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We give a pseudorandom generator that fools m -facet polytopes over {0, 1} n with seed length polylog( m ) · log n . The previous best seed length had superlinear dependence on m . 

There have been conflicting findings on the degree to which rapidly deployed visual attention is selective for depth, and this issue has important implications for attention models. Previous findings have attempted to find depth-based cueing effects on such attention using reaction time (RT) measures for stimuli presented in stereo goggles with a display screen. Results stemming from such approaches have been mixed, depending on whether target/distractor discrimination was required. To help clarify the existence of such depth effects, we have developed a paradigm that measures accuracy rather than RT in an immersive virtual-reality environment, providing a more appropriate context of depth. Three modified Posner Cueing paradigms were run to test for depth-specific rapid attentional selectivity. Participants fixated a cross while attempting to identify a rapidly masked black letter preceded by a red cue that could be valid in depth, side, or both. In Experiment 1a, a potent cueing effect was found for lateral cueing validity, but a weak effect was found for depth despite an extreme difference in virtual depth (1 vs. 300 m). In Experiment 1b, a near-replication of 1a, the lateral effect replicated while the depth effect did not. Finally, in Experiment 2, to increase the depth cue’s effectiveness, the letter matched the cue’s color, and the presentation duration was increased; however, again only a minimal depth-based cueing effect – no greater than that of Experiment 1a – was observed. Thus, we conclude that rapidly deployed attention is driven largely by spatiotopic rather than depth-based information. 

Previous evidence demonstrated that individuals can recall a target’s location in a search display even if location information is completely task-irrelevant. This finding raises the question: does this ability to automatically encode a single item’s location into a reportable memory trace extend to other aspects of spatial information as well? We tested this question using a paradigm designed to elicit attribute amnesia (Chen & Wyble, 2015a). Participants were initially asked to report the location of a target letter among digits with stimuli arranged to form one of two or four spatial configurations varying randomly across trials. After completing numerous trials that matched their expectations, participants were surprised with a series of unexpected questions probing their memory for various aspects of the display they had just viewed. Participants had a profound inability to report which spatial configuration they had just perceived when the target’s location was not unique to a specific configuration (i.e., orthogonal). Despite being unable to report the most recent configuration, answer choices on the surprise trial were focused around previously seen configurations, rather than novel configurations. Thus, there were clear memories of the set of configurations that had been viewed during the experiment but not of the specific configuration from the most recent trial. This finding helps to set boundary conditions on previous findings regarding the automatic encoding of location information into memory.