Flow-graph techniques for epicyclic gear train analysis

Flow-graph techniques are applied in this article for the analysis of an epicyclic gear train. A gear system based on this is designed and constructed for use in Numerical Control Systems.

Acoustic emission source location and damage detection in a metallic structure using a graph-theory-based geodesic pproach

A geodesic-based approach using Lamb waves is proposed to locate the acoustic emission (AE) source and damage in an isotropic metallic structure. In the case of the AE (passive) technique, the elastic waves take the shortest path from the source to the sensor array distributed in the structure. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. The same approach is extended for detection of damage in a structure. The wave response matrix of the given sensor configuration for the healthy and the damaged structure is obtained experimentally. The healthy and damage response matrix is compared and their difference gives the information about the reflection of waves from the damage. These waves are backpropagated from the sensors and the above method is used to locate the damage by finding the point where intersection of geodesics occurs. In this work, the geodesic approach is shown to be suitable to obtain a practicable source location solution in a more general set-up on any arbitrary surface containing finite discontinuities. Experiments were conducted on aluminum specimens of simple and complex geometry to validate this new method.

Using a glow graph to represent data flow and dependency in event logs

The idea of extracting knowledge in process mining is a descendant of data mining. Both mining disciplines emphasise data flow and relations among elements in the data. Unfortunately, challenges have been encountered when working with the data flow and relations. One of the challenges is that the representation of the data flow between a pair of elements or tasks is insufficiently simplified and formulated, as it considers only a one-to-one data flow relation. In this paper, we discuss how the effectiveness of knowledge representation can be extended in both disciplines. To this end, we introduce a new representation of the data flow and dependency formulation using a flow graph. The flow graph solves the issue of the insufficiency of presenting other relation types, such as many-to-one and one-to-many relations. As an experiment, a new evaluation framework is applied to the Teleclaim process in order to show how this method can provide us with more precise results when compared with other representations.

Bond graph model of doubly fed three phase induction motor using the Axis Rotator element for frame transformation

Induction motor is a typical member of a multi-domain, non-linear, high order dynamic system. For speed control a three phase induction motor is modelled as a d–q model where linearity is assumed and non-idealities are ignored. Approximation of the physical characteristic gives a simulated behaviour away from the natural behaviour. This paper proposes a bond graph model of an induction motor that can incorporate the non-linearities and non-idealities thereby resembling the physical system more closely. The model is validated by applying the linearity and idealities constraints which shows that the conventional ‘abc’ model is a special case of the proposed generalised model.

Topological properties of the one dimensional exponential random geometric graph

In this article we study the one-dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008.

Optimal multicommodity flow through the complete graph with random edge capacities

We consider a multicommodity flow problem on a complete graph whose edges have random, independent, and identically distributed capacities. We show that, as the number of nodes tends to infinity, the maximumutility, given by the average of a concave function of each commodity How, has an almost-sure limit. Furthermore, the asymptotically optimal flow uses only direct and two-hop paths, and can be obtained in a distributed manner.

Exact bounds for distributed graph colouring

A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

The hardness of approximating the boxicity, cubicity and threshold dimension of a graph

A k-dimensional box is the Cartesian product R-1 X R-2 X ... X R-k where each R-i is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. A unit cube in k-dimensional space or a k-cube is defined as the Cartesian product R-1 X R-2 X ... X R-k where each R-i is a closed interval oil the real line of the form a(i), a(i) + 1]. The cubicity of G, denoted as cub(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-cubes. The threshold dimension of a graph G(V, E) is the smallest integer k such that E can be covered by k threshold spanning subgraphs of G. In this paper we will show that there exists no polynomial-time algorithm for approximating the threshold dimension of a graph on n vertices with a factor of O(n(0.5-epsilon)) for any epsilon > 0 unless NP = ZPP. From this result we will show that there exists no polynomial-time algorithm for approximating the boxicity and the cubicity of a graph on n vertices with factor O(n(0.5-epsilon)) for any epsilon > 0 unless NP = ZPP. In fact all these hardness results hold even for a highly structured class of graphs, namely the split graphs. We will also show that it is NP-complete to determine whether a given split graph has boxicity at most 3. (C) 2010 Elsevier B.V. All rights reserved.

Simulation and graph mining tools for improving gene mapping efficiency

Gene mapping is a systematic search for genes that affect observable characteristics of an organism. In this thesis we offer computational tools to improve the efficiency of (disease) gene-mapping efforts. In the first part of the thesis we propose an efficient simulation procedure for generating realistic genetical data from isolated populations. Simulated data is useful for evaluating hypothesised gene-mapping study designs and computational analysis tools. As an example of such evaluation, we demonstrate how a population-based study design can be a powerful alternative to traditional family-based designs in association-based gene-mapping projects. In the second part of the thesis we consider a prioritisation of a (typically large) set of putative disease-associated genes acquired from an initial gene-mapping analysis. Prioritisation is necessary to be able to focus on the most promising candidates. We show how to harness the current biomedical knowledge for the prioritisation task by integrating various publicly available biological databases into a weighted biological graph. We then demonstrate how to find and evaluate connections between entities, such as genes and diseases, from this unified schema by graph mining techniques. Finally, in the last part of the thesis, we define the concept of reliable subgraph and the corresponding subgraph extraction problem. Reliable subgraphs concisely describe strong and independent connections between two given vertices in a random graph, and hence they are especially useful for visualising such connections. We propose novel algorithms for extracting reliable subgraphs from large random graphs. The efficiency and scalability of the proposed graph mining methods are backed by extensive experiments on real data. While our application focus is in genetics, the concepts and algorithms can be applied to other domains as well. We demonstrate this generality by considering coauthor graphs in addition to biological graphs in the experiments.

Macroscopic model of city traffic using bond graph modelling

Modelling of city traffic involves capturing of all the dynamics that exist in real-time traffic. Probabilistic models and queuing theory have been used for mathematical representation of the traffic system. This paper proposes the concept of modelling the traffic system using bond graphs wherein traffic flow is based on energy conservation. The proposed modelling approach uses switched junctions to model complex traffic networks. This paper presents the modelling, simulation and experimental validation aspects.

On the Nash-Williams′ Lemma in Graph Reconstruction Theory

A generalization of Nash-Williams′ lemma is proved for the Structure of m-uniform null (m − k)-designs. It is then applied to various graph reconstruction problems. A short combinatorial proof of the edge reconstructibility of digraphs having regular underlying undirected graphs (e.g., tournaments) is given. A type of Nash-Williams′ lemma is conjectured for the vertex reconstruction problem.

A polynomial bound on the number of light cycles in an undirected graph

Let G be an undirected graph with a positive real weight on each edge. It is shown that the number of minimum-weight cycles of G is bounded above by a polynomial in the number of edges of G. A similar bound holds if we wish to count the number of cycles with weight at most a constant multiple of the minimum weight of a cycle of G.

Analysing Message Sequence Graph Specifications

We give a detailed construction of a finite-state transition system for a com-connected Message Sequence Graph. Though this result is well-known in the literature and forms the basis for the solution to several analysis and verification problems concerning MSG specifications, the constructions given in the literature are either not amenable to implementation, or imprecise, or simply incorrect. In contrast we give a detailed construction along with a proof of its correctness. Our transition system is amenable to implementation, and can also be used for a bounded analysis of general (not necessarily com-connected) MSG specifications.

Performance Evaluation of Distance-Hop Proportionality on Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.