Nullity of a graph with a cut-edge

The nullity of a graph is known to be an analytical tool to predict reactivity and conductivity of molecular π-systems. In this paper we consider the change in nullity when graphs with a cut-edge, and others derived from them, undergo geometrical operations. In particular, we consider the deletion of edges and vertices, the contraction of edges and the insertion of an edge at a coalescence vertex. We also derive three inequalities on the nullity of graphs along the same lines as the consequences of the Interlacing Theorem. These results shed light, in the tight-binding source and sink potential model, on the behaviour of molecular graphs which allow or bar conductivity in the cases when the connections are either distinct or ipso.peer-reviewe

Coalescing Fiedler and core vertices

The nullity of a graph G is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique type in the coalescence. Moreover, the nullity of subgraphs obtained by perturbations of the coalescence G is determined relative to the nullity of G. This has direct applications in spectral graph theory as well as in the construction of certain ipso-connected nano-molecular insulators.peer-reviewe

Edge Degree Weight of Sequential Join of Graphs

Let the weight w of an edge e= uv={u,v} of a graph G be defined by w(e)=deg(u)+deg(v)-2 and the weight of G be defined by w(G)= ∑ e ∈ E(G)w(e), where E(G) is the edge set of G. In this paper the weights of joins, sequential joins, unions, intersections, and products (Cartesian and Tensor) of sets of graphs are obtained. This leads to a variety of open questions and new studies

The conductivity of superimposed key-graphs with a common one-dimensional adjacency nullspace

Two connected labelled graphs H1 and H2 of nullity one, with identical one-vertex deleted subgraphs H1 − z1 and H2 − z2 and having a common eigenvector in the nullspace of their 0-1 adjacency matrix, can be overlaid to produce the superimposition Z. The graph Z is H1 + z2 and also H2 + z1 whereas Z + e is obtained from Z by adding the edge {z1, z2}. We show that the nullity of Z cannot take all the values allowed by interlacing. We propose to classify graphs with two chosen vertices according to the type of the vertices occurring by using a 3-type-code. Out of the 27 values it can take, only 9 are hypothetically possible for Z, 8 of which are known to exist. Moreover, the SSP molecular model predicts conduction or insulation at the Fermi level of energy for 11 possible types of devices consisting of a molecule and two prescribed connecting atoms over a small bias voltage. All 11 molecular device types are realizable for general molecules, but the structure of Z and of Z + e restricts the number to just 5.peer-reviewe

Early Life Child Micronutrient Status, Maternal Reasoning, and a Nurturing Household Environment have Persistent Influences on Child Cognitive Development at Age 5 years : Results from MAL-ED

Funding Information: The Etiology, Risk Factors and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project (MAL-ED) is carried out as a collaborative project supported by the Bill & Melinda Gates Foundation, the Foundation for the NIH, and the National Institutes of Health/Fogarty International Center. This work was also supported by the Fogarty International Center, National Institutes of Health (D43-TW009359 to ETR). Author disclosures: BJJM, SAR, LEC, LLP, JCS, BK, RR, RS, ES, LB, ZR, AM, RS, BN, SH, MR, RO, ETR, and LEM-K, no conflicts of interest. Supplemental Tables 1–5 and Supplemental Figures 1–3 are available from the “Supplementary data” link in the online posting of the article and from the same link in the online table of contents at https://academic.oup.com/jn/. Address correspondence to LEM-K (e-mail: [email protected]). Abbreviations used: HOME, Home Observation for Measurement of the Environment inventory; MAL-ED, The Etiology, Risk Factors, and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project; TfR, transferrin receptor; WPPSI, Wechsler Preschool Primary Scales of Intelligence.Peer reviewe

Early life child micronutrient status, maternal reasoning, and a nurturing household environment have persistent influences on child cognitive development at age 5 years: Results from MAL-ED

