A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In the non-four-sided case, this requires a special parameterization technique involving rational curves. Appropriate handling of triangular subpatches and alternative subpatch representations are also discussed.
Purpose This paper aims to investigate the process and business model innovations within the ultra-fast business model (UFBM) that have potential sustainable applications. Design/methodology/approach An exploratory multiple case study research method was used, emphasizing on an integrative literature review and focusing on two successful Chinese-origin companies that have revolutionized the e-commerce market: Shein and Temu. Findings Although the UFBM adopted by these companies remains highly controversial and is commonly associated with harmful business practices and lack of business responsibility, both have managed to develop process and business model innovations that may interest sustainability-driven organizations. They have implemented their unique versions of the customer-to-manufacturer (C2M) production system, which reduces costs and facilitates information exchanges between customers and manufacturers, thereby achieving a better product-market fit. Further still, they have redefined the shopping experience through their interpretations of collaborative consumption, as manifested in live and social commerce, gamification and group buying formats. Originality/value Instead of dismissing the UFBM due to its negative environmental and societal impacts, the study concentrates on process and business model innovations that have a potential for sustainability. That does not mean praising the business model as a whole, but instead indicating its potentially interesting aspects that could serve as inspirations for managers and business leaders who are concerned with sustainability. Learning from others' experiences is a recognized business practice, and in this case, could be particularly beneficial for companies with limited resources or opportunities for experimentation.
In this work, we develop Extraction Theorems for classes of geometric objects with small extraction numbers. These classes include intervals, axis-parallel segments, axis-parallel rays, and octants. We investigate these classes of objects and prove small bounds on the extraction numbers. The tightness of these bounds is demonstrated by examples with matching lower bounds.
Purpose The quest to unravel the mysterious boardroom’s structure that would confer the firm with incremental layers of economic supremacy has emerged as an issue of considerable importance in the corporate governance literature. Despite numerous attempts, corporate governance research has repeatedly failed to establish a clear and unequivocal theoretical linkage between the boardroom type and the corporate performance. Specifically, the optimum boardroom’s structure (i.e. one that would yield maximum economic benefit) remains an elusive dilemma. Undoubtedly, this problematic deserves more scrutiny. This study aims to expose the different layers of dimensional complexities related to boardroom’s research, particularly as it relates to those investigations using the positivist philosophy of research via inferential statistics using hypothetico-deductive reasoning. Design/methodology/approach The author examines the intrinsic complexities of boardroom’s research using thematic analysis. In the first phase, the author conducts a fine-grained systematic review of published studies in scholarly peer-reviewed journals. In the second phase, the author conduct a phenomenological investigation via semi-structured interviews with 35 seasoned corporate governance scholars with sound knowledge and expertise on boardroom’s research. Findings The thematic analysis reveals three overarching complexity dimensions encountered in boardroom’s research: an input dimension related to the ontological complexity of corporations. Research on boardroom’s effectiveness entails the manipulation and analysis of a plethora of convoluted and intertwined corporate performance determinants. Such explanatory variables are difficult to capture, untangle and operationalize; a processing dimension related to the methodological complexity of dealing with imperfect and incomplete information. Positivist research often uses large archival databases marred with endogeneity complications; an output dimension epitomizing the epistemological complexity of ascertaining what really constitutes corporate performance. The currently adopted performance metrics (accounting or market indicators) do not adequately depict the essence of boardroom’s effectiveness and corporate success. Research limitations/implications Boardroom’s research continues to generate high level of interests in academic circles. Specifically, research on the linkage of boardroom’s structure and corporate performance is both unclear and confusing. This lingering deficiency necessitates the adoption of novel epistemological and methodological approaches to broaden the theoretical perspectives of boardroom’s structural effectiveness. Practical implications One key motivation of this study is to entice boardroom’s research to venture in the direction of uncharted territories. Knowledge discovery in this important area would have far-reaching implications on corporate governance best practices, including how to restructure existing boardrooms or how to establish new ones from scratch. Social implications A well-functioning boardroom would justifiably push the firm in the direction of healthier corporate governance. In turn, healthier corporate governance would eventually yield superior corporate performance with positive consequences on key stakeholders, including shareholders, employees, customers, suppliers, regulators and other members of the profession and the society. Originality/value In this paper, the author endeavors to identify and explain the root causes behind the complex nature of boardroom’s research. The author particularly focuses on the factors that blur or distort the causal linkage between boardroom’s type and corporate performance. To the author’s knowledge, this is the first comprehensive investigation that attempts to highlight the inherently complex nature of boardroom’s research. Thus, it fills an important gap in the literature.
