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UC Berkeley (2) UC Davis (5) UC Irvine (4) UCLA (23) UC Merced (16) UC Riverside (2) UC San Diego (4) UCSF (2) UC Santa Barbara (2) UC Santa Cruz (3) UC Office of the President (5) Lawrence Berkeley National Laboratory (0) UC Agriculture & Natural Resources (1)

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Department of Statistics, UCLA (7) Research Grants Program Office (RGPO) (3) University of California Water Resources Center (2) Department of Earth System Science (1) Department of Economics, UCSC (1) Department of Emergency Medicine (UCI) (1)

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Proceedings of the Annual Meeting of the Cognitive Science Society (14) Pacific Basin Law Journal (1) Proceedings of the Vertebrate Pest Conference (1) Western Journal of Emergency Medicine: Integrating Emergency Care with Population Health (1)

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## Scholarly Works (46 results)

The study of how children and adults learn mathematics has given rise to a rich set of psychological phenomena involving mental representation, conceptual understanding, working memory, relational reasoning and problem solving. The subfield of understanding rational number processing and reasoning focuses on mental representation and conceptual understanding of rational numbers, and in particular fractions. Fractions differ from other number types, such as whole numbers, both conceptually and in format. Previous research has highlighted the extent to which fractions and other rational numbers pose challenges for children and adults with respect to magnitude estimation and misconceptions. The goal of this dissertation is to highlight the distinct differences in reasoning with different types of rational numbers. First, a neuroimaging study provides evidence that fractions yield a distinct pattern of neural activation during magnitude estimation that differs from both decimals and integers (Chapter 2). Second, a set of behavioral studies with adults highlights the affordances of the bipartite format of fractions for relational reasoning tasks (Chapter 3). Finally, a developmental study with pre-algebra students provides evidence for a significant relationship between relational understanding of fractions and algebra performance, and specifically algebraic modeling. This work is presented in the context of viewing mathematical notation as a type of conceptual modeling. In particular, decimals have advantages in measurement and representing magnitude. Fractions, on the other hand, have advantages in relational contexts, due to the fact that fractions, with their bipartite (a/b) format, inherently specify a relation between the cardinalities of two sets. When mathematics is viewed as a type of relational modeling, rational expressions provide a gateway to more complex mathematical notations and concepts, such as those in algebra.

Human players in our laboratory experiment converge closely to the symmetric mixed Nash equilibrium when matched in a single population version of the standard Hawk-Dove game. When matched across two populations, the same players show clear movement towards an asymmetric (and very inequitable) pure Nash equilibrium of the same game. These ﬁndings support a distinctive prediction of evolutionary game theory.

Land subsidence caused by the excessive use of groundwater resources has traditionally caused serious and costly damage to the Los Banos-Kettleman City area of California's San Joaquin Valley. Although the arrival of surface water from the Central Valley Project has reduced subsidence in recent decades, the growing instability of surface water supplies has refocused attention on the future of land subsidence in the region. This report develops a three-dimenslonal, numerical simulation model for both groundwater flow and land subsidence. The simulation model is calibrated using observed data from 1972 to 1998. A probable future drought scenario is used to consider the effect on land subsidence of three management alternatives over the next thirty years. Maintaining present practices virtually eliminates unrecoverable land subsidence, but with a growing urban population to the south and concern over the ecological implications of water exportation from the north, it does not appear that the delivery of surface water can be sustained at current levels. The two other proposed management alternatives reduce the dependency on surface water by increasing groundwater withdrawl. Land subsidence is confined to tolerable levels in the more moderate of these proposals, while the more aggressive produces significant long-term subsidence. Finally, an optimization model is formulated to determine maximum groundwater withdrawl from nine water sub-basins without causing irrecoverable subsidence over the forecasted period. The optimization reveals that withdrawl of groundwater supplies can be increased in certain areas in the eastern side of the study area without causing significant subsidence.

Land subsidence caused by the excessive use of ground water resources has traditionally caused serious and costly damage to the Los Banos-Kettleman City area of California's San Joaquin Valley. Although the arrival of surface water from the Central Valley Project has reduced subsidence in recent decades, the growing instability of surface water supplies has refocused attention on the future of land subsidence in the region. This report develops a three dimensional, numerical simulation model for both ground water flow and land subsidence. The simulation model is calibrated using observed data from 1972 to 1998. A probable future drought scenario is used to consider the effect on land subsidence of three management alternatives over the next thirty years. Maintaining present practices virtually eliminates unrecoverable land subsidence, but with a growing urban population to the south and concern over the ecological implications of water exportation from the north, it does not appear that the delivery of surface water can be sustained at current levels. The two other proposed management alternatives reduce the dependency on surface water by increasing ground water withdrawal. Land subsidence is confined to tolerable levels in the more moderate of these proposals, while the more aggressive produces significant long-term subsidence. Finally, an optimization model is formulated to determine maximum ground water withdrawal from nine water sub-basins without causing irrecoverable subsidence over the forecasted period. The optimization reveals that withdrawal of ground water supplies can be increased in certain areas in the eastern side of the study area without causing significant subsidence.