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Reconstructing the history of polar temperature from ice core water isotope (δ¹⁸O) calibration has remained a challenge in paleoclimate research, because of our incomplete understanding of various temperature–δ¹⁸O relationships. This paper resolves this classical problem in a new framework called the unified slope equations (USE), which illustrates the general relations among spatial and temporalδ¹⁸O–surface temperature slopes. The USE is applied to the Antarctica temperature change during the last deglaciation in model simulations and observations. It is shown that the comparable Antarctica-mean spatial slope with deglacial temporal slope inδ¹⁸O–surface temperature reconstruction is caused, accidentally, by the compensation responses between theδ¹⁸O–inversion layer temperature relation and the inversion layer temperature itself. Furthermore, in light of the USE, we propose that the present seasonal slope ofδ¹⁸O–inversion layer temperature is an optimal paleothermometer that is more accurate and robust than the spatial slope. This optimal slope suggests the possibility of reconstructing past Antarctic temperature changes using present and future instrumental observations.

A description is presented of the algorithms used to reconstruct energy deposited in the CMS hadron calorimeter during Run 2 (2015–2018) of the LHC. During Run 2, the characteristic bunch-crossing spacing for proton-proton collisions was 25 ns, which resulted in overlapping signals from adjacent crossings. The energy corresponding to a particular bunch crossing of interest is estimated using the known pulse shapes of energy depositions in the calorimeter, which are measured as functions of both energy and time. A variety of algorithms were developed to mitigate the effects of adjacent bunch crossings on local energy reconstruction in the hadron calorimeter in Run 2, and their performance is compared.

A search for decays to invisible particles of Higgs bosons produced in association with a top-antitop quark pair or a vector boson, which both decay to a fully hadronic final state, has been performed using proton-proton collision data collected at$${\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}}$$$\sqrt{s}=13\text{Te}\text{V}$by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$. The 95% confidence level upper limit set on the branching fraction of the 125$$\,\text {Ge}\hspace{-.08em}\text {V}$$$\text{Ge}\text{V}$Higgs boson to invisible particles,$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$, is 0.54 (0.39 expected), assuming standard model production cross sections. The results of this analysis are combined with previous$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$searches carried out at$${\sqrt{s}=7}$$$\sqrt{s}=7$, 8, and 13$$\,\text {Te}\hspace{-.08em}\text {V}$$$\text{Te}\text{V}$in complementary production modes. The combined upper limit at 95% confidence level on$${\mathcal {B}({\textrm{H}} \rightarrow \text {inv})}$$$B(\text{H}\to \text{inv})$is 0.15 (0.08 expected).