Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

The prevalence, incidence and natural history of primary sclerosing cholangitis in an ethnically diverse population

<p>Abstract</p> <p>Background</p> <p>Primary sclerosing cholangitis (PSC) is a rare chronic cholestatic liver disease often associated with inflammatory bowel diseases (IBD). Current epidemiological data are limited to studies of predominantly Caucasian populations. Our aim was to define the epidemiology of PSC in a large, ethnically diverse US population.</p> <p>Methods</p> <p>The Northern California Kaiser Permanente (KP) database includes records from over 3 million people and was searched for cases of PSC between January 2000 and October 2006. All identified charts were reviewed for diagnosis confirmation, IBD co-morbidity, and major natural history endpoints.</p> <p>Results</p> <p>We identified 169 (101 males) cases fulfilling PSC diagnostic criteria with a mean age at diagnosis of 44 years (range 11-81). The age-adjusted point prevalence was 4.15 per 100,000 on December 31, 2005. The age-adjusted incidence per 100,000 person-years was not significantly greater in men 0.45 (95% CI 0.33 - 0.61) than women 0.37 (95% CI 0.26 - 0.51). IBD was present in 109/169 (64.5%) cases and was significantly more frequent in men than women with PSC (73.3% and 51.5%, respectively, p = 0.005). The cumulative average yearly mortality rate was 1.9%. Age and serum sodium, creatinine and bilirubin at diagnosis and albumin at last entry were identified as significant factors associated with death, liver transplant or cholangiocarcinoma.</p> <p>Conclusions</p> <p>The incidence and prevalence of PSC observed in a representative Northern California population are lower compared to previous studies in Caucasian populations and this might reflect differences in the incidence of PSC among various ethnic groups.</p

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente

Corporate Entrepreneurship:From Structures to Mindset

Corporate entrepreneurship dispersed throughout an organization and leveraging the entrepreneurial potential of all its employees bears significant benefits for those organizations that embrace it. However, it appears more difficult to instill and requires strong investment in the development of human capital and entrepreneurial mindset among the employees and across the organization. In this chapter, we discuss the essence of corporate entrepreneurship mindset and show that across an organization, there might be different entrepreneurial mindsets that correspond to different people, opportunities, and contexts. Although different, they all lead to enactment of entrepreneurial projects. This chapter, thus, contributes to the discussion regarding the nature of corporate entrepreneurial mindsets, and their development and stimulation within an organization, from both academic and practical view

Search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks in proton-proton collisions at root s=13TeV

A search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks is performed in proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the LHC. The analyzed data sample corresponds to an integrated luminosity of 35.9 fb(-1). The signal is characterized by a large missing transverse momentum recoiling against a bottom quark-antiquark system that has a large Lorentz boost. The number of events observed in the data is consistent with the standard model background prediction. Results are interpreted in terms of limits both on parameters of the type-2 two-Higgs doublet model extended by an additional light pseudoscalar boson a (2HDM+a) and on parameters of a baryonic Z simplified model. The 2HDM+a model is tested experimentally for the first time. For the baryonic Z model, the presented results constitute the most stringent constraints to date.Peer reviewe

A Deep Neural Network for Simultaneous Estimation of b Jet Energy and Resolution

We describe a method to obtain point and dispersion estimates for the energies of jets arising from b quarks produced in proton-proton collisions at an energy of s = 13 TeV at the CERN LHC. The algorithm is trained on a large sample of simulated b jets and validated on data recorded by the CMS detector in 2017 corresponding to an integrated luminosity of 41 fb - 1 . A multivariate regression algorithm based on a deep feed-forward neural network employs jet composition and shape information, and the properties of reconstructed secondary vertices associated with the jet. The results of the algorithm are used to improve the sensitivity of analyses that make use of b jets in the final state, such as the observation of Higgs boson decay to b b ¯

Search for the production of W^{\pm} W^{\pm} W^{\mp} events at \sqrt{s} = 13 TeV

A search for the production of events containing three W bosons predicted by the standard model is reported. The search is based on a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the CMS experiment at the CERN LHC and corresponding to a total integrated luminosity of 35.9 fb^{-1}. The search is performed in final states with three leptons (electrons or muons), or with two same-charge leptons plus two jets. The observed (expected) significance of the signal for W^{\pm} W^{\pm} W^{\mp} production is 0.60 (1.78) standard deviations, and the ratio of the measured signal yield to that expected from the standard model is 0.34_{-0.34}^{+0.62}. Limits are placed on three anomalous quartic gauge couplings and on the production of massive axionlike particles

Search for strongly interacting massive particles generating trackless jets in proton-proton collisions at s = 13 TeV

A search for dark matter in the form of strongly interacting massive particles (SIMPs) using the CMS detector at the LHC is presented. The SIMPs would be produced in pairs that manifest themselves as pairs of jets without tracks. The energy fraction of jets carried by charged particles is used as a key discriminator to suppress efficiently the large multijet background, and the remaining background is estimated directly from data. The search is performed using proton-proton collision data corresponding to an integrated luminosity of 16.1 fb - 1 , collected with the CMS detector in 2016. No significant excess of events is observed above the expected background. For the simplified dark matter model under consideration, SIMPs with masses up to 100 GeV are excluded and further sensitivity is explored towards higher masses

Combination of CMS searches for heavy resonances decaying to pairs of bosons or leptons

CMS Collaboration: et al.A statistical combination of searches for heavy resonances decaying to pairs of bosons or leptons is presented. The data correspond to an integrated luminosity of 35.9 fb collected during 2016 by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. The data are found to be consistent with expectations from the standard model background. Exclusion limits are set in the context of models of spin-1 heavy vector triplets and of spin-2 bulk gravitons. For mass-degenerate W′ and Z′ resonances that predominantly couple to the standard model gauge bosons, the mass exclusion at 95% confidence level of heavy vector bosons is extended to 4.5 TeV as compared to 3.8 TeV determined from the best individual channel. This excluded mass increases to 5.0 TeV if the resonances couple predominantly to fermions.Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 752730, and 765710 (European Union); the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias