Search results for: neural petri net

Authors: Sadiq J. Abou-Loukh

Abstract:

The present work deals with implementation of Petri nets, which own the perfect ability of modeling, are used to establish a fault diagnosis model. Fault diagnosis of a control system received considerable attention in the last decades. The formalism of representing neural networks based on Petri nets has been presented. Neural Petri Net (NPN) reasoning model is investigated and developed for the fault diagnosis process of electric control system. The proposed NPN has the characteristics of easy establishment and high efficiency, and fault status within the system can be described clearly when compared with traditional testing methods. The proposed system is tested and the simulation results are given. The implementation explains the advantages of using NPN method and can be used as a guide for different online applications.

Keywords: petri net, neural petri net, electric control system, fault diagnosis

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Authors: Riddhi Jangid, Gajendra Pratap Singh

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Petri nets, a mathematical tool, is used for modeling in different areas of computer sciences, biological networks, chemical systems and many other disciplines. A Petri net model of a given system is created by the graphical representation that describes the properties and behavior of the system. While looking for the behavior of any system, 1-safe Petri nets are of particular interest to many in the application part. Boolean Petri nets correspond to those class in 1- safe Petri nets that generate all the binary n-vectors in their reachability analysis. We study the class by changing different parameters like the token counts in the places and how the structure of the tree changes in the reachability analysis. We discuss here an extended class of Boolean Petri nets that generates n-ary trees in their reachability-based analysis.

Keywords: marking vector, n-vector, petri nets, reachability

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Authors: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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Authors: Riddhi Jangid, Gajendra Pratap Singh

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Petri nets, a formalized modeling language that was introduced back around 50-60 years, have been widely used for modeling discrete event dynamic systems and simulating their behavior. Reachability analysis of Petri nets gives many insights into a modeled system. This idea leads us to study the reachability technique and use it in the reachability problem in the state space of reachable markings. With the same concept, Crisp Boolean Petri nets were defined in which the marking vectors that are boolean are distinct in the reachability analysis of the nets. We generalize the concept and define ‘Crisp’ Petri nets that generate the marking vectors exactly once in their reachability-based analysis, not necessarily Boolean.

Keywords: marking vector, n-vector, Petri nets, reachability

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Authors: K. Shoylekova, K. Grigorova

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The Petri nets are the first standard for business process modeling. Most probably, it is one of the core reasons why all new standards created afterwards have to be so reformed as to reach the stage of mapping the new standard onto Petri nets. The paper presents a Business process repository based on a universal database. The repository provides the possibility the data about a given process to be stored in three different ways. Business process repository is developed with regard to the reformation of a given model to a Petri net in order to be easily simulated two different techniques for business process simulation based on Petri nets - Yasper and Woflan are discussed. Their advantages and drawbacks are outlined. The way of simulating business process models, stored in the Business process repository is shown.

Keywords: business process repository, petri nets, simulation, Woflan, Yasper

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Authors: T. Godwin

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A call-taxi system is a type of taxi service where a taxi could be requested through a phone call or mobile app. A schematic functioning of a call-taxi system is modeled using Petri net, which provides the necessary conditions for a taxi to be assigned by a dispatcher to pick a customer as well as the conditions for the taxi to be released by the customer. A Petri net is a graphical modeling tool used to understand sequences, concurrences, and confluences of activities in the working of discrete event systems. It uses tokens on a directed bipartite multi-graph to simulate the activities of a system. The Petri net model is translated into a simulation model and a call-taxi system is simulated. The simulation model helps in evaluating the operation of a call-taxi system based on the fleet size as well as the operating policies for call-taxi assignment and empty call-taxi repositioning. The developed Petri net based simulation model can be used to decide the fleet size as well as the call-taxi assignment policies for a call-taxi system.

