Laboratory earthquake forecasting: A machine learning competition.

Earthquake prediction, the long-sought holy grail of earthquake science, continues to confound Earth scientists. Could we make advances by crowdsourcing, drawing from the vast knowledge and creativity of the machine learning (ML) community? We used Google's ML competition platform, Kaggle, to engage the worldwide ML community with a competition to develop and improve data analysis approaches on a forecasting problem that uses laboratory earthquake data. The competitors were tasked with predicting the time remaining before the next earthquake of successive laboratory quake events, based on only a small portion of the laboratory seismic data. The more than 4,500 participating teams created and shared more than 400 computer programs in openly accessible notebooks. Complementing the now well-known features of seismic data that map to fault criticality in the laboratory, the winning teams employed unexpected strategies based on rescaling failure times as a fraction of the seismic cycle and comparing input distribution of training and testing data. In addition to yielding scientific insights into fault processes in the laboratory and their relation with the evolution of the statistical properties of the associated seismic data, the competition serves as a pedagogical tool for teaching ML in geophysics. The approach may provide a model for other competitions in geosciences or other domains of study to help engage the ML community on problems of significance.

Density matrices of seniority-zero geminal wavefunctions.

Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analog of Wick's theorem for fermions or bosons. This expression is, in general, intractable, but it is shown how it becomes feasible in three distinct ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals. Both are near exact, suggesting that the incorrect results observed with ground state RG states (a local maximum rather than smooth dissociation) may be fixable using a different RG state.

Reduced density matrices/static correlation functions of Richardson-Gaudin states without rapidities.

Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson-Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical picture, clean expressions for reduced density matrix (RDM) elements, and systematic improvement (with a complete set of eigenvectors). Known expressions for the RDM elements require the computation of rapidities, which are obtained by first solving for the so-called eigenvalue based variables (EBV) and then root-finding a Lagrange interpolation polynomial. In this paper, we obtain expressions for the RDM elements directly in terms of the EBV. The final expressions can be computed at the same cost as the rapidity expressions. Therefore, except, in particular, circumstances, it is entirely unnecessary to compute rapidities at all. The RDM elements require numerically inverting a matrix, and while this is usually undesirable, we demonstrate that it is stable, except when there is degeneracy in the single-particle energies. In such cases, a different construction would be required.

Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field.

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.

Transition density matrices of Richardson-Gaudin states.

Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a mean-field of pairs of electrons (geminals) with a constant pairing strength. To move beyond the mean-field, one must develop the wavefunction on the basis of all the RG states. This requires both practical expressions for transition density matrices and an idea of which states are most important in the expansion. In this contribution, we present expressions for the transition density matrix elements and calculate them numerically for half-filled picket-fence models (reduced BCS models with constant energy spacing). There are no Slater-Condon rules for RG states, though an analog of the aufbau principle proves to be useful in choosing which states are important.

Addressing the Structural Complexity of Fluorinated Glucose Analogues: Insight into Lipophilicities and Solvation Effects.

In this work, we synthesized all mono-, di-, and trifluorinated glucopyranose analogues at positions C-2, C-3, C-4, and C-6. This systematic investigation allowed us to perform direct comparison of 19 F resonances of fluorinated glucose analogues and also to determine their lipophilicities. Compounds with a fluorine atom at C-6 are usually the most hydrophilic, whereas those with vicinal polyfluorinated motifs are the most lipophilic. Finally, the solvation energies of fluorinated glucose analogues were assessed for the first time by using density functional theory. This method allowed the log P prediction of fluoroglucose analogues, which was comparable to the C log P values obtained from various web-based programs.

Probing Slow Earthquakes With Deep Learning.

Slow earthquakes may trigger failure on neighboring locked faults that are stressed sufficiently to break, and slow slip patterns may evolve before a nearby great earthquake. However, even in the clearest cases such as Cascadia, slow earthquakes and associated tremor have only been observed in intermittent and discrete bursts. By training a convolutional neural network to detect known tremor on a single seismic station in Cascadia, we isolate and identify tremor and slip preceding and following known larger slow events. The deep neural network can be used for the detection of quasi-continuous tremor, providing a proxy that quantifies the slow slip rate. Furthermore, the model trained in Cascadia recognizes tremor in other subduction zones and also along the San Andreas Fault at Parkfield, suggesting a universality of waveform characteristics and source processes, as posited from experiments and theory.

