Using the mathematical background for algorithmic complexity developed by Kolmogorov in the sixties, Cilibrasi and Vitanyi have designed a similarity distance named normalized compression distance applicable to the clustering of objects of any kind, such as music, texts or gene sequences. The normalized compression distance is a quasi-universal normalized admissible distance under certain conditions. This paper shows that the compressors used to compute the normalized compression distance are not idempotent in some cases, being strongly skewed with the size of the objects and window size, and therefore causing a deviation in the identity property of the distance if we don’t take care that the objects to be compressed fit the windows. The relationship underlying the precision of the distance and the size of the objects has been analyzed for several well-known compressors, and specially in depth for three cases, bzip2, gzip and PPMZ which are examples of the three main types of compressors: block-sorting, Lempel-Ziv, and statistic.

This paper studies the semi-global robust output regulation problem for the class of nonlinear affine systems in normal form. The same problem was studied before by Khalil under the assumption that the solution of the regulator equations is polynomial. By using the nonlinear internal model approach, we have relaxed the polynomial assumption on the solution of the regulator equations.

“Writing on dirty paper” refers to the communication problem over a channel with both noise and interference, where the interference is known to the encoder non-causally and unknown to the decoder. This problem is regarded as a basic building block in both the single-user and multiuser communications, and it has been extensively investigated by Costa and other researchers. However, little is known in the case that the encoder can have access to feedback from the decoder. In this paper, we study the dirty-paper coding problem for feedback Gaussian channels without or with memory. We provide the most power efficient coding schemes for this problem, i.e., the schemes achieve lossless interference cancelation. These schemes are based on the Kalman filtering algorithm, extend the Schalkwijk-Kailath feedback codes, have low complexity and a doubly exponential reliability function, and reveal the interconnections among information, control, and estimation over dirty-paper channels with feedback. This research may be found useful to, for example, powerconstrained sensor network communication.

In this paper we study the Markovian properties of a system of linear partial differential equations with constant coefficients as initiated by J.C. Willems. In particular, we prove that his conjecture on Markovianity is true if the characteristic variety of the system has dimension zero. For the case when the system is defined by a differential operator, we give conditions under which the conjecture is also valid.