We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory. We also use our methods to deduce spectral properties of positive entro...

Biological sequences from different species are called orthologs if they evolved from a sequence of a common ancestor species and they have the same biological function. Approximations of Kolmogorov complexity or entropy of biological sequences are already well known to be useful in extracting similarity information between such sequences — in the interest, for example, of ortholog detection. A...

The vibration acceleration time history of the cutter holder was separated into three parts; namely, chatter free, transition and chatter processes. The reconstructed attractor and probability distribution of vibration acceleration time series were studied in order to observe the system’s behavior. The Lyapunov exponent andKolmogorov entropy were used to help judge the cutting state. Meanwhile,...

We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (‘algorithmic’) mutual inform...

Role of quality control in industry, software engineering and government. Control schemes: measurement and actuator signals. Process time constants: material balance control, production control, quality control. The concept of quality assurance and quality culture. Control system as a simple teleonomic, purposeful, system. Kolmogorov definition of teleonomic entropy. Realization restrictions in...

Many statements from the classic information theory (the theory of Shannon’s entropy) have natural counterparts in the algorithmic information theory (in the framework of Kolmogorov complexity). In this paper we discuss one simple instance of the parallelism between Shannon’s and Kolmogorov’s theories: we prove in the setting of Kolmogorov complexity a version of Wolf’s characterization of admi...

We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdös-Rényi random graphs, and the recovery of topologic...

We discuss quantum entanglement between fast and slow degrees of freedom, in a two-dimensional (2D) large ${N}_{c}$ gauge theory with Dirac quarks, quantized on the light front. Using 't Hooft wave functions, we construct reduced density matrix for an interval momentum fraction $x$ space, calculate its von Neumann entropy terms structure that are measured by deep inelastic scattering mesons (ha...

Collective emotional behavior of users is frequently observed on various Web portals; however, its complexity and the role of emotions in the acting mechanisms are still not thoroughly understood. In this work, using the empirical data and agent-based modeling, a parallel analysis is performed of two archetypal systems—Blogs and Internet-Relayed-Chats—both of which maintain self-organized dynam...