Multi-fractal processes have been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns a feature that has been found to characterize virtually all financial prices. Furthermore, elementary variants of multi-fractal models are very parsimon...

Fractal and fractal-rate stochastic point processes (FSPPs and FRSPPs) provide useful models for describing a broad range of diverse phenomena, including electron transport in amorphous semiconductors, computer-network traffic, and sequences of neuronal action potentials. A particularly useful statistic of these processes is the fractal exponent α, which may be estimated for any FSPP or FRSPP b...

Due to geological reasons, fractured reservoirs are extremely heterogeneous. Modelling of these reservoirs has so far been considered complex and progress is still inadequate. This paper presents a novel and hybrid method to model discrete fracture networks in naturally fractured reservoirs. It involves investigation and systematic integration of tasks spanning cross-disciplinary areas: geologi...

This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial interactions and the molecule Brownian diffusivities is found to be the bi-fractal mechanism behind multifractal scaling in the inertial range of scales of moderate Rey...

We present a theoretical study of new families of stochastic complex information modules encoded in the hypergraph states which are defined by the fractional entropic descriptor. The essential connection between the Lyapunov exponents and d-regular hypergraph fractal set is elucidated. To further resolve the divergence in the complexity of classical and quantum representation of a hypergraph, w...

The characterization and quantitative description of Internet traffic is becoming increasingly important in light of the rapid growth being observed in the size and usage of the network. Modeling of modern teletraffic and large telecommunications networks with fractal stochastic processes has been investigated by analyzing traffic measurements collected on the “Federico II” university WAN link ...

In this paper, we search for absolute limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal fully weakly self-assembles at temperature 1, and that certain kinds of self-similar fractals do not strictly self-assemble at any temperature....

In this paper, we search for absolute limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal fully weakly self-assembles at temperature 1, and that certain kinds of self-similar fractals do not strictly self-assemble at any temperature....

Discrete-event simulation based optimization is the process of finding the optimum design of a stochastic system when the performance measure(s) could only be estimated via simulation. Randomness in simulation outputs often challenges the correct selection of the optimum. We propose an algorithm that merges Ranking and Selection procedures with a large class of random search methods for continu...

We investigate the application of deterministic chaotic maps to model traffic sources in packet based networks, motivated in part by recent measurement studies which indicate the presence of significant statistical features in packet traffic more characteristic of fractal processes than conventional stochastic processes. We outline one approach whereby traffic sources can be modeled by chaotic ...