Is Solving Graph Neural Tangent Kernel Equivalent to Training Graph Neural Network?

A rising trend in theoretical deep learning is to understand why deep learning works through Neural Tangent Kernel (NTK) [jgh18], a kernel method that is equivalent to using gradient descent to train a multi-layer infinitely-wide neural network. NTK is a major step forward in the theoretical deep learning because it allows researchers to use traditional mathematical tools to analyze properties of deep neural networks and to explain various neural network techniques from a theoretical view. A natural extension of NTK on graph learning is \textit{Graph Neural Tangent Kernel (GNTK)}, and researchers have already provide GNTK formulation for graph-level regression and show empirically that this kernel method can achieve similar accuracy as GNNs on various bioinformatics datasets [dhs+19]. The remaining question now is whether solving GNTK regression is equivalent to training an infinite-wide multi-layer GNN using gradient descent. In this paper, we provide three new theoretical results. First, we formally prove this equivalence for graph-level regression. Second, we present the first GNTK formulation for node-level regression. Finally, we prove the equivalence for node-level regression

Query Complexity of Active Learning for Function Family With Nearly Orthogonal Basis

Many machine learning algorithms require large numbers of labeled data to deliver state-of-the-art results. In applications such as medical diagnosis and fraud detection, though there is an abundance of unlabeled data, it is costly to label the data by experts, experiments, or simulations. Active learning algorithms aim to reduce the number of required labeled data points while preserving performance. For many convex optimization problems such as linear regression and $p$-norm regression, there are theoretical bounds on the number of required labels to achieve a certain accuracy. We call this the query complexity of active learning. However, today's active learning algorithms require the underlying learned function to have an orthogonal basis. For example, when applying active learning to linear regression, the requirement is the target function is a linear composition of a set of orthogonal linear functions, and active learning can find the coefficients of these linear functions. We present a theoretical result to show that active learning does not need an orthogonal basis but rather only requires a nearly orthogonal basis. We provide the corresponding theoretical proofs for the function family of nearly orthogonal basis, and its applications associated with the algorithmically efficient active learning framework

Improved Reconstruction for Fourier-Sparse Signals

We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq k$), from minimum \emph{noisy} samples of $x(t)$ in the time domain. We present a unified framework for this problem by developing a theory of sparse Fourier transforms (SFT) for frequencies lying on a \emph{lattice}, which can be viewed as a ``semi-continuous'' version of SFT in between discrete and continuous domains. Using this framework, we obtain the following results: $\bullet$ **Dimension-free Fourier sparse recovery** We present a sample-optimal discrete Fourier Set-Query algorithm with $O(k^{\omega+1})$ reconstruction time in one dimension, \emph{independent} of the signal's length ($n$) and $\ell_\infty$-norm. This complements the state-of-art algorithm of [Kapralov, STOC 2017], whose reconstruction time is $\tilde{O}(k \log^2 n \log R^*)$, where $R^* \approx \|\hat{x}\|_\infty$ is a signal-dependent parameter, and the algorithm is limited to low dimensions. By contrast, our algorithm works for arbitrary $d$ dimensions, mitigating the $\exp(d)$ blowup in decoding time to merely linear in $d$. A key component in our algorithm is fast spectral sparsification of the Fourier basis. $\bullet$ **High-accuracy Fourier interpolation** In one dimension, we design a poly-time $(3+ \sqrt{2} +\epsilon)$-approximation algorithm for continuous Fourier interpolation. This bypasses a barrier of all previous algorithms [Price and Song, FOCS 2015, Chen, Kane, Price and Song, FOCS 2016], which only achieve $c>100$ approximation for this basic problem. Our main contribution is a new analytic tool for hierarchical frequency decomposition based on \emph{noise cancellation}

A novel high-strength large vibrating screen with duplex statically indeterminate mesh beam structure

Screening is an indispensable unit process for separation of materials. Large vibrating screen is extensively used in coal processing because of its large production capacity. In this study, a novel large vibrating screen with duplex statically indeterminate mesh beam structure (VSDSIMBS) was presented. The dynamic model of VSDSIMBS was proposed, and characteristic parameters were obtained by theoretical calculations. In order to obtain more reliable and believable research results, model of a traditional vibrating screen (TVS) with the same mass was also established for comparisons with VSDSIMBS. The finite element (FE) method was applied to study the performance of VSDSIMBS and FE analysis of VSDSIMBS and TVS was completed by using characteristic parameters. Modal analysis results indicated that VSDSIMBS could avoid the resonance and run more smoothly than TVS. Furthermore, harmonic response analysis results showed that VSDSIMBS could improve the entire stress distribution, reduce high stress areas, and increase the strength of vibrating screen. With DSIMBS, the maximum stress of vibrating screen decreased from 130.53 to 64.54 MPa. The full-scale experimental tests were performed to validate the credibility and accuracy of FE analysis results. The stress and displacements of VSDSIMBS were measured under working conditions. The test results obtained are in good agreement with simulation results, and accord with conclusions made from FE analysis

