Maximal induced matchings in triangle-free graphs

An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. It is known that any $n$-vertex graph has at most $10^{n/5} \approx 1.5849^n$ maximal induced matchings, and this bound is best possible. We prove that any $n$-vertex triangle-free graph has at most $3^{n/3} \approx 1.4423^n$ maximal induced matchings, and this bound is attained by any disjoint union of copies of the complete bipartite graph $K_{3,3}$. Our result implies that all maximal induced matchings in an $n$-vertex triangle-free graph can be listed in time $O(1.4423^n)$, yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.Comment: 17 page

Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Airflow Dynamics of Human Jets: Sneezing and Breathing - Potential Sources of Infectious Aerosols

10.1371/journal.pone.0059970PLoS ONE84

Voice Navigation Effects on Real-World Lane Change Driving Analysis Using an Electroencephalogram

© 2018 IEEE. Improving the degree of assistance given by in-car navigation systems is an important issue for the safety of both drivers and passengers. There is a vast body of research that assesses the usability and interfaces of the existing navigation systems but very few investigations study the impact on the brain activity based on navigation-based driving. In this paper, a real-world experiment is designed to acquire the electroencephalography (EEG) and in-car information to analyze the dynamic brain activity while the driver is performing the lane-changing task based on the auditory instructions from an in-car navigation system. The results show that auditory cues can influence the speed and increase the frontal EEG delta and beta power, which is related to motor preparation and decision making during a lane change. However, there were no significant results on the alpha power. A better lane-change assessment can be obtained using specific vehicle information (lateral acceleration and heading angle) with EEG features for future naturalized driving study

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

Histone deacetylase adaptation in single ventricle heart disease and a young animal model of right ventricular hypertrophy.

BackgroundHistone deacetylase (HDAC) inhibitors are promising therapeutics for various forms of cardiac diseases. The purpose of this study was to assess cardiac HDAC catalytic activity and expression in children with single ventricle (SV) heart disease of right ventricular morphology, as well as in a rodent model of right ventricular hypertrophy (RVH).MethodsHomogenates of right ventricle (RV) explants from non-failing controls and children born with a SV were assayed for HDAC catalytic activity and HDAC isoform expression. Postnatal 1-day-old rat pups were placed in hypoxic conditions, and echocardiographic analysis, gene expression, HDAC catalytic activity, and isoform expression studies of the RV were performed.ResultsClass I, IIa, and IIb HDAC catalytic activity and protein expression were elevated in the hearts of children born with a SV. Hypoxic neonatal rats demonstrated RVH, abnormal gene expression, elevated class I and class IIb HDAC catalytic activity, and protein expression in the RV compared with those in the control.ConclusionsThese data suggest that myocardial HDAC adaptations occur in the SV heart and could represent a novel therapeutic target. Although further characterization of the hypoxic neonatal rat is needed, this animal model may be suitable for preclinical investigations of pediatric RV disease and could serve as a useful model for future mechanistic studies

Airflow Dynamics of Coughing in Healthy Human Volunteers by Shadowgraph Imaging: An Aid to Aerosol Infection Control

Cough airflow dynamics have been previously studied using a variety of experimental methods. In this study, real-time, non-invasive shadowgraph imaging was applied to obtain additional analyses of cough airflows produced by healthy volunteers. Twenty healthy volunteers (10 women, mean age 32.2±12.9 years; 10 men, mean age 25.3±2.5 years) were asked to cough freely, then into their sleeves (as per current US CDC recommendations) in this study to analyze cough airflow dynamics. For the 10 females (cases 1–10), their maximum detectable cough propagation distances ranged from 0.16–0.55 m, with maximum derived velocities of 2.2–5.0 m/s, and their maximum detectable 2-D projected areas ranged from 0.010–0.11 m2, with maximum derived expansion rates of 0.15–0.55 m2/s. For the 10 males (cases 11–20), their maximum detectable cough propagation distances ranged from 0.31–0.64 m, with maximum derived velocities of 3.2–14 m/s, and their maximum detectable 2-D projected areas ranged from 0.04–0.14 m2, with maximum derived expansion rates of 0.25–1.4 m2/s

The effects of symmetry on the dynamics of antigenic variation

In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the dynamics of immune escape of other parasites, as well as for the dynamics of multi-strain diseases.Comment: 21 pages, 4 figures; J. Math. Biol. (2012), Online Firs

Alternative low-cost adsorbent for water and wastewater decontamination derived from eggshellwaste: an overview

As the current global trend towards more stringent environmental standards, technical applicability and cost-effectiveness became key factors in the selection of adsorbents for water and wastewater treatment. Recently, various low-cost adsorbents derived from agricultural waste, industrial by-products or natural materials, have been intensively investigated. In this respect, the eggshells from egg-breaking operations constitute significant waste disposal problems for the food industry, so the development of value-added by-products from this waste is to be welcomed. The egg processing industry is very competitive, with low profit margins due to global competition and cheap imports. Additionally, the costs associated with the egg shell disposal (mainly on landfill sites) are significant, and expected to continue increasing as landfill taxes increase. The aim of the present review is to provide an overview on the development of low-cost adsorbents derived from eggshell by-products