Spectra and structural polynomials of graphs of relevance to the theory of molecular conduction

In chemistry and physics, distortivity of π-systems (stabilisation of bond-alternated structures) is an important factor in the calculation of geometric, energetic, and electronic properties of molecules via graph theoretical methods. We use the spectra of paths and cycles with alternating vertex and edge weights to obtain the eigenvalues and eigenvectors for a class of linear and cyclic ladders with alternating rung and backbone edge weights. We derive characteristic polynomials and other structural polynomials formed from the cofactors of the characteristic matrix for these graphs. We also obtain spectra and structural polynomials for ladders with flipped weights and/or Möbius topology. In all cases, the structural polynomials for the composite graphs are expressed in terms of products of polynomials for graphs of half order. This form of the expressions allows global deductions about the transmission spectra of molecular devices in the graph-theoretical theory of ballistic molecular conduction

A Hidden Twelve-Dimensional SuperPoincare Symmetry In Eleven Dimensions

First, we review a result in our previous paper, of how a ten-dimensional superparticle, taken off-shell, has a hidden eleven-dimensional superPoincare symmetry. Then, we show that the physical sector is defined by three first-class constraints which preserve the full eleven-dimensional symmetry. Applying the same concepts to the eleven dimensional superparticle, taken off-shell, we discover a hidden twelve dimensional superPoincare symmetry that governs the theory.Comment: 13 page

Near omni-conductors and insulators: Alternant hydrocarbons in the SSP model of ballistic conduction

Within the source-and-sink-potential model, a complete characterisation is obtained for the conduction behaviour of alternant π-conjugated hydrocarbons (conjugated hydrocarbons without odd cycles). In this model, an omni-conductor has a molecular graph that conducts at the Fermi level irrespective of the choice of connection vertices. Likewise, an omni-insulator is a molecular graph that fails to conduct for any choice of connections. We give a comprehensive classification of possible combinations of omni-conducting and omni-insulating behaviour for molecular graphs, ranked by nullity (number of non-bonding orbitals). Alternant hydrocarbons are those that have bipartite molecular graphs; they cannot be full omni-conductors or full omni-insulators but may conduct or insulate within well-defined subsets of vertices (unsaturated carbon centres). This leads to the definition of "near omni-conductors" and "near omni-insulators." Of 81 conceivable classes of conduction behaviour for alternants, only 14 are realisable. Of these, nine are realised by more than one chemical graph. For example, conduction of all Kekulean benzenoids (nanographenes) is described by just two classes. In particular, the catafused benzenoids (benzenoids in which no carbon atom belongs to three hexagons) conduct when connected to leads via one starred and one unstarred atom, and otherwise insulate, corresponding to conduction type CII in the near-omni classification scheme

α5β1-Integrin promotes tension-dependent mammary epithelial cell invasion by engaging the fibronectin synergy site.

Tumors are fibrotic and characterized by abundant, remodeled, and cross-linked collagen that stiffens the extracellular matrix stroma. The stiffened collagenous stroma fosters malignant transformation of the tissue by increasing tumor cell tension to promote focal adhesion formation and potentiate growth factor receptor signaling through kinase. Importantly, collagen cross-linking requires fibronectin (FN). Fibrotic tumors contain abundant FN, and tumor cells frequently up-regulate the FN receptor α5β1 integrin. Using transgenic and xenograft models and tunable two- and three-dimensional substrates, we show that FN-bound α5β1 integrin promotes tension-dependent malignant transformation through engagement of the synergy site that enhances integrin adhesion force. We determined that ligation of the synergy site of FN permits tumor cells to engage a zyxin-stabilized, vinculin-linked scaffold that facilitates nucleation of phosphatidylinositol (3,4,5)-triphosphate at the plasma membrane to enhance phosphoinositide 3-kinase (PI3K)-dependent tumor cell invasion. The data explain why rigid collagen fibrils potentiate PI3K activation to promote malignancy and offer a perspective regarding the consistent up-regulation of α5β1 integrin and FN in many tumors and their correlation with cancer aggression

Systematically Searching Empirical Literature in the Social Sciences: Results from Two Meta-Analyses Within the Domain of Education

Introduction. This paper provides an overview of the information retrieval strategy employed for two meta-analyses, conducted by a systematic review team at Concordia University (Montreal, QC, Canada). Both papers draw on standards first articulated by H.M. Cooper and further developed by the Campbell Collaboration, which promote a comprehensive approach to systematically searching an extensive array of resources (bibliographic databases, print resources, citation indices, etc.) in order to locate both published and unpublished research. The goal is to verify if searching comprehensively through multiple resources retrieves studies that are unique, and hence, improve the overall representativeness of a diverse body of literature. We also analyze the sensitivity and specificity of the results by data source. Methods. In order to determine the source sensitivity, we consider percentage of results from each source retrieved for full-text review. In order to determine the source specificity, we derive a percentage from the total number of studies included in the final meta-analysis compared against the overall number of initial results found. Results. Results demonstrate the need to search beyond the subject-specific databases of a particular discipline as unique results can be found in many places. Databases for related disciplines provided 129 unique includes to each meta-analysis, and multidisciplinary databases provided 44 and 99 unique includes for the two meta-analyses in question respectively. Manual search techniques were much more sensitive and specific than electronic searches of databases and yield a higher percentage of final includes. Discussion. The results demonstrate the utility of a comprehensive information retrieval methodology like that proposed by the Campbell Collaboration, which goes beyond the main subject databases to locate the full range of information sources, including grey literature

Molecular graphs and molecular conduction : the d-omni-conductors

Ernzerhof's source-and-sink-potential (SSP) model for ballistic conduction in conjugated π systems predicts transmission of electrons through a two-wire device in terms of characteristic polynomials of the molecular graph and subgraphs based on the pattern of connections. We present here a complete classification of conduction properties of all molecular graphs within the SSP model. An omni-conductor/omni-insulator is a molecular graph that conducts/insulates at the Fermi level (zero of energy) for all connection patterns. In the new scheme, we define d-omni-conduction/insulation in terms of Fermi-level conduction/insulation for all devices with graph distance d between connections. This gives a natural generalisation to all graphs of the concept of near-omni-conduction/insulation previously defined for bipartite graphs only. Every molecular graph can be assigned to a nullity class and a compact code defining conduction behaviour; each graph has 0, 1, >1 zero eigenvalues (non-bonding molecular orbitals), and three letters drawn from {C, I, X} indicate conducting, insulating or mixed behaviour within the sets of devices with connection vertices at odd, even and zero distances d. Examples of graphs (in 28 cases chemical) are given for 35 of the 81 possible combinations of nullity and letter codes, and proofs of non-existence are given for 42 others, leaving only four cases open

A study of meta-analyses reporting quality in the large and expanding literature of educational technology

As the empirical literature in educational technology continues to grow, meta-analyses are increasingly being used to synthesise research to inform practice. However, not all meta-analyses are equal. To examine their evolution over the past 30 years, this study systematically analysed the quality of 52 meta-analyses (1988–2017) on educational technology. Methodological and reporting quality is defined here as the completeness of the descriptive and methodological reporting features of meta-analyses. The study employed the Meta-Analysis Methodological Reporting Quality Guide (MMRQG), an instrument designed to assess 22 areas of reporting quality in meta-analyses. Overall, MMRQG scores were negatively related to average effect size (i.e., the higher the quality, the lower the effect size). Owing to the presence of poor-quality syntheses, the contribution of educational technologies to learning has been overestimated, potentially misleading researchers and practitioners. Nine MMRQG items discriminated between higher and lower average effect sizes. A publication date analysis revealed that older reviews (1988–2009) scored significantly lower on the MMRQG than more recent reviews (2010–2017). Although the increase in quality bodes well for the educational technology literature, many recent meta-analyses still show only moderate levels of quality. Identifying and using only best evidence-based research is thus imperative to avoid bias. Implications for practice or policy: • Educational technology practitioners should make use of meta-analytical findings that systematically synthesise primary research. • Academics, policymakers and practitioners should consider the methodological quality of meta-analyses as they vary in reliability. • Academics, policymakers and practitioners could avoid misleading bias in research evidence by using the MMRQG to evaluate the quality of meta-analyses. • Meta-analyses with lower MMRQG scores should be considered with caution as they seem to overestimate the effect of educational technology on learning