Solving the word problem in real time

The paper is devoted to the study of groups whose word problem can be solved by a Turing machine which operates in real time. A recent result of the first author for word hyperbolic groups is extended to prove that under certain conditions the generalised Dehn algorithms of Cannon, Goodman and Shapiro, which clearly run in linear time, can be programmed on real-time Turing machines. It follows that word-hyperbolic groups, finitely generated nilpotent groups and geometrically finite hyperbolic groups all have real-time word problems

Effect of playing computer games on decision making in people with intellectual disabilities

People with intellectual disabilities have difficulty making decisions and this may hinder their independence and inclusion in society. Interactive computer software may give them the opportunity to practice the underlying components of this skill. This study aimed to discover if repeated sessions playing a computer game involving aspects of decision making, such as collecting relevant information and controlling impulsivity, would improve performance in two non-computer based tests of decision making. 12 adults with intellectual disabilities were randomly assigned to either an intervention group or control group. They were all exposed to 10 twice weekly sessions, playing either the intervention game or the control game, which involved simple reaction time only. After repeated sessions, the intervention group showed a significant improvement in game score, with researcher assistance significantly decreasing. At follow up, the intervention group showed a significant decrease from baseline in the number of guesses made before guessing correctly on both of the decision making tests. The decrease observed in the control group failed to reach significance

Sofic groups: graph products and graphs of groups

We prove that graph products of sofic groups are sofic, as are graphs of groups for which vertex groups are sofic and edge groups are amenable

Minimum fuel control of a pitch motion of a satellite in circular orbit

Time function analysis for optimal control of satellite attitude and control jet fuel consumption in circular orbit

The cutaneous 'rabbit' illusion affects human primary sensory cortex somatopically

We used functional magnetic resonance imaging (fMRI) to study neural correlates of a robust somatosensory illusion that can dissociate tactile perception from physical stimulation. Repeated rapid stimulation at the wrist, then near the elbow, can create the illusion of touches at intervening locations along the arm, as if a rabbit hopped along it. We examined brain activity in humans using fMRI, with improved spatial resolution, during this version of the classic cutaneous rabbit illusion. As compared with control stimulation at the same skin sites (but in a different order that did not induce the illusion), illusory sequences activated contralateral primary somatosensory cortex, at a somatotopic location corresponding to the filled-in illusory perception on the forearm. Moreover, the amplitude of this somatosensory activation was comparable to that for veridical stimulation including the intervening position on the arm. The illusion additionally activated areas of premotor and prefrontal cortex. These results provide direct evidence that illusory somatosensory percepts can affect primary somatosensory cortex in a manner that corresponds somatotopically to the illusory percept