A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariant of 3d Manifolds I

We use the Chern-Simons quantum field theory in order to prove a recently conjectured limitation on the 1/K expansion of the Jones polynomial of a knot and its relation to the Alexander polynomial. This limitation allows us to derive a surgery formula for the loop corrections to the contribution of the trivial connection to Witten's invariant. The 2-loop part of this formula coincides with Walker's surgery formula for Casson-Walker invariant. This proves a conjecture that Casson-Walker invariant is a 2-loop correction to the trivial connection contribution to Witten's invariant of a rational homology sphere. A contribution of the trivial connection to Witten's invariant of a manifold with nontrivial rational homology is calculated for the case of Seifert manifolds.Comment: 28 page

Search for resonant and nonresonant new phenomena in high-mass dilepton final states at root s=13 TeV

A search is presented for physics beyond the standard model (SM) using electron or muon pairs with high invariant mass. A data set of proton-proton collisions collected by the CMS experiment at the LHC at root s = 13 TeV from 2016 to 2018 corresponding to a total integrated luminosity of up to 140 fb(-1) is analyzed. No significant deviation is observed with respect to the SM background expectations. Upper limits are presented on the ratio of the product of the production cross section and the branching fraction to dileptons of a new narrow resonance to that of the Z boson. These provide the most stringent lower limits to date on the masses for various spin-1 particles, spin-2 gravitons in the Randall-Sundrum model, as well as spin-1 mediators between the SM and dark matter particles. Lower limits on the ultraviolet cutoff parameter are set both for four-fermion contact interactions and for the Arkani-Hamed, Dimopoulos, and Dvali model with large extra dimensions. Lepton flavor universality is tested at the TeV scale for the first time by comparing the dimuon and dielectron mass spectra. No significant deviation from the SM expectation of unity is observed.Peer reviewe

Mechanism of accommodation assessed by change in precisely registered ocular images associated with concurrent change in auto-refraction

Purpose: Our purpose was to determine the changes in anterior chamber depth (ACD) and central lens thickness (CLT) during pharmacologically induced accommodation. Methods: Following pupillary dilation with phenylephrine 10%, baseline auto-refractions and swept-source optical coherence tomographic biometric images (Zeiss IOLMaster 700) were obtained from the right eyes of 25 subjects aged 19 to 24 years. Pilocarpine 4% and phenylephrine 10% were then instilled into these right eyes. One hour later, auto-refractions and biometric imaging were repeated. Only data from eight of 25 subjects met the following stringent criteria to be included in the study analysis: pre and post-pilocarpine biometric foveal images were registerable, the images of the corneal centers were shifted by ≤100 μm, pupils >5 mm and the pharmacologically induced refractive change was ≥ −7 diopters. Results: The mean auto-refractive accommodative change for the eight included subjects was −12.45 diopters (± 3.45 diopters). The mean change in CLT was 81 μm (± 54 μm) and the mean change in ACD was −145 μm (± 86 μm). Superimposition of the registered pre and post-pilocarpine biometric images of the sagittal sections of the whole eye from each subject demonstrated that the position of the whole lens did not shift either anteriorly, posteriorly or vertically during pharmacologically induced accommodation. Conclusions: A small increase in lens thickness was associated with a large change in accommodative amplitude and no significant change in lens position as predicted by the Schachar theory

Niche plasticity in invasive fishes in the Great Lakes

© 2015, Springer International Publishing Switzerland. The geographic range of an invasive species is a key determinant of relative impact in the invaded region. Comparison of invasive species that are widespread or rare in invaded ranges can highlight mechanistic traits that determine the risk of impact from invasion. Round Goby (Neogobius melanostomus) is more geographically widespread and abundant than Tubenose Goby (Proterorhinus semilunaris) across invaded ranges of the Laurentian Great Lakes. We used stable isotopes of carbon (δ13C) and nitrogen (δ15N) in liver and muscle to contrast the isotopic niche breadth and niche plasticity of Round Goby and Tubenose Goby near the inflow and outflow of Lake St. Clair and in western Lake Superior. At all sites, Round Goby and Tubenose Goby that matched in size (21–53 mm standard length) had distinct isotopic niches with no overlap, driven by higher δ15N in Round Goby. The variation in isotopic niche, and the mean difference in δ13C and δ15N between muscle and liver, was greater for Round Goby, suggesting both greater seasonal shifts in diet and niche plasticity in this more widely established invader. Round Goby that were significantly larger than Tubenose Goby had broader isotopic niches and greater niche plasticity in the majority of cases and this was associated with isotopic niche overlap with smaller Round Goby and Tubenose Goby. Our findings suggest that a broad and plastic isotopic niche provides scope for wider establishment range in invasive fish species