## About this Research Topic

Nanoscience studies the manipulation or engineering of matter, particles and structures including networks on the nanometer scale, which is the scale of atoms and molecules. Nanotechnology is the technology that is used in the study of nanoscience to design custom-made materials and products with new enhanced ...

A neural network is a computer system inspired by neural networks in the nervous system and modeled on nerve tissues. Many applications of these networks can be found in different areas of studies such as intrusion detection system, image processing, artificial intelligence, localization, medicine, chemical, and environmental sciences.

In particular, neural networks are often applied to perform specific tasks related to; email security enhancement, verification of the signature, identification of an effective ship, localization of damage for bridges as well as detecting resistivity to antibiotics, diagnosing hepatitis, quantification and segmentation of brain tissues from magnetic resonance (MR) images and characterization of genetic variations in toxicological and metabolic responses.

In the context of nanoscience and nanotechnology, mathematical modelling, coding or simulation of nanomaterials and nanosized neural networks play an important role in the study of various physical, biological and chemical properties. Thus, the applications of mathematics in nano and neuroscience is gaining momentum as the mutual benefits of this collaboration become increasingly obvious.

One particular example is the so called graph theory, which has a special impact as it is used to study the pattern classification problem on multiple levels: discrete feed-forward electronics, biological, chemical and neural networks and also, the stability analysis of feedback artificial neural networks. The focus is on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviors in nanomaterials and neural networks at all relevant scales, from the molecular world to the level of cognition.

Specifically, the aim of this Research Topic is providing a general view of the current research in the application of mathematical methods to nanomaterials and neural networks, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. We encourage the submissions of theoretical as well as applied investigations on numerical methods for simulations and analysis of nanomaterials and neural networks based on graph theoretic parameters such as metric dimension, topological indices, graph labeling, entropy and energies, etc.

Potential topics include but are not limited to the following:

● Calculation of metric dimension, entropy, topological indices;

● Energies of nanomaterials and neural networks;

● Labeling of nanomaterials and neural networks;

● Architecture, development, and evolution of brain networks;

● The interaction between biological organisms inside a cell;

● Mathematical modeling in neural network calculation;

● Mathematical calculation and neural network.

**Keywords**:
nanomaterials, neural networks, mathematical methods

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.