Three Partition Refinement Algorithms

We present improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering. Our double lexical ordering algorithm uses a new, efficient method for unmerging two sorted sets

Optimal Equivalence Testing in Exponential Families

We develop uniformly most powerful unbiased (UMPU) two sample equivalence test for a difference of canonical parameters in exponential families. This development involves a non-unique reparameterization. We address this issue via a novel characterization of all possible reparameterizations of interest in terms of a matrix group. Furthermore, our procedure involves an intractable conditional distribution which we reproduce to a high degree of accuracy using saddle point approximations. The development of this saddle point-based procedure involves a non-unique reparameterization, but we show that our procedure is invariant under choice of reparameterization. Our real data example considers the mean-to-variance ratio for normally distributed data. We compare our result to six competing equivalence testing procedures for the mean-to-variance ratio. Only our UMPU method finds evidence of equivalence, which is the expected result. We also perform a Monte Carlo simulation study which shows that our UMPU method outperforms all competing methods by exhibiting an empirical significance level which is not statistically significantly different from the nominal 5% level for all simulation settings

The Hodrick-prescott Filter: A Special Case of Penalized Spline Smoothing

We prove that the Hodrick-Prescott Filter (HPF), a commonly used method for smoothing econometric time series, is a special case of a linear penalized spline model with knots placed at all observed time points (except the first and last) and uncorrelated residuals. This equivalence then furnishes a rich variety of existing data-driven parameter estimation methods, particularly restricted maximum likelihood (REML) and generalized cross-validation (GCV). This has profound implications for users of HPF who have hitherto typically relied on subjective choice, rather than estimation, for the smoothing parameter. By viewing estimates as roots of an appropriate quadratic estimating equation, we also present a new approach for constructing confidence intervals for the smoothing parameter. The method is akin to a parametric bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and provides a fast and accurate alternative to exact methods, when they exist, e.g. REML. More importantly, it is also the only computationally feasible method when no other methods, exact or otherwise, exist, e.g. GCV. The methodology is demonstrated on the Gross National Product (GNP) series originally analyzed by Hodrick and Prescott (1997). With proper attention paid to residual correlation structure, we show that REML-based estimation delivers an appropriate smooth for both the GNP series and its returns

Heat-Transfer and Pressure Measurements on a Flat-Face Cylinder at a Mach Number Range of 2.49 to 4.44

Heat-transfer coefficients and pressure distributions were obtained on a 4-inch-diameter flat-face cylinder in the Langley Unitary Plan wind tunnel. The measured stagnation heat-transfer coefficient agrees well with 55 percent of the theoretical value predicted by the modified Sibulkin method for a hemisphere. Pressure measurements indicated the dimensionless velocity gradient parameter r du\ a(sub t) dx, where x=0 at the stagnation point was approximately 0.3 and invariant throughout the Mach number range from 2.49 to 4.44 and the Reynolds number range from 0.77 x 10(exp 6) to 1.46 x 10(exp 6). The heat-transfer coefficients on the cylindrical afterbody could be predicted with reasonable accuracy by flat-plate theory at an angle of attack of 0 deg. At angles of attack the cylindrical afterbody stagnation-line heat transfer could be computed from swept-cylinder theory for large distances back of the nose when the Reynolds number is based on the distance from the flow reattachment points

Topological Data Analysis for Object Data

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes to vectorize object data and perform statistical analysis. We apply to this pipeline to some biological images that were previously shown to be challenging to study using shape theory. Surprisingly, the most persistent features are shown to be "topological noise" and the statistical analysis depends on the less persistent features which we refer to as the "geometric signal". We also describe the first steps to a new approach to using topology for object data analysis, which applies topology to distributions on object spaces.Comment: 16 pages, 12 figure

Exploring Stakeholders’ Perceptions of Urban Growth Scenarios for Metropolitan Boston (USA): The Relationship Between Urban Trees and Perceived Density

Achieving multiple goals rather than trading one goal off for another is the essence of sustainability. Visualizing alternative futures in a participatory planning process helps disentangle complex planning issues particularly when stakeholders may perceive key goals as imposing potential tradeoffs, such as increased housing for a growing population and availability of green space. This study explored the effects of using visualization and scenarios as planning tools in a workshop with stakeholders in the Boston Metro Area, Massachusetts (USA), in achieving multiple benefits of sustainable future growth of the region. We applied mixed methods sequential explanatory design and a survey instrument with a landscape preference survey designed to garner stakeholders\u27 preference and acceptability of perceived urban density versus urban greening in four future growth scenarios reflecting multiple goals in sustainability. The results of the landscape preference survey demonstrated that increasing tree canopy appears to ameliorate the low ratings of high-rise buildings for the region\u27s urban development. In addition, the scenario planning process, especially the use of small group discussions, represented an effective tool in facilitating stakeholders\u27 discussion about achieving the multiple benefits of the three goals of sustainability: Environment, Economy, Equity. This study provided theoretical and applied insights for planners in the use of visualization and scenario planning methodologies to engage stakeholders in the participatory planning process. It revealed the potential for a policy decision shift among stakeholders in the Boston region, namely that higher density urban development would likely be more acceptable to them when combined with a simultaneous increase in tree canopy cover. Through practices like these, stakeholders are more likely to consider policies and designs that embrace a variety of goals for their community’s future instead of simplistically placing one goal in opposition to another or trading them off against each other

