4 citations · 5 across the 10 of their papers we have counts for
10 papers
Block-hierarchical covariance decompositions for finite-block additive functionals
Abbas Alhakim
We study additive functionals of stationary Markov chains whose observables depend on a fixed finite block of consecutive states. Such block observables arise naturally in sliding-…
Overlapping window tests for correlation and trend
Abbas Alhakim
We develop a general framework for constructing and analyzing overlapping sliding-window statistics for dependence and trend detection. For a fixed window size, the overlapping blo…
Subdivisions of Oriented Cycles in Digraphs with Hamiltonian directed path
Abbas Alhakim, Mouhamad El Joubbeh
Cohen et al. conjectured that for every oriented cycle there exist an integer such that every strong -chromatic digraph contains a subdivision of . El Joubbeh c…
Orientable sequences over non-binary alphabets
Abbas Alhakim, Chris J. Mitchell, Janusz Szmidt +1
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consec…
Nonbinary Counterparts of the Prefer-Same and Prefer-Opposite de Bruijn Sequences
Abbas Alhakim
The well known prefer-one, prefer-opposite, and prefer-same binary de Bruijn sequences are all constructed using simple preference rules. We apply the technique of preference funct…
Efficient constructions of the Prefer-same and Prefer-opposite de Bruijn sequences
Evan Sala, Joe Sawada, Abbas Alhakim
The greedy Prefer-same de Bruijn sequence construction was first presented by Eldert et al.[AIEE Transactions 77 (1958)]. As a greedy algorithm, it has one major downside: it requi…
Hadamard Matrices, Quaternions, and the Pearson Chi-square Statistic
Abbas Alhakim
We present a symbolic decomposition of the Pearson chi-square statistic with unequal cell probabilities, by presenting Hadamard-type matrices whose columns are eigenvectors of the…
Hamiltonicity of the Cross-Join Graph of de Bruijn Sequences
Abbas Alhakim
A generalized de Bruijn digraph generalizes a de Bruijn digraph to the case where the number of vertices need not be a pure power of an integer. Hamiltonian cycles in these digraph…
Spans of Preference Functions for De Bruijn Sequences
Abbas Alhakim
A nonbinary Ford sequence is a de Bruijn sequence generated by simple rules that determine the priorities of what symbols are to be tried first, given an initial word of size w…
De Bruijn Graph Homomorphisms and Recursive De Bruijn Sequences
Abbas Alhakim, Mufutau Akinwande
This paper presents a method to find new De Bruijn cycles based on ones of lesser order. This is done by mapping a De Bruijn cycle to several vertex disjoint cycles in a De Bruijn…