Pole Dancing: 3D Morphs for Tree Drawings

We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\log n)$ steps, while for the latter $\Theta(n)$ steps are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Model Updating for Loading Capacity Estimation of Concrete Structures using Ambient Vibration

This paper presents a model updating approach for determining the loading capacity of a concrete structure utilising measured ambient vibration responses. The proposed method uses Operational Modal Analysis (OMA) with the Enhanced Frequency Domain Decomposition (EFDD) technique to identify the natural frequencies and mode shapes of an experimental replica specimen of a Sydney Harbour Bridge concrete jack arch component. For vibration testing, the structure is excited with ambient vibration recordings from the actual Sydney Harbour Bridge using a vibro tactile transducer. The vibration responses of the structure are measured using an array of strategically placed accelerometers. A numerical model is developed and updated using the vibrational characteristics with the aim of estimating the load capacity of the structure. The results show that the proposed updating method using partitioning has great potential to be used for determining the loading capacity of a structure as part of a Structural Health Monitoring (SHM) system

Euclidean Greedy Drawings of Trees

Greedy embedding (or drawing) is a simple and efficient strategy to route messages in wireless sensor networks. For each source-destination pair of nodes s, t in a greedy embedding there is always a neighbor u of s that is closer to t according to some distance metric. The existence of greedy embeddings in the Euclidean plane R^2 is known for certain graph classes such as 3-connected planar graphs. We completely characterize the trees that admit a greedy embedding in R^2. This answers a question by Angelini et al. (Graph Drawing 2009) and is a further step in characterizing the graphs that admit Euclidean greedy embeddings.Comment: Expanded version of a paper to appear in the 21st European Symposium on Algorithms (ESA 2013). 24 pages, 20 figure

Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition

A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is $x$- and $y$-monotone. Angle-monotone graphs are $\sqrt 2$-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced angle-monotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize angle-monotone geometric graphs. We prove that every point set has a plane geometric graph that is generalized angle-monotone---specifically, we prove that the half-$\theta_6$-graph is generalized angle-monotone. We give a local routing algorithm for Gabriel triangulations that finds a path from any vertex $s$ to any vertex $t$ whose length is within $1 + \sqrt 2$ times the Euclidean distance from $s$ to $t$. Finally, we prove some lower bounds and limits on local routing algorithms on Gabriel triangulations.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Upward Planar Morphs

We prove that, given two topologically-equivalent upward planar straight-line drawings of an $n$-vertex directed graph $G$, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of $O(1)$ morphing steps if $G$ is a reduced planar $st$-graph, $O(n)$ morphing steps if $G$ is a planar $st$-graph, $O(n)$ morphing steps if $G$ is a reduced upward planar graph, and $O(n^2)$ morphing steps if $G$ is a general upward planar graph. Further, we show that $\Omega(n)$ morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an $n$-vertex path.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018) The current version is the extended on

On the Area Requirements of Planar Greedy Drawings of Triconnected Planar Graphs

In this paper we study the area requirements of planar greedy drawings of triconnected planar graphs. Cao, Strelzoff, and Sun exhibited a family $\cal H$ of subdivisions of triconnected plane graphs and claimed that every planar greedy drawing of the graphs in $\mathcal H$ respecting the prescribed plane embedding requires exponential area. However, we show that every $n$-vertex graph in $\cal H$ actually has a planar greedy drawing respecting the prescribed plane embedding on an $O(n)\times O(n)$ grid. This reopens the question whether triconnected planar graphs admit planar greedy drawings on a polynomial-size grid. Further, we provide evidence for a positive answer to the above question by proving that every $n$-vertex Halin graph admits a planar greedy drawing on an $O(n)\times O(n)$ grid. Both such results are obtained by actually constructing drawings that are convex and angle-monotone. Finally, we consider $\alpha$-Schnyder drawings, which are angle-monotone and hence greedy if $\alpha\leq 30^\circ$, and show that there exist planar triangulations for which every $\alpha$-Schnyder drawing with a fixed $\alpha<60^\circ$ requires exponential area for any resolution rule

Effects of Royal Jelly and Tocotrienol Rich Fraction in obesity treatment of calorie-restricted obese rats: A focus on white fat browning properties and thermogenic capacity

Background: Obesity has reached an alarming rate worldwide. Promoting thermogenesis via increasing the function of brown adipose tissue (BAT) or white adipose tissue (WAT) browning has been proposed as a new protective approach against obesity. The goal of this study was to evaluate the effects of Royal Jelly (RJ) and tocotrienol rich fraction (TRF) on BAT activation and WAT browning during calorie restriction diet (CRD) in obesity model. Methods: In this experimental study, 50 obese Wistar rats were randomly divided into 5 groups and then received one of the following treatments for a period of 8-week: High-fat diet (HFD), CRD, RJ + CRD, TRF + CRD, and RJ + TRF + CRD. Effects of RJ and TRF, individually and in combination on body weight and the expression of key thermoregulatory genes in WAT and BAT were examined by quantitative real-time (qRT-PCR). Also, morphological alterations were assessed by hematoxylin and eosin staining. Results: RJ (- 67.21 g ±4.84 g) and RJ + TRF (- 73.29 g ±4.51 g) significantly reduced weight gain relative to the CRD group (- 40.70 g ±6.50 g, P < 0.001). In comparison with the CRD group, RJ and RJ + TRF remarkably enhanced the uncoupling protein1 (UCP1) expression in WAT (5.81, 4.72 fold, P < 0.001) and BAT (4.99, 4.75 fold, P < 0.001). The expression of PR domain containing 16(PRDM 16), cAMP response element-binding protein1 (CREB1), P38 mitogen-activated protein kinases (P38MAPK), and Bone morphogenetic protein8B (BMP8B) have significantly increased following RJ and RJ + TRF treatments (P < 0.001). However, the expression levels of CCAAT/enhancer-binding protein beta (CEBPβ) and Bone morphogenetic protein7 (BMP7) did not remarkably change. Multilocular beige cells in WAT and compacted dense adipocytes were also observed in BAT of RJ and RJ + TRF received groups. TRF showed no substantial effects on the expression of the mentioned thermoregulatory genes and brown fat-like phenotype. Conclusion: Our results suggest that, Royal Jelly promotes thermogenesis and browning of WAT, contributing to an increase in energy expenditure. Thus, Royal Jelly may give rise to a novel dietary choice to attenuate obesity. © 2020 The Author(s)