Shifted shock formation for the 3D compressible Euler equations with damping and variation of the vorticity

In this paper, we consider the shock formation problem for the 3-dimensional(3D) compressible Euler equations with damping inspired by the work \cite{BSV3Dfulleuler}. It will be shown that for a class of large data, the damping can not prevent the formation of point shock, and the damping effect shifts the shock time and the wave amplitude while the shock location and the blow up direction remain the same with the information of this point shock being computed explicitly. Moreover, the vorticity is concentrated in the non-blow-up direction, which varies exponentially due to the damping effect. Our proof is based on the estimates for the modulated self-similar variables and lower bounds for the Lagrangian trajectories

Emerging technologies in ventilation

Innovation in ventilation systems is becoming an increasingly popular and targeted topic of architectural discourse. Architects, consultants and contractors are introducing new products and proposing new systems, subject to client requests for an environmentally responsive architecture. The authors, in compiling the research for this guide, experienced a large increase in Australian constructed buildings that focused specifically on ventilation strategies and systems. This note presents and discusses the underlying principles of different ventilation techniques. Applications of specific ventilation techniques are demonstrated through building examples constructed in Australia as well as overseas. Although a particular building design may demonstrate several ventilation concepts simultaneously, this note illustrates the most dominant ventilation features in each example. <br /

Genetic heterogeneity analysis using genetic algorithm and network science

Through genome-wide association studies (GWAS), disease susceptible genetic variables can be identified by comparing the genetic data of individuals with and without a specific disease. However, the discovery of these associations poses a significant challenge due to genetic heterogeneity and feature interactions. Genetic variables intertwined with these effects often exhibit lower effect-size, and thus can be difficult to be detected using machine learning feature selection methods. To address these challenges, this paper introduces a novel feature selection mechanism for GWAS, named Feature Co-selection Network (FCSNet). FCS-Net is designed to extract heterogeneous subsets of genetic variables from a network constructed from multiple independent feature selection runs based on a genetic algorithm (GA), an evolutionary learning algorithm. We employ a non-linear machine learning algorithm to detect feature interaction. We introduce the Community Risk Score (CRS), a synthetic feature designed to quantify the collective disease association of each variable subset. Our experiment showcases the effectiveness of the utilized GA-based feature selection method in identifying feature interactions through synthetic data analysis. Furthermore, we apply our novel approach to a case-control colorectal cancer GWAS dataset. The resulting synthetic features are then used to explain the genetic heterogeneity in an additional case-only GWAS dataset

Miniature probe for allâ optical double gradientâ index lenses photoacoustic microscopy

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146638/1/jbio201800147.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146638/2/jbio201800147_am.pd