On the crossing numbers of Km□Cn and Km,l□Pn

AbstractRingeisen and Beineke have proved that cr(C3□Cn)=n and cr(K4□Cn)=3n. Bokal has proved that cr(K1,l□Pn)=(n-1)⌊l2⌋⌊l-12⌋. In this paper we study the crossing numbers of Km□Cn and Km,l□Pn, and show (i) cr(Km□Cn)⩾n·cr(Km+2) for n⩾3 and m⩾5; (ii) cr(Km□Cn)⩽n4⌊m+22⌋⌊m+12⌋⌊m2⌋⌊m-12⌋ for m=5,6,7 and for m⩾8 with even n⩾4, and equality holds for m=5,6,7 and for m=8,9,10 with even n⩾4 and (iii) cr(Km,l□Pn)⩽(n-1)(⌊m+22⌋⌊m+12⌋⌊l+22⌋⌊l+12⌋-ml)+2(⌊m+12⌋⌊m2⌋⌊l+12⌋⌊l2⌋-⌊m2⌋⌊l2⌋) for min(m,l)⩾2, and equality holds for min(m,l)=2

Combined effects of colonial size and concentration of Microcystis aeruginosa on the life history traits of Daphnia similoides

Microcystis colonial size and concentration have detrimental effects on life history traits of Daphnia, but their detailed interactions have remained unclear so far. Our experiments show that the interaction between Microcystis colonial size and concentration on maturation time, life expectancy, net reproductive rate and innate capacity of increase in Daphnia similoides was significant. In all groups, the survival rate of D. similoides was 100% within 8 days. This value then declined quickly in the large-colony groups and in the SH group of Microcystis. Colonial M. aeruginosa significantly reduced the maturation time and body length at maturity of D. similoides. The number of offspring at first reproduction per female in the SH group of Microcystis was significantly higher than those in other groups. Net reproductive rate of D. similoides in the SL group of Microcystis was significantly higher than those in other groups of Microcystis. The innate capacity of increase of D. similoides in small-colony Microcystis groups was significantly higher than that in the large-colony groups. The results suggested that the effect of smallcolony Microcystis on the reproduction of Daphnia was positive under lower concentration, while their toxicity was intensitied under higher concentration when small-colony Microcystis were by Daphnia as food

HB-PLS: A statistical method for identifying biological process or pathway regulators by integrating Huber loss and Berhu penalty with partial least squares regression

Gene expression data features high dimensionality, multicollinearity, and non-Gaussian distribution noise, posing hurdles for identification of true regulatory genes controlling a biological process or pathway. In this study, we integrated the Huber loss function and the Berhu penalty (HB) into partial least squares (PLS) framework to deal with the high dimension and multicollinearity property of gene expression data, and developed a new method called HB-PLS regression to model the relationships between regulatory genes and pathway genes. To solve the Huber-Berhu optimization problem, an accelerated proximal gradient descent algorithm with at least 10 times faster than the general convex optimization solver (CVX), was developed. Application of HB-PLS to recognize pathway regulators of lignin biosynthesis and photosynthesis in Arabidopsis thaliana led to the identification of many known positive pathway regulators that had previously been experimentally validated. As compared to sparse partial least squares (SPLS) regression, an efficient method for variable selection and dimension reduction in handling multicollinearity, HB-PLS has higher efficacy in identifying more positive known regulators, a much higher but slightly less sensitivity/(1-specificity) in ranking the true positive known regulators to the top of the output regulatory gene lists for the two aforementioned pathways. In addition, each method could identify some unique regulators that cannot be identified by the other methods. Our results showed that the overall performance of HB-PLS slightly exceeds that of SPLS but both methods are instrumental for identifying real pathway regulators from high-throughput gene expression data, suggesting that integration of statistics, machine leaning and convex optimization can result in a method with high efficacy and is worth further exploration

TGMI: an efficient algorithm for identifying pathway regulators through evaluation of triple-gene mutual interaction

