Related papers: Information Complexity and the Quest for Interacti…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to…
In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by…
The log-rank conjecture is one of the fundamental open problems in communication complexity. It speculates that the deterministic communication complexity of any two-party function is equal to the log of the rank of its associated matrix,…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion.…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
There has been increasing interest in the integrated information theory (IIT) ofconsciousness, which hypothesizes that consciousness is integrated information withinneuronal dynamics. However, the current formulation of IIT poses both…
Entropy or information is a fundamental quantity contained in a system in statistical mechanics and information theory. In this paper, a definition of classical information entropy of parton distribution functions is suggested. The…
Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
Economic complexity reflects the amount of knowledge that is embedded in the productive structure of an economy. It resides on the premise of hidden capabilities - fundamental endowments underlying the productive structure. In general,…
Semantic communication has attracted significant interest recently due to its capability to meet the fast growing demand on user-defined and human-oriented communication services such as holographic communications, eXtended reality (XR),…
The electrical activity of external anal sphincter can be registered with surface electromyography. This signals are known to be highly complex and nonlinear. This work aims in characterisation of the information carried in the signals by…
Shannon mutual information provides a measure of how much information is, on average, contained in a set of neural activities about a set of stimuli. It has been extensively used to study neural coding in different brain areas. To apply a…