Improved estimations of stochastic chemical kinetics by finite-state expansion

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

A Noise-Immune Kalman Filter and Modelling forPedestrian Traffic Loads

The definition of design load with walking crowd excitation on these slender structures is a significant problem to human-induced vibration. To capture the characteristics of walking crowd loads, this article researches both the ground reaction force and ground reaction moment for 36 healthy adults. Firstly, a oscillate system modeling walking leg is used to build a governing equation, which further transformed into the discrete state space. Then the Kalman method is applied to filter the noises for the measured ground reaction force, which can well remove the noises hiding in the measured signals. In addition, the Fourier series are used to model the ground reaction force and ground reaction moment, and the first six corresponding coefficients are obtained and analyzed. This work comprehensively explores the excitation force and moment from walking pedestrian feet. The result of this study provides the reference of load design for these slender structures such as footbridges, grandstands, or stations under crowd excitation.

Closed-Loop Deep Learning: Generating Forward Models With Backpropagation

A reflex is a simple closed-loop control approach that tries to minimize an error but fails to do so because it will always react too late. An adaptive algorithm can use this error to learn a forward model with the help of predictive cues. For example, a driver learns to improve steering by looking ahead to avoid steering in the last minute. In order to process complex cues such as the road ahead, deep learning is a natural choice. However, this is usually achieved only indirectly by employing deep reinforcement learning having a discrete state space. Here, we show how this can be directly achieved by embedding deep learning into a closed-loop system and preserving its continuous processing. We show in z-space specifically how error backpropagation can be achieved and in general how gradient-based approaches can be analyzed in such closed-loop scenarios. The performance of this learning paradigm is demonstrated using a line follower in simulation and on a real robot that shows very fast and continuous learning.