A generalization of the Lyndon--Hochschild--Serre spectral sequence with applications to group cohomology and decompositions of groups

We set up a Grothendieck spectral sequence which generalizes the Lyndon--Hochschild--Serre spectral sequence for a group extension K\mono G\epi Q by allowing the normal subgroup $K$ to be replaced by a subgroup, or family of subgroups which satisfy a weaker condition than normality. This is applied to establish a decomposition theorem for certain groups as fundamental groups of graphs of Poincar\'e duality groups. We further illustrate the method by proving a cohomological vanishing theorem which applies for example to Thompson's group $F$.Comment: 22 page

The Caltech solar site survey, 1965-1967

We describe the Caltech solar site survey in 1965–1967 directed by R. B. Leighton. The solar seeing at 102 locations in 34 sites in Southern California was evaluated by 6009 visual estimates with portable telescopes. Cloud cover and other meteorological factors were also measured, and sunlight recorders were operated at several sites. We have reanalyzed much of the data to determine its consistency and learn what else we could about the sites. The visual estimates show good internal consistency and correlation with photographic data. The seeing was found to be best at various sites associated with water, and we point out the importance of the Bowen ratio in determining the influence of water vapor on seeing. It was found that seeing at the different sites was not well correlated in time. The seeing was found to be best at Lake Elsinore, an inland sink. Good seeing was also found on the Caltech campus and at Big Bear Lake in the San Bernardino Mountains. Taking into account the better sky transparency and the feasibility of constructing an observatory in the lake, we chose Big Bear Lake for the site of a new observatory. The lack of correlation of seeing with transparency suggests the benefits of several smaller telescopes, targeted at specific goals, located at sites chosen for those goals

Basement structure of the northern Ontong Java Plateau

Site surveys conducted in conjunction with Leg 130 on the Ontong Java Plateau reveal a strong seismic reflector at 0.8 to 1.0 s below the seafloor that drilling at Sites 803 and 807 confirmed is Cretaceous basalt. This reflector is generally smooth, except for the northeastern margin of the plateau, where it forms a series of small, irregularly shaped depressions. Correlatable reflectors present at the bottom of the depressions are also present on the adjacent highs, suggesting that these depressions are original volcanic topography. A strong sub-basalt reflector occurs on many seismic profiles on the northeastern portion of the plateau. This reflection may be caused by a density and velocity contrast between pillow lavas and flood basalt flows or it may result from interbedded sediment and thus may represent significant lulls in volcanic activity. The presence of sub-basalt reflectors near Site 803 may indicate that later volcanic episodes occurred there, in contrast to Site 807, where this reflector was not observed and where older basalt ages were obtained

Learning Together: Actionable Approaches for Grantmakers

A majority of grantmakers are struggling to make evaluation and learning meaningful to anyone outside their organizations. Not only is evaluation conducted primarily for internal purposes, but it is usually done by the grantmaker entirely on its own -- with no outside learning partners except perhaps an external evaluator -- and provides little value and may even be burdensome to the grantee. It may be that some funders do not consider expanding the scope of learning efforts beyond their own walls. Or perhaps the gap is driven by funding constraints or funder -- grantee dynamics. In any case, grantees and other stakeholders are critical partners in the achievement of grantmakers' missions and are therefore critical learning partners as well.In this publication, GEO offers actionable ideas and practices to help grantmakers make learning with others a priority. The publication includes stories about foundations that are learning together with a variety of partners, plus a discussion of the key questions that can help shape successful shared learning. It is based on research and interviews conducted from late 2013 to 2015, including extensive outreach to grantmakers, evaluation practitioners and others. The focus of GEO's inquiry: documenting the challenges facing grantmakers as they set out to learn with others, lifting up what it takes to do this work successfully and identifying grantmakers that show a commitment to learning together

Laboratory and Well-Log Velocity and Density Measurements from the Ontong Java Plateau: New in-situ corrections to laboratory data for pelagic carbonates

During Ocean Drilling Program Leg 130, sonic velocity and bulk density/porosity well logs were measured in five separate holes drilled through the sequence of pelagic carbonate oozes, chalks, and limestones that comprise the thick, continuous sedimentary cover on the Ontong Java Plateau. An internally consistent and continuous suite of shipboard laboratory velocity and sediment physical properties measurements were made from the top of each hole down through the entire logged interval. Because of the high quality of the data, extensive overlap of 500 m or more between the log and laboratory measurements at each hole, and the homogeneous nature of the sediments, we have been able to compare laboratory and in-situ log measurements in detail and to evaluate factors that alter laboratory data from their in-situ values. For measurements of bulk density and porosity, differences between laboratory and in-situ log measurements are very small and remain constant over the entire range of depths studied. We have applied a simple hydraulic rebound correction to the laboratory data that compensates for pore fluid expansion after removal of a sediment sample from in-situ conditions. The small, correctable differences between the laboratory and log data imply that mechanical rebound is significantly less than previous estimates (maximum near 5%) of rebound in pelagic carbonates. Furthermore, porosity rebound cannot be used to correct laboratory sonic velocity measurements to in-situ values. Such a rebound correction implicitly requires that laboratory and in-situ data must occupy identical fields on velocity-porosity crossplots. This condition is not met for the Ontong Java Plateau results because laboratory and in-situ logging data occupy distinct trends with little overlap between the two types of measurement. Mechanical rebound in pelagic carbonates cannot be used to correct either laboratory porosity or velocity measurements to in-situ values. The complex porosity systematics of these carbonates resulting from varying abundances of hollow foraminifer grains precluded use of an empirical correction derived from the log porosity and velocity data. Laboratory sonic velocity measurements can be corrected to in-situ values at all of the Ontong Java Plateau sites using a depth-based function derived from downhole differences between log and laboratory velocities in Hole 807A. The applicability of the depth correction implies that the effect of overburden pressure reduction on sediment elastic moduli is the most significant factor affecting laboratory velocity measurements. The depth correction to laboratory velocity measurements appears to be generally applicable to pelagic carbonate oozes and chalks of the Ontong Java Plateau, regardless of depositional depth or sediment age

