Wave-number-explicit bounds in time-harmonic scattering

In this paper we consider the problem of scattering of time-harmonic acoustic waves by a bounded sound soft obstacle in two and three dimensions, studying dependence on the wave number in two classical formulations of this problem. The first is the standard variational/weak formulation in the part of the exterior domain contained in a large sphere, with an exact Dirichletto-Neumann map applied on the boundary. The second formulation is as a second kind boundary integral equation in which the solution is sought as a combined single- and double-layer potential. For the variational formulation we obtain, in the case when the obstacle is starlike, explicit upper and lower bounds which show that the inf-sup constant decreases like k −1 as the wave number k increases. We also give an example where the obstacle is not starlike and the inf-sup constant decreases at least as fast as k −2. For the boundary integral equation formulation, if the boundary is also Lipschitz and piecewise smooth, we show that the norm of the inverse boundary integral operator is bounded independently of k if the coupling parameter is chosen correctly. The methods we use also lead to explicit bounds on the solution of the scattering problem in the energy norm when the obstacle is starlike in which the dependence of the norm of the solution on the wave number and on the geometry are made explicit

On the photodissociation of H2 by the first stars

The first star formation in the universe is expected to take place within small protogalaxies, in which the gas is cooled by molecular hydrogen. However, if massive stars form within these protogalaxies, they may suppress further star formation by photodissociating the H2. We examine the importance of this effect by estimating the timescale on which significant H2 is destroyed. We show that photodissociation is significant in the least massive protogalaxies, but becomes less so as the protogalactic mass increases. We also examine the effects of photodissociation on dense clumps of gas within the protogalaxy. We find that while collapse will be inhibited in low density clumps, denser ones may survive to form stars.Comment: 13 pages, 10 figures. Minor revisions to match version accepted by MNRA

Development of fuzzy logic-base diagnosis expert system for typhoid fever

Typhoid fever (TyF), caused by salmonella typhoid bacteria, represents one of the main public health challenge in various parts of the world. It is often treatable when diagnosed early, but if left untreated could lead to other medical complications. This study proposed an artificial intelligence means (arim) for diagnosis of TyF. The objectives are to find out the leading risk factors for TyF, develop fuzzy logic base-expert system, called Typhoid Responsive Expert System (TyRes), that can predict the ailment from symptoms and use TyRes to predict TyF in patients. Two sets of questionnaires were used for data collection. 325 copies were administered to the patients in 25 hospitals in Lagos, Abeokuta and Ifo, South-west Nigeria. Another set of 200 copies were administered to human medical experts (hme), 70 doctors and 140 qualified nurses, to capture hme knowledge about TyF and its symptoms. The data was analysed using Chi-Square to identify the main symptoms spotted by most of the hme. TyRes was implemented in Matlab 2015a using the main factors as input variables. Vomiting, high-temperature, weakness, abdominal-pains and loss-of-appetite were the input variables used to develop TyRes. When tested to predict TyF in 25 patients, 76% accuracy was derived when comparing hme predictions with TyRes results. It can be concluded that TyRes can mimic hme by 76% of all TyF predictions. The arim is considered reliable and can be used at home, school and health centres where hme are scarce

Two-pathogen model with competition on clustered networks

Networks provide a mathematically rich framework to represent social contacts sufficient for the transmission of disease. Social networks are often highly clustered and fail to be locally tree-like. In this paper, we study the effects of clustering on the spread of sequential strains of a pathogen using the generating function formulation under a complete cross-immunity coupling, deriving conditions for the threshold of coexistence of the second strain. We show that clustering reduces the coexistence threshold of the second strain and its outbreak size in Poisson networks, whilst exhibiting the opposite effects on uniform-degree models. We conclude that clustering within a population must increase the ability of the second wave of an epidemic to spread over a network. We apply our model to the study of multilayer clustered networks and observe the fracturing of the residual graph at two distinct transmissibilities.Publisher PDFPeer reviewe

Exploring Students' Experiences in Occupational Therapy Education:A Phenomenological Study of Professional Identity Development

The existing literature on professional identity enactment and development, subscribes to students’ socializing in a learning environment, where they regularly encounter practicing professionals throughout their education period. However, in most countries with less resourced occupational therapists like Ghana, education in occupational therapy is fraught with inadequate number of same professionals to mentor undergraduate occupational therapy students. The students are thus faced with serious dilemma regarding their professional identity which tends to elicit a bleak perception of their chosen career. The present study was therefore envisaged to interpret and analyse the students’ lived experiences, with the view to capture the process of constructing and developing professional identity. The study focused on purposively sampled group of nine undergraduate occupational therapy students during their practice placement education, and their learning styles on didactic lectures. A hermeneutic phenomenological approach was adopted for the study. The students were followed up throughout their four-year study program for data collection, using one-to-one semi-structured interviews each year. With reference to the threshold concepts, transcribed interview data were analyzed using interpretative phenomenological procedures. The study established a transformational development of professional identity from the novice stage into graduate professionals, amidst complex interaction of co-constructed themes which included: personal knowing, professional knowing and experiential knowing

Degree correlations in graphs with clique clustering

Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).Correlations among the degrees of nodes in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for nodes in the giant component of clustered configuration model networks which are comprised of higher-order subgraphs. We use this model to investigate, in detail, the organisation among nearest-neighbour subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbour in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.PostprintPeer reviewe

Random graphs with arbitrary clustering and their applications

The structure of many real networks is not locally treelike and, hence, network analysis fails to characterize their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, arXiv:2006.06744], we developed analytical solutions to the percolation properties of random networks with homogeneous clustering (clusters whose nodes are degree equivalent). In this paper, we extend this model to investigate networks that contain clusters whose nodes are not degree equivalent, including multilayer networks. Through numerical examples, we show how this method can be used to investigate the properties of random complex networks with arbitrary clustering, extending the applicability of the configuration model and generating function formulation.Publisher PDFPeer reviewe