Powerful sets: a generalisation of binary matroids

A set $S\subseteq\{0,1\}^E$ of binary vectors, with positions indexed by $E$, is said to be a \textit{powerful code} if, for all $X\subseteq E$, the number of vectors in $S$ that are zero in the positions indexed by $X$ is a power of 2. By treating binary vectors as characteristic vectors of subsets of $E$, we say that a set $S\subseteq2^E$ of subsets of $E$ is a \textit{powerful set} if the set of characteristic vectors of sets in $S$ is a powerful code. Powerful sets (codes) include cocircuit spaces of binary matroids (equivalently, linear codes over $\mathbb{F}_2$), but much more besides. Our motivation is that, to each powerful set, there is an associated nonnegative-integer-valued rank function (by a construction of Farr), although it does not in general satisfy all the matroid rank axioms. In this paper we investigate the combinatorial properties of powerful sets. We prove fundamental results on special elements (loops, coloops, frames, near-frames, and stars), their associated types of single-element extensions, various ways of combining powerful sets to get new ones, and constructions of nonlinear powerful sets. We show that every powerful set is determined by its clutter of minimal nonzero members. Finally, we show that the number of powerful sets is doubly exponential, and hence that almost all powerful sets are nonlinear.Comment: 19 pages. This work was presented at the 40th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing (40ACCMCC), University of Newcastle, Australia, Dec. 201

Mixed Statistics on 01-Fillings of Moon Polyominoes

We establish a stronger symmetry between the numbers of northeast and southeast chains in the context of 01-fillings of moon polyominoes. Let \M be a moon polyomino with $n$ rows and $m$ columns. Consider all the 01-fillings of \M in which every row has at most one 1. We introduce four mixed statistics with respect to a bipartition of rows or columns of \M. More precisely, let $S \subseteq \{1,2,..., n\}$ and $\mathcal{R}(S)$ be the union of rows whose indices are in $S$. For any filling $M$, the top-mixed (resp. bottom-mixed) statistic $\alpha(S; M)$ (resp. $\beta(S; M)$) is the sum of the number of northeast chains whose top (resp. bottom) cell is in $\mathcal{R}(S)$, together with the number of southeast chains whose top (resp. bottom) cell is in the complement of $\mathcal{R}(S)$. Similarly, we define the left-mixed and right-mixed statistics $\gamma(T; M)$ and $\delta(T; M)$, where $T$ is a subset of the column index set $\{1,2,..., m\}$. Let $\lambda(A; M)$ be any of these four statistics $\alpha(S; M)$, $\beta(S; M)$, $\gamma(T; M)$ and $\delta(T; M)$, we show that the joint distribution of the pair $(\lambda(A; M), \lambda(\bar A; M))$ is symmetric and independent of the subsets $S, T$. In particular, the pair of statistics $(\lambda(A;M), \lambda(\bar A; M))$ is equidistributed with (\se(M),\ne(M)), where \se(M) and $\ne(M)$ are the numbers of southeast chains and northeast chains of $M$, respectively.Comment: 20 pages, 6 figure

Strategies for Primary Prevention of Coronary Heart Disease Based on Risk Stratification by the ACC/AHA Lipid Guidelines, ATP III Guidelines, Coronary Calcium Scoring...

Background: Several approaches have been proposed for risk-stratification and primary prevention of coronary heart disease (CHD), but their comparative and cost-effectiveness is unknown. Methods: We constructed a state-transition microsimulation model to compare multiple approaches to the primary prevention of CHD in a simulated cohort of men aged 45–75 and women 55–75. Risk-stratification strategies included the 2013 American College of Cardiology/American Heart Association (ACC/AHA) guidelines on the treatment of blood cholesterol, the Adult Treatment Panel (ATP) III guidelines, and approaches based on coronary artery calcium (CAC) scoring and C-reactive protein (CRP). Additionally we assessed a treat-all strategy in which all individuals were prescribed either moderate-dose or high-dose statins and all males received low-dose aspirin. Outcome measures included CHD events, costs, medication-related side effects, radiation-attributable cancers, and quality-adjusted-life-years (QALYs) over a 30-year timeframe. Results: Treat-all with high-dose statins dominated all other strategies for both men and women, gaining 15.7 million QALYs, preventing 7.3 million myocardial infarctions, and saving over $238 billion, compared to the status quo, far outweighing its associated adverse events including bleeding, hepatitis, myopathy, and new-onset diabetes. ACC/AHA guidelines were more cost-effective than ATP III guidelines for both men and women despite placing 8.7 million more people on statins. For women at low CHD risk, treat-all with high-dose statins was more likely to cause a statin-related adverse event than to prevent a CHD event. Conclusions: Despite leading to a greater proportion of the population placed on statin therapy, the ACC/AHA guidelines are more cost-effective than ATP III. Even so, at generic prices, treating all men and women with statins and all men with low-dose aspirin appears to be more cost-effective than all risk-stratification approaches for the primary prevention of CHD. Especially for low-CHD risk women, decisions on the appropriate primary prevention strategy should be based on shared decision making between patients and healthcare providers

