Sublinear variance in Euclidean first-passage percolation

The Euclidean first-passage percolation model of Howard and Newman is a rotationally invariant percolation model built on a Poisson point process. It is known that the passage time between 0 and $ne_1$ obeys a diffusive upper bound: \mbox{Var}\, T(0,ne_1) \leq Cn, and in this paper we improve this inequality to $Cn/\log n$. The methods follow the strategy used for sublinear variance proofs on the lattice, using the Falik-Samorodnitsky inequality and a Bernoulli encoding, but with substantial technical difficulties. To deal with the different setup of the Euclidean model, we represent the passage time as a function of Bernoulli sequences and uniform sequences, and develop several "greedy lattice animal" arguments.Comment: 40 pages, 1 figur

How much of economic growth is fueled by investment-specific technological progress?

Discovering how economies grow is vitally important for economists and policymakers alike. This Commentary shows that more than half of U.S. economic growth can be attributed to technological advance in equipment and structures.Economic development ; Gross domestic product ; Technology

Welfare Reform and Immigrant Participation in the Supplemental Security Income Program

We examine the effect of the 1996 welfare reform legislation on participation in the Supplemental Security Income (SSI) program by immigrants. Although none of the immigrants on the SSI rolls before welfare reform lost eligibility, the potential exists for future impacts on the SSI caseload and the well-being of recent immigrants. We use microdata files from the Social Security Administration’s Continuous Work History Sample matched to administrative data on SSI participation for the period 1993 to 1999. We estimate simple models of SSI participation and compare our results to the existing literature. We then estimate a series of difference-in-differences models of SSI participation. These models compare SSI participation by immigrants relative to nativeborn individuals, and among affected immigrants relative to unaffected immigrants and native-born individuals, before and after welfare reform. Descriptive results indicate that the percentage of immigrants and natives receiving SSI decreased after welfare reform, but by a larger percentage for natives than for immigrants. The probability of SSI participation decreased after welfare reform for immigrants who were affected by the legislation relative to immigrants who were unaffected. The difference-in-differences estimate is positive for immigrants relative to otherwise similar natives, but the estimated effect among affected immigrants is about half as large as the effect for unaffected immigrants. When the sample is limited to low earners as a proxy for the SSI means test, the results are qualitatively unchanged but quantitatively much stronger. Authors’ Acknowledgements We are grateful to Ulyses Balderas for assisting with the collection of some data used here. A previous version of this paper was presented at the 2004 Western Regional Science Association Annual Meeting, February 25-28, 2004, Maui, HI.

Measuring the rate of technological progress in structures

An effort to measure technological progress in structures by using panel data on the age and rents of buildings in a vintage capital model, where buildings are replaced at some chosen periodicity. It finds that there has been significant technological advance in structures, which accounts for a major part of economic growth.Technology ; Capital investments

Free energy functionals for efficient phase field crystal modeling of structural phase transformations

The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory (CDFT), but its single mode free energy functional only leads to lattices with triangular (2D) or BCC (3D) symmetries. By returning to a closer approximation of the CDFT free energy functional, we develop a systematic construction of two-particle direct correlation functions that allow the study of a broad class of crystalline structures. This construction examines planar spacings, lattice symmetries, planar atomic densities and the atomic vibrational amplitude in the unit cell of the lattice and also provides control parameters for temperature and anisotropic surface energies. The power of this new approach is demonstrated by two examples of structural phase transformations.Comment: 4 pages, 4 figure

Collaborative Research: Developing Methods to Study Age-Related Changes in the Physiology of Forest Trees

