Clustering is the unsupervised classification of patterns into groups, which is easy provided the data of patterns are consistent. However, real data are almost always tempered with inconsistencies, which make it a hard problem, and actually, the most widely studied formulations, correlation clustering and hierarchical clustering, are both NP-hard. In the graph representation of data, inconsistencies also frequently present themselves as cycles, also called deadlocks, and to break cycles by removing vertices is the objective of the classical feedback vertex set (FVS) problem. This dissertation studies the three problems, correlation clustering, hierarchical clustering, and disjoint-FVS (a variation of FVS), from a kernelization approach. A kernelization algorithm in polynomial time reduces a problem instance provably to speed up the further processing with other approaches. For each of the problems studied, an efficient kernelization algorithm of linear or sub-quadratic running time is presented. All the kernels obtained in this dissertation have linear size with very small constants. Better parameterized algorithms are also designed based on the kernels for the last two problems. Finally, some concluding remarks on possible directions for future research are briefly mentioned.

The FVS-Sn model was developed by the USDA Forest Service to project and report forest growth and yield predictions for the Southern United States. It is able to project forest growth and yield for different forest types and management prescriptions, but it is a relatively new, complex, and untested model. These limitations notwithstanding, FVS-Sn once tested and validated could meet the critical need of a comprehensive growth and yield model for the mixed hardwood forests of the southern Appalachian region. In this study, sensitivity analyses were performed on the FVS-Sn model using Latin hypercube sampling. Response surfaces were fitted to determine the magnitudes and directions of relationships between FVS-Sn model parameters and predicted 10-year basal area increment. Model sensitivities were calculated for five different test scenarios for both uncorrelated and correlated FVS-Sn input parameters and sub-models. Predicted 10-year basal area increment was most sensitive to parameters and sub-models related to the stand density index and, to a lesser degree, the large tree diameter growth sub-model. The testing procedures and framework developed in this study will serve as a template for further evaluation of FVS-Sn, including a comprehensive assessment of model uncertainties, followed by a recalibration for southern Appalachian mixed hardwood forests. / Master of Science

In order to fully understand the magnitude of the benefits that forests provide, it is crucial to understand the full suite of ecosystem services that they offer. A southern Appalachian red spruce-Fraser fir forest was intensively analyzed using a variety of methodologies to determine the nature and quantity of some of these services. Many hypotheses exist regarding the future of these spruce-fir forests, which were heavily disturbed by the non-native balsam wooly adelgid during the 1980s. Direct measurements over the course of a decade assessed these hypotheses and indicate that this forest is recovering structure and function. The forest is accruing overstory biomass, with vegetation composition on a trajectory towards historic conditions. By using a total forest inventory of all vegetation from overstory trees to understory mosses, rates of productivity and nutrient cycling were determined. Productivity of this forest at low elevations has returned to pre-adelgid levels, while at high elevations productivity is approaching these levels. In the absence of an intact overstory, forest understory vegetation can compensate by disproportionately cycling and retaining nutrients such as nitrogen that would otherwise leach offsite. The understory of this forest provides an important service in nutrient cycling. Our ability to actively manage forests in order to manipulate levels and rates of carbon sequestration was assessed using stand data and the Forest Vegetation Simulator Growth and Yield Model. Silvicultural intervention proved effective at sequestering additional carbon over a no action alternative by the end of our simulation period. This forest provides a variety of ecosystem services and has retained its ability to recover their function after catastrophic disturbance.

The Forest Inventory and Analysis (FIA), the United States’ forest census, measured sixty-six Mexican spotted owl nest stands in order gain insight into the structure and composition of the nest habitat of this threatened species. I used these data, along with the greater FIA database and the Forest Vegetation Simulator to explore questions surrounding the management of Mexican spotted owl habitat, specifically how to balance the objective of sustaining and enhancing nest habitat in face of increasing forest fire size and severity in the Southwest. My research consisted of three studies. The first study quantified the structure and composition of the Mexican spotted owl nest stands and scrutinized current evaluation criteria of nest habitat. The second study estimated how much of the Southwestern landscape is at risk to high-severity crown fire and how much of the landscape is suitable Mexican spotted owl nest habitat. The third study modeled forest dynamics and silvicultural intervention in potential Mexican spotted owl nest stands. The purpose of this research is to assist in management of Southwestern forests in order to decrease fire size and severity while sustaining and enhancing current and future Mexican spotted owl nest habitat.

