Reduced-complexity interpolating control with periodic invariant sets

2021 ◽  
pp. 1-0
Author(s):  
Sheila Scialanga ◽  
Sorin Olaru ◽  
Konstantinos Ampountolas
Keyword(s):  
Invariant Sets ◽  
Reduced Complexity

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

Medicinal Chemistry Database GDBMedChem

2019 ◽  
Author(s):  
Mahendra Awale ◽  
Finton Sirockin ◽  
Nikolaus Stiefl ◽  
Jean-Louis Reymond
Keyword(s):  
Small Molecules ◽  
Natural Product ◽  
Medicinal Chemistry ◽  
3D Visualization ◽  
Molecular Size ◽  
Similarity Searching ◽  
Complex Molecules ◽  
Synthetic Accessibility ◽  
Simple Chemical ◽  
Reduced Complexity

<div>The generated database GDB17 enumerates 166.4 billion possible molecules up to 17 atoms of C, N, O, S and halogens following simple chemical stability and synthetic feasibility rules, however medicinal chemistry criteria are not taken into account. Here we applied rules inspired by medicinal chemistry to exclude problematic functional groups and complex molecules from GDB17, and sampled the resulting subset evenly across molecular size, stereochemistry and polarity to form GDBMedChem as a compact collection of 10 million small molecules.</div><div><br></div><div>This collection has reduced complexity and better synthetic accessibility than the entire GDB17 but retains higher sp 3 - carbon fraction and natural product likeness scores compared to known drugs. GDBMedChem molecules are more diverse and very different from known molecules in terms of substructures and represent an unprecedented source of diversity for drug design. GDBMedChem is available for 3D-visualization, similarity searching and for download at http://gdb.unibe.ch.</div>

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