Keywords: call-taxi, discrete event system, petri net, simulation modeling

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Authors: Sawsen Khlifa, Chiheb AMeur Abid, Belhassan Zouari

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Modular verification approaches have been widely attempted to cope with the well known state explosion problem. This paper deals with the modular verification of modular Petri nets. We propose a reduced version for the modular state space of a given modular Petri net. The new structure allows the creation of smaller modular graphs. Each one draws the behavior of the corresponding module and outlines some global information. Hence, this version helps to overcome the explosion problem and to use less memory space. In this condensed structure, the verification of some generic properties concerning one module is limited to the exploration of its associated graph.

Keywords: distributed systems, modular verification, petri nets, state space explosition

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Authors: Husam Kaid, Abdulrahman Al-Ahmari, Zhiwu Li

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This paper develops a robust deadlock control technique for shared and unreliable resources in automated manufacturing systems (AMSs) based on structural analysis and colored Petri nets, which consists of three steps. The first step involves using strict minimal siphon control to create a live (deadlock-free) system that does not consider resource failure. The second step uses an approach based on colored Petri net, in which all monitors designed in the first step are merged into a single monitor. The third step addresses the deadlock control problems caused by resource failures. For all resource failures in the Petri net model a common recovery subnet based on colored petri net is proposed. The common recovery subnet is added to the obtained system at the second step to make the system reliable. The proposed approach is evaluated using an AMS from the literature. The results show that the proposed approach can be applied to an unreliable complex Petri net model, has a simpler structure and less computational complexity, and can obtain one common recovery subnet to model all resource failures.

Keywords: automated manufacturing system, colored Petri net, deadlocks, siphon

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Authors: Walid Louhichi, Mouhebeddine Berrima, Narjes Ben Rajed

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Elasticity is the essential property of cloud computing. As the name suggests, it constitutes the ability of a cloud system to adjust resource provisioning in relation to fluctuating workload. There are two types of elasticity operations, vertical and horizontal. In this work, we are interested in horizontal scaling, which is ensured by two mechanisms; scaling in and scaling out. Following the sizing of the system, we can adopt scaling in in the event of over-supply and scaling out in the event of under-supply. In this paper, we propose a formal model, based on colored and temporized Petri nets, for the modeling of the duplication and the removal of a virtual machine from a server. This model is based on formal Petri Nets modeling language. The proposed models are edited, verified, and simulated with two examples implemented in CPNtools, which is a modeling tool for colored and timed Petri nets.

Keywords: cloud computing, elasticity, elasticity controller, petri nets, scaling in, scaling out

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Authors: Nidhi Gaur, Padmaja Joshi, Vijay Jain, Rajeev Srivastava

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Web application architecture is important to achieve the desired performance for the application. Performance analysis studies are conducted to evaluate existing or planned systems. Web applications are used by hundreds of thousands of users simultaneously, which sometimes increases the risk of server failure in real time operations. We use Coloured Petri Net (CPN), a very powerful tool for modelling dynamic behaviour of a web application system. CPNs extend the vocabulary of ordinary Petri nets and add features that make them suitable for modelling large systems. The major focus of this work is on server side of web applications. The presented work focuses on modelling restructuring aspects, with major focus on concurrency and architecture, using CPN. It also focuses on bringing out the appropriate architecture for web and database servers given the number of concurrent users.

Keywords: coloured Petri Nets (CPNs), concurrent users, per- formance modelling, web application architecture

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Authors: Abdolghader Pourali, Mohammad V. Malakooti, Muhammad Hussein Yektaie

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A mobile payment system in mobile e-commerce generally have high security so that the user can trust it for doing business deals, sales, paying financial transactions, etc. in the mobile payment system. Since an architecture or payment model in e-commerce only shows the way of interaction and collaboration among users and mortgagers and does not present any evaluation of effectiveness and confidence about financial transactions to stakeholders. In this paper, we try to present a detailed assessment of the reliability of a mobile payment model in the mobile e-commerce using formal models and colored Petri nets. Finally, we demonstrate that the reliability of this system has high value (case study: a secure payment model in mobile commerce.

