Moduli of bundles over rational surfaces and elliptic curves I: simply laced cases

It is well-known that del Pezzo surfaces of degree $9-n$ one-to-one correspond to flat $E_n$ bundles over an elliptic curve. In this paper, we construct $ADE$ bundles over a broader class of rational surfaces which we call $ADE$ surfaces, and extend the above correspondence to all flat $G$ bundles over an elliptic curve, where $G$ is any simply laced, simple, compact and simply-connected Lie group. In the sequel, we will construct $G$ bundles for non-simply laced Lie group $G$ over these rational surfaces, and extend the above correspondence to non-simply laced cases.Comment: 22 pages, 6 figure

Regression Metric Loss: Learning a Semantic Representation Space for Medical Images

Regression plays an essential role in many medical imaging applications for estimating various clinical risk or measurement scores. While training strategies and loss functions have been studied for the deep neural networks in medical image classification tasks, options for regression tasks are very limited. One of the key challenges is that the high-dimensional feature representation learned by existing popular loss functions like Mean Squared Error or L1 loss is hard to interpret. In this paper, we propose a novel Regression Metric Loss (RM-Loss), which endows the representation space with the semantic meaning of the label space by finding a representation manifold that is isometric to the label space. Experiments on two regression tasks, i.e. coronary artery calcium score estimation and bone age assessment, show that RM-Loss is superior to the existing popular regression losses on both performance and interpretability. Code is available at https://github.com/DIAL-RPI/Regression-Metric-Loss.Comment: Accepted by MICCAI202

Polytopes, quasi-minuscule representations and rational surfaces

summary:We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural numerical conditions

Spectral Adversarial MixUp for Few-Shot Unsupervised Domain Adaptation

Domain shift is a common problem in clinical applications, where the training images (source domain) and the test images (target domain) are under different distributions. Unsupervised Domain Adaptation (UDA) techniques have been proposed to adapt models trained in the source domain to the target domain. However, those methods require a large number of images from the target domain for model training. In this paper, we propose a novel method for Few-Shot Unsupervised Domain Adaptation (FSUDA), where only a limited number of unlabeled target domain samples are available for training. To accomplish this challenging task, first, a spectral sensitivity map is introduced to characterize the generalization weaknesses of models in the frequency domain. We then developed a Sensitivity-guided Spectral Adversarial MixUp (SAMix) method to generate target-style images to effectively suppresses the model sensitivity, which leads to improved model generalizability in the target domain. We demonstrated the proposed method and rigorously evaluated its performance on multiple tasks using several public datasets.Comment: Accepted by MICCAI 202

Systematic Fusion of Multi-Source Cognitive Networks With Graph Learning - A Study on Fronto-Parietal Network

Cognitive tasks induce fluctuations in the functional connectivity between brain regions which constitute cognitive networks in the human brain. Although several cognitive networks have been identified, consensus still cannot be achieved on the precise borders and distribution of involved brain regions for each network, due to the multifarious use of diverse brain atlases in different studies. To address the problem, the current study proposed a novel approach to generate a fused cognitive network with the optimal performance in discriminating cognitive states by using graph learning, following the synthesization of one cognitive network defined by different brain atlases, and the construction of a hierarchical framework comprised of one main version and other supplementary versions of the specific cognitive network. As a result, the proposed method demonstrated better results compared with other machine learning methods for recognizing cognitive states, which was revealed by analyzing an fMRI dataset related to the mental arithmetic task. Our findings suggest that the fused cognitive network provides the potential to develop new mind decoding approaches

Integrated single-cell and bulk characterization of cuproptosis key regulator PDHB and association with tumor microenvironment infiltration in clear cell renal cell carcinoma

BackgroundRenal clear cell carcinoma (ccRCC) is one of the most prevalent cancers worldwide. Accumulating evidence revealed that copper-induced cell death played a vital role in various tumors. However, the underlying mechanism of cuproptosis with molecular heterogeneity and tumor microenvironment (TME) in ccRCC remains to be elucidated. The present study aimed to discover the biological function of cuproptosis regulators with the potential to guide clinical therapy.MethodsUsing Single-cell RNA-seq, bulk transcriptome and other multi-omics datasets, we identify essential cuproptosis-related hub gene PDHB for further study. The dysregulation of PDHB in ccRCC was characterized, together with survival outcomes, pathway enrichment and immune infiltration among tumor microenvironments. The functional significance and clinical association of PDHB was validated with loss of function experiments and surgical removal specimens.ResultsPDHB mRNA and protein expression level was significantly downregulated in ccRCC tissues compared with normal and paired normal tissues. Clinicopathological parameters and tissue microarray (TMA) indicated that PDHB was identified as a prognostic factor for survival outcomes among ccRCC patients. Additionally, low PDHB was negatively correlated with Treg cells, indicating an immunosuppressive microenvironment. Mechanistically, knockdown PDHB appeared to promote the RCC cells proliferation, migration, and invasion potentials. Subsequent studies showed that copper-induced cell death activation could overcome sunitinib resistance in RCC cells.ConclusionThis research illustrated a cuproptosis-related hub gene PDHB which could serve as a potential prognostic marker and provide therapeutic benefits for clinical treatment of ccRCC patients