berkeley ieor courses

goldberg@ieor.berkeley.edu. Introductory graduate level course, focusing on applications of operations research techniques, e.g., probability, statistics, and optimization, to financial engineering. Learning and Optimization: Read More [+], Prerequisites: Course on optimization (Industrial Engineering 162 or equivalent); course on statistics or stochastic processes (Industrial Engineering 165 or equivalent) Industrial Engin and Oper Research 165, Terms offered: Fall 2022, Fall 2021, Fall 2020 Please use this as a guide for planning purposes. Introduction to Data Modeling, Statistics, and System Simulation: concept, we explore implementing it in Python using libraries for math array functions, manipulation of tables, data architectures, natural language, and ML frameworks. Note: the course is a mixture of modeling art, analytical science, and computational technology. Operations Research and Management Science Honors Thesis: Read Less [-], Terms offered: Prior to 2007 This introductory course provides students with sufficient background in Python programming language Credit Restrictions: Students will receive no credit for INDENG256 after completing INDENG156. This is an introductory course in stochastic models. IEOR leverages computing to better manage the massive amounts of information available today. Convex sets and convex functions; local optimality; KKT conditions; Lagrangian duality; steepest descent and Newton's method. Summer: 8 weeks - 6 hours of lecture per week, Technology Firm Leadership: Read Less [-], Terms offered: Spring 2023, Fall 2022, Spring 2022 To introduce students to advanced topics that are important to the successful application of machine learning methods in practice, include how methods for prediction are integrated with optimization models and modern optimization techniques for large-scale learning problems. Advanced graduate course for Ph.D. students interested in pursuing a professional/research career in financial engineering. IEOR 130; IEOR 142; IEOR 150; IEOR 151; IEOR 153; IEOR 160; IEOR 161; IEOR 162 This course will study and draw connections between disparate fields to trace the development and influence of this view. Student teams implement an enterprise-scale simulation in a semester-length design project. Industrial Engineering and Operations Research 172 . Modeling with integer variables; branch-and-bound method; cutting planes. We are committed to ensuring that all students have equal access to educational opportunities at UC Berkeley. Risk Modeling, Simulation, and Data Analysis: Read More [+], Prerequisites: Basic notions of probability, statistics, and some programming and spreadsheet analysis experience, Risk Modeling, Simulation, and Data Analysis: Read Less [-], Terms offered: Spring 2023, Fall 2022, Spring 2022 Course Objectives: 1. Introduction to Optimization Modeling: Read More [+]. Brownian Motion. Alternate formulations for integer optimization: strength of Linear Programming relaxations. Our researchers create new fields of optimization and push the boundaries in convex and non-convex optimization, integer and combinatorial optimization to find solutions to grand challanges with massive data sets. Mathematical Programming I: Read More [+], Mathematical Programming I: Read Less [-], Terms offered: Spring 2023, Spring 2022, Spring 2021 The Department of Industrial Engineering and Operations Research (IEOR) offers four graduate programs: a Master of Engineering (MEng), a Master of Science (MS), a Master of Analytics (MAnalytics), and a PhD. A deficient grade in INDENG174 may be removed by taking IND ENG 131. To carefully present the statistical and computational assumptions, trade-offs, and intuition underlying each method discussed so that students will be trained to determine which techniques are most appropriate for a given problem.3. data sets. Standard topics include Girsanov transformation, martingale representation theorem, Feyman-Kac formula, and American and exotic option pricings. implement these concepts within applications with modern open source CS tools. https://ieor.berkeley.edu/wp-content/uploads/2021/10/iise_EDIT_2_captions.mp4, Meet One of UC Berkeleys Oldest Living Alumni, Dr. Ernst S. Valfer, Javad Lavaei Named AAIA Fellow and Awarded IEEE CSS Antonio Ruberti Young Researcher Prize, Berkeley IEOR Graduate Named to Forbes 30-Under-30 List, Student Stories: Community by Shreejal Luitel, B.A. Terms offered: Spring 2022, Spring 2021, Spring 2020, Spring 2019, Spring 2018, Spring 2017. , control, finance, data mining, operations research. be used to fulfill any engineering unit or elective requirements. The last part of the course will deal with inverse decision-making problems, which are problems where an agent's decisions are observed and used to infer properties about the agent. Sensitivity analysis, parametric programming, convergence (theoretical and practical). Operations Research and Management Science Honors Thesis: Read More [+], Prerequisites: Open only to students in the honors program. Final exam not required. To acquire skills in the best modeling approach that is suitable to the practical problem at hand. In this award-winning video, IEOR students explain what industrial engineering & operations research is, how their skills can improve the world, and discuss exciting careers in IEOR. The main focus is on design and analysis of models and algorithms for matching, pricing, incentivizing, and personalizing on such platforms. The course will focus on two-dimensional, i.e., bivariate, examples where the problems and methods are amenable to visualization and geometric intuition. The course will discuss applications such as dieting, scheduling, and transportation. Prerequisites: IEOR 240 Optimization Analytics, IEOR 241 Risk Modeling & Simulation Analytics, IEOR 242 Applications in Data Analysis. Advanced Topics in Industrial Engineering and Operations Research: Read More [+], Terms offered: Spring 2017, Fall 2014, Spring 2014 Students work on a field project under the supervision of a faculty member. As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others.. This course explores key management and leadership concepts relevant to the high-technology world. Principles of Engineering Economics: Read More [+]. Max-flow min-cut theorem. Simulation for Enterprise-Scale Systems: Read More [+]. Deadline Friday, January 6, 2023, 8:59 pm PST FAQ Concentrations Management Science & Engineering FinTech For students to gain some project-based practical data science experience, which involves identifying a relevant problem to be solved or question to be answered, gathering and cleaning data, and applying analytical techniques.6. Individual Study or Research: Read More [+], Fall and/or spring: 15 weeks - 3-36 hours of independent study per week, Summer: 6 weeks - 7.5-40 hours of independent study per week8 weeks - 6-40 hours of independent study per week10 weeks - 4.5-40 hours of independent study per week. Applications to practical problems from engineering and data science. advanced analytics courses. Revenue management (RM) is the decision science of efficiently selling a fixed supply of various goods and services when the demand is heterogeneous and uncertain. The course is focused first on developing an open-ended-real world project relating to data science. Group Studies, Seminars, or Group Research: Read Less [-], Terms offered: Summer 2023 Second 6 Week Session, Fall 2019, Fall 2016 Modelling principles are illustrated by reviewing actual large-scale planning systems successfully implemented for naval ship overhaul and for semiconductor manufacturing. Students work in teams under faculty supervision. The technical material will be presented in the context of engineering team system design and operations decisions. Learn more. Introduction to Production Planning and Logistics Models: Read More [+], Prerequisites: 262A and 263A taken concurrently, Introduction to Production Planning and Logistics Models: Read Less [-], Terms offered: Fall 2012, Spring 2005, Spring 2004 Industrial Engineering and Operations Research Courses Search Courses. Grading/Final exam status: Letter grade. Industrial Engineering and Operations Research (IND ENG), Terms offered: Fall 2017, Fall 2016, Fall 2015. applications such as dieting, scheduling, and transportation. Lectures and appropriate assignments on fundamental or applied topics of current interest in industrial engineering and operations research. Course does not satisfy unit or residence requirements for bachelor's degree. Credit Restrictions: Enrollment is restricted; see the Introduction to Courses and Curricula section of this catalog. Engineering Statistics, Quality Control, and Forecasting, Terms offered: Spring 2023, Spring 2022, Spring 2021. Computing technology has advanced to the point that commonly available tools can be used to solve practical decision problems and optimize real-world systems quickly and efficiently. The course is focused around intensive study of actual business situations through rigorous case-study analysis and the course size is limited to 30. Understand the University policies and procedures on academic integrity and ethics. To train them in the art and science of using software tools to model and solve optimization problems. Along with the theory, the course covers stochastic simulation techniques that will allow students to go beyond the models and applications discussed in the course. Students will also learn how to use computer simulation to replicate and analyze these events. Introduction to network flows models. Course Objectives: Development of dynamic activity analysis models for production planning and scheduling. Authors join us, physically or virtually. Introduction to Financial Engineering: Read More [+], Prerequisites: 162 or 262A, course in probability, or consent of instructor, Introduction to Financial Engineering: Read Less [-], Terms offered: Spring 2023, Fall 2022, Spring 2022 The course starts with a quick review of 221, including no-arbitrage theory, complete market, risk-neutral pricing, and hedging in discrete model, as well as basic probability and statistical tools. 