ItemAlgebraic Curves and Their Applications(American Mathematical Society, 2019) Beshaj, Lubjana; Shaska, TonyThis volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics. ItemThe Tactical Considerations of Augmented and Mixed Reality Implementation(Army University Press, 2022) Kallberg, Jan; Beitelman, Victor; Mitsuoka, Victor; Pittman, Jeremiah; Boyce, Michael; Arnold, Todd W.The U.S. Army, NATO armies, and other advanced nations actively seek to implement augmented reality (AR) and mixed reality (MR) support for their operational forces. These platforms are intended to improve tactical awareness, target acquisition, and situational awareness, and also to develop an information upstream for commanders to act upon... ItemToo Late for Russia to Stop the Foreign Volunteer Army(Center for European Policy Analysis CEPA, 2022) Kallberg, JanThe Kremlin makes dark threats about the fate of foreign volunteers captured on the battlefield, but these are likely to rebound. ItemThe West Has Forgotten How to Keep Secrets(Center for European Policy Analysis CEPA, 2022) Kallberg, JanOpen Source Intelligence (OSINT) has had an extraordinary moment in the spotlight thanks to Russia’s invasion of Ukraine. Viewers have been able to see the effects of antitank weapons and the dreadful realities of war in close to real-time. But OSINT, like all other intelligence, cuts both ways — we look at the Russians, and the Russians look at us. But their interest is almost certainly in freely available material that’s far from televisual — the information a Russian war planner can now use from European Union (EU) states goes far, far beyond what Europe’s well-motivated but slightly innocent data-producing agencies likely realize. ItemThe power of sample size calculations that minimize costs(Elsevier BV, 2023-06) Thomas, Diana M.Nearly every nutrition investigator who has designed a study has performed a power calculation to estimate projected sample size. Even more specifically, investigators want to know what the minimal required sample size should be to statistically test a hypothesis. We are interested in the minimal sample size because the larger the sample size, the higher the cost, labor, and effort required to conduct the study. Power calculations do not, however, provide the sample size calculations that minimize costs. Candel and van Breukelen’s publication in this issue of the Journal presents a refreshing, alternative set of rigorous sample size calculations that minimize costs for different types of study designs. ItemThe Distance Centrality: Measuring Structural Disruption In A Network(Naval Postgraduate School, 2018) Roginski, Jonathan W.This research provides an innovative approach to identifying the influence of vertices on the topology of a graph by introducing and exploring the neighbor matrix and distance centrality. The neighbor matrix depicts the “distance profile” of each vertex, identifying the number of vertices at each shortest path length from the given vertex. From the neighbor matrix, we can derive 11 oft-used graph invariants. Distance centrality uses the neighbor matrix to identify how much influence a given vertex has over graph structure by calculating the amount of neighbor matrix change resulting from vertex removal. We explore the distance centrality in the context of three synthetic graphs and three graphs representing actual social networks. Regression analysis enables the determination that the distance centrality contains different information than four current centrality measures (betweenness, closeness, degree, and eigenvector). The distance centrality proved to be more robust against small changes in graphs through analysis of graphs under edge swapping, deletion, and addition paradigms than betweenness and eigenvector centrality, though less so than degree and closeness centralities. We find that the neighbor matrix and the distance centrality reliably enable the identification of vertices that are significant in different and important contexts than current measures. ItemNeglecting regression to themean continues to lead to unwarranted conclusions: Letter regarding “Themagnitude of weight loss induced bymetformin is independently associated with BMI at baseline in newly diagnosed type 2 diabetes: Post-hoc analysis from data ofa phase IV open-labeled trial”(Advances in Clinical and Experimental Medicine, 2019) Hannon, Bridget A.; Thomas, Diana M.; Siu, Cynthia O.; Allison, David B.As the prevalence of type2 diabetes mellitus and obesity increases worldwide, scientifically rigorous research is needed in this field to determine effective interventions for the prevention and treatment of these chronic diseases. In a recent study published in this journal, Zhou et al. conclude that metformin, a drug used for treatment of type 2 diabetes mellitus, can be used effectively for weight loss, and that this effect is even more pronounced in individuals who weigh more at baseline. Unfortunately, we believe these results to be due to the regression to the mean (RTM) phenomenon, which weakens the causal inference proposed in this study. The conclusions of Zhou et al. that metformin is an effective strategy for weight loss in individuals with type2 diabetes mellitus are not substantiated due to the lack of a control group and failure to consider other factors that may have confounded these results. ItemGoodbye Vladivostok, Hello Hǎishēnwǎi!