A Performance-Based Wind Engineering Framework for Engineered Building Systems Subject to Hurricanes

Over the past decade, significant research efforts have been dedicated to the development of performance-based wind engineering (PBWE). Notwithstanding these efforts, frameworks that integrate the damage assessment of the structural and envelope system are still lacking. In response to this need, the authors have recently proposed a PBWE framework that holistically treats envelope and structural damages through progressive multi-demand fragility models that capture the inherent coupling in the demands and damages. Similar to other PBWE methodologies, this framework is based on describing the hurricane hazard through a nominal straight and stationary wind event with constant rainfall and one-hour duration. This study aims to develop a PBWE framework based on a full description of the hurricane hazard in which the entire evolution of the storm track and time-dependent wind/rain fields is simulated. Hurricane-induced pressures impacting the building envelope are captured through the introduction of a non-stationary/-straight/-Gaussian wind pressure model. Time-dependent wind-driven rain is modeled through a computational fluid dynamics Eulerian multiphase framework with interpolation schemes for the rapid computation of wind-driven rain intensities over the building surface. Through the development of a conditional stochastic simulation algorithm, the envelope performance is efficiently characterized through probabilistic metrics associated with rare events of design interest. The framework is demonstrated through analyzing a 45-story archetype building located in Miami, FL, for which the envelope performance is estimated in terms of a suite of probabilistic damage and loss metrics. A comparative study is carried out in order to provide insights into the differences that can occur due to the use of nominal hurricane models.

Stochastic Simulation Algorithm for effective spreading dynamics on Time-evolving Adaptive NetworX (SSATAN-X)

Modelling and simulating the dynamics of pathogen spreading has been proven crucial to inform public heath decisions, containment strategies, as well as cost-effectiveness calculations. Pathogen spreading is often modelled as a stochastic process that is driven by pathogen exposure on time-evolving contact networks. In adaptive networks, the spreading process depends not only on the dynamics of a contact network, but vice versa, infection dynamics may alter risk behaviour and thus feed back onto contact dynamics, leading to emergent complex dynamics. However, stochastic simulation of pathogen spreading processes on adaptive networks is currently computationally prohibitive. In this manuscript, we propose SSATAN-X, a new algorithm for the accurate stochastic simulation of pathogen spreading on adaptive networks. The key idea of SSATAN-X is to only capture the contact dynamics that are relevant to the spreading process. We show that SSATAN-X captures the contact dynamics and consequently the spreading dynamics accurately. The algorithm achieves a > 10 fold speed-up over the state-of-art stochastic simulation algorithm (SSA). The speed-up with SSATAN-X further increases when the contact dynamics are fast in relation to the spreading process, i.e. if contacts are short-lived and per-exposure infection risks are small, as applicable to most infectious diseases. We envision that SSATAN-X may extend the scope of analysis of pathogen spreading on adaptive networks. Moreover, it may serve to create benchmark data sets to validate novel numerical approaches for simulation, or for the data-driven analysis of the spreading dynamics on adaptive networks. A C++ implementation of the algorithm is available https://github.com/nmalysheva/SSATAN-X

Generalised S-System-Type Equation: Sensitivity of the Deterministic and Stochastic Models for Bone Mechanotransduction

The formalism of a bone cell population model is generalised to be of the form of an S-System. This is a system of nonlinear coupled ordinary differential equations (ODEs), each with the same structure: the change in a variable is equal to a difference in the product of a power-law functions with a specific variable. The variables are the densities of a variety of biological populations involved in bone remodelling. They will be specified concretely in the cases of a specific periodically forced system to describe the osteocyte mechanotransduction activities. Previously, such models have only been deterministically simulated causing the populations to form a continuum. Thus, very little is known about how sensitive the model of mechanotransduction is to perturbations in parameters and noise. Here, we revisit this assumption using a Stochastic Simulation Algorithm (SSA), which allows us to directly simulate the discrete nature of the problem and encapsulate the noisy features of individual cell division and death. Critically, these stochastic features are able to cause unforeseen dynamics in the system, as well as completely change the viable parameter region, which produces biologically realistic results.

The switch of DNA states filtering the extrinsic noise in the system of frequency modulation

There is a special node, which the large noise of the upstream element may not always lead to a broad distribution of downstream elements. This node is DNA, with upstream element TF and downstream elements mRNA and proteins. By applying the stochastic simulation algorithm (SSA) on gene circuits inspired by the fim operon in Escherichia coli, we found that cells exchanged the distribution of the upstream transcription factor (TF) for the transitional frequency of DNA. Then cells do an inverse transform, which exchanges the transitional frequency of DNA for the distribution of downstream products. Due to this special feature, DNA in the system of frequency modulation is able to reset the noise. By probability generating function, we know the ranges of parameter values that grant such an interesting phenomenon.

BiPSim: a flexible and generic stochastic simulator for polymerization processes

Detailed whole-cell modeling requires an integration of heterogeneous cell processes having different modeling formalisms, for which whole-cell simulation could remain tractable. Here, we introduce BiPSim, an open-source stochastic simulator of template-based polymerization processes, such as replication, transcription and translation. BiPSim combines an efficient abstract representation of reactions and a constant-time implementation of the Gillespie’s Stochastic Simulation Algorithm (SSA) with respect to reactions, which makes it highly efficient to simulate large-scale polymerization processes stochastically. Moreover, multi-level descriptions of polymerization processes can be handled simultaneously, allowing the user to tune a trade-off between simulation speed and model granularity. We evaluated the performance of BiPSim by simulating genome-wide gene expression in bacteria for multiple levels of granularity. Finally, since no cell-type specific information is hard-coded in the simulator, models can easily be adapted to other organismal species. We expect that BiPSim should open new perspectives for the genome-wide simulation of stochastic phenomena in biology.

Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

Numerical studies of higher order tau-leaping methods

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

Numerical studies of higher order tau-leaping methods

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation

Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.