Purpose This study aims to intend toward the measurement of corporate governance to identify its maturity levels within Omani public listed companies and also propose to identify whether corporate governance maturity (CGM) levels vary significantly between sectors or not. CGM is an innovation in the field of corporate governance, which assists organizations in achieving their objectives and satisfying shareholders. Design/methodology/approach This study used descriptive cross-sectional survey design. Data are collected by the internet-based tool and analyzed via SPSS. Findings This study found that corporate governance is measurable and can be measured to the levels of maturity. Moreover, this study identified that CGM does not differ among different sectors. From a total of 107 organizations, none of the organizations falls under the forming level and mature level. However, majority of organizations falls under normalized level followed by developing and established levels of maturity. Practical implications This study integrates significant empirical research and literature to broaden the potentials of CGM. This study provides a framework along with a calculation tool, which can be used by organizations, regulators and policymakers. Originality/value To the best of the authors’ knowledge, the maturity levels of Omani organizations are never being measured before. Moreover, past studies demonstrate single constituent relationship with CGM and not all four. Therefore, this study is distinctive from others by testing all four major components or constituents toward CGM.
In a recent article (Auer et al, Algorithmica 2016) it was claimed that every outer-1-planar graph has a planar visibility representation of area $O(n\log n)$. In this paper, we show that this is wrong: There are outer-1-planar graphs that require $Ω(n^2)$ area in any planar drawing. Then wegive a construction (using crossings, but preserving a given outer-1-planar embedding) that results in an orthogonal box-drawing with O(n log n) area and at most two bends per edge.
Let $P$ be a set of $n$ points in $\mathbb{R}^3$ amid a bounded number of obstacles. When obstacles are axis-parallel boxes, we prove that $P$ admits an $8\sqrt{3}$-spanner with $O(n\log^3 n)$ edges with respect to the geodesic distance.
We consider the problem of computing the largest-area bichromatic separating box among a set of $n$ red points and a set of $m$ blue points in three dimensions. Currently, the best-known algorithm to solve this problem takes $O(m^2 (m + n))$ time and $O(m + n)$ space. In this paper, we come up with an improved algorithm for the problem, which takes $O(m^2 + n)$ time.
In 1960, Asplund and Grünbaum proved that every intersection graph of axis-parallel rectangles in the plane admits an $O(ω^2)$-coloring, where $ω$ is the maximum size of a clique. We present the first asymptotic improvement over this six-decade-old bound, proving that every such graph is $O(ω\logω)$-colorable and presenting a polynomial-time algorithm that finds such a coloring. This improvement leads to a polynomial-time $O(\log\log n)$-approximation algorithm for the maximum weight independent set problem in axis-parallel rectangles, which improves on the previous approximation ratio of $O(\frac{\log n}{\log\log n})$.
With the growth of machine learning algorithms with geometry primitives, a high-efficiency library with differentiable geometric operators are desired. We present an optimized Differentiable Geometry Algorithm Library (DGAL) loaded with implementations of differentiable operators for geometric primitives like lines and polygons. The library is a header-only templated C++ library with GPU support. We discuss the internal design of the library and benchmark its performance on some tasks with other implementations.
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly. This approach is based on a new computational characterisation of the singular points of the cutcurve and on how this curve is located with respect to the projection of the considered quadrics (whose boundaries are the so called silhouette curves).
Given a set of radii measured from a fixed point, the existence of a convex configuration with respect to the set of distinct radii in the two-dimensional case is proved when radii are distinct or repeated at most four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.
