The different methods of factor analysis first extract a set a factors from a data set. These factors are almost always orthogonal and are ordered according to the proportion of the variance of the original data that these factors explain. In general, only a (small) subset of factors is kept for further consideration and the remaining factors are considered as either irrelevant or nonexistent (...

We study the reachability problem for finite directed graphs whose independence number is bounded by some constant k. This problem is a generalisation of the reachability problem for tournaments. We show that the problem is first-order definable for all k. In contrast, the reachability problems for many other types of finite graphs, including dags and trees, are not first-order definable. Also ...

To date very few results are known on the critical sets for a set of Mutually Orthogonal Latin Squares(MOLS). In this paper, we consider Orthogonal Array OA(n, k + 2, n, 2) constructed from k mutually orthogonal cyclic latin squares of order n and obtain bounds on the possible sizes of the minimal critical sets. In particular, for n = 7 we exhibit a critical set, thereby improving the bound rep...

We consider three types of set-systems that have interesting applications in algebraic combinatorics and representation theory: maximal collections the so-called strongly, weakly, chord separated subsets a set $$[n]=\{1,2,\ldots ,n\}$$ . These are known to admit nice geometric interpretations; namely, they are, respectively, bijection with rhombus tilings on zonogon Z(n, 2), combined fine zonot...

Setting of this research is Bishop’s constructive mathematics, the mathematics developed on Intuitionistic logic. If (X, =, 6=, θ) is an anti-ordered set, for a coequality q on X we say that it is strongly regular if it is regular and θ ◦ q ⊆ q ◦ θ holds. In this case, θ ◦ q is a quasi-antiorder relation on X such that the relation Θ = π ◦ θ ◦ π−1 on X/q is the maximal anti-order on X/q.

In 1995, Brouwer proved that the toughness of a connected k-regular graph G is at least k/λ − 2, where λ is the maximum absolute value of the non-trivial eigenvalues of G. Brouwer conjectured that one can improve this lower bound to k/λ − 1 and that many graphs (especially graphs attaining equality in the Hoffman ratio bound for the independence number) have toughness equal to k/λ. In this pape...

Recently, stage and cf2 semantics for abstract argumentation attracted specific attention. By distancing from the notion of defense, they are capable to select arguments out of odd-length cycles. In case of cf2 semantics, the SCC-recursive schema guarantees that important evaluation criteria for argumentation semantics, like directionality, weakand CF -reinstatement, are fulfilled. Beside sever...

In this paper, we propose an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets. Instead of assuming the exact convex projection proposed in the literature, we allow each node to compute an approximate projection and communicate it to its neighbors. The communication graph is directed and time-varying. Nodes update their states by we...