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In this lecture, we introduce the three different simulation methodologies (agent-based modeling, system dynamics modeling, and discrete event system simulation) and then focus on how stochastic modeling is used within discrete-event system simulation.
Here at Mayo Clinic, outpatient labs are consistently engaged with patients throughout the week, particularly early in the week and during morning hours. While this congestion was a concern prior to COVID-19, it became a more pressing issue due to the new urgency to create social distancing for patients. Management Engineering and Consulting was asked to lead a project team to develop recommendations to reduce the number of patients in the lab lobbies at peak hours to increase social distancing. Adam Resnick, Health System Engineer Fellow, and host Tony Chihak discuss the challenging process of developing an accurate simulation model to provide recommendations for implementation.
This episode touches on computer simulations, machine learning, and GPU's. How do these aspects of computer science relate and differ? Andy and John dive deep into how they push the boundaries of what is possible and practical in modern medicine by simulating biological systems.Our Team:Host:Angelo KastroulisExecutive Producer: Náture KastroulisProducer: Albert Perrotta; Communications Strategist: Albert Perrotta;Audio Engineer: Ryan ThompsonMusic: All Things Grow by Oliver Worth
Bree Bush, Vice President, Chief Data Officer at GE Healthcare, dives into simulation modeling and advanced analytical tools to optimize inpatient, procedural, and clinic capacity; the concept of “real-time healthcare”; digital transformation in healthcare and medical research, and much more.To find out more about Impetus: https://www.meetwithimpetus.comNatalie Yeadon LinkedIn: https://www.linkedin.com/in/natalieyeadon/Impetus Digital Website: https://www.impetusdigital.com/Impetus Digital LinkedIn: https://www.linkedin.com/company/impetus-digital/Impetus Digital Twitter: https://twitter.com/impetus_digitalImpetus YouTube: https://www.youtube.com/ImpetusDigitalBree Bush: https://www.linkedin.com/in/bree-bush-558a8a34/GE Healthcare: https://www.gehealthcare.com/
In this lecture, we pivot from our general introduction to (quantitative) modeling to a more specific introduction of simulation modeling. System dynamics modeling (SDM), agent-based modeling (ABM), and discrete event system (DES) simulation are introduced, with the most detail on DES that will be the focus for the course. We then motivate the approach of "stochastic modeling" -- using randomness in these models in place of deterministic details.
Here at Mayo Clinic, outpatient labs are consistently engaged with patients throughout the week, particularly early in the week and during morning hours. While this congestion was a concern prior to COVID-19, it became a more pressing issue due to the new urgency to create social distancing for patients. Management Engineering and Consulting was asked to lead a project team to develop … Continue reading Outpatient Simulation Modeling →
In this lecture, we introduce the three different kinds of simulation modeling (system dynamics modeling, agent-based modeling, and discrete event system simulation) and how they differ in the kinds of questions they help answer, the way they are programmed, and the computational resources that they require. We then introduce the fundamental concepts required for discrete event system modeling and start to discuss aspects of stochastic simulation and input modeling.
