Matroids were introduced in the early 20th century as a way of uniting disparate notions of “independence” from across mathematics. Among these notions were linear independence of vectors and graphic independence – defined by acyclicity on the subgraph corresponding to a set of edges. Algebraic independence over a field k, defined by the non-existence of polynomial relations with coefficients i...

OBJECTIVE To investigate the socioeconomic and clinical factors that contribute to the functional independence of the oldest old of a community. METHOD Cross-sectional quantitative study whose sample consisted of 214 elderly people registered in Basic Health Units. Data were collected through structured interviews and application of the Functional Independence Measure. We used descriptive sta...

L2 learners’ individual differences are crucial factors that deserve attention in L2 education. Focusing on 2 main areas of individual differences (i.e., field (in)dependence and multiple intelligences), this study explored their relationships with L2 reading performance. Participants were 64 TEFL undergraduates and postgraduates. To assess the participats’ degree of field (in)dependence and mu...

We investigate efficient algorithms for learning the structure of a Markov network from data using the independence-based approach. Such algorithms conduct a series of conditional independence tests on data, successively restricting the set of possible structures until there is only a single structure consistent with the outcomes of the conditional independence tests executed (if possible). As ...

Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same principle of independence maximization...

Field independence refers to the ability to perceive details from the surrounding context as a whole and to represent the environment by relying on an internal reference frame. Conversely, field dependence individuals tend to focus their attention on single environmental features analysing them individually. This cognitive style affects several visuo-spatial abilities including spatial memory. ...

The minimum rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose (i, j)th entry (for i = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A universally optimal matrix is defined to be an integer matrix A such that every off-diagonal entry of A is 0, 1, or −1, and for all fields F , the rank of A is the minimum rank o...