Since 65 million years ago (Ma), Earth's climate has undergone a significant and complex evolution, the finer details of which are now coming to light through investigations of deep-sea sediment cores. This evolution includes gradual trends of warming and cooling driven by tectonic processes on time scales of 10(5) to 10(7) years, rhythmic or periodic cycles driven by orbital processes with 10(4)- to 10(6)-year cyclicity, and rare rapid aberrant shifts and extreme climate transients with durations of 10(3) to 10(5) years. Here, recent progress in defining the evolution of global climate over the Cenozoic Era is reviewed. We focus primarily on the periodic and anomalous components of variability over the early portion of this era, as constrained by the latest generation of deep-sea isotope records. We also consider how this improved perspective has led to the recognition of previously unforeseen mechanisms for altering climate.

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.

The relation between the partial pressure of atmospheric carbon dioxide (pCO2) and Paleogene climate is poorly resolved. We used stable carbon isotopic values of di-unsaturated alkenones extracted from deep sea cores to reconstruct pCO2 from the middle Eocene to the late Oligocene (approximately 45 to 25 million years ago). Our results demonstrate that pCO2 ranged between 1000 to 1500 parts per million by volume in the middle to late Eocene, then decreased in several steps during the Oligocene, and reached modern levels by the latest Oligocene. The fall in pCO2 likely allowed for a critical expansion of ice sheets on Antarctica and promoted conditions that forced the onset of terrestrial C4 photosynthesis.

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