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Anne Remke
Welcome to the cutting-edge course on Quantitative Model Checking for Markov Chains! As technology permeates every aspect of modern life—Embedded Systems, Cyber-Physical Systems, Communication Protocols, and Transportation Systems—the need for dependable software is at an all-time high. One tiny flaw can lead to catastrophic failures and enormous costs. That's where you come in.
Read more
Welcome to the cutting-edge course on Quantitative Model Checking for Markov Chains! As technology permeates every aspect of modern life—Embedded Systems, Cyber-Physical Systems, Communication Protocols, and Transportation Systems—the need for dependable software is at an all-time high. One tiny flaw can lead to catastrophic failures and enormous costs. That's where you come in.
Read more
Welcome to the cutting-edge course on Quantitative Model Checking for Markov Chains! As technology permeates every aspect of modern life—Embedded Systems, Cyber-Physical Systems, Communication Protocols, and Transportation Systems—the need for dependable software is at an all-time high. One tiny flaw can lead to catastrophic failures and enormous costs. That's where you come in.
The course kicks off with creating a State Transition System, the basic model that captures the intricate dynamics of real-world systems. Soon you'll step into the world of Discrete-time and Continuous-time Markov Chains—powerful mathematical formalisms that are versatile enough to model complex systems yet elegant in their design. These aren't just theories; they are tools actively used across various domains for performance and dependability evaluation.
But we won't stop at modelling. The heart of this course is 'Model Checking,' a formal verification method that scrutinizes the functionality of your system model. Learn how to express dependability properties, track the evolution of Markov chains over time, and verify whether states meet particular conditions—all using advanced computational algorithms.
By the end of this course, you'll be equipped with the skills to:
- Specify dependability properties for a range of transition systems.
- Understand the temporal evolution of Markov chains.
- Analyze and compute the satisfaction set for multiple properties.
Are you ready to become an expert in ensuring the reliability of tomorrow's technologies? Click here to Enroll today and join us in mastering the art and science of model checking.
Register for this course and see more details by visiting:
OpenCourser.com/course/iystbr/quantitative
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What's inside
Syllabus
Module 1: Computational Tree Logic
We introduce Labeled Transition Systems (LTS), the syntax and semantics of Computational Tree Logic (CTL) and discuss the model checking algorithms that are necessary to compute the satisfaction set for specific CTL formulas.
Read more
Syllabus
Module 1: Computational Tree Logic
We introduce Labeled Transition Systems (LTS), the syntax and semantics of Computational Tree Logic (CTL) and discuss the model checking algorithms that are necessary to compute the satisfaction set for specific CTL formulas.
Read more
Discrete Time Markov Chains
We enhance transition systems by discrete time and add probabilities to transitions to model probabilistic choices. We discuss important properties of DTMCs, such as the memoryless property and time-homogeneity. State classification can be used to determine the existence of the limiting and / or stationary distribution.
Probabilistic Computational Tree Logic
We discuss the syntax and semantics of Probabilistic Computational Tree logic and check out the model checking algorithms that are necessary to decide the validity of different kinds of PCTL formulas. We shortly discuss the complexity of PCTL model checking.
Continuous Time Markov Chains
We enhance Discrete-Time Markov Chains with real time and discuss how the resulting modelling formalism evolves over time. We compute the steady-state for different kinds of CMTCs and discuss how the transient probabilities can be efficiently computed using a method called uniformisation.
Continuous Stochastic Logic
We introduce the syntax and semantics of Continuous Stochastic Logic and describe how the different kinds of CSL formulas can be model checked. Especially, model checking the time bounded until operator requires applying the concept of uniformisation, which we have discussed in the previous module.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Develops skills and knowledge in model checking, which is a sought-after skill in industry and academia
Taught by Anne Remke, who is a recognized expert in model checking
Examines quantitative model checking, which is highly relevant to developing dependable software and systems
Strong fit for students with a background in computer science, engineering, or mathematics
Covers the latest algorithms and techniques used in model checking
Teaches skills that are transferable to other fields, such as operations research and optimization
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Reviews summary
Advanced students: model checking
Learners say Quantitative Model Checking is difficult but interesting, especially in weeks 4 and 5.
