Positivity of Δ\Delta-genera for connected polarized demi-normal schemes

In this paper, we show that the $\Delta$-genus $\Delta(X,\mathcal{L})\ge 0$ for any connected polarized demi-normal scheme $(X,\mathcal{L})$. As a direct corollary, we obtain $\Delta(X,K_X+\Lambda)\ge 0$ for any Gorenstein stable log scheme $(X,\Lambda)$, which is an inequality of Noether's type.Comment: 6 page

Does generalization performance of lql^q regularization learning depend on qq? A negative example

$l^q$-regularization has been demonstrated to be an attractive technique in machine learning and statistical modeling. It attempts to improve the generalization (prediction) capability of a machine (model) through appropriately shrinking its coefficients. The shape of a $l^q$ estimator differs in varying choices of the regularization order $q$. In particular, $l^1$ leads to the LASSO estimate, while $l^{2}$ corresponds to the smooth ridge regression. This makes the order $q$ a potential tuning parameter in applications. To facilitate the use of $l^{q}$-regularization, we intend to seek for a modeling strategy where an elaborative selection on $q$ is avoidable. In this spirit, we place our investigation within a general framework of $l^{q}$-regularized kernel learning under a sample dependent hypothesis space (SDHS). For a designated class of kernel functions, we show that all $l^{q}$ estimators for $0< q < \infty$ attain similar generalization error bounds. These estimated bounds are almost optimal in the sense that up to a logarithmic factor, the upper and lower bounds are asymptotically identical. This finding tentatively reveals that, in some modeling contexts, the choice of $q$ might not have a strong impact in terms of the generalization capability. From this perspective, $q$ can be arbitrarily specified, or specified merely by other no generalization criteria like smoothness, computational complexity, sparsity, etc..Comment: 35 pages, 3 figure

Computational illumination for high-speed in vitro Fourier ptychographic microscopy

We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or high resolution, not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixel-scale image having both wide FOV and high resolution, i.e. large space-bandwidth product (SBP). FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (on the order of minutes), limiting throughput. Faster capture times would not only improve imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g. pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4x FOV with sub-second capture times. We propose an improved algorithm and new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time

On canonical bundle formula for fibrations of curves with arithmetic genus one

In this paper, we develop canonical bundle formulas for fibrations of relative dimension one in characteristic $p>0$. For such a fibration from a log pair $f\colon (X, \Delta) \to S$, if $f$ is separable, we can obtain a formula similar to the one due to Witaszek \cite{Wit21}; if $f$ is inseparable, we treat the case when $S$ is of maximal Albanese dimension. As an application, we prove that for a klt pair $(X,\Delta)$ with $-(K_X+\Delta)$ nef, if the Albanese morphism $a_X\colon X \to A$ is of relative dimension one, then $X$ is a fiber space over $A$

PUMA amplifies necroptosis signaling by activating cytosolic DNA sensors.

Necroptosis, a form of regulated necrotic cell death, is governed by RIP1/RIP3-mediated activation of MLKL. However, the signaling process leading to necroptotic death remains to be elucidated. In this study, we found that PUMA, a proapoptotic BH3-only Bcl-2 family member, is transcriptionally activated in an RIP3/MLKL-dependent manner following induction of necroptosis. The induction of PUMA, which is mediated by autocrine TNF-α and enhanced NF-κB activity, contributes to necroptotic death in RIP3-expressing cells with caspases inhibited. On induction, PUMA promotes the cytosolic release of mitochondrial DNA and activation of the DNA sensors DAI/Zbp1 and STING, leading to enhanced RIP3 and MLKL phosphorylation in a positive feedback loop. Furthermore, deletion of PUMA partially rescues necroptosis-mediated developmental defects in FADD-deficient embryos. Collectively, our results reveal a signal amplification mechanism mediated by PUMA and cytosolic DNA sensors that is involved in TNF-driven necroptotic death in vitro and in vivo

CT-based radiomic phenotypes of lung adenocarcinoma: a preliminary comparative analysis with targeted next-generation sequencing

ObjectivesThis study aimed to explore the relationship between computed tomography (CT)-based radiomic phenotypes and genomic profiles, including expression of programmed cell death-ligand 1 (PD-L1) and the 10 major genes, such as epidermal growth factor receptor (EGFR), tumor protein 53 (TP53), and Kirsten rat sarcoma viral oncogene (KRAS), in patients with lung adenocarcinoma (LUAD).MethodsIn total, 288 consecutive patients with pathologically confirmed LUAD were enrolled in this retrospective study. Radiomic features were extracted from preoperative CT images, and targeted genomic data were profiled through next-generation sequencing. PD-L1 expression was assessed by immunohistochemistry staining (chi-square test or Fisher's exact test for categorical data and the Kruskal–Wallis test for continuous data). A total of 1,013 radiomic features were obtained from each patient's CT images. Consensus clustering was used to cluster patients on the basis of radiomic features.ResultsThe 288 patients were classified according to consensus clustering into four radiomic phenotypes: Cluster 1 (n = 11) involving mainly large solid masses with a maximum diameter of 5.1 ± 2.0 cm; Clusters 2 and 3 involving mainly part-solid and solid masses with maximum diameters of 2.1 ± 1.4 cm and 2.1 ± 0.9 cm, respectively; and Cluster 4 involving mostly small ground-glass opacity lesions with a maximum diameter of 1.0 ± 0.9 cm. Differences in maximum diameter, PD-L1 expression, and TP53, EGFR, BRAF, ROS1, and ERBB2 mutations among the four clusters were statistically significant. Regarding targeted therapy and immunotherapy, EGFR mutations were highest in Cluster 2 (73.1%); PD-L1 expression was highest in Cluster 1 (45.5%).ConclusionOur findings provide evidence that CT-based radiomic phenotypes could non-invasively identify LUADs with different molecular characteristics, showing the potential to provide personalized treatment decision-making support for LUAD patients

Combining high-throughput micro-CT-RGB phenotyping and genome-wide association study to dissect the genetic architecture of tiller growth in rice

Manual phenotyping of rice tillers is time consuming and labor intensive and lags behind the rapid development of rice functional genomics. Thus, automated, non-destructive phenotyping of rice tiller traits at a high spatial resolution and high-throughput for large-scale assessment of rice accessions is urgently needed. In this study, we developed a high-throughput micro-CT-RGB (HCR) imaging system to non-destructively extract 730 traits from 234 rice accessions at 9 time points. We could explain 30% of the grain yield variance from 2 tiller traits assessed in the early growth stages. A total of 402 significantly associated loci were identified by GWAS, and dynamic and static genetic components were found across the nine time points. A major locus associated with tiller angle was detected at nine time points, which contained a major gene TAC1. Significant variants associated with tiller angle were enriched in the 3'-UTR of TAC1. Three haplotypes for the gene were found and rice accessions containing haplotype H3 displayed much smaller tiller angles. Further, we found two loci contained associations with both vigor-related HCR traits and yield. The superior alleles would be beneficial for breeding of high yield and dense planting