Book
The Oxford Handbook of Computational and Mathematical Psychology
This chapter provides a review of topics and concepts that are necessary to study and understand 3D shape perception. This includes group theory and their invariants; model-based invariants; Euclidean, affine, and projective geometry; symmetry; inverse problems; simplicity principle; Fechnerian psychophysics; regularization theory; Bayesian inference; shape constancy and shape veridicality; shape recovery; perspective and orthographic projections; camera models; as well as definitions of shape. All concepts are defined and illustrated, and the reader is provided with references providing mathematical and computational details. Material presented here will be a good starting point for students and researchers who plan to study shape, as well as for those who simply want to get prepared for reading the contemporary literature on the subject.
The book contains the official proceedings of The Asian Conference on Psychology & the Behavioral Sciences 2013.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.