Course material is engaging.
"interesting"
Course has challenging weeks.
"difficult in week4&week5"
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Quantitative Model Checking with these
activities:
Organize and Review Course Materials
Show steps
Enhance learning by organizing and reviewing course materials, fostering a clear understanding of the key concepts.
Show steps
-
Gather all course notes, assignments, quizzes, and exams.
-
Create a system for organizing the materials, such as folders or a digital notebook.
-
Review the materials regularly to reinforce learning.
Read Introduction to Probability Models
Show steps
Deepen understanding of probability models, Markov Chains, and related concepts laid out in this course.
View
Introduction to Probability Models
on Amazon
Show steps
-
Read Chapter 1-3 of the book.
-
Summarize main concepts and theorems.
-
Solve 5 practice problems from each chapter.
Review the basics of probability theory
Show steps
Refreshing your knowledge of probability theory will strengthen the foundation for Markov chain concepts.
Browse courses on
Probability Theory
Show steps
-
Review the concepts of probability, randomness, and sample spaces.
-
Brush up on conditional probability, Bayes' theorem, and probability distributions.
-
Go through practice problems to solidify your understanding.
Nine other activities
Expand to see all activities and additional details
Show all 12 activities
Join a Study Group
Show steps
Foster collaborative learning by joining a study group, engaging in discussions, and exchanging diverse perspectives.
Show steps
-
Find a group of peers who are also taking the course.
-
Schedule regular meetings to discuss course materials, assignments, and projects.
-
Actively participate in group discussions and contribute ideas.
Form study groups to discuss CTL and its applications
Show steps
Engaging in peer discussions deepens your understanding of CTL and its real-world applications.
Show steps
-
Identify classmates who share your interests in CTL.
-
Schedule regular meetings to discuss different aspects of CTL.
-
Prepare presentations or summaries on specific topics related to CTL.
-
Collaborate on solving problems and sharing insights.
Explore online tutorials on Markov chain applications
Show steps
Delving into specific applications of Markov chains will enhance your appreciation for their practical relevance.
Show steps
-
Identify reputable online platforms offering tutorials on Markov chain applications.
-
Choose tutorials that align with your interests or areas of curiosity.
-
Follow the tutorials, take notes, and complete any exercises provided.
-
Share your learnings and insights with classmates or online forums.
Practice Markov Chain Analysis
Show steps
Solidify understanding of Markov Chain Analysis, the core technique used in this course
Browse courses on
Markov Chains
Show steps
-
Solve 10 Markov Chain analysis problems from online resources.
-
Create a Markov Chain model for a real-world scenario.
-
Analyze the model to calculate probabilities and steady-state distribution.
Explore NumPy Library for Markov Chain Analysis
Show steps
Enhance practical skills by utilizing the NumPy library for Markov Chain analysis, bridging theory with implementation.
Browse courses on
NumPy
Show steps
-
Install the NumPy library.
-
Find tutorials on Markov Chain analysis using NumPy.
-
Follow the tutorials to apply NumPy functions for Markov Chain operations.
-
Implement a Markov Chain model using NumPy.
Organize and review course notes and materials
Show steps
Organizing and reviewing course materials reinforces learning and aids in retention.
Show steps
-
Consolidate lecture notes, presentations, and handouts into a central location.
-
Highlight key concepts, formulas, and examples.
-
Summarize the main points of each lecture or module.
-
Review the organized materials regularly to strengthen your understanding.
Develop a model checking tool for PCTL
Show steps
Building a model checking tool allows you to apply your knowledge of PCTL and gain practical experience in developing verification tools.
Show steps
-
Design the architecture and algorithms for the tool.
-
Implement the tool using an appropriate programming language.
-
Test the tool on various PCTL formulas and models.
-
Enhance the tool's features and improve its efficiency.
Visualize Markov Chain Models
Show steps
Improve understanding of Markov Chain models by creating visual representations to better comprehend their behavior.
Browse courses on
Data Visualization
Show steps
-
Choose a Markov Chain model to visualize.
