In this paper new and existing approaches are developed to compute the bit error rate for chaos-based communication systems. The multi-user coherent antipodal chaos shift keying system is studied and evaluated in its coherent form, in the sense of perfect synchronization between transmitted and received chaotic sequences. Transmission is through an additive white Gaussian noise channel. Four me...

We study methods to obtain bounds or approximations to u f(A)v where A is a symmetric, positive definite matrix and f is a smooth function. These methods are based on the use of quadrature rules and the Lanczos algorithm. We give some theoretical results on the behavior of these methods based on results for orthogonal polynomials as well as analytical bounds and numerical experiments on a set o...

In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a ...

We provide an introduction to Fredholm theory and discuss using the Fredholm determinant to compute pure-point spectra.

This paper fills a gap in our understanding of the interaction between information and computation. It unifies other approaches to measuring information like Kolmogorov complexity and Shannon information. We define a theory about information flow in deterministic computing based on three fundamental observations: 1) ∀(n ∈ N)I(n) = logn (information is measured in logarithms), 2) all countable s...

We propose an asynchronous protocol for general multiparty computation with perfect security and communication complexity O(n|C|k) where n is the number of parties, |C| is the size of the arithmetic circuit being computed, and k is the size of elements in the underlying field. The protocol guarantees termination if the adversary allows a preprocessing phase to terminate, in which no information...

The utility function u is then extended to a utility function G(u) on G(A)×Θ by assigning each pair (λ, θ) the expectation of the random variable uθ under the measure λ, i.e. Eλ [ uθ ] . Every pure action a ∈ A then can uniquely be identified with the Dirac-measure δa ∈ G(A) and we have u(a, θ) = G(u)(δa, θ) for all (a, θ) ∈ A × Θ. Further, also (1) can easily be extended to randomized actions ...

Frank Gaitan1,2,3 and Franco Nori1,3,4 1Advanced Science Institute, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan 2Department of Physics, Southern Illinois University, Carbondale, Illinois 62901-4401, USA 3CREST, Japan Science and Technology Agency (JST), Kawaguchi, Saitama 332-0012, Japan 4Department of Physics, Center for Theoretical Physics, Unive...