In Distributed Storage Systems (DSSs), usually, data is stored using replicated packets on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes have been introduced, in which, data is replicated in a smart way on distributed servers using a Maximum Distance Separable (MDS) code. In this work, for a non-uniform FR code, bounds on the FR code rate and DSS code rate...

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon’s smoothing prob...

Fractional supersymmetric quantum mechanics of order λ is realized in terms of the generators of a generalized deformed oscillator algebra and a Zλgrading structure is imposed on the Fock space of the latter. This realization is shown to be fully reducible with the irreducible components providing λ sets of minimally bosonized operators corresponding to both unbroken and broken cases. It also f...

In this paper, the problems of the existence and uniqueness of solutions and stability for a class of fractional-order neural networks are studied by using Banach fixed point principle and analysis technique, respectively. A sufficient condition is given to ensure the existence and uniqueness of solutions and uniform stability of solutions for fractional-order neural networks with variable coef...

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon’s smoothing prob...

We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and considering expectation under appropriate distribution functions for unknown contamination of the interaction effects. By considering uniform distributions on symm...

We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed. Introduction The Black-Scholes-Merton model for option prices is an ...

Let B={Bt:t?0} be a real-valued fractional Brownian motion of index H?(0,1). We prove that the macroscopic Hausdorff dimension level sets Lx=t?R+:Bt=x is, with probability one, equal to 1?H for all x?R.