Synchrotron Mössbauer spectroscopic study of ferropericlase at high pressures and temperatures

The electronic spin state of Fe^(2+) in ferropericlase, (Mg_(0.75)Fe_(0.25))O, transitions from a high-spin (spin unpaired) to low-spin (spin paired) state within the Earth’s mid-lower mantle region. To better understand the local electronic environment of high-spin Fe^(2+) ions in ferropericlase near the transition, we obtained synchrotron Mössbauer spectra (SMS) of (Mg_(0.75),Fe_(0.25))O in externally heated and laser-heated diamond anvil cells at relevant high pressures and temperatures. Results show that the quadrupole splitting (QS) of the dominant high-spin Fe^(2+) site decreases with increasing temperature at static high pressure. The QS values at constant pressure are fitted to a temperature-dependent Boltzmann distribution model, which permits estimation of the crystal-field splitting energy (Δ_3) between the d_(xy_ and d_(xz) or d_(zy) orbitals of the t_(2g) states in a distorted octahedral Fe^(2+) site. The derived Δ_3 increases from approximately 36 meV at 1 GPa to 95 meV at 40 GPa, revealing that both high pressure and high temperature have significant effects on the 3d electronic shells of Fe^(2+) in ferropericlase. The SMS spectra collected from the laser-heated diamond cells within the time window of 146 ns also indicate that QS significantly decreases at very high temperatures. A larger splitting of the energy levels at high temperatures and pressures should broaden the spin crossover in ferropericlase because the degeneracy of energy levels is partially lifted. Our results provide information on the hyperfine parameters and crystal-field splitting energy of high-spin Fe^(2+) in ferropericlase at high pressures and temperatures, relevant to the electronic structure of iron in oxides in the deep lower mantle

The Moderating Role of Mindfulness in New Product Evaluation

Mindfulness has the potential to affect new product evaluation since consumers with a higher propensity for mindfulness are more likely to notice and accept differences between existing and new products. This research references piecemeal/category-based processing theory to study the moderating effect of individual mindfulness on information processing in the presence of product category knowledge. We find that mindfulness does not have a direct effect on processing style. However, mindfulness does moderate the relationship between product category knowledge and processing style. Understanding underlying factors during information processing provides important insights for marketers as they implement marketing strategies

Measurement of a topological edge invariant in a microwave network

We report on the measurement of topological invariants in an electromagnetic topological insulator analog formed by a microwave network, consisting of the winding numbers of scattering matrix eigenvalues. The experiment can be regarded as a variant of a topological pump, with non-zero winding implying the existence of topological edge states. In microwave networks, unlike most other systems exhibiting topological insulator physics, the winding can be directly observed. The effects of loss on the experimental results, and on the topological edge states, is discussed.Comment: 10 pages, 10 figure

Latent State Models of Training Dynamics

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the $L_2$ norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.Comment: Accepted at TMLR 2023. Updated Jan 19, 2024 with erratu

A Detailed Procedure for Using Copulas to Classify E-Business Data

Decision support systems are widely implemented to effectively utilize the tremendous amount of data generated by information systems throughout an organization. In one common implementation, the goal is to correctly classify a customer so that appropriate action can take place. This may take the form of a customized purchase incentive given to increase the probability that a transaction is completed, while enhancing profitability. Intelligent agents employing neural network technology that function as Bayesian classifiers are one approach used here. Another approach that has been around for decades, called copulas, to our knowledge has yet to be utilized for classification in e-business applications. Copulas are functions that can describe the dependence among random variables. The very fact that copulas directly address co-dependence among variables may make them especially attractive in e-business applications where large numbers of correlated attributes may be present that could negatively affect the performance of other methods. In this paper, the basics of Bayesian decision making and posterior probabilities are reviewed. A detailed procedure for using copulas as Bayesian classifiers for e-business data is presented. The emphasis in describing the method is placed upon practitioner understanding to facilitate replication in real situations while maintaining technical rigor to ease computerized implementation

Phonon anharmonicity and negative thermal expansion in SnSe

The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the negative thermal expansion within the Sn-Se bilayers. Including the anisotropic strain dependence of the phonon free energy, in addition to the electronic ground state energy, is essential to reproduce the negative thermal expansion. From the phonon DOS obtained with INS and additional calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodynamics is linked to the electronic structure.Comment: 14 pages, 12 figure