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Demixing is the task of identifying multiple signals given only their sum and prior information about their structures. Examples of demixing problems include (i) separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis; (ii) decomposing an observed matrix into low-rank and sparse components; and (iii) identifying a binary codeword with impulsive corruptions. This thesis describes and analyzes a convex optimization framework for solving an array of demixing problems. Our framework includes a random orientation model for the constituent signals that ensures the structures are incoherent. This work introduces a summary parameter, the statistical dimension, that reflects the intrinsic complexity of a signal. The main result indicates that the difficulty of demixing under this random model depends only on the total complexity of the constituent signals involved: demixing succeeds with high probability when the sum of the complexities is less than the ambient dimension; otherwise, it fails with high probability. The fact that a phase transition between success and failure occurs in demixing is a consequence of a new inequality in conic integral geometry. Roughly speaking, this inequality asserts that a convex cone behaves like a subspace whose dimension is equal to the statistical dimension of the cone. When combined with a geometric optimality condition for demixing, this inequality provides precise quantitative information about the phase transition, including the location and width of the transition region.

The Merced County Association of Governments (MCAG) was chosen by the Federal Highway Administration, U.S. Environmental Protection Agency, and the California Department of Transportation to pilot a new program, Partnership for Integrated Planning (PIP), which aimed to: streamline planning and the project-delivery process; avoid environmental impacts; foster collaboration among planning, transportation, and environmental agencies; and engage the public at the beginning of long-term transportation planning. Merced County provides a challenging test case through rapid population growth, cultural diversity, high unemployment, and increasing conflicts between stewardship of sensitive habitats and prime farmland and demands for transportation improvements and housing. The Partnership for Integrated Planning (PIP) included the development of geographic information system (GIS) tools for modeling growth and environmental impacts to produce real-time maps and tables resulting from policy choices at public meetings. PIP engaged all regionally relevant planning, natural resource, and regulatory agencies in data-sharing exercises to integrate data important to each agency into the scenario testing and planning process. Most importantly, the Merced County Association of Governments (MCAG), which is the coordinating partner in PIP, led an extensive outreach program to engage the community in PIP. To project land-use changes, we adapted UPlan, a rule-based land-use model developed at the University of California at Davis. UPlan incorporates user-controlled policy inputs ranging from general plan map choices, housing densities, and household labor rates to the ranking of environmental amenities. These are combined with user-settable infrastructure growth attractors to distribute population-growth estimates into spatially explicit land-use scenarios. UPlan stores all user-specified assumptions so many scenarios may be tested against one another in a transparent fashion. We evaluate

The first fact to know about CARA is that participating groups or individuals collectively felt that scores of sets of facts were critical to their individual or cooperative work with California's rivers. In all, 99 sets of statewide, regional, or local data were integrated directly into CARA. Links were created to another 206 internet providers of information.CARA contains 39 sets of mapped geographical information system(GIS) layers, 60 sets of tabular (database) and textual text) data, as well as links (internet connections) to 510 additional maps, tables and texts located on other servers. All of this data is organized by watershed and theme. CARA makes the data available to interested parties over the internet for a wide variety of analytical and management purposes.

The Sacramento, California, U.S.A, Area Council of Governments (SACOG) commissioned the Information Center for the Environment, University of California, Davis (ICE) to assemble a suite of the best available region-wide GIS data depicting natural resource values and conservation opportunities for the six County, 6,500 square mile (16,830 square kilometer) Sacramento, California region. This region is planned and managed by a large and diverse number of government entities and it contains a population of approximately 2,000,000 with a wide range of natural resource and economic interests. The purpose of this commission was to create a visual, conceptual tool depicting and weighting natural resource variables that are of value to the many parties of interest in land use and conservation planning in the region.