Abstract- We show that a discrete infinite distribution with finite entropy cannot be estimated consistently in information divergence. As a corollary we get that there is no universal source code for an infinite source alphabet over the class of all discrete memoryless sources with finite entropy. Index Terms-Universal source coding, discrete infinite alphabet, distribution estimation, consistency in information divergence. I.

Abstract—We study the minimax redundancy of universal coding for large alphabets over memoryless sources and present two main results: We first complete studies initiated in Orlitsky and Santhanam [12] deriving precise asymptotics of the minimax redundancy for all ranges of the alphabet sizes. Second, we consider the minimax redundancy of a source model in which some symbol probabilities are fixed. The latter model leads to an interesting binomial sum asymptotics with superexponential growth functions. Our findings could be used to approximate numerically the minimax redundancy for various ranges of the sequence length and the alphabet size. These results are obtained by analytic techniques such as tree-like generating functions and the saddle point method. I.

We analyze smoothing algorithms from a universal-compression perspective. Instead of evaluating their performance on an empirical sample, we analyze their performance on the most inconvenient sample possible. Consequently the performance of the algorithm can be guaranteed even on unseen data. We show that universal compression bounds can explain the empirical performance of several smoothing methods. We also describe a new interpolated additive smoothing algorithm, and show that it has lower training complexity and better compression performance than existing smoothing techniques. Key words: Language modeling, universal compression, smoothing 1

Abstract- The quantum Turing machine (QTM) has been introduced by Deutsch as an abstract model of quantum computation. In this paper we try to introduction the new transition function of a QTM can be used for any node configuration in the network. In this paper we introduce the fundamentals of NetQTM like a well-observed lemma and a machine allowing classical and quantum computations is motivated by the emergence of models of quantum computation like the one-way model. Furthermore, this model allows a formal and rigorous treatment of problems requiring classical interactions, like the halting[8] of QTM. Finally, it opens new perspectives for the construction of a universal QTM.

Insurance transfers losses associated with risks to the insurer for a price, the premium. Considering a natural probabilistic framework for the insurance problem, we derive a necessary and sufficient condition on loss models such that the insurer remains solvent despite the losses taken on. In particular, there need not be any upper bound on the loss—rather it is the structure of the model space that decides insurability. Insurance is a way of managing losses associated with risks—for example, floods, network outages, and earthquakes— primarily by transfering risk to another entity—the insurer, for a price, the premium. The insurer attempts to break even by balancing the possible loss that may be suffered by a few (risk) with the guaranteed payments of many

Abstract not found

In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum algorithmic complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs. 1

1) For a real r> 0, let F(r) be the family of all stationary ergodic quantum sources with von Neumann entropy rate less than r. We prove that, for any r> 0, there exists a blind, source-independent block compression scheme which compresses every source from F(r) to rn qubits per input block of size n with arbitrary high fidelity for all large enough n. 2) We show that the stationarity and the ergodicity of a quantum source {ρm} ∞ m=1 are preserved by any trace-preserving completely positive linear map of the tensor product form E⊗m, where a copy of E acts locally on each spin lattice site. We also establish ergodicity criteria for so called classicallycorrelated quantum sources. I.

Abstract: In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs. 1.

For a real r> 0, let F(r) be the family of all stationary ergodic quantum sources with von Neumann entropy rate less than r. We prove that, for any r> 0, there exists a blind, source-independent block compression scheme which compresses every source from F(r) to rn qubits per input block length n with arbitrary high fidelity for all large enough n. As our second result, we show that the stationarity and the ergodicity of a quantum source {ρm} ∞ m=1 are preserved by any trace-preserving completely positive linear map of the tensor product form E⊗m, where a copy of E acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.