相关论文: Survey: Information flow on trees

Consider a tree network $T$, where each edge acts as an independent copy of a given channel $M$, and information is propagated from the root. For which $T$ and $M$ does the configuration obtained at level $n$ of $T$ typically contain…

In this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated…

In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…

Shared information is a measure of mutual dependence among multiple jointly distributed random variables with finite alphabets. For a Markov chain on a tree with a given joint distribution, we give a new proof of an explicit…

Information Theory concepts and methodologies conform the background of how communication systems are studied and understood. They are mainly focused on the source-channel-receiver problem and on the asymptotic limits of accuracy and…

How information spreads through a social network? Can we assume, that the information is spread only through a given social network graph? What is the correct way to compare the models of information flow? These are the basic questions we…

Without having direct access to the information that is being exchanged, traces of information flow can be obtained by looking at temporal sequences of user interactions. These sequences can be represented as causality trees whose…

Life depends as much on the flow of information as on the flow of energy. Here we review the many efforts to make this intuition precise. Starting with the building blocks of information theory, we explore examples where it has been…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

We consider the transmission of a state from the root of a tree towards its leaves, assuming that each transmission occurs through a noisy channel. The states at the leaves are observed, while at deeper nodes we can compute the likelihood…

The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…

Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks.…

Assessing where and how information is stored in biological networks (such as neuronal and genetic networks) is a central task both in neuroscience and in molecular genetics, but most available tools focus on the network's structure as…

We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

Social networks play a fundamental role in the diffusion of information. However, there are two different ways of how information reaches a person in a network. Information reaches us through connections in our social networks, as well as…

Stochastic networks represent very important subject of research because they have been found in almost all branches of modern science, including also sociology and economy. We provide a information theory point of view, mostly based on its…

To analyze the transport of information or material from a source to every node of a network we use two quantities introduced in the study of river networks: the cost and the flow. For a network with $K$ nodes and $M$ levels, we show that…

Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…

Information propagation characterizes how input correlations evolve across layers in deep neural networks. This framework has been well studied using mean-field theory, which assumes infinitely wide networks. However, these assumptions…