A new statistical solution to the generality problem

The Generality Problem is widely recognized to be a serious problem for reliabilist theories of justification. James R. Beebe's Statistical Solution is one of only a handful of attempted solutions that has garnered serious attention in the literature. In their recent response to Beebe, Julien Dutant and Erik J. Olsson successfully refute Beebe's Statistical Solution. This paper presents a New Statistical Solution that countenances Dutant and Olsson's objections, dodges the serious problems that trouble rival solutions, and retains the theoretical virtues that made Beebe's solution so attractive in the first place. There indeed exists a principled, rigorous, conceptually sparse, and plausible solution to the Generality Problem: it is the New Statistical Solution

Generating Molecular Fragmentation Graphs with Autoregressive Neural Networks

The accurate prediction of tandem mass spectra from molecular structures has the potential to unlock new metabolomic discoveries by augmenting the community's libraries of experimental reference standards. Cheminformatic spectrum prediction strategies use a "bond-breaking" framework to iteratively simulate mass spectrum fragmentations, but these methods are (a) slow, due to the need to exhaustively and combinatorially break molecules and (b) inaccurate, as they often rely upon heuristics to predict the intensity of each resulting fragment; neural network alternatives mitigate computational cost but are black-box and not inherently more accurate. We introduce a physically-grounded neural approach that learns to predict each breakage event and score the most relevant subset of molecular fragments quickly and accurately. We evaluate our model by predicting spectra from both public and private standard libraries, demonstrating that our hybrid approach offers state of the art prediction accuracy, improved metabolite identification from a database of candidates, and higher interpretability when compared to previous breakage methods and black box neural networks. The grounding of our approach in physical fragmentation events shows especially high promise for elucidating natural product molecules with more complex scaffolds.Comment: 11 pages, 17 pages with references and appendix, 5 figure

APPLICATION OF DISCRETE BASIS SET METHODS TO THE DIRAC EQUATION.

A variational discrete representation of the relativistic energy spectrum of an electron in a Coulomb field is constructed. It is shown that by a proper choice of the variational basis set, the eigenvalues satisfy a generalized Hylleraas-Undheim theorem. A number of relativistic sum rules which can be evaluated exactly are calculated by means of the basis set to demonstrate that the variational solutions obtained by the diagonalization of the Dirac Hamiltonian with a Coulomb potential yield a discrete representation of the hydrogenic spectrum including both the positive and negative continua. The results strongly suggest that the set of relativistic variational eigenvectors and eigenvalues can be used to construct a discrete representation of the Dirac-Green\u27s function. As applications, the relativistic basis set is used to calculate relativistic values for dipole polarizabilities, electric dipole oscillator strength sums for the ground state with and without retardation, and two-photon decay rates for the metastable 2s(, 1/2) state in hydrogenic ions. The two-photon decay rates differ from previous calculations due to the inclusion of higher order retardation corrections. Our oscillator strength sums from the ground state appear to be much more accurate than earlier calculations. The oscillator strength densities in the continuum are used to calculate photoionization cross-sections by a Stieltjes imaging technique.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1981 .G6424. Source: Dissertation Abstracts International, Volume: 42-03, Section: B, page: 1057. Thesis (Ph.D.)--University of Windsor (Canada), 1981

A physical approach to spherical stars.

Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1977 .G643. Source: Masters Abstracts International, Volume: 40-07, page: . Thesis (M.Sc.)--University of Windsor (Canada), 1977

Prefix-Tree Decoding for Predicting Mass Spectra from Molecules

Computational predictions of mass spectra from molecules have enabled the discovery of clinically relevant metabolites. However, such predictive tools are still limited as they occupy one of two extremes, either operating (a) by fragmenting molecules combinatorially with overly rigid constraints on potential rearrangements and poor time complexity or (b) by decoding lossy and nonphysical discretized spectra vectors. In this work, we use a new intermediate strategy for predicting mass spectra from molecules by treating mass spectra as sets of molecular formulae, which are themselves multisets of atoms. After first encoding an input molecular graph, we decode a set of molecular subformulae, each of which specify a predicted peak in the mass spectrum, the intensities of which are predicted by a second model. Our key insight is to overcome the combinatorial possibilities for molecular subformulae by decoding the formula set using a prefix tree structure, atom-type by atom-type, representing a general method for ordered multiset decoding. We show promising empirical results on mass spectra prediction tasks

MIST-CF: Chemical formula inference from tandem mass spectra

Chemical formula annotation for tandem mass spectrometry (MS/MS) data is the first step toward structurally elucidating unknown metabolites. While great strides have been made toward solving this problem, the current state-of-the-art method depends on time-intensive, proprietary, and expert-parameterized fragmentation tree construction and scoring. In this work we extend our previous spectrum Transformer methodology into an energy based modeling framework, MIST-CF, for learning to rank chemical formula and adduct assignments given an unannotated MS/MS spectrum. Importantly, MIST-CF learns in a data dependent fashion using a Formula Transformer neural network architecture and circumvents the need for fragmentation tree construction. We train and evaluate our model on a large open-access database, showing an absolute improvement of 10% top 1 accuracy over other neural network architectures. We further validate our approach on the CASMI2022 challenge dataset, achieving nearly equivalent performance to the winning entry within the positive mode category without any manual curation or post-processing of our results. These results demonstrate an exciting strategy to more powerfully leverage MS2 fragment peaks for predicting MS1 precursor chemical formula with data driven learning