-
Identify key states and transitions.
-
Create a visual representation using tools like Graphviz or Python's NetworkX.
-
Analyze the visualization to gain insights into the model's dynamics.
Develop a Markov Chain Model for a Real-World Problem
Show steps
Deepen understanding by applying Markov Chains to a real-world problem, fostering critical thinking and problem-solving skills.
Browse courses on
Markov Chains
Show steps
-
Identify a real-world problem that can be modeled using a Markov Chain.
-
Define the states and transitions of the Markov Chain.
-
Estimate the transition probabilities.
-
Analyze the Markov Chain to answer questions about the real-world problem.
Organize and Review Course Materials
Show steps
Enhance learning by organizing and reviewing course materials, fostering a clear understanding of the key concepts.
Show steps
Show steps
Show steps
- Gather all course notes, assignments, quizzes, and exams.
- Create a system for organizing the materials, such as folders or a digital notebook.
- Review the materials regularly to reinforce learning.
Read Introduction to Probability Models
Show steps
Deepen understanding of probability models, Markov Chains, and related concepts laid out in this course.
View
Introduction to Probability Models
on Amazon
Show steps
Show steps
Show steps
- Read Chapter 1-3 of the book.
- Summarize main concepts and theorems.
- Solve 5 practice problems from each chapter.
Review the basics of probability theory
Show steps
Refreshing your knowledge of probability theory will strengthen the foundation for Markov chain concepts.
Browse courses on
Probability Theory
Show steps
Show steps
Show steps
- Review the concepts of probability, randomness, and sample spaces.
- Brush up on conditional probability, Bayes' theorem, and probability distributions.
- Go through practice problems to solidify your understanding.
Nine other activities
Expand to see all activities and additional details
Show all 12 activities
Join a Study Group
Show steps
Foster collaborative learning by joining a study group, engaging in discussions, and exchanging diverse perspectives.
Show steps
Show steps
Show steps
- Find a group of peers who are also taking the course.
- Schedule regular meetings to discuss course materials, assignments, and projects.
- Actively participate in group discussions and contribute ideas.
Form study groups to discuss CTL and its applications
Show steps
Engaging in peer discussions deepens your understanding of CTL and its real-world applications.
Show steps
Show steps
Show steps
- Identify classmates who share your interests in CTL.
- Schedule regular meetings to discuss different aspects of CTL.
- Prepare presentations or summaries on specific topics related to CTL.
- Collaborate on solving problems and sharing insights.
Explore online tutorials on Markov chain applications
Show steps
Delving into specific applications of Markov chains will enhance your appreciation for their practical relevance.
Show steps
Show steps
Show steps
- Identify reputable online platforms offering tutorials on Markov chain applications.
- Choose tutorials that align with your interests or areas of curiosity.
- Follow the tutorials, take notes, and complete any exercises provided.
- Share your learnings and insights with classmates or online forums.
Practice Markov Chain Analysis
Show steps
Solidify understanding of Markov Chain Analysis, the core technique used in this course
Browse courses on
Markov Chains
Show steps
Show steps
Show steps
- Solve 10 Markov Chain analysis problems from online resources.
- Create a Markov Chain model for a real-world scenario.
- Analyze the model to calculate probabilities and steady-state distribution.
Explore NumPy Library for Markov Chain Analysis
Show steps
Enhance practical skills by utilizing the NumPy library for Markov Chain analysis, bridging theory with implementation.
Browse courses on
NumPy
Show steps
Show steps
Show steps
- Install the NumPy library.
- Find tutorials on Markov Chain analysis using NumPy.
- Follow the tutorials to apply NumPy functions for Markov Chain operations.
- Implement a Markov Chain model using NumPy.
Organize and review course notes and materials
Show steps
Organizing and reviewing course materials reinforces learning and aids in retention.
Show steps
Show steps
Show steps
- Consolidate lecture notes, presentations, and handouts into a central location.
- Highlight key concepts, formulas, and examples.
- Summarize the main points of each lecture or module.
- Review the organized materials regularly to strengthen your understanding.
