Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them focuses on one feature of randomness, leading authors to have to use multiple measures. Here we describe and advocate for the use of the accepted universal measure for randomness based on algorithmic complexity, by means of a novel previously presented technique using the the definition of algorithmic probability. A re-analysis of the classical Radio Zenith data in the light of the proposed measure and methodology is provided as a study case of an application.Comment: To appear in Behavior Research Method

Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions

The authors prove existence theorems for the minimum of multiple integrals of the calculus of variations with constraints on the derivatives in classes of BV possibly discontinuous solutions. To this effect the integrals are written in the form proposed by Serrin. Usual convexity conditions are requested, but no growth condition. Preliminary closure and semicontinuity theorems are proved which are analogous to those previously proved by Cesari in Sobolev classes. Compactness in L 1 of classes of BV functions with equibounded total variations is derived from Cafiero-Fleming theorems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47939/1/10231_2005_Article_BF01766143.pd