Related papers: Recognizing and generating knotted molecular struc…

Knotted proteins, when forced through the pores, can get stuck if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, making translocation possible. We construct a simple energy landscape model…

This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does…

Neural network-based algorithms have garnered considerable attention in condensed matter physics for their ability to learn complex patterns from very high dimensional data sets towards classifying complex long-range patterns of…

We present a new method for scaling automatic configuration of computer networks. The key idea is to relax the computationally hard search problem of finding a configuration that satisfies a given specification into an approximate objective…

The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also abound in viral DNA packaged inside bacteriophages. RNA molecules, on the…

Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks:…

As proteins with similar structures often have similar functions, analysis of protein structures can help predict protein functions and is thus important. We consider the problem of protein structure classification, which computationally…

Rapid determination of molecular structures can greatly accelerate workflows across many chemical disciplines. However, elucidating structure using only one-dimensional (1D) NMR spectra, the most readily accessible data, remains an…

Graph Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed…

Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…

Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…

MOTIVATION: Proteins fold into complex structures that are crucial for their biological functions. Experimental determination of protein structures is costly and therefore limited to a small fraction of all known proteins. Hence, different…

We use machine learning to classify examples of braids (or flat braids) as trivial or non-trivial. Our ML takes form of supervised learning using neural networks (multilayer perceptrons). When they achieve good results in classification, we…

In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

The remarkable performance of deep Convolutional neural networks (CNNs) is generally attributed to their deeper and wider architectures, which can come with significant computational costs. Pruning neural networks has thus gained interest…

Molecule property prediction is a fundamental problem for computer-aided drug discovery and materials science. Quantum-chemical simulations such as density functional theory (DFT) have been widely used for calculating the molecule…

In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…

The deep Convolutional Neural Network (CNN) is the state-of-the-art solution for large-scale visual recognition. Following basic principles such as increasing the depth and constructing highway connections, researchers have manually…

A small fraction of all protein structures characterized so far are entangled. The challenge of understanding the properties of these knotted proteins, and the why and the how of their natural folding process, has been taken up in the past…