Fractionally integrated Bessel process

We consider a fractionally integrated Bessel process defined by Y s δ , H = ∫ 0 ∞ ( u H − ( 1 / 2 ) − ( u − s ) + H − ( 1 / 2 ) ) d X u δ , where X δ is the Bessel process of dimension δ  > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder continuity.

Molecular transport in a crowded volume created from vertically aligned carbon nanofibres: a fluorescence recovery after photobleaching study

Rapid and selective molecular exchange across a barrier is essential for emulating the properties of biological membranes. Vertically-aligned carbon nanofibre (VACNF) forests have shown great promise as membrane mimics, owing to their mechanical stability, their ease of integration with microfabrication technologies and the ability to tailor their morphology and surface properties. However, quantifying transport through synthetic membranes having micro- and nanoscale features is challenging. Here, fluorescence recovery after photobleaching (FRAP) is coupled with finite difference and Monte Carlo simulations to quantify diffusive transport in microfluidic structures containing VACNF forests. Anomalous subdiffusion was observed for FITC (hydrodynamic radius of 0.54 nm) diffusion through both VACNFs and SiO(2)-coated VACNFS (oxVACNFs). Anomalous subdiffusion can be attributed to multiple FITC-nanofibre interactions for the case of diffusion through the VACNF forest. Volume crowding was identified as the cause of anomalous subdiffusion in the oxVACNF forest. In both cases the diffusion mode changes to a time-independent, Fickian mode of transport that can be defined by a crossover length (R(CR)). By identifying the space-and time-dependent transport characteristics of the VACNF forest, the dimensional features of membranes can be tailored to achieve predictable molecular exchange.

Self-similar random field models in discrete space

Self-similar random fields are of interest in various areas of image processing since they fit certain types of natural patterns and textures. Current treatments of self-similarity in continuous two-dimensional (2-D) space use a definition that is a direct extension of the one-dimensional definition, which requires invariance of the statistics of a random process to time scaling. Current discrete-space 2-D approaches do not consider scaling, but, instead, are based on ad hoc formulations, such as digitizing continuous random fields. In this paper, we show that the current statistical self-similarity definition in continuous space is restrictive and provide an alternative, more general definition. We also provide a formalism for discrete-space statistical self-similarity that relies on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields and texture images.

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster.