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Revision of the GEOCARB model (Berner, 1991, 1994) for paleolevels of atmospheric CO 2 , has been made with emphasis on factors affecting CO 2 uptake by continental weathering. This includes: (1) new GCM (general circulation model) results for the dependence of global mean surface temperature and runoff on CO 2 , for both glaciated and non-glaciated periods, coupled with new results for the temperature response to changes in solar radiation; (2) demonstration that values for the weathering-uplift factor f R (t) based on Sr isotopes as was done in GEOCARB II are in general agreement with independent values calculated from the abundance of terrigenous sediments as a measure of global physical erosion rate over Phanerozoic time; (3) more accurate estimates of the timing and the quantitative effects on Ca-Mg silicate weathering of the rise of large vascular plants on the continents during the Devonian; (4) inclusion of the effects of changes in paleogeography alone (constant CO 2 and solar radiation) on global mean land surface temperature as it affects the rate of weathering; (5) consideration of the effects of volcanic weathering, both in subduction zones and on the seafloor; (6) use of new data on the 13 C values for Phanerozoic limestones and organic matter; (7) consideration of the relative weathering enhancement by gymnosperms versus angiosperms; (8) revision of paleo land area based on more recent data and use of this data, along with GCM-based paleo-runoff results, to calculate global water discharge from the continents over time. Results show a similar overall pattern to those for GEOCARB II: very high CO 2 values during the early Paleozoic, a large drop during the Devonian and Carbonifer-ous, high values during the early Mesozoic, and a gradual decrease from about 170 Ma to low values during the Cenozoic. However, the new results exhibit considerably higher CO 2 values during the Mesozoic, and their downward trend with time agrees with the independent estimates of Ekart and others (1999). Sensitivity analysis shows that results for paleo-CO 2 are especially sensitive to: the effects of CO 2 fertilization and temperature on the acceleration of plant-mediated chemical weathering; the quantitative effects of plants on mineral dissolution rate for constant temperature and CO 2 ; the relative roles of angiosperms and gymnosperms in accelerating rock weathering ; and the response of paleo-temperature to the global climate model used. This emphasizes the need for further study of the role of plants in chemical weathering and the application of GCMs to study of paleo-CO 2 and the long term carbon cycle.

Dyadic data matrices, such as co-occurrence matrix, rating matrix, and proximity matrix, arise frequently in various important applications. A fundamental problem in dyadic data analysis is to find the hidden block structure of the data matrix. In this paper, we present a new coclustering framework, block value decomposition(BVD), for dyadic data, which factorizes the dyadic data matrix into three components, the row-coefficient matrix R, the block value matrix B, and the column-coefficient matrix C. Under this framework, we focus on a special yet very popular case -non-negative dyadic data, and propose a specific novel co-clustering algorithm that iteratively computes the three decomposition matrices based on the multiplicative updating rules. Extensive experimental evaluations also demonstrate the effectiveness and potential of this framework as well as the specific algorithms for co-clustering, and in particular, for discovering the hidden block structure in the dyadic data.

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