Influenzanet is a system to monitor the activity of influenza-like-illness [ILI] with the aid of internet volunteers. Topological data analysis [TDA] examines the structure of data and contributes to the development of medicine, studying properties of a continuous space by the analysis of a discrete sample of it. Using TDA we analyze the topology of Influenzanet data identifying noise and disti...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

The proposed analysis of the currently available experimental results concerning the neural cell activity in the brain area known as hippocampus suggests a particular mechanism of spatial information and memory processing. Below it is argued that the spatial information available through the analysis of the hippocampal cell activity is predominantly of topological nature. It is pointed out that...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$.

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

The paper provides a method of topological analysis of gray scale images and other images with parameters. The main goal is to count objects in the image and extract them without image segmentation. The approach is simple and context independent. The method is based on algebraic topology, the mathematical theory responsible for these issues.

We propose a new framework for the experimental study of periodic, quasiperiodic and recurrent dynamical systems. These behaviors express themselves as topological features which we detect using persistent cohomology. The resulting 1-cocycles yield circle-valued coordinates associated to the recurrent behavior. We demonstrate how to use these coordinates to perform fundamental tasks like period...