On the Directional Derivative of Kemeny's Constant

In a connected graph, Kemeny's constant gives the expected time of a random walk from an arbitrary vertex $x$ to reach a randomly-chosen vertex $y$. Because of this, Kemeny's constant can be interpreted as a measure of how well a graph is connected. It is generally unknown how the addition or removal of edges affects Kemeny's constant. Inspired by the directional derivative of the normalized Laplacian, we derive the directional derivative of Kemeny's constant for several graph families. In addition, we find sharp bounds for the directional derivative of an eigenvalue of the normalized Laplacian and bounds for the directional derivative of Kemeny's constant

Aquilegia, Vol. 26 No. 2, March-April 2002: Newsletter of the Colorado Native Plant Society

https://epublications.regis.edu/aquilegia/1092/thumbnail.jp

Orthogonal realizations of random sign patterns and other applications of the SIPP

A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228--259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP to initiate the study of conditions under which random sign patterns allow row orthogonality with high probability. Building on prior work, $5\times n$ nowhere zero sign patterns that minimally allow orthogonality are determined. Conditions on zero entries in a sign pattern are established that guarantee any row orthogonal matrix with such a sign pattern has the SIPP

Dressings and securements for the prevention of peripheral intravenous catheter failure in adults (SAVE): a pragmatic, randomised controlled, superiority trial

Background: Two billion peripheral intravenous catheters (PIVCs) are used globally each year, but optimal dressing and securement methods are not well established. We aimed to compare the efficacy and costs of three alternative approaches to standard non-bordered polyurethane dressings. Methods: We did a pragmatic, randomised controlled, parallel-group superiority trial at two hospitals in Queensland, Australia. Eligible patients were aged 18 years or older and required PIVC insertion for clinical treatment, which was expected to be required for longer than 24 h. Patients were randomly assigned (1:1:1:1) via a centralised web-based randomisation service using random block sizes, stratified by hospital, to receive tissue adhesive with polyurethane dressing, bordered polyurethane dressing, a securement device with polyurethane dressing, or polyurethane dressing (control). Randomisation was concealed before allocation. Patients, clinicians, and research staff were not masked because of the nature of the intervention, but infections were adjudicated by a physician who was masked to treatment allocation. The primary outcome was all-cause PIVC failure (as a composite of complete dislodgement, occlusion, phlebitis, and infection [primary bloodstream infection or local infection]). Analysis was by modified intention to treat. This trial is registered with the Australian New Zealand Clinical Trials Registry, number ACTRN12611000769987. Findings: Between March 18, 2013, and Sept 9, 2014, we randomly assigned 1807 patients to receive tissue adhesive with polyurethane (n=446), bordered polyurethane (n=454), securement device with polyurethane (n=453), or polyurethane (n=454); 1697 patients comprised the modified intention-to-treat population. 163 (38%) of 427 patients in the tissue adhesive with polyurethane group (absolute risk difference −4·5% [95% CI −11·1 to 2·1%], p=0·19), 169 (40%) of 423 of patients in the bordered polyurethane group (–2·7% [–9·3 to 3·9%] p=0·44), 176 (41%) of 425 patients in the securement device with poplyurethane group (–1·2% [–7·9% to 5·4%], p=0·73), and 180 (43%) of 422 patients in the polyurethane group had PIVC failure. 17 patients in the tissue adhesive with polyurethane group, two patients in the bordered polyurethane group, eight patients in the securement device with polyurethane group, and seven patients in the polyurethane group had skin adverse events. Total costs of the trial interventions did not differ significantly between groups. Interpretation: Current dressing and securement methods are commonly associated with PIVC failure and poor durability, with simultaneous use of multiple products commonly required. Cost is currently the main factor that determines product choice. Innovations to achieve effective, durable dressings and securements, and randomised controlled trials assessing their effectiveness are urgently needed

Religious socialisation and fertility: transition to third birth in the Netherlands

Although previous studies have demonstrated that religious people in Europe have larger families, the role played by religious socialisation in the context of contemporary fertility behaviour has not yet been analysed in detail. This contribution specifically looks at the interrelation between religious socialisation and current religiosity and their impact on the transition to the third child for Dutch women. It is based on data of the first wave of the Netherlands Kinship Panel Study (2002–2004) and uses event history analysis. The transitions to first, second and third birth are modelled jointly with a control for unobserved heterogeneity. The findings provide evidence for an impact of women’s current church attendance as well as religious socialisation measured by their fathers’ religious affiliation, when they were teenagers. A religious family background remains influential even when a woman has stopped attending church. The effects of religious indicators strengthen over cohorts. Moreover, the combined religious make-up of the respondent’s parents also significantly determines the progression to the third child.S’il est bien établi que les croyants en Europe ont plus d’enfants que les autres, le rôle de la socialisation religieuse dans le contexte de la fécondité contemporaine n’a pas encore été analysé à ce jour. Cette étude s’intéresse au lien entre la socialisation religieuse et la religiosité actuelle, et à leur impact sur la probabilité d’agrandissement de deux à trois enfants de la descendance des femmes néerlandaises. Les données exploitées sont celles de la première vague du Panel Néerlandais d’Etude de la Parenté (the Netherlands Kinship Panel Study, 2002–2004). A l’aide des techniques de l’analyse des biographies, les probabilités d’agrandissement de rang 1, rang 2 et rang 3 ont été modélisées de façon conjointe, en contrôlant l’hétérogénéité non observée. Les résultats mettent en évidence l’impact de la fréquentation actuelle de l’église par les femmes et de leur socialisation religieuse, mesurée par l’appartenance religieuse de leur père quand elles étaient adolescentes. Il apparaît que la religiosité du contexte familial exerce une influence, même quand la femme ne fréquente plus l’église, et que les effets des indicateurs de pratique religieuse se renforcent d’une génération à l’autre. Enfin, l’appartenance religieuse conjointe des parents de la femme détermine significativement la probabilité d’avoir un troisième enfant