Search results for: Business process model and notation

Authors: Hidetoshi Nonaka

Abstract:

This paper presents an interactive modeling system of polyhedra using the isomorphic graphs. Especially, Conway polyhedron notation is implemented. The notation can be observed as interactive animation.

Keywords: Conway polyhedron notation, Polyhedral graph, Visualization.

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Authors: Rozilawati Razali, Paul W. Garratt

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Software maintenance, which involves making enhancements, modifications and corrections to existing software systems, consumes more than half of developer time. Specification comprehensibility plays an important role in software maintenance as it permits the understanding of the system properties more easily and quickly. The use of formal notation such as B increases a specification-s precision and consistency. However, the notation is regarded as being difficult to comprehend. Semi-formal notation such as the Unified Modelling Language (UML) is perceived as more accessible but it lacks formality. Perhaps by combining both notations could produce a specification that is not only accurate and consistent but also accessible to users. This paper presents an experiment conducted on a model that integrates the use of both UML and B notations, namely UML-B, versus a B model alone. The objective of the experiment was to evaluate the comprehensibility of a UML-B model compared to a traditional B model. The measurement used in the experiment focused on the efficiency in performing the comprehension tasks. The experiment employed a cross-over design and was conducted on forty-one subjects, including undergraduate and masters students. The results show that the notation used in the UML-B model is more comprehensible than the B model.

Keywords: Model comprehensibility, formal and semi-formal notation, empirical assessment.

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Authors: Dalyah Y. Al-Jamal, Maryam H. Eshtaiwi, Liyakathunisa Syed

Abstract:

Connecting health services with technology has a huge demand as people health situations are becoming worse day by day. In fact, engaging new technologies such as Internet of Things (IOT) into the medical services can enhance the patient care services. Specifically, patients suffering from chronic diseases such as cardiac patients need a special care and monitoring. In reality, some efforts were previously taken to automate and improve the patient monitoring systems. However, the previous efforts have some limitations and lack the real-time feature needed for chronic kind of diseases. In this paper, an improved process model for patient monitoring system specialized for cardiac patients is presented. A survey was distributed and interviews were conducted to gather the needed requirements to improve the cardiac patient monitoring system. Business Process Model and Notation (BPMN) language was used to model the proposed process. In fact, the proposed system uses the IOT Technology to assist doctors to remotely monitor and follow-up with their heart patients in real-time. In order to validate the effectiveness of the proposed solution, simulation analysis was performed using Bizagi Modeler tool. Analysis results show performance improvements in the heart monitoring process. For the future, authors suggest enhancing the proposed system to cover all the chronic diseases.

Keywords: Business process model and notation, cardiac patient, cardiac monitoring, heart monitoring, healthcare, internet of things, remote patient monitoring system, process model, telemedicine, wearable sensors.

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Authors: Kashif Kamran, Farooque Azam

Abstract:

The policies governing the business of any organization are well reflected in her business rules. The business rules are implemented by data validation techniques, coded during the software development process. Any change in business policies results in change in the code written for data validation used to enforce the business policies. Implementing the change in business rules without changing the code is the objective of this paper. The proposed approach enables users to create rule sets at run time once the software has been developed. The newly defined rule sets by end users are associated with the data variables for which the validation is required. The proposed approach facilitates the users to define business rules using all the comparison operators and Boolean operators. Multithreading is used to validate the data entered by end user against the business rules applied. The evaluation of the data is performed by a newly created thread using an enhanced form of the RPN (Reverse Polish Notation) algorithm.

Keywords: Business Rules, data validation, multithreading, Reverse Polish Notation

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Authors: Gionata Carmignani, Mario G. C. A. Cimino, Franco Failli

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Business Processes (BPs) are the key instrument to understand how companies operate at an organizational level, taking an as-is view of the workflow, and how to address their issues by identifying a to-be model. In last year’s, the BP Model and Notation (BPMN) has become a de-facto standard for modeling processes. However, this standard does not incorporate explicitly the Problem- Solving (PS) knowledge in the Process Modeling (PM) results. Thus, such knowledge cannot be shared or reused. To narrow this gap is today a challenging research area. In this paper we present a framework able to capture the PS knowledge and to improve a workflow. This framework extends the BPMN specification by incorporating new general-purpose elements. A pilot scenario is also presented and discussed.

