Scale-Change Symmetry in the Rules Governing Neural Systems.

Similar universal phenomena can emerge in different complex systems when those systems share a common symmetry in their governing laws. In physical systems operating near a critical phase transition, the governing physical laws obey a fractal symmetry; they are the same whether considered at fine or coarse scales. This scale-change symmetry is responsible for universal critical phenomena found across diverse systems.

Robust entropy requires strong and balanced excitatory and inhibitory synapses.

It is widely appreciated that balanced excitation and inhibition are necessary for proper function in neural networks. However, in principle, balance could be achieved by many possible configurations of excitatory and inhibitory synaptic strengths and relative numbers of excitatory and inhibitory neurons. For instance, a given level of excitation could be balanced by either numerous inhibitory neurons with weak synapses or a few inhibitory neurons with strong synapses.

Emergence of Persistent Infection due to Heterogeneity.

We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual. We investigate the persistence of contagion qualitatively and quantitatively, under increasing heterogeneity in the partitioning of the population into different disease compartments, as well as increasing heterogeneity in the phases of the disease among individuals within a compartment. We observe that when the initial population is uniform, consisting of individuals at the same stage of disease progression, infection arising from a contagious seed does not persist.