I solve a conjecture originally studied by M. Ajtai. It states that for different primes q, p the matching principles Count(q) and Count(p) are logically independent. I prove that this indeed is the case. Actually I show that Count(q) implies Count(p) exactly when each prime factor in p also is a factor in q. 1 The logic of elementary counting “She loves me, she loves me not, she loves me,. . ....

Normalization, which divisively scales neuronal responses to multiple stimuli, is thought to underlie many sensory, motor, and cognitive processes. In every study where it has been investigated, neurons measured in the same brain area under identical conditions exhibit a range of normalization, ranging from suppression by nonpreferred stimuli (strong normalization) to additive responses to comb...