Develop a model checking tool for PCTL
Show steps
Building a model checking tool allows you to apply your knowledge of PCTL and gain practical experience in developing verification tools.
Show steps
Show steps
Show steps
- Design the architecture and algorithms for the tool.
- Implement the tool using an appropriate programming language.
- Test the tool on various PCTL formulas and models.
- Enhance the tool's features and improve its efficiency.
Visualize Markov Chain Models
Show steps
Improve understanding of Markov Chain models by creating visual representations to better comprehend their behavior.
Browse courses on
Data Visualization
Show steps
Show steps
Show steps
- Choose a Markov Chain model to visualize.
- Identify key states and transitions.
- Create a visual representation using tools like Graphviz or Python's NetworkX.
- Analyze the visualization to gain insights into the model's dynamics.
Develop a Markov Chain Model for a Real-World Problem
Show steps
Deepen understanding by applying Markov Chains to a real-world problem, fostering critical thinking and problem-solving skills.
Browse courses on
Markov Chains
Show steps
Show steps
Show steps
- Identify a real-world problem that can be modeled using a Markov Chain.
- Define the states and transitions of the Markov Chain.
- Estimate the transition probabilities.
- Analyze the Markov Chain to answer questions about the real-world problem.
Career center
Learners who complete Quantitative Model Checking will develop knowledge and skills
that may be useful to these careers:
Software Engineer
Software Engineer
Software Engineers are responsible for designing, developing, and maintaining software systems. They use their knowledge of programming languages, software development tools, and software engineering principles to create software that meets the needs of users. The Quantitative Model Checking course can be a valuable asset for Software Engineers, as it teaches them how to verify the reliability and correctness of software systems. This knowledge can help Software Engineers to develop software that is more reliable and less likely to fail.
Systems Analyst
Systems Analyst
Systems Analysts are responsible for analyzing and designing business systems. They use their knowledge of business processes, systems analysis techniques, and software development tools to create systems that meet the needs of businesses. The Quantitative Model Checking course can be a valuable asset for Systems Analysts, as it teaches them how to verify the reliability and correctness of business systems. This knowledge can help Systems Analysts to design systems that are more reliable and less likely to fail.
Quality Assurance Analyst
Quality Assurance Analyst
Quality Assurance Analysts are responsible for testing and evaluating software systems. They use their knowledge of software testing techniques and quality assurance principles to identify and fix defects in software. The Quantitative Model Checking course can be a valuable asset for Quality Assurance Analysts, as it teaches them how to verify the reliability and correctness of software systems. This knowledge can help Quality Assurance Analysts to identify and fix defects more efficiently.
Financial Analyst
Financial Analyst
Financial Analysts are responsible for analyzing and interpreting financial data. They use their knowledge of financial analysis techniques and tools to develop recommendations for investment decisions. The Quantitative Model Checking course can be a valuable asset for Financial Analysts, as it teaches them how to verify the reliability and correctness of financial analysis models. This knowledge can help Financial Analysts to develop models that are more reliable and less likely to produce false recommendations.
Risk Analyst
Risk Analyst
Risk Analysts are responsible for identifying and assessing risks. They use their knowledge of risk management techniques and tools to develop strategies to mitigate risks. The Quantitative Model Checking course can be a valuable asset for Risk Analysts, as it teaches them how to verify the reliability and correctness of risk assessment models. This knowledge can help Risk Analysts to develop models that are more reliable and less likely to produce false alarms.
Actuary
Actuary
Actuaries are responsible for assessing and managing financial risks. They use their knowledge of mathematics, statistics, and finance to develop models to predict future events. The Quantitative Model Checking course can be a valuable asset for Actuaries, as it teaches them how to verify the reliability and correctness of financial risk assessment models. This knowledge can help Actuaries to develop models that are more reliable and less likely to produce false alarms.
