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Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
Given an event log as a collection of recorded real-world process traces, process mining aims to automatically construct a process model that is both simple and provides a useful explanation of the traces. Conformance checking techniques…
The presented article attempts to characterize the encryption dynamics of delayed dynamics based block ciphers, designed for the encryption of binary data. For such encryption algorithms, the encryption process relies on a coupling dynamics…
In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…
Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these…
The relationship between entropy and information is reviewed, taking into account that information is stored in macroscopic degrees of freedom, such as the order parameter in a system exhibiting spontaneous symmetry breaking. It is shown…
It was recently pointed out that identifiability of quantum random walks and hidden Markov processes underlie the same principles. This analogy immediately raises questions on the existence of hidden states also in quantum random walks and…
We initiate a rigorous study of computational entanglement theory, inspired by the emerging usefulness of ideas from quantum information theory in computational complexity. We define new operational computational measures of entanglement --…
Street networks may be planned according to clear organizing principles or they may evolve organically through accretion, but their configurations and orientations help define a city's spatial logic and order. Measures of entropy reveal a…
Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and thermodynamic properties. Such stealthy and…
Behavior of hysteretic trajectories for cyclical input is investigated as a function of the internal structure of a system modeled by the classical random network of binary spins. Different regimes of hysteretic behavior are discovered for…
We consider a unified framework of sequential change-point detection and hypothesis testing modeled by means of hidden Markov chains. One observes a sequence of random variables whose distributions are functionals of a hidden Markov chain.…
Living entities in a group communicate and transfer information to one another for a variety of reasons. It might be for foraging food, migration, or escaping threats and obstacles, etc. They do so by interacting with each other and also…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…
To understand and explain process behaviour we need to be able to see it, and decide its significance, i.e. be able to tell a story about its behaviours. This paper describes a few of the modelling challenges that underlie monitoring and…
A broad class of blocked or jammed configurations of particles on the one-dimensional lattice can be characterized in terms of local rules involving only the lengths of clusters of particles (occupied sites) and of holes (empty sites).…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…
In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography.…