## Graduate Students

### Doctoral Candidates

Nick Allgaier PhD CandidateDepartment of Mathematics and Statistics website Advisor, Christopher Danforth Research Interests: Weather & Climate Prediction; Reverse Engineering the Brain Degrees Received: Graduate Certificate in Complex Systems |

Cathy Bliss PhD CandidateDepartment of Mathematics and Statistics website Advisor, Peter Dodds Research Interests: Inference on Social Networks with Missing Data Degrees Received: Graduate Certificate in Complex Systems |

Eitan Pechenick PhD CandidateDepartment of Mathematics and Statistics website Advisor, Peter Dodds Research Interests: Computational Linguistics Degree Received: Graduate Certificate in Complex Systems |

Andy Reagan PhD CandidateDepartment of Mathematics and Statistics website Advisors, Christopher Danforth and Yves Dubief Data Assimilation and Uncertainty Quantification Masters in Mathematics, 2013 Title: Predicting Flow Reversals in a Computational Fluid Dynamics Simulated Thermosyphon Using Data AssimilationAbstract: A thermal convection loop is a circular chamber filled with water, heated on the bottom half and cooled on the top half. with sufficiently large forcing of heat, the direction of fluid flow in the loop oscillates chaotically, forming an analog to the Earth’s weather. As is the case for state-of-the-art weather models, we only observe the statistics over a small region of state space, making prediction difficult. To overcome this challenge, data assimilation (da) methods, and specifically ensemble methods, use the computational model itself to estimate the uncertainty of the model to optimally combine these observations into an initial condition for predicting the future state. First, we build and verify four distinct d.a. methods. Then, a computational fluid dynamics simulation of the loop and a reduced order model are both used by these d.a. methods to predict flow reversals. The results contribute to a testbed for algorithm development. |

Jake Williams PhD CandidateDepartment of Mathematics and Statistics Advisor, Peter Dodds Research Interests: Computational Linguistics; Quantifying Stories |

Tom Mcandrew PhD CandidateDepartment of Mathematics and Statistics Advisor, Peter Dodds Research Interests: Computational Linguistics; Quantifying Stories |

Mark Wagy PhD CandidateDepartment of Computer Science Degree Received: Graduate Certificate in Complex Systems |

Bob Swain PhD CandidateDepartment of Computer Science Degree Received: Graduate Certificate in Complex Systems |

Emily Cody, PhD CandidateDepartment of Mathematics and Statistics Advisor, Chris Danforth Research Interests: NSF Igert; Small Grid & Human Behavior |

Goodarz Ghanavati, PhD CandidateDepartment of Electrical Engineering Advisor, Paul Hines Research Interests: Power system dynamic stability |

Anton Bernatskiy PhD Candidate |

### Masters Students

Sharon Alajajian, Masters StudentDepartment of Mathematics and Statistics Advisor, Peter Dodds Research Interests: Food Systems & Eating Behavior Via Social Media |

Mike Foley, Masters StudentDepartment of Mathematics and Statistics Advisor, Brian Tivnan Research Interests: Computational Finance |

Kayla Horak, Masters StudentDepartment of Mathematics and Statistics Advisor, Chris Danforth Research Interests: Statistical Hedonometrics |

David Buckingham, Masters StudentDepartment of Computer Science Research Interests: Cellular Communication with the Snowcloud Wireless Sensor Network |

### Students Earning Graduate Certificates in Complex Systems

Javier Garcia-BernardoCurrently a Computer Science Masters Student |

Scott HamshawOwner of Hamshaw Design; Research Assistant |

Christopher PierceCurrently an employee at PharMerica Corporation |

Curtis SaundersCurrently a PhD candidate in Mechanical Engineering |

### Alumni

Amanda Casari, AlumnaDegree Earned: Graduate Certificate in Complex Systems Currently Data Scientist at Mantis Technology Group (A ProKarma Company) |