Optimal combination of MYCN differential gene and cellular senescence gene predicts adverse outcomes in patients with neuroblastoma

IntroductionNeuroblastoma (NB) is a common extracranial tumor in children and is highly heterogeneous. The factors influencing the prognosis of NB are not simple.MethodsTo investigate the effect of cell senescence on the prognosis of NB and tumor immune microenvironment, 498 samples of NB patients and 307 cellular senescence-related genes were used to construct a prediction signature.ResultsA signature based on six optimal candidate genes (TP53, IL-7, PDGFRA, S100B, DLL3, and TP63) was successfully constructed and proved to have good prognostic ability. Through verification, the signature had more advantages than the gene expression level alone in evaluating prognosis was found. Further T cell phenotype analysis displayed that exhausted phenotype PD-1 and senescence-related phenotype CD244 were highly expressed in CD8+ T cell in MYCN-amplified group with higher risk-score.ConclusionA signature constructed the six MYCN-amplified differential genes and aging-related genes can be used to predict the prognosis of NB better than using each high-risk gene individually and to evaluate immunosuppressed and aging tumor microenvironment

Human Leukocyte Antigens-B and -C Loci Associated with Posner-Schlossman Syndrome in a Southern Chinese Population

The etiology of Posner-Schlossman syndrome (PSS) remains unknown. The association of human leukocyte antigens (HLA) allelic diversity with PSS has been poorly investigated. To evaluate the association of allelic polymorphisms of class I HLA-A, -B and -C and class II HLA-DRB1 and -DQB1 with PSS, 100 unrelated patients with PSS and 128 age- and ethnically matched control subjects were recruited from a southern Chinese Han population. Polymorphisms in exons 2–4 for HLA-A, -B, -C loci, exon 2 for HLA-DRB1 and exons 2,3 for HLA-DQB1 were analyzed for association with PSS at allele and haplotype levels. The allele frequency of HLA-C*1402 in PSS patients was significantly higher than that in controls (P = 0.002, OR = 4.12). This association survived the Bonferroni correction (Pc = 0.04). The allele frequency of HLA-B*1301 in PSS patients was lower than that in the control group (P = 0.003, OR = 0.21), although this association did not survive the Bonferroni correction (Pc = 0.16). In PSS patients, the haplotype frequencies of HLA-A*1101~C*1402 and B*5101~C*1402 were higher than that in controls (P = 0.03, OR = 4.44; P = 0.02, OR = 3.20; respectively), while the HLA-B*1301~C*0304 was lower than that in controls (P = 0.007, OR = 0.23), although these associations did not survive the Bonferroni correction (Pc > 0.16). This study for the first time demonstrated that polymorphisms at the HLA-B and HLA-C loci were nominally associated with PSS in the southern Chinese Han population. Our results suggest that HLA-C*1402, A*1101~C*1402 and B*5101~C*1402 might be risk factors for PSS, whereas HLA-B*1301 plus B*1301~C*0304 might be protective factors against PSS, but even larger datasets are required to confirm these findings. Findings from this study provide valuable new clues for investigating the mechanisms and development of new diagnosis and treatment for PSS

Connection of the proto-Yangtze River to the East China Sea traced by sediment magnetic properties

The evolution of the Yangtze River, and specifically how and when it connected to the East China Sea, has been hotly debated with regard to possible linkages with the so-called ‘Cenozoic Topographic Reversal’ (tectonic tilting of continental east China in the Cenozoic) and particularly the relationship to the uplift history of the Tibetan Plateau. Resolving this key question would shed light on the development of large Asian rivers and related changes in landforms and monsoon climate during this interval. Here, we use the magnetic properties of both Plio-Quaternary sediments in the Yangtze delta and of surficial river sediments to identify a key mid-late Quaternary switch in sediment source-sink relationships. Our results reveal a fundamental shift in sediment magnetic properties at this time; the upper 145 m of sediment has magnetic mineral concentrations 5 to 10 times higher than those of the underlying late Pliocene/early Quaternary sediments. We show that the distinctive magnetic properties of the upper core sediments closely match those of surficial river sediments of the upper Yangtze basin, where the large-scale E'mei Basalt block (2.5 × 105 km2) is the dominant magnetic mineral source. This switch in sediment magnetic properties occurred at around the Jaramillo event (~ 1.2–1.0 Ma), which indicates that both the westward extension of the proto-Yangtze River into the upper basin and completion of the connection to the East China Sea occurred no later than at that age

