We present an approximation algorithm for computing the diameter of a point-set in $\Re^d$. The new algorithm is sensitive to the ``hardness'' of computing the diameter of the given input, and for most inputs it is able to compute the exact diameter extremely fast. The new algorithm is simple, robust, has good empirical performance, and can be implemented quickly. As such, it seems to be the algorithm of choice in practice for computing/approximating the diameter.
We prove that, for every plane graph $G$ and every smooth convex curve $C$ not on a single line, there exists a straight-line drawing of $G$ for which every face is crossed by $C$.
We resolve a conjecture posed by Covella, Frati and Patrignani by proving the straight-line orthogonal drawing of the complete ternary tree with $n$ nodes satisfying the subtree separation property with smallest area has area $Ω(n^{1.031})$. We also improve the upper bound of this area to $O(n^{1.032})$.
We initiate the study of spanners under the Hausdorff and Fréchet distances. We show that any $t$-spanner of a planar point-set $S$ is a $\frac{\sqrt{t^2-1}}{2}$-Hausdorff-spanner and a $\min\{\frac{t}{2},\frac{\sqrt{t^2-t}}{\sqrt{2}}\}$-Fréchet spanner. We also prove that for any $t > 1$, there exist a set of points $S$ and an $\varepsilon_1$-Hausdorff-spanner of $S$ and an $\varepsilon_2$-Fréchet-spanner of $S$, where $\varepsilon_1$ and $\varepsilon_2$ are constants, such that neither of them is a $t$-spanner.
Abstract The immune signaling pathway mediated by Dectin-1 is important in mammals to modulate the production of IL-17 and TNF-α. Recently, IL-17 and TNF have also been characterized in invertebrates to play crucial roles in antibacterial immune responses, although the immune recognition and regulation mechanisms to produce IL-17 and TNF are still not well investigated. In the current study, a novel C-type lectin receptor (named CgCLec-HTM) with a signal peptide, a carbohydrate recognition domain, a transmembrane domain, and a nonclassical ITAM (hemITAM) in the cytoplasmic tail was identified from oyster Crassostrea gigas. CgCLec-HTM could bind LPS and various bacteria. After binding to its ligands, CgCLec-HTM was associated with the Src homology 2 (SH2) domain of spleen tyrosine kinase (CgSyk) by the hemITAM in its cytoplasmic tail to promote ERK (CgERK) phosphorylation. The activated CgERK could interact with CgRel to induce CgRel nuclear translocation. The CgRel in the nucleus eventually induced the transcription of CgIL-17s and CgTNF. The results demonstrated that CgCLec-HTM with a broad binding spectrum of bacteria could be associated with CgSyk to transfer immune signals into the intracellular ERK–Rel pathway to induce CgIL-17 and CgTNF production.
We describe a data structure that can maintain a dynamic set of points given by their Cartesian coordinates, and maintain the point whose product of ranks within the two coordinate orderings is minimum or maximum, in time $O(\sqrt{n\log n})$ per update.
We study the problem of how to breakup many point sets in $\mathbb{R}^d$ into smaller parts using a few splitting (shared) hyperplanes. This problem is related to the classical Ham-Sandwich Theorem. We provide a logarithmic approximation to the optimal solution using the greedy algorithm for submodular optimization.
We show that every polycube tree can be unfolded with a 4x4 refinement of the grid faces. This is the first constant refinement unfolding result for polycube trees that are not required to be well-separated.
Leticia Pérez-Calero, Ma del Mar Villegas, Carmen Barroso
PurposeThe purpose of this paper is to examine in greater depth the concept of “board capital”, which the authors consider to be a bundle of three types of capital, and believe to be a clear antecedent of the board’s ability to perform its roles, which have positive consequences for the firm’s performance.Design/methodology/approachThrough 83 firms listed on The Madrid Stock Exchange during the period 2005-2010, the authors test empirically the relationships between different dimensions of board capital and firm performance, and specially how internal social capital moderates the relationships between board human capital and external social capital with firm performance.FindingsThe results show that certain characteristics of human capital (average board tenure) and external social capital (directors’ interlocks) are positively related to the firm performance. The empirical findings also indicate that the internal social capital, measured by board density, is positively related to the firm performance and moderates these above relationships, increasing the potential of the resources contributed by the board members and influencing to a large extent on a firm’s performance.Practical implicationsThe results of the investigation will help both executives and scholar in two ways. First, they will assist firms when they have to select board members, as they can now understand how the resources that board members bring with them can affect the firm performance. To be more effective, boards need to have members that have experience as firm’s directors, external connections to other boards and many internal ties among them. Second, in this context, internal social capital is especially relevant, so the firms should look for possible ways of encouraging internal ties between directors. In this paper, the authors have opted for study the participation of directors in committees.Originality/valueThe authors propose that these three types of capital (human, external and internal social capital) need to be synergistically combined to create a group of directors with access to a complete set of skills, knowledge and connections, but which can still work as a compact social group when making decisions.
