Gravitational Thermodynamics of Causal Diamonds in (A)dS

The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a "first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the "entanglement equilibrium" result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.Comment: v3: 64 pages, 6 appendices, 8 figures; matches published versio

What grid cells convey about rat location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code

Spinning Black Holes as Particle Accelerators

It has recently been pointed out that particles falling freely from rest at infinity outside a Kerr black hole can in principle collide with arbitrarily high center of mass energy in the limiting case of maximal black hole spin. Here we aim to elucidate the mechanism for this fascinating result, and to point out its practical limitations, which imply that ultra-energetic collisions cannot occur near black holes in nature.Comment: 3 pages; v2: references added, minor modifications to match version published in PR

Over-spinning a black hole with a test body

It has long been known that a maximally spinning black hole can not be over-spun by tossing in a test body. Here we show that if instead the black hole starts out with below maximal spin, then indeed over-spinning can be achieved when adding either orbital or spin angular momentum. We find that requirements on the size and internal structure of the test body can be met as well. Our analysis neglects radiative and self-force effects,which may prevent the over-spinning.Comment: 4 pages; v2: reference added, incorporates the missed case of an oblate test body, which appears with the published version only as an erratum, other minor edits (with respect to v1

HEDGING FEEDER STEERS AND HEIFERS IN THE CASH-SETTLED FEEDER CATTLE FUTURES MARKET

Recent changes in the feeder cattle futures contract specifications are expected to reduce hedging risk and may result in changes in optimal hedging levels. This study provides an estimate of feeder cattle hedge ratios associated with the new cash-settled feeder cattle futures contract and compares the levels of hedging risk present under the cash settled contract with the physical delivery contract. Hedging risks are compared for several weights of feeder steers and heifers and are analyzed across four market locations. Results indicate that hedging risk is generally, though not always, lower with cash settlement than under the physical delivery contract specifications.Livestock Production/Industries, Marketing,

Novel individualized power training protocol preserves physical function in adult and older mice

Sarcopenia, the age-related loss of muscle mass and strength, contributes to frailty, functional decline, and reduced quality of life in older adults. Exercise is a recognized therapy for sarcopenia and muscle dysfunction, though not a cure. Muscle power declines at an increased rate compared to force, and force output declines earlier than mass. Thus, there is a need for research of exercise focusing on improving power output and functionality in older adults. Our primary purpose was proof-of-concept that a novel individualized power exercise modality would induce positive adaptations in adult mice, before the exercise program was applied to an aged cohort. We hypothesized that after following our protocol, both adult and older mice would show improved function, though there would be evidence of anabolic resistance in the older mice. Male C57BL/6 mice (12 months of age at study conclusion) were randomized into control (n = 9) and exercise (n = 6) groups. The trained group used progressive resistance (with a weighted harness) and intensity (~ 4-10 rpm) on a custom motorized running wheel. The mice trained similarly to a human workout regimen (4-5 sets/session, 3 sessions/week, for 12 weeks). We determined significant (p < 0.05) positive adaptations post-intervention, including: neuromuscular function (rotarod), strength/endurance (inverted cling grip test), training physiology (force/power output per session), muscle size (soleus mass), and power/velocity of contraction (in vitro physiology). Secondly, we trained a cohort of older male mice (28 months old at conclusion): control (n = 12) and exercised (n = 8). While the older exercised mice did preserve function and gain benefits, they also demonstrated evidence of anabolic resistance.F31 AG044108 - NIA NIH HHS; R01 AG017768 - NIA NIH HHS; TL1 TR001440 - Institute for Translational Sciences, University of Texas Medical BranchAccepted manuscrip

Stellar Populations and the White Dwarf Mass Function: Connections To Supernova Ia Luminosities

We discuss the luminosity function of SNe Ia under the assumption that recent evidence for dispersion in this standard candle is related to variations in the white dwarf mass function (WDMF) in the host galaxies. We develop a simple parameterization of the WDMF as a function of age of a stellar population and apply this to galaxies of different morphological types. We show that this simplified model is consistent with the observed WDMF of Bergeron et al. (1992) for the solar neighborhood. Our simple models predict that WDMF variations can produce a range of more than 1.8 mag in M$_B$(SN Ia), which is comparable to the observed value using the data of Phillips (1993) and van den Bergh (1996). We also predict a galaxy type dependence of M$_B$(SN Ia) under standard assumptions of the star formation history in these galaxies and show that M$_B$(SN Ia) can evolve with redshift. In principle both evolutionary and galaxy type corrections should be applied to recover the intrinsic range of M$_B$(SN Ia) from the observed values. Our current inadequate knowledge of the star formation history of galaxies coupled with poor physical understanding of the SN Ia mechanism makes the reliable estimation of these corrections both difficult and controversial. The predictions of our models combined with the observed galaxy and redshift correlations may have the power to discriminate between the Chandrasekhar and the sub-Chandrasekhar progenitor scenarios for SNe Ia.Comment: 20 pages, latex + 7 postscript figures, to be published in AJ, September 199

Some considerations for interpretation of soil tests for phosphorus and potassium

Digitized 2007 AES MoU.Includes bibliographical references (page 36)