A formula for Pl\"ucker coordinates associated with a planar network

For a planar directed graph G, Postnikov's boundary measurement map sends positive weight functions on the edges of G onto the appropriate totally nonnegative Grassmann cell. We establish an explicit formula for Postnikov's map by expressing each Pluecker coordinate as a ratio of two combinatorially defined polynomials in the edge weights, with positive integer coefficients. In the non-planar setting, we show that a similar formula holds for special choices of Pluecker coordinates.Comment: 15 pages, 6 figures. Extensive additions, including a generalization for arbitrarily oriented planar graphs and a formula for some Pluecker coordinates of non-planar perfectly oriented graph

Positivity for Gaussian graphical models

Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient condition in terms of the graph for when a subdeterminant is zero for all covariance matrices that belong to the Gaussian graphical model. Here we extend this result to give explicit cancellation-free formulas for the expansions of nonzero subdeterminants.Comment: 16 pages, 3 figure

A comparison of two protein supplements on the healing of stage III and IV pressure injuries in enterally fed, ventilator dependent long – term care residents

The purpose of this study was to evaluate the change in stage III or IV pressure injury size of enterally fed, ventilator dependent, long-term care residents after receiving one of two protein supplements in addition to enteral feeding meeting 100% of calculated needs. The two protein supplements were Beneprotein™ (powder) and Pro T Gold™ (liquid). The injuries were evaluated for change in size at two weeks and four weeks post initiation of protein supplement. Sixty subjects were reviewed – 30 for each supplement. Subjects included 20 males (33%) and 40 females (67%). The analysis indicated for the total sample, a significant reduction in injury size for those receiving Beneprotein™ compared to those receiving Pro T Gold™ (p\u3c0.05) after two weeks of supplementation. However, there was no significant difference between the supplement groups after four weeks of continued supplementation (p = .261). Injury healing for subjects with an existing comorbidity of diabetes or chronic kidney disease were compared to subjects without these comorbidities. Overall, the comorbidity group experienced greater injury healing compared to the non-comorbidity group after both two weeks (p\u3c0.05) and four weeks of supplementation (p\u3c0.05). This research showed that Beneprotein™ provided more rapid wound healing in the first two weeks of supplementation and that the comorbidity group experienced greater benefit from protein supplementation. Further research needs to be conducted with a larger sample size for a longer monitoring time

Incidência de COVID-19 (Sars-Cov-2) e fluxos de deslocamentos para serviços de saúde na Região AMAUC: Geotecnologias aplicadas aos estudos demográficos

The scientific and technological transformations that configure the current moment of society make with that perfecting of methods that aim achieve excellence in terms of knowledge and treatment of spatial data will be always on the order of days. With this understanding, the proposal was to elaborate thematic maps applied to the monitoring of the diffusion of COVID-19 (Sars-Cov-2) in the region of the Associação dos Municípios do Alto Uruguai Catarinense (AMAUC). The geotechnological procedures applied in the generation of cartographic product are described, which relates the incidence of confirmed cases of Covid-19 (Sars-cov2) for groups of 1.000 people and the displacement of the resident population for access to health services. The final cartographic product is important for analysis, visual communication and interpretation of spatial phenomena, contributing to territorial planning and management.Las transformaciones científicas y tecnológicas que configuran el momento actual de la sociedad con ese perfeccionamiento de los métodos que apuntan a alcanzar la excelencia en términos de conocimiento y tratamiento de datos espaciales estarán siempre en el orden de los días. Con este entendimiento, la propuesta fue elaborar mapas temáticos aplicados al monitoreo de la difusión de COVID-19 (Sars-Cov-2) en la región de la Asociación de Municipios del Alto Uruguay Catarinense (AMAUC). Se describen los procedimientos geotecnológicos aplicados en la generación del producto cartográfico, que relaciona la incidencia de casos confirmados de Covid-19 (Sars-cov2) para grupos de 1.000 personas y el desplazamiento de la población residente para acceder a los servicios de salud. El producto cartográfico final es importante para el análisis, la comunicación visual y la interpretación de fenómenos espaciales, contribuyendo a la planificación y gestión territorial.As transformações científicas e tecnológicas que configuram o momento atual da sociedade fazem com que o aperfeiçoamento de métodos que visam alcançar a excelência em termos de conhecimento e tratamento de dados espaciais estejam sempre na ordem do dia. Com este entendimento, a proposta foi elaborar mapas temáticos aplicados ao  monitoramento da difusão do COVID-19 (Sars-Cov-2) na região da Associação dos Municípios do Alto Uruguai Catarinense (AMAUC). Assim, descreve-se os procedimentos geotecnológicos aplicados na geração de produto cartográfico, que relaciona a incidência dos casos confirmados de Covid-19 (Sars-cov2) para grupos de 1.000 habitantes e os deslocamentos da população residente para o acesso aos serviços de saúde. O produto cartográfico final se mostra importante para análises, comunicação visual e interpretação de fenômenos espaciais que importam ao planejamento e gestão territorial

Rehabilitation strategies to overcome quadriceps weakness for athletes with anterior cruciate ligament (ACL) reconstruction

This poster was presented at the Great Plains Honors Conference in Canyon, Texas.https://scholarworks.uttyler.edu/student_posters/1018/thumbnail.jp

Trek separation for Gaussian graphical models

Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases. Our new trek separation criterion generalizes the familiar $d$-separation criterion. Proofs are based on the trek rule, the resulting matrix factorizations and classical theorems of algebraic combinatorics on the expansions of determinants of path polynomials.Comment: Published in at http://dx.doi.org/10.1214/09-AOS760 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estrutura agrária e agricultura familiar em Santa Catarina

Considerando as modificações realizadas no arcabouço conceitual de interpretação da realidade agrária brasileira nas últimas décadas, este artigo revela a supressão e a inclusão normativa de conceitos importantes para a interpretação da estrutura agrária e fundiária do país. O debate centra-se em torno da categoria latifúndio, que, segundo o Estatuto da Terra de 1964, deveria ter sido extinto gradualmente do território brasileiro. Fato que acabou acontecendo, eficientemente, no texto das leis, cunhadas por interesses de classe, mas, que, comprovadamente, se mostram persistentes na realidade agrária brasileira e, inclusive, na realidade do estado de Santa Catarina, onde se apresenta de forma concomitante com a agricultura familiar e, principalmente, com a agricultura não familiar. Este artigo apresenta, além de pressupostos teóricos para a permanência dos latifúndios, evidências que permitem a sua identificação na realidade agrária brasileira à luz da sua definição originária de 1964