On the minimization of Dirichlet eigenvalues of the Laplace operator

We study the variational problem \inf \{\lambda_k(\Omega): \Omega\ \textup{open in}\ \R^m,\ |\Omega| < \infty, \ \h(\partial \Omega) \le 1 \}, where $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, \h(\partial \Omega) is the $(m-1)$- dimensional Hausdorff measure of the boundary of $\Omega$, and $|\Omega|$ is the Lebesgue measure of $\Omega$. If $m=2$, and $k=2,3, \cdots$, then there exists a convex minimiser $\Omega_{2,k}$. If $m \ge 2$, and if $\Omega_{m,k}$ is a minimiser, then $\Omega_{m,k}^*:= \textup{int}(\overline{\Omega_{m,k}})$ is also a minimiser, and $\R^m\setminus \Omega_{m,k}^*$ is connected. Upper bounds are obtained for the number of components of $\Omega_{m,k}$. It is shown that if $m\ge 3$, and $k\le m+1$ then $\Omega_{m,k}$ has at most $4$ components. Furthermore $\Omega_{m,k}$ is connected in the following cases : (i) $m\ge 2, k=2,$ (ii) $m=3,4,5,$ and $k=3,4,$ (iii) $m=4,5,$ and $k=5,$ (iv) $m=5$ and $k=6$. Finally, upper bounds on the number of components are obtained for minimisers for other constraints such as the Lebesgue measure and the torsional rigidity.Comment: 16 page

GBDTMO: as new option for early-stage breast cancer detection and classification using machine learning

Breast cancer is the second leading cause of disease death in women, after lung and bronchus cancer. According to measurements, mammography misses breast cancer in 10% to 15% of cases for women aged 50 to 69 years. In the current study, we used the Wisconsin breast cancer dataset to develop a two-stage model for breast cancer diagnosis. The main goal of this study effort is to effectively carry out feature selection and classification tasks. Gradient Boosting Decision Tree-based Mayfly Optimisation (GBDTMO), an innovative and efficient breast cancer diagnostic machine learning system, is provided. In the second stage, we employ a Mayfly search to determine which subset of traits is the best. Two more well-known datasets on breast cancer, the ICCR and the Cancer Corpus, were also compared for classification accuracy. The accuracy of the suggested GBDTMO model was higher than that of the existing GBDT and Practical Federated Gradient Boosting Decision Tree (PFGBDT), which had accuracy values of 93.25% and 94.25%, respectively. Similarly, the recall, F-measure, and ROC area values were 98.52%, 97.52%, and 96.32%, respectively. Furthermore, it demonstrated a lower RMSE of 0.98 than the existing GBDT and PFGBDT

Salvia miltiorrhiza water-soluble extract, but not its constituent salvianolic acid B, abrogates LPS-induced NF-kappaB signalling in intestinal epithelial cells

Herbal medicine has become an increasing popular therapeutic alternative among patients suffering from various inflammatory disorders. The Salvia miltiorrhizae water-soluble extract (SME) have been shown to possess antioxidant and anti-inflammatory properties in vitro. However, the mechanism of action and impact of SME on LPS-induced gene expression is still unknown. We report that SME significantly abrogated LPS-induced IκB phosphorylation/degradation, NF-κB transcriptional activity and ICAM-1 gene expression in rat IEC-18 cells. Chromatin immunoprecipitation assay demonstrated that LPS-induced RelA recruitment to the ICAM-1 gene promoter was inhibited by SME. Moreover, in vitro kinase assay showed that SME directly inhibits LPS induced IκB kinase (IKK) activity in IEC-18 cells. To investigate the physiological relevance of SME inhibitory activity on NF-κB signalling, we used small intestinal explants and primary intestinal epithelial cells derived from a transgenic mouse expressing the enhanced green fluorescent protein (EGFP) under the transcriptional control of NF-κB cis-elements (cis-NF-κBEGFP). SME significantly blocked LPS-induced EGFP expression and IκBα phosphorylation in intestinal explants and primary IECs, respectively. However, salvianolic acid B, an activate component of SME did not inhibit NF-κB transcriptional activity and IκB phosphorylation/degradation in IEC-18 cells. These results indicate that SME blocks LPS-induced NF-κB signalling pathway by targeting the IKK complex in intestinal epithelial cells. Modulation of bacterial product-mediated NF-κB signalling by natural plant extracts may represent an attractive strategy towards the prevention and treatment of intestinal inflammation

Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Changes in hemlock looper [Lepidoptera: Geometridae] pupal distribution through a 3-year outbreak cycle

La distribution des chrysalides de l’arpenteuse de la pruche, Lambdina fiscellaria, a été étudiée au cours d’un cycle épidémique d’une durée de trois ans près du Lac Princeton sur l’île d’Anticosti au Québec. Au total, 10 sapins ont été coupés et toutes les chrysalides ont été comptées sur le tronc et les branches (partie non-foliée vs foliée) de la cime inférieure, médiane et supérieure, ainsi que sur le tronc sous la cime. En condition préépidémique, les chrysalides ont principalement été trouvées sur les branches des cimes médianes et supérieures. Durant l’épidémie, la densité des chrysalides n’a pas augmenté dans ces sites de pupaison et les larves se sont surtout transformées en chrysalides sur le tronc, à partir du sol jusque dans la cime médiane, ainsi que sur les branches de la cime inférieure. Peu de chrysalides ont été trouvées sur la partie foliée des branches en période post-épidémique, la plupart étant trouvées sur la partie basale non-foliée qui apparaît comme un endroit préférentiel pour la pupaison de l'arpenteuse de la pruche. De façon à optimiser la détection des augmentations de populations dans les réseaux de surveillance, des pièges à chrysalides devraient être placés à hauteur de poitrine sur le tronc de sapins baumiers.The hemlock looper, Lambdina fiscellaria, pupal distribution was studied through a 3-year outbreak cycle near Lac Princeton on Anticosti Island in Quebec. Over the 3 years, 10 balsam fir trees were cut and all pupae were counted on the stem and branches (non-foliated vs foliated parts) of the lower, middle and upper crowns and on the stem below crown. In pre-outbreak conditions, pupae were mostly found on branches of the middle and upper crowns. During the outbreak, pupal density did not increase on these parts of the trees, since pupae were mostly found on the stem, from the ground to the middle crown, and on branches of the lower crown. Few pupae were found on the foliated portion of branches in post-outbreak conditions but most were found on the basal non-foliated part of branches, which appears to be a preferred location for hemlock looper pupation. In order to optimize detection of population increases in monitoring networks, we suggest using pupal traps at breast height on balsam fir trees

Diagnosis of tuberculosis in wildlife: a systematic review

[EN] Animal tuberculosis (TB) is a multi-host disease caused by members of the Mycobacterium tuberculosis complex (MTC). Due to its impact on economy, sanitary standards of milk and meat industry, public health and conservation, TB control is an actively ongoing research subject. Several wildlife species are involved in the maintenance and transmission of TB, so that new approaches to wildlife TB diagnosis have gained relevance in recent years. Diagnosis is a paramount step for screening, epidemiological investigation, as well as for ensuring the success of control strategies such as vaccination trials. This is the first review that systematically addresses data available for the diagnosis of TB in wildlife following the Preferred Reporting Items of Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The article also gives an overview of the factors related to host, environment, sampling, and diagnostic techniques which can affect test performance. After three screenings, 124 articles were considered for systematic review. Literature indicates that post-mortem examination and culture are useful methods for disease surveillance, but immunological diagnostic tests based on cellular and humoral immune response detection are gaining importance in wildlife TB diagnosis. Among them, serological tests are especially useful in wildlife because they are relatively inexpensive and easy to perform, facilitate large-scale surveillance and can be used both ante- and post-mortem. Currently available studies assessed test performance mostly in cervids, European badgers, wild suids and wild bovids. Research to improve diagnostic tests for wildlife TB diagnosis is still needed in order to reach accurate, rapid and cost-effective diagnostic techniques adequate to a broad range of target species and consistent over space and time to allow proper disease monitoring.SIThis work has been funded by project MYCOTRAINING SBPLY/19/180501/000174 (Junta de Castilla-La Mancha), Agencia Estatal de Investigación grant WildDriver CGL2017-89866 (MINECO, Spain and EU FEDER), project RTI2018-096010-B-C21 (MCIU and AEI; FEDER co-funded), and PCTI 2018–2020 (GRUPIN: IDI2018-000237) (Gobierno del Principado de Asturias and FEDER). J. Thomas was supported by a grant from the Indian Council of Agricultural Research-International Fellowship 2014–2015 (ICAR-IF 2014–2015)

