Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Harary [10, p. 7] claims that Veblen [20, p. 2] first suggested to formalize simple graphs using simplicial complexes. We have developed basic terminology for simple graphs as at most 1-dimensional complexes. We formalize this new setting and then reprove Mycielski’s [12] construction resulting in a triangle-free graph with arbitrarily large chromatic number. A different formalization of similar material is in [15].This work has been partially supported by the NSERC grant OGP 9207Rudnicki Piotr - University of Alberta, Edmonton, CanadaStewart Lorna - University of Alberta, Edmonton, CanadaGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.Grzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007, doi:10.2478/v10037-007-0011-x.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Frank Harary. Graph theory. Addison-Wesley, 1969.Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.J. Mycielski. Sur le coloriage des graphes. Colloquium Mathematicum, 3:161-162, 1955.Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.Piotr Rudnicki and Lorna Stewart. The Mycielskian of a graph. Formalized Mathematics, 19(1):27-34, 2011, doi: 10.2478/v10037-011-0005-6.Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Oswald Veblen. Analysis Situs, volume V. AMS Colloquium Publications, 193

Stability of a frictional, cohesive layer on a viscous substratum: validity of asymptotic solution and influence of material properties

This study deals with the stability of a stratified structure composed of a cohesive and frictional overburden, a viscous substratum, and a rigid basement. That structure should be seen as a prototype for various salt tectonics and lithospheric plates stability analyses. The destabilizing factors are the density contrast, the tectonic compressive stress, and the possible erosion and deposition at the top surface. The overburden stiffness, a nonlinear function of in situ stress, has a stabilizing role. Two solutions are extracted from the variational formulation of the stability problem previously proposed [Leroy and Triantafyllidis, 1996]: the first is analytical and is obtained by disregarding gravity, and the second is numerical and is based on the finite element method. The latter is used to assess the validity of the previously presented asymptotic solution. It is shown that the asymptotic solution is accurate even for values of the small parameter, defined as the perturbation wavenumber times the overburden thickness, as large as 0.4. Furthermore, the possibility for the cohesive material in the overburden to accommodate part of the deformation by slip along a population of small pervasive faults is accounted for by the introduction of a deformation theory of plasticity. Stability predictions based on this theory indicate that structural modes, such as folding, and localized faulting modes are triggered for similar stress magnitudes. The parametric study presented includes the previously undetected influences of the stress gradient with depth and of the work hardening properties of the competent overburden. The role of erosion and deposition in destabilizing shallow overburdens, regardless of the magnitude of the tectonic stress, is also established. The stability predictions are then applied to a folded section through the Campos basin, offshore Brazil, revealing that the deformation theory of plasticity is necessary to explain the buckling that occurred during the Albian

Screensaver: an open source lab information management system (LIMS) for high throughput screening facilities

<p>Abstract</p> <p>Background</p> <p>Shared-usage high throughput screening (HTS) facilities are becoming more common in academe as large-scale small molecule and genome-scale RNAi screening strategies are adopted for basic research purposes. These shared facilities require a unique informatics infrastructure that must not only provide access to and analysis of screening data, but must also manage the administrative and technical challenges associated with conducting numerous, interleaved screening efforts run by multiple independent research groups.</p> <p>Results</p> <p>We have developed Screensaver, a free, open source, web-based lab information management system (LIMS), to address the informatics needs of our small molecule and RNAi screening facility. Screensaver supports the storage and comparison of screening data sets, as well as the management of information about screens, screeners, libraries, and laboratory work requests. To our knowledge, Screensaver is one of the first applications to support the storage and analysis of data from both genome-scale RNAi screening projects and small molecule screening projects.</p> <p>Conclusions</p> <p>The informatics and administrative needs of an HTS facility may be best managed by a single, integrated, web-accessible application such as Screensaver. Screensaver has proven useful in meeting the requirements of the ICCB-Longwood/NSRB Screening Facility at Harvard Medical School, and has provided similar benefits to other HTS facilities.</p