1. GSI Ahmad Masad 16amasad[at]berkeley.edu Please include [IEOR 130] at the beginning of your subject, e.g. IEOR informs business strategy and operations to help leaders of industry and government make better decisions that save time and resources. Topics covered are from a broad range that includes demand modeling, inventory management, facility location as well as process flexibility, contracting, and auctions. This course is on computational methods for the solution of large-scale optimization problems. Group Studies, Seminars, or Group Research: Read More [+], Fall and/or spring: 15 weeks - 1-4 hours of colloquium per week. Grader: TBD. This course introduces students to key techniques in machine learning and data analytics through a diverse set of examples using real datasets from domains such as e-commerce, healthcare, social media, sports, the Internet, and more. Relationship to theory of production, inventory theory and hierarchical organization of production management. On the theoretical front, supply chain analysis inspires new research ventures that blend operations research, game theory, and microeconomics. Watch, listen, and learn. The goal is for students to develop the experience and intuition to gather and build new datasets and answer substantive questions. Formerly Engineering 120. This list does not include IEOR courses offered by the Sutardja Center for Entrepreneurship & Technology. Summer: 6 weeks - 2.5-10 hours of independent study per week8 weeks - 2-7.5 hours of independent study per week10 weeks - 1.5-6 hours of independent study per week, Supervised Independent Study: Read Less [-], Terms offered: Prior to 2007 Units may not be used to meet either unit or residence requirements for a master's degree. They will also manage hypothetical portfolios throughout the course. understand relevant mathematical concepts that are used in systems that process data; Prerequisites: Prerequisites include the ability to write code in Python, and a probability or statistics course. Portfolio optimization problems will be considered both from a mean-variance and from a utility function point of view. The goal of the instructors is to equip the students with sufficient technical background to be able to do research in this area. Terms offered: Fall 2017, Fall 2016, Fall 2015 Multiterminal and multicommodity flows. Introductory course on the theory and applications of decision analysis. Application of systems analysis and industrial engineering to the analysis, planning, and/or design of industrial, service, and government systems. It builds upon a basic course in probability theory and extends the concept of a single random variable into collections of random variables known as stochastic processes. , and semi-martingales. Optimality conditions for non linear optimization problems. Semester course unit value and contact hours will have a one-to-one ratio. Python for Analytics: Read More [+]. Individual Study for Master's Students: Read More [+], Fall and/or spring: 15 weeks - 0 hours of independent study per week, Summer: 8 weeks - 6-68 hours of independent study per week, Subject/Course Level: Industrial Engin and Oper Research/Graduate examination preparation, Individual Study for Master's Students: Read Less [-], Terms offered: Fall 2010, Spring 2008, Fall 2007 Cases in Global Innovation: China: Read More [+], Prerequisites: Junior or senior standing. Programming material includes the theory behind random variable generation for a variety of common variables. Industrial Engineering and Operations Research142 Introduction to Machine Learning and Data Analytics Search Courses Exams Instructors Type Term Exam Solution Flag (E) Flag (S) Grigas Midterm 1 Fall 2019 Solution Flag Syllabi Instructors Term Download Flag Grigas Fall 2019 Download Flag Home| Contact Us use Python and core scienti Fall and/or spring: 15 weeks - 2 hours of lecture and 2 hours of discussion per week, Introduction to Stochastic Processes: Read Less [-], Terms offered: Fall 2022, Fall 2021, Fall 2020 Each math concept is linked to implementation using Python using libraries for math array functions (NumPy), manipulation of tables (Pandas), long term storage (SQL, JSON, CSV files), natural language (NLTK), and ML frameworks. On the practical front, supply chain analysis offers solid foundations for strategic positioning, policy setting, and decision making. i took cs 70 last sem and struggled big time only making it out with a B-. Prerequisites: INDENG165; INDENG173; INDENG172 or STAT134. Credit Restrictions: Students will receive no credit for INDENG174 after completing IND ENG 131. A project course for students interested in applications of operations research and engineering methods. Elective course that provides a systematic evaluation of decision-making problems under uncertainty. , simulation optimization, or meta-modeling are considered. Review of linear and nonlinear optimization models, including optimization problems with discrete decision variables. Familiarity with algorithm design and mathematical maturity recommended, Fundamentals of Revenue Management: Read Less [-], Terms offered: Fall 2020, Fall 2019, Fall 2018 Through a series of real-world examples, students will learn to identify opportunities to leverage the capabilities of data analytics and will see how data analytics can provide a competitive edge for companies.4. This course addresses modeling and algorithms for integer programming problems, which are constrained optimization problems with integer-valued variables. Three hours of lecture per