Defective and Clustered Choosability of Sparse Graphs

An (improper) graph colouring has "defect" $d$ if each monochromatic subgraph has maximum degree at most $d$, and has "clustering" $c$ if each monochromatic component has at most $c$ vertices. This paper studies defective and clustered list-colourings for graphs with given maximum average degree. We prove that every graph with maximum average degree less than $\frac{2d+2}{d+2} k$ is $k$-choosable with defect $d$. This improves upon a similar result by Havet and Sereni [J. Graph Theory, 2006]. For clustered choosability of graphs with maximum average degree $m$, no $(1-\epsilon)m$ bound on the number of colours was previously known. The above result with $d=1$ solves this problem. It implies that every graph with maximum average degree $m$ is $\lfloor{\frac{3}{4}m+1}\rfloor$-choosable with clustering 2. This extends a result of Kopreski and Yu [Discrete Math., 2017] to the setting of choosability. We then prove two results about clustered choosability that explore the trade-off between the number of colours and the clustering. In particular, we prove that every graph with maximum average degree $m$ is $\lfloor{\frac{7}{10}m+1}\rfloor$-choosable with clustering $9$, and is $\lfloor{\frac{2}{3}m+1}\rfloor$-choosable with clustering $O(m)$. As an example, the later result implies that every biplanar graph is 8-choosable with bounded clustering. This is the best known result for the clustered version of the earth-moon problem. The results extend to the setting where we only consider the maximum average degree of subgraphs with at least some number of vertices. Several applications are presented

Simulation Video Games as Learning Tools: An Examination of Instructor Guided Reflection on Cognitive Outcomes

Simulation video games potentially offer students the opportunity to participate in activities designed to bring about higher order thinking. Gee (2005b, 2007) elucidates that without the guidance of instructors, humans involved in a simulation experience have a high probability of finding creative but spurious patterns and generalizations that send learners down miseducative paths. The focus of this study is an examination of the function of instructor guided reflection and prior participant interest and exposure to video games in promoting affective and cognitive learning during participant use of single and multiplayer simulation video games in the classroom. One hundred twenty- eight students enrolled in World History classes at a suburban high school located in the Southeastern United States participated in this research study. Participants completed a survey of their interest and prior exposure to video games, played a tutorial of the simulation video game, played a single player or multiplayer version of the game with or without instructor guided reflection, and completed a posttest of reasoning and knowledge ability. The researcher used independent samples t tests, analysis of variance, and descriptive statistical analysis in combination with qualitative methods outlined by Miles and Huberman (1994) to analyze the data. Thomas (2003) described the mixed methodology used to analyze and interpret the data in this research study. Quantitative analysis of the data revealed that participants who engaged in both reflection and multiplayer groups scored significantly higher on posttest of reasoning ability at the .05 level. Furthermore, qualitative analysis revealed that participants in the multiplayer and reflection treatment groups were more likely to be engaged in the lesson, participate in more cognitive discussions, and made more connections to the large context of the lesson. Participants with a high level of prior interest in video games scored significantly higher on a posttest of reasoning ability at the .05 level of significance and were more likely to participate actively during the lesson. The findings from this study suggest the need for teaching educators to utilize reflective and collaborative practices in the incorporation of digital technology in the classroom

Near-Shortest and K-Shortest Simple Paths

2005, Networks, 46, pp. 98-109

Mints not Mines: a macroscale investigation of Roman silver coinage

Although silver coins have been investigated through the lens of geological provenance to locate argentiferous ore deposits exploited in their production, we consider that this avenue of research may be a cul-de-sac, especially for studies that rely heavily on deciphering lead and silver isotope signatures that may have been altered by the addition of lead and copper (and their associated impurities) during silver refining and debasement, and by ancient recycling of coinage. Instead, we focus our attention on mints, by analysing the compositions of over 1000 silver coins from the early 1st century BC to AD 100. We propose that lead from the west Mediterranean was used exclusively to refine silver at mints in the West, and that an unknown lead supply (possibly from Macedonia), used in the East by the Late Seleucid ruler Philip I Philadelphus and later Mark Antony, was mixed with western lead. Extensive mixing of lead and/or silver coins is particularly evident under Nero and Vespasian, aligning with historically attested periods of recycling following currency reform. We further propose that coins minted in the kingdom of Mauretania used different lead and silver sources from the majority of coins minted in the western Mediterranean, and that silver coins minted at Tyre are derived from silver refined in the west Mediterranean. Coinage minted at Alexandria is consistent with debasement of recycled Roman denarii, thereby suggesting that denarii were deliberately removed from circulation to mint tetradrachms during the early Imperial Roman period

Crisis? What crisis? Recycling of silver for Roman Republican coinage

Dated measurements of lead pollution in deep Greenland ice have become a useful proxy to monitor historical events because interruptions in lead-silver production result in fluctuations in lead emissions. However, the application of the lead emission record has not perhaps received the attention it deserves because of the difficulty in connecting macroscale events, such as wars and plagues, to their economic repercussions. For instance, although debasement of silver coinage with copper has been proposed as a reasonable response to interruptions in silver production, reductions in fineness of the silver denarius, the backbone of Roman coinage from the late third century BC, are not always coincident with decreases in lead deposited in Greenland. We propose that extensive recycling of silver that is evident in the numismatic record can better explain drops in lead emissions and, thereby, the responses to major historical events, such as warfare in the silver-producing areas of the Iberian Peninsula and southern France during the middle and late Roman Republic

Response to comment of Albarède and colleagues

Our purpose is to better understand the actions and behaviours of people in the past, often with a focus on ancient economies, and we are willing to use tools from any discipline that allow us to explore these issues. This is why it is so important that the limitations of techniques applied to archaeology are presented as explicitly as their utility

A stochastic program for optimizing military sealift subject to attack

We describe a stochastic program for planning the wartime, sealift deployment of military cargo subject to attack. The cargo moves on ships from US or allied seaports of embarkation through seaports of debarkation (SPODs) near the theater of war where it is unloaded and sent on to final , in-theater destinations. The question we ask is: Can a deployment-planning model, with probabilistic knowledge of the time and location of potential enemy attacks on SPODs, successfully hedge against those attacks? That is, can this knowledge be used to reduce the expected disruption caused by such attacks? A specialized, multi-stage stochastic mixed-integer program is developed and answers that question in the affirmative. Furthermore, little penalty is incurred with the stochastic solution when no attack occurs, and worst-case scenarios are better. In the short term, insight gained from the stochastic-programming approach also enables better scheduling using current rule-based methods

Monte Carlo Bounding Techniques for Determining Solution Quality in Stochastic Programs

Operations Research Letters, 24, pp. 47-56

Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators

We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors characteristic of a variety of considerably more complicated models. In addition, we study the microscopic basis of synchronization above threshold and detail the counterintuitive subtleties relating measurements of time averaged frequencies and mean field oscillations. Most notably, we observe a state of suprathreshold partial synchronization in which time-averaged frequency measurements from individual oscillators do not correspond to the frequency of macroscopic oscillations observed in the population