A friendship graph is a graph consisting of cliques sharing a common vertex. In this paper we investigate the maximum number of elements in an optimal friendship decomposition of graphs of order n. We obtain upper and lower bounds for this number. These bounds relate this problem with the classical Ramsey numbers.

Spreadsheets are among the most popular programming languages in the world. Unfortunately, spreadsheet systems were not tailored from scratch with modern programming language features that guarantee, as much as possible, program correctness. As a consequence, spreadsheets are populated with unacceptable amounts of errors. In other programming language settings, model-based approaches have been proposed to increase productivity and program effectiveness. Within spreadsheets, this approach has also been followed, namely by ClassSheets. In this paper, we propose an extension to ClassSheets to allow the specification of spreadsheets that can be viewed as relational databases. Moreover, we present a transformation from ClassSheet models to UML class diagrams enriched with OCL constraints. This brings to the spreadsheet realm the entire paraphernalia of model validation techniques that are available for UML.

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In this paper, the use of non-optimality spheres in a simplicial branch and bound (B&B) algorithm is investigated. In this context, some considerations regarding the use of bisection on the longest edge in relation with ideas of Reiner Horst are reminded. Three arguments highlight the merits of bisection of simplicial subsets in B&B schemes.

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The concept of H-decompositions of graphs was first introduced by Erdös, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let Ф(n,H) be the smallest number Ф, such that, any graph of order n admits an H-decomposition with at most Ф parts. The exact computation of Ф(n,H) for an arbitrary H is still an open problem. Recently, a few papers have been published about this problem. In this survey we will bring together all the results about H-decompositions. We will also introduce two new related problems, namely Weighted H-Decompositions of graphs and Monochromatic H-Decompositions of graphs.

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The close structural similarity between the two cyclooxygenase (COXs) isoforms and the absence of selective inhibitors without side effects continues to stimulate the development of novel approaches towards selective anti-inflammatory drugs. In the present study a small library of new indolic compounds involving two different substitutions patterns at the indole scaffold was synthesized. In order to establish a relation between the spatial distribution of known functional groups related with inhibitory activity, two substitution patterns were explored: one with substituents at N-1, C-3, C-5 positions and another at C-2, C-3 and C5 positions. Accordingly, indole positions C-5, C-3 and N-1 were substituted with: sulfonamide or methylsulfone at C-5, p-halo-benzyl group at C-3, and an alkyl chain with a trifluoromethyl group at N-1. Alternatively, a p-halo-benzyl group was introduced at C-2, leaving the indolic nitrogen free. Inhibitory studies were performed and the activity results obtained against both COXs isoforms were rationalized based on docking and NMR studies. Docking studies show that dialkyation at C-2 and C-3 favors a binding with an orientation similar to that of the known selective inhibitor SC-558. From the tested compounds, this substitution pattern is correlated with the highest inhibitory activity and selectivity: 70% COX-2 inhibition at 50 M, and low COX-1 inhibition (18±9%). Additionally, Saturation Transfer Difference NMR experiments reveal different interaction patterns with both COXs isoforms that may be related with different orientations of the sulfonamide group in the binding pocket. Despite the moderated inhibitory activities found, this study represents an innovative approach towards COXs inhibitory activity rationalization and to the design of anti-inflammatory drugs.

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Green and lean paradigms have been adopted by companies in order to manage their relationships with suppliers in a supply chain management context, but nearly always separately and with little understanding of their influence on company performance. This paper proposes a theoretical framework for the analysis of the influence of green and lean upstream supply chain management practices on the sustainable development of businesses. To attend this objective, a set of performance measures covering economic (operational cost, environmental cost, and inventory cost), environmental (business wastage, green image, and CO2 emission), and social (corruption risk, supplier screening and local supplier) perspectives is proposed. An explanatory case study was conducted at a Portuguese automaker to test qualitatively the validity of the proposed theoretical framework. From the case study, a model is suggested, which encompasses the relationships between green and lean upstream supply chain practices and sustainable business development.

We present a generalization to symmetric optimization of interior-point methods for linear optimization based on kernel functions. Symmetric optimization covers the three most common conic optimization problems: linear, second-order cone and semi-definite optimization problems. Namely, we adapt the interior-point algorithm described in Peng et al. [Self-regularity: A New Paradigm for Primal–Dual Interior-point Algorithms. Princeton University Press, Princeton, NJ, 2002.] for linear optimization to symmetric optimization. The analysis is performed through Euclidean Jordan algebraic tools and a complexity bound is derived.

Techniques for estimating the condition number of a nonsingular matrix are developed. It is shown that Hager's 1-norm condition number estimator is equivalent to the conditional gradient algorithm applied to the problem of maximizing the 1-norm of a matrix-vector product over the unit sphere in the 1-norm. By changing the constraint in this optimization problem from the unit sphere to the unit simplex, a new formulation is obtained which is the basis for both conditional gradient and projected gradient algorithms. In the test problems, the spectral projected gradient algorithm yields condition number estimates at least as good as those obtained by the previous approach. Moreover, in some cases, the spectral gradient projection algorithm, with a careful choice of the parameters, yields improved condition number estimates.

A clutch of several crushed eggs and embryos from the Late Jurassic (near the Kimmeridgian-Tithonian
boundary), Lourinhã Formation, Portugal contains a complete maxilla, erupted and scattered teeth,
and presacral vertebrae. The maxilla bears four teeth separated by individualized interdental plates,
the dorsal process of the maxilla is confluent with the maxillary body, the ventral rim of the antorbital
fossa is parallel to the tooth row, and the anterior border of the maxilla forms a right angle with the
ventral margin. The teeth are conical and recurved distally with carinae on mesial and distal sides. The
vertebrae are amphiplatyan, with a ventral pair of neurovascular foramina and heavily pitted articular
facets. These fossils allow unambiguous association of basal theropod osteology (Megalosauroidea) with
a new eggshell morphotype. Synchrotron micro-computed tomographic scanning (SRμCT), scanning
electron microscopy, and thin-sections under polarized and normal light revealed that the outer
ornamentation of the eggshell is composed of anastomosing ridges and islets, the pores communicate
near the outer region of the eggshells, and in radial section they are irregular canals that ramify towards
the surface. Micro-proto induced x-ray emission (micro-PIXE) analysis of the eggshell (excluding pores)
revealed the presence of Mg, Fe, Mn (0.33%, 0.27% and 0.18%, respectively) and several trace elements,
with a corresponding loss of Ca (39.4% detected but 40.0% expected for calcite), which suggests minimal
eggshell diagenesis. The eggshells do not luminesce, which could imply that no diagenetic alteration
took effect. However, the quenching effect of Fe2+ has to be taken into consideration. Conversely,
luminescence is observed in the pores since they are filled with sediment, composed of phyllosilicates,
as revealed by SRμCT, micro-PIXE and x-ray diffraction analyses.

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Supply chains (SCs) may experience instability induced by disturbances such as extreme climate conditions or accidents. These events can cause severe negative effects on SCs, jeopardising the on-time delivery of products and services to customers. This paper proposes a mapping framework to improve SC resilience to such events, avoiding possible failure modes. The proposed mapping framework allows identification of the current SC operation and possible transition states, together with points of vulnerability. An illustrative example of the framework applied to a real-life wine SC is presented.