A Markov embedding of ranked unlabelled trees reduces state space, enabling efficient Fréchet means, arbitrary-order F-matrix moments via phase-type theory, and improved neutrality tests under coalescent models.
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For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
An explicit Fejér-kernel-power construction yields matrix-exponential distributions with closed-form parameters that asymptotically surpass the Erlang variance bound for unit delay.
Random-reward discrete phase-type distributions are defined and used to construct the two-parameter Inertia-Escalation model for latent severity, with parameter inference and validation on warfare and churn data.
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Markov embedding of ranked unlabelled evolutionary trees and its applications
A Markov embedding of ranked unlabelled trees reduces state space, enabling efficient Fréchet means, arbitrary-order F-matrix moments via phase-type theory, and improved neutrality tests under coalescent models.
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Solving linear-rate ODE hierarchies (like master equations) using closures and operator splitting
For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
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Optimization-Free Concentrated Matrix-Exponentials
An explicit Fejér-kernel-power construction yields matrix-exponential distributions with closed-form parameters that asymptotically surpass the Erlang variance bound for unit delay.
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Random Reward Phase-Type Distributions with Applications in Latent Severity Modeling
Random-reward discrete phase-type distributions are defined and used to construct the two-parameter Inertia-Escalation model for latent severity, with parameter inference and validation on warfare and churn data.