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We review recent progress in understanding Quantum Field Theory. The new results connect three thorny and fundamental questions: The symmetries of second order phase transitions, monotonicity of the renormalization group flow, and the entanglement entropy of the vacuum. We give examples of various applications for theories ranging from boiling water to Quantum Chromodynamics.

While single-cell activity may be well correlated with simple aspects of sensory stumuli, rich stimuli or subtly differing stimuli require concomitant coding by several neurons in a population. It is then natural to ask whether the nature of the coding is ‘orchestral’ in that it relies upon correlation and physiological diversity among cells. Positive correlations in the activity of neurons are widely observed in the brain and previous studies stipulate that these are at best marginally favorable, if not detrimental, to the fidelity of population codes, compared to independent codes. Here, we put forth a scenario in which positive correlations can enhance coding performance by astronomical factors. Specifically, the probability of discrimination error can be suppressed by many orders of magnitude.
Likewise, the number of stimuli encoded—the capacity—can be enhanced by similarly large factors. These effects do not necessitate unrealistic correlation values and can occur for populations with as little as a few tens of neurons. The scenario relies upon ‘lock-in’
patterns of activity with which correlation relegates the noise in irrelevant modes. We further demonstrate that, quite generically, coding fidelity is enhanced by physiological heterogeneity. Finally, we formulate heuristic arguments as to the plausibility of ‘lock-in’
patterns and possible experimental tests of the theoretical proposal.