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%'e investigate the structure of metastable states (states of local-energy minima) in a random Ising chain. It is shown that one can always achieve a unique reduction of a metastable state into a series of irreducible spin clusters. In a certain sense each irreducible spin cluster is equivalent to a two-level system. e present the exact degeneracy for a random Ising chain by a very simple argument. %e obtain an analytical expression for the distribution function of the barrier heights r and the excitation energies e of the clusters -D(e, r). This includes contributions from all the possible spin clusters of various shapes and sizes, Even though the numerical results of this paper have been obtained for a Gaussian distribution, all the formulas of the distribution functions obtained are general, independent of the concrete form of any random continuous distribution. To illustrate how these results can be applied, we recover the "logarithmic law" for energy versus relaxation times at different temperatures, a well-known characteristic of spin-glasses.

PurposeMultidrug-resistant tuberculosis (MDR-TB) requires long-term treatment, has a high fatality rate, and constitutes a global threat. Earlier detection of treatment failure is required to predict therapeutic efficacy.Patients and methodsWe enrolled MDR-TB patients consecutively from January 2011 through December 2012 in Lianyungang, China. Sputum smear microscopy tests and sputum cultures were performed once a month for the first 6 months following initiation of antituberculosis treatment and once every 2 months thereafter until the end of therapy. The sensitivity, specificity and area under the receiver operating characteristic curve (AUC) were used with a 95% CI to estimate the role of sputum bacteriology conversion in predicting treatment outcomes.ResultsAmong the 92 MDR-TB patients enrolled in this study, 40.2% had poor treatment outcomes. The median initial sputum bacteriology conversion time was 1 month. Patients having 2-month sputum smear conversions (adjusted odds ratio [OR]: 7.19, 95% CI: 2.60–19.84) or culture conversions (adjusted OR: 2.88, 95% CI: 1.11–7.45) were more likely to experience good outcomes. The sensitivity and specificity obtained when using two-month sputum smear conversions to predict treatment outcomes were 67.6% (95% CI: 50.2–82.0) and 76.4% (95% CI: 63.0–86.8), respectively. The sensitivity and specificity obtained when using 2-month culture conversions to predict treatment outcomes were 48.6% (95% CI: 32.0–65.6) and 74.5% (95% CI: 61.0–85.3), respectively. The AUC for two-month smear conversions was 0.72 (95% CI: 0.62–0.81), significantly higher than that obtained for 2-month culture conversions (0.62, 95% CI: 0.52–0.72) (χ2 = 4.18, P = 0.041).ConclusionThe prognoses of MDR-TB patients displaying persistent sputum positivity were inferior to those for whom sputum bacteriology conversion was observed. Thus, sputum smear conversion results obtained 2 months after treatment initiation may provide a potential means for predicting MDR-TB treatment outcomes.

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Obesity is associated with increased sensitivity to pain, including neuropathic pain, but the precise mechanisms are not fully understood. Recent evidence has revealed that AMP-activated protein kinase (AMPK) in the central nervous system (CNS) regulates the neuropeptide calcitonin gene-related peptide (CGRP), a principal neurotransmitter of the class C nerve fiber, which serves an important role in initiating and maintaining neuropathic pain. AMPK has been demonstrated to be downregulated in the CNS in obesity. The present study hypothesized that obesity may lead to increased sensitivity to neuropathic pain by downregulating AMPK and upregulating CGRP expression levels in the CNS. Sprague-Dawley rats consuming a high-fat diet (HF) for 12 weeks developed obesity; they exhibited significantly decreased levels of phospho (p)-AMPK and increased CGRP expression levels in the spinal cord (SC) and dorsal root ganglion (DRG), respectively, compared with rats consuming a low-fat (LF) diet. HF-fed rats that underwent spared nerve injury (SNI) also exhibited lower p-AMPK and higher CGRP expression levels in the SC and DRG, compared with the corresponding LF-diet rats. The 50% paw withdrawal threshold (PWT; as measured by Von Frey testing) was significantly lower in HF-fed compared with LF-fed rats, with or without SNI. Through intrathecal treatment, the AMPK activator 5-aminoimidazole-4-carboxamide riboside (AICAR) or the CGRP antagonist CGRP8-37 decreased CGRP expression levels and increased the 50% PWT; however, the AMPK inhibitor dorsomorphin augmented CGRP expression levels and further reduced the 50% PWT in HF-fed rats, but not LF-fed rats, with or without SNI. The results indicated that blocking the AMPK-CGRP pathway may enhance neuropathic pain in HF-induced obesity, with or without nerve injury. Targeting AMPK in the CNS may be a novel strategy for the prevention and treatment of obesity-associated neuropathic pain.

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We study the problem of existence of homoclinic and heteroclinic orbits of Chen's system. For the case of 2c > a > c > 0 and b ≥ 2a, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits.

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