Keywords: reliability, colored Petri net, assessment, payment models, m-commerce

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Authors: I. Bentchikou, A. Tlemcani, F. Boudjema, D. Boukhetala, N. Ould Cherchali

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In this paper, hybrid approach is proposed to regulate the voltages of the floating capacitor multicell inverter and the current in the load. This structure makes it possible to ensure the distribution of the voltage stresses on the various low-voltage semiconductor components connected in series. And as the problem and to keep a constant voltage across the capacitors. Thus, it is necessary to ensure a distribution balanced voltages at the terminals of floating capacitors thanks to Algorithm develop for this, using the Petri nets. So we consider a three-cell converter represented as a hybrid system with eight modes of operation. The operating modes of the system are governed by the control reference voltage and a reference current. Finally, we present the results of the simulation with MATLAB/SIMULINK to illustrate the performances of this approach.

Keywords: hybrid control, floating condensers, multicellular converter, petri nets

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Authors: Joselito Medina-Marin, Alexandr Karelin, Ana Tarasenko, Juan Carlos Seck-Tuoh-Mora, Norberto Hernandez-Romero, Eva Selene Hernandez-Gress

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A production line designer faces with several challenges in manufacturing system design. One of them is the assignment of buffer slots in between every machine of the production line in order to maximize the throughput of the whole line, which is known as the Buffer Allocation Problem (BAP). The BAP is a combinatorial problem that depends on the number of machines and the total number of slots to be distributed on the production line. In this paper, we are proposing a Petri Net (PN) Model to obtain the throughput in unreliable production lines, based on PN mathematical tools and the decomposition method. The results obtained by this methodology are similar to those presented in previous works, and the number of machines is not a hard restriction.

Keywords: buffer allocation problem, Petri Nets, throughput, production lines

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Authors: C. Baidada, M. H. Abidi, A. Jakimi, E. H. El Kinani

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Reverse engineering has become a viable method to measure an existing system and reconstruct the necessary model from tis original. The reverse engineering of behavioral models consists in extracting high-level models that help understand the behavior of existing software systems. In this paper, we propose an approach for the reverse engineering of sequence diagrams from the analysis of execution traces produced dynamically by an object-oriented application using petri nets. Our methods show that this approach can produce state diagrams in reasonable time and suggest that these diagrams are helpful in understanding the behavior of the underlying application. Finally we will discuss approachs and tools that are needed in the process of reverse engineering UML behavior. This work is a substantial step towards providing high-quality methodology for effectiveand efficient reverse engineering of sequence diagram.

Keywords: reverse engineering, UML behavior, sequence diagram, execution traces, petri nets

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

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The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: flow-shop scheduling problem, makespan, Petri nets, state equation

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Authors: Hichem Kmimech, Achref Jabeur Telmoudi, Lotfi Nabli

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The estimation of the initial marking minimum (MIM) is a crucial problem in labeled Petri nets. In the case of multiple choices, the search for the initial marking leads to a problem of optimization of the minimum allocation of resources with two constraints. The first concerns the firing sequence that could be legal on the initial marking with respect to the firing vector. The second deals with the total number of tokens that can be minimal. In this article, the MIM problem is solved by the meta-heuristic particle swarm optimization (PSO). The proposed approach presents the advantages of PSO to satisfy the two previous constraints and find all possible combinations of minimum initial marking with the best computing time. This method, more efficient than conventional ones, has an excellent impact on the resolution of the MIM problem. We prove through a set of definitions, lemmas, and examples, the effectiveness of our approach.

Keywords: marking, production system, labeled Petri nets, particle swarm optimization

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Authors: Daniel Li

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We present a novel application of neural rendering methods to confocal microscopy. Neural rendering and implicit neural representations have developed at a remarkable pace, and are prevalent in modern 3D computer vision literature. However, they have not yet been applied to optical microscopy, an important imaging field where 3D volume information may be heavily sought after. In this paper, we employ neural rendering on confocal microscopy focus stack data and share the results. We highlight the benefits and potential of adding neural rendering to the toolkit of microscopy image processing techniques.

