The Indefinite Logarithm, Logarithmic Units, and the Nature of Entropy

We define the indefinite logarithm [log x] of a real number x>0 to be a mathematical object representing the abstract concept of the logarithm of x with an indeterminate base (i.e., not specifically e, 10, 2, or any fixed number). The resulting indefinite logarithmic quantities naturally play a mathematical role that is closely analogous to that of dimensional physical quantities (such as length) in that, although these quantities have no definite interpretation as ordinary numbers, nevertheless the ratio of two of these entities is naturally well-defined as a specific, ordinary number, just like the ratio of two lengths. As a result, indefinite logarithm objects can serve as the basis for logarithmic spaces, which are natural systems of logarithmic units suitable for measuring any quantity defined on a logarithmic scale. We illustrate how logarithmic units provide a convenient language for explaining the complete conceptual unification of the disparate systems of units that are presently used for a variety of quantities that are conventionally considered distinct, such as, in particular, physical entropy and information-theoretic entropy.Comment: Manuscript of a 15 pp. review article. Suggestions for additional appropriate references to relevant prior work are solicited from the communit

Isometric Tensor Network States in Two Dimensions

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD$^2$) for approximating the ground state of a Hamiltonian as an isometric TNS, which we demonstrate for the 2D transverse field Ising model.Comment: 5 pages, 4 figure

Stated Choice Experiments with Complex Ecosystem Changes: The Effect of Information Formats on Estimated Variances and Choice Parameters

Stated choice experiments about ecosystem changes involve complex information. This study examines whether the format in which ecosystem information is presented to respondents affects stated choice outcomes. Our analysis develops a utility-maximizing model to describe respondent behavior. The model shows how alternative questionnaire formats alter respondents’ use of filtering heuristics and result in differences in preference estimates. Empirical results from a large-scale stated choice experiment confirm that different format presentations of the same information lead to different preference parameter estimates and error variances. A tabular format results in choice parameter estimates with statistically smaller variances than parameters estimated from data obtained with a text-based format. A text-based format also appears to induce greater use of decision heuristics than does a tabular format.choice experiments, heuristics, stated preference, valuation, web surveys, wetland mitigation, Crop Production/Industries, Demand and Price Analysis,

Cow serum and colostrum immunoglobulin (IgG1) concentration of five suckler cow breed types and subsequent immune status of their calves

peer-reviewedB. Murphy would like to gratefully acknowledge receipt of a Walsh Fellowship provided by Teagasc.The objective of this study was to determine the effect of cow breed type on (a) cow serum and colostrum immunoglobulin (IgG1) concentrations and (b) subsequent calf serum IgG1 concentration and zinc sulphate turbidity (ZST) units. Five cow breed types were examined: LF (Limousin × Friesian), LLF (Limousin × (Limousin × Friesian)), L (Limousin), C (Charolais) and SLF (Simmental × (Limousin × Friesian)). Three blood samples were taken by jugular venipuncture from the cows at approximately 90, 60 and 30 days pre partum, at parturition and at 15 days or more post partum and from the calves at 48 (40 to 56) h post partum. Prior to suckling a 20 ml sample of colostrum was obtained. Milk yield was estimated using the weigh-suckleweigh technique. The decrease in serum IgG1 concentration in cows between 90 days pre partum and parturition was greater (P < 0.01) for LF cows than all other breed types, except SLF. There was no difference between LLF, L, C and SLF cows. There was no effect of cow breed type on colostrum IgG1 concentration. Milk yield was higher (P < 0.001) for LF cows than all other breed types, while that of SLF was higher than the three remaining breed types, which were similar. Calf serum IgG1 concentration and ZST units were higher (P < 0.01) for the progeny of LF cows than all others except SLF. There was no difference between the progeny of LLF, L, C and SLF cows. Calf serum IgG1 was affected by cow breed type and showed a positive relationship with cow serum IgG1 decreases in late pregnancy