Scheduling coupled tasks on parallel identical machines

In many applications in the context of patient appointment scheduling there are recurring tasks with fixed delays between them. These tasks are commonly referred to as coupled-task jobs. In the coupled-task settings, each job consists of two tasks whereby the second task must start processing after an exact time lag following the completion of the first task. In this paper, we introduce the problem of scheduling a set of coupled-task jobs on parallel identical machines with the objective function of minimizing the makespan. We study the computational complexity of the general problem, as well as its special cases. We prove that the majority of these problems are (strongly) NP-hard. Nonetheless, we provide the optimal scheduling policy for two settings consisting of identical jobs. An important result of our work includes showing that the existence of a (2−ε)-approximation algorithm for the problem implies P=NP. The latter result improves a recently proposed bound for the open-shop counterpart as well

The influence of radiofrequency ablation patterns on length, histological and mechanical properties of tendons

The use of radiofrequency ablation for thermomodulation of connective tissues has gained acceptance with some surgeons. It is now mainly used for shoulder instability, and two techniques are commonly applied – ablation in a uniform pattern (paintbrush) and ablation in a linearly dispersed fashion (grid). The use of these techniques for shrinkage of tendons or cruciate ligaments is not widely accepted but may be utilized in selected cases. We assessed the effects of thermomodulation via monopolar radiofrequency ablation using these two techniques on the histological and biomechanical properties of rabbit Achilles tendons. 16 paired rabbit achilles tendons were divided into two treatment groups. Using a Monopolar RF device, eight tendons were treated using the paintbrush technique, and eight using the grid technique. The tendons were shrunk to about 90% of their original length, and the paired tendons were used as control. Following thermomodulation, tendons were pulled to tear using the Instron 4502 (Instron, Mass.) device. We found treated tendons were significantly less resistant to tear when compared to control; the average load to failure of the treatment group was 19.4% lower (p=0.05) than the control group values and the average tissue stiffness in the treatment group was 11.3% lower (p=0.051) than the control group. We found a tendency towards a lower resistance to pull in the tendon group treated using the grid technique. Histological analysis demonstrated areas of collagen denaturation correlated to areas of thermomodulation. A random point of failure was found along the tendons in the paintbrush group whereas the typical point of failure in the grid group was located at the treatment point or at its margins. Our findings demonstrate that use of the grid technique in ablation of tendons creates typical failure points (locus minoris resistenci) which bring about failure and alter the biomechanical properties of the thermomodulated tendons. Thermomodulation of tendons may be used efficiently in selected cases but its detrimental effects to the biomechanical attributes of the tissue should be considered

Widefield lensless imaging through a fiber bundle via speckle correlations

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