Keywords: Business Process Management, BPMN, Problem Solving, Process mapping.

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Authors: Wararat Rungworawut, Twittie Senivongse

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Business process model describes process flow of a business and can be seen as the requirement for developing a software application. This paper discusses a BPM2CD guideline which complements the Model Driven Architecture concept by suggesting how to create a platform-independent software model in the form of a UML class diagram from a business process model. An important step is the identification of UML classes from the business process model. A technique for object-oriented analysis called domain analysis is borrowed and key concepts in the business process model will be discovered and proposed as candidate classes for the class diagram. The paper enhances this step by using ontology search to help identify important classes for the business domain. As ontology is a source of knowledge for a particular domain which itself can link to ontologies of related domains, the search can give a refined set of candidate classes for the resulting class diagram.

Keywords: Business Process Model, Model DrivenArchitecture, Ontology, UML Class Diagram.

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Authors: Somayeh Sobati Moghadam

Abstract:

Business processes are crucial for organizations and help businesses to evaluate and optimize their performance and processes against current and future-state business goals. Outsourcing business processes to the cloud becomes popular due to a wide varsity of benefits and cost-saving. However, cloud outsourcing raises enterprise data security concerns, which must be incorporated in Business Process Model and Notation (BPMN). This paper, presents SeCloudBPMN, a lightweight extension for BPMN which extends the BPMN to explicitly support the security threats in the cloud as an outsourcing environment. SeCloudBPMN helps business’s security experts to outsource business processes to the cloud considering different threats from inside and outside the cloud. In this way, appropriate security countermeasures could be considered to preserve data security in business processes outsourcing to the cloud.

Keywords: BPMN, security threats, cloud computing, graphical representation.

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Authors: Bernhard G. Humm, Janina Fengel

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Business process modeling has become an accepted means for designing and describing business operations. Thereby, consistency of business process models, i.e., the absence of modeling faults, is of upmost importance to organizations. This paper presents a concept and subsequent implementation for detecting faults in business process models and for computing a measure of their consistency. It incorporates not only syntactic consistency but also semantic consistency, i.e., consistency regarding the meaning of model elements from a business perspective.

Keywords: Business process modeling, model analysis, semantic consistency, Semantic Web

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Authors: Ahmad F. Subahi, Anthony J. H. Simons

Abstract:

This Paper presents an on-going research in the area of Model-Driven Engineering (MDE). The premise is that UML is too unwieldy to serve as the basis for model-driven engineering. We need a smaller, simpler notation with a cleaner semantics. We propose some ideas for a simpler notation with a clean semantics. The result is known as μML, or the Micro-Modelling Language.

Keywords: Model-driven engineering, model transformations, domain-specific languages, end-user development.

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Authors: Adla Bentellis, Zizette Boufaïda

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Nowadays, the pace of business change is such that, increasingly, new functionality has to be realized and reliably installed in a matter of days, or even hours. Consequently, more and more business processes are prone to a continuous change. The objective of the research in progress is to use the MAP model, in a conceptual modeling method for flexible and adaptive business process. This method can be used to capture the flexibility dimensions of a business process; it takes inspiration from modularity concept in the object oriented paradigm to establish a hierarchical construction of the BP modeling. Its intent is to provide a flexible modeling that allows companies to quickly adapt their business processes.

Keywords: Business Process, Business process modeling, flexibility, MAP Model.

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Authors: Ljubica Milanović Glavan

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Because of the increasing business pressures, companies must be adaptable and flexible in order to withstand them. Inadequate business processes and low level of business process orientation, that in its core accentuates business processes as opposed to business functions and focuses on process performance and customer satisfaction, hider the ability to adapt to changing environment. It has been shown in previous studies that the companies which have reached higher business process maturity level consistently outperform those that have not reached them. The aim of this paper is to provide a basic understanding of business process orientation concept and business process maturity model. Besides that the paper presents the state of business process orientation in Croatia that has been captured with a study conducted in 2013. Based on the results some practical implications and guidelines for managers are given.