(Center for European Policy Analysis CEPA, 2022) Kallberg, JanIn 1997, the First Opium War officially ended with the British administration and forces leaving Hong Kong. The Second Opium War is still ongoing, since the Russian Federation continues to occupy the Amur region and Outer Manchuria. This land area was extorted from China in 1860 during the Second Opium War, under threat to set Beijing ablaze... ItemDrones Will not Liberate Ukraine – but Tanks Will(Center for European Policy Analysis CEPA, 2022) Kallberg, JanDrones have changed the battlefield, providing additional situation awareness and the ability to strike targets, but their high success rates in the Ukraine war is a result of unique conditions unlikely to be replicated elsewhere. ItemEmergency First Response to a Crisis Event: A Multi-Agent Simulation Approach(Naval Postgraduate School, 2006) Roginski, Jonathan W.Homeland Security Presidential Directive #8 led to the establishment of the National Exercise Program and the Top Officials exercise series to test and evaluate first response agency integration and effectiveness. The last TOPOFF exercise cost $16M and involved over 10,000 people, but did not effectively leverage simulation techniques to make efficient use of resources. This research adapts an existing organizational learning process, integrating low- and high resolution simulation to provide decision support. This process led to the development of a multi-agent simulation methodology for emergency first response, specifically applied to analyze a notional vehicle bomb attack during a festival in the Baltimore Inner Harbor. This simulation demonstrates the potential benefits of low resolution simulation, using efficient experimental design and high-performance computing. Combined, these two ideas result in examining a 48-dimensional response surface and using over 156 CPU centuries of computer time. All experiments were completed in less than three weeks. The analysis of this data set provided insight into several areas, including the importance of standing operating procedures in the early moments of a crisis. Analysis showed that effective procedures may even be more important than the effectiveness of communications devices early in a first response operation. ItemDiscrete Zombie Apocalypse: A Mathematical Modeling Course Project(Informa UK Limited, 2023-04-20) Lee, Andrew C.; Czerniakowski, Frank; McDermott, Kyle C.; Reynolds, JeremyFor undergraduate mathematical modeling courses, a successful semester project can reinforce key learning objectives while enabling creativity and developing critical thinking skills. However, course directors often struggle in developing novel project ideas and balancing the tradeoff between grading burden and project complexity. At the U.S Military Academy, we take an open-ended and discovery-learning approach to the freshman level math modeling project. This article outlines one successful project involving a Zombie Apocalypse scenario along with student responses. To assist the students, we promote flexibility, scaffold the modeling process with in-progress reviews, and train students on how to write concise executive summaries. ItemBest (but oft-forgotten) practices: identifying and accounting for regression to the mean in nutrition and obesity research(Elsevier BV, 2020-02) Thomas, Diana M.; Clark, Nicholas J.; Turner, Dusty; Siu, Cynthia; Halliday, Tanya M.; Hannon, Bridget A.; Kahathuduwa, Chanaka N.; Kroeger, Cynthia M.; Zoh, Roger; Allison, David B.Background: Regression to the mean (RTM) is a statistical phenomenon where initial measurements of a variable in a nonrandom sample at the extreme ends of a distribution tend to be closer to the mean upon a second measurement. Unfortunately, failing to account for the effects of RTM can lead to incorrect conclusions on the observed mean difference between the 2 repeated measurements in a nonrandom sample that is preferentially selected for deviating from the population mean of the measured variable in a particular direction. Study designs that are susceptible to misattributing RTM as intervention effects have been prevalent in nutrition and obesity research. This field often conducts secondary analyses of existing intervention data or evaluates intervention effects in those most at risk (i.e., those with observations at the extreme ends of a distribution). Objectives: To provide best practices to avoid unsubstantiated conclusions as a result of ignoring RTM in nutrition and obesity research. Methods: We outlined best practices for identifying whether RTM is likely to be leading to biased inferences, using a flowchart that is available as a web-based app at https://dustyturner.shinyapps.io/DecisionTreeMeanRegression/. We also provided multiple methods to quantify the degree of RTM. Results: Investigators can adjust analyses to include the RTM effect, thereby plausibly removing its biasing influence on estimating the true intervention