High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

A 233 km Tunnel for Lepton and Hadron Colliders

A decade ago, a cost analysis was conducted to bore a 233 km circumference Very Large Hadron Collider (VLHC) tunnel passing through Fermilab. Here we outline implementations of $e^+e^-$, $p \bar{p}$, and $\mu^+ \mu^-$ collider rings in this tunnel using recent technological innovations. The 240 and 500 GeV $e^+e^-$ colliders employ Crab Waist Crossings, ultra low emittance damped bunches, short vertical IP focal lengths, superconducting RF, and low coercivity, grain oriented silicon steel/concrete dipoles. Some details are also provided for a high luminosity 240 GeV $e^+ e^-$ collider and 1.75 TeV muon accelerator in a Fermilab site filler tunnel. The 40 TeV $p \bar{p}$ collider uses the high intensity Fermilab $\bar{p}$ source, exploits high cross sections for $p \bar{p}$ production of high mass states, and uses 2 Tesla ultra low carbon steel/YBCO superconducting magnets run with liquid neon. The 35 TeV muon ring ramps the 2 Tesla superconducting magnets at 9 Hz every 0.4 seconds, uses 250 GV of superconducting RF to accelerate muons from 1.75 to 17.5 TeV in 63 orbits with 71% survival, and mitigates neutrino radiation with phase shifting, roller coaster motion in a FODO lattice.Comment: LaTex, 6 pages, 1 figure, Advanced Accelerator Concepts Workshop, Austin, TX, 10-15 June 201

The accelerating influence of humans on mammalian macroecological patterns over the late Quaternary

The transition of hominins to a largely meat-based diet ~1.8 million years ago led to the exploitation of other mammals for food and resources. As hominins, particularly archaic and modern humans, became increasingly abundant and dispersed across the globe, a temporally and spatially transgressive extinction of large-bodied mammals followed; the degree of selectivity was unprecedented in the Cenozoic fossil record. Today, most remaining large-bodied mammal species are confined to Africa, where they coevolved with hominins. Here, using a comprehensive global dataset of mammal distribution, life history and ecology, we examine the consequences of “body size downgrading” of mammals over the late Quaternary on fundamental macroecological patterns. Specifically, we examine changes in species diversity, global and continental body size distributions, allometric scaling of geographic range size with body mass, and the scaling of maximum body size with area. Moreover, we project these patterns toward a potential future scenario in which all mammals currently listed as vulnerable on the IUCN\u27s Red List are extirpated. Our analysis demonstrates that anthropogenic impact on earth systems predates the terminal Pleistocene and has grown as populations increased and humans have become more widespread. Moreover, owing to the disproportionate influence on ecosystem structure and function of megafauna, past and present body size downgrading has reshaped Earth\u27s biosphere. Thus, macroecological studies based only on modern species yield distorted results, which are not representative of the patterns present for most of mammal evolution. Our review supports the concept of benchmarking the “Anthropocene” with the earliest activities of Homo sapiens

Standard Model Top Quark Asymmetry at the Fermilab Tevatron

Top quark pair production at proton-antiproton colliders is known to exhibit a forward-backward asymmetry due to higher-order QCD effects. We explore how this asymmetry might be studied at the Fermilab Tevatron, including how the asymmetry depends on the kinematics of extra hard partons. We consider results for top quark pair events with one and two additional hard jets. We further note that a similar asymmetry, correlated with the presence of jets, arises in specific models for parton showers in Monte Carlo simulations. We conclude that the measurement of this asymmetry at the Tevatron will be challenging, but important both for our understanding of QCD and for our efforts to model it.Comment: 26 p., 10 embedded figs., comment added, version to appear in PR