Keywords: Business process orientation, business process maturity, Croatia, maturity score.

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Authors: K. Shoylekova, K. Grigorova

Abstract:

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: Hadia Abdel Aziz, Raghda El Ebrashi

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Business models are shaped by their design space or the environment they are designed to be implemented in. The rapidly changing economic, technological, political, regulatory and market external environment severely affects business logic. This is particularly true for social enterprises whose core mission is to transform their environments, and thus, their whole business logic revolves around the interchange between the enterprise and the environment. The context in which social business operates imposes different business design constraints while at the same time, open up new design opportunities. It is also affected to a great extent by the impact that successful enterprises generate; a continuous loop of interaction that needs to be managed through a dynamic capability in order to generate a lasting powerful impact. This conceptual research synthesizes and analyzes literature on social enterprise, social enterprise business models, business model innovation, business model design, and the open system view theory to propose a new business model design process for social enterprises that takes into account the critical role of environmental factors. This process would help the social enterprise develop a dynamic capability that ensures the alignment of its business model to its environmental context, thus, maximizing its probability of success.

Keywords: Social enterprise, business model, business model design.

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Authors: Orkide Donma, Mustafa M. Donma

Abstract:

Basal metabolic rate is questioned as a risk factor for weight gain. The relations between basal metabolic rate and body composition have not been cleared yet. The impact of fat mass on basal metabolic rate is also uncertain. Within this context, indices based upon total body mass as well as total body fat mass are available. In this study, the aim is to investigate the potential clinical utility of these indices in the adult population. 287 individuals, aged from 18 to 79 years, were included into the scope of the study. Based upon body mass index values, 10 underweight, 88 normal, 88 overweight, 81 obese, and 20 morbid obese individuals participated. Anthropometric measurements including height (m), and weight (kg) were performed. Body mass index, diagnostic obesity notation model assessment index I, diagnostic obesity notation model assessment index II, basal metabolic rate-to-weight ratio were calculated. Total body fat mass (kg), fat percent (%), basal metabolic rate, metabolic age, visceral adiposity, fat mass of upper as well as lower extremities and trunk, obesity degree were measured by TANITA body composition monitor using bioelectrical impedance analysis technology. Statistical evaluations were performed by statistical package (SPSS) for Windows Version 16.0. Scatterplots of individual measurements for the parameters concerning correlations were drawn. Linear regression lines were displayed. The statistical significance degree was accepted as p < 0.05. The strong correlations between body mass index and diagnostic obesity notation model assessment index I as well as diagnostic obesity notation model assessment index II were obtained (p < 0.001). A much stronger correlation was detected between basal metabolic rate and diagnostic obesity notation model assessment index I in comparison with that calculated for basal metabolic rate and body mass index (p < 0.001). Upon consideration of the associations between basal metabolic rate-to-weight ratio and these three indices, the best association was observed between basal metabolic rate-to-weight and diagnostic obesity notation model assessment index II. In a similar manner, this index was highly correlated with fat percent (p < 0.001). Being independent of the indices, a strong correlation was found between fat percent and basal metabolic rate-to-weight ratio (p < 0.001). Visceral adiposity was much strongly correlated with metabolic age when compared to that with chronological age (p < 0.001). In conclusion, all three indices were associated with metabolic age, but not with chronological age. Diagnostic obesity notation model assessment index II values were highly correlated with body mass index values throughout all ranges starting with underweight going towards morbid obesity. This index is the best in terms of its association with basal metabolic rate-to-weight ratio, which can be interpreted as basal metabolic rate unit.

Keywords: Basal metabolic rate, body mass index, children, diagnostic obesity notation model assessment index, obesity.