Planning for Change in the Boston Metropolitan Area (USA): Exploring the relationship between urban greening and socio-economic processes

Global population growth is increasingly concentrated in urban areas, degrading natural resources and threatening long-term sustainability of both human and biotic systems. Even in a developed nation like the United States, urban areas are expected to double in population and land area over the next fifty years (UNFPA, 2007). In order to plan for a more sustainable urban future, there is a need to understand the relationship between the socio-economic forces that are driving land use and land cover change, and the resulting impacts upon the ecosystem state and structure of the urban forest (Colding, 2007). In particular, this study will focus upon the role of urban greening projects in preserving urban open space, restoring ecological processes, and building stewardship of urban nature by local residents. Urban greening is a spatially distributed form of land use-land cover change with diverse drivers and potential outcomes. In this framework changes in ecosystem state and structure, including the delivery of ecosystem services and other benefits to human well-being, are recognized as the aggregate outcomes of many local acts (e.g. tree-planting, riparian restoration, and community gardening). Each can be treated as opportunistic experiments, with testable predictions regarding their consequences, (e.g., for biodiversity, air quality, and fluxes in water and nutrients). From this perspective urban greening can be placed in the context of broader scale processes of urban-associated land use/land cover change. In order to explore these issues, an interdisciplinary team was formed to develop a long-term research study for the Boston Metropolitan Area to provide a model for scientific investigation and to address the critical needs of urban communities

Sustaining Urban Forests in Post-Industrial Cities: Place Attachment, Ecology, and Stewardship Potential

People value urban green spaces for enjoying nature and socializing with friends, family, and other park users. However, overgrown urban forests without clear access points can be perceived as dark, dangerous, and wild places. As many cities experience reduced budgets, they struggle to maintain green spaces established in more prosperous times. We conducted a descriptive analysis of how constrained parks budgets and subsequent city decisions about maintenance are associated with patterns of forest use, place attachment, and social capital and their impacts on the potential for stewardship of forested parks. We selected Springfield, Massachusetts for our study because it is typical of former industrial cities with highly constrained budgets. We used both qualitative and quantitative analyses of field observations and interviews with park users and nearby residents. We found that access to forests and park use were the strongest predictors of place attachment, and that on-site services, access, and maintenance level were the strongest predictors of use rather than surrounding socioeconomic conditions. Users valued the ecology of the sites, even while park managers highlighted invasive plants as a major maintenance issue. Even though many sites had low levels of use, there remains a strong sense of ownership, community, and safety. Taken together, there is a great deal of untapped stewardship potential in the city, with few organized avenues for users and residents to engage in stewardship. The findings support the hypothesized ‘virtuous circle’ whereby higher levels of maintenance and access beget greater use and attachment, which motivates stewardship. Alternatively, the more neglected forested parks become, the less use they will have, and the more unknown and unloved they will become. In high use sites, some outreach may be all that is needed to move into the ‘virtuous circle,’ while greater interventions will be needed in low use sites with no facilities, and these sites are the ones at greatest risk. Since the long-term sustainability of urban forests requires that local residents appreciate, use, and steward them, Springfield and other post-industrial cities need to find creative models for supporting greater involvement of residents in park stewardship while recognizing these residents frequently inhabit communities under stress

Scenario Planning for the Boston Metropolitan Region: Exploring Environmental and Social Implications of Alternative Futures

The Boston Metropolitan Area Urban Long-term Ecological Research Area (BMA-ULTRA-EX) Project is an interdisciplinary project that is studying the effects of socio-economic and biophysical drivers on urban ecosystems. The Boston region is experiencing low-density urban sprawl (suburbanization) on the rural-urban fringes of the metropolitan area that is creating environmental impacts to natural resources. At the same time, central cities such as Boston are seeing disinvestment in some low-income neighborhoods causing property abandonment, along with limited infill development (densification) near the commercial core and transit hubs. These competing socio-economic forces of suburbanization, densification, and disinvestment have environmental implications for urban ecosystems, including urban forest canopy, water quantity and quality, and biodiversity. Landscape planning initiatives to address these issues will require a pro-active approach to concentrating development on currently built lands and in the suburban fringe to protect forests, farms and other natural resources, while greening and enhancing ecosystem services in the current high-density urban core. It is within this landscape planning setting that the research team used a stakeholder- driven process to develop a set of four planning scenarios to explore the future of the region. This paper will describe the planning process with stakeholders to develop these plans, along with the preliminary analyses. It will conclude with insights for other landscape planners engaged in scenario planning