MedZIM: Mediation analysis for Zero-Inflated Mediators with applications to microbiome data

The human microbiome can contribute to the pathogenesis of many complex diseases such as cancer and Alzheimer's disease by mediating disease-leading causal pathways. However, standard mediation analysis is not adequate in the context of microbiome data due to the excessive number of zero values in the data. Zero-valued sequencing reads, commonly observed in microbiome studies, arise for technical and/or biological reasons. Mediation analysis approaches for analyzing zero-inflated mediators are still lacking largely because of challenges raised by the zero-inflated data structure: (a) disentangling the mediation effect induced by the point mass at zero; and (b) identifying the observed zero-valued data points that are actually not zero (i.e., false zeros). We develop a novel mediation analysis method under the potential-outcomes framework to fill this gap. We show that the mediation effect of the microbiome can be decomposed into two components that are inherent to the two-part nature of zero-inflated distributions. The first component corresponds to the mediation effect attributable to a unit-change over the positive relative abundance and the second component corresponds to the mediation effect attributable to discrete binary change of the mediator from zero to a non-zero state. With probabilistic models to account for observing zeros, we also address the challenge with false zeros. A comprehensive simulation study and the applications in two real microbiome studies demonstrate that our approach outperforms existing mediation analysis approaches.Comment: Corresponding: Zhigang L

Gut microbiota and probiotics in colon tumorigenesis

The human gastrointestinal tract harbors a complex and abundant microbial community reaching as high as 1013–1014 microorganisms in the colon. This endogenous microbiota forms a symbiotic relationship with their eukaryotic host and this close partnership helps maintain homeostasis by performing essential and non-redundant tasks (e.g. nutrition/energy and, immune system balance, pathogen exclusion). Although this relationship is essential and beneficial to the host, various events (e.g. infection, diet, stress, inflammation) may impact microbial composition, leading to the formation of a dysbiotic microbiota, further impacting on health and disease states. For example, Crohn’s disease and ulcerative colitis, collectively termed inflammatory bowel diseases (IBD), have been associated with the establishment of a dysbiotic microbiota. In addition, extra-intestinal disorders such as obesity and metabolic syndrome are also associated with the development of a dysbiotic microbiota. Consequently, there is an increasing interest in harnessing the power of the microbiome and modulating its composition as a means to alleviate intestinal pathologies/disorders and maintain health status. In this review we will discuss the emerging relationship between the microbiota and development of colorectal cancer as well as present evidence that microbial manipulation (probiotic, prebiotic) impacts disease development

Toll-Like Receptor 9-Dependent Macrophage Activation by Entamoeba histolytica DNA

Activation of the innate immune system by bacterial DNA and DNA of other invertebrates represents a pathogen recognition mechanism. In this study we investigated macrophage responses to DNA from the intestinal protozoan parasite Entamoeba histolytica. E. histolytica genomic DNA was purified from log-phase trophozoites and tested with the mouse macrophage cell line RAW 264.7. RAW cells treated with E. histolytica DNA demonstrated an increase in levels of tumor necrosis factor alpha (TNF-α) mRNA and protein production. TNF-α production was blocked by pretreatment with chloroquine or monensin. In fact, an NF-κB luciferase reporter assay in HEK cells transfected with human TLR9 demonstrated that E. histolytica DNA signaled through Toll-like receptor 9 (TLR9) in a manner similar to that seen with CpG-ODN. Immunofluorescence assays confirmed NF-κB activation in RAW cells, as seen by nuclear translocation of the p65 subunit. Western blot analysis demonstrated mitogen-activated protein kinase activation by E. histolytica DNA. E. histolytica DNA effects were abolished in MYD88−/− mouse-derived macrophages. In the context of disease, immunization with E. histolytica DNA protected gerbils from an E. histolytica challenge infection. Taken together, these results demonstrate that E. histolytica DNA is recognized by TLR9 to activate macrophages and may provide an innate defense mechanism characterized by the induction of the inflammatory mediator TNF-α