We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
We present linear-time algorithms for both maximum hidden set and minimum convex cover in funnel polygons. These algorithms show that funnel polygons are "homestead" polygons, i.e. polygons for which the hidden set number and the convex cover number coincide. We extend the algorithm to apply to maximum hidden vertex set and use the result to give a 2-approximation for all three problems in pseudotriangles.
Jue Hua Lau, Anitha Jeyagurunathan, Saleha Shafie
et al.
AbstractBackgroundImpulsivity has been linked to risky behaviours amongst patients with schizophrenia or other psychotic disorders. However, there is a dearth of studies examining impulsivity amongst this population in Singapore. Moreover, to date, scales to measure impulsivity have not been validated in this population. The present study seeks to examine the underlying factor structure of the Barratt Impulsiveness Scale (BIS-11) and explore sociodemographic and clinical correlates of impulsivity within this group.MethodsConfirmatory factor analyses (CFA) were conducted to test factor structures of the BIS-11 proposed in extant literature. However, due to poor fit statistics, the sample (n = 397) was split into two groups, with Exploratory Factor Analyses (EFA) conducted in the first subgroup (n = 200). The final model of the EFA was then tested within the second subgroup (n = 197) with CFA. Multivariable linear regressions were conducted to examine sociodemographic and clinical correlates of each underlying factor.ResultsCFA indicated a three-factor structure amongst 16-items of the BIS-11 with acceptable fit: i) Non-planning impulsivity (5-items; α = 0.94), ii) Motor impulsiveness (6-items α = 0.84), and iii) Lack of self-control (5-items, α = 0.85). Lower education was associated with higher non-planning impulsivity. While age, ethnicity, marital status, and general psychiatric symptom severity were significant correlates of motor impulsiveness, problematic alcohol use and general psychiatric symptom severity were related to a greater lack of self-control.ConclusionFactor structures of the BIS-11 suggested by extant literature were not applicable, and we propose an alternative factor structure for BIS-11. Significant correlates of impulsivity are highlighted, and avenues for future research are suggested.
$\renewcommand{\Re}{\mathbb{R}}$Given a set $P$ of $n$ points in $\Re^d$, consider the problem of computing $k$ subsets of $P$ that form clusters that are well-separated from each other, and each of them is large (cardinality wise). We provide tight upper and lower bounds, and corresponding algorithms, on the quality of separation, and the size of the clusters that can be computed, as a function of $n,d,k,s$, and $Φ$, where $s$ is the desired separation, and $Φ$ is the spread of the point set $P$.
We show that several types of graph drawing in the hyperbolic plane require features of the drawing to be separated from each other by sub-constant distances, distances so small that they can be accurately approximated by Euclidean distance. Therefore, for these types of drawing, hyperbolic geometry provides no benefit over Euclidean graph drawing.
Given a simple polygon $P$ on $n$ vertices, and a set $D$ of $m$ pairwise intersecting geodesic disks in $P$, we show that five points in $P$ are always sufficient to pierce all the disks in $D$. This improves the previous bound of 14, obtained by Bose, Carmi, and Shermer.
In this note, a simple description of zone theorem in three dimensions is given.Arrangements in three dimensions are useful for constructing higher-order Voronoi diagrams in plane. An elementary and very intuitive treatment of this result is also given.
For a set of curves, Ahn et al. introduced the notion of a middle curve and gave algorithms computing these with run time exponential in the number of curves. Here we study the computational complexity of this problem: we show that it is NP-complete and give approximation algorithms.
We study self-improving sorting with hidden partitions. Our result is an optimal algorithm which runs in expected time O(H(π(I)) + n), where I is the given input which contains n elements to be sorted, π(I) is the output which are the ranks of all element in I, and H(π(I)) denotes the entropy of the output.
Purpose This paper aims to examine jointly the CEO inside debt and firm debt to further investigate the compensation incentives on risky decision-making and the resulting financial policy decisions concerning the debt structure of the firm. Design/methodology/approach Using S&P 1500 data from CRSP, Compustat, Execucomp and Capital IQ between 2006 and 2011, statistical analysis and regression models are used to determine potential correlations between the variable of interest, inside debt and debt control variables, including specialization. Findings Firms with high inside debt specialize in commercial loans and drawn credit lines. Larger firms diversify their debt holdings among commercial instruments and senior bonds. As firm size increases with inside debt, the effects are counteracted. Larger firms with high CEO inside debt have lower interest rates on these debt instruments and shorter maturities, suggesting a more conservative financing policy with regards to debt. Research limitations/implications Debt diversification is partially affected by compensation in the form of inside debt. Future studies of debt diversification should include CEO compensation controls. Practical implications For struggling companies or for those that want to return to a conservative financial policy, they can influence the CEO to make this decision by deferring his compensation to retirement. Originality/value This paper considers debt policy through the lens of a key decision maker, the CEO, and uses compensation as an incentive to determine what choices are made concerning debt.
Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani
Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations. Aim of this survey is to describe the main research directions in this area, the most prominent known results, and some of the most challenging open problems.
In this note we show that the volume of axis-parallel boxes in $\mathbb{R}^d$ which do not intersect an admissible lattice $\mathbb{L}\subset\mathbb{R}^d$ is uniformly bounded. In particular, this implies that the dispersion of the dilated lattices $N^{-1/d}\mathbb{L}$ restricted to the unit cube is of the (optimal) order $N^{-1}$ as $N$ goes to infinity. This result was obtained independently by V.N. Temlyakov (arXiv:1709.08158).
Purpose This paper aims to explore the importance of meaningful participation for Indigenous peoples within the complex and highly political context of mining and mineral extraction. The aim is to consider the multi-dimensional nature of the mining context that takes into account the discursive landscape that frames the often disparate perspectives of corporate, state and Indigenous communities. Design/methodology/approach The paper is a conceptual offering that examines the complex environment within which “meaningful participation” between mining corporates and Indigenous communities operate. Findings This paper highlights the multi-dimensional nature of a proposed relationship between the mining corporates, the state and the Indigenous Māori community within New Zealand. The facilitation of “meaningful participation” requires that any negotiated agreement is undertaken within a framework of meaning that makes sense to the Indigenous community, in addition to the appropriate legislative and corporate initiatives to be in place. Originality/value The paper highlights the complex considerations that must be included in any form of negotiation between mining corporates and Indigenous peoples to achieve meaningful participation in the form that it was intended under international accords. While recognising the different contextual circumstance of Indigenous peoples around the world, this paper illustrates a pathway towards meaningful participation that takes into account economic, socio-cultural and environmental variables.
In this paper, we give a characterization of the visibility graphs of pseudo-polygons. We first identify some key combinatorial properties of pseudo-polygons, and we then give a set of five necessary conditions based off our identified properties. We then prove that these necessary conditions are also sufficient via a reduction to a characterization of vertex-edge visibility graphs given by O'Rourke and Streinu.
Adaptive grid generation is an active research topic for numer- ical solution of differential equations. In this paper, we propose a variational method which generates transformations with prescribed Jacobian determinant and curl. Then we use this transformation to achieve adaptive grid generation task, and show the importance of curl in a transformation.
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved approximation guarantees.
The purpose of this note is to describe of a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for level persistence. The paper provides the opportunity to compare level persistence with the persistence introduced by Edelsbrunner- Letscher-Zomorodian called in this paper, as sub-level persistence.
We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse) and the simplest degenerate critical points.