In order to fully understand the magnitude of the benefits that forests provide, it is crucial to understand the full suite of ecosystem services that they offer. A southern Appalachian red spruce-Fraser fir forest was intensively analyzed using a variety of methodologies to determine the nature and quantity of some of these services. Many hypotheses exist regarding the future of these spruce-fir forests, which were heavily disturbed by the non-native balsam wooly adelgid during the 1980s. Direct measurements over the course of a decade assessed these hypotheses and indicate that this forest is recovering structure and function. The forest is accruing overstory biomass, with vegetation composition on a trajectory towards historic conditions. By using a total forest inventory of all vegetation from overstory trees to understory mosses, rates of productivity and nutrient cycling were determined. Productivity of this forest at low elevations has returned to pre-adelgid levels, while at high elevations productivity is approaching these levels. In the absence of an intact overstory, forest understory vegetation can compensate by disproportionately cycling and retaining nutrients such as nitrogen that would otherwise leach offsite. The understory of this forest provides an important service in nutrient cycling. Our ability to actively manage forests in order to manipulate levels and rates of carbon sequestration was assessed using stand data and the Forest Vegetation Simulator Growth and Yield Model. Silvicultural intervention proved effective at sequestering additional carbon over a no action alternative by the end of our simulation period. This forest provides a variety of ecosystem services and has retained its ability to recover their function after catastrophic disturbance.

Little information is available to nonindustrial-private forest (NIPF) owners regarding economic tradeoffs between managing pine plantations for timber production or wildlife habitat. Loblolly (Pinus taeda) and longleaf (Pinus palustris) pine plantations were modeled to quantify economic tradeoffs for competing management scenarios utilizing densities aimed at wildlife habitat or timber production in Mississippi. Models contained a range of site indices, planting densities, and rotation lengths for timber maximization and white-tailed deer (Odocoileus virginianus) or northern bobwhite (Colinus virginianus) habitat production. All management scenarios in loblolly plantations produced positive Land Expectation Values (LEVs), while one fifth of the management scenarios in longleaf plantations produced positive LEVs. Comparison to the regional hunting lease rate the compensatory lease rates from the study could be realized, making wildlife management as valuable as timber management. The results of this study will help landowners be more informed about economic tradeoffs when making management decisions on their property.

The purpose of this research was to model the growth and yield of bottomland hardwood forests of the Lower Mississippi Alluvial Valley and to explain the economic tradeoffs of even- and uneven-aged management. The US Forest Service (USFS) Forest Vegetation Simulator was used to model growth and yield for four different bottomland hardwood forest types using USFS inventory data. Even- and uneven-aged management scenarios were optimized for timber revenue maximization using the Land Expectation Value formula. Analyses suggested that growth and yield of even-aged and uneven-aged management approaches differ in terms of end products and harvesting time. The even-aged management scenarios performed better over the uneven-aged management scenarios with few exceptions; however, the magnitude of the economic tradeoff depended upon initial stand conditions and required rates of return. These analyses will allow landowners to understand how much economic gain or loss they may realize by adopting an alternative management.

I utilized forest growth model (FVS-FFE) and fire simulation software (FlamMap, Randig), integrated through GIS software (ArcMap9.3), to quantify the impacts varied landscape-scale fuel treatments have on short-term onsite carbon loss, long-term onsite carbon storage, burn probability, conditional flame length, and mean fire size. Thirteen fuel treatment scenarios were simulated on a 42,000 hectare landscape in northern California: one untreated, three proposed by the US Forest Service, and nine that were spatially-optimized and developed with the Treatment Optimization Model in FlamMap. The nine scenarios developed in FlamMap varied by treatment intensity (10%, 20%, and 30% of the landscape treated) and treatment type (prescribed fire, mastication and thin + burn). Each scenario was subjected to 10,000 simulated wildfires with random ignition locations in order to develop burn probability and average flame length values for each scenario. I also recorded mean fire size for each scenario. I used the burn probability values to represent the likelihood of future wildfire occurrence, which I incorporated into our long-term onsite carbon storage projections. Our results suggest that the influence landscape-scale fuel treatments have on carbon dynamics and fire behavior metrics (mean burn probability, flame length and mean fire size) are highly dependent upon the treatment arrangement, type, and intensity. The results suggest that treating 20% of the landscape maximizes long-term carbon storage and that prescribed fire minimizes short-term carbon loss and maximizes onsite long-term carbon storage. Treating 20% of the landscape also appears to be the optimal treatment intensity for reducing fire behavior metrics, and treating beyond this level produces diminishing returns in reduction of fire behavior. When treating 20% of the landscape, site-specific treatments appear to perform well in comparison to spatially-optimized treatments.

