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Abstract The Hubble diagram of quasars, as candidates to “standardizable” candles, has been used to measure the expansion history of the Universe at late times, up to very high redshifts (z∼ 7). It has been shown that this history, as inferred from the quasar dataset, deviates at ≳ 3σlevel from the concordance (ΛCDM) cosmology model preferred by the cosmic microwave background (CMB) and other datasets. In this article, we investigate whether new physics beyond ΛCDM (BΛCDM) or beyond the Standard Model (BSM) could make the quasar data consistent with the concordance model. We first show that an effective redshift-dependent relation between the quasar UV and X-ray luminosities, complementing previous phenomenological work in the literature, can potentially remedy the discrepancy. Such a redshift dependence can be realized in a BSM model with axion-photon conversion in the intergalactic medium (IGM), although the preferred parameter space is in tension with various other astrophysical constraints on axions, at a level depending on the specific assumptions made regarding the IGM magnetic field. We briefly discuss a variation of the axion model that could evade these astrophysical constraints. On the other hand, we show that models beyond ΛCDM such as one with a varying dark energy equation of state (wCDM) or the phenomenological cosmographic model with a polynomial expansion of the luminosity distance, cannot alleviate the tension. The code for our analysis, based onemcee[1] andcorner.py[2], is publicly available atgithub.com/ChenSun-Phys/high_z_candles. 

There is considerable interest in MnOH x moieties, particularly in the stepwise changes in those O–H bonds in tandem with Mn oxidation state changes. The reactivity of aquo-derived ligands, {MOH x }, is also heavily influenced by the electronic character of the other ligands. Despite the prevalence of oxygen coordination in biological systems, preparation of mononuclear Mn complexes of this type with all O-donors is rare. Herein, we report several Mn complexes with perfluoropinacolate (pin F ) 2− including the first example of a crystallographically characterized mononuclear {Mn( iii )OH} with all O-donors, K 2 [Mn(OH)(pin F ) 2 ], 3. Complex 3 is prepared via deprotonation of K[Mn(OH 2 )(pin F ) 2 ], 1, the p K a of which is estimated to be 18.3 ± 0.3. Cyclic voltammetry reveals quasi-reversible redox behavior for both 1 and 3 with an unusually large Δ E p , assigned to the Mn( iii / ii ) couple. Using the Bordwell method, the bond dissociation free energy (BDFE) of the O–H bond in {Mn( ii )–OH 2 } is estimated to be 67–70 kcal mol −1 . Complex 3 abstracts H-atoms from 1,2-diphenylhydrazine, 2,4,6-TTBP, and TEMPOH, the latter of which supports a PCET mechanism. Under basic conditions in air, the synthesis of 1 results in K 2 [Mn(OAc)(pin F ) 2 ], 2, proposed to result from the oxidation of Et 2 O to EtOAc by a reactive Mn species, followed by ester hydrolysis. Complex 3 alone does not react with Et 2 O, but addition of O 2 at low temperature effects the formation of a new chromophore proposed to be a Mn( iv ) species. The related complexes K(18C6)[Mn( iii )(pin F ) 2 ], 4, and (Me 4 N) 2 [Mn( ii )(pin F ) 2 ], 5, have also been prepared and their properties discussed in relation to complexes 1–3. 

In collaborative problem solving (CPS), people's actions are interactive, interdependent, and temporal. However, it is unclear how actions temporally relate to each other and what are the temporal similarities and differences between successful vs. unsuccessful CPS processes. As such, we apply a temporal analysis approach, Multilevel Vector Autoregression (mlVAR) to investigate CPS processes. Our data were collected from college students who collaborated in triads via a video-conferencing tool (Zoom) to collaborately engage a physics learning game. Video recordings of their verbal interactions were transcribed, coded using a validated CPS framework, and organized into sequences of 10-second windows. Then, mlVAR was applied to the successful vs. unsuccessful CPS sequences to build temporal models for each. A comparison of the models together with a qualitative analysis of the transcripts revealed six temporal relationships common to both, six unique to successful level attempts, and another eight unique to unsuccessful level attempts only. Generally, for successful outcomes, people were likely to answer clarification questions with reasons and to ask for suggestions according to the current game situation, while for unsuccessful CPS level attempts, people were more likely to struggle with unclear instructions and to respond to inappropriate ideas. Overall, our results suggest that mlVAR is an effective approach for temporal analyses of CPS processes by identifying relationships that go beyond a coding and counting approach.