Kameron D. Harris, AlumnusReceived Masters in Mathematics from University of Vermont, 2012 Currently at the University of WashingtonTitle of Masters Thesis: On-off Threshold Models of Social BehaviorAbstract: We study binary state dynamics on a social network, where nodes act according to individual response functions of the average state of their neighborhood. These response functions model the competing tendencies of imitation and non-conformity by incorporating an “off-threshold” into standard threshold models of behavior. In this way, we attempt to capture important aspects of fashions and general societal trends allowing varying amounts of stochasticity in both the network and response functions, we find different outcomes in the random and deterministic versions of the model. In the limit of a large, dense network, however, these dynamics coincide. The dynamical behavior of the system ranges from steady state to chaotic depending on network connectivity and update synchronicity. A mean field theory is laid out in detail for general random networks. In the undirected case, the mean field theory predicts that the dynamics on the network are a smoothed version of the response function dynamics. The theory is compared to simulations on Poisson random graphs with response functions that average to the chaotic tent map.Received Undergraduate Honors in Mathematics & Physics from University of Vermont, 2009 Title of Undergraduate Honors Thesis: Predicting Climate Regime Change in Chaotic ConvectionAbstract: A toy climate analogous to the famous lorenz system is derived and compared to computational ﬂuid dynamics simulations in order to test new modeling techniques. In particular, methods of data assimilation and ensemble forecasting are used to predict regime changes and residencies in this toy climate. A climate “truth” is created using a finite-element simulation of a thermal convection loop, a physical apparatus designed to be the simplest model of convection in the Earth’s atmosphere. Forecasts of the climate are made using low-dimensional lorenz-like models and synchronized to noisy observations of the truth using various Kalman filters. Forecasting of regime changes has been successfully demonstrated when the same model is used to create both the observations and the forecast, but never for realistic chaotic convection. |

Ahmed Ragab NabhanDegree Earned: Graduate Certificate in Complex Systems Currently a Senior Software Engineer at Sears Holdings Corporation |

Ross Lieb-Lappen, Alumnus 2011Received a Masters in Mathematics & Statistics from University of Vermont, 2010 Currently at the Dartmouth College in the Thayer School of EngineeringTitle of Masters Thesis: Aggressive Shadowing of a Low-Dimensional Model of Atmospheric Dynamics Modeling Earth’s atmospheric conditions is difficult due to the size of the system, and predictions of its future state suffer from the consequences of chaos. As a result, current weather forecast models quickly diverge from observations as uncertainty in the initial state is amplified by nonlinearity. One measure of the strength of a forecast is its shadowing time, the period for which the forecast is a reasonable description of reality. The present work uses the Lorenz ’96 coupled system, a simplified nonlinear model of atmospheric conditions, to extend a recently developed technique for lengthening the shadowing time of a dynamical system. An ensemble of initial states, systematically perturbed using knowledge of the local dynamics, is used to make a forecast. The experiment is then repeated using inflation, whereby the ensemble is regularly expanded along dimensions whose uncertainty is contracting. The first goal of this work is to compare the two forecasts to reality, chosen to be an imperfect version of the same model, and determine whether variance inflation succeeds. The second goal is to establish whether inflation can increase the maximum shadowing time for a single member of the ensemble. In the second experiment the trajectory of reality is known a priori, and only the closest ensemble members are considered at each time step. When inflation is introduced to this technique, it is called stalking. Variance inflation was shown to have the potential to be successful, with the extent dependent upon algorithm parameters (e.g. size of state space, inflation amount). Under idealized conditions, the technique was shown to improve forecasts over 50% of the time. Under these same conditions, stalking also exhibited the potential to be useful. When only the best ensemble members were considered at each time step, the known trajectory could be shadowed for an entire 50-day forecast 50-75% of the time. However, if inflation occurs in directions incommensurate with the true trajectory, inflation can actually reduce stalking times. Thus, utilized appropriately, inflation has the potential to improve predictions of the future state of atmospheric conditions, and possibly other physical systems.Abstract: |

Josh Auerbach, PhDDepartment of Computer Science Currently a Post Doctoral Fellow at the Laboratory of Intelligent Systems at EPFL |

Peter FroncekDegree Received: Graduate Certificate in Complex Systems Currently a Graduate Teaching Assistant at the University of Vermont |

Karim Chichakly, PhDDepartment of Computer Science Advisor, Maggie Eppstein Currently Co-Owner of ieee Systems in Lebanon, NH and Adjunct Faculty at WPI |

Jo Krupa, Masters of Computer ScienceAdvisors, Maggie Eppstein and Donna Rizzo Currently City Engineer for the city of New Haven, CT |

Shreya Mukherjee, Masters of Computer ScienceAdvisors, Maggie Eppstein Research Interest: Genetic Programming Currently a Software Engineer at Data Innovations LLC, S |

Joshua Payne, PhDDepartment of Computer Science Advisors, Maggie Eppstein Currently a Post Doctoral Fellow with Andrea Wagner at the Institute of Evolutionary Biology and Environmental Studies at the University of Zurich |

Paul Haake, Masters of Computer ScienceAdvisors, Maggie Eppstein Currently a Software Development Engineer II at Amazon.com |

Paul BeliveauDegree Earned: Graduate Certificate in Computer Science Adjunct Faculty at Champlain College |