The Contraction Checking problem asks, given two graphs H and G as input, whether H can be obtained from G by a sequence of edge contractions. Contraction Checking remains NP-complete, even when H is fixed. We show that this is not the case when G is embeddable in a surface of fixed Euler genus. In particular, we give an algorithm that solves Contraction Checking in f(h, g) · |V (G)|3 steps, wh...

Estrogen exerts protective effects against cardiovascular diseases in premenopausal women, but is associated with an increased risk of both coronary heart disease and stroke in older postmenopausal women. Studies have shown that activation of the G-protein-coupled estrogen receptor 1 (GPER) can cause either relaxation or contraction of arteries. It is highly likely that these dual actions of GP...

The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...

In this paper, we apply the idea of integral type contraction and prove some coupled fixed point theorems for such contractions in ordered $G$-metric space. Also, we support the main results by an illustrative example.

The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction F-Khan-type contraction mappings on a metric space with graph. At the end, we give an illustrative example.

Abstract. In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a necessary and sufficient condi...

We have shown that myosin light chain kinase (MLCK) was required for the off-contraction in response to the electrical field stimulation (EFS) of feline esophageal smooth muscle. In this study, we investigated whether protein kinase C (PKC) may require the on-contraction in response to EFS using feline esophageal smooth muscle. The contractions were recorded using an isometric force transducer....

Lower esophageal sphincter (LES) tone depends on PGF(2alpha) and thromboxane A(2) acting on receptors linked to G(i3) and G(q) to activate phospholipases and produce second messengers resulting in muscle contraction. We therefore examined PGF(2alpha) signal transduction in circular smooth muscle cells isolated by enzymatic digestion from cat esophagus (Eso) and LES. In Eso, PGF(2alpha)-induced ...

For a family of graphs F , the F-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists S ⊆ E(G) of size at most k such that G/S belongs to F . Here, G/S is the graph obtained from G by contracting all the edges in S. Heggernes et al. [Algorithmica (2014)] were the first to study edge contraction problems in the realm of Parameterized Complex...