. The significant alternation is that while, in the former case, the elementary siphons and dependent ones are sufficient for supervisor synthesis, here, in the later case, the GPNs and their siphons have to satisfy the max cs property. [ABSTRACT FROM AUTHOR]

In this paper we purpose a Stochastic Petri Net based approach for analysis of communication system with fuzzy sets. There are two stages to the method that is being given. In terms of transition firing rates, the first stage is identical to that of regular stochastic petri nets with steady-state probability and continuous time Markov chain (CTMC) generated. Fuzzy steady state probabilities are computed in the second step after the transition firing rates are represented by triangular fuzzy numbers. A numerical example of communication system considered to analyse the pertinence of proposed method. The significance of this method is to study the dimensions of uncertainty and stochastic variability in system modelling. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of NO2 emissions in Mashhad City utilizing statistical evaluations and the Cisco Network Model. The present study begins by evaluating NO2 emissions through statistical analysis, followed by the application of histograms and radar statistical appraisals. Subsequently, a model execution logic is developed using the Cisco Network Model to further understand the distribution and sources of NO2 emissions in the city. Additionally, the research incorporates managerial insights by employing Petri Net modeling, which enables a deeper understanding of the dynamic interactions within the air quality management system. This approach aids in identifying critical control points and optimizing response strategies, thus enhancing the overall effectiveness of urban air pollution mitigation efforts. The findings of this study provide valuable insights into the levels of NO2 pollution in Mashhad City and offer a structured approach to modeling NO2 emissions for effective air quality management strategies which can be extended to the other megacities as well. [ABSTRACT FROM AUTHOR]

Process mining is a field of computer science that deals with the discovery and analysis of process models based on automatically generated event logs. Currently, many companies are using this technology to optimize and improve their business processes. However, a discovered process model may be too detailed, sophisticated, and difficult for experts to understand. In this paper, we consider a problem of discovering the hierarchical business process model from a low-level event log, i. e., the problem of the automatic synthesis of more readable and understandable process models based on the data stored in the event logs of information systems. The discovery of better-structured and more readable process models is extensively studied in the framework of process mining research from different perspectives. In this paper, we present an algorithm for discovering hierarchical process models represented as two-level workflow Petri nets. The algorithm is based on predefined event partitioning so that this partitioning defines a sub-process corresponding to a high-level transition at the top level of a two-level net. In contrast to existing solutions, our algorithm does not impose restrictions on the process control flow and allows for concurrency and iterations.

NFV (Network Function Virtualization) is an innovative paradigm that seeks to improve the flexibility and efficiency of network services. NFV focuses on virtualizing network functions, allowing them to be executed on generic hardware, which decouples software and hardware and allows for more agile and scalable implementations. Through NFV, the concept of SFC (Service Function Chain) emerges, which consists of a sequence of VNFs (Virtual Network Functions), such as gateways, firewalls, and routers, arranged in an orderly manner. A critical challenge faced by SFC is its sensitivity to latency: delay increases as the chain of VNFs lengthens, which can compromise the quality of service. Minimizing this latency is crucial to ensure the efficiency of SFC systems. However, testing different SFC architectures in real environments is costly. As a solution, this study proposes using Stochastic Petri Nets (SPNs) for a performance evaluation of SFC architectures. The developed SPN model allows for analyzing different configurations of VNFs in sequential, parallel, and hybrid architectures. Four case studies were carried out exploring the behavior of the proposed model under different analyses and scenarios. The results obtained were validated through simulations in GNS3 (Graphical Network Simulator-3). The data demonstrate that changes in the SFC architecture can result in significant performance improvements and latency reduction. [ABSTRACT FROM AUTHOR]

Studies in the area of mobile robotics have advanced in recent years, mainly due to the evolution of technology and the growing need for automated and dynamic solutions in sectors such as industry, transport, and agriculture. These devices are complex and the ideal method for localizing, mapping, and navigating autonomous mobile robots changes depending on the application. Thus, the general objective of this work is to propose a simultaneous localization and mapping method for autonomous mobile robots in indoor environments, using computer vision (CV) and Petri net (PN). A landmark was placed next to each door in the analyzed region and images were acquired as the rooms in the environment were explored. The algorithm processes the images to count and identify the doors. A transition is created in the PN for each door found and the rooms connected by these doors are represented by the places in the PN. Then, one of the doors is crossed, new images are obtained and the process is repeated until all rooms are explored. The algorithm generates a PN, which can be represented by an image file (.png) and a file with the extension.pnml. The results compare the layout of four environments with the respective generated PNs. Furthermore, six evaluation criteria are proposed for validating Petri nets as a topological map of environments. It is concluded that using PN for this purpose presents originality and potential innovation, being a SLAM technique for indoor environments, which demands low computational cost. [ABSTRACT FROM AUTHOR]

