Total Positivity of the Cubic Trigonometric Bézier Basis

Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009) forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm

Competition-cooperation mechanism between Escherichia coli and Staphylococcus aureus based on systems mapping

IntroductionInterspecies interactions are a crucial driving force of species evolution. The genes of each coexisting species play a pivotal role in shaping the structure and function within the community, but how to identify them at the genome-wide level has always been challenging.MethodsIn this study, we embed the Lotka-Volterra ordinary differential equations in the theory of community ecology into the systems mapping model, so that this model can not only describe how the quantitative trait loci (QTL) of a species directly affects its own phenotype, but also describe the QTL of the species how to indirectly affect the phenotype of its interacting species, and how QTL from different species affects community behavior through epistatic interactions.ResultsBy designing and implementing a co-culture experiment for 100 pairs of Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus), we mapped 244 significant QTL combinations in the interaction process of the two bacteria using this model, including 69 QTLs from E. coli and 59 QTLs from S. aureus, respectively. Through gene annotation, we obtained 57 genes in E. coli, among which the genes with higher frequency were ypdC, nrfC, yphH, acrE, dcuS, rpnE, and ptsA, while we obtained 43 genes in S. aureus, among which the genes with higher frequency were ebh, SAOUHSC_00172, capF, gdpP, orfX, bsaA, and phnE1.DiscussionBy dividing the overall growth into independent growth and interactive growth, we could estimate how QTLs modulate interspecific competition and cooperation. Based on the quantitative genetic model, we can obtain the direct genetic effect, indirect genetic effect, and genome-genome epistatic effect related to interspecific interaction genes, and then further mine the hub genes in the QTL networks, which will be particularly useful for inferring and predicting the genetic mechanisms of community dynamics and evolution. Systems mapping can provide a tool for studying the mechanism of competition and cooperation among bacteria in co-culture, and this framework can lay the foundation for a more comprehensive and systematic study of species interactions

Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a C1 positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the G1 continuous conditions are deduced for the joining of two patches

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at root s=13 TeV

Peer reviewe

Performance of the CMS muon trigger system in proton-proton collisions at √s = 13 TeV

The muon trigger system of the CMS experiment uses a combination of hardware and software to identify events containing a muon. During Run 2 (covering 2015-2018) the LHC achieved instantaneous luminosities as high as 2 × 10 cm s while delivering proton-proton collisions at √s = 13 TeV. The challenge for the trigger system of the CMS experiment is to reduce the registered event rate from about 40 MHz to about 1 kHz. Significant improvements important for the success of the CMS physics program have been made to the muon trigger system via improved muon reconstruction and identification algorithms since the end of Run 1 and throughout the Run 2 data-taking period. The new algorithms maintain the acceptance of the muon triggers at the same or even lower rate throughout the data-taking period despite the increasing number of additional proton-proton interactions in each LHC bunch crossing. In this paper, the algorithms used in 2015 and 2016 and their improvements throughout 2017 and 2018 are described. Measurements of the CMS muon trigger performance for this data-taking period are presented, including efficiencies, transverse momentum resolution, trigger rates, and the purity of the selected muon sample. This paper focuses on the single- and double-muon triggers with the lowest sustainable transverse momentum thresholds used by CMS. The efficiency is measured in a transverse momentum range from 8 to several hundred GeV

Measurement of the W gamma Production Cross Section in Proton-Proton Collisions at root s=13 TeV and Constraints on Effective Field Theory Coefficients

A fiducial cross section for W gamma production in proton-proton collisions is measured at a center-of-mass energy of 13 TeV in 137 fb(-1) of data collected using the CMS detector at the LHC. The W -> e nu and mu nu decay modes are used in a maximum-likelihood fit to the lepton-photon invariant mass distribution to extract the combined cross section. The measured cross section is compared with theoretical expectations at next-to-leading order in quantum chromodynamics. In addition, 95% confidence level intervals are reported for anomalous triple-gauge couplings within the framework of effective field theory.Peer reviewe

Search for top squark production in fully hadronic final states in proton-proton collisions at root s=13 TeV

A search for production of the supersymmetric partners of the top quark, top squarks, is presented. The search is based on proton-proton collision events containing multiple jets, no leptons, and large transverse momentum imbalance. The data were collected with the CMS detector at the CERN LHC at a center-of-mass energy of 13 TeV, and correspond to an integrated luminosity of 137 fb(-1). The targeted signal production scenarios are direct and gluino-mediated top squark production, including scenarios in which the top squark and neutralino masses are nearly degenerate. The search utilizes novel algorithms based on deep neural networks that identify hadronically decaying top quarks and W bosons, which are expected in many of the targeted signal models. No statistically significant excess of events is observed relative to the expectation from the standard model, and limits on the top squark production cross section are obtained in the context of simplified supersymmetric models for various production and decay modes. Exclusion limits as high as 1310 GeVare established at the 95% confidence level on the mass of the top squark for direct top squark production models, and as high as 2260 GeV on the mass of the gluino for gluino-mediated top squark production models. These results represent a significant improvement over the results of previous searches for supersymmetry by CMS in the same final state.Peer reviewe