42 citations · 110 across the 10 of their papers we have counts for
11 papers
An Explicit Bound for the First Dirichlet Eigenvalue via Two Moments
Thomas Schürmann
Let , , be a compact connected Riemannian manifold with smooth nonempty boundary, for , and nonnegative outward boundary mean…
A First-Order Entropy Law for Canonical T-Complexity of Finite-Alphabet i.i.d. Sources
Thomas Schürmann
Let be an exact length- block from a strictly positive i.i.d. source on a fixed finite alphabet. We prove that the canonical T-complexity satisfies \[ \f…
Non-Simple T-Prescriptions Yield T-Complexity Gains Infinitely Often
Thomas Schürmann
Titchener et al. (2005) asked whether non-simple T-prescriptions can achieve larger T-complexity than simple T-prescriptions for infinitely many finite values of the maximum codewo…
On the experimental verification of the uncertainty principle of position and momentum
Thomas Schürmann, Ingo Hoffmann, Winfrid Görlich
Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice sh…
A note on entropy estimation
Thomas Schürmann
We compare an entropy estimator recently discussed in [10] with two estimators and introduced in [6][7]. We prove the identity , which has not bee…
Unbiased Estimators for Entropy and Class Number
Stephen Montgomery-Smith, T. Schürmann
We introduce unbiased estimators for the Shannon entropy and the class number, in the situation that we are able to take sequences of independent samples of arbitrary length.
A closer look at the uncertainty relation of position and momentum
Thomas Schürmann, Ingo Hoffmann
We consider particles prepared by the von Neumann-Lüders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviati…
The predictability of letters in written english
Thomas Schürmann, Peter Grassberger
We show that the predictability of letters in written English texts depends strongly on their position in the word. The first letters are usually the least easy to predict. This ag…
The entropy of 'strange' billiards inside n-simplexes
Thomas Schürmann, Ingo Hoffmann
In the present work we investigate a new type of billiards defined inside n-simplex regions. We determine an invariant ergodic (SRB) measure of the dynamics for any dimension. In u…
Scaling behaviour of entropy estimates
Thomas Schürmann
Entropy estimation of information sources is highly non trivial for symbol sequences with strong long-range correlations. The rabbit sequence, related to the symbolic dynamics of t…
The entropy of ``strange'' billiards inside n-simplexes
Thomas Schürmann, Ingo Hoffmann
In the present work we investigate a new type of billiards defined inside of --simplex regions. We determine an invariant ergodic (SRB) measure of the dynamics for any dimension…