There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

The Analysis of Time Series: An Introduction, 4th edn. By C. Chatfield. ISBN 0 412 31820 2. Chapman and Hall, London, 1989. 242 pp. £13.50.

The Analysis of Time Series: An Introduction

This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

Parameterized Algorithms

We consider a network design problem arising in the development of an all-optical future generation Internet network called a flex-grid. An optical island is a set of core nodes that can be fully interconnected by transparent wavelength routes. We present a mathematical model for finding an optimal optical island, show that it is an NP-hard problem, and present a decomposition for solving it. In a first phase, we choose network links and route the traffic over the resulting network. In the second phase, we allocate the light-paths associated with the traffic requests to individual fibres and spectrum segments on the fibres. This so-called routing and spectrum assignment (RSA) problem is a generalisation of the well-known routing and wavelength assignment problem (RWA) of conventional optical networks. Flex-grid optical networks allow us to bundle higher capacity connection requests by allocating channels in a number of contiguous frequency slots, providing increased throughput, as long as the connection length is below technological limits. We solve the first part of the decomposition with a large neighborhood search, and the second with a CP model using a single GEOST global constraint. Results for Ireland and Italy show that solutions of high quality can be found by this decomposition.

Designing an Optical Island in the Core Network: From Routing to Spectrum Allocation

We introduce new CP models for the many-to-many stable matching problem. We use the notion of rotation to give a novel encoding that is linear in the input size of the problem. We give extra filtering rules to maintain arc consistency in quadratic time. Our experimental study on hard instances of sex-equal and balanced stable matching shows the efficiency of one of our propositions as compared with the state-of-the-art constraint programming approach.

Rotation-Based Formulation for Stable Matching

Call control features (e.g., call-divert, voice-mail) are primitive options to which users can subscribe off-line to personalise their service. The configuration of a feature subscription involves choosing and sequencing features from a catalogue and is subject to constraints that prevent undesirable feature interactions at run-time. When the subscription requested by a user is inconsistent, one problem is to find an optimal relaxation. In this paper, we show that this problem is NP-hard and we present a constraint programming formulation using the variable weighted constraint satisfaction problem framework. We also present simple formulations using partial weighted maximum satisfiability and integer linear programming. We experimentally compare our formulations of the different approaches; the results suggest that our constraint programming approach is the best of the three overall.

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Solving a Telecommunications Feature Subscription Configuration Problem

We show that previous filtering propositions on two-sided stability problems do not enforce arc consistency (AC), however they maintain bound(\(\mathcal{D}\)) consistency (BC(D)). We propose an optimal algorithm achieving BC(D) with O(L) time complexity where L is the length of the preference lists. We also show an adaptation of this filtering approach to achieve AC. Next, we report the first polynomial time algorithm for solving the hospital/resident problem with forced and forbidden pairs. Furthermore, we show that the particular case of this problem for stable marriage can be solved in \(O(n^2)\) which improves the previously best complexity by a factor of \(n^2\). Finally, we present a comprehensive set of experiments to evaluate the filtering propositions.

Revisiting Two-Sided Stability Constraints

Mass deployment of fibre access networks is without doubt the next short to medium term goal of many network operators around the globe. Long-Reach Passive Optical Network (LR-PON) has been proposed as a solution to help spreading mass deployment of Fibre-to-the-premises (FTTP), by sensibly reducing the cost per customer compared to current commercially available technologies. This paper addresses the issue of reducing protection costs on LR-PON deployment by reducing active network protection resources by spreading the load generated by a node failure over the network. Here we present a novel scalable optimisation approach to this problem that is able to find solutions for typical sized European countries in very limited time (i.e., within 30 minutes). We present a constraint optimisation formulation of the problem and propose a hybrid approach that decomposes the problem in to two subproblems and solves them using local search and systematic search respectively. The scalability of our approach is demonstrated by performing experiments using real datasets corresponding to three European countries: Ireland, UK and Italy. Our results show that the LR-PON deployment strategy that minimises the overall protection capacity rather than just minimising fibre distances in the LR-PON can indeed significantly reduce total over-provision by increasing the total distance-based cost marginally.

Barry O'Sullivan

Papers

Designing an Optical Island in the Core Network: From Routing to Spectrum Allocation

Rotation-Based Formulation for Stable Matching

Solving a Telecommunications Feature Subscription Configuration Problem

Revisiting Two-Sided Stability Constraints

A scalable optimisation approach to minimising IP protection capacity for Long-Reach PON