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mathematics
information-theory
renyi-entropy
shannon-entropy
hidden-markov-models
bernoulli-convolutions
| \begin{table}[htbp] | |
| \centering\small | |
| \setlength{\tabcolsep}{4pt} | |
| \begin{tabular}{lrrrrr} | |
| \toprule | |
| Source / base & $n$ & $q$ & Lower & Upper & Peak states\\ | |
| \midrule | |
| $\varphi$, fair iid & 128 & 2 & 0.458519 & 0.481101 & 7 \\ | |
| $\varphi$, zero-edge Markov & 128 & 2 & 0.391238 & 0.419235 & 14 \\ | |
| Salem, fair iid & 64 & 2 & 0.395946 & 0.543536 & 1477 \\ | |
| Salem, zero-edge Markov & 64 & 2 & 0.216449 & 0.419235 & 10 \\ | |
| Salem, fair iid & 16 & 3 & 0.028764 & 0.543536 & 2493 \\ | |
| $\varphi$, unequal clocks & 24 & 2 & 0.135801 & 0.419235 & 114 \\ | |
| $\varphi$, three-state hidden & 16 & 2 & 0.226595 & 0.652983 & 2403 \\ | |
| Base $2$, stationary mixture & 16 & 2 & 0.000000 & 0.000000 & 3 \\ | |
| Salem, positive correlated & 64 & 2 & 0.284357 & 0.487144 & 3286 \\ | |
| $\varphi$, positive correlated & 128 & 2 & 0.398994 & 0.426991 & 18 \\ | |
| \bottomrule | |
| \end{tabular} | |
| \caption{Exact-rational rate certificates, displayed outwards to six decimal places. Rates are in nats per branch; peak states are observed layer sizes, not asymptotic bounds.} | |
| \label{tab:certs} | |
| \end{table} | |