Reaction rates for a generalized reaction-diffusion master equation

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm, which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules

Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity

MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools, a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments

Interpretable Polynomial Neural Ordinary Differential Equations

Neural networks have the ability to serve as universal function approximators, but they are not interpretable and don't generalize well outside of their training region. Both of these issues are problematic when trying to apply standard neural ordinary differential equations (neural ODEs) to dynamical systems. We introduce the polynomial neural ODE, which is a deep polynomial neural network inside of the neural ODE framework. We demonstrate the capability of polynomial neural ODEs to predict outside of the training region, as well as perform direct symbolic regression without additional tools such as SINDy

Reaction rates for mesoscopic reaction-diffusion kinetics

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework, frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a mixed boundary condition at the reaction radius of two molecules. We also establish fundamental limits for the range of mesh resolutions for which this approach yields accurate results, and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics

Are Large Language Models Ready for Healthcare? A Comparative Study on Clinical Language Understanding

Large language models (LLMs) have made significant progress in various domains, including healthcare. However, the specialized nature of clinical language understanding tasks presents unique challenges and limitations that warrant further investigation. In this study, we conduct a comprehensive evaluation of state-of-the-art LLMs, namely GPT-3.5, GPT-4, and Bard, within the realm of clinical language understanding tasks. These tasks span a diverse range, including named entity recognition, relation extraction, natural language inference, semantic textual similarity, document classification, and question-answering. We also introduce a novel prompting strategy, self-questioning prompting (SQP), tailored to enhance LLMs' performance by eliciting informative questions and answers pertinent to the clinical scenarios at hand. Our evaluation underscores the significance of task-specific learning strategies and prompting techniques for improving LLMs' effectiveness in healthcare-related tasks. Additionally, our in-depth error analysis on the challenging relation extraction task offers valuable insights into error distribution and potential avenues for improvement using SQP. Our study sheds light on the practical implications of employing LLMs in the specialized domain of healthcare, serving as a foundation for future research and the development of potential applications in healthcare settings.Comment: 19 pages, preprin

Advances in Deep Space Exploration via Simulators & Deep Learning

The NASA Starlight and Breakthrough Starshot programs conceptualize fast interstellar travel via small relativistic spacecraft that are propelled by directed energy. This process is radically different from traditional space travel and trades large and slow spacecraft for small, fast, inexpensive, and fragile ones. The main goal of these wafer satellites is to gather useful images during their deep space journey. We introduce and solve some of the main problems that accompany this concept. First, we need an object detection system that can detect planets that we have never seen before, some containing features that we may not even know exist in the universe. Second, once we have images of exoplanets, we need a way to take these images and rank them by importance. Equipment fails and data rates are slow, thus we need a method to ensure that the most important images to humankind are the ones that are prioritized for data transfer. Finally, the energy on board is minimal and must be conserved and used sparingly. No exoplanet images should be missed, but using energy erroneously would be detrimental. We introduce simulator-based methods that leverage artificial intelligence, mostly in the form of computer vision, in order to solve all three of these issues. Our results confirm that simulators provide an extremely rich training environment that surpasses that of real images, and can be used to train models on features that have yet to be observed by humans. We also show that the immersive and adaptable environment provided by the simulator, combined with deep learning, lets us navigate and save energy in an otherwise implausible way