Seismic Response Analysis of Pile-Supported Structure: Assessment of Commonly Used Approximations

The seismic response of a pile-supported structure is formulated by the approach developed by the first author. Using this formulation, some of the crude approximations frequently used in the seismic response analysis of a soil-pile-structure system are examined. Those involved in the analysis procedure are assessed under the linear elastic condition. A commonly used nonlinear soil model for the dynamic pile response analysis is also assessed. It is found that those approximations routinely used in the analysis procedure and numerical modelling can cause significant errors in the computed response of a pile-supported structure

Seismic stratigraphy of the Ontong Java Plateau

The Ontong Java Plateau, a large, deep-water carbonate plateau in the western equatorial Pacific, is an ideal location for studying responses of carbonate sedimentation to the effects of changing paleoceanographic conditions. These carbonate responses are often reflected in the physical properties of the sediment, which in turn control the appearance of seismic reflection profiles. Seismic stratigraphy analyses, correlating eight reflector horizons to each drill site, have been conducted in an attempt to map stratigraphic data. Accurate correlation of seismic stratigraphic data to drilling results requires conversion of traveltime to depth in meters. Synthetic seismogram models, using shipboard physical properties data, have been generated in an attempt to provide this correlation. Physical properties, including laboratory-measured and well-log data, were collected from sites drilled during Deep Sea Drilling Project Legs 30 and 89, and Ocean Drilling Program Leg 130, on the top and flank of the Ontong Java Plateau. Laboratory-measured density is corrected to in-situ conditions by accounting for porosity rebound resulting from removal of the sediment from its overburden. The correction of laboratory-measured compressional velocity to in situ appears to be largely a function of increases in elastic moduli (especially shear rigidity) with depth of burial, more than a function of changes in temperature, pressure, or density (porosity rebound). Well-log velocity and density data for the ooze intervals were found to be greatly affected by drilling disturbance; hence, they were disregarded and replaced by lab data for these intervals. Velocity and density data were used to produce synthetic seismograms. Correlation of seismic reflection data with synthetic data, and hence with depth below seafloor, at each drill site shows that a single velocity-depth function exists for sediments on the top and flank of the Ontong Java Plateau. A polynomial fit of this function provides an equation for domain conversion: Depth (mbsf) = 44.49 + 0.800(traveltime[ms]) + 3.308 × 10 4 (traveltime[ms]2 ) Traveltime (ms) = -35.18 + 1.118(depth[mbsf]) - 1.969 × KT* (depth[mbsf]2 ) Seismic reflection profiles down the flank of the plateau undergo three significant changes: (1) a drastic thinning of the sediment column with depth, (2) changes in the echo-character of the profile (development of seismic facies), and (3) loss of continuous, coherent reflections. Sediments on the plateau top were largely deposited by pelagic processes, with little significant postdepositional or syndepositional modification. Sediments on the flank of the plateau are also pelagic, but they have been modified by faulting, erosion, and mass movement. These processes result in disrupted and incoherent reflectors, development of seismic facies, and redistribution of sediment on the flank of the plateau. Seismic stratigraphic analyses have shown that the sediment section decreases in thickness by as much as 65% between water depths of 2000 m water depth (at the top of the plateau) and 4000 m (near the base of the plateau). Thinning is attributed to increasing carbonate dissolution with depth. If this assumption is correct, then changes in the relative thicknesses of seismostratigraphic units at each drill site are indicative of changes in the position of the lysocline and the dissolution gradient between the lysocline and the carbonate compensation depth. We think that a shallow lysocline in the early Miocene caused sediment thinning. A deepening of the lysocline in the late-early Miocene caused relative thickening at each site. Within the middle Miocene, a sharp rise in lysoclinal depth occurs, concurrent with a steepening of the dissolution gradient. These events result in sediment thinning at all four sites. The thicker sections in the late Miocene likely correspond to a deepening of the lysocline, and a subsequent rise in the lysocline again hinders accumulation of sediment in the very late Miocene and Pliocene

Scales for co-compact embeddings of virtually free groups

Let $\Gamma$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(\Gamma)$ be the family of totally disconnected, locally compact groups containing $\Gamma$ as a co-compact lattice. We prove that the values of the scale function with respect to groups in $\mathcal{F}_{td}(\Gamma)$ evaluated on the subset $\Gamma$ have only finitely many prime divisors. This can be thought of as a uniform property of the family $\mathcal{F}_{td}(\Gamma)$.Comment: 12 pages; key words: uniform lattice, virtually free group, totally disconnected group, scale function (Error in references corrected in version 2