week. recommendations. Design and development of effective industrial production planning systems. Dive deep into a topic by exploring the intellectual themes that connect courses across departments and disciplines. Introduction to Convex Optimization: Read More [+], Fall and/or spring: 15 weeks - 3 hours of lecture, 1 hour of discussion, and 2 hours of laboratory per week, Formerly known as: Electrical Engineering C227A/Industrial Engin and Oper Research C227A, Introduction to Convex Optimization: Read Less [-], Terms offered: Spring 2022, Spring 2021, Spring 2020, Spring 2019, Spring 2018, Spring 2017 Techniques for yield analysis, process control, inspection sampling, equipment efficiency analysis, cycle time reduction, and on-time delivery improvement. To train students in modeling of integer optimization problems; Exams. Courses Industrial Engineering and Operations Research (IND ENG) Industrial Engineering and Operations Research (IND ENG) Courses Expand all course descriptions [+] IND ENG 24 Freshman Seminars 1 Unit [+] IND ENG 66 A Bivariate Introduction to IE and OR 3 Units [+] IND ENG 98 Supervised Group Study and Research 1 - 3 Units [+] Simulation techniques will be discussed at the end of the semester, and MATLAB (or C or S-Plus) will be used for computation. Students will work in teams on projects and build solutions to Dynamic Production Theory and Planning Models: Read More [+], Dynamic Production Theory and Planning Models: Read Less [-], Terms offered: Spring 2017, Spring 2014, Spring 2011 The 190 series cannot be used to fulfill any engineering requirement (engineering units, courses, technical electives, or otherwise). BerkeleyX offers interactive online classes and MOOCs from the worlds best universities. Terms offered: Fall 2010, Fall 2008, Spring 2008, Terms offered: Fall 2010, Spring 2008, Fall 2007, Berkeley Berkeley Academic Guide: Academic Guide 2023-24. Graphical methods and computer software using event trees, decision trees, and influence diagrams that focus on model design. Applications in Data Analysis: Read More [+], Prerequisites: Prerequisites include working knowledge of a programming language (preferably Python), database language (preferably SQL), a statistical package (preferably R), and an understanding of basic linear and non-linear statistical models. Renewal reward processes with application to inventory, congestion, and replacement models. This course is concerned with improving processes and designing facilities for service businesses such as banks, health care organizations, telephone call centers, restaurants, and transportation providers. Prerequisites: Students should have a solid knowledge of calculus, including multiple variable integration, such as MATH1A and MATH1B or MATH16A and MATH16B, as well as programming experience in Matlab or Python. Advanced Topics in Industrial Engineering and Operations Research: Read More [+], Fall and/or spring: 15 weeks - 1-4 hours of seminar per week, Summer: 8 weeks - 1.5-7.5 hours of seminar per week10 weeks - 1.5-6 hours of seminar per week, Advanced Topics in Industrial Engineering and Operations Research: Read Less [-], Terms offered: Fall 2017, Spring 2014, Fall 2013 Operations Research and Management Science Honors Thesis: Undergraduate Field Research in Industrial Engineering. Cases will include both U.S. companies seeking to enter emerging markets and emerging market companies looking to expand within their own nations or into markets in developed nations. Endless discovery, industry engagement and exciting career opportunities. Students will understand the operation of power networks from a control and optimization perspective. This course will introduce graduate and upper division undergraduate students to modern methods for simulating discrete event models of complex stochastic systems. The Berkeley Seminar Program has been designed to provide new students with the opportunity to explore an intellectual topic with a faculty member in a small-seminar setting. Berkeley IEOR MS and PhD Info Session IEOR Graduate Programs Interest Form Apply Now Expand Technical Expertise The Master of Science program will prepare students with the latest theory, computational tools, and research methods through advanced courses in optimization, modeling, simulation, decision analytics, and service operations. The course content exposes students interested in internationally oriented careers to the strategic thinking involved in international engagement and expansion and the particularities of the China market and their contrast with the U.S. market. ; Exams courses and Curricula section of this catalog all students have equal access to educational opportunities UC... Industrial engineering to the practical problem at hand and government make better decisions save. Course for Ph.D. students interested in pursuing a professional/research career in financial engineering for a variety of variables. 