Conditions implying regularity of the three dimensional Navier-Stokes equation

We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foias, Guillope and Temam.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints/ (Changes: this is a substantial rewrite of the previous version.

On the blow up criterion for the 2-D compressible Navier-Stokes equations

summary:Motivated by [10], we prove that the upper bound of the density function $\rho$ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain

Efficacy and safety of combination of ulinastatin and meglumine cyclic adenosine monophosphate in the treatment of acute myocardial infarction, and its effect on serum levels of hs-CRP, cTnI and CK

Purpose: To determine the efficacy and safety of a combination of ulinastatin and meglumine cyclic adenosine monophosphate (cAMP) in the treatment of acute myocardial infarction (AMI), and its effect on serum levels of hypersensitive-c-reactive protein (hs-CRP), cardiac troponin I (cTnI), creatine kinase (CK).Methods: A total of 90 AMI patients admitted to The Second Affiliated Hospital of Qiqihar Medical College, Qiqihar City, Heilongjiang Province, China from January 2019 to January 2020 were selected and randomized (in a 1:1 ration) into control group and study group. Patients in the two groups received meglumine cAMP, while those in the study group were, in addition, treated with ulinastatin. The two groups were compared with regard to clinical efficacy, cardiac function indices, serum biochemical indices, incidence of drug-related side effects, duration and number of episodes of angina pectoris, and levels of neuroendocrine hormones.Results: The study group exhibited remarkably higher treatment effectiveness and cardiac function indices compared to the control group (p < 0.05). However, lower levels of serum biochemical indices, lower total incidence of drug toxicity, smaller number and shorter duration of angina pectoris, and lower levels of panel reactive antibodies (PRA) were observed in the study when compared to control group (p< 0.001).Conclusion: Treatment of AMI patients with the combination of ulinastatin and meglumine cAMP significantly reduces the clinical symptoms of the patients, with remarkable efficacy and high safety. Furthermore, it down-regulates serum levels of hs-CRP, cTnI and CK. Thus, the combination treatment seems superior to the conventional therapy

Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation

Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions

Easy Begun is Half Done: Spatial-Temporal Graph Modeling with ST-Curriculum Dropout

Spatial-temporal (ST) graph modeling, such as traffic speed forecasting and taxi demand prediction, is an important task in deep learning area. However, for the nodes in graph, their ST patterns can vary greatly in difficulties for modeling, owning to the heterogeneous nature of ST data. We argue that unveiling the nodes to the model in a meaningful order, from easy to complex, can provide performance improvements over traditional training procedure. The idea has its root in Curriculum Learning which suggests in the early stage of training models can be sensitive to noise and difficult samples. In this paper, we propose ST-Curriculum Dropout, a novel and easy-to-implement strategy for spatial-temporal graph modeling. Specifically, we evaluate the learning difficulty of each node in high-level feature space and drop those difficult ones out to ensure the model only needs to handle fundamental ST relations at the beginning, before gradually moving to hard ones. Our strategy can be applied to any canonical deep learning architecture without extra trainable parameters, and extensive experiments on a wide range of datasets are conducted to illustrate that, by controlling the difficulty level of ST relations as the training progresses, the model is able to capture better representation of the data and thus yields better generalization

CNTF Induces Regeneration of Cone Outer Segments in a Rat Model of Retinal Degeneration

Cone photoreceptors are responsible for color and central vision. In the late stage of retinitis pigmentosa and in geographic atrophy associated with age-related macular degeneration, cone degeneration eventually causes loss of central vision. In the present work, we investigated cone degeneration secondary to rod loss in the S334ter-3 transgenic rats carrying the rhodopsin mutation S334ter.Recombinant human ciliary neurotrophic factor (CNTF) was delivered by intravitreal injection to the left eye of an animal, and vehicle to the right eye. Eyes were harvested 10 days after injection. Cone outer segments (COS), and cell bodies were identified by staining with peanut agglutinin and cone arrestin antibodies in whole-mount retinas. For long-term treatment with CNTF, CNTF secreting microdevices were implanted into the left eyes at postnatal day (PD) 20 and control devices into the right eyes. Cone ERG was recorded at PD 160 from implanted animals. Our results demonstrate that an early sign of cone degeneration is the loss of COS, which concentrated in many small areas throughout the retina and is progressive with age. Treatment with CNTF induces regeneration of COS and thus reverses the degeneration process in early stages of cone degeneration. Sustained delivery of CNTF prevents cones from degeneration and helps them to maintain COS and light-sensing function.Loss of COS is an early sign of secondary cone degeneration whereas cell death occurs much later. At early stages, degenerating cones are capable of regenerating outer segments, indicating the reversal of the degenerative process. Sustained delivery of CNTF preserves cone cells and their function. Long-term treatment with CNTF starting at early stages of degeneration could be a viable strategy for preservation of central vision for patients with retinal degenerations

Scutellarin Ameliorates Renal Injury via Increasing CCN1 Expression and Suppressing NLRP3 Inflammasome Activation in Hyperuricemic Mice

Considerable evidences have indicated that elevated uric acid (UA) was involved in renal tubular injury leading to hyperuricemic nephropathy (HN). Scutellarin is a biologically active flavonoid derived from the Chinese traditional herb Erigeron breviscapus Hand-Mazz, which has been widely used in the treatment of cardiovascular and cerebrovascular diseases. In the present study, we analyzed the effect of scutellarin on HN, by using C57BL/6 mice and human renal tubular epithelial cell line HK-2 which was subjected to adenine/potassium oxonate and UA to mimic a HN injury. The HN mice showed a significant decrease in renal function with the increased SCr and blood urea nitrogen (BUN) (p < 0.05). Hematoxylin-eosin staining results showed a histological injury in HN mice kidney tissues with severe tubular damage. Scutellarin dose dependently alleviated the renal injury of the HN model (p < 0.05), and a dose of 20 mg/kg/day remarkably reduced the Scr level (26.10 +/- 3.23 mu mol/ml vs. 48.39 +/- 7.51 mu mol/ml, p < 0.05) and BUN (151.12 +/- 30.24 mmol/L vs. 210.43 +/- 45.67 mmol/L, p < 0.05) compared with the HN model group. Similarly, scutellarin decreased NGAL, Kim-1, cystatin C, and IL-18 protein expression levels in HN mouse (p < 0.05). Overexpressed CCN1 could not induce NLRP3 inflammasome activation, with no change of mRNA and protein expression levels of NLRP3, ASC, and pro-caspase-1 compared with the control HK-2. However, HK-2 showed a significant NLRP3 inflammasome activation and apoptosis. Importantly, knockdown of CCN1 not only aggravated NLRP3 inflammasome activation and apoptosis but also abrogated the protective effect of scutellarin in UA-induced HK-2 injury. Thus, scutellarin might alleviate HN progression via a mechanism involved in CCN1 regulation on NLRP3 inflammasome activation

Invasiveness of the Yersinia pestis ail protein contributes to host dissemination in pneumonic and oral plague

Yersinia pestis, a Gram-negative bacterium, is the etiologic agent of plague. A hallmark of Y. pestis infection is the organism's ability to rapidly disseminate through an animal host. Y. pestis expresses the outer membrane protein, Ail (Attachment invasion locus), which is associated with host invasion and serum resistance. However, whether Ail plays a role in host dissemination remains unclear. In this study, C57BL/6J mice were challenged with a defined Y. pestis strain, KimD27, or an isogenic ail-deleted mutant derived from KimD27 via metacarpal paw pad inoculation, nasal drops, orogastric infection, or tail vein injection to mimic bubonic, pneumonic, oral, or septicemic plague, respectively. Our results showed that ail-deleted Y. pestis KimD27 lost the ability to invade host cells, leading to failed host dissemination in the pneumonic and oral plague models but not in the bubonic or septicemic plague models, which do not require invasiveness. Therefore, this study demonstrated that whether Ail plays a role in Y. pestis pathogenesis depends on the infection route.Peer reviewe