The neural network learned to recognize the knots in polymers

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.

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