Min-Max Theorems for Packing and Covering Odd (u,v)(u,v)-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated vertices but no repeated edges. We call a trail odd if the number of edges in the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd $(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that intersects every odd $(u,v)$-trail. We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$. Our proof also yields a polynomial-time algorithm for finding a cover and a collection of trails satisfying the above bounds. Our proof is simple and has two main ingredients. We show that (loosely speaking) the problem can be reduced to the problem of packing and covering odd $(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or the size of the cover). Complementing this, we show that the odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting a powerful min-max result of [Chudnovsky et al 2006] for packing vertex-disjoint nonzero $A$-paths in group-labeled graphs

Religious leaders\u27 perceptions of advance care planning: a secondary analysis of interviews with Buddhist, Christian, Hindu, Islamic, Jewish, Sikh and Bahai leaders

Background: International guidance for advance care planning (ACP) supports the integration of spiritual and religious aspects of care within the planning process. Religious leaders’ perspectives could improve how ACP programs respect patients’ faith backgrounds. This study aimed to examine: (i) how religious leaders understand and consider ACP and its implications, including (ii) how religion affects followers’ approaches to end-of-life care and ACP, and (iii) their implications for healthcare. Methods: Interview transcripts from a primary qualitative study conducted with religious leaders to inform an ACP website, ACPTalk, were used as data in this study. ACPTalk aims to assist health professionals conduct sensitive conversations with people from different religious backgrounds. A qualitative secondary analysis conducted on the interview transcripts focussed on religious leaders’ statements related to this study’s aims. Interview transcripts were thematically analysed using an inductive, comparative, and cyclical procedure informed by grounded theory. Results: Thirty-five religious leaders (26 male; mean 58.6-years-old), from eight Christian and six non-Christian (Jewish, Buddhist, Islamic, Hindu, Sikh, Bahá’í) backgrounds were included. Three themes emerged which focussed on: religious leaders’ ACP understanding and experiences; explanations for religious followers’ approaches towards end-of-life care; and health professionals’ need to enquire about how religion matters. Most leaders had some understanding of ACP and, once fully comprehended, most held ACP in positive regard. Religious followers’ preferences for end-of-life care reflected family and geographical origins, cultural traditions, personal attitudes, and religiosity and faith interpretations. Implications for healthcare included the importance of avoiding generalisations and openness to individualised and/ or standardised religious expressions of one’s religion. Conclusions: Knowledge of religious beliefs and values around death and dying could be useful in preparing health professionals for ACP with patients from different religions but equally important is avoidance of assumptions. Community-based initiatives, programs and faith settin

USING NONLINEAR GROWTH CURVES TO ESTIMATE HEAT STRESS IN PROCESSING FEEDLOT CATTLE

Summertime heat waves cause excessive discomfort and, in extreme cases, death of feedlot cattle. During such emergencies, extension specialists are called upon for recommendations of management practices to minimize heat stress. Since moving cattle is believed to raise body temperature 1 degree, one recommendation is to move cattle before mid-day or reschedule to another day. More knowledge of body temperature dynamics could lead to more specific recommendations of how far cattle can be moved without stress. Several models are investigated - especially those involving exponential growth(challenge) and decay (recovery) such as the bi-exponential, single compartment and other models in pharmacokinetics. Data from feedlot trials can be messy and judgement calls involving starting and ending times, model parametrization, and statistical assumptions can influence the results. Analyzes from SAS: proc NLIN and checks on nonlinear assumptions are discussed

USING THE BI-LOGISTIC MODEL TO ESTIMATE BODY TEMPERATURE IN FEEDLOT CATTLE

Processing and handling cattle require an expenditure of energy causing an elevation of body temperature, depending on the ambient conditions. More knowledge of body temperature, Tb, dynamics could lead to more specific recommendations of how far cattle can be moved without stress. The bi-Iogistic model has been used to describe the handling process. This model estimates several important biological parameters: rate of increase in Tb (rate of heat challenge), the maximum Tb (max Tb), time to reach maximum Tb (tmax) and recovery rate (rate of decrease in Tb). The objectives of this study are: to compare parameter estimates from the bi-Iogistic model with a segmented version of the model; to investigate the robustness of the model for different definitions of recovery; and, to check for hormetic behavior using switching functions

Hydrodynamic lift of vesicles under shear flow in microgravity

The dynamics of a vesicle suspension in a shear flow between parallel plates has been investigated under microgravity conditions, where vesicles are only submitted to hydrodynamic effects such as lift forces due to the presence of walls and drag forces. The temporal evolution of the spatial distribution of the vesicles has been recorded thanks to digital holographic microscopy, during parabolic flights and under normal gravity conditions. The collected data demonstrates that vesicles are pushed away from the walls with a lift velocity proportional to $\dot{\gamma} R^3/z^2$ where $\dot{\gamma}$ is the shear rate, $R$ the vesicle radius and $z$ its distance from the wall. This scaling as well as the dependence of the lift velocity upon vesicle aspect ratio are consistent with theoretical predictions by Olla [J. Phys. II France {\bf 7}, 1533--1540 (1997)].Comment: 6 pages, 8 figure

