Many theorists argue that deduction is based on the construction of mental models or simulations of descriptions. Individuals tend to reason intuitively from a single mental model, but on occasion they make a deliberate search for alternative models. Previous computer implementations of the theory were deterministic, but evidence from empirical studies suggested that a stochastic algorithm woul...

Previous research has shown that stochastic models are advantageous tools for representation of the real world. Due to actual spread of fast and inexpensive computational power everywhere in the world, the best approach is to model a real phenomenon as faithfully as possible, and then rely on a simulation study to analyse it. Based on theoretical fundamentals in stochastic modelling and simulat...

We present a positivity preserving numerical scheme for the pathwise solution of nonlinear stochastic differential equations driven by a multi-dimensional Wiener process and governed by non-commutative linear and non-Lipschitz vector fields. This strong order one scheme uses: (i) Strang exponential splitting, an approximation that decomposes the stochastic flow separately into the drift flow, a...

Here, Tj is a time period that species X spent in state n, and Tsim is the total simulation time. For the species X1 shown in Figure 1 of the manuscript, as first sight, one might think that P (X1 = 0) << P (X1 = 1) because X1 = 1 during 19 of the 20 simulated time steps. In stochastic simulations, reaction events are irregular due to their stochastic nature. In this particular example, the fir...

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and paramete...

Stochastic seismic inversion is a family of inversion algorithms in which the inverse solution was carried out using geostatistical simulation. In this work, a new 3D stochastic seismic inversion was developed in the MATLAB programming software. The proposed inversion algorithm is an iterative procedure that uses the principle of cross-over genetic algorithms as the global optimization techniqu...

Single-cell and single-molecule measurements indicate the importance of stochastic phenomena in cell biology. Stochasticity creates spontaneous differences in the copy numbers of key macromolecules and the timing of reaction events between genetically-identical cells. Mathematical models are indispensable for the study of phenotypic stochasticity in cellular decision-making and cell survival. T...

Title (Swedish) Abstract A comparison of the mesoscopic and macroscopic reaction-diffusion modelling has been performed. The comparison has been done on a full 3D model using Monte Carlo simulation, solving the reaction-diffusion master equation, and deterministic simulation, solving partial differential equations. All simulations were done on the Min-system in E. coli. In many cases the stocha...

Simulation is defined to be a technique to imitate the evolution of a real system by studying a model of the system (Winston, 1994, p. 23; Ripley, 1987, p. 2). The model is an abstraction, a simplified and convenient mathematical representation of the actual system typically coded and run as a computer program. If the model has a stochastic1 element, then we have stochastic simulation. The term...