In this paper, we address the unison problem. We consider the self-stabilizing algorithm proposed by Boulinier et al. We exhibit a bound on the step complexity of its stabilization time. In more details, the stabilization time of this algorithm is at most 2Dn + (α + 1)n + (α− 2D)n steps, where n is the number of processes, D is the diameter of the network, and α is a parameter of the algorithm.

We reduce the problem of proving the convergence of a randomized self-stabilizing algorithm under k-bounded policies to the convergence of the same algorithm under a specific policy. As a consequence, all k-bounded schedules are equivalent : a given algorithm is self-stabilizing under one of them if and only if it is self-stabilizing under any of them.

This paper deals with quadratic stabilization of discrete-time multiple-input (MI) systems by means of quantized static feedback. We consider the minimization of quantization density, which is still an open problem for MI systems. Our first contribution in this regard is to partially derive the structure that a quantizer that minimizes density for a MI system should have. The second and main co...

stabilization of river terraces and natural soil slopes in rangelands by means of tree roots as a reinforcement agent is an environmental adopted method which needs to be developed. in this research a series of tests was carried out on soil blocks containing willow roots and without roots using a large scale in situ direct shear test apparatus. the results were analyzed based on direct shear th...

The biomechanical performance of a locking compression plate system was compared to an intramedullary photodynamic bone stabilization system in a femur and humerus osteotomy model. The photodynamic bone stabilization system utilizes an angioplasty-like balloon that is introduced into the intramedullary canal of a fractured bone, filled with monomer that is then polymerized and hardened by visib...

conclusions the trunk stabilization exercises are more effective than conventional back care exercises in the rehabilitation of patients with chronic lbp. results the results of the study demonstrated significant improvements in abdominal muscle endurance and reduction in vas and modq score of both groups (p = 0.001). the trunk stabilization exercise group showed greater gains in abdominal musc...

We show that, contrary to common belief, Dijkstra’s K-state mutual exclusion algorithm on a ring also stabilizes when the number K of states per process is one less than the number N + 1 of processes in the ring. We formalize the algorithm and verify the proof in PVS, based on Qadeer and Shankar’s work. We show that K = N is sharp by giving a counter-example for K = N − 1. ACM CCS

Self-stabilizing algorithms are designed to guarantee convergence to some desired stable state from arbitrary initial states arising out of an arbitrarily large number of faults. However, in a well-designed system, the simultaneous occurrence of a large number of faults is rare. It is therefore desirable to design algorithms that are not only self-stabilizing, but also have the ability to recov...