Related papers: A simpler derivation of the coding theorem
Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called…
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
In computer science, we can theoretically neatly separate transmission and processing of information, hardware and software, and programs and their inputs. This is much more intricate in biology, Nevertheless, I argue that Shannon's concept…
Substantial progress has recently been made in the understanding of the cutoff phenomenon for Markov processes, using an information-theoretic statistics known as varentropy [Sal23; Sal24; Sal25a; PS25]. In the present paper, we propose an…
We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
Despite its obvious relevance, meaning has been outside most theoretical approaches to information in biology. As a consequence, functional responses based on an appropriate interpretation of signals has been replaced by a probabilistic…
Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the…
We begin the study of how to extend few variable means to several variable ones and how to shrink means of several variables to less variables. With the help of one of the techniques we show that it is enough to check an inequality between…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
The present work continues investigation of the capacities of measurement (quantum-classical) channels in the most general setting, initiated in~\cite{HCT}. The proof of coding theorems is given for the classical capacity and…
In general, if there is one device A with the same performance as many devices B, it would be better to replace many devices with one device. In order to determine the number of devices that can be reduced, it is important to determine the…