Schrödinger

About: Schrödinger is a based out in . It is known for research contribution in the topics: Sputtering & Ion. The organization has 1621 authors who have published 2200 publications receiving 81554 citations.

Parabolic Geometries I

Abstract: The first monograph on parabolic geometry in the literature following several ground-braking results achieved by the authors and their collaborators in the last two decades. The volume will be followed by the second one focused on mathematical applications

'Sum over surfaces' form of loop quantum gravity

Abstract: We derive a spacetime formulation of quantum general relativity from (Hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the three-geometry in proper time. We show that the perturbation expansion of this operator is finite and computable order by order. By giving a graphical representation in the manner of Feynman of this expansion, we find that the theory can be expressed as a sum over topologically inequivalent (branched, colored) two-dimensional (2D) surfaces in 4D. The contribution of one surface to the sum is given by the product of one factor per branching point of the surface. Therefore branching points play the role of elementary vertices of the theory. Their value is determined by the matrix elements of the Hamiltonian constraint, which are known. The formulation we obtain can be viewed as a continuum version of Reisenberger's simplicial quantum gravity. Also, it has the same structure as the Ooguri-Crane-Yetter 4D topological field theory, with a few key differences that illuminate the relation between quantum gravity and topological quantum field theory. Finally, we suggest that certain new terms should be added to the Hamiltonian constraint in order to implement a ``crossing'' symmetry related to 4D diffeomorphism invariance.

Analysis and comparison of 2D fingerprints: Insights into database screening performance using eight fingerprint methods

Abstract: Virtual screening is a widely used strategy in modern drug discovery and 2D fingerprint similarity is an important tool that has been successfully applied to retrieve active compounds from large datasets. However, it is not always straightforward to select an appropriate fingerprint method and associated settings for a given problem. Here, we applied eight different fingerprint methods, as implemented in the new cheminformatics package Canvas, on a well-validated dataset covering five targets. The fingerprint methods include Linear, Dendritic, Radial, MACCS, MOLPRINT2D, Pairwise, Triplet, and Torsion. We find that most fingerprints have similar retrieval rates on average; however, each has special characteristics that distinguish its performance on different query molecules and ligand sets. For example, some fingerprints exhibit a significant ligand size dependency whereas others are more robust with respect to variations in the query or active compounds. In cases where little information is known about the active ligands, MOLPRINT2D fingerprints produce the highest average retrieval actives. When multiple queries are available, we find that a fingerprint averaged over all query molecules is generally superior to fingerprints derived from single queries. Finally, a complementarity metric is proposed to determine which fingerprint methods can be combined to improve screening results.