We propose to employ scale spaces of mathematical morphology to hierarchically simplify fracture surfaces of complementarity fitting archaeological fragments. This representation preserves complementarity and is insensitive to different kinds of abrasion affecting the exact fitting of the original fragments. We present a pipeline for morphologically simplifying fracture surfaces, based on their Lipschitz nature; its core is a new embedding of fracture surfaces to simultaneously compute both closing and opening morphological operations, using distance transforms.
PurposeInvestors are called to be good stewards/trustees of their investments, often on behalf of third parties. In light of this fiduciary responsibility, and the conundrum of public criticism potentially impacting on share price, this paper aims to use the basis of the UK governance code to explore what important dialogue investors really have with their holdings to support good governance.Design/methodology/approachSemi-structured telephone interviews with eight institutional investors explore governance issues and investor company dialogue, giving insights into the aspects of the importance of their part in the UK corporate governance code.FindingsRather than being sleeping lions, investors positively engage with companies, with regular communication being high on their agenda and not always via the annual general meeting. There is a preference to engage directly with the company rather than in public view or via share dumptin. Thus, we often do not see their actions around their fiduciary duties as often they avoid public criticism or any visibility that could do reputational harm and decrease company value.Research limitations/implicationsThis dialogue was just before the point of the exposure of the financial crisis; however, it shows the importance that investors give to taking their responsibilities seriously. Importantly, it provides a springboard for further debate following the financial crises and the updates of the financial environment.Practical implicationsEven though policy seeks engagement, the nuances of the investor dialogue are under explored compared to visible quantitative metrics. This dialogue assures that investors are active, even if their engagement is not public and can be deemed as hidden.Originality/valueComplementing quantitative studies, this paper explores a qualitative approach, uniquely sharing insights into a hidden and little explored world of fiduciary dialogue.
We study the point location problem in incremental (possibly disconnected) planar subdivisions, that is, dynamic subdivisions allowing insertions of edges and vertices only. Specifically, we present an $O(n\log n)$-space data structure for this problem that supports queries in $O(\log^2 n)$ time and updates in $O(\log n\log\log n)$ amortized time. This is the first result that achieves polylogarithmic query and update times simultaneously in incremental (possibly disconnected) planar subdivisions. Its update time is significantly faster than the update time of the best known data structure for fully-dynamic (possibly disconnected) planar subdivisions.
How many copies of a parallelepiped are needed to ensure that for every point in the parallelepiped a copy of each other point exists, such that the distance between them equals the distance of the pair of points when the opposite sites of the parallelepiped are identified? This question is answered in Euclidean space by constructing the smallest domain that fulfills the above condition. We also describe how to obtain all primitive cells of a lattice (i.e., closures of fundamental domains) that realise the smallest number of copies needed and give them explicitly in 2D and 3D.
The goal in the min-\# curve simplification problem is to reduce the number of the vertices of a polygonal curve without changing its shape significantly. We study curve-restricted min-\# simplification of polygonal curves, in which the vertices of the simplified curve can be placed on any point of the input curve, provided that they respect the order along that curve. For local directed Hausdorff distance from the input to the simplified curve in $\mathbb{R}^2$, we present an approximation algorithm that computes a curve whose number of links is at most twice the minimum possible.
The VC-dimension plays an important role for the algorithmic problem of guarding art galleries efficiently. We prove that inside a simple polygon at most $5$ points can be shattered by $L_1$-visibility polygons and give an example where 5 points are shattered. The VC-dimension is exactly $5$. The proof idea for the upper bound is different from previous approaches. Keywords: Art gallery, VC-dimension, $L_1$-visibility, polygons
We show that every 4-connected planar graph has a $B_3$-EPG representation, i.e., every vertex is represented by a curve on the grid with at most three bends, and two vertices are adjacent if and only if the corresponding curves share an edge of the grid. Our construction is based on a modification of the representation by touching thickened $L$-shapes proposed by Gonçalves et al.