Related papers: Bounds from a Card Trick
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…
We introduce the swap-or-not shuffle and show that the technique gives rise to a new method to convert a pseudorandom function (PRF) into a pseudorandom permutation (PRP) (or, alternatively, to directly build a confusion/diffusion…
We consider overdamped physical systems evolving under a feedback-controlled fluctuating potential and in contact with a thermal bath at temperature $T$. A Markovian description of the dynamics, which keeps only the last value of the…
Grammar compression represents a string as a context free grammar. Achieving compression requires encoding such grammar as a binary string; there are a few commonly used encodings. We bound the size of practically used encodings for several…
Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
We propose a model of card shuffling where a pack of cards, spread as points on a square table, are repeatedly gathered locally at random spots and then spread towards a random direction. A shuffling of the cards is then obtained by…
The definition of $k^{th}$-order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
A short note to propose a procedure to construct excess maps, probability maps and to calculate point source flux upper limits.
The pit recording of file, the coefficient of compression are introduced. The theoretical limit of the information compression as minimal coefficient of compression for the given length of alphabet are found.
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
We present a new data structure called the \emph{Compressed Random Access Memory} (CRAM) that can store a dynamic string $T$ of characters, e.g., representing the memory of a computer, in compressed form while achieving asymptotically…
We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging…
We study Markov tree-shifts given by $k$ transition matrices, one for each of its $k$ directions. We provide a method to characterize the complexity function for these tree-shifts, used to calculate the tree entropies defined by Ban and…
The entropy of a graph was first introduced by Rashevsky \cite{Rashevsky} and Trucco \cite{Trucco} to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of…
In this article, we introduce the Sharma-Mittal entropy of a graph, which is a generalization of the existing idea of the von-Neumann entropy. The well-known R{\'e}nyi, Thallis, and von-Neumann entropies can be expressed as limiting cases…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to…