Any polyhedron accommodates a type of potential theoretic skeleton called a mother body. The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov and developed by Björn Gustafson and Makoto Sakai. In this paper, we attempt to apply the brilliant idea of mother body to Electrostatics to compute the potentials of electric fields.
Purpose The purpose of this paper is to frame the development and directions of business sustainability efforts. Design/methodology/approach A qualitative study was undertaken with respect to a convenience sample of reputable companies in Norway, which have implemented significant business sustainability efforts within their organisations, their business networks, the marketplace and in the society, beyond the level of mere compliance. Findings Different directions are associated with the development of corporate efforts in connection with business sustainability. Business sustainability efforts are not static, but dynamic and based upon continuous flexibility to changes and adaptations over time. Research Limitations/implications The current study highlights the need for further research into the development and directions of corporate efforts in connection with business sustainability in the marketplace and society. A key suggestion for further research is to further explore the existence of other directions. Practical Implications The directions reported, provide a framework to assess the development or the status of companies’ business sustainability efforts in the marketplace and society. Corporate efforts in connection with business sustainability develop over time as experiences are gained and personal impressions move the identified directions forward. Originality/value This study contributes to seven interconnected directions of corporate efforts in connection with business sustainability that are both relevant and potentially fruitful to both scholars and practitioners.
Purpose The purpose of this paper is to offer a political perspective on modifications in corporate governance regulation. In the wake of the financial crisis, the investment rationale of institutional investors is being pushed away from a focus on financial market liquidity and short-term trading. From a political perspective, this modification entails consideration both of investment horizon and of the definition of corporate value. Design/methodology/approach The paper narrates the historical policy debate on institutional investors as corporate governors. Building on this point, a conceptual framework is developed to further the understanding of the current shifts in policy debate of institutional investors as governors. Findings The authors find a strong policy impetus to move away from certain liberal market assumptions of efficient financial markets and the positive effects of privatization, toward viewing markets as institutionally embedded. Based on their knowledge of corporate governance regimes’ political economy, the authors argue that this shift brings intensified engagement of institutional investors in corporate affairs. The reasons for why and how this might be politically contested are specified. In conclusion, propositions regarding the outcome of such contestation in different national corporate governance regimes are offered. Originality/value Pointing to the predominantly European stakeholder value versus shareholder value discussion, the authors claim that the corporate governance policy debate related to intensified engagement of institutional investors in corporate affairs is still in its infancy. Their political perspective, including propositions for further elaboration, offers a contribution to further academic debate.
In this paper we present an interesting gadget based on the chain pair simplification problem under the discrete Fréchet distance (CPS-3F), which allows the construction of arbitrarily long paths that must be chosen in the simplification of the two curves. A pseudopolynomial time reduction from set partition is given as an example. For clarification, CPS-3F was recently shown to be in \textbf{P}, and the reduction is merely to show how the gadget works.
A novel topological segmentation of retinal images represents blood vessels as connected regions in the continuous image plane, having shape-related analytic and geometric properties. This paper presents topological segmentation results from the DRIVE retinal image database.
Given a set of points in the plane each colored either red or blue, we find non-self-intersecting geometric spanning cycles of the red points and of the blue points such that each edge of the red spanning cycle is crossed at most three times by the blue spanning cycle and vice-versa.
In this note we prove that, if $S_n$ is the greatest area of a rectangle which can be covered with $n$ unit disks, then $2\leq S_n/n<3 \sqrt{3}/2$, and these are the best constants; moreover, for $Δ(n):=(3\sqrt{3}/2)n-S_n$, we have $0.727384<\liminfΔ(n)/\sqrt{n}<2.121321$ and $0.727384<\limsupΔ(n)/\sqrt{n}<4.165064$.
We present a new algorithm for lune-based $β$-skeletons for sets of $n$ points in the plane, for $β\in (2,\infty]$, the only case when optimal algorithms are not known. The running time of the algorithm is $O(n^{3/2} \log^{1/2} n)$, which is the best known and is an improvement of Rao and Mukhopadhyay \cite{rm97} result. The method is based on point location in monotonic subdivisions of arrangements of curve segments.
Given two combinatorial triangulations, how many edge flips are necessary and sufficient to convert one into the other? This question has occupied researchers for over 75 years. We provide a comprehensive survey, including full proofs, of the various attempts to answer it.