Keywords: neural rendering, implicit neural representations, confocal microscopy, medical image processing

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Authors: José Luis Carrillo-Medina, Roberto Latorre

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Experimental evidence has revealed that different living neural systems can sign their output signals with some specific neural signature. Although experimental and modeling results suggest that neural signatures can have an important role in the activity of neural networks in order to identify the source of the information or to contextualize a message, the functional meaning of these neural fingerprints is still unclear. The existence of cellular mechanisms to identify the origin of individual neural signals can be a powerful information processing strategy for the nervous system. We have recently built different models to study the ability of a neural network to process information based on the emission and recognition of specific neural fingerprints. In this paper we further analyze the features that can influence on the information processing ability of this kind of networks. In particular, we focus on the role that the duration of a refractory period in each neuron after emitting a signed message can play in the network collective dynamics.

Keywords: neural signature, neural fingerprint, processing based on signal identification, self-organizing neural network

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Authors: Andreev V. A., Kovalenko T. N., Privolnev V. V., Chernavin A. V., Knyazeva E. R.

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Aim: To evaluate the antagonistic activity of Streptococcus salivarius K12 (SsK12) against ENT and oral cavity infection pathogens (S. pneumoniae, S. pyogenes, S. aureus), gram-negative bacteria (E. coli, P. aeruginosa) and C. albicans. Materials and methods: The probiotic strain SsK12 was isolated from the dietary supplement containing at least 1 × 109 CFU per tablet. The tablet was dissolved in the enrichment broth. The resulting suspension was seeded on 5% blood agar and incubated at 35°C in 4-6% CO2 for 48 hours. The raised culture was identified as Streptococcus salivarius with MALDI-TOF mass spectrometry method. The evaluation of SsK12 antagonistic activity was carried out using a perpendicular streak technique. The daily SsK12 culture was inoculated as heavy streaks with a loop at one side of Petri dish with the Muller-Hinton agar (MHA) and incubated for 24 hours at 350 C in anaerobic conditions. It was supposed that bacteriocins would diffuse over the whole area of the agar media. On the next day S. pneumoniae, S. pyogenes, S. aureus, E. coli, P. aeruginosa and C. albicans clinical isolates were streaked at the clear side of MHA Petri dish. MHA Petri dish inoculated with SsK12 (one part) and with the respective clinical isolates (another part) streaked perpendicularly on the same day was used as the control. Results: There was no growth of S. pyogenes on the Petri dish with SsK12 daily culture; the growth of a few colonies of S. pneumonia was noted. The growth of S. aureus, E. coli, P. aeruginosa and C. albicans was noted along the inoculated streak. On the control Petri dish with simultaneous inoculating of the SsK12 strain and the test cultures, the growth of all the testes isolates was noted. Conclusions: (1) SsK12 possesses perfect antagonistic activity against S. pyogenes and good activity against S. pneumoniae. (2) There was no antagonistic activity of SsK12 against S. aureus, E. coli, P. aeruginosa and C. albicans. (3) SsK12 antagonistic properties make it possible to use this probiotic strain for prophylaxis of recurrent ENT infections.

Keywords: probiotics, SsK12, streptococcus salivarius K12, antagonistic activity

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Authors: Amel Ltifi, Ahmed Zouinkhi, Med Salim Bouhlel

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Spontaneous networks such as VANET are in general deployed in an open and thus easily accessible environment. Therefore, they are vulnerable to attacks. Trust management is one of a set of security solutions dedicated to this type of networks. Moreover, the strong mobility of the nodes (in the case of VANET) makes the establishment of a trust management system complex. In this paper, we present a concept of ‘Active Vehicle’ which means an autonomous vehicle that is able to make decision about trustworthiness of alert messages transmitted about road accidents. The behavior of an “Active Vehicle” is modeled using Petri Nets.

