Experience Implementing a Performant Category-Theory Library in Coq

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to cope with large categorical constructions without slowing proof script processing unacceptably. In this paper, we share the lessons we have learned about how to represent very abstract mathematical objects and arguments in Coq and how future proof assistants might be designed to better support such reasoning. One particular encoding trick to which we draw attention allows category-theoretic arguments involving duality to be internalized in Coq's logic with definitional equality. Ours may be the largest Coq development to date that uses the relatively new Coq version developed by homotopy type theorists, and we reflect on which new features were especially helpful.Comment: The final publication will be available at link.springer.com. This version includes a full bibliography which does not fit in the Springer version; other than the more complete references, this is the version submitted as a final copy to ITP 201

Vapour reactive distillation process for hydrogen production by hi decomposition from hi-i2-h2o solutions

In this contribution, a sequential and hierarchical approach for the feasibility analysis and the preliminary design of reactive distillation columns is extended to systems involving vapour phase chemical reaction and is successfully applied to the HI vapour phase decomposition to produce H2. The complex phase and physico chemical behaviour of the quaternary HI-H2-I2-H2O system is represented by the Neumann’s thermodynamic model and instantaneous vapour phase chemical equilibrium is assumed. Then, from minimal information concerning the physicochemical properties of the system, three successive steps lead to the design of the unit and the specification of its operating conditions: the feasibility analysis, the synthesis and the design step. First, the analysis of reactive condensation curve map method (rCCM), assuming infinite internal liquid and vapour flow rate and infinite reflux ratio, is used to assess the feasibility of the process. It determines the column structure and estimates the attainable compositions. These results are used as inputs data for the synthesis step. Based on the boundary value design method (BVD), considering finite internal liquid and vapour flow rate and finite reflux ratio while neglecting all thermal effects and assuming a constant heat of vaporisation, the synthesis step provides more precise information about the process configuration (minimum reflux ratio, number of theoretical stages, localisation and number of reactive plates, position of the feed plate). Finally, the BVD method results are used to initialise rigorous simulations, based on an equilibrium stage model with energy balance, to estimate the reflux ratio taking into account thermal effect on the process. The resulting design configuration consists in a single feed and entirely reactive distillation column. The column operates under a pressure of 22 bars. The feed of the reactive distillation column, coming from the Bunsen reaction section [xHI=0.10; xI2=0.39 xH2O=0.51], is at its boiling temperature. The residue consists in pure iodine. Water and produced hydrogen are recovered at the distillate. The column operates at a reflux ratio of 5 and is composed of 11 theoretical plates including the reboiler and the partial condenser with the feed at the stage 10 (counted downwards). The obtained HI dissociation yield is 99.6%

Hydraulic Responses of Shrubs and Grasses to Fire Frequency and Drought in a Tallgrass Prairie Experiencing Bush Encroachment

The increase in abundance and density of woody plants in herbaceous ecosystems (i.e. bush encroachment) is occurring globally and is driven by reduced fire frequency, climate change, and the utilization of deeper, more reliable soil water by woody plants. Thus, a comprehensive understanding of the physiological processes through which woody and herbaceous plants use water will provide greater insight into the mechanisms of bush encroachment, as well as the trajectory of encroachment in a changing climate. Our objective was to assess how experimental changes in water availability and fire frequency impact belowground water-use traits in Cornus drummondii, the primary encroaching shrub within North American tallgrass prairies, and Andropogon gerardii, a dominant C4 grass. Shelters that reduced precipitation by 50% (drought) and 0% (control) were built over mature shrubs growing in sites that were burned at 1-year and 4-year frequencies. We assessed the water transport capability of shrubs and grasses growing in each treatment by measuring the maximum hydraulic conductance (Kmax) of entire root systems. We also assessed the vulnerability of shrub root segments to loss of hydraulic function by measuring the pressure at which 50% of the maximum hydraulic conductivity is lost (P50). Grass and shrub roots had opposite responses to drought and these patterns varied with fire treatment. Grasses growing in drought plots had lower root Kmax than control grasses. Conversely, root Kmax did not differ significantly between treatments in shrubs. However, drought shrub roots were less vulnerable to water stress than control roots (P50=-1.5 and -0.20 MPa, respectively). These results suggest that the ability of grass roots to use water declined with drought, while the ability of shrub roots to resist water stress increased with drought. Future work should investigate whether these drought responses are associated with altered root growth patterns

