The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem. We show that Bisection is FPT w.r.t. the minimum c...

BACKGROUND Some metazoa have the capacity to regenerate lost body parts. This phenomenon in adults has been classically described in echinoderms, especially in sea stars (Asteroidea). Sea star bipinnaria larvae can also rapidly and effectively regenerate a complete larva after surgical bisection. Understanding the capacity to reverse cell fates in the larva is important from both a developmenta...

This communication presents a new method for evaluating phase response curves (PRCs). A PRC describes the phase shifts produced in an oscillator by stimuli applied at different initial phase-states of that oscillator. In the PRC bisection tests, we repeatedly cut in half the circular distribution of the initial phase-states of the oscillator when stimuli are given. Empirically, we locate that o...

Line bisection has long been a routine test for unilateral neglect, along with a range of tests requiring cancellation, copying or drawing. However, several studies have reported that line bisection, as classically administered, correlates relatively poorly with the other tests of neglect, to the extent that some authors have questioned its status as a valid test of neglect. In this article, we...

We show stability of the $L^2$-projection onto Lagrange finite element spaces with respect to (weighted) $L^p$ and $W^{1,p}$-norms for any polynomial degree space dimension under suitable conditions on mesh grading. This includes $W^{1,2}$-stability in two dimensions meshes generated by newest vertex bisection. Under realistic but conjectured assumptions grading three we all degrees. also propo...

The bisection method for kinetically constrained models (KCM) of Cancrini, Martinelli, Roberto and Toninelli is a vital technique applied also beyond KCM. In this note we present new way performing it, based on novel two-block dynamics with probabilistic proof instead the original spectral one. We illustrate by very directly proving an upper bound relaxation time KCM like one East model in stri...

Bisecting a visually presented stimulus is a sensitive test for attentional and motor biases in both healthy and brain-damaged participants. There are, in addition, perceptual effects on performance and several idiosyncratic biases. Experiments that manipulated the stimulus attributes have suggested that higher-level cognitive processes can also influence bisection accuracy. These observations ...

In this work some preliminary numerical results obtained by large scale simulations of the sequential dynamics of a neural network model for the graph bisection problem on random geometrically connected graphs are presented. It can be concluded that the sequential dynamic is a low cost, effective and very fast local minima optimization heuristic for the Graph Bisection Problem.