The Forest Vegetation Simulator (FVS) is a growth and yield modeling system widely-used for predicting stand and tree-level attributes for management and planning applications in North American forests. The accuracy of FVS predictions for a range of tree and stand level attributes depends a great deal on the performance of the diameter increment model and its predictions of change in diameter at breast height (DBH) over time. To address the challenge of predicting growth in highly variable and geographically expansive forest systems, FVS was designed to include an internal calibration algorithm that makes use of growth observations, when available, from permanent inventory plots. The basic idea is that observed growth rates on a collection of remeasured trees are used to adjust or "calibrate" FVS diameter growth predictions. Therefore, DBH modeling was the focus of this investigation. Five methods were proposed for local calibration of individual tree DBH growth predictions and compared to two sets of results generated without calibration. Data from the US Forest Service's Forest Inventory and Analysis (FIA) program were used to test the methods for eleven widely-distributed forest tree species in Virginia. Two calibration approaches were based on median prediction errors from locally-observed DBH increments spanning a five year average time interval. Two were based on simple linear regression models fitted to the locally-observed prediction errors, and one method employed a mixed effects regression model with a random intercept term estimated from locally-observed DBH increments. Data witholding, specifically a leave-one-out cross-validation was used to compare results of the methods tested. Results showed that any of the calibration approaches tested in general led to improved accuracy of DBH growth predictions, with either of the median-based methods or regression based methods performing better than the random-effects-based approach. Equivalence testing showed that median or regression-based local calibration methods met error tolerances within ± 12% of observed DBH increments for all species with the random effects approach meeting a larger tolerance of ± 17%. These results showed improvement over uncalibrated models, which failed to meet tolerances as high as ± 30% for some species in a newly-fitted DBH growth model for Virginia, and as high as ± 170% for an existing model fitted to data from a much larger region of the Southeastern United States. Local calibration of regional DBH increment models provides an effective means of substantially reducing prediction errors when a relatively small set of observations are available from local sources such as permanent forest inventory plots, or the FIA database. / MS / The Forest Vegetation Simulator (FVS) is a growth and yield model widely-used for predicting stand dynamics, management and decision support in North American forests. Diameter increment is a major component in modeling tree growth. The system of integrated analytical tools in FVS is primarily based on the performance of the diameter increment model and the subsequent use of predicted in diameter at breast height (DBH) over time in forecasting tree attributes. To address the challenge of predicting growth in highly variable and geographically expansive forest systems, FVS was designed to include an internal calibration algorithm that makes use of growth observations, when available, from permanent inventory plots. The basic idea was that observed growth rates on a small set of remeasured trees are used to adjust or “calibrate” FVS growth predictions. The FVS internal calibration was the subject being investigated here. Five alternative methods were proposed attributed to a specific site or stand of interest and compared to two sets of results, which were based on median prediction errors, generated without calibration. Results illustrated that median-based methods or regression based methods performed better than the random-effects-based approach using independently observed growth data from Forest Service FIA re-measurements in Virginia. Local calibration of regional DBH increment models provides an effective means of substantially reducing prediction errors. The results of this study should also provide information to evaluate the efficiency of FVS calibration alternatives and a possible method for future implementation.

Cette thèse est consacrée au développement de méthodes numériques pour la simulation de plaques et coques fissurées. Pour ce problème, les méthodes classiques sont basées sur la Méthode des Elements Finis (MEF). En raison de la présence d'une singularité en fond de fissure, la MEF souffre de plusieurs défauts. Son taux de convergence n'est pas optimal. De plus, en cas de propagation de la fissure, le domaine doit être remaillé. Une nouvelle méthode d'éléments finis, introduite en 1999 et baptisée XFEM, permet de s'affranchir de ces inconvénients. Dans cette méthode, la base éléments finis est enrichie par des fonctions de forme spécifiques qui représentent la séparation du matériau et la singularité de fond de fissure. Ainsi, domaine et fissure sont indépendants et le taux de convergence est optimal. Dans cette thèse, on développe deux formulations XFEM adaptées à un modèle de plaques minces. Ces méthodes ont pu être implémentées dans la bibliothèque d'éléments finis Getfem++, et testées sur des exemples où la solution exacte est connue. L'étude d'erreur montre que la méthode XFEM possède un taux de convergence optimal, alors que la MEF montre une convergence plus lente. L'autre contribution de cette thèse concerne le calcul de Facteurs d'Intensité de Contraintes (FIC) : ces grandeurs indiquent le risque de propagation de la fissure. Nous proposons deux méthodes de calcul originales, basées sur nos formulations XFEM. La première méthode utilise l'intégrale-J, et la deuxième fournit une estimation directe, sans post-traitement.