The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to ...

In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related to the solution of linear three–term recurrences. We show through some simple examples how these triangular arrays appe...

A method of constructzon is presented for rectangular quaszorthogonal code arrays over the ring Z+ The proposed arrays are easy to generate: The four-phase lznear recurrzng sequences constructed by Bozta8 et. al. are utilized to generate the arrays by modulo 4 subtractcon. The perzodzc autoand cross-correlataon propertaes of these arrays are then dersved in a strasghtforward manner. The maximum...

To overcome the drawbacks of premature and poor convergence of classical PSO, a new particle swarm optimization is proposed by combining extrapolation technique and orthogonal design. Orthogonal design is introduced to design self-adaptive orthogonal crossover operator (SOC) which self-adaptively adjusts the number of orthogonal array’s factors and the location for dividing the parent particles...

We study a class of interacting particle systems with asymmetric interaction showing self-duality property. The includes the ASEP(q,θ), exclusion process, repulsive interaction, allowing up to θ∈N particles in each site, and ASIP(q,θ), θ∈R+, inclusion that is its attractive counterpart. extend setting investigation orthogonal duality properties done [8] for symmetric processes. analysis leads m...

We explore the orthogonal decomposition of tensors (also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebr...

Stacked chloroplast membranes isolated from Chlamydomonas reinhardtii have differentiated particle arrays when examined by freeze-fracture electron microscopy. When the membranes are isolated unstacked, these particle arrays are lost and the fracture faces have a homogeneous appearance. The changes in appearance are due to rearrangement of existing membrane components by lateral particle moveme...

The effectiveness of Quasi-Monte Carlo methods for numerical integration has led to the study of (T,M, S)-nets, which are uniformly distributed point sets in the Euclidean unit cube. A recent result, proved independently by Schmid/Mullen and Lawrence, establishes an equivalence between (T,M, S)-nets and ordered orthogonal arrays. In a paper of Martin and Stinson, a linear programming technique ...

Differential microphone arrays have the potential to be widely deployed in hands-free communication systems thanks to their frequency-invariant beampatterns, high directivity factors, and small apertures. Traditionally, they are designed and implemented in a multistage way with uniform linear geometries. This paper presents an approach to the design of differential microphone arrays with orthog...

In this paper we develop a class of two-level designs that allow orthogonal estimation of certain main e ects and two-factor interactions when other main e ects and two-factor interactions are present but not of interest. The designs can be easily generated using block-crossed arrays. The application is clearly to settings in which one might apply either Taguchi’s crossed arrays or single-array...