A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

Surface and capillary transitions in an associating binary mixture model

We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere the physical mechanism involved in the appearance of these phase diagrams, leading to an enhanced tendency to phase separate below the lower critical solution point. Three different cases are considered: a planar solid surface in contact with a bulk fluid, while the other two represent two models of porous systems, namely a slit and an array on infinitely long parallel cylinders. We confirm that surface transitions, as well as capillary transitions for a large area/volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed.Comment: 12 two-column pages, 12 figures, accepted for publication in Physical Review E; corrected versio

Diurnal shifts in nutritive value of alfalfa harvested as hay and evaluated by animal intake and digestion

Forages accumulate nonstructural carbohydrates during the day, with animals showing preference and improved daily responses from afternoon compared with morning cut hays. This study evaluated alfalfa (Medicago sativa L.) hay harvested at 0700, 1000, 1300, 1600, and 1900 h to determine how nutritive value changes during the day and to assess the impact of these changes on animal preference using cattle (Bos taurus L.), sheep (Ovis aries L.), and goat (Capra hircus L.) responses. Total nonstructural carbohydrates were altered by time of cut (cubic contrast, P < 0.01) ranging from 85 g kg?1 at 0700 h to 83 g kg?1 at 1000 h, then increasing to 97 g kg?1 by 1600 h with little change at 1900 h (96 g kg?1). Fiber fractions also varied diurnally, with a quadratic decrease from 418 g kg?1 at 0700 h to 387 g kg?1 by 1900 h in neutral detergent fiber. A combined analysis of three animal trials showed a linear increase in dry matter intake (DMI) with later hay harvest, a cubic response for dry matter digestion (DMD), and a linear increase in digestible DMI. Mean DMI increased from 27.5 g kg?1 body weight at 0700 h to a maximum of 30.8 g kg?1 body weight at 1600 h, whereas DMD decreased from 658 g kg?1 at 0700 to 647 g kg?1 at 1300 h and peaked at 664 g kg?1 at 1600 h. Digestible DMI increased from 18.1 g kg?1 body weight at 0700 h to a maximum of 20.5 g kg?1 body weight at 1600 h. No additional advantages in animal responses were noted by cutting after 1600 h

Preference by sheep and goats among hay of eight tall fescue cultivars

Grazing ruminants use both visual cues and taste in selecting their diet. Preference during grazing may not be the same when forage is dried for hay and cut into lengths prior to feeding in confinement. Eight cultivars of tall fescue (Festuca arundinacea Schreb.), previously evaluated for preference while grazed, were harvested three times over a period of 2 yr. The hays were air-dried, baled, and passed through a hydraulic bale processor prior to feeding. Five experiments were conducted. All three harvests were evaluated with sheep and the last two also with goats, using six animals each time. During an adaptation phase, hays were offered alone as meals. In the experimental phase, every possible pair of hays (28 pairs) was presented for a meal. Data were analyzed by multidimensional scaling and by traditional analyses. Preference was significant among cultivars in all experiments. Multidimensional scaling showed that selection was based on two criteria with two dimensions being significant. Sheep preferred KENHY followed by KENTUCKY 31 and STARGRAZER but preferenced against BARCEL. HIMAG, MO-96, and C1 were intermediate and MOZARK was variable. Goats were similar to sheep in preferring KENHY followed by STARGRAZER and selected against MOZARK and BARCEL. KENTUCKY 31, HIMAG, MO-96, and Cl were intermediate. In all five experiments, the general association was positive for available carbohydrate fractions and negative for fiber fractions that contribute to cell wall rigidity

Ruminant selection among switchgrass hays cut at either sundown or sunup

As a result of photosynthesis, plants typically have greater concentrations of nonstructural carbohydrates at the end of the photoperiod. The preference of ruminants for hays harvested within the same 24-h period can be greater for plants harvested late in the photoperiod with increased soluble carbohydrate. To test for variation in ruminant preference for afternoon versus morning harvested hays in a C4 grass harvested in the humid east, established fields of 'Kanlow' and 'Alamo' switchgrass (Panicum virgatum L.) were used to produce hays in 1998, 1999, and 2000 near Raleigh, NC. Harvests were paired so that each cutting in the evening (PM) was followed by a cutting the next morning (AM). We harvested in this manner three times in 1998 to produce six Kanlow hays; twice with Kanlow and once with Alamo at two levels of nitrogen fertility in 1999 to produce eight hays; and three times in 2000 to produce six Alamo hays. The hays were field-dried, baled, and passed through a hydraulic bale processor. Hays from each year were tested with cattle (Bos taurus L.), goats (Capra hircus L.), and sheep (Ovis aries L.). During an adaptation phase, hays were offered individually. In the experimental phase, all possible pairs of hays were presented. Data were analyzed by multidimensional scaling and by traditional analyses. Multidimensional scaling indicated that selection was based on multiple criteria. The suite of improvements associated with PM-harvested hays in fiber content, digestibility, and nonstructural carbohydrate observed for alfalfa and fescue hays in the western USA was difficult to reproduce with switchgrass hay in the southeastern USA. This difficulty is likely related to the less favorable environment for haymaking as well as the physiology, anatomy, and morphology of this C4 grass

Investment in Electricity Networks with Transmission Switching

We consider the application of Dantzig-Wolfe decomposition to stochastic integer programming problems arising in the capacity planning of electricity trans-mission networks that have some switchable transmission elements. The decomposition enables a column-generation algorithm to be applied, which allows the solution of large problem instances. The methodology is illustrated by its application to a problem of determining the optimal investment in switching equipment and transmission capacity for an existing network. Computational tests on IEEE test networks with 73 nodes and 118 nodes confirm the efficiency of the approach

Ring exchange, the Bose metal, and bosonization in two dimensions

Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase which underlies the spin-charge separation scenario for high-T_c superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the *Bose metal*. The Bose metal is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the Bose metal with the aid of an exact plaquette duality transformation, which motivates a universal low energy description of the Bose metal. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well-known one-dimensional bosonization approach. We verify the validity of the low energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-T_c superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two dimensional fermionic ring model

A simple two-module problem to exemplify building-block assembly under crossover

Theoretically and empirically it is clear that a genetic algorithm with crossover will outperform a genetic algorithm without crossover in some fitness landscapes, and vice versa in other landscapes. Despite an extensive literature on the subject, and recent proofs of a principled distinction in the abilities of crossover and non-crossover algorithms for a particular theoretical landscape, building general intuitions about when and why crossover performs well when it does is a different matter. In particular, the proposal that crossover might enable the assembly of good building-blocks has been difficult to verify despite many attempts at idealized building-block landscapes. Here we show the first example of a two-module problem that shows a principled advantage for cross-over. This allows us to understand building-block assembly under crossover quite straightforwardly and build intuition about more general landscape classes favoring crossover or disfavoring it

Crossover from 2-dimensional to 1-dimensional collective pinning in NbSe3

We have fabricated NbSe$_3$ structures with widths comparable to the Fukuyama-Lee-Rice phase-coherence length. For samples already in the 2-dimensional pinning limit, we observe a crossover from 2-dimensional to 1-dimensional collective pinning when the crystal width is less than 1.6 $\mu$m, corresponding to the phase-coherence length in this direction. Our results show that surface pinning is negligible in our samples, and provide a means to probe the dynamics of single domains giving access to a new regime in charge-density wave physics.Comment: 4 pages, 2 figures, and 1 table. Accepted for publication in Physical Review