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Authors: Eakong Atiptamvaree, Twittie Senivongse

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A new paradigm for software design and development models software by its business process, translates the model into a process execution language, and has it run by a supporting execution engine. This process-oriented paradigm promotes modeling of software by less technical users or business analysts as well as rapid development. Since business process models may be shared by different organizations and sometimes even by different business domains, it is interesting to apply a technique used in traditional software component technology to design reusable business processes. This paper discusses an approach to apply a technique for software component fabrication to the design of process-oriented software units, called process components. These process components result from decomposing a business process of a particular application domain into subprocesses with an aim that the process components can be reusable in different process-based software models. The approach is quantitative because the quality of process component design is measured from technical features of the process components. The approach is also strategic because the measured quality is determined against business-oriented component management goals. A software tool has been developed to measure how good a process component design is, according to the required managerial goals and comparing to other designs. We also discuss how we benefit from reusable process components.

Keywords: Business process model, process component, component management goals, measurement

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Authors: Mohammad Ehson Rangiha, Bill Karakostas

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Social Business Process Management (SBPM) promises to overcome limitations of traditional BPM by allowing flexible process design and enactment through the involvement of users from a social community. This paper proposes a meta-model and architecture for socially driven business process management systems. It discusses the main facets of the architecture such as goalbased role assignment that combines social recommendations with user profile, and process recommendation, through a real example of a charity organization.

Keywords: Business Process Management, Goal-Based Modelling, Process Recommendation Social Collaboration, Social BPM.

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Authors: Andreas Jede, Frank Teuteberg

Abstract:

Cloud computing (CC) has already gained overall appreciation in research and practice. Whereas the willingness to integrate cloud services in various IT environments is still unbroken, the previous CC procurement processes run mostly in an unorganized and non-standardized way. In practice, a sufficiently specific, yet applicable business process for the important acquisition phase is often lacking. And research does not appropriately remedy this deficiency yet. Therefore, this paper introduces a field-tested approach for CC procurement. Based on an extensive literature review and augmented by expert interviews, we designed a model that is validated and further refined through an in-depth real-life case study. For the detailed process description, we apply the event-driven process chain notation (EPC). The gained valuable insights into the case study may help CC research to shift to a more socio-technical area. For practice, next to giving useful organizational instructions we will provide extended checklists and lessons learned.

Keywords: Cloud Procurement Process, IT-Organization, Event-driven Process Chain, In-depth Case Study.

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Authors: Faisal A. Aburub

Abstract:

Organizations today need to invest in software in order to run their businesses, and to the organizations’ objectives, the software should be in line with the business process. This research presents an approach for linking process models and system models. Particularly, the new approach aims to synthesize sequence diagram based on role activity diagram (RAD) model. The approach includes four steps namely: Create business process model using RAD, identify computerized activities, identify entities in sequence diagram and identify messages in sequence diagram. The new approach has been validated using the process of student registration in University of Petra as a case study. Further research is required to validate the new approach using different domains.

Keywords: Business process modelling, system models, role activity diagrams, sequence diagrams.

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Authors: Eakong Atiptamvaree, Twittie Senivongse

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Process-oriented software development is a new software development paradigm in which software design is modeled by a business process which is in turn translated into a process execution language for execution. The building blocks of this paradigm are software units that are composed together to work according to the flow of the business process. This new paradigm still exhibits the characteristic of the applications built with the traditional software component technology. This paper discusses an approach to apply a traditional technique for software component fabrication to the design of process-oriented software units, called process components. These process components result from decomposing a business process of a particular application domain into subprocesses, and these process components can be reused to design the business processes of other application domains. The decomposition considers five managerial goals, namely cost effectiveness, ease of assembly, customization, reusability, and maintainability. The paper presents how to design or decompose process components from a business process model and measure some technical features of the design that would affect the managerial goals. A comparison between the measurement values from different designs can tell which process component design is more appropriate for the managerial goals that have been set. The proposed approach can be applied in Web Services environment which accommodates process-oriented software development.

Keywords: Business Process Model, Managerial Goals, ProcessComponent.

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Authors: Reza Davoodi, Jahangir Yadollahi Farsi, Roya Naseri

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In the way of growing and developing firms especially high-tech firms, on many occasions manager of firm is mainly involved in solving problems of his business and decision making about executive activities of the firm, while besides executive measures, attention to planning of firm's success and growth way and application of long experience and sagacity in designing business model are vital and necessary success in a business is achieved as a result of different factors, one of the most important of them is designing and performing an optimal business model at the beginning of the firm's work. This model is determining the limit of profitability achieved by innovation and gained value added. Therefore, business model is the process of connecting innovation environment and technology with economic environment and business and is important for succeeding modern businesses considering their traits.