Parental Influences on Hmong University Students\u27 Success

This study reports findings from a series of focus groups conducted on Hmong American university students. The purpose of the focus groups was to understand how, from the perspective of Hmong American students themselves, acculturative stress and parents influenced academic success. Findings of a thematic analysis centered on general themes across focus group respondents that related to parental socialization, gendered socialization, and ethnic identification. Each identified themes is discussed in reference to gendered patterns of experiences in Hmong American families and in reference to academic success

Identification and characterization of dysregulated P-element induced wimpy testis-interacting RNAs in head and neck squamous cell carcinoma.

It is clear that alcohol consumption is a major risk factor in the pathogenesis of head and neck squamous cell carcinoma (HNSCC); however, the molecular mechanism underlying the pathogenesis of alcohol-associated HNSCC remains poorly understood. The aim of the present study was to identify and characterize P-element-induced wimpy testis (PIWI)-interacting RNAs (piRNAs) and PIWI proteins dysregulated in alcohol-associated HNSCC to elucidate their function in the development of this cancer. Using next generation RNA-sequencing (RNA-seq) data obtained from 40 HNSCC patients, the piRNA and PIWI protein expression of HNSCC samples was compared between alcohol drinkers and non-drinkers. A separate piRNA expression RNA-seq analysis of 18 non-smoker HNSCC patients was also conducted. To verify piRNA expression, reverse transcription-quantitative polymerase chain reaction (RT-qPCR) was performed on the most differentially expressed alcohol-associated piRNAs in ethanol and acetaldehyde-treated normal oral keratinocytes. The correlation between piRNA expression and patient survival was analyzed using Kaplan-Meier estimators and multivariate Cox proportional hazard models. A comparison between alcohol drinking and non-drinking HNSCC patients demonstrated that a panel of 3,223 piRNA transcripts were consistently detected and differentially expressed. RNA-seq analysis and in vitro RT-qPCR verification revealed that 4 of these piRNAs, piR-35373, piR-266308, piR-58510 and piR-38034, were significantly dysregulated between drinking and non-drinking cohorts. Of these four piRNAs, low expression of piR-58510 and piR-35373 significantly correlated with improved patient survival. Furthermore, human PIWI-like protein 4 was consistently upregulated in ethanol and acetaldehyde-treated normal oral keratinocytes. These results demonstrate that alcohol consumption may cause dysregulation of piRNA expression in HNSCC and in vitro verifications identified 4 piRNAs that may be involved in the pathogenesis of alcohol-associated HNSCC

Nanoparticles and their applications in cell and molecular biology

Nanoparticles can be engineered with distinctive compositions, sizes, shapes, and surface chemistries to enable novel techniques in a wide range of biological applications. The unique properties of nanoparticles and their behavior in biological milieu also enable exciting and integrative approaches to studying fundamental biological questions. This review will provide an overview of various types of nanoparticles and concepts of targeting nanoparticles. We will also discuss the advantages and recent applications of using nanoparticles as tools for drug delivery, imaging, sensing, and for the understanding of basic biological processes

Wellbore Permeability Estimates from Vertical Interference Testing of Existing Wells

AbstractWellbore integrity is considered an important risk factor for leakage of CO2 and formation fluids out of geological CO2 storage sites. Quantifying the effective hydraulic parameters that control vertical migration of fluids along the wellbore involves data collection through numerous field and laboratory experiments. The vertical interference test (VIT) is a downhole test designed to measure hydraulic communication of the outside-of-casing wellbore barrier system over a selected well section. Results from these tests can be analyzed numerically to determine the average permeability of the section. Several field surveys of existing wells have resulted in 9 VIT datasets, of which three are presented here. The effective permeability estimates for the three tests span two orders of magnitude, from approximately 1 mD to more than 100 mD. When compared with companion sidewall core analyses of the cement matrix that have permeabilities in the microD range, the VIT data suggest that interfaces or defects in the cement sheath are responsible for flow. Initial analysis of the remaining 6 datasets suggests an even larger range in effective permeability values, as low as microD to more than 1 D, indicating that well permeability can be highly variable from well to well and that high values of permeability are possible. These data provide important insights into realistic wellbore integrity of typical wells in N. America, and help us constrain models for understanding and mitigating risk of leakage during CO2 storage operations