Scientists tested

the ability of neural networks to classify emerging in the chemistry of polymers the nodes. Researchers

tested several different architectures, the best of which showed

correct recognition in 99% of all cases in the analysis of cyclic molecules

of the one hundred segments. Such precision today enough for some

applications, and in the case of the future progress of neural network defining nodes can

become a full-fledged method as in the case of physico-chemical systems and in

the context of the mathematics, write the authors in the journal Physical Review E.

Nodes in ubiquitous environment

the reality of the tangled headphones in your pocket to the climber

strapping. They also arise in many branches of science, including physics,

chemistry and biology. For example, there are knotted currents in the fluid, the nodes are also

curl many molecules, in particular proteins and DNA.

From the point of view of mathematics

the host is the attachment of a circle in three-dimensional space, with the same

the accuracy of continuous transformations (without breaks) nodes are considered to be

equivalent. It is known that the problem of classifying nodes algorithmically

solvable, but not yet invented algorithm of polynomial complexity even for recognition

trivial nodes, that is the usual circles with an accuracy of deformations.

The standard approach

is to find topological invariants, by which one can distinguish

nodes. Here are two directions: polynomial invariants (Alexander,

Jones and others) and homotopy invariants (Jovanova, hagara — Floer and others).

However, all proposed methods have shortcomings. In particular, infinitely

many different nodes are indistinguishable when using the Alexander polynomial and homotopy in the General case, it is unrealistic difficult to calculate.

Researchers from China and

Singapore under the leadership of Liang Dai (Dai Liang) from City University

Hong Kong tested a fundamentally different method based on neural networks. Unlike

analytical algorithms it is not possible to achieve absolute certainty

the answer is, but could theoretically work in secret ways

cases. The authors wanted to test the possibility of using

neural networks to identify the nodes, therefore, limited to five different sites and

two neural networks.

The researchers used a neural network

with a direct link and a recurrent neural network. Training and test sample was

conducted Monte-Carlo simulation of the configuration of the polymer in the form of a ring

one hundred monomers. In each case the type of the node is determined by means of a polynomial

Alexander, and neural networks were selected in 200 thousand or 2 million each

five types of receive nodes. As a further test of the neural network

also determined the type of site a million polymers of 60 and 80 monomers, which are not

it was in the training set.