In this paper we characterize the group of affine transformations a flat simply connected manifold whose developing map is diffeomorphism. This proved by making use some simple facts about homeomorphisms $\mathbb{R}^n$ preserving open sets. We show examples where characterization useful.

We say that the sequence gn, n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module Kn over commutative ring K is a sequence of stable degree if the order of gn is growing with n and the degree of each nonidentical polynomial map of kind gn is an independent constant c. Transformation b = τgnkτ−1, where τ is the affine bijection, n is large and k is relatively small, can be use...

Non-malleable code is a relaxed version of errorcorrection codes and the decoding of modified codewords results in the original message or a completely unrelated value. Thus, if an adversary corrupts a codeword then he cannot get any information from the codeword. This means that non-malleable codes are useful to provide a security guarantee in such situations that the adversary can overwrite t...

Prior work on diagnosing Alzheimer’s disease from magnetic resonance images of the brain established that convolutional neural networks (CNNs) can leverage high-dimensional image information for classifying patients. However, little research focused how these models utilize usually low-dimensional tabular information, such as patient demographics or laboratory measurements. We introduce Dynamic...

This paper is a shortened exposition of the theory of shrinkings, with particular emphasis on the relations between shrinkings and geometries at infinity or affine expansions. To make things easier, we shall only consider locally affine geometries, referring the reader to [A. Pasini, C. Wiedorn, Local parallelisms, shrinkings and geometries at infinity, in: A. Pasini (Ed.), Topics in Diagram Ge...

For $\mathfrak g$ a Kac-Moody algebra of affine type, we show that there is an $\text{Aut}\, \mathcal O$-equivariant identification between $\text{Fun}\,\text{Op}_{\mathfrak g}(D)$, the functions on space ${\mathfrak g}$-opers disc, and $W\subset \pi_0$, intersection kernels screenings inside vacuum Fock module $\pi_0$. This kernel $W$ generated by two states: conformal vector, state $\delta_{-...

We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further references) as messages and use the iterative process to walk on such graph as encryption process. To hide such encryption (graph and walk on it) we will use two affine transfor...

An exact C-function, which is an action for the Virasoro master equation, is obtained on affine-Virasoro space. The solutions of the master equation are fixed points of an associated flow, which obeys a C-theorem. The closed sub-flow SO(n)diag is a flow on the space of graphs, and the associated Morse polynomials are known generating functions in graph theory. The general flow also implies a me...