Information geometric bound on general chemical reaction networks

We investigate the dynamics of chemical reaction networks (CRNs) with the goal of deriving an upper bound on their reaction rates. This task is challenging due to the nonlinear nature and discrete structure inherent in CRNs. To address this, we employ an information geometric approach, using the natural gradient, to develop a nonlinear system that yields an upper bound for CRN dynamics. We validate our approach through numerical simulations, demonstrating faster convergence in a specific class of CRNs. This class is characterized by the number of chemicals, the maximum value of stoichiometric coefficients of the chemical reactions, and the number of reactions. We also compare our method to a conventional approach, showing that the latter cannot provide an upper bound on reaction rates of CRNs. While our study focuses on CRNs, the ubiquity of hypergraphs in fields from natural sciences to engineering suggests that our method may find broader applications, including in information science.

Mol-PECO: a deep learning model to predict human olfactory perception from molecular structures

While visual and auditory information conveyed by wavelength of light and frequency of sound have been decoded, predicting olfactory information encoded by the combination of odorants remains challenging due to the unknown and potentially discontinuous perceptual space of smells and odorants. Herein, we develop a deep learning model called Mol-PECO (Molecular Representation by Positional Encoding of Coulomb Matrix) to predict olfactory perception from molecular structures. Mol-PECO updates the learned atom embedding by directional graph convolutional networks (GCN), which model the Laplacian eigenfunctions as positional encoding, and Coulomb matrix, which encodes atomic coordinates and charges. With a comprehensive dataset of 8,503 molecules, Mol-PECO directly achieves an area-under-the-receiver-operating-characteristic (AUROC) of 0.813 in 118 odor descriptors, superior to the machine learning of molecular fingerprints (AUROC of 0.761) and GCN of adjacency matrix (AUROC of 0.678). The learned embeddings by Mol-PECO also capture a meaningful odor space with global clustering of descriptors and local retrieval of similar odorants. Our work may promote the understanding and decoding of the olfactory sense and mechanisms.

Forward and Backward Bellman equations improve the efficiency of EM algorithm for DEC-POMDP

Decentralized Partially Observable Markov Decision Process (DEC-POMDP) models sequential decision making problems by a team of agents. Since the planning of DEC-POMDP can be interpreted as the maximum likelihood estimation for the latent variable model, DEC-POMDP can be solved by EM algorithm. However, in EM for DEC-POMDP, the forward-backward algorithm needs to be calculated up to the infinite horizon, which impairs the computational efficiency. In this paper, we propose Bellman EM algorithm (BEM) and Modified Bellman EM algorithm (MBEM) by introducing the forward and backward Bellman equations into EM. BEM can be more efficient than EM because BEM calculates the forward and backward Bellman equations instead of the forward-backward algorithm up to the infinite horizon. However, BEM cannot always be more efficient than EM when the size of problems is large because BEM calculates an inverse matrix. We circumvent this shortcoming in MBEM by calculating the forward and backward Bellman equations without the inverse matrix. Our numerical experiments demonstrate that the convergence of MBEM is faster than that of EM.