On the role of vortex stretching in energy optimal growth of three dimensional perturbations on plane parallel shear flows

The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille, and mixing layer shear profiles is robust and resembles localized plane-waves in regions where the background shear is large. The waves are tilted with the shear when the span-wise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification reflects on the optimal energy growth. This perspective provides an understanding of the three dimensional growth solely from the two dimensional dynamics on the shear plane

Universal interactive preferences

We prove that a universal preference type space exists under much more general conditions than those postulated by Epstein and Wang (1996). To wit, it is enough that preferences can be encoded by a countable collection of continuous functionals, while the preferences themselves need not necessarily be continuous or regular, like, e.g., in the case of lexicographic preferences. The proof relies on a far-reaching generalization of a method developed by Heifetz and Samet (1998)

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given

Predicting Residence Time of GPCR Ligands with Machine Learning

Drug-target residence time, the duration of binding at a given protein target, has been shown in some protein families to be more significant for conferring efficacy than binding affinity. To carry out efficient optimization of residence time in drug discovery, machine learning models that can predict that value need to be developed. One of the main challenges with predicting residence time is the paucity of data. This chapter outlines all of the currently available ligand kinetic data, providing a repository that contains the largest publicly available source of GPCR-ligand kinetic data to date. To help decipher the features of kinetic data that might be beneficial to include in computational models for the prediction of residence time, the experimental evidence for properties that influence residence time are summarized. Finally, two different workflows for predicting residence time with machine learning are outlined. The first is a single-target model trained on ligand features; the second is a multi-target model trained on features generated from molecular dynamics simulations

Liberal parentalism

What normative constraints should bind parents (or policy makers) if they intervene in the choices of children (or constituencies) whose preferences evolve over time? For a sophisticated child who anticipates correctly his preference change, we prove that generically there exist parental interventions that are Pareto improving over the backward induction path that the child will follow on his own. If, in contrast, the child misperceives his future preferences, Pareto improving interventions might not exist, and even nudges might be painfully sobering. The parent may then choose to minimize the maximal disappointment along time that her benevolent intervention would cause

Leading Boldly: Foundations Can Move Past Traditional Approaches to Create Social Change Through Imaginative -- Even Controversial -- Leadership

Rarely do foundations publicly communicate their dissatisfaction with their grantees, withhold funds, or use tactics that carry the risks of creating ill will. Yet extraordinary results can be achieved if foundations were more imaginative, visible, and controversial. Three foundations shocked the city of Pittsburgh in 2002 by abruptly suspending their funding to local public schools. The foundations announced their decision in a news conference that attracted both local and national coverage -- a sharp departure from their usual approach of working quietly behind the scenes. Foundation executives explained that they had completely lost confidence in the ability of the local school board to run the district. Their action yielded a community-wide process that led to real change. Here's how foundations can exercise Adaptive Leadership without misusing authority

On the normal form of synchronization and resonance between vorticity waves in shear flow instability

A central mechanism of linearised two dimensional shear instability can be described in terms of a nonlinear, action-at-a-distance, phase-locking resonance between two vorticity waves which propagate counter to their local mean flow as well as counter to each other. Here we analyze the prototype of this interaction as an autonomous, nonlinear dynamical system. The wave interaction equations can be written in a generalized Hamiltonian action-angle form. The pseudo-energy serves as the Hamiltonian of the system, the action coordinates are the contribution of the vorticity waves to the wave-action, and the angles are the phases of the vorticity waves. The term "generalized action-angle" emphasizes that the action of each wave is generally time dependent, which allows instability. The synchronization mechanism between the wave phases depends on the cosine of their relative phase, rather than the sine as in the Kuramoto model. The unstable normal modes of the linearised dynamics correspond to the stable fixed points of the dynamical system and vice versa. Furthermore, the normal form of the wave interaction dynamics reveals a new type of inhomogeneous bifurcation -- annihilation of a pair of stable and unstable fixed points yields the emergence of two neutral center fixed points of opposite circulation

Rapid and Accurate Assessment of GPCR-Ligand Interactions Using the Fragment Molecular Orbital-Based Density-Functional Tight-Binding Method

The reliable and precise evaluation of receptor–ligand interactions and pair-interaction energy is an essential element of rational drug design. While quantum mechanical (QM) methods have been a promising means by which to achieve this, traditional QM is not applicable for large biological systems due to its high computational cost. Here, the fragment molecular orbital (FMO) method has been used to accelerate QM calculations, and by combining FMO with the density-functional tight-binding (DFTB) method we are able to decrease computational cost 1000 times, achieving results in seconds, instead of hours. We have applied FMO-DFTB to three different GPCR–ligand systems. Our results correlate well with site directed mutagenesis data and findings presented in the published literature, demonstrating that FMO-DFTB is a rapid and accurate means of GPCR–ligand interactions

Synergistic Use of GPCR Modeling and SDM Experiments to Understand Ligand Binding

There is a substantial amount of historical ligand binding data available from site-directed mutagenesis (SDM) studies of many different GPCR subtypes. This information was generated prior to the wave of GPCR crystal structure, in an effort to understand ligand binding with a view to drug discovery. Concerted efforts to determine the atomic structure of GPCRs have proven extremely successful and there are now more than 80 GPCR crystal structure in the PDB database, many of which have been obtained in the presence of receptor ligands and associated G proteins. These structural data enable the generation of computational model structures for all GPCRs, including those for which crystal structures do not yet exist. The power of these models in designing novel ligands, especially those with improved residence times, and for better understanding receptor function can be enhanced tremendously by combining them synergistically with historic SDM ligand binding data. Here, we describe a protocol by which historic SDM binding data and receptor models may be used together to identify novel key residues for mutagenesis studies