We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse hemispheres. This approach has a natural extension to the presence of additive white noise prior to quantization. Noisy one-bit mappings are shown to satisfy an RIP ...

We present a short survey of some very recent results on the finitely additive white noise theory. We discuss the Markov property of the solution of a stochastic differential equation driven directly by a white noise, study the Radon-Nikodym derivative of the measure induced by nonlinear transformation on a Hilbert space with respect to the canonical Gauss measure thereon and obtain a represent...

We continue the study of cellular automata (CA) directional dynamics, i.e. the behavior of the joint action of CA and shift maps. This notion has been investigated for general CA in the case of expansive dynamics by Boyle and by Sablik for sensitivity and equicontinuity. In this paper we give a detailed classification for the class of additive CA providing non-trivial examples for some classes ...

Here we describe a method for separating the sum of chaotic signals into the individual components, using the inherent underlying dynamics of the chaotic sources. Capabilities of the method are demostrated on example of discrete-time systems, one-dimensional logistic maps. We demonstrate that the proposed approach based on backward iteration of the mapping equations describing the chaotic sourc...

In a previous article ([2]), we computed the Betti numbers and an additive basis for the Chow ring A(M0,2(P , 2)) of the moduli space of degree two stable maps from 2-pointed curves to projective space of arbitrary dimension r. These are the first steps in a program to give presentations for these Chow rings. In the present paper, we will complete this program for the special case r = 1 by show...

A non-additive version of the thermodynamic formalism is developed. This allows us to obtain lower and upper bounds for the dimension of a broad class of Cantor-like sets. These are constructed with a decreasing sequence of closed sets that may satisfy no asymptotic behavior. Moreover, they are coded by an arbitrary symbolic dynamics, and the geometry of the construction may depend on all the s...

In the present article, we investigate a possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor’s K-group of the real numbers into the additive group of real numbers. Usi...

The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

We present a mostly numerical investigation on randomly perturbed piecewise contracting maps (PCM) with the goal to study the extreme value limit distribution of observables related to local recurrence. Our analysis will focus on PCM under additive noise, but we will also consider the hyperbolic attractor of the Baker’s map when perturbed with another kind of noise, namely, the randomly applied...

As an attempt to understand motives over k[x]/(xm), we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. Rülling on 0-dimensional cycles. We give an explicit construction of regulator maps on the groups of 1-cycles with an aid of the residue theory of A. Parshin and V. Lomadze.