A Recipe for State Dependent Distributed Delay Differential Equations

We use the McKendrick equation with variable ageing rate and randomly distributed maturation time to derive a state dependent distributed delay differential equation. We show that the resulting delay differential equation preserves non-negativity of initial conditions and we characterise local stability of equilibria. By specifying the distribution of maturation age, we recover state dependent discrete, uniform and gamma distributed delay differential equations. We show how to reduce the uniform case to a system of state dependent discrete delay equations and the gamma distributed case to a system of ordinary differential equations. To illustrate the benefits of these reductions, we convert previously published transit compartment models into equivalent distributed delay differential equations.Comment: 28 page

Bringing an Occupational Therapy Perspective to Linden Waldorf School

Through this project, an occupational therapy doctoral student brought an occupational therapy perspective to Linden Waldorf School and provided the school with direct observations, educational presentations, and various educational materials on the topics of fine motor development, sensory processing, and behavior management in order to help empower Waldorf faculty and staff to best meet the needs of their students

Theoretical and practical aspects of variography: in particular, estimation and modelling of semi-variograms over areas of limited and clustered or widely spaced data in a two-dimensional South African gold mining context.

This thesis provides a detailed study of the semi-variogram. Included is a thorough presentation of the theory of semi-variograms, ranging from the probabilistic model of geostatistics to validity, estimation and modelling of the semi-variogram. A detailed study of the nugget effect parameter is included in which the composition of the nugget effect and the concept of measurement error being part of the nugget effect are explored. The influence that support size has on the semi-variogram parameters is also presented. Practical guidelines into modelling the best semi-variogram are given, and the problems associated with modelling semi-variograms over limited and clustered or widely spaced data is investigated in detail. This thesis looks at semi-variograms from a South African deep-level gold mining standpoint, and its ultimate goal is to provide a thorough investigation of the semi-variogram from both a theoretical and a practical perspective. Much of the theory presented is tested against real-life gold mining data sets, and the theoretical as well as practical implications of semi-variogram estimation and modelling are discussed. A particularly interesting observation is the potential under-estimation of the sill, nugget and range parameters of the semi-variogram when faced with limited, clustered gold mining data. However, most of the theory presented in this thesis can be generalized to situations outside of the gold mining industry, and it is believed that many of the practical results observed can also be used outside of gold mining. Therefore, although targeted primarily at the gold mining professional, this thesis is equally valid to interested persons involved in other spatial disciplines

Analysing spatial data via geostatistical methods

Faculty of Science School of Statistics snd Acturial Science 9907894x [email protected] dissertation presents a detailed study of geostatistics. Included in this work are details of the development of geostatistics and its usefulness both in and outside of the mining industry, a comprehensive presentation of the theory of geostatistics, and a discussion of the application of this theory to practical situations. A published debate over the validity of geostatistics is also examined. The ultimate goal of this dissertation is to provide a thorough investigation of geostatistics from both a theoretical and a practical perspective. The theory presented in this dissertation is thus tested on various spatial data sets, and from these tests it is concluded that geostatistics can be effectively used in practice provided that the practitioner fully understands the theory of geostatistics and the spatial data being analyzed. A particularly interesting conclusion to come out of this dissertation is the importance of using additive regionalized variables in all geostatistical analyses

Custer State Park : An Area Study

This thesis is a systematic geographic analysis of Custer State Park. Because Custer State Park has definite geopolitical boundaries. this study is limited to that particular political region in the Black Hills. The systematic study of this area is not limited to one criterion such as location, climate or human occupance. Rather, it incorporates the sum total of all the criteria included in a traditional regional study. Custer State Park is located in the southern portion of the Black Hills of western South Dakota. Described by numerous authors as an is land of green in a vast sea of grass, the Black Hills lie roughly between 43 and 45 degrees north latitude and 103 to 104 degrees west longitude and comprise an area about 60 miles in width and 100 miles in length, or approximately 20,600 square miles. About two-thirds of the Black Hills lie in South Dakota; the remaining one-third is in Wyoming. (Figure 2) Hundreds of books and articles have been written about the Black Hills. Many of these works may briefly give mention to certain general aspects of Custer State Park, but very few of them mention any specific, up-to-date details of the park. The last major geographic work about Custer State Park was compiled by the Federal Writer\u27s Project in 1938. A much more general study of the park was later written by Tom Baskette Jr. and Jerry Sanders in l977. It is because of this lack of current information about Custer State Park that the author chose the park as a thesis topic. The last major geographic study of South Dakota was done by Stephen Sargent Visher in 1917. It is because of this that the Department of Geography has set as a goal the completion of a set of master\u27s theses updating the geographic knowledge of the state. The author hopes that this thesis brings the science of geography in South Dakota into a more modern time frame. The following study of Custer State Park was undertaken using an outline that divides the park\u27s attributes into several categories. Chapter 2 deals with the physical environment of the park. Chapter 3 concerns itself with the exploration and settlement of the Black Hills and the later creation of Custer State Park. Chapter 4 is about the cultural environment of Custer State Park. Chapter 5 summarizes this study\u27s findings and takes a look at the future of Custer State Park

The Use of Virtual Instruments by Australian Screen Composers

Recent technological advancements, strong competition and targeted marketing strategies by virtual instrument merchants have established virtual instruments and digital instrument samples as essential components of a professional screen composer's toolset. The democratisation of these powerful tools has led to broad accessibility to virtual instruments and the digital sequencing software required to run them. Virtual instruments are portable, powerful, and affordable––they are no longer the exclusive domain of expensive recording studios. This thesis aims to quantify and qualify the parameters surrounding screen music composition in this digital age and introduce to the literature new empirical data together with the experiences of working screen music professionals. This is achieved by following a mixed methods sequential exploratory methodology starting with a survey of Australian screen composers (n=102) where they are asked to answer questions with a recent cue in mind. Informed by the results of the survey, semistructured interviews were conducted and recorded with working Australian screen composers (n=22). When combined the meta-inferences confirm that virtual instruments are vital for Australian screen composers to do their job, especially now that their tools are democratised. Screen composers are able to swiftly create cues that are finished products and not demos for their director and film-team. These changes have also shaped a new paradigm of film and television directors to expect final and completed versions of cues from Australian screen composers and not working drafts

‘It’s Mental Health, Not Mental Police’: A human rights approach to mental health triage and Section 136 of the Mental Health Act 1983

A human rights approach to the policing of mental ill-health raises fundamental questions about the vulnerability of people in the care of the police, the appropriateness of police interventions, and how societies define and delineate the role and function of the police and health sectors. It is the challenge of understanding and interpreting the police–health nexus and its associated points of intervention that this article addresses. The article uses a human rights framework to explore the challenges that emerge when policing mental ill-health through the use of Section 136 of the Mental Health Act 1983 and recent experimental use of mental health triage in England and Wales. The article explores the potential of triage to alleviate some of the human rights concerns associate with the use of Section 136 through interviews with police officers involved with the triage pilots. The final discussion situates experiments with mental health triage against a backcloth of mental health’s increasingly prominent position on the global public policy agenda. The article concludes with call for a reassessment and realignment of thinking about the police–health nexus that aligns with the United Nations’ sustainable development goals for 2030

Development and piloting of a food-based intervention to increase vitamin E intake in pregnant women in a randomised controlled trial

Acknowledgement This study was funded by the University of Aberdeen and an unrestricted grant from Baxters Food Group Ltd. LC acknowledges funding from the RESAS programme of the Scottish Government.Peer reviewedPublisher PD