Entropy and Hausdorff Dimension in Random Growing Trees

We investigate the limiting behavior of random tree growth in preferential attachment models. The tree stems from a root, and we add vertices to the system one-by-one at random, according to a rule which depends on the degree distribution of the already existing tree. The so-called weight function, in terms of which the rule of attachment is formulated, is such that each vertex in the tree can have at most K children. We define the concept of a certain random measure mu on the leaves of the limiting tree, which captures a global property of the tree growth in a natural way. We prove that the Hausdorff and the packing dimension of this limiting measure is equal and constant with probability one. Moreover, the local dimension of mu equals the Hausdorff dimension at mu-almost every point. We give an explicit formula for the dimension, given the rule of attachment

Adaptive constraints for feature tracking

In this paper extensions to an existing tracking algorithm are described. These extensions implement adaptive tracking constraints in the form of regional upper-bound displacements and an adaptive track smoothness constraint. Together, these constraints make the tracking algorithm more flexible than the original algorithm (which used fixed tracking parameters) and provide greater confidence in the tracking results. The result of applying the new algorithm to high-resolution ECMWF reanalysis data is shown as an example of its effectiveness

Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II

The strong convergence of Wong-Zakai approximations of the solution to the reflecting stochastic differential equations was studied in [2]. We continue the study and prove the strong convergence under weaker assumptions on the domain.Comment: To appear in "Stochastic Analysis and Applications 2014-In Honour of Terry Lyons", Springer Proceedings in Mathematics and Statistic

Major features and forcing of high‐latitude northern hemisphere atmospheric circulation using a 110,000‐year‐long glaciochemical series

The Greenland Ice Sheet Project 2 glaciochemical series (sodium, potassium, ammonium, calcium, magnesium, sulfate, nitrate, and chloride) provides a unique view of the chemistry of the atmosphere and the history of atmospheric circulation over both the high latitudes and mid‐low latitudes of the northern hemisphere. Interpretation of this record reveals a diverse array of environmental signatures that include the documentation of anthropogenically derived pollutants, volcanic and biomass burning events, storminess over marine surfaces, continental aridity and biogenic source strength plus information related to the controls on both high‐ and low‐frequency climate events of the last 110,000 years. Climate forcings investigated include changes in insolation of the order of the major orbital cycles that control the long‐term behavior of atmospheric circulation patterns through changes in ice volume (sea level), events such as the Heinrich events (massive discharges of icebergs first identified in the marine record) that are found to operate on a 6100‐year cycle due largely to the lagged response of ice sheets to changes in insolation and consequent glacier dynamics, and rapid climate change events (massive reorganizations of atmospheric circulation) that are demonstrated to operate on 1450‐year cycles. Changes in insolation and associated positive feedbacks related to ice sheets may assist in explaining favorable time periods and controls on the amplitude of massive rapid climate change events. Explanation for the exact timing and global synchroneity of these events is, however, more complicated. Preliminary evidence points to possible solar variability‐climate associations for these events and perhaps others that are embedded in our ice‐core‐derived atmospheric circulation records

Comparison of Two Systems of Pasture Allocation on Milking Intervals and Total Daily Milk Yield of Dairy Cows in a Pasture-Based Automatic Milking System

In pasture-based automatic milking systems (AMS), cows usually have a lower milking frequency (MF, the number of milking events in any 24 h period) than those reported in indoor housing systems (García and Fulkerson 2005). Moreover, milking intervals (MI, the interval between consecutive milking events, measured at every milking session in hours since the previous milking event) are higher, with up to 30% of milking events occurring with intervals above 16 h in grazing systems (NA Lyons unpublished data). Milking events occurring with long intervals have a negative effect on milk yield (Schmidt 1960) and udder health (Hammer et al. 2012). Recognising that feed is the main incentive to achieve voluntary cow traffic (Prescott et al. 1998), some initial reports have depicted the potential importance and effect of incentives put in place per day (Jago et al. 2007). Yet to date no research has been published that quantifies the actual impact of number of feed allocations, on animal performance in pasture-based systems. The aim of this study was to determine the impact of 2 different grazing treatments (2-way grazing [2WG] versus 3-way grazing [3WG] allocations of feed per 24 h period), on MI, MF and daily milk yield (DY, in kg milk/d). It was hypothesised that an increase in frequency of feed allocation would result in increased cow traffic, MF and DY