The Cauchy-Lorentz family is the unique connected two-dimensional family of continuous probability densities invariant under projective transport induced by Riccati dynamics, via reformulation on the circle and stereographic projection.
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A path-integral DMFT for periodic phase oscillators yields a self-consistent single-oscillator stochastic equation that handles arbitrary 2π-periodic couplings and predicts synchronization thresholds from iPRC-fitted neuron data.
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Geometric Origin of Exact Mean-Field Reductions: M{\"o}bius Symmetry and the Lorentzian Ansatz
The Cauchy-Lorentz family is the unique connected two-dimensional family of continuous probability densities invariant under projective transport induced by Riccati dynamics, via reformulation on the circle and stereographic projection.
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Compact Dynamical Mean-Field Theory of Oscillator Networks
A path-integral DMFT for periodic phase oscillators yields a self-consistent single-oscillator stochastic equation that handles arbitrary 2π-periodic couplings and predicts synchronization thresholds from iPRC-fitted neuron data.