Finding Dominators via Disjoint Set Union

The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-linear-time algorithms exist, they use sophisticated data structures. We develop an algorithm for finding dominators that uses only a "static tree" disjoint set data structure in addition to simple lists and maps. The algorithm runs in near-linear or linear time, depending on the implementation of the disjoint set data structure. We give several versions of the algorithm, including one that computes loop nesting information (needed in many kinds of global code optimization) and that can be made self-certifying, so that the correctness of the computed dominators is very easy to verify

Development of an algebraic turbulence model for analysis of propulsion flows

A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC

Alignment via friction for nonisothermal multicomponent fluid systems

The derivation of an approximate Class-I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class-II model is justified, by validating the Chapman-Enskog expansion performed from the Class-II model towards the Class-I model. The analysis proceeds by comparing two thermomechanical theories via relative entropy

Uniqueness of renormalized solutions for the Maxwell-Stefan system

We give conditions that guarantee uniqueness of renormalized solutions for the Maxwell-Stefan system. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we derive the identity for two renormalized solutions and use information on the spectrum of the Maxwell-Stefan matrix to estimate the symmetrized relative entropy and show uniqueness

Understanding chronic pain in the ubiquitous community: the role of open data

The combined use of social media, open data, and Artificial Intelligence has the potential to support practitioners and empower patients/citizens living with persistent pain, both as local and online communities. Given the wide availability of digital technology today, both practitioners and interested individuals can be connected with virtual communities and can support each other from the comfort of their homes. Digital means may represent new avenues for exploring the complexity of the pain experience. Online interactions of patients, data on effective treatments, and data collected by wearable devices may represent an incredible source of psychological, sociological, and physiological pain-related information. Digital means might provide several solutions that enhance inclusiveness and motivate patients to share personal experiences, limiting the sense of isolation in both rural and metropolitan areas. Building on the consensus of the usefulness of social media in enhancing the understanding of persistent pain and related subjective experiences via online communities and networks, we provide relevant scenarios where the effectiveness and efficiency of healthcare delivery might be improved by the adoption of the digital technologies mentioned above and repeated subsequently. The aim of this perspective paper is to explore the potential of open data, social media, and Artificial Intelligence in improving the prevention and management of persistent pain by adopting innovative non-biomedical approaches