Background: Child cognitive development is influenced by early-life insults and protective factors. To what extent these factors have a long-term legacy on child development and hence fulfillment of cognitive potential is unknown. Objective: The aim of this study was to examine the relation between early-life factors (birth to 2 y) and cognitive development at 5 y. Methods: Observational follow-up visits were made of children at 5 y, previously enrolled in the community-based MAL-ED longitudinal cohort. The burden of enteropathogens, prevalence of illness, complementary diet intake, micronutrient status, and household and maternal factors from birth to 2 y were extensively measured and their relation with the Wechsler Preschool Primary Scales of Intelligence at 5 y was examined through use of linear regression. Results: Cognitive T-scores from 813 of 1198 (68%) children were examined and 5 variables had significant associations in multivariable models: mean child plasma transferrin receptor concentration (β: −1.81, 95% CI: −2.75, −0.86), number of years of maternal education (β: 0.27, 95% CI: 0.08, 0.45), maternal cognitive reasoning score (β: 0.09, 95% CI: 0.03, 0.15), household assets score (β: 0.64, 95% CI: 0.24, 1.04), and HOME child cleanliness factor (β: 0.60, 95% CI: 0.05, 1.15). In multivariable models, the mean rate of enteropathogen detections, burden of illness, and complementary food intakes between birth and 2 y were not significantly related to 5-y cognition. Conclusions: A nurturing home context in terms of a healthy/clean environment and household wealth, provision of adequate micronutrients, maternal education, and cognitive reasoning have a strong and persistent influence on child cognitive development. Efforts addressing aspects of poverty around micronutrient status, nurturing caregiving, and enabling home environments are likely to have lasting positive impacts on child cognitive development.publishedVersio

Measurement of quark- and gluon-like jet fractions using jet charge in PbPb and pp collisions at 5.02 TeV

The momentum-weighted sum of the electric charges of particles inside a jet, known as jet charge, is sensitive to the electric charge of the particle initiating the parton shower. This paper presents jet charge distributions in root sNN = 5.02 TeV lead-lead (PbPb) and proton-proton (pp) collisions recorded with the CMS detector at the LHC. These data correspond to integrated luminosities of 404 mu b(-1)and 27.4 pb(-1)for PbPb and pp collisions, respectively. Leveraging the sensitivity of the jet charge to fundamental differences in the electric charges of quarks and gluons, the jet charge distributions from simulated events are used as templates to extract the quark- and gluon-like jet fractions from data. The modification of these jet fractions is examined by comparing pp and PbPb data as a function of the overlap of the colliding Pb nuclei (centrality). This measurement tests the color charge dependence of jet energy loss due to interactions with the quark-gluon plasma. No significant modification between different centrality classes and with respect to pp results is observed in the extracted quark- and gluon-like jet fractions.Peer reviewe

Penilaian Kinerja Keuangan Koperasi di Kabupaten Pelalawan

This paper describe development and financial performance of cooperative in District Pelalawan among 2007 - 2008. Studies on primary and secondary cooperative in 12 sub-districts. Method in this stady use performance measuring of productivity, efficiency, growth, liquidity, and solvability of cooperative. Productivity of cooperative in Pelalawan was highly but efficiency still low. Profit and income were highly, even liquidity of cooperative very high, and solvability was good

Juxtaposing BTE and ATE – on the role of the European insurance industry in funding civil litigation

One of the ways in which legal services are financed, and indeed shaped, is through private insurance arrangement. Two contrasting types of legal expenses insurance contracts (LEI) seem to dominate in Europe: before the event (BTE) and after the event (ATE) legal expenses insurance. Notwithstanding institutional differences between different legal systems, BTE and ATE insurance arrangements may be instrumental if government policy is geared towards strengthening a market-oriented system of financing access to justice for individuals and business. At the same time, emphasizing the role of a private industry as a keeper of the gates to justice raises issues of accountability and transparency, not readily reconcilable with demands of competition. Moreover, multiple actors (clients, lawyers, courts, insurers) are involved, causing behavioural dynamics which are not easily predicted or influenced. Against this background, this paper looks into BTE and ATE arrangements by analysing the particularities of BTE and ATE arrangements currently available in some European jurisdictions and by painting a picture of their respective markets and legal contexts. This allows for some reflection on the performance of BTE and ATE providers as both financiers and keepers. Two issues emerge from the analysis that are worthy of some further reflection. Firstly, there is the problematic long-term sustainability of some ATE products. Secondly, the challenges faced by policymakers that would like to nudge consumers into voluntarily taking out BTE LEI