Related papers: Entropy Encoding, Hilbert Space and Karhunen-Loeve…
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed meta-converse\, -- \,are equivalent in terms of success…
Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific,…
Many common types of data can be represented as functions that map coordinates to signal values, such as pixel locations to RGB values in the case of an image. Based on this view, data can be compressed by overfitting a compact neural…
In this article we consider means of positive bounded linear operators on a Hilbert space. We present a complete theory that provides a framework which extends the theory of the Karcher mean, its approximating matrix power means, and a…
A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space $(X,\mu)$. These have…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…
Real world scenarios can be captured with lifted probability distributions. However, distributions are usually encoded in a table or list, requiring an exponential number of values. Hence, we propose a method for extracting first-order…
We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…
This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the…
We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example, where a complete proof is still awaited, but where…
A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
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…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…