Online Covering with Sum of ellqell_q-Norm Objectives

We consider fractional online covering problems with lq-norm objectives. The problem of interest is of the form min{ f(x) : Ax >= 1, x >= 0} where f(x) is the weighted sum of lq-norms and A is a non-negative matrix. The rows of A (i.e. covering constraints) arrive online over time. We provide an online O(log d+log p)-competitive algorithm where p is the maximum to minimum ratio of A and A is the row sparsity of A. This is based on the online primal-dual framework where we use the dual of the above convex program. Our result expands the class of convex objectives that admit good online algorithms: prior results required a monotonicity condition on the objective which is not satisfied here. This result is nearly tight even for the linear special case. As direct applications, we obtain (i) improved online algorithms for non-uniform buy-at-bulk network design and (ii) the first online algorithm for throughput maximization under lq-norm edge capacities

Biocompatible tumour implant systems: towards an integrated biophotonic system

There is a need to perform comprehensive cell biology studies transferable across culture platforms using innovative cellular models. The higher purpose is to bridge the gap between in vitro cell culture and in vivo models. In this thesis a significant advance is presented in the embedding of an innovative optical biophotonic capability for the dynamic interrogation and single cell tracking of human osteosarcoma cells encapsulated in the hollow fiber (HF) platform. Two approaches have been implemented: quantum dot (QD) nanoparticles providing proliferative and cell cycle readouts and an in-fiber light illumination providing global features of particle and cell density. An in vitro HF encapsulation model was developed and characterised against standard two-dimensional tissue culture (TC) using the human osteosarcoma U-2 OS cell line expressing a cell cycle fluorescent reporter (cyclin Bl-GFP). Analysis of the packing and orientation of cells in the HF revealed that they grow like an anchorage dependent adherent layer. Overall cells in the fiber displayed a slower cell cycle traverse and a differential sensitivity to clinically relevant doses of the anticancer mitosis-inhibiting agent Taxol compared to cells under normal TC conditions. Comprehensive gene profiling, with bioinformatics and ontology network analysis, showed that the HF cells presented high steroid related but low differentiation gene expression. Specific biomarkers were indentified, and it is suggested that the HF model displays features that are closer to an in vivo tumour. A flow cytometry cell-tracking approach using QD labelling was validated and applied to the HF model for the first time. This represents an "embedded" biophotonic system where the QD sensors are integrated directly into the seeded cell population and then redistributed through the daughter cells, thus reflecting patterns of lineage expansion. This provides sub-population parameterized information on cell-cell heterogeneity and cell division. A biophotonic HF prototype comprising the integration of direct coupled-light excitation in the HF was conceived, this revealed the potential and limitations to detect die presence of cells inside the HF lumen by analysing light attenuation changes. Finally a "systems cytometry" acquisition concept has been proposed, comprising the use of embedded engineered nanoparticles as single cell "nano-memory" biophotonic intracellular probes