Existence of solutions for fourth order differential equation with four-point boundary conditions

AbstractIn this paper we investigate the existence of solutions of a class of four-point boundary value problems for a fourth order ordinary differential equation. Our analysis relies on a nonlinear alternative of Leray–Schauder type

Corrections to LRT on Large Dimensional Covariance Matrix by RMT

In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension is large compared to the sample size. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tests to cope with high-dimensional effects. The asymptotic distributions of these corrected tests under the null are given. Simulations demonstrate that the corrected LR tests yield a realized size close to nominal level for both moderate p (around 20) and high dimension, while the traditional LR tests with chi-square approximation fails. Another contribution from the paper is that for testing the equality between two covariance matrices, the proposed correction applies equally for non-Gaussian populations yielding a valid pseudo-likelihood ratio test.Comment: 25 pages, 2 figures and 3 table

Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say $p\le 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension $p$ and a large sample size $n$. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

Dual-agonist occupancy of orexin receptor 1 and cholecystokinin A receptor heterodimers decreases G-protein-dependent signaling and migration in the human colon cancer cell line HT-29

The orexin (OX1R) and cholecystokinin A (CCK1R) receptors play opposing roles in the migration of the human colon cancer cell line HT-29, and may be involved in the pathogenesis and pathophysiology of cancer cell invasion and metastasis. OX1R and CCK1R belong to family A of the G-protein-coupled receptors (GPCRs), but the detailed mechanisms underlying their functions in solid tumor development remain unclear. In this study, we investigated whether these two receptors heterodimerize, and the results revealed novel signal transduction mechanisms. Bioluminescence and Förster resonance energy transfer, as well as proximity ligation assays, demonstrated that OX1R and CCK1R heterodimerize in HEK293 and HT-29 cells, and that peptides corresponding to transmembrane domain 5 of OX1R impaired heterodimer formation. Stimulation of OX1R and CCK1R heterodimers with both orexin-A and CCK decreased the activation of Gαq, Gαi2, Gα12, and Gα13 and the migration of HT-29 cells in comparison with stimulation with orexin-A or CCK alone, but did not alter GPCR interactions with β-arrestins. These results suggest that OX1R and CCK1R heterodimerization plays an anti-migratory role in human colon cancer cells. [Abstract copyright: Copyright © 2017. Published by Elsevier B.V.

Micro-object pose estimation with sim-to-real transfer learning using small dataset

International audience<span style="color: rgb(34, 34, 34); font-family: -apple-system, BlinkMacSystemFont, &quot;Segoe UI&quot;, Roboto, Oxygen-Sans, Ubuntu, Cantarell, &quot;Helvetica Neue&quot;, sans-serif; font-size: 18px;"&gtThree-dimensional (3D) pose estimation of micro/nano-objects isessential for the implementation of automatic manipulation inmicro/nano-robotic systems. However, out-of-plane pose estimationof a micro/nano-object is challenging, since the images aretypically obtained in 2D using a scanning electron microscope (SEM)or an optical microscope (OM). Traditional deep learning basedmethods require the collection of a large amount of labeled datafor model training to estimate the 3D pose of an object from amonocular image. Here we present a sim-to-real learning-to-matchapproach for 3D pose estimation of micro/nano-objects. Instead ofcollecting large training datasets, simulated data is generated toenlarge the limited experimental data obtained in practice, whilethe domain gap between the generated and experimental data isminimized via image translation based on a generative adversarialnetwork (GAN) model. A learning-to-match approach is used to mapthe generated data and the experimental data to a low-dimensionalspace with the same data distribution for different pose labels,which ensures effective feature embedding. Combining the labeleddata obtained from experiments and simulations, a new trainingdataset is constructed for robust pose estimation. The proposedmethod is validated with images from both SEM and OM, facilitatingthe development of closed-loop control of micro/nano-objects withcomplex shapes in micro/nano-robotic systems.</span&g

Electroacupuncture Improves Neurobehavioral Function Through Targeting of SOX2-Mediated Axonal Regeneration by MicroRNA-132 After Ischemic Stroke

Our previous studies have shown that electroacupuncture (EA) enhances neurobehavioral functional recovery after ischemic stroke, however, the underlying regulatory mechanisms remain unclear. MicroRNAs (miRNAs) are abundant in the brain and are involved in post-transcriptional gene regulation. During cerebral ischemia reperfusion, miRNAs perform numerous biological functions in the central nervous system related to regeneration and repair of damaged nerves. Our previous studies also have shown that the expression of miRNA-132 (miR-132) is obviously down-regulated after stroke by middle cerebral artery occlusion (MCAO), which can be up-regulated by EA. This study aimed to identify whether up-regulation of miR-132 by EA improved the damaged nerves after stroke and to screen the potential target of miR-132. The results showed that EA up-regulated miR-132 thus suppressing SOX2 expression in vivo after MCAO, which obviously ameliorated neurobehavioral functional recovery. Moreover, our results also suggested that up-regulated miR-132 suppressed SOX2 in primary neurons after oxygen-glucose deprivation (OGD), which promoted neurite outgrowth. In conclusion, EA enhances neurobehavioral functional recovery against ischemic stroke through targeting of SOX2-mediated axonal regeneration by miR-132