Figure-ground organization as a 3D visual operation

The main purpose of the article is to codify the theoretical resources of the sociology of everyday life. The author focuses on the two research programmes of the contemporary sociology of everyday world: the frame theory and the practice theory. The author reveals basic conceptualizations of practice-orientated sociology and frame-analysis, their constructive features; analyses their inherent axiomatics and logics, trying to find their theoretical implications for the sociology of everyday life in particular and the sociological theory in the whole. The method of codification used by the author - description, distinguishing constitutive features of the basic conceptualizations, reconstructing the logic and pointing to the theoretical implications - is also the object of critical reflection in this article.

Added: Sep 25, 2012

Integrality of Framing and Geometric Origin of 2-functions

Vologodsky V., Walcher J., Schwarz A. math. arxive. Cornell University, 2017. No. 1702.07135.

We say that a formal power series $\sum a_n z^n$ with rational coefficients is a 2-function if the numerator of the fraction $a_{n/p}-p^2 a_n$ is divisible by $p^2$ for every prime number $p$. One can prove that 2-functions with rational coefficients appear as building block of BPS generating functions in topological string theory. Using the Frobenius map we define 2-functions with coefficients in algebraic number fields. We establish two results pertaining to these functions. First, we show that the class of 2-functions is closed under the so-called framing operation (related to compositional inverse of power series). Second, we show that 2-functions arise naturally in geometry as $q$-expansion of the truncated normal function associated with an algebraic cycle extending a degenerating family of Calabi-Yau 3-folds.

Added: Nov 8, 2017

Detection of skewed symmetry

Sawada T., Pizlo Z. Journal of Vision. 2008. Vol. 8. No. 5:14. P. 1-18.

Added: Oct 7, 2014

Gamma conjecture via mirror symmetry

Galkin S., Iritani H. arxiv.org. math. Cornell University, 2015. No. 1508.00719.

The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors claims that the principal asymptotic class A_F equals the Gamma class G_F associated to Euler's Γ-function. We illustrate in the case of toric varieties, toric complete intersections and Grassmannians how this conjecture follows from mirror symmetry. We also prove that Gamma conjecture is compatible with taking hyperplane sections, and give a heuristic argument how the mirror oscillatory integral and the Gamma class for the projective space arise from the polynomial loop space.

Added: Aug 5, 2015

The conifold point

Galkin S. arxiv.org. math. Cornell University, 2014. No. 1404.7388.

Consider a Laurent polynomial with real positive coefficients such that the origin is strictly inside its Newton polytope. Then it is strongly convex as a function of real positive argument. So it has a distinguished Morse critical point --- the unique critical point with real positive coordinates. As a consequence we obtain a positive answer to a question of Ostrover and Tyomkin: the quantum cohomology algebra of a toric Fano manifold contains a field as a direct summand. Moreover, it gives a good evidence that the same statement holds for any Fano manifold.

Added: May 4, 2014

Direct and reverse projection procedures in problems of 3D objects reconstruction from images

Veselov E. A., Uvaysov S. U., Lvov B. G. et al. In bk.: Innovative Information Technologies: Materials of the International scientific–practical conference. Part 2. Prt. 2. M.: HSE, 2014. Ch. 2. P. 710-716.

This article presents a research of direct and reverse projection procedures. Presents Mathematical calculations of spatial situated point projection are presented as particular case for obtaining the expressions which describe this process. The application of these processes in problems of three-dimensional object reconstruction from images is demonstrated by a simple 3D object.

Added: Jun 23, 2014