[1] We present a 5.3-Myr stack (the ''LR04'' stack) of benthic d 18 O records from 57 globally distributed sites aligned by an automated graphic correlation algorithm. This is the first benthic d 18 O stack composed of more than three records to extend beyond 850 ka, and we use its improved signal quality to identify 24 new marine isotope stages in the early Pliocene. We also present a new LR04 age model for the Pliocene-Pleistocene derived from tuning the d 18 O stack to a simple ice model based on 21 June insolation at 65°N. Stacked sedimentation rates provide additional age model constraints to prevent overtuning. Despite a conservative tuning strategy, the LR04 benthic stack exhibits significant coherency with insolation in the obliquity band throughout the entire 5.3 Myr and in the precession band for more than half of the record. The LR04 stack contains significantly more variance in benthic d 18 O than previously published stacks of the late Pleistocene as the result of higherresolution records, a better alignment technique, and a greater percentage of records from the Atlantic. Finally, the relative phases of the stack's 41-and 23-kyr components suggest that the precession component of d 18 O from 2.7-1.6 Ma is primarily a deep-water temperature signal and that the phase of d 18 O precession response changed suddenly at 1.6 Ma.

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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.

(2015) 'Sea-level rise due to polar ice-sheet mass loss during past warm periods. ', Science., 349 (6244). aaa4019.Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

Climate over the past million years has been dominated by glaciation cycles with periods near 23,000, 41,000, and 100,000 years. In a linear version of the Milankovitch theory, the two shorter cycles can be explained as responses to insolation cycles driven by precession and obliquity. But the 100,000-year radiation cycle (arising from eccentricity variation) is much too small in amplitude and too late in phase to produce the corresponding climate cycle by direct forcing. We present phase observations showing that the geographic progression of local responses over the 100,000-year cycle is similar to the progression in the other two cycles, implying that a similar set of internal climatic mechanisms operates in all three. But the phase sequence in the 100,000-year cycle requires a source of climatic inertia having a time constant (--15,000 years) much larger than the other cycles (--5,000 years). Our conceptual model identifies massive northern hemisphere ice sheets as this larger inertial source. When these ice sheets, forced by precession and obliquity, exceed a critical size, they cease responding as linear Milankovitch slaves and drive atmospheric and oceanic responses that mimic the externally forced responses. In our model, the coupled system acts as a nonlinear amplifier that is particularly sensitive to eccentricity-driven modulations in the 23,000-year sea level cycle. During an interval when sea level is forced upward from a major low stand by a Milankovitch response acting either alone or in combination with an internally driven, higher-frequency process, ice sheets grounded on continental shelves become unstable, mass wasting accelerates, and the resulting deglaciation sets the phase of one wave in the train of 100,000-year oscillations.Whether a glacier or ice sheet influences the climate depends very much on the scale .... The interesting aspect is that an effect on the local climate can still make an ice mass grow larger and larger, thereby gradually increasing its radius of influence. Johannes Oerlemans [1991, p. 155] 1. BACKGROUND AND PURPOSE Climate over the past half-million years has been dominated by glacial cycles with periods near 23, 41, and 100 kyr [Hays 14 DSDP607 A•5•3C index of ventilation 3427

Time series of ocean properties provide a measure of global ice volume and monitor key features of the wind-driven and density-driven circulations over the past 400,000 years. Cycles with periods near 23,000, 41,000, and 100,000 years dominate this climatic narrative. When the narrative is examined in a geographic array of time series, the phase of each climatic oscillation is seen to progress through the system in essentially the same geographic sequence in all three cycles. We argue that Paper number 92PA02253 0883-8305/92/92PA-02253510.00 the 23,000-and 41,000-year cycles of glaciation are continuous, linear responses to orbitally driven changes in the Arctic radiation budget; and we use the phase progression in each climatic cycle to identify the main pathways along which the initial, local responses to radiation are propagated by the atmosphere and ocean. Early in this progression, deep waters of the Southern Ocean appear to act as a carbon trap. To stimulate new observations and modeling efforts, we offer a process model that gives a synoptic view of climate at the four end-member states needed to describe the system's evolution, and we propose a dynamic system model that explains the phase progression along causal pathways by specifying inertial constants in a chain of four subsystems. "Solutions to problems involving systems of such complexity are not born full grown like Athena from the head of Zeus. Rather they evolve slowly, in stages, each of which requires a pause to examine data at great lengths in order to guarantee a sure footing and to properly choose the next step." --Victor P. Starr Imbrie et al.' Linear Responses to Milankovitch Forcing 705 MODEL SYSTEM STATE IG G IG 1 3 PHASE © DG PG 1 4 3 2 TIME

Abs~ract. We analy:ro five high-resolution time series spanmng the last 1.65 m.y.: benthic foraminiferal 5110 and 5'~C. percent CaC03o and estimated sea surface temperature (SS1) at Nonh Atlantic Deep Sea Drilling Project site 007 and percent CaC~ at site 609. E ach record is a multicore compo<;ite verifiC;d fo~ c?nti.nuity by splicing among multiple hole~. The~e chmauc. mdtces portray changes in northern hemtsphere tee sheet stze and in North Atlantic surface and deep circulation. By tuning obliquity and precession components in the 5 11 0 record to orbital variations we have devised a time scale (TP607) for the entire Pleist~ene that agrees in age with aU K/Ar-dated magnetic reversals to within 1.5%. The Brunhes time scale is taken from Imbrie et al. (1984], except for differences near the stage 17/16 transition (0.70 to 0.64 Ma). All indicators show a similar evolution from the ~uyama to the B.runhes chrons: orbital eccentricity and_ prece~1o.n responses mcreased in amplitude; those at orbttal obliqutty decreased. The change in dominance from Paper number 89PA00434. 0883-8305/89/89PA-00434$10.00 obliquity to eccentricity occurred over several hundred thousand years, with fa stest changes around 0.7 to 0.6 Ma. The coherent, in-phase responses of 5"0. 5 1 3C, CaC03 and SST at these rhythms indicate that northern hemisphere ice volume changes have controlled most of the North Atlantic surfaceocean and deep-ocean responses for the last 1.6 m.y. Tbe 5 1 3C, percent CaCO; and SST records at site 607 also show prominent changes at low frequencies, including a prominent long-wavelength oscillation toward glacial conditions that is centered between 0.9 and 0.6 Ma These changes appear to be associated neither with orbital forcing nor with changes in ice volume.

The Milankovitch theory of climate change proposes that glacial-interglacial cycles are driven by changes in summer insolation at high northern latitudes. The timing of climate change in the Southern Hemisphere at glacial-interglacial transitions (which are known as terminations) relative to variations in summer insolation in the Northern Hemisphere is an important test of this hypothesis. So far, it has only been possible to apply this test to the most recent termination, because the dating uncertainty associated with older terminations is too large to allow phase relationships to be determined. Here we present a new chronology of Antarctic climate change over the past 360,000 years that is based on the ratio of oxygen to nitrogen molecules in air trapped in the Dome Fuji and Vostok ice cores. This ratio is a proxy for local summer insolation, and thus allows the chronology to be constructed by orbital tuning without the need to assume a lag between a climate record and an orbital parameter. The accuracy of the chronology allows us to examine the phase relationships between climate records from the ice cores and changes in insolation. Our results indicate that orbital-scale Antarctic climate change lags Northern Hemisphere insolation by a few millennia, and that the increases in Antarctic temperature and atmospheric carbon dioxide concentration during the last four terminations occurred within the rising phase of Northern Hemisphere summer insolation. These results support the Milankovitch theory that Northern Hemisphere summer insolation triggered the last four deglaciations.