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

Coupled plasma-neutral transport model for the scrape-off region

Analysis of the scrape-off region requires treatment of the plasma transport along and across the field lines and inclusion of the neutral transport effects. A method for modeling the scrape-off region that is presented here uses separate models for each of these aspects that are coupled together through an iteration procedure that requires only minimal numerical effort. The method is applied here to estimate the neutral pumping rates in the pump-limiter and divertor options for a proposed deuterium-tritium (D-T) ignition experiment. High neutral recycling in the vicinity of the neutralizer plate dramatically affects pumping rates for both the pump-limiter and divertor. In both cases, the plasma flow into the channel surrounding the neutralizer plate is greatly reduced by the neutral recycling. The fraction of this flow that is pumped can be large (> 50%), but in general it is dependent on the particular geometry and plasma conditions. It is estimated that pumping speeds approximately greater than 10/sup 5/ L/s are adequate for the exhaust requirements in the pump-limiter and the divertor cases. Also, high neutral recycling on the front surface of the limiter tends to increase the neutral pumping rate

Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model

Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The HMS model is syntax-free, which precludes the simple option to rely on formal language to induce lattices, and represents uncertainty and unawareness with one entangled construct, making it difficult to assess the properties of either. Here, we present a model based on a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show the models to be equivalent by defining transformations between them which preserve formula satisfaction, and obtain completeness through our and HMS' results.Comment: 18 pages, 2 figures, proceedings of DaLi conference 202

Computational Methods Used in Hit-to-Lead and Lead Optimization Stages of Structure-Based Drug Discovery

GPCR modeling approaches are widely used in the hit-to-lead (H2L) and lead optimization (LO) stages of drug discovery. The aims of these modeling approaches are to predict the 3D structures of the receptor-ligand complexes, to explore the key interactions between the receptor and the ligand and to utilize these insights in the design of new molecules with improved binding, selectivity or other pharmacological properties. In this book chapter, we present a brief survey of key computational approaches integrated with hierarchical GPCR modeling protocol (HGMP) used in hit-to-lead (H2L) and in lead optimization (LO) stages of structure-based drug discovery (SBDD). We outline the differences in modeling strategies used in H2L and LO of SBDD and illustrate how these tools have been applied in three drug discovery projects

Reasoning with global assumptions in arithmetic modal logics

We establish a generic upper bound ExpTime for reasoning with global assumptions in coalgebraic modal logics. Unlike earlier results of this kind, we do not require a tractable set of tableau rules for the in- stance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that offers potential for practical reasoning