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

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

Changes in the diet and body size of a small herbivorous mammal (hispid cotton rat, \u3ci\u3eSigmodon hispidus\u3c/i\u3e) following the late Pleistocene megafauna extinction

The catastrophic loss of large-bodied mammals during the terminal Pleistocene likely led to cascading effects within communities. While the extinction of the top consumers probably expanded the resources available to survivors of all body sizes, little work has focused on the responses of the smallest mammals. Here, we use a detailed fossil record from the southwestern United States to examine the response of the hispid cotton rat Sigmodon hispidus to biodiversity loss and climatic change over the late Quaternary. In particular, we focus on changes in diet and body size. We characterize diet through carbon (δ13C) and nitrogen (δ15N) isotope analysis of bone collagen in fossil jaws and body size through measurement of fossil teeth; the abundance of material allows us to examine population level responses at millennial scale for the past 16 ka. Sigmodon was not present at the cave during the full glacial, first appearing at ~16 ka after ice sheets were in retreat. It remained relatively rare until ~12 ka when warming tempera­tures allowed it to expand its species range northward. We find variation in both diet and body size of Sigmodon hispidus over time: the average body size of the population varied by ~20% (90–110 g) and mean δ13C and δ15N values ranged between −13.5 to −16.5‰ and 5.5 to 7.4‰ respectively. A state–space model suggested changes in mass were influenced by diet, maximum temperature and community structure, while the modest changes in diet were most influenced by community structure. Sigmodon maintained a fairly similar dietary niche over time despite contemporaneous changes in climate and herbivore community composition that followed the megafauna extinc­tion. Broadly, our results suggest that small mammals may be as sensitive to shifts in local biotic interactions within their ecosystem as they are to changes in climate and large-scale biodiversity loss

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

Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

Flows driven by Banach space-valued rough paths

We show in this note how the machinery of C^1-approximate flows devised in the work "Flows driven by rough paths", and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path, can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force in a simple way.Comment: 8 page

Semantic Memory Functional MRI and Cognitive Function After Exercise Intervention in Mild Cognitive Impairment

Mild cognitive impairment (MCI) is associated with early memory loss, Alzheimer\u27s disease (AD) neuropathology, inefficient or ineffective neural processing, and increased risk for AD. Unfortunately, treatments aimed at improving clinical symptoms or markers of brain function generally have been of limited value. Physical exercise is often recommended for people diagnosed with MCI, primarily because of its widely reported cognitive benefits in healthy older adults. However, it is unknown if exercise actually benefits brain function during memory retrieval in MCI. Here, we examined the effects of exercise training on semantic memory activation during functional magnetic resonance imaging (fMRI). Seventeen MCI participants and 18 cognitively intact controls, similar in sex, age, education, genetic risk, and medication use, volunteered for a 12-week exercise intervention consisting of supervised treadmill walking at a moderate intensity. Both MCI and control participants significantly increased their cardiorespiratory fitness by approximately 10% on a treadmill exercise test. Before and after the exercise intervention, participants completed an fMRI famous name discrimination task and a neuropsychological battery, Performance on Trial 1 of a list-learning task significantly improved in the MCI participants. Eleven brain regions activated during the semantic memory task showed a significant decrease in activation intensity following the intervention that was similar between groups (p-values ranged 0.048 to 0.0001). These findings suggest exercise may improve neural efficiency during semantic memory retrieval in MCI and cognitively intact older adults, and may lead to improvement in cognitive function. Clinical trials are needed to determine if exercise is effective to delay conversion to AD

Arterial pathology in canine mucopolysaccharidosis-I and response to therapy.

Mucopolysaccharidosis-I (MPS-I) is an inherited deficiency of α-L-iduronidase (IdU) that causes lysosomal accumulation of glycosaminoglycans (GAG) in a variety of parenchymal cell types and connective tissues. The fundamental link between genetic mutation and tissue GAG accumulation is clear, but relatively little attention has been given to the morphology or pathogenesis of associated lesions, particularly those affecting the vascular system. The terminal parietal branches of the abdominal aorta were examined from a colony of dogs homozygous (MPS-I affected) or heterozygous (unaffected carrier) for an IdU mutation that eliminated all enzyme activity, and in affected animals treated with human recombinant IdU. High-resolution computed tomography showed that vascular wall thickenings occurred in affected animals near branch points, and associated with low endothelial shear stress. Histologically these asymmetric 'plaques' entailed extensive intimal thickening with disruption of the internal elastic lamina, occluding more than 50% of the vascular lumen in some cases. Immunohistochemistry was used to show that areas of sclerosis contained foamy (GAG laden) macrophages, fibroblasts and smooth muscle cells, with loss of overlying endothelial basement membrane and claudin-5 expression. Lesions contained scattered cells expressing nuclear factor-κβ (p65), increased fibronectin and transforming growth factor β-1 signaling (with nuclear Smad3 accumulation) in comparison to unaffected vessels. Intimal lesion development and morphology was improved by intravenous recombinant enzyme treatment, particularly with immune tolerance to this exogenous protein. The progressive sclerotic vasculopathy of MPS-I shares some morphological and molecular similarities to atherosclerosis, including formation in areas of low shear stress near branch points, and can be reduced or inhibited by intravenous administration of recombinant IdU

Raman Scattering and Anomalous Current Algebra: Observation of Chiral Bound State in Mott Insulators

Recent experiments on inelastic light scattering in a number of insulating cuprates [1] revealed a new excitation appearing in the case of crossed polarizations just below the optical absorption threshold. This observation suggests that there exists a local exciton-like state with an odd parity with respect to a spatial reflection. We present the theory of high energy large shift Raman scattering in Mott insulators and interpret the experiment [1] as an evidence of a chiral bound state of a hole and a doubly occupied site with a topological magnetic excitation. A formation of these composites is a crucial feature of various topological mechanisms of superconductivity. We show that inelastic light scattering provides an instrument for direct measurements of a local chirality and anomalous terms in the electronic current algebra.Comment: 18 pages, TeX, C Version 3.