Guest Name : Greg Schlegel - Founder at The Supply Chain Management Risk Consortium. Language : English, Publication date: Feb, 10. 2020 Greg has been a supply chain executive for over 30 years with several Fortune 100 companies and spent seven years as an IBM supply chain Executive Consultant. He has presented papers on and has managed consulting engagements in supply chain management, Risk Management, Lean/Six Sigma and Theory of Constraints throughout the US and around the globe. Greg is then founded the The Supply Chain Management Risk Consortium; The Consortium has grown to include (22) companies who bring unique core competencies in supply chain risk. These range from education, insurance risk quantification, Simulation/Modeling, Business Continuity Planning, Supply Chain Mapping and much more. Connect Greg on his Linkedin: https://www.linkedin.com/in/greg-schlegel-cpim-csp-jonah-4163951/ Highlighted: Learn on why is risk management an important part of supply chain management ? How to identify a supply chain risks ? Is there any systematic-approach on how to identify the risks ? Global issues on corona-virus : Supply chain management risks's perspective --- Send in a voice message: https://anchor.fm/bicarasupplychain/message
Host: Benjamin SchumannTopic: In this episode Ben sits down and explains what Simulation Modeling actually isSocial/OtherJacob on TwitterBen on TwitterBen's WebsiteBroken Jar's Patreon
Dr. Raafat Zaini, Research Scientist at Worcester Polytechnic Institute discusses the dynamic enrollment model for university expansion he created at WPI and the interdependence between enrollment factors and cost centers to create a scalable model for growth detailed in his research study, Let’s Talk Change in a University: A Simple Model for Addressing a Complex Agenda. Dr. Raafat Zaini's research interest is in the area of organizational dynamics and innovation sustainability with a focus on a multi-perspective design approach and dynamic modeling of R&D organizations and higher education institutions. Raafat holds a B.S in mechanical engineering (KFUPM 1990), M.S. in aeronautical and industrial engineering (Purdue 1999) and Ph.D. in system dynamics and organization behavior (WPI 2017). You can reach Dr. Zaini at rzaini@wpi.edu and on both Twitter and LinkedIn @raafatzaini
This is the last of four conversation Gudrun had during the British Applied Mathematics Colloquium which took place 5th – 8th April 2016 in Oxford. Andrea Bertozzi from the University of California in Los Angeles (UCLA) held a public lecture on The Mathematics of Crime. She has been Professor of Mathematics at UCLA since 2003 and Betsy Wood Knapp Chair for Innovation and Creativity (since 2012). From 1995-2004 she worked mostly at Duke University first as Associate Professor of Mathematics and then as Professor of Mathematics and Physics. As an undergraduate at Princeton University she studied physics and astronomy alongside her major in mathematics and went through a Princeton PhD-program. For her thesis she worked in applied analysis and studied fluid flow. As postdoc she worked with Peter Constantin at the University of Chicago (1991-1995) on global regularity for vortex patches. But even more importantly, this was the moment when she found research problems that needed knowledge about PDEs and flow but in addition both numerical analysis and scientific computing. She found out that she really likes to collaborate with very different specialists. Today hardwork can largely be carried out on a desktop but occasionally clusters or supercomputers are necessary. The initial request to work on Mathematics in crime came from a colleague, the social scientist Jeffrey Brantingham. He works in Anthropology at UCLA and had well established contacts with the police in LA. He was looking for mathematical input on some of his problems and raised that issue with Andrea Bertozzi. Her postdoc George Mohler came up with the idea to adapt an earthquake model after a discussion with Frederic Paik Schoenberg, a world expert in that field working at UCLA. The idea is to model crimes of opportunity as being triggered by crimes that already happend. So the likelihood of new crimes can be predicted as an excitation in space and time like the shock of an earthquake. Of course, here statistical models are necessary which say how the excitement is distributed and decays in space and time. Mathematically this is a self-exciting point process. The traditional Poisson process model has a single parameter and thus, no memory - i.e. no connections to other events can be modelled. The Hawkes process builds on the Poisson process as background noise but adds new events which then are triggering events according to an excitation rate and the exponential decay of excitation over time. This is a memory effect based on actual events (not only on a likelihood) and a three parameter model. It is not too difficult to process field data, fit data to that model and make an extrapolation in time. Meanwhile the results of that idea work really well in the field. Results of field trials both in the UK and US have just been published and there is a commercial product available providing services to the police. In addition to coming up with useful ideas and having an interdisciplinary group of people committed to make them work it was necessery