Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting Totally Positive Differential Systems: A Tutorial and New
  Results   A matrix is called totally nonnegative (TN) if all its minors are
nonnegative, and totally positive (TP) if all its minors are positive.
Multiplying a vector by a TN matrix does not increase the number of sign
variations in the vector. In a largely forgotten paper, Schwarz (1970)
considered matrices whose exponentials are TN or TP. He also analyzed the
evolution of the number of sign changes in the vector solutions of the
corresponding linear system.
  In a seemingly different line of research, Smillie (1984), Smith (1991), and
others analyzed the stability of nonlinear tridiagonal cooperative systems by
using the number of sign variations in the derivative vector as an
integer-valued Lyapunov function.
  We provide a tutorial on these fascinating research topics and show that they
are intimately related. This allows to derive generalizations of the results by
Smillie (1984) and Smith (1991) while simplifying the proofs. It also opens the
door to many new and interesting research directions.

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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: hep-lat