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Well-trained classifiers and their complete weight distributions provide us with a well-motivated and practicable method to test generative networks in particle physics. We illustrate their benefits for distribution-shifted jets,…

Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…

Graph neural networks are currently leading the performance charts in learning-based molecule property prediction and classification. Computational chemistry has, therefore, become the a prominent testbed for generic graph neural networks,…

We lay the foundation of a circuit theory for chemical reaction networks. Chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic, as electrical devices by their…

Discovering new drug molecules is a pivotal yet challenging process due to the near-infinitely large chemical space and notorious demands on time and resources. Numerous generative models have recently been introduced to accelerate the drug…

The calculation of the full counting statistics of the charge within a finite interval of an interacting one-dimensional system of electrons is a fundamental, yet as of now unresolved problem. Even in the non-interacting case, charge…

Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions. Most models for molecule generation rely on the decomposition of molecules into frequently occurring…

Applying machine learning to molecules is challenging because of their natural representation as graphs rather than vectors.Several architectures have been recently proposed for deep learning from molecular graphs, but they suffer from…

How to identify influential nodes in social networks is of theoretical significance, which relates to how to prevent epidemic spreading or cascading failure, how to accelerate information diffusion, and so on. In this Letter, we make an…

Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…

Searching for novel molecules with desired chemical properties is crucial in drug discovery. Existing work focuses on developing neural models to generate either molecular sequences or chemical graphs. However, it remains a big challenge to…

Spectroscopic techniques are essential tools for determining the structure of molecules. Different spectroscopic techniques, such as Nuclear magnetic resonance (NMR), Infrared spectroscopy, and Mass Spectrometry, provide insight into the…

Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…

Generative deep learning has become pivotal in molecular design for drug discovery, materials science, and chemical engineering. A widely used paradigm is to pretrain neural networks on string representations of molecules and fine-tune them…

The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…

Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from…

The ability to reason beyond established knowledge allows Organic Chemists to solve synthetic problems and to invent novel transformations. Here, we propose a model which mimics chemical reasoning and formalises reaction prediction as…

Discovery of atomistic systems with desirable properties is a major challenge in chemistry and material science. Here we introduce a novel, autoregressive, convolutional deep neural network architecture that generates molecular equilibrium…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Chemical reaction networks (CRNs) model the behavior of chemical reactions in well-mixed solutions and they can be designed to perform computations. In this tutorial we give an overview of various computational models for CRNs. Moreover, we…