Machine Learning With Tree Tensor Networks, CP Rank Constraints, and Tensor Dropout.

Tensor networks developed in the context of condensed matter physics try to approximate order- N tensors with a reduced number of degrees of freedom that is only polynomial in N and arranged as a network of partially contracted smaller tensors. As we have recently demonstrated in the context of quantum many-body physics, computation costs can be further substantially reduced by imposing constraints on the canonical polyadic (CP) rank of the tensors in such networks. Here, we demonstrate how tree tensor networks (TTN) with CP rank constraints and tensor dropout can be used in machine learning.

Targeting the Main Protease (M, nsp5) by Growth of Fragment Scaffolds Exploiting Structure-Based Methodologies.

The main protease M, nsp5, of SARS-CoV-2 (SCoV2) is one of its most attractive drug targets. Here, we report primary screening data using nuclear magnetic resonance spectroscopy (NMR) of four different libraries and detailed follow-up synthesis on the promising uracil-containing fragment Z604 derived from these libraries. Z604 shows time-dependent binding.

Large-Scale Crystallographic Fragment Screening Expedites Compound Optimization and Identifies Putative Protein-Protein Interaction Sites.

The identification of starting points for compound development is one of the key steps in early-stage drug discovery. Information-rich techniques such as crystallographic fragment screening can potentially increase the efficiency of this step by providing the structural information of the binding mode of the ligands in addition to the mere binding information. Here, we present the crystallographic screening of our 1000-plus-compound F2X-Universal Library against the complex of the yeast spliceosomal Prp8 RNaseH-like domain and the snRNP assembly factor Aar2.

Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems.

We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions.

The 3-triangle method preserves the posterior tibial slope during high tibial valgus osteotomy: first preliminary data using a mathematical model.

Purpose: Despite much improved preoperative planning techniques accurate intraoperative assessment of the high tibial valgus osteotomy (HTO) remains challenging and often results in coronal over- and under-corrections as well as unintended changes of the posterior tibial slope. Noyes et al. reported a novel method for accurate intraoperative coronal and sagittal alignment correction based on a three-dimensional mathematical model.