A direct optical method for the study of grain boundary melting

The structure and evolution of grain boundaries underlies the nature of polycrystalline materials. Here we describe an experimental apparatus and light reflection technique for measuring disorder at grain boundaries in optically clear material, in thermodynamic equilibrium. The approach is demonstrated on ice bicrystals. Crystallographic orientation is measured for each ice sample. The type and concentration of impurity in the liquid can be controlled and the temperature can be continuously recorded and controlled over a range near the melting point. The general methodology is appropriate for a wide variety of materials.Comment: 8 pages, 8 figures, updated with minor changes made to published versio

COMPARATIVE STUDY OF TIME SERIES AND MULTIPLE REGRESSION FOR MODELING DEPENDENCE OF CATTLE BODY TEMPERATURE ON ENVIRONMENTAL VARIABLES DURING HEAT STRESS

During the summer, a challenging thermal environment is known to cause a significant reduction in food intake, growth, milk production, reproduction and even death in cattle. In this study, we attempt to characterize the relationship of cattle body temperature with several environmental variables, such as air temperature, soil surface temperature, relative humidity, solar radiation, wind speed, incoming and outgoing short and long wave radiation. For these variables, the measurements taken over time are correlated. This places severe restrictions on the applicability of many conventional statistical methods that depend on the assumption of independent and identically distributed errors. In addition to these assumptions, there is serious collinearity among several weather variables and the variables are not stationary. Commonly used multiple regression models can be misleading when predictor variables are stochastic and issues of collinearity and non-stationary are ignored. In this paper, time series analysis is used as a tool to investigate the adequacy of classical regression models. Various aspects of dynamics of cattle body temperature and its relationship to environmental variables are discussed using the frequency and time domain analysis. Finally, we present a detailed approach for fitting cattle body temperature using a transfer function model with multiple environmental variables as inputs

COMPARING EXPERIMENTAL DESIGNS FOR A BI-LOGISTICAL MODEL USED TO ESTIMATE HEAT STRESS WHEN MOVING FEEDLOT CATTLE

Processing and handling cattle requires expenditure of energy causing an elevation of body temperature, depending on the ambient conditions. Therefore, caution should be exercised in moving cattle, especially during summer. More knowledge of the dynamics of body temperature, (Tb), could lead to specific recommendations on how far and under what conditions cattle can be moved before becoming thermally challenged. Data comes from feedlot trials conducted over four days. A bi-logistic mixed model of Tb is used to describe the effects of moving and handling on Tb. This model provides estimates for several important biological parameters describing the thermal challenge and recovery: the maximum Tb challenge, challenge rate constant (rate constant for increase in Tb), time to maximum rate of challenge (challenge inflection point), baseline for recovery, recovery rate constant (rate constant for decrease in Tb) and time to maximum recovery rate (recovery inflection point). Fitting a nonlinear mixed model with six parameters under extremely variable animal and environmental conditions is difficult especially when the treatment factor (distance) is introduced into the model. Additional difficulties in fitting the model arise as the experimental design increases in complexity from a CRD to a replicated Latin square. The objectives of this study are: to examine the bi-logistic model with distance as a treatment factor and estimate the relative efficiencies as the experimental design is simplified

LOGISTIC REGRESSION ANALYSIS TO DETERMINE FACTORS CONTRIBUTING TO SUMMER FEEDLOT DEATHS

Summer heat has already been identified as a major factor for cattle deaths in the feedlot. This study attempts to assess what other factors contribute to and/or influence cattle deaths. Identifying multiple factors that contribute to summer feedlot deaths could aid feedlot managers in implementation of mitigation strategies and minimize the loss of nearly finished cattle. Daily pen, cattle, and nutritional characteristics were recorded and included in this generalized linear mixed model analysis. Cattle data were obtained from cattle pens at a single location from July 1, 2010 to July 31, 2010. Hourly weather data were acquired from this feed yard while solar radiation was received from a neighboring town. Rather than using multiple weather variables, a single comprehensive climate index that summarizes several weather variables is used to capture the apparent feel of the weather. After reviewing the data, a statistical model is developed and odds ratios are computed for statistical inference. According to these odds ratios, cattle fed on severe west slopes had significantly higher odds of death than other types of slopes. Analysis of feed intake indicates pens consuming 16 pounds of feed per head or less during July 16 – 18 have higher odds of death than other consumption levels