Related papers: Perspectives on information-based complexity
"Information Processing" is a recently launched buzzword whose meaning is vague and obscure even for the majority of its users. The reason for this is the lack of a suitable definition for the term "information". In my attempt to amend this…
In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
This work builds on a rich discourse surrounding the social brain hypothesis as well as the definition and quantification of social complexity. We believe this manuscript provides a new perspective on the topic by pairing a conceptual…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
The possibility to describe the laws of the Universe in a computational way seems to be correlated to a principle that the density of information is bounded. This principle, that is dual to that of a finite velocity of information, has…
The article considers the quantitative assessment approach to the innovativeness of different objects. The proposed assessment model is based on the object data retrieval from various databases including the Internet. We present an object…
This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…
Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Concept-based explainability methods provide insight into deep learning systems by constructing explanations using human-understandable concepts. While the literature on human reasoning demonstrates that we exploit relationships between…
Complex network theory is being widely used to study many real-life systems. One of the fields that can benefit from complex network theory approach is transportation network. In this paper, we briefly review the complex network theory…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…