Related papers: Network theory approach for data evaluation in the…
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's…
Neural networks are being used to make new types of empirical chemical models as inexpensive as force fields, but with accuracy close to the ab-initio methods used to build them. Besides modeling potential energy surfaces, neural-nets can…
This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…
Single-molecule narrowfield microscopy is a versatile tool to investigate a diverse range of protein dynamics in live cells and has been extensively used in bacteria. Here, we describe how these methods can be extended to larger eukaryotic,…
Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models…
Heterogeneity in biological molecules, resulting in molecule-to-molecule variations in their dynamics and function, is an emerging theme. To elucidate the consequences of heterogeneous behavior at the single molecule level, we propose an…
Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…
We present mathematical models based on persistent homology for analyzing force distributions in particulate systems. We define three distinct chain complexes: digital, position, and interaction, motivated by different capabilities of…
Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of…
Numerous social, medical, engineering and biological challenges can be framed as graph-based learning tasks. Here, we propose a new feature based approach to network classification. We show how dynamics on a network can be useful to reveal…
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed,…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
The forced rupture of single chemical bonds under external load is addressed. A general framework is put forward to optimally utilize the experimentally observed rupture force data for estimating the parameters of a theoretical model. As an…
Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict studies in…
This paper describes a novel approach to modeling homphily, i.e. the tendency of nodes that share (or differ in) certain attributes to be linked; we consider dynamic networks in which nodes can be added over time but not removed. Our…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
Dynamic gene-regulatory networks are complex since the number of potential components involved in the system is very large. Estimating dynamic networks is an important task because they compromise valuable information about interactions…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…