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Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general logical axioms is an open problem. We develop a method to enable principled derivations of models of natural phenomena from axiomatic knowledge and experimental data by combining logical reasoning with symbolic regression. We demonstrate these concepts for Kepler's third law of planetary motion, Einstein's relativistic time-dilation law, and Langmuir's theory of adsorption. We show we can discover governing laws from few data points when logical reasoning is used to distinguish between candidate formulae having similar error on the data., (© 2023. The Author(s).)

Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into theorem provers to improve their performance automatically. In this work, we describe TRAIL (Trial Reasoner for AI that Learns), a deep learning-based approach to theorem proving that characterizes core elements of saturation-based theorem proving within a neural framework. TRAIL leverages (a) an effective graph neural network for representing logical formulas, (b) a novel neural representation of the state of a saturation-based theorem prover in terms of processed clauses and available actions, and (c) a novel representation of the inference selection process as an attention-based action policy. We show through a systematic analysis that these components allow TRAIL to significantly outperform previous reinforcement learning-based theorem provers on two standard benchmark datasets (up to 36% more theorems proved). In addition, to the best of our knowledge, TRAIL is the first reinforcement learning-based approach to exceed the performance of a state-of-the-art traditional theorem prover on a standard theorem proving benchmark (solving up to 17% more theorems).

The synthesis of 2,6-bis-anilino-3-nitropyridines that are alkylated or acylated at the anilino nitrogen atoms is described. These derivatives show characteristic differences in the 1H-NMR spectra compared with the unsubstituted parent compound. These differences are used to determine structure-conformation relationships of this type of compounds. The conclusions drawn from the 1H-NMR spectra in this respect are supported by X-ray crystallographic data and by 1H-NMR data of conformationally restricted analogues. Preliminary investigations indicate that these relationships can in principle be extended to other diarylamines.

Benzimidazole 5-carboxamide derivatives from a combinatorial screening library were discovered as specific inhibitors of the NS5B polymerase of the hepatitis C virus (HCV). Initial hit-to-lead activities taking advantage of high-throughput parallel synthetic techniques, identified a 1,2-disubstituted benzimidazole 5-carboxylic acid scaffold as the minimum core for biological activity. Potent analogues in this series inhibit the polymerase at low micromolar concentrations and provide an attractive "drug-like" lead structure for further optimization and the development of potential HCV therapeutics.

Label-free optical detection methods are of particular value for the investigation of biomolecular interactions. A label-free method based on reflectometric interference spectroscopy is described which enables both the on-line monitoring of solid phase peptide syntheses and subsequently the determination of antibody binding to these peptides without cleavage from the support. The method uses SiO(2) transducers that were modified with diaminopolyethylene glycol. The stepwise coupling of different amino acids to the transducer surface was investigated and the complete monitoring of the synthesis of a viral epitope was performed. The success of the synthesis was proven via binding of a specific monoclonal antibody to the transducer-bound product. In order to demonstrate specificity the binding was inhibited with the same peptide epitope added in solution. The approach is attractive especially in the field of high throughput screening since both the synthesis and the interaction with the biological receptor can be monitored using the same technique., ((c)2001 Elsevier Science.)

A strategy of practical drug design is developed on the basis of the theory of sets. This strategy accounts for the fact that new drugs are required to optimally approach a certain activity profile rather than showing maximal intrinsic activity. In addition, modern structure selection techniques as well as qualitative and quantitative structure-activity relationships are incorporated in the strategy so as to optimally contribute to an economical use of experimental capacity.

A new type of cardiotonic compounds is developed by applying a systematic drug design procedure based on the theory of sets. With the aid of clinical and pharmacological experience in the field of cardiotonic drugs and from biomolecular considerations a structural field (set) is selected which is likely to contain compounds which show the desired activity profile. By systematic exclusion of inappropriate parts of this structural field (subsets) the original set is reduced to a small structural area (residue set) the structures (elements) of which have a high potential of being new cardiotonic drugs with an activity profile superior to hitherto known compounds. In our case one of the elements, 2-[(2-methoxy-4-methylsulfinyl)phenyl]-1H-imidazo[4,5-b]pyridine (AR-L 115 BS), proved to fulfil all the requirements of the medicinal objective. The structure of AR-L 115 differs significantly from all other cardiotonic principles and therefore represents an entirely new type of positive inotropic agents.

A simple steric parameter Sb is formulated on the basis of substituent branching. This parameter can be calculated for every conceivable substituent and gives an estimate of steric effects which is sufficient for most purposes in practical drug design. Sb may also be applied to quantitative structure-activity relationships.