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

Critique graphs were introduced as a device for analysing the behaviour of conversational recommender systems. A conversational recommender allows a user to critique a recommended product with statements such as "I'd like a similar product to this one, but cheaper". A critique graph is a directed multigraph in which the nodes represent products, and a directed edge between a pair of products represents how a user can move from one product to another by tweaking a particular product feature. It has been shown that critique graphs are not symmetric: if a user critiques a product pi and is presented with product pj, critiquing product pj in the opposite manner does not necessarily return product pi. Furthermore, it might not be possible to reach all products in a catalogue starting from a given product, or as a consequence of a particular critique some products become unreachable. This latter point is quite unsatisfactory since a user would assume that it is possible to explore the full catalogue by critiquing alone. A number of approaches to overcoming this problem have been proposed in the literature. In this paper we propose a novel approach that exploits the critique graph directly. Specifically, the unreachability is a consequence of a critique graph having more than one strongly connected component. We show how the critique graph can be modified in a minor way, thereby modifying the semantics of critiquing for a given catalogue, so that all products are always reachable.

Improving Navigation in Critique Graphs

We study the problem of matching a set of applicants to a set of posts, where each applicant has an ordinal preference list, which may contain ties, ranking a subset of posts. A matching M is popular if there exists no matching M' where more applicants prefer M' to M . Several notions of optimality are studied in the literature for the case of strictly ordered preference lists. In this paper we address the case involving ties and propose novel algorithmic and complexity results for this variant. Next, we focus on the NP-hard case where additional copies of posts can be added in the preference lists, called Popular Matching with Copies. We define new dominance rules for this problem and present several novel graph properties characterising the posts that should be copied with priority. We present a comprehensive set of experiments for the popular matching problem with copies to evaluate our dominance rules as well as the different branching strategies. Our experimental study emphasizes the importance of the dominance rules and characterises the key aspects of a good branching strategy.

New Models for Two Variants of Popular Matching

We present a greedy version of an existing metaheuristic al-gorithm for a special version of the Cutting Stock Problem(CSP). For this version, it is only possible to have indirectcontrol over the patterns via a vector of continuous valueswhich we refer to as a weights vector. Our algorithm itera-tively generates new weights vectors by making local changesover the best weights vector computed so far. This allows usto achieve better solutions much faster than is possible withthe original metaheuristic.

An improved metaheuristic algorithm for maximizing demand satisfaction in the population harvest Cutting Stock Problem

Search effort is typically measured in terms of the number of backtracks, constraint checks, or nodes in the search tree, but measures such as the number of incorrect decisions have also been proposed. Comparisons based on mean and median effort are common. However, other researchers focus on studying runtime distributions, where one can observe a (non-)heavy-tailed distribution under certain conditions [2, 3].

Failure analysis in backtrack search for constraint satisfaction

Product catalogues are usually represented as tables. They are regularly updated with new variants and, over time, various forms of inconsistencies or undesirable properties can be introduced, especially when global changes are made. We argue that by compiling product catalogues into decision diagrams we can support a number of high-level queries for detecting and checking for various forms of inconsistency, as well as verifying other properties relevant for user interaction. In particular, a class of functional dependency-based inconsistencies can be detected efficiently. An example is verifying properties such as: "each identical configuration of a product has the same price". This paper presents a number of algorithmic advances. We illustrate the usefulness of our approach by evaluating these high-level properties over real-world publicly available product catalogues.

Barry O'Sullivan

Papers

Improving Navigation in Critique Graphs

New Models for Two Variants of Popular Matching

An improved metaheuristic algorithm for maximizing demand satisfaction in the population harvest Cutting Stock Problem

Failure analysis in backtrack search for constraint satisfaction

Uncovering functional dependencies in MDD-compiled product catalogues