The development of quantifiable measurements to characterise the epidermal integrity of the equine hoof capsule.

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On local search and LP and SDP relaxations for k-Set Packing

Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set problem. In this thesis we study the k-set packing problem where given a universe U and a collection C of subsets over U, each of cardinality k, one needs to find the maximum collection of mutually disjoint subsets. Local search techniques have proved to be successful in the search for approximation algorithms, both for the unweighted and the weighted version of the problem where every subset in C is associated with a weight and the objective is to maximise the sum of the weights. We make a survey of these approaches and give some background and intuition behind them. In particular, we simplify the algebraic proof of the main lemma for the currently best weighted approximation algorithm of Berman ([Ber00]) into a proof that reveals more intuition on what is really happening behind the math. The main result is a new bound of k/3 + 1 + epsilon on the integrality gap for a polynomially sized LP relaxation for k-set packing by Chan and Lau ([CL10]) and the natural SDP relaxation [NOTE: see page iii]. We provide detailed proofs of lemmas needed to prove this new bound and treat some background on related topics like semidefinite programming and the Lovasz Theta function. Finally we have an extended discussion in which we suggest some possibilities for future research. We discuss how the current results from the weighted approximation algorithms and the LP and SDP relaxations might be improved, the strong relation between set packing and the independent set problem and the difference between the weighted and the unweighted version of the problem.Comment: There is a mistake in the following line of Theorem 17: "As an induced subgraph of H with more edges than vertices constitutes an improving set". Therefore, the proofs of Theorem 17, and hence Theorems 19, 23 and 24, are false. It is still open whether these theorems are tru

(De)humanizing metaphors of people in pain and their association with the perceived quality of nurse-patient relationship

Metaphors are central in communication and sense-making processes in health-related contexts. Yet how the metaphors used by health-care-professionals to make sense of their patients and their relations to them are associated to the perceived valence of their clinical encounters is underexplored. Drawing-upon the ABC Model of Dehumanization, this study investigated how the humanizing or dehumanizing metaphors nurses’ use for making sense of their pain patients are associated with how they perceived their relationships with them. Fifty female nurses undertook individual narrative-episodic interviews about easy/difficult cases in pain care. A content analysis classified the metaphors, identifying eight classes reflecting different types of patients (de)humanization. A multiple correspondence analysis extracted patterns of metaphors and their association with the perceived characteristics of the patient-nurse relationship. It showed how these patterns were not associated with patient sex or socioeconomic status (SES) but were related to the perceived valence of the clinical relationship. By uncovering how patient metaphors guide nurses’ sense-making and potentially modulate interactions in clinical encounters, these findings may contribute to improve quality of pain care.Fundação para a Ciência e Tecnologiainfo:eu-repo/semantics/publishedVersio