Hyperledger Fabric is a platform for permissioned blockchain networks that enables secure and auditable distributed data storage for enterprise applications. There is a growing interest in applications based on this platform, but its use requires the configuration of different blockchain parameters. Various configurations impact the system's non-functional qualities, especially performance and cost. In this article, we propose a Stochastic Petri Net to model the performance of the Hyperledger Fabric platform with different blockchain parameters, computer capacity, and transaction rates. We also present a set of case studies to demonstrate the feasibility of the proposed model. This model serves as a practical guide to help administrators of permissioned blockchain networks find the best performance for their applications. The proposed model allowed us to identify the block size that leads to a high mean response time (ranging from 1 to 25 seconds) caused by a change in the arrival rate. [ABSTRACT FROM AUTHOR]

Petri nets are a graphical notation for describing a class of discrete event dynamic systems whose behaviours are characterised by concurrency, synchronisation, mutual exclusion and conflict. They have been used over the years for the modelling of various distributed systems applications. With the advent of pervasive systems and the Internet of Things, the Calculus of Context-aware Ambients (CCA) has emerged as a suitable formal notation for analysing the behaviours of these systems. In this paper, we are interested in comparing the expressive power of Petri nets to that of CCA. That is, can the class of systems represented by Petri nets be modelled in CCA? To answer this question, an algorithm is proposed that maps any Petri net onto a CCA process. We prove that a Petri net and its corresponding CCA process are behavioural equivalent. It follows that CCA is at least as expressive as Petri nets, i.e., any system that can be specified in Petri nets can also be specified in CCA. Moreover, tools developed for CCA can also be used to analyse the behaviours of Petri nets.

Critical systems, in which failure and malfunction may result in severe human, environmental, and financial damages, are essential components in various sectors and particularly in energy domains. Although undesirable, integration error problems in the supervision of critical systems do occur, incurring significant expenses due to an operator's subjective analysis and hardware topology failures. In this work, a malleable model design approach is proposed to formulate and solve the integration error problem in critical systems' supervision in terms of reliability. A real hybrid power plant (HPP) case is considered for a case study with simulated data. A method framework with an informal approach (C4 diagram) and formal approach (hierarchical colored Petri nets) in a radial spectrum is applied to the HPP supervision design. In using formal methods, a formulation and solution to this problem through structured, scalable, and compact mathematical representations are possible. This malleable model is intended to guarantee the functional correctness and also reliability of the plant supervision system based on system software architecture. The outcomes suggest that the malleable model is appropriate for the energy domain and can be used for other types of critical systems, bringing all the benefits of this methodology to the context in which it will be applied. [ABSTRACT FROM AUTHOR]

The article discusses the concept of Self-Learning Meta (SLeM) and its applications in Auto Machine Learning (AutoML). SLeM is a framework that aims to automate various components of the machine learning process, such as data selection, model adjustment, loss setting, and algorithm designing. The framework utilizes meta-data or meta-knowledge to evaluate and predict the optimal learning methodology for different tasks. The text presents several SLeM algorithms, including data auto-selection, model auto-adjustment, loss auto-setting, and algorithm auto-designing. These algorithms have been implemented and released on an open-source platform. The text also highlights the challenges and future research directions in developing more automated and comprehensive SLeM algorithms. The work was supported by funding from the National Key Research and Development Program of China and the National Natural Science Foundation of China. [Extracted from the article]

In process mining, conformance checking determines the quality of discrete‐event process models through several measures computed with respect to a set of event sequences λ from which the model N is obtained. Precision is a measure that evaluates the surplus language of the model LN with respect to λ. This article outlines four precision evaluation approaches for Petri net (PN) workflow models obtained through process discovery techniques. First, the basics of the quality measures of process models stablished in conformance checking are summarised. Then, the methods for model precision evaluation in literature are outlined and analysed. Finally, the advantages and limitations of the methods are pointed out and compared. [ABSTRACT FROM AUTHOR]

