Categorical formulation of quantum algebras

We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between finite-dimensional C*-algebras and certain types of dagger-Frobenius monoids in the category of Hilbert spaces. Using this technology, we recast the spectral theorems for commutative C*-algebras and for normal operators into an explicitly categorical language, and we examine the case that the results of measurements do not form finite sets, but rather objects in a finite Boolean topos. We describe the relevance of these results for topological quantum field theory.Comment: 34 pages, to appear in Communications in Mathematical Physic

Best practices for addressing missing data through multiple imputation

A common challenge in developmental research is the amount of incomplete and missing data that occurs from respondents failing to complete tasks or questionnaires, as well as from disengaging from the study (i.e., attrition). This missingness can lead to biases in parameter estimates and, hence, in the interpretation of findings. These biases can be addressed through statistical techniques that adjust for missing data, such as multiple imputation. Although multiple imputation is highly effective, it has not been widely adopted by developmental scientists given barriers such as lack of training or misconceptions about imputation methods. Utilizing default methods within statistical software programs like listwise deletion is common but may introduce additional bias. This manuscript is intended to provide practical guidelines for developmental researchers to follow when examining their data for missingness, making decisions about how to handle that missingness and reporting the extent of missing data biases and specific multiple imputation procedures in publications

Comparison of two soil quality indexes to evaluate cropping systems in northern Colorado

Various soil management or quality assessment tools have been proposed to evaluate the effects of land management practices on soil, air, and water resources. Two of them are the Soil Management Assessment Framework and the Soil Conditioning Index (SCI). This study was conducted to test the hypothesis that the Soil Quality Index (SQI) estimated by the Soil Management Assessment Framework can detect more minute changes in soil management than SCI and to test SCI response to other soil quality (SQ) indicators. These SQ indexes were tested on irrigated cropping systems near Fort Collins, Colorado, that included no-till and conventionally-tilled corn (Zea mays L.), and no-till corn with rotations including barley (Hordeum distichon L.), soybean (Glycine max (L.) Merr.), and dry bean (Phaeseolus vulgaris L.) at three levels of nitrogen varying from 0 to 224 kg N ha–1 (0 to 200 lb ac–1). Both SQ indexes clearly separated the plots with very high levels of N from plots with no N. However, for SQI the mid-level of N was statistically the same as both extreme levels. Statistical differences were observed among all N levels for the SCI. The SQI seemed to make more detailed differentiation among crop management systems than the SCI. The SCI separated the cropping systems into three groups with no overlap among groups. All no-till systems had the statistically same higher SCI than the conventionally-tilled continual corn system. The SQI separated the cropping systems into three groups with decreasing SQI as tillage intensity increased and as lower residue crops were introduced into the cropping system. The systems that included tillage and a low residue crop (soybean) had the lowest SQI. The SQI allowed overlap among cropping groups not recognized by SCI. Selection of the most appropriate SQ index seems to be a tradeoff between data requirements, resolution required, and the desired use of the evaluation tool

Saline seep diagnosis, control and reclamation

Please contact the NWISRL if you have a copy of this publication

Saline seep diagnosis, control and reclamation

Please contact the NWISRL if you have a copy of this publication