The complexity of counting poset and permutation patterns

We introduce a notion of pattern occurrence that generalizes both classical permutation patterns as well as poset containment. Many questions about pattern statistics and avoidance generalize naturally to this setting, and we focus on functional complexity problems -- particularly those that arise by constraining the order dimensions of the pattern and text posets. We show that counting the number of induced, injective occurrences among dimension 2 posets is #P-hard; enumerating the linear extensions that occur in realizers of dimension 2 posets can be done in polynomial time, while for unconstrained dimension it is GI-complete; counting not necessarily induced, injective occurrences among dimension 2 posets is #P-hard; counting injective or not necessarily injective occurrences of an arbitrary pattern in a dimension 1 text is #P-hard, although it is in FP if the pattern poset is constrained to have bounded intrinsic width; and counting injective occurrences of a dimension 1 pattern in an arbitrary text is #P-hard, while it is in FP for bounded dimension texts. This framework easily leads to a number of open questions, chief among which are (1) is it #P-hard to count the number of occurrences of a dimension 2 pattern in a dimension 1 text, and (2) is it #P-hard to count the number of texts which avoid a given pattern?Comment: 15 page

Limits of geometries

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transform into another. We develop a general framework to describe transitions in the context that both geometries involved are represented as sub-geometries of a larger ambient geometry. Specializing to the setting of real projective geometry, we classify the geometric limits of any sub-geometry whose structure group is a symmetric subgroup of the projective general linear group. As an application, we classify all limits of three-dimensional hyperbolic geometry inside of projective geometry, finding Euclidean, Nil, and Sol geometry among the limits. We prove, however, that the other Thurston geometries, in particular $\mathbb{H}^2 \times \mathbb{R}$ and $\widetilde{\operatorname{SL}_2 \mathbb{R}}$, do not embed in any limit of hyperbolic geometry in this sense.Comment: 40 pages, 2 figures. new in v2: figure 2 added, minor edits to Sections 1,2,

Detecting Starting Point Bias in Dichotomous-Choice Contingent Valuation Surveys

We examine starting point bias in CV surveys with dichotomous choice payment questions and follow-ups, and double-bounded models of the WTP responses. We wish to investigate (1) the seriousness of the biases for the location and scale parameters of WTP in the presence of starting point bias; (2) whether or not these biases depend on the distribution of WTP and on the bids used; and (3) how well a commonly used diagnostic for starting point bias—a test of the null that bid set dummies entered in the right-hand side of the WTP model are jointly equal to zero—performs under various circumstances. Because starting point bias cannot be separately identified in any reliable manner from biases caused by model specification, we use simulation approaches to address this issue. Our Monte Carlo simulations suggest that the effect of ignoring starting point bias is complex and depends on the true distribution of WTP. Bid set dummies tend to soak up misspecifications in the distribution assumed by the researcher for the latent WTP, rather than capturing the presence of starting point bias. Their power in detecting starting point bias is low.Anchoring, Dichotomous choice contingent valuation, Starting point bias, Double-bounded models, Estimation bias

Korea\u27s Explosive Declaration of Independence: Complex Influences Leading Up to the March First Movement of 1919

The March First Movement of 1919 was a widespread independence movement in colonized Korea. This Movement began with the reading of Korea’s Declaration of Independence in a restaurant in Seoul and quickly spread throughout the country, amassing over two million Korean participants who demonstrated in 1500 protests. This significant Movement in Korean history resulted from a culmination of factors, but is often defined by modern historians as an effort against Japan’s oppressive colonization. However, this simplified description of the Movement’s origins understates the complex influences that lead to this Movement. This work then studies how this Movement came to be: specifically, Japan’s influence was never welcomed or accepted by Korea, so a combination of harsh Japanese colonization practices, anti-imperial global ideology after WWI, and the establishment of Protestant missionaries in Korea all contributed to the development and creation of an independence movement that quickly spread throughout the entire country. Each one of these influences helped determine when the Movement occurred, and why it occurred. Because the complexity of this Movement is better understood through a consideration of all its major influences, this work contributes to the contemporary state of scholarly work on Korea by offering a comprehensive but critical history into the Movement’s inspirations

Willingness to Pay for Mortality Risk Reductions: Does Latency Matter?

Using results from two contingent valuation surveys conducted in Canada and the United States, we explore the effect of a latency period on willingness to pay (WTP) for reduced mortality risk using both structural and reduced form approaches. We find that delaying the time at which the risk reduction occurs by 10 to 30 years significantly reduces WTP for respondents aged 40 to 60 years. Additionally, we estimate implicit discount rates equal to 8% for Canada and 4.5% for the United States—both well within the range established previously in the literature.value of a statistical life, mortality risks, cost–benefit analysis

Change in active travel and changes in recreational and total physical activity in adults: longitudinal findings from the iConnect study.

BACKGROUND: To better understand the health benefits of promoting active travel, it is important to understand the relationship between a change in active travel and changes in recreational and total physical activity. METHODS: These analyses, carried out in April 2012, use longitudinal data from 1628 adult respondents (mean age 54 years; 47% male) in the UK-based iConnect study. Travel and recreational physical activity were measured using detailed seven-day recall instruments. Adjusted linear regression models were fitted with change in active travel defined as 'decreased' (15 min/week) as the primary exposure variable and changes in (a) recreational and (b) total physical activity (min/week) as the primary outcome variables. RESULTS: Active travel increased in 32% (n=529), was maintained in 33% (n=534) and decreased in 35% (n=565) of respondents. Recreational physical activity decreased in all groups but this decrease was not greater in those whose active travel increased. Conversely, changes in active travel were associated with commensurate changes in total physical activity. Compared with those whose active travel remained unchanged, total physical activity decreased by 176.9 min/week in those whose active travel had decreased (adjusted regression coefficient -154.9, 95% CI -195.3 to -114.5) and was 112.2 min/week greater among those whose active travel had increased (adjusted regression coefficient 135.1, 95% CI 94.3 to 175.9). CONCLUSION: An increase in active travel was associated with a commensurate increase in total physical activity and not a decrease in recreational physical activity