71 research outputs found
Positive definite metric spaces
Magnitude is a numerical invariant of finite metric spaces, recently
introduced by T. Leinster, which is analogous in precise senses to the
cardinality of finite sets or the Euler characteristic of topological spaces.
It has been extended to infinite metric spaces in several a priori distinct
ways. This paper develops the theory of a class of metric spaces, positive
definite metric spaces, for which magnitude is more tractable than in general.
Positive definiteness is a generalization of the classical property of negative
type for a metric space, which is known to hold for many interesting classes of
spaces. It is proved that all the proposed definitions of magnitude coincide
for compact positive definite metric spaces and further results are proved
about the behavior of magnitude as a function of such spaces. Finally, some
facts about the magnitude of compact subsets of l_p^n for p \le 2 are proved,
generalizing results of Leinster for p=1,2, using properties of these spaces
which are somewhat stronger than positive definiteness.Comment: v5: Corrected some misstatements in the last few paragraphs. Updated
reference
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Toward critical evaluation of the role(s) of molecular biomarkers in the management of bladder cancer
Among genitourinary malignancies, bladder cancer is a common, potentially dangerous and exceedingly costly disease entity. Predicated on substantial gains in our understanding of the natural history and molecular biology of bladder cancer, recent years have seen an explosion of new applied technologies to aid clinicians in the management of bladder cancer. Herein we present a systematic overview of general conceptual issues and specific strategies of potential relevance to the clinical evaluation of patients with bladder cancer. A number of basic epidemiological issues provide the relevant background within which we should consider candidate biomarkers. Within this framework, we highlight a number of important recent research findings representative of the large number of candidate bladder cancer biomarkers that have emerged. With several markers already having obtained regulatory approval for clinical use, this topic is of clear relevance not only to researchers but also to the practicing physician. Bladder cancer is a common, costly, and potentially dangerous disease with the opportunity for significant technological inroads in the area of applied biomarkers. An appreciation of basic epidemiological considerations informs our consideration of the state of the art and identifies specific strategies amenable to further innovation
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The role of deoxyribonucleic acid methylation in development, diagnosis, and prognosis of bladder cancer
Alterations in global levels and regional patterns of deoxyribonucleic acid methylation are among the earliest and most common events known to occur in human cancer. The mutational and epigenetic effects of this covalent deoxyribonucleic acid modification to the development of bladder cancer are well recognized. The contribution of aberrant methylation to mutational hot spots located within genes, transcriptional silencing, and chromosomal instability is reviewed in the context of its relevance to bladder carcinogenesis. Understanding how such processes evolve during the progression of bladder cancer is essential for using these molecular changes in the clinical setting. The recent development of sensitive and specific techniques for quantifying methylation changes in urine specimens and bodily fluids underscores the potential use of this molecular marker for early detection and surveillance of bladder cancer. Further refinement of these molecular biological techniques holds much promise for the use of methylation markers for bladder cancer diagnosis, risk stratification, and disease prognostication
1323: Outcomes of Patients with Aborted Cystectomy for Intraoperative Findings of Metastatic Disease
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PATHOLOGIC UPSTAGING AT THE TIME OF RADICAL CYSTECTOMY IS ASSOCIATED WITH WORSE RECURRENCE FREE SURVIVAL IN PATIENTS WITH BCG-REFRACTORY BLADDER CANCER
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