相关论文: On a conditional inequality in Kolmogorov complexi…

We present an information-theoretic approach to lower bound the oracle complexity of nonsmooth black box convex optimization, unifying previous lower bounding techniques by identifying a combinatorial problem, namely string guessing, as a…

One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…

Given $n>0$, let $S\subset [0,1]^2$ be a set of $n$ points, chosen uniformly at random. Let $R\cup B$ be a random partition, or coloring, of $S$ in which each point of $S$ is included in $R$ uniformly at random with probability $1/2$.…

Entanglement is one of important resources for quantum communication tasks. Most of results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We firstly derive an…

We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction…

We study two dual settings of information processing. Let $ \mathsf{Y} \rightarrow \mathsf{X} \rightarrow \mathsf{W} $ be a Markov chain with fixed joint probability mass function $ \mathsf{P}_{\mathsf{X}\mathsf{Y}} $ and a mutual…

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…

Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open…

We survey the diverse approaches to the notion of information content: from Shannon entropy to Kolmogorov complexity. The main applications of Kolmogorov complexity are presented namely, the mathematical notion of randomness (which goes…

The standard population protocol model assumes that when two agents interact, each observes the entire state of the other agent. We initiate the study of $\textit{message complexity}$ for population protocols, where the state of an agent is…

We consider the network consisting of three nodes $1, 2, 3$ connected by two open channels $1\rightarrow 2$ and $1\rightarrow 3$. The information present in the node 1 consists of four strings $x,y,z,w$. The nodes $2, 3$ know $x,w$ and need…

We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be…

Multimodal learning seeks to integrate information from heterogeneous sources, where signals may be shared across modalities, specific to individual modalities, or emerge only through their interaction. While self-supervised multimodal…

The decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), asks to list all fragments of $T$ that are at edit distance at…

Let $K\ < x_i\ >$ be the free associative algebra generated by a finite or countable number of variables $x_i$. The notion of "letterplace correspondence" introduced in [1,2] for the graded (two-sided) ideals of $K\ < x_i\ >$ is extended in…

When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behaviour of the modified orthogonal polynomials is expected to have different properties…

Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content…

Information Causality is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of…

We consider online packing problems where we get a stream of axis-parallel rectangles. The rectangles have to be placed in the plane without overlapping, and each rectangle must be placed without knowing the subsequent rectangles. The goal…

This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement…