Existence theorems for a crystal surface model involving the p-Laplace operator

The manufacturing of crystal films lies at the heart of modern nanotechnology. How to accurately predict the motion of a crystal surface is of fundamental importance. Many continuum models have been developed for this purpose, including a number of PDE models, which are often obtained as the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. In this paper we offer an analytical perspective into some of these models. To be specific, we study the existence of a weak solution to the boundary value problem for the equation - \Delta e^{-\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right)}+au=f, where $p>1, a>0$ are given numbers and $f$ is a given function. This problem is derived from a crystal surface model proposed by J.L.~Marzuola and J.~Weare (2013 Physical Review, E 88, 032403). The mathematical challenge is due to the fact that the principal term in our equation is an exponential function of a p-Laplacian. Existence of a suitably-defined weak solution is established under the assumptions that $p\in(1,2], \ N\leq 4$, and $f\in W^{1,p}$. Our investigations reveal that the key to our existence assertion is how to control the set where -\mbox{div}\left(|\nabla u|^{p-2}\nabla u\right) is $\pm\infty$

Biomechanical comparison of lumbar spine instability between laminectomy and bilateral laminotomy for spinal stenosis syndrome – an experimental study in porcine model

<p>Abstract</p> <p>Background</p> <p>The association of lumbar spine instability between laminectomy and laminotomy has been clinically studied, but the corresponding <it>in vitro </it>biomechanical studies have not been reported. We investigated the hypothesis that the integrity of the posterior complex (spinous process-interspinous ligament-spinous process) plays an important role on the postoperative spinal stability in decompressive surgery.</p> <p>Methods</p> <p>Eight porcine lumbar spine specimens were studied. Each specimen was tested intact and after two decompression procedures. All posterior components were preserved in Group A (Intact). In Group B (Bilateral laminotomy), the inferior margin of L4 lamina and superior margin of L5 lamina were removed, but the L4–L5 supraspinous ligament was preserved. Fenestrations were made on both sides. In Group C (Laminectomy) the lamina and spinous processes of lower L4 and upper L5 were removed. Ligamentum flavum and supraspinous ligament of L4–L5 were removed. A hydraulic testing machine was used to generate an increasing moment up to 8400 N-mm in flexion and extension. Intervertebral displacement at decompressive level L4–L5 was measured by extensometer</p> <p>Results</p> <p>The results indicated that, under extension motion, intervertebral displacement between the specimen in intact form and at two different decompression levels did not significantly differ (<it>P </it>> 0.05). However, under flexion motion, intervertebral displacement of the laminectomy specimens at decompression level L4–L5 was statistically greater than in intact or bilateral laminotomy specimens (<it>P </it>= 0.0000963 and <it>P </it>= 0.000418, respectively). No difference was found between intact and bilateral laminotomy groups. (<it>P </it>> 0.05).</p> <p>Conclusion</p> <p>We concluded that a lumbar spine with posterior complex integrity is less likely to develop segment instability than a lumbar spine with a destroyed anchoring point for supraspinous ligament.</p

Predicting Transition Temperature of Superconductors with Graph Neural Networks

Predicting high temperature superconductors has long been a great challenge. The difficulty lies in how to predict the transition temperature (Tc) of superconductors. Although recent progress in material informatics has led to a number of machine learning models predicting Tc, prevailing models have not shown adequate generalization ability and physical rationality to find new high temperature superconductors, yet. In this work, a bond sensitive graph neural network (BSGNN) was developed to predict the Tc of various superconductors. In BSGNN, communicative message passing and graph attention methods were utilized to enhance the model's ability to process bonding and interaction information in the crystal lattice, which is crucial for the superconductivity. Consequently, our results revealed the relevance between chemical bond attributes and Tc. It indicates that shorter bond length is favored by high Tc. Meanwhile, some specific chemical elements that have relatively large van der Waals radius is favored by high Tc. It gives a convenient guidance for searching high temperature superconductors in materials database, by ruling out the materials that could never have high Tc

CR3 and Dectin-1 Collaborate in Macrophage Cytokine Response through Association on Lipid Rafts and Activation of Syk-JNK-AP-1 Pathway

Copyright: © 2015 Huang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited Acknowledgments We are grateful to the Second Core Laboratory of Research Core Facility at the National Taiwan University Hospital for confocal microscopy service and providing ultracentrifuge. We thank Dr. William E. Goldman (University of North Carolina, Chapel Hill, NC) for kindly providing WT and ags1-null mutant of H. capsulatum G186A. Funding: This work is supported by research grants 101-2320-B-002-030-MY3 from the Ministry of Science and Technology (http://www.most.gov.tw) and AS-101-TP-B06-3 from Academia Sinica (http://www.sinica.edu.tw) to BAWH. GDB is funded by research grant 102705 from Welcome Trust (http://www.wellcome.ac.uk). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD

Direction controllable linearly polarized laser from a dye-doped cholesteric liquid crystal

We demonstrate a direction controllable linearly polarized laser from a dye-doped cholesteric liquid crystal (CLC) in a homogeneous cell coated with a metallic mirror on the inner side of a glass substrate. Due to coherent superposition of two orthogonal polarization states, the output laser light becomes linearly polarized and its output energy is greatly enhanced. Moreover, the linear polarization direction angle is proportional to the product of the CLC effective birefringence and cell gap. Hence direction tunable laser devices can be demonstrated by controlling the cell gap and the operating temperature

CXCL-8 Regulates Head and Neck Carcinoma Progression through NOD Signalling Pathway

Head and neck squamous cell carcinoma (HNSCC) ranks sixth among the most common cancers in the world. Interlukin-8 (CXCL-8), a major role in inflammatory response and tumor microenvironment, correlates with tumor progression, metastasis and invasion. We explored CXCL-8 promotes tumor progression in different differentiation HNSCC cells. This project would apply to development on biomarker and target in HNSCC as well as provide a basis of early diagnosis and treatment for clinical. CXCL-8, NOD1 (nucleotide-binding oligomerization domain-containing protein 1) and receptor-interacting protein kinase (RIPK2) levels were detected statistically higher in patient tissue with HNSCC than in non-cancerous matched tissue (NCMT) in the microarray and qRT-PCR study, whereas NOD2 was weakly expressed. Similar results were obtained for CXCL-8, NOD1, NOD2 and RIP2 from RT-PCR and western blotting. High CXCL-8, NOD1 and RIP2 expressions were found on HNSCC patient tissue than that of NCMT, whereas NOD2 was weakly expressed. The analytical results indicate that CXCL-8 is required in NOD 1-mediated signalling pathways in HNSCC

The Relationship between Qi Deficiency, Cancer-related Fatigue and Quality of Life in Cancer Patients

AbstractBackgroundQi (氣 qì) refers to the vital energy of the body in Traditional Chinese medicines (TCM). Qi deficiency (氣虛 qì xū) is the most common symptom in cancer patients according to the concept of TCM. We hypothesized that cancer patients with Qi deficiency suffer from poor quality of life (QOL) and fatigue.MethodAmong the 256 registered cancer patients screened at our outpatient clinic, a total of 198 were enrolled. The inclusion criteria were (1) age between 18 and 70years, (2) cancer diagnosis confirmed by the professional physician, (3) being Chinese, and (4) Eastern Cooperative Oncology Group (ECOG) performance status rating (PSR)≤3. The major outcome is the difference in QOL score in cancer patients with and without Qi deficiency.ResultsThe initial results showed statistically significant differences in WHO-QOL scores in physical, psychological, and social domains between the groups with and without Qi deficiency as well as the groups with and without cancerrelated fatigue (CRF). All patients with CRF present were also diagnosed as Qi deficient. In addition, among the patients with no CRF, 39.9% (69/173) were diagnosed as suffering from Qi deficiency, which led to poor QOL.ConclusionsThe present study showed statistically significant difference in WHO-QOL scores in physical, psychological, and social domains between the groups with and without Qi deficiency as well as the groups with and without CRF. Cancer patients diagnosed with Qi deficiency or CRF have poor QOL. The concept of Qi deficiency in TCM might be applied to cancer health care