An influence network is a graph where each node changes its state according to a function of the states of its neighbors. We present bounds for the stabilization time of such networks. We derive a general bound for the classic “Democrats and Republicans” problem and study different model modifications and their influence on the way of stabilizing and their stabilization time. Our main contribut...

A systematic method of designing TSC checker for Q class (even code length) of Borden’s code [l] is proposed, where a modular approach is used. In a comparative study, it is found that the proposed method is much better than [2,3] and it has a larger capability than [4,5] in designing the checker. For instance, the 3/12 code in C(12,2) can be identified in one of four ways, corresponding to PT’...

It is a well known fact that if C is an [n, k, d] formally self-dual even code with n > 30, then d ≤ 2[n/8]. A formally self-dual even code with d = 2[n/8] is called nearextremal. Kim and Pless [9] conjecture that there does not exist a near-extremal formally self dual even (not Type II) code of length n ≥ 48 with 8|n. In this paper, we prove that if n ≥ 72 and 8|n, then there is no near-extrem...

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even-odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

Hyperb Med 2009; 36: 407–8 14 Souday V, Radermacher P, Asfar P. Cerebral arterial gas embolism— a race against time! Crit Care Med 2013; 41: 1817–9 15 Ploner F, Saltuari L, Marosi MJ, Dolif R, Salsa A. Cerebral air emboli with use of central venous catheter in mobile patient. Lancet 1991; 338: 1331 16 Fracasso T, Karger B, Schmidt PF, Reinbold WD, Pfeiffer H. Retrograde venous cerebral air embo...

Let C be a binary linear self-dual doubly-even code of length n and minimal weight d. Such codes exist only if 12 = 0 (mod 8). We put II = 24r + 8s, s = 0, 1, 2. It follows from the work of Gleason [2] and of Mallows and Sloane [6] that d s 4r + 4. C is called extremal if d = 4r + 4. In the following, an extremal code means a binary linear self-dual doubly-even extremal code. We use the set-the...

We argue for breaking data-parallel jobs in compute clusters into tiny tasks that each complete in hundreds of milliseconds. Tiny tasks avoid the need for complex skew mitigation techniques: by breaking a large job into millions of tiny tasks, work will be evenly spread over available resources by the scheduler. Furthermore, tiny tasks alleviate long wait times seen in today’s clusters for inte...

We show that the ring of the weight enumerators of a self-dual doubly even code dn in arbitrary genus is finitely generated. Indeed enough elements to generate it are given. The latter result is applied to obtain a minimal set of generators of the ring in genus two.