Learning theory: stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization

Solutions of learning problems by Empirical Risk Minimization (ERM) – and almost-ERM when the minimizer does not exist – need to be consistent, so that they may be predictive. They also need to be well-posed in the sense of being stable, so that they might be used robustly. We propose a statistical form of stability, defined as leave-one-out (LOO) stability. We prove that for bounded loss classes LOO stability is (a) sufficient for generalization, that is convergence in probability of the empirical error to the expected error, for any algorithm satisfying it and, (b) necessary and sufficient for consistency of ERM. Thus LOO stability is a weak form of stability that represents a sufficient condition for generalization for symmetric learning algorithms while subsuming the classical conditions for consistency of ERM. In particular, we conclude that a certain form of well-posedness and consistency are equivalent for ERM. Dedicated to Charles A. Micchelli on his 60th birthday Mathematics subject classifications (2000) 68T05, 68T10, 68Q32, 62M20. Tomaso Poggio: Corresponding author.     

Quantifying energy condition violations in traversable wormholes

The ‘theoretical’ existence of traversable Lorentzian wormholes in the classical, macroscopic world is plagued by the violation of the well-known energy conditions of general relativity. In this brief article we show: (i) how the extent of violation can be quantified using certain volume integrals and (ii) whether this ‘amount of violation’ can be minimised for some specific cut-and-paste geometric constructions. Examples and possibilities are also outlined.     

In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T₀), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Electronic structure theories such as AFQMC can accurately predict the low-lying excited state energetics of organic chromophores involved in triplet–triplet annihilation upconversion. A novel class of benzothiadiazole annihilators is discovered.     

Tweaking Nickel with Minimal Silver in a Heterogeneous Alloy of Decahedral Geometry to Deliver Platinum-like Hydrogen Evolution Activity

Five-fold intertwined Ag_xNi_1−x (x=0.01–0.25) heterogeneous alloy nanocrystal (NC) catalysts, prepared through unique reagent combinations, are presented. With only ca. 5 at % Ag (AgNi-5), Pt-like activity has been achieved at pH 14. To reach a current density of 10 mA cm⁻² the extremely stable AgNi-5 requires an overpotential of 24.0±1.2 mV as compared to 20.1±0.8 mV for 20 % Pt/C, both with equal catalyst loading of 1.32 mg cm⁻². The turnover frequency (TOF) is as high as 2.1 H₂ s⁻¹ at 50 mV (vs. RHE). Site-specific elemental analyses show the Ag:Ni compositional variation, where the apex and edges of the decahedra are Ag-rich, thereby exposing Ni onto the faces to achieve maximum charge transport for an exceptional pH universal HER activity. DFT calculations elucidate the relative H-atom adsorption capability of the Ni centers as a function of their proximity to Ag atom.     

Tweaking Nickel with Minimal Silver in a Heterogeneous Alloy of Decahedral Geometry to Deliver Platinum‐like Hydrogen Evolution Activity

Five‐fold intertwined Ag_xNi_1?x (x=0.01–0.25) heterogeneous alloy nanocrystal (NC) catalysts, prepared through unique reagent combinations, are presented. With only ca. 5 at % Ag (AgNi‐5), Pt‐like activity has been achieved at pH 14. To reach a current density of 10 mA cm^?2 the extremely stable AgNi‐5 requires an overpotential of 24.0±1.2 mV as compared to 20.1±0.8 mV for 20 % Pt/C, both with equal catalyst loading of 1.32 mg cm^?2. The turnover frequency (TOF) is as high as 2.1 H₂ s^?1 at 50 mV (vs. RHE). Site‐specific elemental analyses show the Ag:Ni compositional variation, where the apex and edges of the decahedra are Ag‐rich, thereby exposing Ni onto the faces to achieve maximum charge transport for an exceptional pH universal HER activity. DFT calculations elucidate the relative H‐atom adsorption capability of the Ni centers as a function of their proximity to Ag atom.     

Effect of silica on the crystallization of sodium perborate tetrahydrate

Effects of SiO₂ additive on sodium perborate tetrahydrate crystallization (via chemical reaction of NaBO₂ and H₂O₂) has been studied in a MSMPR-type reaction crystallizer. CSD and microscopic observations are used to evaluate the secondary nucleation behaviour. Secondary nucleation rate decreases in case of SiO₂ addition of up to 200 ppm. Higher SiO₂ content results in higher primary nucleation rates. Abrasion resistance increases with the amount of SiO₂ additive.     

Development of a microsecond X‐ray protein footprinting facility at the Advanced Light Source

X‐ray footprinting (XF) is an important structural biology tool used to determine macromolecular conformations and dynamics of both nucleic acids and proteins in solution on a wide range of timescales. With the impending shut‐down of the National Synchrotron Light Source, it is ever more important that this tool continues to be developed at other synchrotron facilities to accommodate XF users. Toward this end, a collaborative XF program has been initiated at the Advanced Light Source using the white‐light bending‐magnet beamlines 5.3.1 and 3.2.1. Accessibility of the microsecond time regime for protein footprinting is demonstrated at beamline 5.3.1 using the high flux density provided by a focusing mirror in combination with a micro‐capillary flow cell. It is further reported that, by saturating samples with nitrous oxide, the radiolytic labeling efficiency is increased and the imprints of bound versus bulk water can be distinguished. These results both demonstrate the suitability of the Advanced Light Source as a second home for the XF experiment, and pave the way for obtaining high‐quality structural data on complex protein samples and dynamics information on the microsecond timescale.     

Mussel-inspired Ag/poly(norepinephrine)/MnO2 heterogeneous nanocatalyst for efficient reduction of 4-nitrophenol and 4-nitroaniline: an alternative approach

Research on Chemical Intermediates - Noble metal-based surface chemistry is a well-practiced domain on interest in catalysis. A newborn in mussel-inspired coating based on catecholic chemistry,...     

Acid-promoted multicomponent allylic amidation towards 7-acetamido tetrahydroindole derivatives

An acid-promoted multicomponent reaction for the direct C(sp³)N bond formation was achieved through intermolecular allylic amidation in a one-pot operation to synthesize 7-acetamido tetrahydroindole derivatives from simple and readily available arylglyoxal monohydrates, acetonitriles, and enamines of 5,5-dimethyl-1,3-cyclohexadione (dimedone) has been developed. Here acetonitrile acts both as solvent and reagent. These tetahydroindole derivatives are formed through domino condensation of the enamines and arylglyoxals followed by annulation and allylic amidation.