The association of lesion eccentricity with plaque morphology and components in the superficial femoral artery: a high-spatial-resolution, multi-contrast weighted CMR study

<p>Abstract</p> <p>Background</p> <p>Atherosclerotic plaque morphology and components are predictors of subsequent cardiovascular events. However, associations of plaque eccentricity with plaque morphology and plaque composition are unclear. This study investigated associations of plaque eccentricity with plaque components and morphology in the proximal superficial femoral artery using cardiovascular magnetic resonance (CMR).</p> <p>Methods</p> <p>Twenty-eight subjects with an ankle-brachial index less than 1.00 were examined with 1.5T high-spatial-resolution, multi-contrast weighted CMR. One hundred and eighty diseased locations of the proximal superficial femoral artery (about 40 mm) were analyzed. The eccentric lesion was defined as [(Maximum wall thickness- Minimum wall thickness)/Maximum wall thickness] ≥ 0.5. The arterial morphology and plaque components were measured using semi-automatic image analysis software.</p> <p>Results</p> <p>One hundred and fifteen locations were identified as eccentric lesions and sixty-five as concentric lesions. The eccentric lesions had larger wall but similar lumen areas, larger mean and maximum wall thicknesses, and more calcification and lipid rich necrotic core, compared to concentric lesions. For lesions with the same lumen area, the degree of eccentricity was associated with an increased wall area. Eccentricity (dichotomous as eccentric or concentric) was independently correlated with the prevalence of calcification (odds ratio 3.78, 95% CI 1.47-9.70) after adjustment for atherosclerotic risk factors and wall area.</p> <p>Conclusions</p> <p>Plaque eccentricity is associated with preserved lumen size and advanced plaque features such as larger plaque burden, more lipid content, and increased calcification in the superficial femoral artery.</p

The unique immune ecosystems in pediatric brain tumors: integrating single-cell and bulk RNA-sequencing

BackgroundThe significant progress of immune therapy in non-central nervous system tumors has sparked interest in employing the same strategy for adult brain tumors. However, the advancement of immunotherapy in pediatric central nervous system (CNS) tumors is not yet on par. Currently, there is a lack of comprehensive comparative studies investigating the immune ecosystem in pediatric and adult CNS tumors at a high-resolution single-cell level.MethodsIn this study, we comprehensively analyzed over 0.3 million cells from 171 samples, encompassing adult gliomas (IDH wild type and IDH mutation) as well as four major types of pediatric brain tumors (medulloblastoma (MB), ependymoma (EPN), H3K27M-mutation (DIPG), and pediatric IDH-mutation glioma (P-IDH-M)). Our approach involved integrating publicly available and newly generated single-cell datasets. We compared the immune landscapes in different brain tumors, as well as the detailed functional phenotypes of T-cell and myeloid subpopulations. Through single-cell analysis, we identified gene sets associated with major cell types in the tumor microenvironment (gene features from single-cell data, scFes) and compared them with existing gene sets such as GSEA and xCell. The CBTTC and external GEO cohort was used to analyze and validate the immune-stromal-tumor patterns in pediatric brain tumors which might potentially respond to the immunotherapy.ResultsFrom the perspective of single-cell analysis, it was observed that major pediatric brain tumors (MB, EPN, P-IDH-M, DIPG) exhibited lower immune contents compared with adult gliomas. Additionally, these pediatric brain tumors displayed diverse immunophenotypes, particularly in regard to myeloid cells. Notably, the presence of HLA-enriched myeloid cells in MB was found to be independently associated with prognosis. Moreover, the scFes, when compared with commonly used gene features, demonstrated superior performance in independent single-cell datasets across various tumor types. Furthermore, our study revealed the existence of heterogeneous immune ecosystems at the bulk-RNA sequencing level among different brain tumor types. In addition, we identified several immune-stromal-tumor patterns that could potentially exhibit significant responses to conventional immune checkpoint inhibitors.ConclusionThe single-cell technique provides a rational path to deeply understand the unique immune ecosystem of pediatric brain tumors. In spite of the traditional attitudes of “cold” tumor towards pediatric brain tumor, the immune-stroma-tumor patterns identified in this study suggest the feasibility of immune checkpoint inhibitors and pave the way for the upcoming tide of immunotherapy in pediatric brain tumors