  The computation of rank ordering plays a fundamental role in cognitive tasks
and offers a basic building block for computing arbitrary digital functions.
Spiking neural networks have been demonstrated to be capable of identifying the
largest k out of N analog input signals through their collective nonlinear
dynamics. By finding partial rank orderings, they perform k-winners-take-all
computations. Yet, for any given study so far, the value of k is fixed, often
to k equal one. Here we present a concept for spiking neural networks that are
capable of (re)configurable computation by choosing k via one global system
parameter. The spiking network acts via pulse-suppression induced by inhibitory
pulse-couplings. Couplings are proportional to each units' state variable
(neuron voltage), constituting an uncommon but straightforward type of leaky
integrate-and-fire neural network. The result of a computation is encoded as a
stable periodic orbit with k units spiking at some frequency and others at
lower frequency or not at all. Orbit stability makes the resulting
analog-to-digital computation robust to sufficiently small variations of both,
parameters and signals. Moreover, the computation is completed quickly within a
few spike emissions per neuron. These results indicate how reconfigurable
k-winners-take-all computations may be implemented and effectively exploited in
simple hardware relying only on basic dynamical units and spike interactions
resembling simple current leakages to a common ground.

Adaptation and Self-Organizing Systems