Keywords: Business Model (BM), Nanotechnology, High- TechFirms.

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Authors: Felix Baumann, Aleksandar Milutinovic, Dieter Roller

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Up to this point business process management projects in general and business process modelling projects in particular could not rely on a practical and scientifically validated method to estimate cost and effort. Especially the model development phase is not covered by a cost estimation method or model. Further phases of business process modelling starting with implementation are covered by initial solutions which are discussed in the literature. This article proposes a method of filling this gap by deriving a cost estimation method from available methods in similar domains namely software development or software engineering. Software development is regarded as closely similar to process modelling as we show. After the proposition of this method different ideas for further analysis and validation of the method are proposed. We derive this method from COCOMO II and Function Point which are established methods of effort estimation in the domain of software development. For this we lay out similarities of the software development process and the process of process modelling which is a phase of the Business Process Management life-cycle.

Keywords: Cost Estimation, Effort Estimation, Process Modelling, Business Process Management, COCOMO.

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Authors: María Fernández-Ropero, Ricardo Pérez-Castillo, Ismael Caballero, Mario Piattini

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Appropriate description of business processes through standard notations has become one of the most important assets for organizations. Organizations must therefore deal with quality faults in business process models such as the lack of understandability and modifiability. These quality faults may be exacerbated if business process models are mined by reverse engineering, e.g., from existing information systems that support those business processes. Hence, business process refactoring is often used, which change the internal structure of business processes whilst its external behavior is preserved. This paper aims to choose the most appropriate set of refactoring operators through the quality assessment concerning understandability and modifiability. These quality features are assessed through well-proven measures proposed in the literature. Additionally, a set of measure thresholds are heuristically established for applying the most promising refactoring operators, i.e., those that achieve the highest quality improvement according to the selected measures in each case.

Keywords: business process model, modifiability, refactoring, understandability

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Authors: Ora Geiger

Abstract:

This paper discusses the question whether a person diagnosed with dyslexia will necessarily have difficulty in reading musical notes. The author specifies the characteristics of alphabet reading in comparison to musical notation reading, and concludes that there should be no contra-indication for teaching standard music reading to children with dyslexia if an appropriate process is offered. This conclusion is based on a long term case study and relies on two main characteristics of music reading: (1) musical notation system is a systematic, logical, relative set of symbols written on a staff; and (2) music reading learning connected with playing a musical instrument is a multi-sensory activity that combines sight, hearing, touch, and movement. The paper describes music reading teaching procedures, using soprano recorders, and provides unique teaching methods that have been found to be effective for students who were diagnosed with dyslexia. It provides theoretical explanations in addition to guidelines for music education practices.

Keywords: Alphabet reading, music reading, multisensory teaching method, dyslexia, recorder playing.

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Authors: Eckhard M. Ammann

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Knowledge development in companies relies on knowledge-intensive business processes, which are characterized by a high complexity in their execution, weak structuring, communication-oriented tasks and high decision autonomy, and often the need for creativity and innovation. A foundation of knowledge development is provided, which is based on a new conception of knowledge and knowledge dynamics. This conception consists of a three-dimensional model of knowledge with types, kinds and qualities. Built on this knowledge conception, knowledge dynamics is modeled with the help of general knowledge conversions between knowledge assets. Here knowledge dynamics is understood to cover all of acquisition, conversion, transfer, development and usage of knowledge. Through this conception we gain a sound basis for knowledge management and development in an enterprise. Especially the type dimension of knowledge, which categorizes it according to its internality and externality with respect to the human being, is crucial for enterprise knowledge management and development, because knowledge should be made available by converting it to more external types. Built on this conception, a modeling approach for knowledgeintensive business processes is introduced, be it human-driven,e-driven or task-driven processes. As an example for this approach, a model of the creative activity for the renewal planning of a product is given.

Keywords: Conception of knowledge, knowledge dynamics, modeling notation, knowledge-intensive business processes.

