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1. Approximate Majority With Catalytic Inputs

   Amir, Talley; Aspnes, James; Lazarsfeld, John (January 2020, OPODIS 2020)

   null (Ed.)

   Third-state dynamics (Angluin et al. 2008; Perron et al. 2009) is a well-known process for quickly and robustly computing approximate majority through interactions between randomly-chosen pairs of agents. In this paper, we consider this process in a new model with persistent-state catalytic inputs, as well as in the presence of transient leak faults. Based on models considered in recent protocols for populations with persistent-state agents (Dudek et al. 2017; Alistarh et al. 2017; Alistarh et al. 2020), we formalize a Catalytic Input (CI) model comprising n input agents and m worker agents. For m = Θ(n), we show that computing the parity of the input population with high probability requires at least Ω(n2) total interactions, demonstrating a strong separation between the CI and standard population protocol models. On the other hand, we show that the third-state dynamics can be naturally adapted to this new model to solve approximate majority in O(n log n) total steps with high probability when the input margin is Ω(√(n log n)), which preserves the time and space efficiency of the corresponding protocol in the original model. We then show the robustness of third-state dynamics protocols to the transient leak faults considered by (Alistarh et al. 2017; Alistarh et al 2020). In both the original and CI models, these protocols successfully compute approximate majority with high probability in the presence of leaks occurring at each time step with probability β ≤ O(√(n log n}/n). The resilience of these dynamics to adversarial leaks exhibits a subtle connection to previous results involving Byzantine agents. 

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2. Imaging rotational energy transfer: comparative stereodynamics in CO + N ₂ and CO + CO inelastic scattering

   https://doi.org/10.1039/D3CP02229C  

   Sun, Zhong-Fa; Scheidsbach, Roy J.; van Hemert, Marc C.; van der Avoird, Ad; Suits, Arthur G.; Parker, David H. (July 2023, Physical Chemistry Chemical Physics)

   State-to-state rotational energy transfer in collisions of ground ro-vibrational state 13 CO molecules with N 2 molecules has been studied using the crossed molecular beam method under kinematically equivalent conditions used for 13 CO + CO rotationally inelastic scattering described in a previously published report (Sun et al. , Science , 2020, 369 , 307–309). The collisionally excited 13 CO molecule products are detected by the same (1 + 1′ + 1′′) VUV (Vacuum Ultra-Violet) resonance enhanced multiphoton ionization scheme coupled with velocity map ion imaging. We present differential cross sections and scattering angle resolved rotational angular momentum alignment moments extracted from experimentally measured 13 CO + N 2 scattering images and compare them with theoretical predictions from quasi-classical trajectories (QCT) on a newly calculated 13 CO–N 2 potential energy surface (PES). Good agreement between experiment and theory is found, which confirms the accuracy of the 13 CO–N 2 potential energy surface for the 1460 cm −1 collision energy studied by experiment. Experimental results for 13 CO + N 2 are compared with those for 13 CO + CO collisions. The angle-resolved product rotational angular momentum alignment moments for the two scattering systems are very similar, which indicates that the collision induced alignment dynamics observed for both systems are dominated by a hard-shell nature. However, compared to the 13 CO + CO measurements, the primary rainbow maximum in the DCSs for 13 CO + N 2 is peaked consistently at more backward scattering angles and the secondary maximum becomes much less obvious, implying that the 13 CO–N 2 PES is less anisotropic. In addition, a forward scattering component with high rotational excitation seen for 13 CO + CO does not appear for 13 CO–N 2 in the experiment and is not predicted by QCT theory. Some of these differences in collision dynamics behaviour can be predicted by a comparison between the properties of the PESs for the two systems. More specific behaviour is also predicted from analysis of the dependence on the relative collision geometry of 13 CO + N 2 trajectories compared to 13 CO + CO trajectories, which shows the special ‘do-si-do’ pathway invoked for 13 CO + CO is not effective for 13 CO + N 2 collisions. 

