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Reconnect 2023 Workshop: Exploring Risk Assessment

Reconnect 2023 focused on Risk Assessment, emphasizing the importance of identifying, analyzing, and preparing for potential risks, such as natural or man-made disasters, to ensure organizational continuity and the well-being of stakeholders. The workshop explored the importance of understanding vulnerabilities and possible impacts on organizations and people and prescribing control measures and contingency plans to minimize potential repercussions.

The workshop reviewed traditional methods and tools for risk assessment across different risks and hazards, using real-world case studies to illustrate practical applications, as shared by SENTRY researchers. The following modules are the direct outcome of discussions and insights from the 2023 workshop.

SENTRY Educational Modules

An Introduction to Centrality Measures with a Transportation Network Defense Exercise

This module serves as a resource for introductory discrete math courses. Tailored for first- and second-year college students, it seamlessly integrates into discrete math courses with an emphasis on graph theory. Prior knowledge in precalculus, basic matrices, and sigma notation is recommended. The objectives encompass introducing graphs, measures of centrality, and their application in real-world scenarios such as soft target defense and natural disaster response.

Centrality Measures Module

Block Maximum Techniques and River Flooding

This module introduces Block Maximum Techniques in Statistics, utilizing river flooding as a practical example. It emphasizes understanding the probabilities associated with events like 100-year and 500-year floods, aiding students in grasping risk assessment within their communities. Class activities are suggested to familiarize students with river flooding risk assessment, along with instructions for data analysis using Excel, R, and Minitab.

Statistics Module

Big Blow Can Blow the Budget

This module serves as a mathematical and quantitative literacy activity focused on data interpretation, leveraging information from various sources, including the Federal Emergency Management Agency’s National Risk Index tool, the National Oceanic and Atmospheric Administration’s Historical Hurricane Tracks tool, and the Natural Hazards Research and Applications Information Center’s Children and Disasters Special Collection of research.

Budget Analysis Module

Investigating Risk in Our Environment

This module harnesses FEMA’s National Risk Index interactive map as a captivating tool for exploring risk areas across the United States. Through its user-friendly visual interface, students delve into patterns in risk-related variables, fostering critical analysis of their interrelationships and personal relevance. Tailored for first-year students in Math Literacy or Quantitative Reasoning courses, the module cultivates skills in pattern recognition, critical thinking, and quantitative analysis.

Investigating Risk Module

Neighborhood Walk

This module introduces undergraduates across a variety of disciplines to the vital field of risk assessment. Drawing upon students’ life experiences, this module challenges students to identify soft targets in their neighborhood, identify their vulnerabilities, and consider how to protect them from natural and manmade threats. They will analyze and display the foot traffic data they gather in order to determine the time of day and day of the week when their facility has highest occupancy and determine an evacuation plan.

Neighborhood Walk Module

Transportation Network Risk and Disruption

This module offers an introduction to analyzing the vulnerability of transportation systems through graph or network modeling, employing fundamental concepts from graph theory. It covers defining and illustrating measures of node centrality, which are pivotal for assessing the susceptibility of transportation networks to failures or attacks. Geared towards undergraduate students in mathematics, engineering, or environmental science, the module aims to familiarize learners with modeling threats to transportation networks efficiently.

Transportation Risk Module

Reconnect 2022 Workshop: Optimization

Reconnect 2022 explored the topic of optimization, a concept pervasive in daily decision-making. The broad field of “optimization” equips us with tools to tackle complex problems in diverse areas, such as biology and finance. These tools enhance our lives through efficient supply chains, improved traffic management, and secure power grids. Over time, mathematical optimization has advanced from handling hundreds of variables to over a million, with widely available solvers for linear, integer, and nonlinear programming.

The workshop covered classic linear and integer programming methods and showcased real-world applications like disaster resource allocation, as shared by SENTRY researchers. The following modules are the direct outcome of discussions and insights from the 2022 workshop.

SENTRY Educational Modules with Professional Development

String Art: Creating, Constructing, and Computing

This module includes an introduction to String Art and the work of Mary Everest Boole and then an application of optimization using string art in differential calculus. It is designed to be flexible in its deployment in the classroom. The first part requires no prerequisite knowledge and is an ideal opportunity to highlight marginalized mathematicians while engaging a general education audience in finding patterns related to modular arithmetic. It is formatted as a guided worksheet for student use. The second part is a research question using Desmos and is formatted to guide the instructor supervising the research project. The module in its entirety is appropriate for a Calculus I audience to demonstrate another use for tangent lines that also provides an example of optimization beyond the traditional single-variable calculus optimization problems.

String Art Module

Legos Optimization

We seek to introduce the field of optimization to these students through an engaging activity that both reinforces concepts from Linear Algebra and develops a conceptual framework that will be useful for students who go on to study optimization in a later course. After a fun, hands-on activity, we introduce optimization modeling and a simple (albeit computationally expensive) algorithm for solving linear optimization models, commonly called Linear Programs or LPs, with bounded feasible regions. The algorithm relies on the basic geometry of systems of linear inequalities. The ideas in this simple algorithm are fundamental to the Simplex Method, the linear optimization algorithm that is implemented in commercial optimization solvers and that is typically taught in a first course in optimization.

Legos Optimization Module

The Simplex Algorithm

The simplex algorithm is a common method of solving linear programs. This module will define common terms used for linear programs; provide a step by step explanation of the method; provide a two dimensional graphical interpretation of the method; and demonstrate a free software tool that replicates the simplex method. In linear algebra, the goal is to find the point that satisfies a set of equations. In linear programs, we have a set of equations that form a feasible space. Any point within that space satisfies those constraints. Another function is introduced where the goal is to maximize or minimize its value. This function is called the objective. So, the goal is to find the best solution from that set of solutions in the feasible space.

Simplex Algorithm Module

SENTRY Educational Modules

Rank, Predict, Program, Play, Repeat: An Introduction to Linear Programming

This module is aimed to provide students beginning Linear Algebra an opportunity to play with advanced ideas of optimization and linear programming, typically reserved for a course in Optimization or Operations Research. The module builds upon introductory Linear Algebra ideas and implements code in MATLAB (using the Symbolic and Optimization Toolboxes) to allow students the ability to explore complex systems through framed examples and research questions. No previous knowledge of MATLAB or programming is required. It can be used as a classroom exercise or an out-of-class project.

Linear Programming Module

Data Analytics Using Linear Programming and the AMPL Algebraic Modelling Language

Data analytics explores information contained in data sets. We start from building simple linear integer programming models, then use nonlinear and linear programming to find the optimal parameter values by minimizing the error between the observed data and the predicted results. We utilize the algebraic modeling language AMPL to build our models and then call a solver like CPLEX to find optimizers to our models. The module will introduce students to AMPL and optimization through several examples of increasing complexity.

Data Analytics Module

Simplex Introduction to Optimization from Theory to Data

The mathematical concept of optimization is the one that is used in everyday life constantly. Almost every situation (financial, economic, business, etc.) can be modeled as an optimization problem. The mathematical field of optimization offers various principles and methods for solving quantitative problems that require maximizing or minimizing a quantity. This module aims to introduce some of these methods and algorithms (such as the linear optimization and the simplex algorithm) to an undergraduate audience. Specific class activities are suggested to be performed that will help students become familiar with the optimization in real-life problems.

Simplex Module