The Importance of Attention in the Twinkle Goes Effect

How do we perceive the location of moving objects? The position and motion literature is currently divided. Predictive accounts of object tracking propose that the position of moving objects is anticipated ahead of sensory signals, whilst non-predictive accounts claim that an anticipatory mechanism is not necessary. A novel illusion called the twinkle goes effect, describing a forward shift in the perceived final location of a moving object in the presence of dynamic noise, presents a novel opportunity to disambiguate these accounts. Across three experiments, we compared the predictions of predictive and non-predictive theories of object tracking by combining the twinkle goes paradigm with a multiple object tracking task. Specifically, we tested whether the size of the twinkle goes illusion would be smaller with greater attentional load (as entailed by the non-predictive, tracking continuation theory) or whether it would not be affected by attentional load (as entailed by predictive extrapolation theory). Our results failed to align with either of these theories of object localisation and tracking. Instead, we found evidence that the twinkle goes effect may be stronger with greater attentional load. We discuss whether this result may be a consequence of an essential, but previously unexplored relationship between the twinkle goes effect and representational momentum. In addition, this study was the first to reveal critical individual differences in the experience of the twinkle goes effect, and in the mislocalisation of moving objects. Together, our results continue to demonstrate the complexity of position and motion perception.

Singular integrals and sublinear operators on amalgam spaces and Hardy-amalgam spaces

In this paper, we establish the extrapolation theory for the amalgam spaces and the Hardy-amalgam spaces. By using the extrapolation theory, we obtain the mapping properties for the Calderón-Zygmund operators and its commutator, the Carleson operators and establish the Rubio de Francia inequalities for Littlewood-Paley functions of arbitrary intervals to the amalgam spaces. We also obtain the boundedness of the Calder{ó}n-Zygmund operators and the intrinsic square function on the Hardy-amalgam spaces.

Calderón Operator on Local Morrey Spaces with Variable Exponents

In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.

Extrapolation to mixed norm spaces and applications

This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.

Extrapolation to weighted Morrey spaces with variable exponents and applications

This paper establishes the mapping properties of pseudo-differential operators and the Fourier integral operators on the weighted Morrey spaces with variable exponents and the weighted Triebel–Lizorkin–Morrey spaces with variable exponents. We obtain these results by extending the extrapolation theory to the weighted Morrey spaces with variable exponents. This extension also gives the mapping properties of Calderón–Zygmund operators on the weighted Hardy–Morrey spaces with variable exponents and the wavelet characterizations of the weighted Hardy–Morrey spaces with variable exponents.

Extrapolation to product Herz spaces and some applications

This paper extends the extrapolation theory to product Herz spaces. To prove the main result, we first investigate the dual space of the product Herz space, and then show the boundedness of the strong maximal operator on product Herz spaces. By using this extrapolation theory, we establish the John–Nirenberg inequality, the characterization of little bmo, the Fefferman–Stein vector-valued inequality, the boundedness of the bi-parameter singular integral operator, the strong fractional maximal operator, and the bi-parameter fractional integral operator on product Herz spaces. We also give a new characterization of little bmo via the boundedness of the commutators of some bi-parameter operators on product Herz spaces. Even in the one-parameter setting, some of our results are new.

Hallucination of moving objects revealed by a dynamic noise background

We show that on a dynamic noise background, the perceived disappearance location of a moving object is shifted in the direction of motion. This “twinkle goes” illusion has little dependence on the luminance- or chromaticity-based confusability of the object with the background, or on the amount of background motion energy in the same direction as the object motion. This suggests that the illusion is enabled by the dynamic noise masking the offset transients that otherwise accompany an object’s disappearance. While these results are consistent with an anticipatory process that pre-activates positions ahead of the object’s current position, additional findings suggest an alternative account: a continuation of attentional tracking after the object disappears. First, the shift was greatly reduced when attention was divided between two moving objects. Second, the illusion was associated with a prolonging of the perceived duration of the object, by an amount that matched the extent of extrapolation inferred from the effect of speed on the size of the illusion (~50 ms). While the anticipatory extrapolation theory does not predict this, the continuation of attentional tracking theory does. Specifically, we propose that in the absence of offset transients, attentional tracking keeps moving for several tens of milliseconds after the target disappearance, and this causes one to hallucinate a moving object at the position of attention.

On the theory of integral manifolds for some delayed partial differential equations with nondense domain}

UDC 517.9 Integral manifolds are very useful in studying dynamics of nonlinear evolution equations. In this paper, we consider the nondensely-defined partial differential equation ⅆ u ⅆ t = ( A + B ( t ) ) u ( t ) + f ( t , u t ) , t ∈ R , ( 1 ) where ( A , D ( A ) ) satisfies the Hille – Yosida condition, ( B ( t ) ) t ∈ R is a family of operators in ℒ ( D ( A ) ¯ , X ) satisfying some measurability and boundedness conditions, and the nonlinear forcing term f satisfies ‖ f ( t , ϕ ) - f ( t , ψ ) ‖ ≤ φ ( t ) ‖ ϕ - ψ ‖ 𝒞 , here, φ belongs to some admissible spaces and ϕ , ψ ∈ 𝒞 : = C ( [ - r ,0 ] , X ) . We first present an exponential convergence result between the stable manifold and every mild solution of (1). Then we prove the existence of center-unstable manifolds for such solutions.Our main methods are invoked by the extrapolation theory and the Lyapunov – Perron method based on the admissible functions properties.