相关论文: Information disclosure in the framework of Kolmogo…
Multiple players are each given one independent sample, about which they can only provide limited information to a central referee. Each player is allowed to describe its observed sample to the referee using a channel from a family of…
Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
During an epidemic, the information available to individuals in the society deeply influences their belief of the epidemic spread, and consequently the preventive measures they take to stay safe from the infection. In this paper, we develop…
Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$ denotes mutual…
Symmetry of information states that $C(x) + C(y|x) = C(x,y) + O(\log C(x))$. We show that a similar relation for online Kolmogorov complexity does not hold. Let the even (online Kolmogorov) complexity of an n-bitstring $x_1x_2... x_n$ be…
We investigate the use of network coding for information dissemination over a wireless network. Using network coding allows for a simple, distributed and robust algorithm where nodes do not need any information from their neighbors. In this…
In this paper, we first introduce the notion of channel leakage as the minimum mutual information between the channel input and channel output. As its name indicates, channel leakage quantifies the minimum information leakage to the…
We consider the problem of source coding with receiver side information for the simple network proposed by R. Gray and A. Wyner in 1974. In this network, a transmitter must reliably transport the output of two correlated information sources…
Given two events $A$ and $B$, Bayes' law is based on the argument that the probability of $A$ given $B$ is proportional to the probability of $B$ given $A$. When probabilities are interpreted in the Bayesian sense, Bayes' law constitutes a…
We consider the problem where a group of n nodes, connected to the same broadcast channel (e.g., a wireless network), want to generate a common secret bitstream, in the presence of an adversary Eve, who tries to obtain information on the…
We investigate and quantify the interplay between topology and ability to send specific signals in complex networks. We find that in a majority of investigated real-world networks the ability to communicate is favored by the network…
In this note, we show that the operator theoretic concept of Kolmogorov numbers and the number of degrees of freedom at level $\epsilon$ of a communication channel are closely related. Linear communication channels may be modeled using…
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The…
Knowledge networks can be defined as social networks that enable the transfer of the knowledge, which is defined as the intellectual product formed as a result of the work of human intelligence, to be transferred to any other means of…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
In this paper, we address hypothesis testing in a distributed network of nodes, where each node has only partial information about the State of the World (SotW) and is tasked with determining which hypothesis, among a given set, is most…
Humans communicate using systems of interconnected stimuli or concepts -- from language and music to literature and science -- yet it remains unclear how, if at all, the structure of these networks supports the communication of information.…
There is currently growing interest in modeling the information diffusion on social networks across multi-disciplines. The majority of the corresponding research has focused on information diffusion independently, ignoring the network…