  We combine extensive data analyses with a modeling approach to measure,
disentangle, and reconstruct the actual functional form of interactions
involved in the coordination of swimming in Rummy-nose tetra (Hemigrammus
rhodostomus). This species of fish performs burst-and-coast swimming behavior
that consists of sudden heading changes combined with brief accelerations
followed by quasi-passive, straight decelerations. We quantify the spontaneous
stochastic behavior of a fish and the interactions that govern wall avoidance
and the attraction and alignment to a neighboring fish, the latter by
exploiting general symmetry constraints for the interactions. In contrast with
previous experimental works, we find that both attraction and alignment
behaviors control the reaction of fish to a neighbor. We then exploit these
results to build a model of spontaneous burst-and-coast swimming and
interactions of fish, with all parameters being estimated or directly measured
from experiments. This model quantitatively reproduces the key features of the
motion and spatial distributions observed in experiments with a single fish and
with two fish. This demonstrates the power of our method that exploits large
amounts of data for disentangling and fully characterizing the interactions
that govern collective behaviors in animals groups. Moreover, we introduce the
notions of "dumb" and "intelligent" active matter and emphasize and clarify the
strong differences between them.