to find funding in order to support students to work on that topic. The first grant came from the National Science Foundation and from this time on the group included George Tita (UC Irvine) a criminology expert in LA-Gangs and Lincoln Chayes as another mathematician in the team. The practical implementation of this crime prevention method for the police is as follows: Before the policemen go out on a shift they ususally meet to divide their teams over the area they are serving. The teams take the crime prediction for that shift which is calculated by the computer model on the basis of whatever data is available up to shift. According to expected spots of crimes they especially assign teams to monitor those areas more closely. After introducing this method in the police work in Santa Cruz (California) police observed a significant reduction of 27% in crime. Of course this is a wonderful success story. Another success story involves the career development of the students and postdocs who now have permanent positions. Since this was the first group in the US to bring mathematics to police work this opened a lot of doors for young people involved. Another interesting topic in the context of Mathematics and crime are gang crime data. As for the the crime prediction model the attack of one gang on a rival gang usually triggers another event soon afterwards. A well chosen group of undergraduates already is mathematically educated enough to study the temporary distribution of gang related crime in LA with 30 street gangs and a complex net of enemies. We are speaking about hundreds of crimes in one year related to the activity of gangs. The mathematical tool which proved to be useful was a maximum liklihood penalization model again for the Hawkes process applied on the expected retaliatory behaviour. A more complex problem, which was treated in a PhD-thesis, is to single out gangs which would be probably responsable for certain crimes. This means to solve the inverse problem: We know the time and the crime and want to find out who did it. The result was published in Inverse Problems 2011. The tool was a variational model with an energy which is related to the data. The missing information is guessed and then put into the energy . In finding the best guess related to the chosen energy model a probable candidate for the crime is found. For a small number of unsolved crimes one can just go through all possible combinations. For hundreds or even several hundreds of unsolved crimes - all combinations cannot be handled. We make it easier by increasing the number of choices and formulate a continuous instead of the discrete problem, for which the optimization works with a standard gradient descent algorithm. A third topic and a third tool is Compressed sensing. It looks at sparsitiy in data like the probability distribution for crime in different parts of the city. Usually the crime rate is high in certain areas of a city and very low in others. For these sharp changes one needs different methods since we have to allow for jumps. Here the total variation enters the model as the -norm of the gradient. It promotes sparsity of edges in the solution. Before coming up with this concept it was necessary to cross-validate quite a number of times, which is computational very expensive. So instead of in hours the result is obtained in a couple minutes now. When Andrea Bertozzi was a young child she spent a lot of Sundays in the Science museum in Boston and wanted to become a scientist when grown up. The only problem was, that she could not decide which science would be the best choice since she liked everything in the museum. Today she says having chosen applied mathematics indeed she can do all science since mathematics works as a connector between sciences and opens a lot of doors. References Press coverage of Crime prevention collected Website of Mathematical and Simulation Modeling of Crime Examples for work of undergraduates M. Allenby, e.a.: A Point Process Model for Simulating Gang-on-Gang Violence, Project Report, 2010. K. Louie: Statistical Modeling of Gang Violence in Los Angeles, talk at AMS Joint meetings San Francisco, AMS Session on Mathematics in the Social Sciences, 2010] Publications of A. Bertozzi and co-workers on Crime prevention G.O. Mohler e.a.: Randomized controlled field trials of predictive policing, J. Am. Stat. Assoc., 111(512), 1399-1411, 2015. J. T. Woodworth e.a.: Nonlocal Crime Density Estimation Incorporating Housing Information, Phil. Trans. Roy. Soc. A, 372(2028), 20130403, 2014. J. Zipkin, M. B. Short & A. L. Bertozzi: Cops on the dots in a mathematical model of urban crime and police response, Discrete and Continuous Dynamical Systems B, 19(5), pp. 1479-1506, 2014. H. Hu e.a.: A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme, SIAM J. Appl. Math., 73(6), pp. 2224-2246, 2013. L.M. Smith e.a.: Adaptation of an Ecological Territorial Model to Street Gang Spatial Patterns in Los Angeles Discrete and Continuous Dynamical Systems A, 32(9), pp. 3223 - 3244, 2012. G. Mohler e.a.. (2011): Self- exciting point process modeling of crime, Journal of the American Statistical Association, 106(493):100–108, 2011. A. Stomakhin, M. Short, and A. Bertozzi: Reconstruction of missing data in social networks based on temporal patterns of interactions. Inverse Problems, 27, 