相关论文: Shannon capacity, Chess, DNA and Umbrellas
Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy…
Shannon defined channel capacity as the highest rate at which there exists a sequence of codes of block length $n$ such that the error probability goes to zero as $n$ goes to infinity. In this definition, it is implicit that the block…
We develop a notion of containment for independent sets in hypergraphs. For every $r$-uniform hypergraph $G$, we find a relatively small collection $C$ of vertex subsets, such that every independent set of $G$ is contained within a member…
There has been interest recently in maximizing the number of independent sets in graphs. For example, the Kahn-Zhao theorem gives an upper bound on the number of independent sets in a $d$-regular graph. Similarly, it is a corollary of the…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…
We quantify a social organization's potentiality, that is its ability to attain different configurations. The organization is represented as a network in which nodes correspond to individuals and (multi-)edges to their multiple…
The classical problem of reliable point-to-point digital communication is to achieve a low probability of error while keeping the rate high and the total power consumption small. Traditional information-theoretic analysis uses `waterfall'…
Information-theoretic limits of {\it cognitive radio} networks have been under exploration for more than a decade. Although such limits are unknown for many networks, including the simplest case with two pairs of transmitter-receiver, there…
Finding a Maximum Clique is a classic property test from graph theory; find any one of the largest complete subgraphs in an Erd\"os-R\'enyi G(N, p) random graph. We use Maximum Clique to explore the structure of the problem as a function of…
We survey the prospects for an Information Dynamics which can serve as the basis for a fundamental theory of information, incorporating qualitative and structural as well as quantitative aspects. We motivate our discussion with some basic…
We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper…
Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…
How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? The n-queens problem in higher dimensions is a generalization of the well-known n-queens problem. We provide a comprehensive overview of…
This letter reports a novel application of game theory to quantum informational processes which can be used to optimally classify data generated by these processes. To this end, the notion of simultaneously distinguishing a pure quantum…
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption…
There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets…
Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a…
We show that a graph with $n$ vertices and vertex cover of size $k$ has at most $4^k + n$ potential maximal cliques. We also show that for each positive integer $k$, there exists a graph with vertex cover of size $k$, $O(k^2)$ vertices, and…
In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set $\Theta(2^{n})$ bits with respect to classical…