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1. Bounds for the smallest eigenvalue of the NTK for arbitrary spherical data of arbitrary dimension

   Karhadkar, Kedar; Murray, Michael; Montufar, Guido (September 2024, 38th Conference on Neural Information Processing Systems (NeurIPS 2024))

   Bounds on the smallest eigenvalue of the neural tangent kernel (NTK) are a key ingredient in the analysis of neural network optimization and memorization. How- ever, existing results require distributional assumptions on the data and are limited to a high-dimensional setting, where the input dimension d0 scales at least log- arithmically in the number of samples n. In this work we remove both of these requirements and instead provide bounds in terms of a measure of distance between data points: notably these bounds hold with high probability even when d0 is held constant versus n. We prove our results through a novel application of the hemisphere transform. 

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2. Bootstrapping ground state correlators in matrix theory. Part I

   https://doi.org/10.1007/JHEP01(2025)190  

   Lin, Henry W; Zheng, Zechuan (January 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> The D0-brane/Banks-Fischler-Shenker-Susskind matrix theory is a strongly coupled quantum system with an interesting gravity dual. We develop a scheme to derive bootstrap bounds on simple correlators in the matrix theory at infiniteNat zero energy by imposing the supercharge equations of motion. By exploiting SO(9) symmetry, we are able to consider single-trace operators involving words of length up to 9 using very modest computational resources. We interpret our initial results as strong evidence that the bootstrap method can efficiently access physics in the strongly coupled, infiniteNregime. 

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3. Thermochemical properties of small rhenium molecules: ReC, ReN, ReO, ReS, and ReC2

   https://doi.org/10.1063/5.0302138  

   Tomchak, Kimberly H; Tieu, Erick; Kawagoe, Thomas T; Derbidge, Jordan; Clark, Keith T; Morse, Michael D; Welch, Bradley; Wilson, Angela K (November 2025, The Journal of Chemical Physics)

   The rhenium-containing molecules ReC, ReN, ReO, ReS, and ReC2 have been investigated using a pulsed laser ablation supersonic beam molecular source in resonant two-photon ionization experiments with time-of-flight mass spectrometric detection. Sharp predissociation thresholds have been observed, allowing precise bond dissociation energies (BDEs) to be measured as D0(ReC) = 5.731(3) eV, D0(ReN) = 5.635(3) eV, D0(ReO) = 5.510(3) eV, D0(ReS) = 3.947(3) eV, and D0(Re–C2) = 5.359(3) eV. The threshold for two-photon ionization was also measured for ReC, ReN, and ReO, providing ionization energies (IEs) of IE(ReC) = 8.425(12) eV, IE(ReN) = 8.193(20) eV, and IE(ReO) = 8.561(11) eV. These are the first measurements of these thermochemical quantities to be reported in the literature. The combination of BDEs and IEs allowed the BDEs of the cations ReC+, ReN+, and ReO+ to be determined via a thermochemical cycle as D0(Re+-C) = 5.140(12) eV, D0(Re+-N) = 5.275(20) eV, and D0(Re+-O) = 4.783(11) eV. In addition, computations of these thermochemical values were performed using density functional theory [B3LYP/aug-cc-pVQZ(-PP)] to determine the ground states and their geometric parameters. These were further studied at the CCSD(T) level with extrapolation to the complete basis set limit using aug-cc-pVXZ(-PP) basis sets (X = 3, 4, 5) to obtain computational values of the BDEs and IEs as well. The high-level super correlation consistent composite approach (s-ccCA) was also utilized, providing an additional approach for the prediction of thermochemical values. The electronic structure of the molecules is discussed, along with the periodic trends as the ligand is varied. 

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4. Bond dissociation energies of diatomic transition metal nitrides

   https://doi.org/10.1063/5.0141182  

   Merriles, Dakota M.; Knapp, Annie S.; Barrera-Casas, Yexalen; Sevy, Andrew; Sorensen, Jason J.; Morse, Michael D. (February 2023, The Journal of Chemical Physics)

   Resonant two-photon ionization (R2PI) spectroscopy has been used to measure the bond dissociation energies (BDEs) of the diatomic transition metal nitrides ScN, TiN, YN, MoN, RuN, RhN, HfN, OsN, and IrN. Of these, the BDEs of only TiN and HfN had been previously measured. Due to the many ways electrons can be distributed among the d orbitals, these molecules possess an extremely high density of electronic states near the ground separated atom limit. Spin–orbit and nonadiabatic interactions couple these states quite effectively, so that the molecules readily find a path to dissociation when excited above the ground separated atom limit. The result is a sharp drop in ion signal in the R2PI spectrum when the molecule is excited above this limit, allowing the BDE to be readily measured. Using this method, the values D0(ScN) = 3.905(29) eV, D0(TiN) = 5.000(19) eV, D0(YN) = 4.125(24) eV, D0(MoN) = 5.220(4) eV, D0(RuN) = 4.905(3) eV, D0(RhN) = 3.659(32) eV, D0(HfN) = 5.374(4) eV, D0(OsN) = 5.732(3) eV, and D0(IrN) = 5.115(4) eV are obtained. To support the experimental findings, ab initio coupled-cluster calculations extrapolated to the complete basis set limit (CBS) were performed. With a semiempirical correction for spin–orbit effects, these coupled-cluster single double triple-CBS calculations give a mean absolute deviation from the experimental BDE values of 0.20 eV. A discussion of the periodic trends, summaries of previous work, and comparisons to isoelectronic species is also provided. 

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5. Bond Dissociation Energies of RuC, RhC, OsC, IrC, and PtC Measured by Resonant Three-Photon Ionization Spectroscopy

   https://doi.org/10.1021/acs.jpca.5c04466  

   Tomchak, Kimberly H; Morse, Michael D (September 2025, The Journal of Physical Chemistry A)

   Resonant three-photon ionization spectroscopy has been used to study the late 4d and 5d transition metal carbides RuC, RhC, OsC, IrC, and PtC. These species, like most diatomic transition metals with open nd subshells, exhibit an exceptionally high density of states near the ground separated atom limit. Spin-orbit and nonadiabatic interactions provide a means for the molecules to rapidly dissociate as soon as the bond dissociation energy (BDE) is exceeded. The result is a sharp predissociation threshold that is identified as the BDE. The high BDEs of these five molecules required the use of two tunable lasers to reach the BDE. Measured values of D0(RuC) = 6.312(2) eV, D0(RhC) = 6.007(2) eV, D0(OsC) = 6.427(2) eV, D0(IrC) = 6.404(2) eV, and D0(PtC) = 6.260(2) eV were obtained, where the value is parentheses represents the estimated error limit in units of the last quoted digit. A new electronic state of PtC, tentatively assigned as the c(_^3)Σ_1^+ state, has been found with T0 = 22442 cm-1. These BDEs are combined with recently measured ionization energies to obtain BDEs of the associated cations. Electronic structure calculations are also reported to investigate the chemical bonding in more detail. Trends in the BDEs of the diatomic transition metal carbides are also discussed. 

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