2011. N. Rodriguez & A. Bertozzi: Local Existence and Uniqueness of Solutions to a PDE model for Criminal Behavior , M3AS, special issue on Mathematics and Complexity in Human and Life Sciences, Vol. 20, Issue supp01, pp. 1425-1457, 2010. Related Podcasts AMS - Mathematical Moments Podcast: MM97 - Forecasting Crime British Applied Mathematics Colloquium 2016 Special J.Dodd: Crop Growth, Conversation with G. Thäter in the Modellansatz Podcast episode 89, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2016. http://modellansatz.de/crop-growth H. Wilson: Viscoelastic Fluids, Conversation with G. Thäter in the Modellansatz Podcast episode 92, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2016. http://modellansatz.de/viscoelastic-fluids A. Hosoi: Robots, Conversation with G. Thäter in the Modellansatz Podcast, episode 108, Department for Mathematics, Karlsruhe Institute of Technologie (KIT), 2016. http://modellansatz.de/robot A. Bertozzi: Crime Prevention, Conversation with G. Thäter in the Modellansatz Podcast, episode 109, Department for Mathematics, Karlsruhe Institute of Technologie (KIT), 2016. http://modellansatz.de/crime-prevention
This is the last of four conversation Gudrun had during the British Applied Mathematics Colloquium which took place 5th – 8th April 2016 in Oxford. Andrea Bertozzi from the University of California in Los Angeles (UCLA) held a public lecture on The Mathematics of Crime. She has been Professor of Mathematics at UCLA since 2003 and Betsy Wood Knapp Chair for Innovation and Creativity (since 2012). From 1995-2004 she worked mostly at Duke University first as Associate Professor of Mathematics and then as Professor of Mathematics and Physics. As an undergraduate at Princeton University she studied physics and astronomy alongside her major in mathematics and went through a Princeton PhD-program. For her thesis she worked in applied analysis and studied fluid flow. As postdoc she worked with Peter Constantin at the University of Chicago (1991-1995) on global regularity for vortex patches. But even more importantly, this was the moment when she found research problems that needed knowledge about PDEs and flow but in addition both numerical analysis and scientific computing. She found out that she really likes to collaborate with very different specialists. Today hardwork can largely be carried out on a desktop but occasionally clusters or supercomputers are necessary. The initial request to work on Mathematics in crime came from a colleague, the social scientist Jeffrey Brantingham. He works in Anthropology at UCLA and had well established contacts with the police in LA. He was looking for mathematical input on some of his problems and raised that issue with Andrea Bertozzi. Her postdoc George Mohler came up with the idea to adapt an earthquake model after a discussion with Frederic Paik Schoenberg, a world expert in that field working at UCLA. The idea is to model crimes of opportunity as being triggered by crimes that already happend. So the likelihood of new crimes can be predicted as an excitation in space and time like the shock of an earthquake. Of course, here statistical models are necessary which say how the excitement is distributed and decays in space and time. Mathematically this is a self-exciting point process. The traditional Poisson process model has a single parameter and thus, no memory - i.e. no connections to other events can be modelled. The Hawkes process builds on the Poisson process as background noise but adds new events which then are triggering events according to an excitation rate and the exponential decay of excitation over time. This is a memory effect based on actual events (not only on a likelihood) and a three parameter model. It is not too difficult to process field data, fit data to that model and make an extrapolation in time. Meanwhile the results of that idea work really well in the field. Results of field trials both in the UK and US have just been published and there is a commercial product available providing services to the police. In addition to coming up with useful ideas and having an interdisciplinary group of people committed to make them work it was necessery to find funding in order to support students to work on that topic. The first grant came from the National Science Foundation and from this time on the group included George Tita (UC Irvine) a criminology expert in LA-Gangs and Lincoln Chayes as another mathematician in the team. The practical implementation of this crime prevention method for the police is as follows: Before the policemen go out on a shift they ususally meet to divide their teams over the area they are serving. The teams take the crime prediction for that shift which is calculated by the computer model on the basis of whatever data is available up to shift. According to expected spots of crimes they especially assign teams to monitor those areas more closely. After introducing this method in the police work in Santa Cruz (California) police observed a significant reduction of 27% in crime. Of course this is a wonderful success story. Another success story involves the career development of the students and postdocs who now have permanent positions. Since this was the first group in the US to bring mathematics to police work this opened a lot of doors for young people involved. Another