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis.

Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution, we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim [Phys. Rev. B 84, 224503 (2011)]. In each case, the expressions scale like O(N4), with the most expensive step being the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step toward practical mean-field methods to treat strongly correlated electrons.

Richardson-Gaudin mean-field for strong correlation in quantum chemistry.

Ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian are employed as a wavefunction Ansatz to model strong electron correlation in quantum chemistry. This wavefunction is a product of weakly interacting pairs of electrons. While other geminal wavefunctions may only be employed in a projected Schrödinger equation, the present approach may be solved variationally with polynomial cost. The resulting wavefunctions are used to compute expectation values of Coulomb Hamiltonians, and we present results for atoms and dissociation curves that are in agreement with doubly occupied configuration interaction data. The present approach will serve as the starting point for a many-body theory of pairs, much as Hartree-Fock is the starting point for weakly correlated electrons.

Fluorine effect in nucleophilic fluorination at C4 of 1,6-anhydro-2,3-dideoxy-2,3-difluoro-ß-D-hexopyranose.

In this work, we have developed a simple synthetic approach using Et3N·3HF as an alternative to the DAST reagent. We controlled the stereochemistry of the nucleophilic fluorination at C4 of 1,6-anhydro-2,3-dideoxy-2,3-difluoro-4-O-triflate-ß-ᴅ-talopyranose using Et3N·3HF or in situ generated Et3N·1HF. The influence of the fluorine atom at C2 on reactivity at C4 could contribute to a new fluorine effect in nucleophilic substitution. Finally, with the continuous objective of synthesizing novel multi-vicinal fluorosugars, we prepared one difluorinated and one trifluorinated alditol analogue.

From Stress Chains to Acoustic Emission.

A numerical scheme using the combined finite-discrete element method is employed to study a model of an earthquake system comprising a granular layer embedded in a formation. When the formation is driven so as to shear the granular layer, a system of stress chains emerges. The stress chains endow the layer with resistance to shear and on failure launch broadcasts into the formation. These broadcasts, received as acoustic emission, provide a remote monitor of the state of the granular layer of the earthquake system.

Fortnightly modulation of San Andreas tremor and low-frequency earthquakes.

Earth tides modulate tremor and low-frequency earthquakes (LFEs) on faults in the vicinity of the brittle-ductile (seismic-aseismic) transition. The response to the tidal stress carries otherwise inaccessible information about fault strength and rheology. Here, we analyze the LFE response to the fortnightly tide, which modulates the amplitude of the daily tidal stress over a 14-d cycle. LFE rate is highest during the waxing fortnightly tide, with LFEs most strongly promoted when the daily stress exceeds the previous peak stress by the widest margin. This pattern implies a threshold failure process, with slip initiated when stress exceeds the local fault strength. Variations in sensitivity to the fortnightly modulation may reflect the degree of stress concentration on LFE-producing brittle asperities embedded within an otherwise aseismic fault.

Simple and inexpensive perturbative correction schemes for antisymmetric products of nonorthogonal geminals.

A new multireference perturbation approach has been developed for the recently proposed AP1roG scheme, a computationally facile parametrization of an antisymmetric product of nonorthogonal geminals. This perturbation theory of second-order closely follows the biorthogonal treatment from multiconfiguration perturbation theory as introduced by Surján et al., but makes use of the additional feature of AP1roG that the expansion coefficients within the space of closed-shell determinants are essentially correct already, which further increases the predictive power of the method. Building upon the ability of AP1roG to model static correlation, the perturbation correction accounts for dynamical electron correlation, leading to absolute energies close to full configuration interaction results. Potential surfaces for multiple bond dissociation in H2O and N2 are predicted with high accuracy up to bond breaking. The computational cost of the method is the same as that of conventional single-reference MP2.

Assessing the accuracy of new geminal-based approaches.