Advancing Social Determinants of Health Through Investments in Postsecondary Attainment and Sustaining Employment

In 2018, the Humana Foundation shifted the focus of its work to the social determinants of health, with the key aim of promoting health equity. With this new focus came a recognition that larger, long-term investments would be needed to support strategies addressing upstream determinants of health. The foundation also recognized the need to co-create processes with communities to understand how to provide essential holistic supports. This article explores one area of the foundation’s new efforts, the Strategic Community Investment Program, which focuses in part on postsecondary attainment and sustaining employment. The foundation partnered with the University of Louisville’s Center for Health Organization Transformation to systematically review models in the literature of successful postsecondary attainment strategies to evaluate the results in communities. This article shares key learnings from the literature and coordinated practice in communities that were used to revise the foundation’s strategy, and concludes with suggestions for other foundations interested in addressing postsecondary attainment and other social determinants of health to better meet the challenges and opportunities of the communities they serve

Predictive validity of the UK clinical aptitude test in the final years of medical school:a prospective cohort study

Peer reviewedPublisher PD

The Common Factors of Grit, Hope, and Optimism Differentially Influence Suicide Resilience

No study to date has simultaneously examined the commonalities and unique aspects of positive psychological factors and whether these factors uniquely account for a reduction in suicide risk. Using a factor analytic approach, the current study examined the relationships between grit, hope, optimism, and their unique and overlapping relationships in predicting suicide ideation. Results of principle axis factor analysis demonstrated close relationships between these variables at both the construct and item level. Item-level analyses supported a five-factor solution (Stick-to-Itiveness, Poor Future, Consistency of Interest, Positive Future, and Poor Pathways). Four of the five factors (excluding Stick-to-Itiveness) were associated with suicide ideation. Additionally, results of a multiple regression analysis indicated that two of the five factors (Consistency of Interest and Positive Future) negatively predicted suicide ideation while Poor Future positively predicted suicide ideation. Implications regarding the interrelationships between grit, hope, and optimism with suicide ideation are discussed

Increased homozygosity in the first Hispanic patient with plantar lipomatosis, unusual facies, and developmental delay (Pierpont syndrome): a case report

BACKGROUND: Pierpont syndrome was first described in 1998 with key characteristics including developmental delay, dysmorphic facial features, fat pads on hands and feet, and feeding difficulties. To date the mechanism of inheritance is unknown. Nine out of ten previously described patients with Pierpont syndrome were boys. This is the first report of a case of a non-white patient with Pierpont syndrome and she is the second female patient to be described as having Pierpont syndrome. CASE PRESENTATION: Our patient is a 16-month-old Hispanic girl with extreme developmental delay, microcephaly, large ears, short and thick upper lip, broad philtrum, widely spaced teeth, constipation, dysphagia, fat pads on feet and hands, autistic behavior and seizure-like episodes. She had a normal karyotype (46,XX), and array testing showed greater than 8 % homozygosity with otherwise normal results. Genes within these areas of homozygosity may provide clues to an etiology and suggest autosomal recessive inheritance. This case report highlights the possibility of ethnic variations in this syndrome’s presentation, which may have ramifications in uncovering the pathogenesis as well as expanding the phenotype. CONCLUSION: Pierpont syndrome should be considered in the evaluation of children with the described features, regardless of their gender and ethnicity

Representational capacity of a set of independent neurons

The capacity with which a system of independent neuron-like units represents a given set of stimuli is studied by calculating the mutual information between the stimuli and the neural responses. Both discrete noiseless and continuous noisy neurons are analyzed. In both cases, the information grows monotonically with the number of neurons considered. Under the assumption that neurons are independent, the mutual information rises linearly from zero, and approaches exponentially its maximum value. We find the dependence of the initial slope on the number of stimuli and on the sparseness of the representation.Comment: 19 pages, 6 figures, Phys. Rev. E, vol 63, 11910 - 11924 (2000