Chains, Antichains, and Complements in Infinite Partition Lattices

We consider the partition lattice $\Pi_\kappa$ on any set of transfinite cardinality $\kappa$ and properties of $\Pi_\kappa$ whose analogues do not hold for finite cardinalities. Assuming the Axiom of Choice we prove: (I) the cardinality of any maximal well-ordered chain is always exactly $\kappa$; (II) there are maximal chains in $\Pi_\kappa$ of cardinality $> \kappa$; (III) if, for every cardinal $\lambda < \kappa$, we have $2^{\lambda} < 2^\kappa$, there exists a maximal chain of cardinality $< 2^{\kappa}$ (but $\ge \kappa$) in $\Pi_{2^\kappa}$; (IV) every non-trivial maximal antichain in $\Pi_\kappa$ has cardinality between $\kappa$ and $2^{\kappa}$, and these bounds are realized. Moreover we can construct maximal antichains of cardinality $\max(\kappa, 2^{\lambda})$ for any $\lambda \le \kappa$; (V) all cardinals of the form $\kappa^\lambda$ with $0 \le \lambda \le \kappa$ occur as the number of complements to some partition $\mathcal{P} \in \Pi_\kappa$, and only these cardinalities appear. Moreover, we give a direct formula for the number of complements to a given partition; (VI) Under the Generalized Continuum Hypothesis, the cardinalities of maximal chains, maximal antichains, and numbers of complements are fully determined, and we provide a complete characterization.Comment: 24 pages, 2 figures. Submitted to Algebra Universalis on 27/11/201

DNA expression microarrays may be the wrong tool to identify biological pathways

DNA microarray expression signatures are expected to provide new insights into patho- physiological pathways. Numerous variant statistical methods have been described for each step of the signal analysis. We employed five similar statistical tests on the same data set at the level of gene selection. Inter-test agreement for the identification of biological pathways in BioCarta, KEGG and Reactome was calculated using Cohen&#x2019;s k- score. The identification of specific biological pathways showed only moderate agreement (0.30 &#x3c; k &#x3c; 0.79) between the analysis methods used. Pathways identified by microarrays must be treated cautiously as they vary according to the statistical method used

Examining agreement between clinicians when assessing sick children.

BACKGROUND: Case management guidelines use a limited set of clinical features to guide assessment and treatment for common childhood diseases in poor countries. Using video records of clinical signs we assessed agreement among experts and assessed whether Kenyan health workers could identify signs defined by expert consensus. METHODOLOGY: 104 videos representing 11 clinical sign categories were presented to experts using a web questionnaire. Proportionate agreement and agreement beyond chance were calculated using kappa and the AC1 statistic. 31 videos were selected and presented to local health workers, 20 for which experts had demonstrated clear agreement and 11 for which experts could not demonstrate agreement. PRINCIPAL FINDINGS: Experts reached very high level of chance adjusted agreement for some videos while for a few videos no agreement beyond chance was found. Where experts agreed Kenyan hospital staff of all cadres recognised signs with high mean sensitivity and specificity (sensitivity: 0.897-0.975, specificity: 0.813-0.894); years of experience, gender and hospital had no influence on mean sensitivity or specificity. Local health workers did not agree on videos where experts had low or no agreement. Results of different agreement statistics for multiple observers, the AC1 and Fleiss' kappa, differ across the range of proportionate agreement. CONCLUSION: Videos provide a useful means to test agreement amongst geographically diverse groups of health workers. Kenyan health workers are in agreement with experts where clinical signs are clear-cut supporting the potential value of assessment and management guidelines. However, clinical signs are not always clear-cut. Video recordings offer one means to help standardise interpretation of clinical signs

Accuracy Measures for the Comparison of Classifiers

The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on the measure used to assess the classification performance and rank the algorithms. We present the most popular measures and discuss their properties. Despite the numerous measures proposed over the years, many of them turn out to be equivalent in this specific case, to have interpretation problems, or to be unsuitable for our purpose. Consequently, classic overall success rate or marginal rates should be preferred for this specific task.Comment: The 5th International Conference on Information Technology, amman : Jordanie (2011

Stroke Quality Measures in Mexican Americans and Non-Hispanic Whites

Mexican Americans (MAs) have been shown to have worse outcomes after stroke than non-Hispanic Whites (NHWs), but it is unknown if ethnic differences in stroke quality of care may contribute to these worse outcomes. We investigated ethnic differences in the quality of inpatient stroke care between MAs and NHWs within the population-based prospective Brain Attack Surveillance in Corpus Christi (BASIC) Project (February 2009- June 2012). Quality measures for inpatient stroke care, based on the 2008 Joint Commission Primary Stroke Center definitions were assessed from the medical record by a trained abstractor. Two summary measure of overall quality were also created (binary measure of defect-free care and the proportion of measures achieved for which the patient was eligible). 757 individuals were included (480 MAs and 277 NHWs). MAs were younger, more likely to have hypertension and diabetes, and less likely to have atrial fibrillation than NHWs. MAs were less likely than NHWs to receive tPA (RR: 0.72, 95% confidence interval (CI) 0.52, 0.98), and MAs with atrial fibrillation were less likely to receive anticoagulant medications at discharge than NHWs (RR 0.73, 95% CI 0.58, 0.94). There were no ethnic differences in the other individual quality measures, or in the two summary measures assessing overall quality. In conclusion, there were no ethnic differences in the overall quality of stroke care between MAs and NHWs, though ethnic differences were seen in the proportion of patients who received tPA and anticoagulant at discharge for atrial fibrillation

Spartan Daily, December 10, 1951

Volume 40, Issue 51https://scholarworks.sjsu.edu/spartandaily/11638/thumbnail.jp

Spartan Daily, May 10, 1955

Volume 42, Issue 138https://scholarworks.sjsu.edu/spartandaily/12187/thumbnail.jp