One way to define the “randomness” of a fixed individual sequence is to ask how hard it is to predict. When prediction error is measured via squared loss, it has been established that memoryless sequences (which are, in a precise sense, hard to predict) have some of the stochastic attributes of truly random sequences. In this paper, we ask how changing the loss function used changes the set of ...

Von Neumann entropy rate for open quantum systems is, in general, written terms of production and flow rates, encompassing the second law thermodynamics. When open-quantum-system evolution corresponds to a dynamical semigroup, we find decomposition infinitesimal generator dynamics, that allows relate von with divergence-based Fisher information, at any time. Applied Gaussian channels are semigr...

This paper considers the covert identification problem in which a sender aims to reliably convey an (ID) message set of receivers via binary-input discrete memoryless channel (BDMC), and simultaneously guarantee that communication is with respect warden who monitors another independent BDMC. We prove square-root law for problem. states ID size exp(exp(Θ(√{ n})) can be transmitted over n uses. t...

We formulate and study a fundamental search and detection problem, Schedule Optimization, motivated by a variety of real-world applications, ranging from monitoring content changes on the web, social networks, and user activities to detecting failure on large systems with many individual machines. We consider a large system consists of many nodes, where each node has its own rate of generating ...