entity; it is always tied to a physical representation. It is represented by engraving on a stone tablet, a spin, a charge, a hole in a punched card, a mark on a paper, or some other equivalent.” (1996, p. 188; see also Landauer 1991). This view is also adopted by some philosophers of science; for instance, Peter Kosso states that “information is transferred between states through interaction.”...

As a novel data mining approach, a wavelet entropy algorithm is used to perform entropy statistics on wavelet coefficients (or reconstructed signals) at various wavelet scales on the basis of wavelet decomposition and entropy statistic theory. Shannon wavelet energy entropy, one kind of wavelet entropy algorithm, has been taken into consideration and utilized in many areas since it came into be...

We consider the problem of communicating the state of a dynamical system via a Shannon Gaussian channel with a given power constraint and no feedback. The transmitter observes a possibly noisy measurement of the state. These measurements are then used to encode the message to be transmitted over a noisy Gaussian channel, where a power constraint is imposed on the transmitted message. The receiv...

Claude Shannon founded information theory in the 1940s. The theory has long been known to be closely related to thermodynamics and physics through the similarity of Shannon's uncertainty measure to the entropy function. Recent work using information theory to understand molecular biology has unearthed a curious fact: Shannon's channel capacity theorem only applies to living organisms and their ...

Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.

In this paper the capacity achievable by Abelian group codes when employed over symmetric channels is determined. For certain important examples, like the AWGN channel with m-PSK modulation, it follows that this capacity coincides with the corresponding Shannon capacity of these channels. In other words using Abelian group codes in this case there is no loss of capacity (as it happens for binar...

A sampling theorem for regular sampling in shift invariant subspaces is established. The sufficient-necessary condition for which it holds is found. Then, the theorem is modified to the shift sampling in shiftinvariant subspaces by using the Zak transform. Finally, some examples are presented to show the generality of the theorem.

We calculate the Shannon entropy of a time series by using the probability density functions of the characteristic sizes of the long-range correlated clusters introduced in [A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69 (2004) 026105]. We define three different measures of the entropy related, respectively, to the length, the duration and the area of the clusters. For all the three cas...