Computer system resilience refers to the ability of a computer system to continue functioning even in the face of unexpected events or disruptions. These disruptions can be caused by a variety of factors, such as hardware failures, software glitches, cyber attacks, or even natural disasters. Modern computational environments need applications that can recover quickly from major disruptions while also being environmentally sustainable. Balancing system resilience with energy efficiency is challenging, as efforts to improve one can harm the other. This paper presents a method to enhance disaster survivability in microservice architectures, particularly those using Kubernetes in cloud-based environments, focusing on optimizing electrical energy use. Aiming to save energy, our work adopt the consolidation strategy that means grouping multiple microservices on a single host. Our aproach uses a widely adopted analytical model, the Generalized Stochastic Petri Net (GSPN). GSPN are a powerful modeling technique that is widely used in various fields, including engineering, computer science, and operations research. One of the primary advantages of GSPN is its ability to model complex systems with a high degree of accuracy. Additionally, GSPN allows for the modeling of both logical and stochastic behavior, making it ideal for systems that involve a combination of both. Our GSPN models compute a number of metrics such as: recovery time, system availability, reliability, Mean Time to Failure, and the configuration of cloud-based microservices. We compared our approach against others focusing on survivability or efficiency. Our approach aligns with Recovery Time Objectives during sudden disasters and offers the fastest recovery, requiring 9% less warning time to fully recover in cases of disaster with alert when compared to strategies with similar electrical consumption. It also saves about 27% energy compared to low consolidation strategies and 5% against high consolidation under static conditions. [ABSTRACT FROM AUTHOR]

In this article we show that the conformal nets corresponding to WZW models are rational, resolving a long-standing open problem. Specifically, we show that the Jones-Wassermann subfactors associated with these models have finite index. This result was first conjectured in the early 90s but had previously only been proven in special cases, beginning with Wassermann's landmark results in type A. The proof relies on a new framework for the systematic comparison of tensor products (a.k.a. 'fusion') of conformal net representations with the corresponding tensor product of vertex operator algebra modules. This framework is based on the geometric technique of 'bounded localized vertex operators,' which realizes algebras of observables via insertion operators localized in partially thin Riemann surfaces. We obtain a general method for showing that Jones-Wassermann subfactors have finite index, and apply it to additional families of important examples beyond WZW models. We also consider applications to a class of positivity phenomena for VOAs, and use this to outline a program for identifying unitary tensor product theories of VOAs and conformal nets even for badly-behaved models. [ABSTRACT FROM AUTHOR]

Effective quality management plays a pivotal role in ensuring the smooth operation of smart city systems, which have significant implications for safety, accessibility, affordability, and maintainability. Dependability of autonomous systems is of utmost importance, as achieving satisfactory levels of availability and reliability poses considerable challenges. Smart cities are characterized by interconnected sub-architectures, encompassing vehicle monitoring, sidewalk monitoring, and building monitoring, all of which need to function efficiently. Analytical models such as Petri nets, Markov chains, and fault trees are well-suited for evaluating complex scenarios in the context of smart cities. This paper presents analytical models that utilize fault tree and Markov chain techniques to assess the availability and reliability of smart city monitoring systems. The model is divided into shared and non-shared components, with non-shared components being specific to certain contextual applications, while shared components, such as data processing and electrical power, are essential for all smart city monitoring and management systems. The study underscores the ease with which the fault tree model can enhance availability by modifying failure requirements and resources. Case studies provide concrete examples of how availability improved from 95.3 to 99.8% by varying a configuration known as "KooN" in multiple components. This paper takes a comprehensive approach to evaluating the dependability of smart city architectures and contributes advancements, such as hierarchical modeling, sequential sensitivity analysis, and the "KooN" analytic method. These contributions expand the existing knowledge and methodologies in smart city dependability analysis. Moreover, this work aims to serve as a practical tool to assist smart city managers in optimizing their proposals. All modeling aspects and parameters are detailed thoroughly to enable effective implementation of the proposed approach by anyone using it. [ABSTRACT FROM AUTHOR]