In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spac...

In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical syste...

A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that families of binary block codes with appropriately rescaled binomial multiplicity enumerators used on binary classical-quantum channels and decoded by the su...

In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and statitical independence of the constituent parts. An example of interacting Bernoulli units is used to illustrate the nature of these invariants. 1 Conditional exp...

We analyze the tubular phase of self-avoiding anisotropic crystalline membranes. A careful analysis using renormalization group arguments together with symmetry requirements motivates the simplest form of the large-distance free energy describing fluctuations of tubular configurations. The non-self-avoiding limit of the model is shown to be exactly solvable. For the full self-avoiding model we ...

The pinch-off of a two-dimensional region of inviscid fluid is investigated using numerical and analytical techniques. We find that pinch-off occurs when a sufficiently deformed 2D drop is released from rest. The asymptotic collapse of the pinching region is characterized by an anomalous, nonrational similarity exponent , indicating the existence of self-similarity of the second kind. Numerical...

Hans Peter Graf AT&T Bell Laboratories Holmdel, NJ 07733 The back propagation algorithm has been modified to work without any multiplications and to tolerate comput.ations with a low resolution, which makes it. more attractive for a hardware implementatioll. Numbers are represented in float.ing point format with 1 bit mantissa and 3 bits in the exponent for the states, and 1 bit mantissa and 5 ...

In this work, we introduce the notion of the error exponent region for a multi-user channel. This region specifies the set of error-exponent vectors that are simultaneously achievable by all users in the multi-user channel. This is done by associating different probabilities of error for different users, contrary to the traditional approach where a single probability of system error is consider...

We are interesting in the error exponent for source coding with fidelity criterion. For each fixed distortion level ∆, the maximum attainable error exponent at rate R, as a function of R, is called the reliability function. The minimum rate achieving the given error exponent is called the minimum achievable rate. For memoryless sources with finite alphabet, Marton (1974) gave an expression of t...