Publication informationNanomedicine: Nanotechnology, Biology and Medicine, 7 (6):
818-826Publisher Elsevier Central to understanding how nanoscale objects interact with living matter is the need for reproducible and verifiable data that can be interpreted with confidence. Likely this will be the basis of durable advances in nanomedicine and nanosafety. To develop these fields, there is also considerable interest in advancing the first generation of theoretical models of nanoparticle uptake into cells, and nanoparticle biodistribution in general. Here we present an uptake study comparing the outcomes for free molecular dye and nanoparticles labeled with the same dye. A simple flux-based approach is presented to model nanoparticle uptake. We find that the intracellular nanoparticle concentration grows linearly in time, and that the uptake is essentially irreversible, with the particles accumulating in lysosomes. A wide range of practical challenges, from labile dye release, to nanoparticle aggregation and the need to account for cell division, are addressed to ensure these studies yield meaningful kinetic information.
We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D(1) 5 . In particular for the double of S 3 , 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors.
Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a sort of Shannon's entropy per unit of time, from the recurrence times of chaotic systems. One formula provides the KS entropy and is more theoretically oriented since one has to measure also the low probable very long returns. The other provides a lower bound for the KS entropy and is more experimentally oriented since one has to measure only the high probable short returns. These formulas are a consequence of the fact that the series of returns do contain the same information of the trajectory that generated it. That suggests that recurrence times might be valuable when making models of complex systems.
Let f be an expansive Markov interval map with finite transition matrix A f . Then for every point, we yield an irreducible representation of the Cuntz-Krieger algebra O A f and show that two such representations are unitarily equivalent if and only if the points belong to the same generalized orbit. The restriction of each representation to the gauge part of O A f is decomposed into irreducible representations, according to the decomposition of the orbit.
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