Data Scientist
Data Scientist
Data Scientists are responsible for collecting, analyzing, and interpreting data. They use their knowledge of data science techniques and tools to extract insights from data. The Quantitative Model Checking course can be a valuable asset for Data Scientists, as it teaches them how to verify the reliability and correctness of data analysis models. This knowledge can help Data Scientists to develop models that are more reliable and less likely to produce false results.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts are responsible for developing and implementing mathematical models to solve operational problems. They use their knowledge of mathematics, statistics, and operations research techniques to develop models that can improve efficiency and productivity. The Quantitative Model Checking course can be a valuable asset for Operations Research Analysts, as it teaches them how to verify the reliability and correctness of operational research models. This knowledge can help Operations Research Analysts to develop models that are more reliable and less likely to produce false conclusions.
Statistician
Statistician
Statisticians are responsible for collecting, analyzing, and interpreting data. They use their knowledge of statistics and statistical methods to develop models to understand and predict the world around us. The Quantitative Model Checking course can be a valuable asset for Statisticians, as it teaches them how to verify the reliability and correctness of statistical models. This knowledge can help Statisticians to develop models that are more reliable and less likely to produce false conclusions.
Computer Scientist
Computer Scientist
Computer Scientists are responsible for developing new computing technologies and solving computational problems. They use their knowledge of computer science fundamentals and computer science theories to create new algorithms, new data structures, and new programming languages. The Quantitative Model Checking course can be a valuable asset for Computer Scientists, as it teaches them how to verify the reliability and correctness of new algorithms and new数据结构. This knowledge can help Computer Scientists to develop new technologies that are more reliable and less likely to fail.
Mathematician
Mathematician
Mathematicians are responsible for developing new mathematical theories and solving mathematical problems. They use their knowledge of mathematics fundamentals and mathematical theories to create new theorems, new proofs, and new mathematical models. The Quantitative Model Checking course can be a valuable asset for Mathematicians, as it teaches them how to verify the reliability and correctness of new mathematical models. This knowledge can help Mathematicians to develop new theories that are more reliable and less likely to be false.
Data Engineer
Data Engineer
Data Engineers are responsible for designing, building, and maintaining data pipelines. They use their knowledge of data engineering tools and techniques to create pipelines that can collect, transform, and store data. The Quantitative Model Checking course can be a valuable asset for Data Engineers, as it teaches them how to verify the reliability and correctness of data pipelines. This knowledge can help Data Engineers to build pipelines that are more reliable and less likely to produce errors.
Software Architect
Software Architect
Software Architects are responsible for designing the architecture of software systems. They use their knowledge of software design principles and software architecture tools to create architectures that meet the needs of users. The Quantitative Model Checking course can be a valuable asset for Software Architects, as it teaches them how to verify the reliability and correctness of software architectures. This knowledge can help Software Architects to design architectures that are more reliable and less likely to fail.
Physicist
Physicist
Physicists are responsible for studying the laws of nature and the behavior of matter and energy. They use their knowledge of physics fundamentals and physics theories to create new models, new theories, and new experiments. The Quantitative Model Checking course can be a valuable asset for Physicists, as it teaches them how to verify the reliability and correctness of new physics models. This knowledge can help Physicists to develop new theories that are more reliable and less likely to be false.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers are responsible for designing, developing, and deploying machine learning models. They use their knowledge of machine learning algorithms, machine learning libraries, and machine learning engineering tools to build models that can solve complex problems. The Quantitative Model Checking course can be a valuable asset for Machine Learning Engineers, as it teaches them how to verify the reliability and correctness of machine learning models. This knowledge can help Machine Learning Engineers to develop models that are more reliable and less likely to produce false predictions.
For more career information including salaries, visit:
OpenCourser.com/course/iystbr/quantitative
Reading list
We've selected 31 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Quantitative Model Checking.
This classic textbook provides a comprehensive introduction to the theory and practice of model checking. It covers a wide range of topics, from the basics of temporal logic to advanced techniques for model checking complex systems.
Provides a comprehensive introduction to model checking and covers both the theoretical foundations and practical applications.
Focuses on probabilistic model checking and covers both the theoretical foundations and practical applications.
This textbook provides a comprehensive introduction to the theory and practice of formal verification of real-time systems. It covers a wide range of topics, from the basics of temporal logic to advanced techniques for model checking real-time systems.
