Health care quality improvement interventions are often evaluated in randomized trials in which individual physicians serve as the unit of randomization. These cluster randomized trials present a unique data structure that consists of many clusters of highly variable size. The appropriate method of analysis for these trials is unknown. We conducted a simulation study to compare several methods ...

Magnetic flux ropes immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Each collision results in magnetic field line reconnection and the generation of a quasi-separatrix layer. Three-dimensional magnetic field lines are computed by conditionally aver...

We consider rational functions of the form V(x)/U(x), where both V(x) and U(x) are relatively prime polynomials over finite field \(\mathbb {F}_q\). Polynomials that permute elements a field, called permutation (PPs), have been subject research for decades. Let \({\mathcal {P}}^1(\mathbb {F}_q)\) denote {F}_q\cup \{\infty \}\). If function, permutes {F}_q)\), it is function (PRF). \(N_d(q)\) nu...

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinational design, communication theory and so on. Permutation binomials and trinomials attract people’s interest due to their simple algebraic form and additional extraordinary properties. In t...

The Discrete Memory Machine (DMM) is a theoretical parallel computing model that captures the essence of the shared memory access of GPUs. The bank conflicts should be avoided for maximizing the bandwidth of the shared memory access. Offline permutation of an array is a task to copy all elements in array a into array b along a permutation given in advance. The main contribution of this paper is...