Word Free Recall Search Scales Linearly With Number of Items Recalled

I find that the total search time in word free recall, averaged over item position, increases linearly with the number of items recalled. Thus the word free recall search algorithm scales the same as the low-error recognition of integers (Sternberg, 1966). The result suggests that both simple integer recognition and the more complex word free recall use the same search algorithm. The proportionality constant of 2-4 seconds per item (a hundred times larger than for integer recognition) is a power function of the proportion not remembered and seems to be the same function for word free recall in young and old subjects, high and low presentation rates and delayed and immediate free recall. The linear scaling of the search algorithm is different from what is commonly assumed to be the word free recall search algorithm, search by random sampling. The linearity of the word free recall extends down to 3 items which presents a challenge to the prevalent working memory theory in which 3-5 items are proposed to be stored in a separate high-availability store

An algorithm for the word entropy

For any infinite word $w$ on a finite alphabet $A$, the complexity function $p_w$ of $w$ is the sequence counting, for each non-negative $n$, the number $p_w(n)$ of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$ and the the entropy of $w$ is the quantity $E(w)=\lim\limits_{n\to\infty}\frac 1n\log p_w(n)$. For any given function $f$ with exponential growth, Mauduit and Moreira introduced in [MM17] the notion of word entropy $E_W(f) = \sup \{E(w), w \in A^{{\mathbb N}}, p_w \le f \}$ and showed its links with fractal dimensions of sets of infinite sequences with complexity function bounded by $f$. The goal of this work is to give an algorithm to estimate with arbitrary precision $E_W(f)$ from finitely many values of $f$

List-Decoding Gabidulin Codes via Interpolation and the Euclidean Algorithm

We show how Gabidulin codes can be list decoded by using a parametrization approach. For this we consider a certain module in the ring of linearized polynomials and find a minimal basis for this module using the Euclidean algorithm with respect to composition of polynomials. For a given received word, our decoding algorithm computes a list of all codewords that are closest to the received word with respect to the rank metric.Comment: Submitted to ISITA 2014, IEICE copyright upon acceptanc