Save
Provides a comprehensive theoretical foundation for Markov chains and includes plenty of worked examples, exercises, and computational algorithms.
Provides a comprehensive overview of the numerical techniques used for solving Markov chains, with a focus on applications in areas such as queueing theory, reliability theory, and financial mathematics.
Provides a comprehensive introduction to Markov decision processes and covers a wide range of topics, including value iteration, policy iteration, and linear programming.
Provides a comprehensive introduction to statistical methods for reliability data and covers a wide range of topics, including data collection, analysis, and modeling.
Provides a comprehensive introduction to reliability engineering and covers a wide range of topics, including reliability assessment, prediction, and improvement.
Provides a comprehensive introduction to reliability theory and covers a wide range of topics, including reliability assessment, prediction, and improvement.
This textbook provides a rigorous introduction to the theory of Markov chains and stochastic processes. It covers a wide range of topics, from the basics of probability theory to advanced topics such as martingales and Brownian motion.
Provides a comprehensive introduction to the theory of probability and stochastic processes. It covers a wide range of topics, from the basics of probability theory to advanced topics such as Markov chains and queuing theory.
Provides a comprehensive introduction to the theory of stochastic models. It covers a wide range of topics, from the basics of probability theory to advanced topics such as Markov chains and queuing theory.
Provides a comprehensive overview of numerical methods for solving Markov chains. It valuable resource for students and researchers in the field of numerical methods.
Provides a comprehensive overview of Markov chains and stochastic processes. It valuable resource for students and researchers in the field of Markov chains and stochastic processes.
Provides a comprehensive overview of stochastic modeling. It valuable resource for students and researchers in the field of stochastic modeling.
Provides a comprehensive overview of applied probability models. It valuable resource for students and researchers in the field of applied probability models.
Provides a comprehensive overview of stochastic processes. It valuable resource for students and researchers in the field of stochastic processes.
Provides a comprehensive overview of discrete-time Markov chains. It valuable resource for students and researchers in the field of discrete-time Markov chains.
Provides a comprehensive overview of continuous-time Markov chains. It valuable resource for students and researchers in the field of continuous-time Markov chains.
Provides a comprehensive overview of performance evaluation of computer and communication systems. It valuable resource for students and researchers in the field of performance evaluation of computer and communication systems.
Provides a comprehensive overview of queueing networks. It valuable resource for students and researchers in the field of queueing networks.
Provides a comprehensive overview of applied stochastic processes. It valuable resource for students and researchers in the field of applied stochastic processes.
Provides an introduction to the theory of continuous-time Markov chains, with a focus on applications in areas such as queueing theory, reliability theory, and financial mathematics.
Provides a comprehensive introduction to performance modeling and analysis and covers a wide range of topics, including Markov chains, queuing theory, and simulation.
Provides a comprehensive introduction to stochastic processes and covers a wide range of topics, including Markov chains, queuing theory, and simulation.
Provides a comprehensive introduction to simulation modeling and analysis and covers a wide range of topics, including simulation languages, model development, and data analysis.
Save
Provides a comprehensive introduction to numerical methods for Markov chains and covers a wide range of topics, including matrix methods, iterative methods, and Monte Carlo methods.
Save
Provides a comprehensive introduction to continuous-time Markov chains and covers a wide range of topics, including birth-death processes, queuing theory, and reliability theory.
Provides an introduction to the theory and practice of probabilistic model checking, a technique for verifying the correctness of probabilistic systems.
Provides an introduction to the use of logic in computer science, with a focus on modeling and reasoning about systems.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/iystbr/quantitative
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Effort
5 weeks of study, each with around 2.h hours work
Level
Intermediate
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Institution
EIT Digital
Instructor
Anne Remke
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English
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Good to know
Develops skills and knowledge in model checking, which is a sought-after skill in industry and academia
Taught by Anne Remke, who is a recognized expert in model checking
Examines quantitative model checking, which is highly relevant to developing dependable software and systems
Strong fit for students with a background in computer science, engineering, or mathematics
Covers the latest algorithms and techniques used in model checking
Teaches skills that are transferable to other fields, such as operations research and optimization
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