Iteration in Tracts

This thesis is focused on the iteration of transcendental entire and meromorphic functions within a particular domain of the complex plane called a direct tract. Many new results are given on the rates of escape and the dimension of points of bounded orbit in a direct tract, as well as the geometry of direct tracts. First, we study iterates of points within one of these tracts. The points that escape to infinity are of particular interest in the iteration of entire functions due both to their simple definition and, in contrast to rational functions, the interesting phenomena and structures they exhibit. We expand on work of Rippon and Stallard to show that in many cases there exist points that escape to infinity within a direct tract as slowly as desired. In order to accomplish this, we develop several tools based both on the expansion of the hyperbolic metric and estimates on the function value in these direct tracts. Next, we relate the geometry of a direct tract to how well behaved the entire function is inside this direct tract. We consider a particular type of direct tract, called a logarithmic tract. Many results are known for functions with this type of direct tract, so the ability to identify them from their geometric properties is important. In particular, we give new descriptions of when a direct tract is a logarithmic tract or contains logarithmic tracts. Finally, we show that, for functions with a specific restriction on the geometry of the direct tract, the Hausdorff dimension of the set of points with bounded orbit in the Julia set is strictly greater than one. To do this, we prove new results related to Wiman–Valiron theory

Bounded Fatou and Julia components of meromorphic functions

We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior. We do so by constructing meromorphic functions with wandering continua using approximation theory.Comment: 15 pages, 4 figures. V2: We have revised the introduction, and introduced two new sections: Section 2 discusses and compare topological properties of Fatou components, while Section 3 establishes that certain bounded regular domains cannot arise as eventually periodic Fatou components of meromorphic function

Human-macaque encounters in Ifrane National Park, Morocco: behavioural, spatial, and temporal coping strategies of the Barbary macaque (Macaca sylvanus)

Wild animals in human-dominated landscapes are exposed to a broad range of human activities and infrastructure that have the potential to alter their fitness and behaviour. Understanding wildlife responses to human disturbance is an important conservation goal, particularly when the fate of many wildlife populations depends on their capacity to coexist with humans. Most field studies have focussed on the effects of one type of disturbance only (i.e. a single disturbance type per study), however in heavily human-modified habitats animals must often deal with numerous different types of human activity and infrastructure, and less is known about whether different types differentially affect animal behavioural responses. This study examined the responses of 5 wild Barbary macaque (Macaca sylvanus) groups in Ifrane National Park, Morocco, to a range of human activities and infrastructure on a short-term behavioural scale (individual focal follows) and a longer-term spatio-temporal scale (individual scan sampling). Using a series of GLMMs I first compared pre-, during-, and post- human-macaque encounter levels of escape, affiliative, and self-directed behaviours (behaviours that may serve as components of a coping strategy) to determine whether different encounter types differentially affect macaque behavioural responses. Using logistic regression to estimate resource selection functions I then examined the behaviour-specific habitat use of macaques to determine whether (and how) different types of human activity and infrastructure influence habitat selection within home ranges. Two broadly consistent responses to human encounters were observed; the first in association with potentially threatening encounters (those that involved/potentially involved dogs), and the second with potentially rewarding encounters (those that involved human provisioning). In response to potentially threatening encounters macaques made extensive use of escape behaviours, varied use of affiliative behaviours, and limited use of self-directed behaviours. In response to potentially rewarding encounters, macaques made use of escape, affiliative, and self-directed behaviours. Three broadly consistent patterns of habitat selection/avoidance were observed in response to human activities and infrastructure within macaque home ranges. Macaques exhibited a general spatial preference for areas close to roads and a general spatial avoidance of both open areas (i.e. with no tree cover) and areas close to herding routes. Macaques also selected/avoided potentially threatening and rewarding areas (i.e. shepherd herding routes and provisioning loci) on a flexible temporal scale, only using potentially threatening areas when the probability of a human encounter was low, and preferentially using rewarding areas only when the risk/benefit balance associated with human provisioning was most heavily in their favour. The results of this study highlight the value of considering the effects of multiple different types of human activity and infrastructure (at different spatio-temporal scales) on wildlife behaviour and welfare, and of assessing human impact on habitat selection separately for different types of behaviour. Such detailed studies on the effects of human activities on wild animal populations can enhance our understanding of, and ability to manage, the impacts of increasing human expansion into wildlife habitat

Glaucoma, dementia and the 'precipice of care': transitions between states of medication adherence