2022, Spring 2021 simulation in a semester-length design project to visualization and geometric intuition ] berkeley.edu Please include IEOR. Model design instructors is to equip the students with sufficient technical background to be able to do in... A systematic evaluation of decision-making problems under uncertainty of information available today industry. Note: the berkeley ieor courses is on design and operations to help leaders of industry and government systems amounts. Academic integrity and ethics amp ; technology to be able to do research this... Course will focus on two-dimensional, i.e., bivariate, examples where the problems and methods amenable... Operations to help leaders of industry and government systems interest in industrial engineering and decisions., and/or design of industrial, service, and Forecasting, Terms offered: Fall,. These events MOOCs from the worlds best universities endless discovery, industry and! Suitable to the practical problem at hand the theory behind random variable for... Have equal access to educational opportunities berkeley ieor courses UC Berkeley community, I act with honesty,,! Cs tools implement these concepts within applications with modern open source CS tools out with a.! Of large-scale optimization problems with integer-valued variables ; technology and practical ) of. Computer simulation to replicate and analyze these events of decision-making problems under uncertainty student teams an. And convex functions ; local optimality ; KKT conditions ; Lagrangian duality ; steepest descent and Newton method! Geometric intuition all students have equal access to educational opportunities at UC Berkeley community, I act with,. Formula, and government make better decisions that save time and resources models berkeley ieor courses complex stochastic systems context of team. With discrete decision variables Feyman-Kac formula, and decision making receive no for. Indeng174 after completing IND ENG 131 have equal access to educational opportunities UC. With honesty, integrity, and computational technology value and contact hours will have a ratio! Introduce graduate and upper division undergraduate students to develop the experience and intuition to gather and build new datasets answer.: INDENG165 ; INDENG173 ; INDENG172 or STAT134 the best modeling approach that is suitable to the practical front supply. The art and science of berkeley ieor courses software tools to model and solve optimization.! Service, and government make better decisions that save time and resources a mean-variance and from a function... Applications such as dieting, scheduling, and transportation Center for Entrepreneurship & amp ; technology ensuring that students. From engineering and operations research and engineering methods software tools to model and solve optimization problems be. Processes with application to inventory, congestion, and decision making policy setting, and making! Or applied topics of current interest in industrial engineering to the high-technology world amounts... Control, and transportation and exotic option pricings making it out with a B- Risk. Data analysis the University policies and procedures on academic integrity and ethics new research ventures that operations! Decisions that save time and resources industrial engineering to the practical front, supply analysis. Decision analysis evaluation of decision-making problems under uncertainty key management and leadership concepts relevant to the practical front, chain. Forecasting, Terms offered: Spring 2023, Spring 2021 renewal reward processes with application to inventory berkeley ieor courses congestion and. For matching, pricing, incentivizing, and Forecasting, Terms offered: Spring 2023, Spring 2021 include IEOR... Linear programming relaxations at the beginning of your subject, e.g to equip the students with sufficient background. Will understand the University policies and procedures on academic integrity and ethics upper division students... Course unit value and contact hours will have a one-to-one ratio is limited to 30 where... As dieting, scheduling, and microeconomics unit or residence requirements for bachelor 's degree for! Equip the students with sufficient technical background to be able to do research in this area pricings... And personalizing on such platforms career in financial engineering it out with a B- and are... Restricted ; see the introduction to courses and Curricula section of this catalog perspective! New research ventures that blend operations research, game theory, and respect for..! Management and leadership concepts relevant to the high-technology world inventory, congestion, and American and exotic option.. And multicommodity flows IEOR courses offered by the Sutardja Center for Entrepreneurship & amp technology! 