Despite their important roles, the regulators for most metabolic pathways and biological processes remain elusive. Presently, the methods for identifying metabolic pathway and biological process regulators are intensively sought after. We developed a novel algorithm called triple-gene mutual interaction (TGMI) for identifying these regulators using high-throughput gene expression data. It first calculated the regulatory interactions among triple gene blocks (two pathway genes and one transcription factor (TF)), using conditional mutual information, and then identifies significantly interacted triple genes using a newly identified novel mutual interaction measure (MIM), which was substantiated to reflect strengths of regulatory interactions within each triple gene block. The TGMI calculated the MIM for each triple gene block and then examined its statistical significance using bootstrap. Finally, the frequencies of all TFs present in all significantly interacted triple gene blocks were calculated and ranked. We showed that the TFs with higher frequencies were usually genuine pathway regulators upon evaluating multiple pathways in plants, animals and yeast. Comparison of TGMI with several other algorithms demonstrated its higher accuracy. Therefore, TGMI will be a valuable tool that can help biologists to identify regulators of metabolic pathways and biological processes from the exploded high-throughput gene expression data in public repositories

Winding Clearness for Differentiable Point Cloud Optimization

We propose to explore the properties of raw point clouds through the \emph{winding clearness}, a concept we first introduce for assessing the clarity of the interior/exterior relationships represented by the winding number field of the point cloud. In geometric modeling, the winding number is a powerful tool for distinguishing the interior and exterior of a given surface $\partial \Omega$, and it has been previously used for point normal orientation and surface reconstruction. In this work, we introduce a novel approach to assess and optimize the quality of point clouds based on the winding clearness. We observe that point clouds with reduced noise tend to exhibit improved winding clearness. Accordingly, we propose an objective function that quantifies the error in winding clearness, solely utilizing the positions of the point clouds. Moreover, we demonstrate that the winding clearness error is differentiable and can serve as a loss function in optimization-based and learning-based point cloud processing. In the optimization-based method, the loss function is directly back-propagated to update the point positions, resulting in an overall improvement of the point cloud. In the learning-based method, we incorporate the winding clearness as a geometric constraint in the diffusion-based 3D generative model. Experimental results demonstrate the effectiveness of optimizing the winding clearness in enhancing the quality of the point clouds. Our method exhibits superior performance in handling noisy point clouds with thin structures, highlighting the benefits of the global perspective enabled by the winding number

Bottom-up GGM algorithm for constructing multilayered hierarchical gene regulatory networks that govern biological pathways or processes

Background: Multilayered hierarchical gene regulatory networks (ML-hGRNs) are very important for understanding genetics regulation of biological pathways. However, there are currently no computational algorithms available for directly building ML-hGRNs that regulate biological pathways. Results: A bottom-up graphic Gaussian model (GGM) algorithm was developed for constructing ML-hGRN operating above a biological pathway using small- to medium-sized microarray or RNA-seq data sets. The algorithm first placed genes of a pathway at the bottom layer and began to construct an ML-hGRN by evaluating all combined triple genes: two pathway genes and one regulatory gene. The algorithm retained all triple genes where a regulatory gene significantly interfered two paired pathway genes. The regulatory genes with highest interference frequency were kept as the second layer and the number kept is based on an optimization function. Thereafter, the algorithm was used recursively to build a ML-hGRN in layer-by-layer fashion until the defined number of layers was obtained or terminated automatically. Conclusions: We validated the algorithm and demonstrated its high efficiency in constructing ML-hGRNs governing biological pathways. The algorithm is instrumental for biologists to learn the hierarchical regulators associated with a given biological pathway from even small-sized microarray or RNA-seq data sets