effect. Conclusions: The identification of RTM and implementation of proper statistical practices will help advance the field by improving scientific rigor and the accuracy of conclusions. This trial was registered at clinicaltrials.gov as NCT00427193. ItemA Troubling Silence on Prisoners of War(Center for European Policy Analysis CEPA, 2022) Kallberg, JanWith a few exceptions in the Balkans in the 1990s, Europe has not experienced a large number of captured personnel since 1945. The American experience is close to 50 years away, ending with the War in Vietnam. Years of counterinsurgency operations have bred complacency; the notion that potentially thousands of soldiers could become prisoners of war (PoWs) has until the events in Ukraine been seen as unlikely. Preparing soldiers for captivity, confinement and interrogation has also lapsed, and that risks mistakes and unnecessary harm in a conflict. ItemA Potemkin Military? Russia’s Over-Estimated Legions(Center for European Policy Analysis CEPA, 2022) Kallberg, JanDates should not matter very much in war, but May 9 is not a day like any other. For the men in the Kremlin, Victory Day is a chance to burnish their credentials as inheritors of what many Russians still see as their greatest generation — the men and women who paid the price in blood to defeat the Nazi invaders. ItemDefending NATO in the High North(Center for European Policy Analysis CEPA, 2022) Kallberg, JanThe entry of two wealthy and well-defended Nordic states mark a genuinely transformational moment for the alliance in the High North. The decision, which still has to be confirmed by the other 30 member state parliaments, is only the latest self-harming consequence of Vladimir Putin’s largest invasion of Ukraine on February 24, coming just days after the European Union (EU) gave the country candidate status, and NATO pledged more arms... ItemModelling Nuclear Weapon Effects in Wargaming Using Monte Carlo Simulations(United States Military Academy, 2023) Guetzke, Tyler; Withenbury, Alexander; Dugger, Zachary; Kendall, ThomasThe United States Army’s interpretation of nuclear weapon effects needs change and modernization. Wargaming exercises are commonplace in today’s military, however, despite the growing threat of non-strategic nuclear weapons (NSNW), little has been done to inform battlefield commanders on their true effects. Our research seeks to develop a tool for commanders to easily interpret quantifiable effects of a NSNW. Utilizing Monte Carlo simulation, we are developing a new methodology to analyze NSNW effects. Our model allows a commander to calculate the expected unit strength following a NSNW strike which will aid in their operational decision-making ability. The Monte Carlo simulation method for analyzing nuclear effects offers a novel approach to account for variation while giving the commander an analytically interpretable output as descriptive statistics that avoids probabilities. ItemThe New Army Combat Fitness Test: An Opportunity to Improve Recruitment and Retainment(Obesity, 2019) Bigelman, Kevin A.; East, Whitfield B.; Thomas, Diana M.; Turner, Dusty; Hertling, MarkOn July 5, 1950, Lieutenant Colonel Charles Smith led United States soldiers against an advancing North Korea at the Battle of Osan. The US soldiers recently arrived from constabulary duty in Japan, where they had been conducting peacetime service and were not accustomed to Korean mountain combat. The Task Force Smith soldiers became "winded and overwhelmed" as they moved across the hilly terrain, and the Army partly attributed the massive casualties resulting from the action to reduced fitness and increasing obesity... ItemUS Army performance appraisal policy analysis: a simulation optimization approach(Journal of Defense Modeling & Simulation, 2018) Evans, Lee; Bae, Ki-Hwan G.An effective performance appraisal system is critical in identifying officers with the knowledge, skills, and abilities to lead the future military force. The US Army uses a forced distribution performance appraisal system that limits the number of above average evaluations raters can award to their subordinates. Aside from job performance, multiple factors contribute to the rating an individual receives in such systems. These factors include a rater’s span of control (the number of subordinates being rated), the frequency at which individuals change raters, regulatory constraints pertaining to the number of top evaluations a rater can award, and the rater behavior. Using performance appraisal data provided by the US Army Human Resources Command, we develop a discrete-event simulation model that represents Army officers in the current forced distribution performance appraisal system. We then apply ranking and selection simulation optimization techniques to evaluate and optimize controllable input parameters in the simulated system. Our results show the potential of reducing the number of officers not receiving the number of above average evaluations commensurate with their performance level by as much as 24%. The results also further indicate the general applicability of simulation optimization in the fields of manpower modeling and policy analysis.