Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms.

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in generalization, and provide dimension reduction. In this work, we introduce a fast-to-compute, translationally invariant and rotationally equivariant wavelet scattering network (EqWS) and filter bank of wavelets (triglets). We demonstrate the interpretability and quantify the invariance/equivariance of the coefficients, briefly commenting on difficulties with implementing scale equivariance. On MNIST, we show that training on a rotationally invariant reduction of the coefficients maintains rotational invariance when generalized to test data and visualize residual symmetry breaking terms. Rotation equivariance is leveraged to estimate the rotation angle of digits and reconstruct the full rotation dependence of each coefficient from a single angle. We benchmark EqWS with linear classifiers on EMNIST and CIFAR-10/100, introducing a new second-order, cross-color channel coupling for the color images. We conclude by comparing the performance of an isotropic reduction of the scattering coefficients and RWST, a previous coefficient reduction, on an isotropic classification of magnetohydrodynamic simulations with astrophysical relevance.

Phase-induced topological superconductivity in a planar heterostructure.

Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A major cause of this ambiguity is the side effects of applying a magnetic field: induced in-gap states, vortices, and alignment issues. Here we propose a planar semiconductor-superconductor heterostructure as a platform for realizing topological superconductivity without applying a magnetic field to the two-dimensional electron gas hosting the topological state. Time-reversal symmetry is broken only by phase biasing the proximitizing superconductors, which can be achieved using extremely small fluxes or bias currents far from the quasi-one-dimensional channel. Our platform is based on interference between this phase biasing and the phase arising from strong spin-orbit coupling in closed electron trajectories. The principle is demonstrated analytically using a simple model, and then shown numerically for realistic devices. We show a robust topological phase diagram, as well as explicit wavefunctions of Majorana zero modes. We discuss experimental issues regarding the practical implementation of our proposal, establishing it as an accessible scheme with contemporary experimental techniques.

High-energy quasiparticle injection into mesoscopic superconductors.

At non-zero temperatures, superconductors contain excitations known as Bogoliubov quasiparticles (QPs). The mesoscopic dynamics of QPs inform the design of quantum information processors, among other devices. Knowledge of these dynamics stems from experiments in which QPs are injected in a controlled fashion, typically at energies comparable to the pairing energy1-5. Here we perform tunnel spectroscopy of a mesoscopic superconductor under high electric fields. We observe QP injection due to field-emitted electrons with 106 times the pairing energy, an unexplored regime of QP dynamics. Upon application of a gate voltage, the QP injection decreases the critical current and, at sufficiently high electric field, a field-emission current (<0.1 nA in our device) switches the mesoscopic superconductor into the normal state, consistent with earlier observations6. We expect that high-energy injection will be useful for developing QP-tolerant quantum information processors, will allow rapid control of resonator quality factors and will enable the design of electric-field-controlled superconducting devices with new functionality.

Development of an Improved System for the Carboxylation of Aryl Halides through Mechanistic Studies.

The nickel-catalyzed carboxylation of organic halides or pseudohalides using carbon dioxide is an emerging method to prepare synthetically valuable carboxylic acids. Here, we report a detailed mechanistic investigation of these reactions using the carboxylation of aryl halides with (PPh3)2NiIICl2 as a model reaction. Our studies allow us to understand several general features of nickel-catalyzed carboxylation reactions. For example, we demonstrate that both a Lewis acid and halide source are beneficial for catalysis. To this end, we establish that heterogeneous Mn(0) and Zn(0) reductants are multifaceted reagents that generate noninnocent Mn(II) or Zn(II) Lewis acids upon oxidation. In a key result, a rare example of a well-defined nickel(I) aryl complex is isolated, and it is demonstrated that its reaction with carbon dioxide results in the formation of a carboxylic acid in high yield (after workup). The carbon dioxide insertion product undergoes rapid decomposition, which ca These three oxidation states correspond to the onbe circumvented by a ligand metathesis reaction with a halide source. Our studies have led to both a revised mechanism and the development of a broadly applicable strategy to improve reductive carboxylation reactions. A critical component of this strategy is that we have replaced the heterogeneous Mn(0) reductant typically used in catalysis with a well-defined homogeneous organic reductant. Through its use, we have increased the range of ancillary ligands, additives, and substrates that are compatible with the reaction. This has enabled us to perform reductive carboxylations at low catalyst loadings. Additionally, we demonstrate that reductive carboxylations of organic (pseudo)halides can be achieved in high yields in more practically useful, non-amide solvents. Our results describe a mechanistically guided strategy to improve reductive carboxylations through the use of a homogeneous organic reductant, which may be broadly translatable to a wide range of cross-electrophile coupling reactions.

A Possible Path to Prebiotic Peptides Involving Silica and Hydroxy Acid-Mediated Amide Bond Formation.

The formation of alanine and glycine oligomers in films produced by drying aqueous mixtures of lactic acid and silica nanoparticles has been studied as a model prebiotic reaction. The addition of silica results in alanine or glycine enrichment in the polymers. Oligomerization proceeds through ester-mediated peptide bond formation in an acidic and evaporative environment at temperatures as low as 85 °C. For both amino acids, the dominant species produced in the presence of silica and lactic acid are rich in amide bonds and deficient in ester linkages. At higher temperatures, glycine and alanine oligomers contain only a single hydroxy acid residue conjugated to the peptide N terminus. Similar product distributions occur with silica particles prereacted with lactic acid, which suggests the catalytic role of a functionalized surface. This work highlights the role minerals might have served in transitioning from oligomers with both ester and amide linkages (depsipeptides) to peptides in a prebiotic context.

A Photoresponsive Orthogonal Supramolecular Complex Based on Host-Guest Interactions.

We synthesized a novel green-light-responsive tetra-ortho-isopropoxy-substituted azobenzene (ipAzo). Cis-ipAzo forms a strong host-guest complex with γ-cyclo dextrin (γ-CD) whereas trans-ipAzo binds weakly. This new photoresponsive host-guest interaction is reverse to the well-known azobenzene (Azo)/α-cyclodextrin (α-CD) complex, which is strong only between trans-Azo and α-CD. By combining the UV-light-responsive Azo/α-CD and green-light-responsive ipAzo/γ-CD host-guest complexes, a photoresponsive orthogonal supramolecular system is developed.