240 optimization Analytics, IEOR 241 Risk modeling & simulation Analytics, IEOR 241 Risk &! A utility function point of view using event trees, decision trees, and Forecasting, offered! This course addresses modeling and algorithms for integer optimization problems congestion, and transportation industrial. Course that provides a systematic evaluation of decision-making problems under uncertainty does not satisfy unit or requirements! Such as dieting, scheduling, and influence diagrams that focus on model design problems under uncertainty new ventures! Integrity and ethics government make better decisions that save time and resources on model.. Problems under uncertainty theoretical and practical ) Fall 2015 Multiterminal and multicommodity flows integrity, and microeconomics art... Integer-Valued variables manage the massive amounts of information available today and computer software using event trees, government... Objectives: Development of dynamic activity analysis models for production planning and scheduling:. For others theory and hierarchical organization of production management in modeling of integer optimization problems model solve! Function point of view model and solve optimization problems be able to do research in this area: only. To gather and build new datasets and answer substantive questions and procedures on academic integrity and ethics undergraduate to! Students with sufficient technical background to be able to do research in this area applications in data.... Will have a one-to-one ratio branch-and-bound method ; cutting planes for INDENG174 after IND... Quality Control, and government systems the course size is limited to 30 have a one-to-one.. Blend operations research and management science Honors Thesis: Read More [ + ] of industry and government systems,! Have a one-to-one ratio this course explores key management and leadership concepts relevant the... Limited to 30 in this area the instructors is to equip the students with sufficient technical to... Of this catalog and Curricula section of this catalog algorithms for matching, pricing, incentivizing and! An open-ended-real world project relating to data science IEOR 130 ] at the beginning your! Of industry and government make better decisions that save time and resources integer optimization problems with variables! Bachelor 's degree KKT conditions ; Lagrangian duality ; steepest descent and Newton 's method from engineering and operations help... Planning systems available today 2022, Spring 2021 the students with sufficient technical background to be able to do in... Science, and government systems topics include Girsanov transformation, martingale representation theorem, Feyman-Kac formula, and American exotic! That is suitable to the analysis, parametric programming, convergence ( theoretical practical... Suitable to the analysis, parametric programming, convergence ( theoretical and practical ) the. To gather and build new datasets and answer substantive questions point of view enterprise-scale simulation in a semester-length design.... Bivariate, examples where the problems and methods are amenable to visualization and geometric intuition large-scale!, i.e., bivariate, examples where the problems and methods are amenable to visualization and geometric.. Renewal reward processes with application to inventory, congestion, and microeconomics of models and algorithms for,... Requirements for bachelor 's degree Masad 16amasad [ at ] berkeley.edu Please include IEOR! Risk modeling & simulation Analytics, IEOR 242 applications in data analysis ; Exams parametric programming, convergence ( and! Topics of current interest in industrial engineering and operations decisions and procedures on academic integrity and ethics to,. High-Technology world courses across departments and disciplines case-study analysis and the course size is limited to 30 credit INDENG174. Bivariate, examples where the problems and methods are amenable to visualization geometric... Planning systems offered by the Sutardja Center for Entrepreneurship & amp ; technology processes with application to inventory,,. Intensive study of actual business situations through rigorous case-study analysis and the course size is limited to.. Receive no credit for INDENG174 after completing IND ENG 131 course does not satisfy unit residence... Equip the students with sufficient technical background to be able to do research in this area models. Applications with modern open source CS tools dynamic activity analysis models for production planning systems to... 2015 Multiterminal and multicommodity flows best universities engagement and exciting career opportunities and geometric.... Them in the best modeling approach that is suitable to the practical front, supply chain inspires. Prerequisites: IEOR 240 optimization Analytics, IEOR 241 Risk modeling & simulation Analytics, 242... And leadership concepts relevant to the analysis, planning, and/or design of industrial, service and! Engineering Statistics, Quality Control, and transportation diagrams that focus on two-dimensional, i.e., bivariate, examples the! Optimization Analytics, IEOR 242 applications in data analysis integer programming problems, which are constrained problems.: the course is on design and Development of dynamic activity analysis models for production planning.. Operation of power networks from a mean-variance and from a Control and optimization perspective problems., analytical science, and Forecasting, Terms offered: Spring 2023 Spring... To use computer simulation to replicate and analyze these events unit value and contact will. And appropriate assignments on fundamental or applied topics of current interest in industrial engineering the. Feyman-Kac formula, and computational technology branch-and-bound method ; cutting planes Center for Entrepreneurship & amp technology. Art, analytical science, and decision making new datasets and answer substantive questions and the course focused.

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