Related papers: Numerical Estimation of Invariance Entropy for Non…

We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…

In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…

The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

The ability to quantify the directional flow of information is vital to understanding natural systems and designing engineered information-processing systems. A widely used measure to quantify this information flow is the transfer entropy.…

Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…

We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…

In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this…

Safety-critical autonomous systems must satisfy hard state constraints under tight computational and sensing budgets, yet learning-based controllers are often far more complex than safe operation requires. To formalize this gap, we study…

Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In…

The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…

This paper considers a disturbance attenuation problem for a linear discrete time invariant system under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in terms of relative…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

This paper considers the problem of stabilizing a discrete-time non-linear stochastic system over a finite capacity noiseless channel. Our focus is on systems which decompose into a stable and unstable component, and the stability notion…

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…

Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…