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3. Equality on a Scale vs Equal Sign in a Mathematical Equation

   Haider, Q. M. (January 2019, Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Plenty of literature has highlighted elementary students’ misinterpretation and difficulty in dealing with an equal sign at different grade levels (e.g., Jones, Inglis, Gilmore & Evans, 2013; Sherman & Bisanz, 2009; Stephens et al., 2013). Studies have suggested various tools to develop a relational understanding of equality (e.g., Ellis & Yeh, 2008; Jones & Pratt, 2006). Leavy, Hourigan, and McMahon (2013) reported evidence of a relational understanding of the equal sign, rather than an operational understanding, in elementary students’ work when using a physical balance. In this study, we investigate how often elementary students use their relational understanding of equality using a balance to write a balanced equation of the given situation. 

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4. Comparison of the predictions of Langevin Dynamics-based diffusion charging collision kernel models with canonical experiments

   https://doi.org/https://doi.org/10.1016/j.jaerosci.2019.105481  

   Li, Li Chahl (February 2020, Journal of aerosol science)

   Based on the prior work of Chahl and Gopalakrishnan (2019) to infer particle-ion collision time distributions using a Langevin Dynamics (LD) approach, we develop a model for the non-dimensional diffusion charging collision kernel β_i or H that is applicable for 0≤Ψ_E≤60,0≤Ψ_I/Ψ_E ≤1,Kn_D≤2000 (defined in the main text). The developed model for β_i for attractive Coulomb and image potential interactions, along with the model for β_i for repulsive Coulomb and image potential interactions from Gopalakrishnan et al. (2013b), is tested against published diffusion charging experimental data. Current state of the art charging models, Fuchs (1963) and Wiedensohler (1988) regression for bipolar charging, are also evaluated and discussed. Comparisons reveal that the LD-based model accurately describes unipolar fractions for 10 – 100 nm particles measured in air (Adachi et al., 1985), nitrogen and argon but not in helium (Adachi et al., 1987). Fuchs model and the LD-based model yield similar predictions in the experimental conditions considered, except in helium. In the case of bipolar charging, the LD-based model captures the experimental trends quantitatively (within ±20%) across the entire size range of 4 – 40 nm producing superior agreement than Wiedensohler’s regression. The latter systematically underpredicts charge fraction below ~20 nm in air (by up to 40%) for the data presented in Adachi et al. (1985). Comparison with the data of Gopalakrishnan et al. (2015), obtained in UHP air along with measurements of the entire ion mass-mobility distribution, shows excellent agreement with the predictions of the LD-based model. This demonstrates the capability to accommodate arbitrary ion populations in any background gas, when such data is available. Wiedensohler’s regression, derived for bipolar charging in air using average ion mass-mobility, also describes the data reasonably well in the conditions examined. However, both models failed to capture the fraction of singly and doubly charged particles in carbon dioxide warranting further investigation. 

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5. Stereodynamics of cold HD and D2 collisions with He

   https://doi.org/10.1063/5.0250522  

   Mandal, Bikramaditya; Patkowski, Konrad; Jambrina, Pablo G; Aoiz, F Javier; Balakrishnan, Naduvalath (March 2025, The Journal of Chemical Physics)

   We present a comprehensive quantum mechanical study of stereodynamic control of HD + He and D2 + He collisions that have been probed experimentally by Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] using Stark-induced adiabatic Raman passage (SARP) techniques. Our calculations utilize a highly accurate full-dimensional H2 + He interaction potential with diagonal Born–Oppenheimer correction appropriate for HD and D2 isotopomers. The results show that rotational quenching of HD from j = 2 → j′ = 0 in v = 2, j = 2 → j′ = 1 in v = 2 and v = 4, and j = 4 → j′ = 3 in v = 4 is dominated by an l = 1 shape resonance located between 0.1 and 1.0 cm−1. For collision energies less than 0.1 cm−1, isotropic scattering prevails. An l = 1 resonance centered around 0.02 cm−1 is also found to dominate the j = 2 → j′ = 0 and j = 4 → j′ = 2 transitions in v = 4 for He–D2 collisions consistent with our prior studies of Δj = −2 transition in He + D2(v = 2, j = 2) collisions. Our analysis does not support the hypothesis of Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] that a strong l = 2 resonance controls the angular distribution for Δj = −2 transition for both systems. Despite improvements in the development of the potential energy surface, a good agreement with SARP experiments for v = 2 is achieved only when contributions from collision energies less than 1.0 cm−1 were excluded in the computation of velocity averaged differential rate coefficients for both systems. This could be due to some uncertainties in the velocity spread in the experiment that employs co-propagation of the collision partners and possibly, the neglect of transverse velocities in the simulation of the experiment. 

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