A controversial area in covariance structure models is the assessment of overall model fit. Researchers have expressed concern over the influence of sample size on measures of fit. Many contradictory claims have been made regarding which fit statistics are affected by N. Part of the confusion is due to there being two types of sample size effects that are confounded. The first is whether N dire...

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve cluster quality and promote interpretability process has become a hot research topic at intersection mathematical optimization machine research. problem taking advantage information in data called semi-su...

The minimum sum-of-squares clustering problem (MSSC) consists of partitioning $n$ observations into $k$ clusters in order to minimize the sum squared distances from points centroid their cluster. In this paper, we propose an exact algorithm for MSSC based on branch-and-bound technique. lower bound is computed by using a cutting-plane procedure where valid inequalities are iteratively added Peng...

Motivated by a question of Defant and Propp (Electron J Combin 27:Article P3.51, 2020) regarding the connection between degrees noninvertibility functions those their iterates, we address combinatorial optimization problem minimizing sum squares over partitions n with nonnegative rank. Denoting sequence minima $$(m_n)_{n\in {\mathbb {N}}}$$ , prove that $$m_n=\Theta \left( n^{4/3}\right) $$ . C...

A magic square of order n consists of the numbers 1 to n placed such that the sum of each row, column and principal diagonal equals the magic sum n(n +1)/2. In addition, an odd ordered magic square is associative or self-complementary if diagonally opposite elements have the same sum (n +1)/2. The magic square is said to be regular Greco-Latin if it can be decomposed as a sum of a pair of Latin...