Two Triads of Squares

Sums of Two Squares

n = 1: 1 = 0 + 1; n = 2 (prime): 2 = 1 + 1; n = 3 (prime) is not a sum of two squares. n = 4: 4 = 2 + 0. n = 5 (prime): 5 = 2 + 1. n = 6 is not a sum of two squares. n = 7 (prime) is not a sum of two squares. n = 8: 8 = 2 + 2. n = 9: 9 = 3 + 0. n = 10: 10 = 3 + 1. n = 11 (prime) is not a sum of two squares. n = 12 is not a sum of two squares. n = 13 (prime): 13 = 3 + 2. n = 14 is not a sum of t...

Morphology of isolated triads

The triad is the junctional association of transverse tubule with sarcoplasmic reticulum terminal cisternae. A procedure for the isolation of highly enriched triads from skeletal muscle has been described in the previous paper. In the present study, the structural features of isolated triads have been examined by thin-section, negative-staining, and freeze-fracture electron microscopy. In isola...

Two Squares Canonical Factorization

We present a new combinatorial structure in a string: a canonical factorization for any two squares that occur at the same position and satisfy some size restrictions. We believe that this canonical factorization will have application to related problems such as the New Periodicity Lemma, Crochemore-Rytter Three Squares Lemma, and ultimately the maximum-number-of-runs conjecture.

The Sum of Two Squares

Least-squares two-sample test

The goal of the two-sample test (a.k.a. the homogeneity test) is, given two sets of samples, to judge whether the probability distributions behind the samples are the same or not. In this paper, we propose a novel non-parametric method of two-sample test based on a least-squares density ratio estimator. Through various experiments, we show that the proposed method overall produces smaller type-...