In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannancontractions dened on modular spaces endowed with a graph. We do not impose the Δ2-conditionor the Fatou property on the modular spaces to give generalizations of some recent results. Thegiven results play as a modular version of metric xed point results.

This incursion into the realm of elementary and probabilistic number theory of continued fractions, via modular forms, allows us to study the alternating sum of coeecients of a continued fraction, thus solving the longstanding open problem of their limit law.

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

We present properties of multihead two-way probabilistic nite automata that parallel those of their deterministic and nondeterministic counterparts. We deene multihead proba-bilistic nite automata with log-space constructible transition probabilities, and we describe a simple technique to simulate these automata by standard log-space probabilistic Turing machines. Next, we represent log-space p...

In this paper, we investigate a modular architecture for ECG beat classification. The feature space is divided into distinct regions and individual classifiers are developed for each region. We compare different combination strategies, and feature space partition strategies. We also describe a novel, batch modular learning method that can be used to incrementally improve the performance of the ...

We launch the new probabilistic model checker Storm. It features the analysis of discreteand continuous-time variants of both Markov chains and MDPs. It supports the Prism and JANI modeling languages, probabilistic programs, dynamic fault trees and generalized stochastic Petri nets. It has a modular set-up in which solvers and symbolic engines can easily be exchanged. It offers a Python API for...

This paper gives an overview of recent results concerning the modular derivation of (i) modal specification logics, (ii) notions of simulation together with logical characterisations, and (iii) sound and complete axiomatisations, for systems modelled as coalgebras of functors on Set. Our approach applies directly to an inductivelydefined class of coalgebraic types, which subsumes several types ...

The aim of our participation in the topic distillation and the named page finding tasks of the Web track is the evaluation of a well-founded modular probabilistic framework for Web Information Retrieval, which integrates content and link analyses. The link analysis component of the framework employs a new probabilistic approach, called the Absorbing Model, for calculating a measure of popularit...

We investigate hierarchical properties and log-space reductions of languages recognized by log-space probabilistic Turing machines, Arthur-Merlin games and Games against Nature with log-space probabilistic veriiers. For each log-space complexity class, we decompose it into a hierarchy based on corresponding multihead two-way nite automata and we (eventually) prove the separation of the hierarch...