Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising

The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy image. The algorithm relies on the following two observations: (1) the low-index eigenvectors of the diffusion, or graph Laplacian, operators are very robust to random perturbations of the weights and random changes in the connections of the patch-graph; and (2) patches extracted from smooth regions of the image are organized along smooth low-dimensional structures in the patch-set, and therefore can be reconstructed with few eigenvectors. Experiments demonstrate that our denoising algorithm outperforms the denoising gold-standards

A skewed Kalman filter

AbstractThe popularity of state-space models comes from their flexibilities and the large variety of applications they have been applied to. For multivariate cases, the assumption of normality is very prevalent in the research on Kalman filters. To increase the applicability of the Kalman filter to a wider range of distributions, we propose a new way to introduce skewness to state-space models without losing the computational advantages of the Kalman filter operations. The skewness comes from the extension of the multivariate normal distribution to the closed skew-normal distribution. To illustrate the applicability of such an extension, we present two specific state-space models for which the Kalman filtering operations are carefully described

Simultaneous mesoscopic and two-photon imaging of neuronal activity in cortical circuits.

Spontaneous and sensory-evoked activity propagates across varying spatial scales in the mammalian cortex, but technical challenges have limited conceptual links between the function of local neuronal circuits and brain-wide network dynamics. We present a method for simultaneous cellular-resolution two-photon calcium imaging of a local microcircuit and mesoscopic widefield calcium imaging of the entire cortical mantle in awake mice. Our multi-scale approach involves a microscope with an orthogonal axis design where the mesoscopic objective is oriented above the brain and the two-photon objective is oriented horizontally, with imaging performed through a microprism. We also introduce a viral transduction method for robust and widespread gene delivery in the mouse brain. These approaches allow us to identify the behavioral state-dependent functional connectivity of pyramidal neurons and vasoactive intestinal peptide-expressing interneurons with long-range cortical networks. Our imaging system provides a powerful strategy for investigating cortical architecture across a wide range of spatial scales

Identification of immune-associated genes in diagnosing osteoarthritis with metabolic syndrome by integrated bioinformatics analysis and machine learning

BackgroundIn the pathogenesis of osteoarthritis (OA) and metabolic syndrome (MetS), the immune system plays a particularly important role. The purpose of this study was to find key diagnostic candidate genes in OA patients who also had metabolic syndrome.MethodsWe searched the Gene Expression Omnibus (GEO) database for three OA and one MetS dataset. Limma, weighted gene co-expression network analysis (WGCNA), and machine learning algorithms were used to identify and analyze the immune genes associated with OA and MetS. They were evaluated using nomograms and receiver operating characteristic (ROC) curves, and finally, immune cells dysregulated in OA were investigated using immune infiltration analysis.ResultsAfter Limma analysis, the integrated OA dataset yielded 2263 DEGs, and the MetS dataset yielded the most relevant module containing 691 genes after WGCNA, with a total of 82 intersections between the two. The immune-related genes were mostly enriched in the enrichment analysis, and the immune infiltration analysis revealed an imbalance in multiple immune cells. Further machine learning screening yielded eight core genes that were evaluated by nomogram and diagnostic value and found to have a high diagnostic value (area under the curve from 0.82 to 0.96).ConclusionEight immune-related core genes were identified (FZD7, IRAK3, KDELR3, PHC2, RHOB, RNF170, SOX13, and ZKSCAN4), and a nomogram for the diagnosis of OA and MetS was established. This research could lead to the identification of potential peripheral blood diagnostic candidate genes for MetS patients who also suffer from OA

beta-Cell function or insulin resistance was associated with the risk of type 2 diabetes among women with or without obesity and a history of gestational diabetes

Introduction To evaluate the single association of postpartum beta-cell dysfunction and insulin resistance (IR), as well as different combinations of postpartum beta-cell dysfunction, IR, obesity, and a history of gestational diabetes mellitus (GDM) with postpartum type 2 diabetes risk. Research design and methods The study included 1263 women with prior GDM and 705 women without GDM. Homeostatic model assessment was used to estimate homeostatic model assessment of beta-cell secretory function (HOMA-%beta) and homeostatic model assessment of insulin resistance (HOMA-IR). Results Multivariable-adjusted ORs of diabetes across quartiles of HOMA-%beta and HOMA-IR were 1.00, 1.46, 2.15, and 6.25 (p(trend) Conclusions beta-cell dysfunction or IR was significantly associated with postpartum diabetes. IR and beta-cell dysfunction, together with obesity and a history of GDM, had the highest ORs of postpartum diabetes risk.Peer reviewe