Max flow vitality in general and stst-planar graphs

The \emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after determining the vitality of arcs and/or nodes, and given a planar embedding of the graph, we can determine the vitality of a `contiguous' set of arcs/nodes in time proportional to the size of the set.Comment: 12 pages, 3 figure

206— Binding of Telomeric DNA G-Quadruplexes by Abietane Diterpene Natural Products

G-quadruplexes are non-canonical higher order DNA structures formed from guanine rich sequences, made up of stacked G-tetrads stabilized by Hoogsteen base pairing and K+ ions. G-quadruplexes are overrepresented in the promoter regions of oncogenes and the 5’UTR of mRNA1. As a result, G-Quadruplexes have been implicated as targets for possible anti-cancer therapeutic agents to treat previously “undruggable” targets like the c-myc and ras oncogenes1. The human telomeric repeat, [5’G3(T2AG3)3], is a repeating, single stranded DNA sequence that can form G-quadruplexes. Telomerase, an enzyme expressed in ~90% of all cancers, is responsible for extending telomeric repeats, making cancer cells immortal. It has been shown that stabilization of telomeric G-quadruplexes can inhibit telomerase activity and therefore block the survival of cancer cells2. The compounds used in the study are a group of abietane diterpene natural products from Hyptis verticillata, a plant native to the Caribbean and central America that has been used traditionally as an ethnomedicine that has been shown to have therapeutic effects. Some of these effects include anti-microbial, anti-inflammatory, and even anti-cancer activities3. Using several biophysical techniques, we have investigated the binding characteristics of these compounds to G-quadruplex DNA as a possible rationale for their observed anti-cancer therapeutic effects

Computing Lengths of Shortest Non-Crossing Paths in Planar Graphs

Given a plane undirected graph $G$ with non-negative edge weights and a set of $k$ terminal pairs on the external face, it is shown in Takahashi et al., (Algorithmica, 16, 1996, pp. 339-357) that the lengths of $k$ non-crossing shortest paths joining the $k$ terminal pairs (if they exist) can be computed in $O(n \log n)$ worst-case time, where $n$ is the number of vertices of $G$. This technique only applies when the union $U$ of the computed shortest paths is a forest. We show that given a plane undirected weighted graph $U$ and a set of $k$ terminal pairs on the external face, it is always possible to compute the lengths of $k$ non-crossing shortest paths joining the $k$ terminal pairs in linear worst-case time, provided that the graph $U$ is the union of $k$ shortest paths, possibly containing cycles. Moreover, each shortest path $\pi$ can be listed in $O(\ell+\ell\log\lceil{\frac{k}{\ell}}\rceil)$, where $\ell$ is the number of edges in $\pi$. As a consequence, the problem of computing multi-terminal distances in a plane undirected weighted graph can always be solved in $O(n \log k)$ worst-case time in the general case.Comment: 17 pages, 11 figure

Parametric variational analysis of compliant sheet metal assemblies with shell elements

One of most demanding tasks in the manufacturing field is controlling the variability of parts as it may affect strongly the deliverability of key characteristics defined at the final (product) assembly level. Current CAT systems offer a good solution to the tolerance analysis/synthesis task, but to handle flexible objects with shape errors more effort is needed to include methods able to capture the elastic behaviour of parts that adds more variability on the final assembly. Usually, sheet metal assemblies require dedicated fixtures and clamps layout to control the gap between parts in the specific location where a join must be placed. Due to the variability of parts the position of clamps can also be varied. The paper describes a FEM-based method able take into account part flexibility and shape error to parametrically analyse sheet metal assemblies by acting on some key parameters to look for the optimal clamp layout that guarantee the gap between parts to be under control after joining parts together. This method offers, with respect to commercial solutions, the ability to model fixtures, clamps and different joint types with no matter on the mesh nodes’ position. Locations of such elements are based on the shape functions defined at element (shell) mesh level and modelled as local constraints. So the user can generate a mesh without a previous knowledge of the exact positions of clamps, for example. This allows to conduit a faster parametric analysis without remeshing the surfaces and with no need to physically model the clamps. An aeronautic case study is described with a four-part assembly riveted on a quite complex fixture by using several clamps

Spatio-temporal adaptive sampling for effective coverage measurement planning during quality inspection of free form surfaces using robotic 3D optical scanner

In-line dimensional inspection of free form surfaces using robotic 3D-optical scanners provide an opportunity to reduce the mean-time-to-detection of product quality defects and has thus emerged as a critical enabler in Industry 4.0 to achieve near-zero defects. However, the time needed to inspect large industrial size sheet metal parts by 3D-optical scanners frequently exceeds the production cycle time (CT), consequently, limiting the application of in-line measurement systems for high production volume manufacturing processes such as those used in the automotive industry. This paper addresses the aforementioned challenge by developing the Spatio-Temporal Adaptive Sampling (STAS) methodology which has the capability for (i) estimation of whole part deviations based on partial measurement of a free form surface; and, (ii) adaptive selection of the next region to be measured in order to satisfy pre-defined measurement criterion. This is achieved by first, modelling spatio-temporal correlations in the high dimensional Cloud-of-Points measurement data by using a dimension reduced space-time Kalman filter; then, dynamically updating the model parameters during the inspection process by incorporating partial measurement data to predict entire part deviations and adaptively choose the next critical region of the part to be measured

Quality and productivity driven trajectory optimisation for robotic handling of compliant sheet metal parts in multi-press stamping lines

This paper investigates trajectory generation for multi-robot systems that handle compliant parts in order to minimise deformations during handling, which is important to reduce the risk of affecting the part’s dimensional quality. An optimisation methodology is proposed to generate deformation-minimal multi-robot coordinated trajectories for predefined robot paths and cycle-time. The novelty of the proposed optimisation methodology is that it efficiently estimates part deformations using a precomputed Response Surface Model (RSM), which is based on data samples generated by Finite Element Analysis (FEA) of the handled part and end-effector. The end-effector holding forces, plastic part deformations, collision-avoidance and multi-robot coordination are also considered as constraints in the optimisation model. The optimised trajectories are experimentally validated and the results show that the proposed optimisation methodology is able to significantly reduce the deformations of the part during handling, i.e. up to 12% with the same cycle-time in the case study that involves handling compliant sheet metal parts. This investigation provides insights into generating specialised trajectories for material handling of compliant parts that can systematically minimise part deformations to ensure final dimensional quality

Shape error modelling and analysis by conditional simulations of Gaussian random fields for compliant non-ideal sheet metal parts

Accurate modelling of geometric and dimensional errors of sheet metal parts is crucial in designing correct GD&T and preventing unnecessary design changes during the development and launch of a new assembly process. A novel conditional simulation based methodology to probabilistically model and generate non-ideal sheet metal part geometric variations is developed. The methodology generates part geometric variations, which accurately emulate part fabrication process in terms of covariance of generated deviations. The methodology uses as inputs one or more of the following: measurement data of current parts, historical measurements of similar parts or FEM-based simulations. The proposed methodology emulates real processes and products accurately by generating non-ideal part representatives based on the aforementioned input data. Results provide an easy engineering interpretation to the designer. The methodology is demonstrated using automotive door hinge reinforcement