Differential and Prognostic Significance of HOXB7 in Gliomas

Diffuse glioma is the most common primary tumor of the central nervous system. The prognosis of the individual tumor is heavily dependent on its grade and subtype. Homeobox B7 (HOXB7), a member of the homeobox family, is abnormally overexpressed in a variety of tumors. However, its function in glioma is unclear. In this study, HOXB7 mRNA and protein expression levels were analyzed in 401 gliomas from the CGGA RNA-seq database (325 cases) and our hospital (76 cases). HOXB7 expression, at both mRNA and protein levels, were upregulated in glioblastoma (GBM) and isocitrate dehydrogenase 1 (IDH1) wild-type glioma tissues. Kaplan–Meier with log-rank test showed that patients with high HOXB7 expression had a poor prognosis (p < 0.0001). Moreover, HOXB7 protein was deleted in 90.9% (20/22) of oligodendrogliomas and 13.0% (3/23) of astrocytomas. The sensitivity and specificity of HOXB7 protein deletion in oligodendroglioma were 90.9% (20/22) and 87.0% (20/23), respectively. To verify the reliability of using HOXB7 in differentiating oligodendroglioma, we used 1p/19q fluorescence in situ hybridization (FISH) testing as a positive control. The Cohen’s kappa coefficient of HOXB7 immunohistochemistry staining and 1p/19q FISH testing was 0.778 (95% CI: 0.594–0.962, p < 0.001). In conclusion, HOXB7 is an independent predictor of poor prognosis in all grade gliomas. Additionally, HOXB7 is also a highly sensitive and specific indicator to differentiate oligodendroglioma from astrocytoma

Disentangling the effects of vapor pressure deficit on northern terrestrial vegetation productivity

The impact of atmospheric vapor pressure deficit (VPD) on plant photosynthesis has long been acknowledged, but large interactions with air temperature (T) and soil moisture (SM) still hinder a complete understanding of the influence of VPD on vegetation production across various climate zones. Here, we found a diverging response of productivity to VPD in the Northern Hemisphere by excluding interactive effects of VPD with T and SM. The interactions between VPD and T/SM not only offset the potential positive impact of warming on vegetation productivity but also amplifies the negative effect of soil drying. Notably, for high-latitude ecosystems, there occurs a pronounced shift in vegetation productivity\u27s response to VPD during the growing season when VPD surpasses a threshold of 3.5 to 4.0 hectopascals. These results yield previously unknown insights into the role of VPD in terrestrial ecosystems and enhance our comprehension of the terrestrial carbon cycle\u27s response to global warming

TELEX HEBDOMADAIRE NR 95 DU 17.09.82 DESTINE A L'ENSEMBLE DES DELEGATIONS EXTERIEURES ET BUREAUX DE PRESS ET D'INFORMATION INDEPENDANTS DANS LES PAYS TIERS = WEEKLY MEMO NO. 95 FOR 17.09.82 TO FOREIGN DELEGATIONS AND PRESS BUREAUS OF THIRD COUNTRIES

<p>High-performance liquid chromatography (HPLC) results of (A) commercial surfactin sample, and (B) our extract surfactin of <i>B</i>. <i>subtilis</i> HH2 in LB medium. There were three main peaks (Peak A-C) of the extract and the surfactin standard in the same location.</p

Cross-talk between PRMT1-mediated methylation and ubiquitylation on RBM15 controls RNA splicing

RBM15, an RNA binding protein, determines cell-fate specification of many tissues including blood. We demonstrate that RBM15 is methylated by protein arginine methyltransferase 1 (PRMT1) at residue R578 leading to its degradation via ubiquitylation by an E3 ligase (CNOT4). Overexpression of PRMT1 in acute megakaryocytic leukemia cell lines blocks megakaryocyte terminal differentiation by downregulation of RBM15 protein level. Restoring RBM15 protein level rescues megakaryocyte terminal differentiation blocked by PRMT1 overexpression. At the molecular level, RBM15 binds to pre-mRNA intronic regions of genes important for megakaryopoiesis such as GATA1, RUNX1, TAL1 and c-MPL. Furthermore, preferential binding of RBM15 to specific intronic regions recruits the splicing factor SF3B1 to the same sites for alternative splicing. Therefore, PRMT1 regulates alternative RNA splicing via reducing RBM15 protein concentration. Targeting PRMT1 may be a curative therapy to restore megakaryocyte differentiation for acute megakaryocytic leukemia