Synthesis and conformational analysis of pyran inter-halide analogues of á´ -talose.

In this work, we describe the synthesis of halogenated pyran analogues of ᴅ-talose using a halo-divergent strategy from known 1,6-anhydro-2,3-dideoxy-2,3-difluoro-ß-ᴅ-mannopyranose. In solution and in the solid-state, all analogues adopt standard 4 C 1-like conformations despite 1,3-diaxial repulsion between the F2 and the C4 halogen. Moreover, the solid-state conformational analysis of halogenated pyrans reveals deviation in the intra-annular torsion angles arising from repulsion between the axial fluorine at C2 and the axial halogen at C4, which increases with the size of the halogen at C4 (F < Cl < Br < I). Crystal packing arrangements of pyran inter-halides show hydrogen bond acceptor and nonbonding interactions for the halogen at C4. Finally, density functional theory (DFT) calculations corroborate the preference of talose analogues to adopt a 4 C 1-like conformation and a natural bonding orbital (NBO) analysis demonstrates the effects of hyperconjugation from C-F antibonding orbitals.

ModelHamiltonian: A Python-scriptable library for generating 0-, 1-, and 2-electron integrals.

ModelHamiltonian is a free, open source, and cross-platform Python library designed to express model Hamiltonians, including spin-based Hamiltonians (Heisenberg and Ising models) and occupation-based Hamiltonians (Pariser-Parr-Pople, Hubbard, and Hückel models) in terms of 1- and 2-electron integrals, so that these systems can be easily treated by traditional quantum chemistry software programs. ModelHamiltonian was originally intended to facilitate the testing of new electronic structure methods using HORTON but emerged as a stand-alone research tool that we recognize has wide utility, even in an educational context. ModelHamiltonian is written in Python and adheres to modern principles of software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. While we anticipate that most users will use ModelHamiltonian as a Python library, we include a graphical user interface so that models can be built without programming, based on connectivity/parameters inferred from, for example, a SMILES string. We also include an interface to ChatGPT so that users can specify a Hamiltonian in plain language (without learning ModelHamiltonian's vocabulary and syntax). This article marks the official release of the ModelHamiltonian library, showcasing its functionality and scope.

Beyond a Richardson-Gaudin Mean-Field: Slater-Condon Rules and Perturbation Theory.

Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.

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.

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.

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.

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.

Predicting fault slip via transfer learning.

Data-driven machine-learning for predicting instantaneous and future fault-slip in laboratory experiments has recently progressed markedly, primarily due to large training data sets. In Earth however, earthquake interevent times range from 10's-100's of years and geophysical data typically exist for only a portion of an earthquake cycle. Sparse data presents a serious challenge to training machine learning models for predicting fault slip in Earth. Here we describe a transfer learning approach using numerical simulations to train a convolutional encoder-decoder that predicts fault-slip behavior in laboratory experiments. The model learns a mapping between acoustic emission and fault friction histories from numerical simulations, and generalizes to produce accurate predictions of laboratory fault friction. Notably, the predictions improve by further training the model latent space using only a portion of data from a single laboratory earthquake-cycle. The transfer learning results elucidate the potential of using models trained on numerical simulations and fine-tuned with small geophysical data sets for potential applications to faults in Earth.

Autonomous extraction of millimeter-scale deformation in InSAR time series using deep learning.

Systematically characterizing slip behaviours on active faults is key to unraveling the physics of tectonic faulting and the interplay between slow and fast earthquakes. Interferometric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformation at a global scale every few days, may hold the key to those interactions. However, atmospheric propagation delays often exceed ground deformation of interest despite state-of-the art processing, and thus InSAR analysis requires expert interpretation and a priori knowledge of fault systems, precluding global investigations of deformation dynamics. Here, we show that a deep auto-encoder architecture tailored to untangle ground deformation from noise in InSAR time series autonomously extracts deformation signals, without prior knowledge of a fault's location or slip behaviour. Applied to InSAR data over the North Anatolian Fault, our method reaches 2 mm detection, revealing a slow earthquake twice as extensive as previously recognized. We further explore the generalization of our approach to inflation/deflation-induced deformation, applying the same methodology to the geothermal field of Coso, California.

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.

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.

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.

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.

An exponential build-up in seismic energy suggests a months-long nucleation of slow slip in Cascadia.

Slow slip events result from the spontaneous weakening of the subduction megathrust and bear strong resemblance to earthquakes, only slower. This resemblance allows us to study fundamental aspects of nucleation that remain elusive for classic, fast earthquakes. We rely on machine learning algorithms to infer slow slip timing from statistics of seismic waveforms. We find that patterns in seismic power follow the 14-month slow slip cycle in Cascadia, arguing in favor of the predictability of slow slip rupture. Here, we show that seismic power exponentially increases as the slowly slipping portion of the subduction zone approaches failure, a behavior that shares a striking similarity with the increase in acoustic power observed prior to laboratory slow slip events. Our results suggest that the nucleation phase of Cascadia slow slip events may last from several weeks up to several months.

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.

Synthesis and Properties of Conjugated Polymers Based on a Ladderized Anthanthrene Unit.

Polycyclic aromatic hydrocarbons (PAHs) are interesting building blocks for the preparation of conjugated polymers due to their extended π surface and planar conformation. However, their use as comonomer in conjugated polymers often leads to nonplanar main chains as a consequence of high steric hindrance at the linking point. Herein, we report the synthesis of a ladderized anthanthrene unit using an sp3 carbon bridge. Three conjugated copolymers with fluorene, isoindigo, and bithiophene derivatives have been synthesized and characterized to study the effect of such ladderization on the electronic properties. The dihedral angle between the ladderized anthanthrene and adjacent units has been significantly reduced by the formation of the sp3 carbon bridge, thus eliminating the steric hindrance with the proton at the peri position of the anthanthrene unit and red-shifting the absorption spectrum by 25 nm.

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.