相关论文: An information theoretic necessary condition for p…

We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…

The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…

A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely…

We consider the problem of developing a method to reconstruct a potential $q$ from the partial data Dirichlet-to-Neumann map for the Schr\"odinger equation $(-\Delta_g+q)u=0$ on a fixed admissible manifold $(M,g)$. If the part of the…

We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and…

While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to asses the amount and quality of information inside a noisy optical channel. A number of theoretical…

We study sparse recovery when observations come from mixed-quality sources: a small collection of high-quality measurements with small noise variance and a larger collection of lower-quality measurements with higher variance. For this…

Information theory has provided foundations for the theories of several application areas critical for modern society, including communications, computer storage, and AI. A key aspect of Shannon's 1948 theory is a sharp lower bound on the…

The information entropy budget and the rate of information transfer between variables is studied in the context of a nonlinear reduced-order atmospheric model. The key ingredients of the dynamics are present in this model, namely the…

We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined…

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive…

We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however…

We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…

Two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel, in which a stochastic channel output is generated based on a compressed description of the…

Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…

We investigate the amount of primordial information that can be reconstructed from spectroscopic galaxy surveys, as well as what sets the noise in reconstruction at low wavenumbers, by studying a simplified universe in which galaxies are…

In communications, unknown variables are usually modelled as random variables, and concepts such as independence, entropy and information are defined in terms of the underlying probability distributions. In contrast, control theory often…

In the beautifully simple-to-state problem of trace reconstruction, the goal is to reconstruct an unknown binary string $x$ given random "traces" of $x$ where each trace is generated by deleting each coordinate of $x$ independently with…

The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error…