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.

Block-based feature detection and matching for mosaicing of camera-captured document images

In this paper, we present a new feature-based approach for mosaicing of camera-captured document images. A novel block-based scheme is employed to ensure that corners can be reliably detected over a wide range of images. 2-D discrete cosine transform is computed for image blocks defined around each of the detected corners and a small subset of the coefficients is used as a feature vector A 2-pass feature matching is performed to establish point correspondences from which the homography relating the input images could be computed. The algorithm is tested on a number of complex document images casually taken from a hand-held camera yielding convincing results.

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.

Data fusion and matching by maximizing statistical dependencies

The core aim of machine learning is to make a computer program learn from the experience. Learning from data is usually defined as a task of learning regularities or patterns in data in order to extract useful information, or to learn the underlying concept. An important sub-field of machine learning is called multi-view learning where the task is to learn from multiple data sets or views describing the same underlying concept. A typical example of such scenario would be to study a biological concept using several biological measurements like gene expression, protein expression and metabolic profiles, or to classify web pages based on their content and the contents of their hyperlinks. In this thesis, novel problem formulations and methods for multi-view learning are presented. The contributions include a linear data fusion approach during exploratory data analysis, a new measure to evaluate different kinds of representations for textual data, and an extension of multi-view learning for novel scenarios where the correspondence of samples in the different views or data sets is not known in advance. In order to infer the one-to-one correspondence of samples between two views, a novel concept of multi-view matching is proposed. The matching algorithm is completely data-driven and is demonstrated in several applications such as matching of metabolites between humans and mice, and matching of sentences between documents in two languages.

Empirical Studies on Labor Market Matching (summary section only)

This thesis analyzes how matching takes place at the Finnish labor market from three different angles. The Finnish labor market has undergone severe structural changes following the economic crisis in the early 1990s. The labor market has had problems adjusting from these changes and hence a high and persistent unemployment has followed. In this thesis I analyze if matching problems, and in particular if changes in matching, can explain some of this persistence. The thesis consists of three essays. In the first essay Finnish Evidence of Changes in the Labor Market Matching Process the matching process at the Finnish labor market is analyzed. The key finding is that the matching process has changed thoroughly between the booming 1980s and the post-crisis period. The importance of the number of unemployed, and in particular long-term unemployed, for the matching process has vanished. More unemployed do not increase matching as theory predicts but rather the opposite. In the second essay, The Aggregate Matching Function and Directed Search -Finnish Evidence, stock-flow matching as a potential micro foundation of the aggregate matching function is studied. In the essay I show that newly unemployed match mainly with the stock of vacancies while longer term unemployed match with the inflow of vacancies. When aggregating I still find evidence of the traditional aggregate matching function. This could explain the huge support the aggregate matching function has received despite its odd randomness assumption. The third essay, How do Registered Job Seekers really match? -Finnish occupational level Evidence, studies matching for nine occupational groups and finds that very different matching problems exist for different occupations. In this essay also misspecification stemming from non-corresponding variables is dealt with through the introduction of a completely new set of variables. The new outflow measure used is vacancies filled with registered job seekers and it is matched by the supply side measure registered job seekers.

Voting Paths

We consider a variant of the popular matching problem here. The input instance is a bipartite graph $G=(\mathcal{A}\cup\mathcal{P},E)$, where vertices in $\mathcal{A}$ are called applicants and vertices in $\mathcal{P}$ are called posts. Each applicant ranks a subset of posts in an order of preference, possibly involving ties. A matching $M$ is popular if there is no other matching $M'$ such that the number of applicants who prefer their partners in $M'$ to $M$ exceeds the number of applicants who prefer their partners in $M$ to $M'$. However, the “more popular than” relation is not transitive; hence this relation is not a partial order, and thus there need not be a maximal element here. Indeed, there are simple instances that do not admit popular matchings. The questions of whether an input instance $G$ admits a popular matching and how to compute one if it exists were studied earlier by Abraham et al. Here we study reachability questions among matchings in $G$, assuming that $G=(\mathcal{A}\cup\mathcal{P},E)$ admits a popular matching. A matching $M_k$ is reachable from $M_0$ if there is a sequence of matchings $\langle M_0,M_1,\dots,M_k\rangle$ such that each matching is more popular than its predecessor. Such a sequence is called a length-$k$ voting path from $M_0$ to $M_k$. We show an interesting property of reachability among matchings in $G$: there is always a voting path of length at most 2 from any matching to some popular matching. Given a bipartite graph $G=(\mathcal{A}\cup\mathcal{P},E)$ with $n$ vertices and $m$ edges and any matching $M_0$ in $G$, we give an $O(m\sqrt{n})$ algorithm to compute a shortest-length voting path from $M_0$ to a popular matching; when preference lists are strictly ordered, we have an $O(m+n)$ algorithm. This problem has applications in dynamic matching markets, where applicants and posts can enter and leave the market, and applicants can also change their preferences arbitrarily. After any change, the current matching may no longer be popular, in which case we are required to update it. However, our model demands that we switch from one matching to another only if there is consensus among the applicants to agree to the switch. Hence we need to update via a voting path that ends in a popular matching. Thus our algorithm has applications here.

Max-Coloring Paths: Tight Bounds and Extensions

The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V, E) with a non-negative weight function w on V such that Sigma(k)(i=1) max(v epsilon Ci) w(v(i)) is minimized, where C-1, ... , C-k are the various color classes. Max-coloring general graphs is as hard as the classical vertex coloring problem, a special case where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring abroad class of trees and show it can be solved in time O(vertical bar V vertical bar+time for sorting the vertex weights). When vertex weights belong to R, we show a matching lower bound of Omega(vertical bar V vertical bar log vertical bar V vertical bar) in the algebraic computation tree model.

Popular Matchings with Variable Job Capacities

We consider the problem of matching people to jobs, where each person ranks a subset of jobs in an order of preference, possibly involving ties. There are several notions of optimality about how to best match each person to a job; in particular, popularity is a natural and appealing notion of optimality. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not adroit popular matchings. This motivates the following extension of the popular rnatchings problem:Given a graph G; = (A boolean OR J, E) where A is the set of people and J is the set of jobs, and a list < c(1), c(vertical bar J vertical bar)) denoting upper bounds on the capacities of each job, does there exist (x(1), ... , x(vertical bar J vertical bar)) such that setting the capacity of i-th, job to x(i) where 1 <= x(i) <= c(i), for each i, enables the resulting graph to admit a popular matching. In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c is 1 or 2.

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.

Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, ..., d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4 − 2/d for an even d; and in graphs with maximum degree Δ, to within 4 − 2/(Δ − 1) for an odd Δ and to within 4 − 2/Δ for an even Δ. These approximation ratios are tight for all values of d and Δ: there are matching lower bounds.

Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.