Related papers: Monotone measures of statistical complexity
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
In this paper, we consider the fundamental problem of testing for monotone trend in a time series. While the term "trend" is commonly used and has an intuitive meaning, it is first crucial to specify its exact meaning in a hypothesis…
We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
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…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
This study is focused on the qualitative and quantitative characterization of chaotic systems with the use of symbolic description. We consider two famous systems: Lorenz and R\"ossler models with their iconic attractors, and demonstrate…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
Quantifying coherence is a key task in both quantum mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a…
We study the statistical monotonicity of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data we are led to some conjectures about quantum alpha-geometries…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
In a recent result, Knop, Lovett, McGuire and Yuan (STOC 2021) proved the log-rank conjecture for communication complexity, up to log n factor, for any Boolean function composed with AND function as the inner gadget. One of the main tools…
How much information a fermionic state contains? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock…
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…
We discuss why regular observables can not be proper entanglement measures, and how observables in a generalized setting can be used to make an entanglement monotone a directly observable quantity for the case of pure states. For the case…