Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. We establish sufficient conditions to ensure...

A methodology for automatically identifying and clustering semantic features or topics in a heterogeneous text collection is presented. Textual data is encoded using a low rank nonnegative matrix factorization algorithm to retain natural data nonnegativity, thereby eliminating the need to use subtractive basis vector and encoding calculations present in other techniques such as principal compon...

Denote by H(t, q), t ≤ q, the incidence matrix (with respect to inclusion) of the t–sets versus the q–sets of the n–set {1, 2, . . . , n}. This matrix is considered as a linear map of Q–vector spaces Cq(n) −→ Ct(n), where Cs(n) is the Q–vector space having the s–sets as a basis (s ≤ n). As a basic tool, we introduce a connection of the vector spaces to a graded Q–algebra (which is at the same t...

The q-numerical range (0 ≤ q ≤ 1) of an n × n matrix polynomial P (λ) = Amλ m + · · ·+ A1λ + A0 is defined by Wq(P ) = {λ ∈ C : y∗P (λ)x = 0, x, y ∈ C, x∗x = y∗y = 1, y∗x = q}. In this paper, we investigate the boundary and the shape of Wq(P ), using the notion of local dimension. We also obtain that the q-numerical range of first order matrix polynomials is always simply connected. Moreover, t...

In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental matrix solution Φ(t) is a canonical decomposition of the form Φ(t) = Q(t)e, where Q(t) is a real periodic matrix and R is a constant matrix. To compute rigorously the Fl...

Generalized Hadamard matrices of order qn−1 (q a prime power, n ≥ 2) over GF (q) are related to symmetric nets in affine 2-(qn, qn−1, (qn−1 − 1)/(q − 1)) designs invariant under an elementary abelian group of order q acting semi-regularly on points and blocks. The rank of any such matrix over GF (q) is greater than or equal to n− 1. It is proved that a matrix of minimum q-rank is unique up to a...

Given any natural number q > 3 we show there exists an integer t ≤ [2 log2 (q – 3)] such that an Hadamard matrix exists for every order 2q where s > t. The Hadamard conjecture is that s = 2. This means that for each q there is a finite number of orders 2q for which an Hadamard matrix is not known. This is the first time such a statement could be made for arbitrary q. In particular it is already...

Let 4n2 be the order of a Bush-type Hadamard matrix with q = (2n − 1)2 a prime power. It is shown that there is a weighing matrix W (4(q + qm−1 + · · ·+ q + 1)n, 4qn) which includes two symmetric designs with the Ionin–type parameters ν = 4(q + qm−1 + · · ·+ q + 1)n, κ = q(2n − n), λ = q(n − n) for every positive integer m. Noting that Bush–type Hadamard matrices of order 16n2 exist for all n f...