Purpose: “She wouldn’t remember. Even when I go through, and she’s decided to go to bed, I’ll say I’ll come and do her drops. If I didn’t say that, they wouldn’t be done.” Dementia is widely considered a key factor in whether patients take their medication as prescribed. However, few studies have examined the effect of dementia upon medication management strategies for glaucoma including how patient and carer needs impact adherence and long term prognosis. We report findings from a qualitative grounded theory study incorporating the views of patients, carers and healthcare professionals. Patients and methods: 83 semi-structured interviews were conducted with 35 patients, 22 lay carers and nine healthcare professionals across sites in Wales and Scotland. These explored understanding of eye drop regimens, barriers and facilitators to drop administration, as well as attitudes towards glaucoma, dementia and other comorbidities. Results: Using Pandora Pound’s synthesis of adherence behaviour, we identified categories of active and passive acceptance of medicines, alongside modification or rejection of eye drop regimens. In relation to dementia, participants highlighted transitions between such categories, with a shift from active to passive acceptance commonly reported. This loss of self-medicating capability was referred to as the precipice of care, where entwinement of multiple conditions (eg heart disease, glaucoma and dementia) and socio-cultural influences (eg living alone) contributed to accelerated health declines. That said, numerous factors mitigated this, with a key role being the lay carer. Spouses and family members often acted as the monitor of eye drops for patients, seeking intervention when any behavioural changes influenced their administration. Conclusion: Though dementia was associated with progression towards the precipice of care, factors such as communication with healthcare professionals appeared to affect patient adherence. Recommendations for healthcare practice include better recording of dementia diagnoses and integrating eye drops into pre-existing routines

Let me Google that for you:a time series analysis of seasonality in internet search trends for terms related to foot and ankle pain

BACKGROUND: The analysis of internet search traffic may present the opportunity to gain insights into general trends and patterns in information seeking behaviour related to medical conditions at a population level. For prevalent and widespread problems such as foot and ankle pain, this information has the potential to improve our understanding of seasonality and trends within these conditions and their treatments, and may act as a useful proxy for their true incidence/prevalence characteristics. This study aimed to explore seasonal effects, general trends and relative popularity of internet search terms related to foot and ankle pain over the past decade. METHODS: We used the Google Trends tool to obtain relative search engine traffic for terms relating to foot and ankle pain and common treatments from Google search and affiliated pages for major northern and southern hemisphere English speaking nations. Analysis of overall trends and seasonality including summer/winter differences was carried out on these terms. RESULTS: Searches relating to general foot pain were on average 3.4 times more common than those relating to ankle pain, and twice as common as searches relating to heel pain. Distinct seasonal effects were seen in the northern hemisphere, with large increases in search volumes in the summer months compared to winter for foot (p = 0.004, 95 % CI [22.2–32.1]), ankle (p = 0.0078, 95 % CI [20.9–35.5]), and heel pain (p = 0.004, 95 % CI [29.1–45.6]). These seasonal effects were reflected by data from Australia, with the exception of ankle pain. Annual seasonal effects for treatment options were limited to terms related to foot surgery and ankle orthoses (p = 0.031, 95 % CI [3.5–20.9]; p = 0.004, 95 % CI [7.6–25.2] respectively), again increasing in the summer months. CONCLUSIONS: A number of general trends and annual seasonal effects were found in time series internet search data for terms relating to foot and ankle pain. This data may provide insights into these conditions at population levels. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13047-015-0074-9) contains supplementary material, which is available to authorized users

PREGNANT AND LACTATING Macaca nigra: BEHAVIOR AND FOOD SELECTION

Pregnancy and lactation are reproductive phases that require large amounts of energy. Females in the reproductive period need good quality and quantity of food to provide nutrition for the fetus, milk production and child care. The mother will adapt to changes in behavior patterns and food type to meet these needs. The influence of parity and environmental conditions can affect the behavior patterns of females. During pregnancy, the Macaca nigra is known to have different proportion of activities in each period, while the behavior during the lactation phase in each mester is unknown. Therefore, this study aimed to analyze the behavior patterns in each mester and the food selection of Macaca nigra during the pregnancy and lactation phases, as well as the influence of female parity and environmental toward the behavior patterns. There were 39 females Macaca nigra observed from two groups from August 2018 to July 2019. An instantaneous focal sampling method was performed to observe females’ daily activities, continuous focal sampling to monitor food types and a selectivity index to analyze food type preferences. The results showed that the female Macaca nigra pattern was influenced by the reproductive phase, female parity and environmental conditions. Females at the end of the pregnancy and lactation phases had a high proportion of feeding and eat more arthropods. Primiparous females mostly performed resting activities. Food preference was influenced by reproductive factors and food availability. The choice of fruit could be affected by fruit availability, and their favorite food was D. mangiferum and Euginia sp.