Stochastic diffusion search review

Stochastic Diffusion Search, first incepted in 1989, belongs to the extended family of swarm intelligence algorithms. In contrast to many nature-inspired algorithms, stochastic diffusion search has a strong mathematical framework describing its behaviour and convergence. In addition to concisely exploring the algorithm in the context of natural swarm intelligence systems, this paper reviews various developments of the algorithm, which have been shown to perform well in a variety of application domains including continuous optimisation, implementation on hardware and medical imaging. This algorithm has also being utilised to argue the potential computational creativity of swarm intelligence systems through the two phases of exploration and exploitatio

An Introduction to Non-diffusive Transport Models

The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and finance. However, in recent decades, non-diffusive transport processes with non-Brownian statistics were observed experimentally in a multitude of scientific fields. Examples include human travel, in-cell dynamics, the motion of bright points on the solar surface, the transport of charge carriers in amorphous semiconductors, the propagation of contaminants in groundwater, the search patterns of foraging animals and the transport of energetic particles in turbulent plasmas. These examples showed that the assumptions of the classical diffusion paradigm, assuming an underlying uncorrelated (Markovian), Gaussian stochastic process, need to be relaxed to describe transport processes exhibiting a non-local character and exhibiting long-range correlations. This article does not aim at presenting a complete review of non-diffusive transport, but rather an introduction for readers not familiar with the topic. For more in depth reviews, we recommend some references in the following. First, we recall the basics of the classical diffusion model and then we present two approaches of possible generalizations of this model: the Continuous-Time-Random-Walk (CTRW) and the fractional L\'evy motion (fLm)

Stochastic models of intracellular transport

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self–organization of subcellular structures

Computational models for large-scale simulations of facilitated diffusion

The binding of site-specific transcription factors to their genomic target sites is a key step in gene regulation. While the genome is huge, transcription factors belong to the least abundant protein classes in the cell. It is therefore fascinating how short the time frame is that they require to home in on their target sites. The underlying search mechanism is called facilitated diffusion and assumes a combination of three-dimensional diffusion in the space around the DNA combined with one-dimensional random walk on it. In this review, we present the current understanding of the facilitated diffusion mechanism and identify questions that lack a clear or detailed answer. One way to investigate these questions is through stochastic simulation and, in this manuscript, we support the idea that such simulations are able to address them. Finally, we review which biological parameters need to be included in such computational models in order to obtain a detailed representation of the actual process. © 2012 The Royal Society of Chemistry

Landau theory of restart transitions

We develop a Landau like theory to characterize the phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two phases is characterized by the behavioral change in the order parameter of the system namely the optimal restart rate. Like in the original theory of Landau, the optimal restart rate can undergo a first or second order transition depending on the details of the system. Nonetheless, there exists no unified framework which can capture the onset of such novel phenomena. We unravel this in a comprehensive manner and show how the transition can be understood by analyzing the first passage time moments. Power of our approach is demonstrated in two canonical paradigm setup namely the Michaelis Menten chemical reaction and diffusion under restart

Pricing average price advertising options when underlying spot market prices are discontinuous

Advertising options have been recently studied as a special type of guaranteed contracts in online advertising, which are an alternative sales mechanism to real-time auctions. An advertising option is a contract which gives its buyer a right but not obligation to enter into transactions to purchase page views or link clicks at one or multiple pre-specified prices in a specific future period. Different from typical guaranteed contracts, the option buyer pays a lower upfront fee but can have greater flexibility and more control of advertising. Many studies on advertising options so far have been restricted to the situations where the option payoff is determined by the underlying spot market price at a specific time point and the price evolution over time is assumed to be continuous. The former leads to a biased calculation of option payoff and the latter is invalid empirically for many online advertising slots. This paper addresses these two limitations by proposing a new advertising option pricing framework. First, the option payoff is calculated based on an average price over a specific future period. Therefore, the option becomes path-dependent. The average price is measured by the power mean, which contains several existing option payoff functions as its special cases. Second, jump-diffusion stochastic models are used to describe the movement of the underlying spot market price, which incorporate several important statistical properties including jumps and spikes, non-normality, and absence of autocorrelations. A general option pricing algorithm is obtained based on Monte Carlo simulation. In addition, an explicit pricing formula is derived for the case when the option payoff is based on the geometric mean. This pricing formula is also a generalized version of several other option pricing models discussed in related studies.Comment: IEEE Transactions on Knowledge and Data Engineering, 201