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Authors: Marcel Rojahn, Edzard Weber, Norbert Gronau

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Terminology is a critical instrument for each researcher. Different terminologies for the same research object may arise in different research communities. By this inconsistency, many synergistic effects get lost. Theories and models will be more understandable and reusable if a common terminology is applied. This paper examines the terminological (in)consistence for the research field of job-shop scheduling by a literature review. There is an enormous variety in the choice of terms and mathematical notation for the same concept. The comparability, reusability and combinability of scheduling methods is unnecessarily hampered by the arbitrary use of homonyms and synonyms. The acceptance in the community of used variables and notation forms is shown by means of a compliance quotient. This is proven by the evaluation of 240 scientific publications on planning methods.

Keywords: Job-shop scheduling, JSP, terminology, notation, standardization.

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Authors: Soe Winn, May Thwe Oo

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Business process automation is an important task in an enterprise business environment software development. The requirements of processing acceleration and automation level of enterprises are inherently different from one organization to another. We present a methodology and system for automation of business process management system architecture by multi-agent collaboration based on SOA. Design layer processes are modeled in semantic markup language for web services application. At the core of our system is considering certain types of human tasks to their further automation across over multiple platform environments. An improved abnormality processing with model for automation of BPMS architecture by multi-agent collaboration based on SOA is introduced. Validating system for efficiency of process automation, an application for educational knowledge base instance would also be described.

Keywords: Business process management system, businessprocess automation, multi-agent collaboration, Service OrientedArchitecture, extensible service application

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Authors: M. Klimavicius

Abstract:

This paper proposes a modeling methodology for the development of data analysis solution. The Author introduce the approach to address data warehousing issues at the at enterprise level. The methodology covers the process of the requirements eliciting and analysis stage as well as initial design of data warehouse. The paper reviews extended business process model, which satisfy the needs of data warehouse development. The Author considers that the use of business process models is necessary, as it reflects both enterprise information systems and business functions, which are important for data analysis. The Described approach divides development into three steps with different detailed elaboration of models. The Described approach gives possibility to gather requirements and display them to business users in easy manner.

Keywords: Data warehouse, data analysis, business processmanagement.

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Authors: Kannanut Chamsri

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Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.

Keywords: Darcy’s Law, Homogenization method, Indicial notation

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Authors: Mamoun Sqali, Mohamed Wassim Trojet

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The requirements analysis, modeling, and simulation have consistently been one of the main challenges during the development of complex systems. The scenarios and the state machines are two successful models to describe the behavior of an interactive system. The scenarios represent examples of system execution in the form of sequences of messages exchanged between objects and are a partial view of the system. In contrast, state machines can represent the overall system behavior. The automation of processing scenarios in the state machines provide some answers to various problems such as system behavior validation and scenarios consistency checking. In this paper, we propose a method for translating scenarios in state machines represented by Discreet EVent Specification and procedure to detect implied scenarios. Each induced DEVS model represents the behavior of an object of the system. The global system behavior is described by coupling the atomic DEVS models and validated through simulation. We improve the validation process with integrating formal methods to eliminate logical inconsistencies in the global model. For that end, we use the Z notation.

Keywords: Scenarios, DEVS, synthesis, validation and verification, simulation, formal verification, z notation.

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Authors: Mario Mastriani, Marcelo Naiouf

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This paper introduces a Quantum Correlation Matrix Memory (QCMM) and Enhanced QCMM (EQCMM), which are useful to work with quantum memories. A version of classical Gram-Schmidt orthogonalisation process in Dirac notation (called Quantum Orthogonalisation Process: QOP) is presented to convert a non-orthonormal quantum basis, i.e., a set of non-orthonormal quantum vectors (called qudits) to an orthonormal quantum basis, i.e., a set of orthonormal quantum qudits. This work shows that it is possible to improve the performance of QCMM thanks QOP algorithm. Besides, the EQCMM algorithm has a lot of additional fields of applications, e.g.: Steganography, as a replacement Hopfield Networks, Bilevel image processing, etc. Finally, it is important to mention that the EQCMM is an extremely easy to implement in any firmware.

Keywords: Quantum Algebra, correlation matrix memory, Dirac notation, orthogonalisation.

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