Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Heider balance - a continuous approach   The Heider balance (HB) is investigated in a fully connected graph of $N$
nodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N.
In a social group, nodes represent group members and links represent relations
between them, positive (friendly) or negative (hostile). At the balanced state,
r(i,j)r(j,k)r(k,i)>0 for all the triads (i,j,k). As follows from the structure
theorem of Cartwright and Harary, at this state the group is divided into two
subgroups, with friendly internal relations and hostile relations between the
subgroups. Here the system dynamics is proposed to be determined by a set of
differential equations. The form of equations guarantees that once HB is
reached, it persists. Also, for N=3 the dynamics reproduces properly the
tendency of the system to the balanced state. The equations are solved
numerically. Initially, r(i,j) are random numbers distributed around zero with
a symmetric uniform distribution of unit width. Calculations up to N=500 show
that HB is always reached. Time to get the balanced state varies with the
system size N as N^{-1/2}. The spectrum of relations, initially narrow, gets
very wide near HB. This means that the relations are strongly polarized. In our
calculations, the relations are limited to a given range around zero. With this
limitation, our results can be helpful in an interpretation of somestatistical
data.

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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn