Research in Mathematics and Public Policy (Association for Women in Mathematics Series Book 23)

This volume features a variety of research projects at the intersection of mathematics and public policy. The topics included here fall in the areas of cybersecurity and climate change, two broad and impactful issues that benefit greatly from mathematical techniques. Each chapter in the book is a mathematical look into a specific research question related to one of these issues, an approach that offers the reader insight into the application of mathematics to important public policy questions. The articles in this volume are papers inspired by a Workshop for Women in Mathematics and Public Policy, held January 22-25, 2019 at the Institute for Pure and Applied Mathematics and the Luskin Center at the University of California, Los Angeles. The workshop was created to promote and develop women at all levels of their careers as researchers in mathematics and public policy. The idea was modeled after other successful Research Collaboration Conferences for Women, where junior and senior women come together at week-long conferences held at mathematics institutes to work on pre-defined research projects. The workshop focused on how mathematics can be used in public policy research and was designed to foster collaborative networks for women to help address the gender gap in mathematics and science. Preface 7 Contents 9 Exploring the Application of Machine Learning for Downscaling Climate Projections 10 1 Introduction 11 2 Data and Methods 13 2.1 Description of Datasets Used 14 2.2 Machine Learning Techniques 15 2.3 Data Preparation 16 3 Results 18 3.1 Experiment 1: Predicting Training Data 19 3.2 Experiment 2: Predicting ERAi Data 20 3.3 Experiment 3: Predicting Weather Station Data 21 4 Discussion and Conclusions 23 References 25 Approaches to Analyzing the Vulnerability of Community Water Systems to Groundwater Contamination in Los Angeles County 27 1 Introduction 28 2 Workshop Objectives 29 3 Data Cleaning and Processing 29 4 Method Selection and Description 31 5 Discussion 34 References 35 The Measurement of Disaster Recovery Efficiency Using Data Envelopment Analysis: An Application to Electric Power Restoration 37 1 Introduction 37 2 Previous Literature Assessing Power Restoration Performance 38 3 Methodology 41 3.1 Framework 41 3.2 Empirical Strategy 41 3.2.1 Stage 1: Radial Super-Efficiency DEA Method 42 3.2.2 Stage 2: Environmental Harshness 43 3.2.3 Stage 3: Adjusted Super-Efficiency DEA Model 44 3.3 Sample and Variables 44 3.3.1 Output Variables 45 3.3.2 Input Variables 45 3.3.3 Environmental Variables 45 4 Results 48 4.1 Stage 1 Super-Efficient Values 48 4.2 Stage 2 48 4.3 Stage 3 Final Super-Efficiency Values 48 5 Discussion 51 References 53 Transparency Tools for Fairness in AI (Luskin) 55 1 Introduction 56 1.1 The Toolkit 58 1.2 Prior Fairness Definitions and Our Contributions 59 1.3 Additional Related Work 62 1.4 Organization 63 2 Preliminaries 63 3 Controlled Fairness 64 3.1 Algorithm 1: Synthetic Data via Selective Risk Adjustment 66 3.2 Algorithm 2: Synthetic Data via Risk Based Flipping 69 3.3 Choice of Dataset 70 3.4 Type of Models for Our Algorithms 73 3.5 Experimental Result 75 4 Fairness via Classification Parity 79 4.1 Classification Parity 80 4.2 With Prior Knowledge of the Protected Attribute 81 4.3 Without Prior Knowledge of the Protected Attribute 82 4.4 Experimental Results 83 4.4.1 Feature Preprocessing 83 4.4.2 With Prior Knowledge 84 4.4.3 Without Prior Knowledge 85 References 87 The Hidden Price of Convenience: A Cyber-Inclusive Cost-Benefit Analysis of Smart Cities 89 1 Background and Introduction 90 2 A Hypothetical Catastrophe 92 2.1 A Concocted Catastrophe 93 3 Analysis and Mathematical Approach 95 4 Research Process and Resources 97 5 Conclusion 98 6 Future Research 99 References 99 Security of NewHope Under Partial Key Exposure 101 1 Introduction 102 1.1 Leaky RLWE Assumptions–Search and Decision Versions 103 1.2 Our Results 103 1.3 Technical Overview 105 1.3.1 Overview of NewHope Algorithm 105 1.3.2 Resilience of NewHope to Partial Key Exposure 105 1.4 Related Work 106 2 Preliminaries 107 2.1 Lattices and Background 108 2.2 Volume of Hypercube Clipped by One Hyperplane 109 2.3 Algebraic Number Theory 109 2.4 Ring of Integers and Its Ideals 110 2.5 Ring-LWE 111 2.6 Number Theoretic Transform (NTT) 111 2.7 Min-Entropy and Average Min-Entropy 112 3 Search and Decisional RLWE with Leakage 112 4 Leakage Analysis of New Hope Key Exchange 113 4.1 New Hope Key Exchange Scheme 113 4.2 Security with Auxiliary Inputs 116 4.3 Instantiating the Parameters 129 4.4 On the Non-generic Part of the Analysis 130 References 130 Front Matter ....Pages i-ix Exploring the Application of Machine Learning for Downscaling Climate Projections (Kristin Van Abel, Amanda Back, M. Kathleen Brennan, Oriana S. Chegwidden, Mimi Hughes, Marielle Pinheiro et al.)....Pages 1-17 Approaches to Analyzing the Vulnerability of Community Water Systems to Groundwater Contamination in Los Angeles County (Michelle E. Miro, Kelsea Best, Nur Kaynar, Rachel Kirpes, Aisha Najera Chesler)....Pages 19-28 The Measurement of Disaster Recovery Efficiency Using Data Envelopment Analysis: An Application to Electric Power Restoration (Priscillia Hunt, Kelly Klima)....Pages 29-46 Transparency Tools for Fairness in AI (Luskin) (Mingliang Chen, Aria Shahverdi, Sarah Anderson, Se Yong Park, Justin Zhang, Dana Dachman-Soled et al.)....Pages 47-80 The Hidden Price of Convenience: A Cyber-Inclusive Cost-Benefit Analysis of Smart Cities (Ummugul Bulut, Emily Frye, Jillian Greene, Yuanchun Li, Mary Lee)....Pages 81-92 Security of NewHope Under Partial Key Exposure (Dana Dachman-Soled, Huijing Gong, Mukul Kulkarni, Aria Shahverdi)....Pages 93-125