Background: Surgery and accurate removal of the brain tumor in the operating room and after opening the scalp is one of the major challenges for neurosurgeons due to the removal of skull pressure and displacement and deformation of the brain tissue. This displacement of the brain changes the location of the tumor relative to the MR image taken preoperatively. Methods: This study, which is done...

We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by FominGreene-Reiner-Shimozono, and we extend this notion to affine permutations. The balanced labellings give a natural encoding of the reduced decompositions of affine permutations. We show that the sum of weight monomials of the column...

We show that it is impossible to compute (or even to approximate) the topological entropy of a continuous piecewise affine function in dimension four. The same result holds for saturated linear functions in unbounded dimension. We ask whether the topological entropy of a piecewise affine function is always a computable real number, and conversely whether every non-negative computable real numbe...

A Boolean function f :F2 → F2 is called an affine disperser of dimension d, if f is not constant on any affine subspace of F2 of dimension at least d. Recently Ben-Sasson and Kopparty gave an explicit construction of an affine disperser for sublinear d. The main motivation for studying such functions comes from extracting randomness from structured sources of imperfect randomness. In this paper...

Abstract The scope of our investigation is to study the geometric properties normalized form combination generalized Lommel–Wright function $J_{\nu ,\lambda }^{\mu ,m}$ J ? , ? ? m </mm...