An Intermittent Live Cell Imaging Screen for siRNA Enhancers and Suppressors of a Kinesin-5 Inhibitor

Kinesin-5 (also known as Eg5, KSP and Kif11) is required for assembly of a bipolar mitotic spindle. Small molecule inhibitors of Kinesin-5, developed as potential anti-cancer drugs, arrest cell in mitosis and promote apoptosis of cancer cells. We performed a genome-wide siRNA screen for enhancers and suppressors of a Kinesin-5 inhibitor in human cells to elucidate cellular responses, and thus identify factors that might predict drug sensitivity in cancers. Because the drug's actions play out over several days, we developed an intermittent imaging screen. Live HeLa cells expressing GFP-tagged histone H2B were imaged at 0, 24 and 48 hours after drug addition, and images were analyzed using open-source software that incorporates machine learning. This screen effectively identified siRNAs that caused increased mitotic arrest at low drug concentrations (enhancers), and vice versa (suppressors), and we report siRNAs that caused both effects. We then classified the effect of siRNAs for 15 genes where 3 or 4 out of 4 siRNA oligos tested were suppressors as assessed by time lapse imaging, and by testing for suppression of mitotic arrest in taxol and nocodazole. This identified 4 phenotypic classes of drug suppressors, which included known and novel genes. Our methodology should be applicable to other screens, and the suppressor and enhancer genes we identified may open new lines of research into mitosis and checkpoint biology

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Efficacy of Mesenchymal Stromal Cell Therapy for Acute Lung Injury in Preclinical Animal Models: A Systematic Review

<div><p>The Acute Respiratory Distress Syndrome (ARDS) is a devastating clinical condition that is associated with a 30–40% risk of death, and significant long term morbidity for those who survive. Mesenchymal stromal cells (MSC) have emerged as a potential novel treatment as in pre-clinical models they have been shown to modulate inflammation (a major pathophysiological hallmark of ARDS) while enhancing bacterial clearance and reducing organ injury and death. A systematic search of MEDLINE, EMBASE, BIOSIS and Web of Science was performed to identify pre-clinical studies that examined the efficacy MSCs as compared to diseased controls for the treatment of Acute Lung Injury (ALI) (the pre-clinical correlate of human ARDS) on mortality, a clinically relevant outcome. We assessed study quality and pooled results using random effect meta-analysis. A total of 54 publications met our inclusion criteria of which 17 (21 experiments) reported mortality and were included in the meta-analysis. Treatment with MSCs, as compared to controls, significantly decreased the overall odds of death in animals with ALI (Odds Ratio 0.24, 95% Confidence Interval 0.18–0.34, I² 8%). Efficacy was maintained across different types of animal models and means of ALI induction; MSC origin, source, route of administration and preparation; and the clinical relevance of the model (timing of MSC administration, administration of fluids and or antibiotics). Reporting of standard MSC characterization for experiments that used human MSCs and risks of bias was generally poor, and although not statistically significant, a funnel plot analysis for overall mortality suggested the presence of publication bias. The results from our meta-analysis support that MSCs substantially reduce the odds of death in animal models of ALI but important reporting elements were sub optimal and limit the strength of our conclusions.</p></div

Correction to: Cluster identification, selection, and description in Cluster randomized crossover trials: the PREP-IT trials

An amendment to this paper has been published and can be accessed via the original article

The Mycielskian of a Graph

Let ω(G) and χ(G) be the clique number and the chromatic number of a graph G. Mycielski [11] presented a construction that for any n creates a graph Mn which is triangle-free (ω(G) = 2) with χ(G)&gt; n. The starting point is the complete graph of two vertices (K2). M(n+1) is obtained from Mn through the operation µ(G) called the Mycielskian of a graph G. We first define the operation µ(G) and then show that ω(µ(G)) = ω(G) and χ(µ(G)) = χ(G) + 1. This is done for arbitrary graph G, see also [10]. Then we define the sequence of graphs Mn each of exponential size in n and give their clique and chromatic numbers

Mizar Verification of Algorithms for Recognizing Chordal Graphs

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