Keywords: active vehicle, cooperation, petri nets, trust management, VANET

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Authors: Taha Benarbia, Kay W. Axhausen, Anugrah Ilahi

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Electric car sharing system as ecologic transportation increasing in the world. The complexity of managing electric car sharing systems, especially one-way trips and battery autonomy have direct influence to on supply and demand of system. One must be able to precisely model the demand and supply of these systems to better operate electric car sharing and estimate its effect on mobility management and the accessibility that it provides in urban areas. In this context, our work focus to develop performances optimization model of the system based on discrete event simulation and stochastic Petri net. The objective is to search optimal decisions and management parameters of the system in order to fulfil at best demand while minimizing undesirable situations. In this paper, we present new model of electric cars sharing with relocation based on monitoring system. The proposed approach also help to precise the influence of battery charging level on the behaviour of system as important decision parameter of this complex and dynamical system.

Keywords: electric car-sharing systems, smart mobility, Petri nets modelling, discrete event simulation

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Authors: Elabed Saud

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This paper introduces the new ability of Artificial Neural Networks (ANNs) in estimating speed and controlling the separately excited DC motor. The neural control scheme consists of two parts. One is the neural estimator which is used to estimate the motor speed. The other is the neural controller which is used to generate a control signal for a converter. These two neutrals are training by Levenberg-Marquardt back-propagation algorithm. ANNs are the standard three layers feed-forward neural network with sigmoid activation functions in the input and hidden layers and purelin in the output layer. Simulation results are presented to demonstrate the effectiveness of this neural and advantage of the control system DC motor with ANNs in comparison with the conventional scheme without ANNs.

Keywords: Artificial Neural Network (ANNs), excited DC motor, convenional controller, speed Controller

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Authors: A. A. Behroozpoor, M. M. Mazarei

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In this paper, a fuzzy recurrent neural network is proposed for solving the classical quadratic control problem subject to linear equality and bound constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed.

Keywords: REFERENCES [1] Xia, Y, A new neural network for solving linear and quadratic programming problems. IEEE Transactions on Neural Networks, 7(6), 1996, pp.1544–1548. [2] Xia, Y., & Wang, J, A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Transactions on Neural Networks, 16(2), 2005, pp. 379–386. [3] Xia, Y., H, Leung, & J, Wang, A projection neural network and its application to constrained optimization problems. IEEE Transactions Circuits and Systems-I, 49(4), 2002, pp.447–458.B. [4] Q. Liu, Z. Guo, J. Wang, A one-layer recurrent neural network for constrained seudoconvex optimization and its application for dynamic portfolio optimization. Neural Networks, 26, 2012, pp. 99-109.

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Authors: Najmeh Mohsenifar, Narjes Mohsenifar, Abbas Kargar

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In this paper, has been presented a stable method for predicting the ECG signals through the RBF neural networks, by the PSO algorithm. In spite of quasi-periodic ECG signal from a healthy person, there are distortions in electro cardiographic data for a patient. Therefore, there is no precise mathematical model for prediction. Here, we have exploited neural networks that are capable of complicated nonlinear mapping. Although the architecture and spread of RBF networks are usually selected through trial and error, the PSO algorithm has been used for choosing the best neural network. In this way, 2 second of a recorded ECG signal is employed to predict duration of 20 second in advance. Our simulations show that PSO algorithm can find the RBF neural network with minimum MSE and the accuracy of the predicted ECG signal is 97 %.

Keywords: electrocardiogram, RBF artificial neural network, PSO algorithm, predict, accuracy

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Authors: J. Barilla, M. Lokajíček, H. Pisaková, P. Simr

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The final biological effect of ionizing particles may be influenced strongly by some chemical substances present in cells mainly in the case of low-LET radiation. The influence of oxygen may be particularly important because oxygen is always present in living cells. The corresponding processes are then running mainly in the chemical stage of radio biological mechanism. The radical clusters formed by densely ionizing ends of primary or secondary charged particles are mainly responsible for final biological effect. The damage effect depends then on radical concentration at a time when the cluster meets a DNA molecule. It may be strongly influenced by oxygen present in a cell as oxygen may act in different directions: at small concentration of it the interaction with hydrogen radicals prevails while at higher concentrations additional efficient oxygen radicals may be formed. The basic radical concentration in individual clusters diminishes, which is influenced by two parallel processes: chemical reactions and diffusion of corresponding clusters. The given simultaneous evolution may be modeled and analyzed well with the help of Continuous Petri nets. The influence of other substances present in cells during irradiation may be studied, too. Some results concerning the impact of oxygen content will be presented.

