Local dimension is unbounded for planar posets

In 1981, Kelly showed that planar posets can have arbitrarily large dimension. However, the posets in Kelly's example have bounded Boolean dimension and bounded local dimension, leading naturally to the questions as to whether either Boolean dimension or local dimension is bounded for the class of planar posets. The question for Boolean dimension was first posed by Nešetřil and Pudlák in 1989 and remains unanswered today. The concept of local dimension is quite new, introduced in 2016 by Ueckerdt. Since that time, researchers have obtained many interesting results concerning Boolean dimension and local dimension, contrasting these parameters with the classic Dushnik-Miller concept of dimension, and establishing links between both parameters and structural graph theory, path-width and tree-width in particular. Here we show that local dimension is not bounded on the class of planar posets. Our proof also shows that the local dimension of a poset is not bounded in terms of the maximum local dimension of its blocks, and it provides an alternative proof of the fact that the local dimension of a poset cannot be bounded in terms of the tree-width of its cover graph, independent of its height

Study protocol: the effects of work-site exercise on the physical fitness and work-ability of older workers

BACKGROUND: Older workers have a higher rate and cost of injury than younger workers and with a rapidly ageing work force there is a need to identify strategies to address this problem. Older workers are less physically active and fit than younger workers and so have reduced work ability. The reduced work ability means they are more likely to be fatigued at work and so at greater risk of injury. Exercise could potentially assist this problem. Exercise training has been previously shown to improve fitness in older people however there has been no evaluation of workplace exercise program for older workers. We do not know if the programs are feasible and can improve the fitness and work ability of older workers. We have designed a randomised controlled trial to evaluate whether exercise improves fitness and perceived work-ability of older workers. METHODS/DESIGN: This paper describes the protocol for a trial examining the effects of a 12-week physical training program in workers over the age of 45. Participants will be randomized to an exercise or no-intervention control group. The primary outcomes are cardiorespiratory endurance, lifting capacity, upper and lower limb strength and perceived work-ability. DISCUSSION: This trial will test the feasibility of implementing a worksite-based exercise program as a means of improving the physical fitness and work-ability of older workers performing physically demanding work. If we demonstrate the feasibility of the program we will conduct a larger trial that additionally measures injury outcomes

Dying well with reduced agency: a scoping review and thematic synthesis of the decision-making process in dementia, traumatic brain injury and frailty

Background In most Anglophone nations, policy and law increasingly foster an autonomy-based model, raising issues for large numbers of people who fail to fit the paradigm, and indicating problems in translating practical and theoretical understandings of ‘good death’ to policy. Three exemplar populations are frail older people, people with dementia and people with severe traumatic brain injury. We hypothesise that these groups face some over-lapping challenges in securing good end-of-life care linked to their limited agency. To better understand these challenges, we conducted a scoping review and thematic synthesis. Methods To capture a range of literature, we followed established scoping review methods. We then used thematic synthesis to describe the broad themes emerging from this literature. Results Initial searches generated 22,375 references, and screening yielded 49, highly heterogeneous, studies that met inclusion criteria, encompassing 12 countries and a variety of settings. The thematic synthesis identified three themes: the first concerned the processes of end-of-life decision-making, highlighting the ambiguity of the dominant shared decision-making process, wherein decisions are determined by families or doctors, sometimes explicitly marginalising the antecedent decisions of patients. Despite this marginalisation, however, the patient does play a role both as a social presence and as an active agent, by whose actions the decisions of those with authority are influenced. The second theme examined the tension between predominant notions of a good death as ‘natural’ and the drive to medicalise death through the lens of the experiences and actions of those faced with the actuality of death. The final theme considered the concept of antecedent end-of-life decision-making (in all its forms), its influence on policy and decision-making, and some caveats that arise from the studies. Conclusions Together these three themes indicate a number of directions for future research, which are likely to be applicable to other conditions that result in reduced agency. Above all, this review emphasises the need for new concepts and fresh approaches to end of life decision-making that address the needs of the growing population of frail older people, people with dementia and those with severe traumatic brain injury

ON-LINE DIMENSION FOR POSETS EXCLUDING TWO LONG INCOMPARABLE CHAINS

For a positive integer k, let k + k denote the poset consisting of two disjoint k-element chains, with all points of one chain incomparable with all points of the other. Bosek, Krawczyk and Szczypka showed that for each k ≥ 1, there exists a constant ck so that First Fit will use at most ckw 2 chains in partitioning a poset P of width at most w, provided the poset excludes k+k as a subposet. This result played a key role in the recent proof by Bosek and Krawczyk that O(w 16logw) chains are sufficient to partition on-line a poset of width w into chains. This result was the first improvement in Kierstead’s exponential bound: (5 w − 1)/4 in nearly 30 years. Subsequently, Joret and Milans improved the Bosek-Krawczyk-Szczypka bound for the performance of First Fit to 8(k − 1) 2 w, which in turn yields the modest improvement to O(w 14logw) for the general on-line chain partitioning result. In this paper, we show that this classof posets admits a notion ofon-line dimension. Specifically, we show that when k and w are positive integers, there exists an integer t = t(k,w) and an on-line algorithm that will construct an on-line realizer of size t for any poset P having width at most w, provided that the poset excludes k+k as a subposet

Physical activity in an air-polluted environment: behavioral, psychological and neuroimaging protocol for a prospective cohort study (Healthy Aging in Industrial Environment study – Program 4)

BackgroundAir pollution has been linked to increased mortality and morbidity. The Program 4 of the Healthy Aging in Industrial Environment study investigates whether the health and wellbeing benefits of physical activity (PA) can be fully realized in individuals living in highly polluted environments. Herein, we introduce the behavioral, psychological and neuroimaging protocol of the study.MethodsThis is a prospective cohort study of N=1500 individuals aged 18-65years comparing: (1) individuals living in the highly polluted, industrial region surrounding the city of Ostrava (n=750), and (2) controls from the comparison region with relative low pollution levels in Southern Bohemia (n=750). Quota sampling is used to obtain samples balanced on age, gender, PA status (60% active runners vs. 40% insufficiently active). Participants are screened and complete baseline assessments through online questionnaires and in-person lab-based assessments of physiological, biomechanical, neuroimaging and cognitive function parameters. Prospective 12-month intensive monitoring of air pollution and behavioral parameters (PA, inactivity, and sleep) follows, with a focus on PA-related injuries and psychological factors through fitness trackers, smartphones, and mobile apps. Subsequently, there will be a 5-year follow-up of the study cohort.DiscussionThe design of the study will allow for (1) the assessment of both short-term variation and long-term change in behavioral parameters, (2) evaluation of the incidence of musculoskeletal injuries and psychological factors impacting behavior and injury recovery, and (3) the impact that air pollution status (and change) has on behavior, psychological resilience, and injury recovery. Furthermore, the integration of MRI techniques and cognitive assessment in combination with data on behavioral, biological and environmental variables will provide an opportunity to examine brain structure and cognitive function in relation to health behavior and air pollution, as well as other factors affecting resilience against and vulnerability to adverse changes in brain structure and cognitive aging. This study will help inform individuals about personal risk factors and decision-makers about the impact of environmental factors on negative health outcomes and potential underlying biological, behavioral and psychological mechanisms. Challenges and opportunities stemming from the timing of the study that coincided with the COVID-19 pandemic are also discussed.Web of Science211art. no. 12