Related papers: Recognizing and generating knotted molecular struc…

We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an…

Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the…

In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…

Simulated configurations of flexible knotted rings confined inside a spherical cavity are fed into long-short term memory neural networks (LSTM NNs) designed to distinguish knot types. The results show that they perform well in knot…

Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…

Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular…

Classifying the topology of closed curves is a central problem in low dimensional topology with applications beyond mathematics spanning protein folding, polymer physics and even magnetohydrodynamics. The central problem is how to determine…

In this work, we introduce a method to fine-tune a Transformer-based generative model for molecular de novo design. Leveraging the superior sequence learning capacity of Transformers over Recurrent Neural Networks (RNNs), our model can…

The weights of a neural network are typically initialized at random, and one can think of the functions produced by such a network as having been generated by a prior over some function space. Studying random networks, then, is useful for a…

Knowledge embedded in the weights of the artificial neural network can be used to improve the network structure, such as in network compression. However, the knowledge is set up by hand, which may not be very accurate, and relevant…

Spiking Neural Networks (SNNs) are biologically inspired machine learning models that build on dynamic neuronal models processing binary and sparse spiking signals in an event-driven, online, fashion. SNNs can be implemented on neuromorphic…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…

Proteins are linear molecular chains that often fold to function. The topology of folding is widely believed to define its properties and function, and knot theory has been applied to study protein structure and its implications. More that…

Active nematics is an emerging paradigm for characterising biological systems. One aspect of particularly intense focus is the role active nematic defects play in these systems, as they have been found to mediate a growing number of…

Knitted sensors frequently suffer from inconsistencies due to innate effects such as offset, relaxation, and drift. These properties, in combination, make it challenging to reliably map from sensor data to physical actuation. In this paper,…

Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…

We explore the application of automated reasoning techniques to unknot detection, a classical problem of computational topology. We adopt a two-pronged experimental approach, using a theorem prover to try to establish a positive result…

Artificial neural networks which are inspired from the learning mechanism of brain have achieved great successes in many problems, especially those with deep layers. In this paper, we propose a nucleus neural network (NNN) and corresponding…

The field of machine learning has taken a dramatic twist in recent times, with the rise of the Artificial Neural Network (ANN). These biologically inspired computational models are able to far exceed the performance of previous forms of…