Trees continue to increase in size and complexity over life spans that may last many centuries, and each year the growing regions of their shoots produce new foliage and reproductive structures. As they grow older and larger, forest trees appear to grow more slowly, produce thicker foliage and more reproductive structures. These changes are likely to be associated with age-related declines in the growth rates of forest stands, which occur before the mid-point of the lifespan of important timber species. Although similar patterns of age- and size-related change in the morphology and physiology of foliage have been described for numerous species, the mechanisms governing these changes are virtually unknown. Possible explanations for these phenomena range from decreased photosynthesis due to increased resistance of water flow to a genetically controlled ageing process that slows growth and photosynthesis. Processes regulating maturation, ageing and senescence are fundamental to biology, and some of these processes are probably unique to large, long-lived trees. A more complete understanding of the basis for this decline is necessary to model and accurately predict the growth of forests over time.Reciprocal grafting of shoots between trees of different ages offers great potential as a tool to distinguish among explanations for changes in growth behavior. In this approach, shoots from old growth trees are grafted onto juvenile and young-mature trees, and shoots from juvenile and young-mature trees are grafted into the crowns of old-growth trees. The extent, direction and time-course of changes in the growth, morphology, and physiology of foliage produced by the grafted shoots will provide insight into the mechanisms governing age-related change. This study will attempt reciprocal grafting on two species of long-lived trees, red spruce and Douglas fir. These species are adapted to substantially different climatic regimes, so a comparative study will provide insights into the universality or variability of processes associated with age-related changes in tree growth

Mineralogy and Geochemistry of Pleistocene Volcanics at Embagai Caldera and Natron Basin, Tanzania: Potential Constraints on the Stratigraphy of Olduvai Gorge

Olduvai Gorge is a paleoanthropologically significant site on the shoulder of the East African Rift Valley of north-central Tanzania, hosting Pleistocene-aged hominid fossils and stone tools. Several volcanoes in the adjacent Ngorongoro Volcanic Highlands (NVH) have erupted volcanic material into Olduvai and other nearby sedimentary basins. Embagai (Elanairobi) is a Pleistocene caldera within the NVH. It is a potential source volcano for Olduvai tuffs, particularly for Bed II and younger deposits, as it is consistent in overall composition (nephelinite and trachybasalt) and general age. Nephelinitic and phonolitic lava and tuff samples were collected from the caldera floor and the western, eastern, and northeastern sides of the caldera. Common primary minerals included nepheline, clinopyroxenes, titanomagnetite, and andradite garnets exclusive to alkaline volcanic settings. Secondary alteration significantly affected the quality of the geochemical and mineralogical results, with analcime, phillipsite, and calcite as the dominant secondary minerals. Unaffected samples plot as nephelinites. The compositions of phenocrysts of augite, feldspar, and titanomagnetite sampled from both Embagai and the Olduvai beds were compared. High-Mg augite compositions from the northern rim and western flank of Embagai are most similar to those of Olduvai Bed II. Feldspars are rare and distinctively K-rich in Embagai samples, which are dominated by nepheline compared to Olduvai tuffs. Overall, the mineral compositions and assemblage of Embagai appear to be a better match for a younger Olduvai Bed III tuff. The Pleistocene Peninj Group, exposed to the north of the NVH along the western margin of Lake Natron, is also paleoanthropologically important. It is comprised of the Humbu and Moinik Formations, which contain clastic sediments along with tephras and lavas likely associated with local eruptions from nearby volcanoes. The Main Tuff within the Humbu Formation is interlaid with the Wa Mbugu Basalt to the south of Peninj. This study compares the geochemistry and paleomagnetism of both well-constrained and unknown samples of the Wa Mbugu and other basaltic lavas in the vicinity to constrain the various units in this highly faulted and fragmented region. Samples were variably altered, with zeolites dominating the alteration assemblage. Geochemical results indicate that bulk major and minor elements alone are not enough to distinguish between some lavas of different stratigraphic positions but similar compositions, and would require further study using trace elements, phenocryst compositions, or other means. An oriented sample of the Wa Mbugu appears to indicate transitional polarity as opposed to the normal polarity commonly found with this unit. A second oriented lava sample had reversed polarity, however is not compositionally similar to the nearby Hajaro lava (reversed). This second lava may represent a previously undocumented flow. With further study of both Embagai and the Natron basin lavas focusing on phenocryst mineralogy in unaltered samples, additional correlations could lead to a higher resolution inter-basin stratigraphic framework for the NVH and for the surrounding paleontologically and archaeologically important sedimentary basins