We present a systematic theoretical study on the dissociation of diatomic molecules and their spectroscopic constants using our recently presented geminal-based wave function ansätze. Specifically, the performance of the antisymmetric product of rank two geminals (APr2G), the antisymmetric product of 1-reference-orbital geminals (AP1roG) and its orbital-optimized variant (OO-AP1roG) are assessed against standard quantum chemistry methods. Our study indicates that these new geminal-based approaches provide a cheap, robust, and accurate alternative for the description of bond-breaking processes in closed-shell systems requiring only mean-field-like computational cost. In particular, the spectroscopic constants obtained from OO-AP1roG are in very good agreement with reference theoretical and experimental data.

Effects of acoustic waves on stick-slip in granular media and implications for earthquakes.

It remains unknown how the small strains induced by seismic waves can trigger earthquakes at large distances, in some cases thousands of kilometres from the triggering earthquake, with failure often occurring long after the waves have passed. Earthquake nucleation is usually observed to take place at depths of 10-20 km, and so static overburden should be large enough to inhibit triggering by seismic-wave stress perturbations. To understand the physics of dynamic triggering better, as well as the influence of dynamic stressing on earthquake recurrence, we have conducted laboratory studies of stick-slip in granular media with and without applied acoustic vibration. Glass beads were used to simulate granular fault zone material, sheared under constant normal stress, and subject to transient or continuous perturbation by acoustic waves. Here we show that small-magnitude failure events, corresponding to triggered aftershocks, occur when applied sound-wave amplitudes exceed several microstrain. These events are frequently delayed or occur as part of a cascade of small events. Vibrations also cause large slip events to be disrupted in time relative to those without wave perturbation. The effects are observed for many large-event cycles after vibrations cease, indicating a strain memory in the granular material. Dynamic stressing of tectonic faults may play a similar role in determining the complexity of earthquake recurrence.

Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal.

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases.

Proximal Ultrasound-Guided Posterior Tibial Nerve Block for the Removal of Calcaneal Hardware.

The anesthetic technique for calcaneal surgery has been reported to include peripheral nerve blocks, such as a sciatic block in the popliteal fossa, followed by intraoperative sedation. Sciatic nerve blocks are associated with limb weakness and fall risk. We present a case of a patient presenting for outpatient calcaneal surgery. The anesthetic plan consisted of a proximal, ultrasound-guided, single-injection selective posterior tibial nerve block followed by intraoperative sedation. The nerve block was performed, surgery concluded, and the patient received six hours of postoperative analgesia. Once the nerve block effects receded, the postoperative pain was managed with only over-the-counter analgesics while the patient was at home. We recommend an ultrasound-guided proximal posterior tibial nerve block for outpatient surgery involving the calcaneus to preserve lower extremity motor strength and provide postoperative analgesia.

Nonlinear ultrasound: potential of the cross-correlation method for osseointegration monitoring.

Recently the concept of probing nonlinear elasticity at an interface prosthesis/bone has been proposed as a promising method to monitor the osseointegration/sealing of a prosthesis. However, the most suitable method to achieve this goal is a point of debate. To this purpose, two approaches termed the scaling subtraction method and the cross-correlation method are compared here. One nonlinear parameter derived from the cross-correlation method is as sensitive as a clinical device based on linear elasticity measurement. Further, this study shows that cross-correlation based methods are more sensitive than those based on subtraction/addition, such like pulse inversion and similar methods.

Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models.

This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.

Accurate O-H bond dissociation energy differences of hydroxylamines determined by EPR spectroscopy: computational insight into stereoelectronic effects on BDEs and EPR spectral parameters.

Differences in O-H bond dissociation enthalpies (ΔBDEs) between the hydroxylamine of (15)N-labeled TEMPONE and 10 N,N-di-tert-alkyl hydroxylamines were determined by EPR. These ΔBDEs, together with the g and a(N) values of the derived nitroxide radicals, are discussed in relation to various geometric, intramolecular dipole/dipole, and steric effects and in relation to the results from DFT calculations. We find that dipole/dipole interactions are the dominant factors in dictating a(N) values and O-H BDEs in all of these structurally similar nitroxides and hydroxylamines, respectively. The importance of including the Boltzmann distribution of conformations for each nitroxide in the a(N) calculations is emphasized.