Irrelevant Singletons in Visual Search Do Not Capture Attention but Can Produce Nonspatial Filtering Costs

It is not clear how salient distractors affect visual processing. The debate concerning the issue of whether irrelevant salient items capture spatial attention [e.g., Theeuwes, J., Atchley, P., & Kramer, A. F. On the time course of top–down and bottom–up control of visual attention. In S. Monsell & J. Driver (Eds.), Attention and performance XVIII: Control of cognitive performance (pp. 105–124). Cambridge, MA: MIT Press, 2000] or produce only nonspatial interference in the form of, for example, filtering costs [Folk, Ch. L., & Remington, R. Top–down modulation of preattentive processing: Testing the recovery account of contingent capture. Visual Cognition, 14, 445–465, 2006] has not yet been settled. The present ERP study examined deployment of attention in visual search displays that contained an additional irrelevant singleton. Display-locked N2pc showed that attention was allocated to the target and not to the irrelevant singleton. However, the onset of the N2pc to the target was delayed when the irrelevant singleton was presented in the opposite hemifield relative to the same hemifield. Thus, although attention was successfully focused on the target, the irrelevant singleton produced some interference resulting in a delayed allocation of attention to the target. A subsequent probe discrimination task allowed for locking ERPs to probe onsets and investigating the dynamics of sensory gain control for probes appearing at relevant (target) or irrelevant (singleton distractor) positions. Probe-locked P1 showed sensory gain for probes positioned at the target location but no such effect for irrelevant singletons in the additional singleton condition. Taken together, the present data support the claim that irrelevant singletons do not capture attention. If they produce any interference, it is rather due to nonspatial filtering costs.

SINGLETON CONDITIONS AND QUANTUM DE FINETTI'S THEOREM

We investigate the validity of quantum De Finetti's Theorem for algebraic random processes satisfying the singleton condition. We first prove a conditional version of the theorem, then we give some natural conditions which guarantee the full validity of De Finetti's Theorem.

Notions of Independence Related to the Free Group

The central limit problem for algebraic probability spaces associated with the Haagerup states on the free group with countably many generators leads to a new form of statistical independence in which the singleton condition is not satisfied. This circumstance allows us to obtain nonsymmetric distributions from the central limit theorems deduced from this notion of independence. In the particular case of the Haagerup states, the role of the Gaussian law is played by the Ullman distribution. The limit process is explicitly realized on the finite temperature Boltzmannian Fock space. The role of entangled ergodic theorems in the proof of the central limit theorems is discussed.