Keywords: radiobiological mechanism, chemical phase, DSB formation, Petri nets

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Authors: Diego De Almeida Pereira, Diana Borchenko

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Artificial neural networks are used for many applications as they are able to learn complex nonlinear relationships between input and output data. As the number of neurons and layers in a neural network increases, it is possible to represent more complex behaviors. The present study proposes that artificial neural networks are a valuable tool for architecture and engineering professionals concerned with understanding how buildings influence human and social well-being based on theories of environmental psychology.

Keywords: environmental psychology, architecture, neural networks, human and social well-being

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Authors: Sofiane Bendoukha, Daniel Moldt, Hayat Bendoukha

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Workflow concepts are essential for the development of remote sensing applications. They can help users to manage and process satellite data and execute scientific experiments on distributed resources. The objective of this paper is to introduce an approach for the specification and the execution of complex scientific workflows in Cloud-like environments. The approach strives to support scientists during the modeling, the deployment and the monitoring of their workflows. This work takes advantage from Petri nets and more pointedly the so-called reference nets formalism, which provides a robust modeling/implementation technique. RENEWGRASS is a tool that we implemented and integrated into the Petri nets editor and simulator RENEW. It provides an easy way to support not experienced scientists during the specification of their workflows. It allows both modeling and enactment of image processing workflows from the remote sensing domain. Our case study is related to the implementation of vegetation indecies. We have implemented the Normalized Differences Vegetation Index (NDVI) workflow. Additionally, we explore the integration possibilities of the Cloud technology as a supplementary layer for the deployment of the current implementation. For this purpose, we discuss migration patterns of data and applications and propose an architecture.

Keywords: cloud computing, scientific workflows, petri nets, RENEWGRASS

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Authors: Mohammad Reza Rahimi Khoygani, Reza Ghasemi

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In this paper, designing direct adaptive neural controller is applied for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) is used for the Neural network (NN). The adaptive neural controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are the merits of this paper. The promising performance of the proposed controllers investigates in simulation results.

Keywords: adaptive control, pendulum dynamical system, nonlinear control, adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: H. Y. Jung, Jing Wang, J. H. Park, Hao Shen

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This brief addresses the passivity problem for neural networks with time-varying delays. The aim is focus on establishing the passivity condition of the considered neural networks.

Keywords: neural networks, passivity analysis, time-varying delays, linear matrix inequality

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Authors: Karen C. Olufokunbi, Odetunji A. Odejobi

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The discourse of this paper is the examination of the generation, accumulation and growth of e-waste in a developing country. Images and other data about computer e-waste were collected using a digital camera, 290 copies of questionnaire and three structured interviews using Obafemi Awolowo University (OAU), Ile-Ife, Nigeria environment as a case study. The numerical data were analysed using R data analysis and process tool. Automata-based techniques and Petri net modeling tool were used to design and simulate a computational model for the recovery of saleable materials from e-waste. The R analysis showed that at a 95 percent confidence level, the computer equipment that will be disposed by 2020 will be 417 units. Compared to the 800 units in circulation in 2014, 50 percent of personal computer components will become e-waste. This indicates that personal computer components were in high demand due to their low costs and will be disposed more rapidly when replaced by new computer equipment Also, 57 percent of the respondents discarded their computer e-waste by throwing it into the garbage bin or by dumping it. The simulated model using Coloured Petri net modelling tool for the process showed that the e-waste dynamics is a forward sequential process in the form of a pipeline meaning that an e-waste recovery of saleable materials process occurs in identifiable discrete stages indicating that e-waste will continue to accumulate and grow in volume with time.

Keywords: Coloured Petri net, computational modelling, electronic waste, electronic waste process dynamics

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