This paper deals with the development of mathematical structures suitable to include a variety of Boltzmann type models for social competition.
Weisberg (2013), building on many insights from Giere's work, presents a broad view of modeling that includes mathematical structures that are "trajectories in state spaces" (29), but also permits concrete objects and computational structures such as algorithms to be deemed models.
However, a large part of the appeal of the DA is that it classes intangible, mathematical structures — geometry — as mere representation, and tangible things — matter (including fields) and its properties — as real.
Furthermore, deterministic ODEs are only one of several mathematical structures used to model gene regulatory networks; other possibilities include boolean networks, Petri nets, Markov chains, stochastic ODEs, and so on.
Mathematical structures with an addition operation but not a subtraction operation include commutative semigroups, commutative monoids and semirings.
Finally, there are certain hybrids of these two branches of mathematical logic, including "partial structures" (e.g., da Costa and French 1990, 2003; Bueno 1997; French and Ladyman 1999, 2003; Vickers 2009; Bueno, French, and Ladyman 2012).
But rather than supporting the existence of mathematical objects, the argument would only support commitment to modal-structural translations of mathematical theories and the possibility of mathematical structures.
In the case where lattice equations including the positive and negative lattices by using the semi-direct sums of Lie algebras have been present [12, 13], their mathematical structures such as Hamiltonian structures usually investigated by the variational identity [14].
Even Shakespeare's poetry is full of interesting mathematical structures.
But some mathematical structures have symmetries that persist across scales.
