Compositional Data in Biomedical Research

Modern methods of compositional data analysis are not well known in biomedical research. Moreover, there appear to be few mathematical and statistical researchers working on compositional biomedical problems. Like the earth and environmental sciences, biomedicine has many problems in which the relevant scienti c information is encoded in the relative abundance of key species or categories. I introduce three problems in cancer research in which analysis of compositions plays an important role. The problems involve 1) the classi cation of serum proteomic pro les for early detection of lung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostic tumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it's role in breast cancer patient prognosis. For each of these problems I outline a partial solution. However, none of these problems is \solved". I attempt to identify areas in which additional statistical development is needed with the hope of encouraging more compositional data analysts to become involved in biomedical research

All-Optical Label Stacking: Easing the Trade-offs Between Routing and Architecture Cost in All-Optical Packet Switching

All-optical label swapping (AOLS) forms a key technology towards the implementation of all-optical packet switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the way in which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This paper studies all-optical label stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this paper, an integer lineal program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more