Informational entropy : a failure tolerance and reliability surrogate for water distribution networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies

Central loop Versus Conventional H-reflex in Diabetic Neuropathic Patients

ABSTRACT: Introduction & Objective: Diabetes mellitus is the most prevalent endocrine disease and one of the most common causes of peripheral neuropathy. Neither conventional electrodiagnostic nor imaging studies (even MRI of lumbosacral vertebrae) can precisely differentiate concomitant radiculopathy (e.g. S1-root irritation) and diabetic peripheral polyneuropathy. This usually leads to unnecessary surgical interventions and its complications. In this study, S1-roots of diabetic neuropathic patients with impaired conventional H-reflexes were evaluated by the central loop of gastrocnemius-soleus H-reflexes. Materials & Methods: This descriptive study was performed in the clinics of Shiraz medical school in 1387(2008). Forty two diabetic patients (14 males and 28 females with a mean age of 48.2 years) with unobtainable or abnormal conventional gastrocnemius-soleus H-reflexes and peripheral neuropathy were enrolled. The central loop of H-reflex was performed bilaterally by stimulating S1-root with a monopolar needle and recorded in the half way of the line from popliteal crease to the medial malleolus. Collected data were analyzed by McNemar test, using SPSS software. Results: Of 84 limbs with impaired conventional H-reflexes, 82 limbs (97.6%) had the central loop of H-reflexes with latencies less than 8 ms. All the limbs with abnormally prolonged conventional H-reflexes' latencies had the central loop of H-reflexes' latencies in the range of 5.5-7.85 ms. The latency of central loop of H-reflex in this study was 6.34 ± 0.96 ms with the range of 4.3-7.85 ms. Conclusion: In case the conventional H-reflex is impaired, the central loop of H-reflex in diabetic neuropathic patients offers a valuable approach for investigating S1-root. It seems that this approach leads to a better diagnosis of the absence of radiculopathy and a decrease in the rate of unnecessary surgical interventions and its complications in diabetics. Keywords: Central loop, H-reflex, Diabetic neuropath