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

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

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

Strong Completeness for Markovian Logics

In this paper we present Hilbert-style axiomatizations for three logics for reasoning about continuous-space Markov processes (MPs): (i) a logic for MPs defined for probability distributions on measurable state spaces, (ii) a logic for MPs defined for sub-probability distributions and (iii) a logic defined for arbitrary distributions.These logics are not compact so one needs infinitary rules in order to obtain strong completeness results. We propose a new infinitary rule that replaces the so-called Countable Additivity Rule (CAR) currently used in the literature to address the problem of proving strong completeness for these and similar logics. Unlike the CAR, our rule has a countable set of instances; consequently it allows us to apply the Rasiowa-Sikorski lemma for establishing strong completeness. Our proof method is novel and it can be used for other logics as well

Leading with heart: Academic leadership during the COVID-19 crisis

The COVID-19 pandemic has impacted every sphere of life. It has brought into sharp focus not only the critical role that leaders have to play in taking charge of their organisations and employees, but the complexity of that leadership role, too. The authors of this paper are both psychologists who occupy leadership positions in a university. The paper briefly explores the evolution of leadership theory, leadership in times of crises, generally, and leadership during the time of COVID-19. In addition, one of the authors offers a personal note on the leadership experience during COVID-19. What became clear during the reflections was that empathy, vulnerability, self-awareness and agility were some of the qualities needed during this crisis. In addition, the psychodynamic concept of containment appears very relevant in managing the affective intensity experienced by staff and students. Leaders were expected to not only fully understand the meaning of empathy and compassion, but to know how to sincerely demonstrate these qualities to staff and students alike

Identity is About us: Leadership Lessons Learned During an Accreditation Journey

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156444/2/jls21694_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156444/1/jls21694.pd

Instability in stratified shear flow: Review of a physical interpretation based on interacting waves

Instability in homogeneous and density stratified shear flows may be interpreted in terms of the interaction of two (or more) otherwise free waves in the velocity and density profiles. These waves exist on gradients of vorticity and density, and instability results when two fundamental conditions are satisfied: (I) the phase speeds of the waves are stationary with respect to each other ("phase-locking"), and (II) the relative phase of the waves is such that a mutual growth occurs. The advantage of the wave interaction approach is that it provides a physical interpretation to shear flow instability. This paper is largely intended to purvey the basics of this physical interpretation to the reader, while both reviewing and consolidating previous work on the topic. The interpretation is shown to provide a framework for understanding many classical and nonintuitive results from the stability of stratified shear flows, such as the Rayleigh and Fjørtoft theorems, and the destabilizing effect of an otherwise stable density stratification. Finally, we describe an application of the theory to a geophysical-scale flow in the Fraser River estuary