interesting topic in the context of Mathematics and crime are gang crime data. As for the the crime prediction model the attack of one gang on a rival gang usually triggers another event soon afterwards. A well chosen group of undergraduates already is mathematically educated enough to study the temporary distribution of gang related crime in LA with 30 street gangs and a complex net of enemies. We are speaking about hundreds of crimes in one year related to the activity of gangs. The mathematical tool which proved to be useful was a maximum liklihood penalization model again for the Hawkes process applied on the expected retaliatory behaviour. A more complex problem, which was treated in a PhD-thesis, is to single out gangs which would be probably responsable for certain crimes. This means to solve the inverse problem: We know the time and the crime and want to find out who did it. The result was published in Inverse Problems 2011. The tool was a variational model with an energy which is related to the data. The missing information is guessed and then put into the energy . In finding the best guess related to the chosen energy model a probable candidate for the crime is found. For a small number of unsolved crimes one can just go through all possible combinations. For hundreds or even several hundreds of unsolved crimes - all combinations cannot be handled. We make it easier by increasing the number of choices and formulate a continuous instead of the discrete problem, for which the optimization works with a standard gradient descent algorithm. A third topic and a third tool is Compressed sensing. It looks at sparsitiy in data like the probability distribution for crime in different parts of the city. Usually the crime rate is high in certain areas of a city and very low in others. For these sharp changes one needs different methods since we have to allow for jumps. Here the total variation enters the model as the -norm of the gradient. It promotes sparsity of edges in the solution. Before coming up with this concept it was necessary to cross-validate quite a number of times, which is computational very expensive. So instead of in hours the result is obtained in a couple minutes now. When Andrea Bertozzi was a young child she spent a lot of Sundays in the Science museum in Boston and wanted to become a scientist when grown up. The only problem was, that she could not decide which science would be the best choice since she liked everything in the museum. Today she says having chosen applied mathematics indeed she can do all science since mathematics works as a connector between sciences and opens a lot of doors. References Press coverage of Crime prevention collected Website of Mathematical and Simulation Modeling of Crime Examples for work of undergraduates M. Allenby, e.a.: A Point Process Model for Simulating Gang-on-Gang Violence, Project Report, 2010. K. Louie: Statistical Modeling of Gang Violence in Los Angeles, talk at AMS Joint meetings San Francisco, AMS Session on Mathematics in the Social Sciences, 2010] Publications of A. Bertozzi and co-workers on Crime prevention G.O. Mohler e.a.: Randomized controlled field trials of predictive policing, J. Am. Stat. Assoc., 111(512), 1399-1411, 2015. J. T. Woodworth e.a.: Nonlocal Crime Density Estimation Incorporating Housing Information, Phil. Trans. Roy. Soc. A, 372(2028), 20130403, 2014. J. Zipkin, M. B. Short & A. L. Bertozzi: Cops on the dots in a mathematical model of urban crime and police response, Discrete and Continuous Dynamical Systems B, 19(5), pp. 1479-1506, 2014. H. Hu e.a.: A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme, SIAM J. Appl. Math., 73(6), pp. 2224-2246, 2013. L.M. Smith e.a.: Adaptation of an Ecological Territorial Model to Street Gang Spatial Patterns in Los Angeles Discrete and Continuous Dynamical Systems A, 32(9), pp. 3223 - 3244, 2012. G. Mohler e.a.. (2011): Self- exciting point process modeling of crime, Journal of the American Statistical Association, 106(493):100–108, 2011. A. Stomakhin, M. Short, and A. Bertozzi: Reconstruction of missing data in social networks based on temporal patterns of interactions. Inverse Problems, 27, 2011. N. Rodriguez & A. Bertozzi: Local Existence and Uniqueness of Solutions to a PDE model for Criminal Behavior , M3AS, special issue on Mathematics and Complexity in Human and Life Sciences, Vol. 20, Issue supp01, pp. 1425-1457, 2010. Related Podcasts AMS - Mathematical Moments Podcast: MM97 - Forecasting Crime British Applied Mathematics Colloquium 2016 Special J.Dodd: Crop Growth, Conversation with G. Thäter in the Modellansatz Podcast episode 89, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2016. http://modellansatz.de/crop-growth H. Wilson: Viscoelastic Fluids, Conversation with G. Thäter in the Modellansatz Podcast episode 92, Department of Mathematics, Karlsruhe Institute of Technology (KIT), 2016. http://modellansatz.de/viscoelastic-fluids A. Hosoi: Robots, Conversation with G. Thäter in the Modellansatz Podcast, episode 108, Department for Mathematics, Karlsruhe Institute of Technologie (KIT), 2016. http://modellansatz.de/robot A. Bertozzi: Crime Prevention, Conversation with G. Thäter in the Modellansatz Podcast, episode 109, Department for Mathematics, Karlsruhe Institute of Technologie (KIT), 2016. http://modellansatz.de/crime-prevention