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

Bids submitted in auctions are usually treated as enforceable commitments in most bidding and auction theory literature. In reality bidders often withdraw winning bids before the transaction when it is in their best interests to do so. Given a bid withdrawal in a combinatorial auction, finding an alternative repair solution of adequate revenue without causing undue disturbance to the remaining winning bids in the original solution may be difficult or even impossible. We have called this the "Bid-taker's Exposure Problem". When faced with such unreliable bidders, it is preferable for the bid-taker to preempt such uncertainty by having a solution that is robust to bid withdrawal and provides a guarantee that possible withdrawals may be repaired easily with a bounded loss in revenue.In this paper, we propose an approach to addressing the Bid-taker's Exposure Problem. Firstly, we use the Weighted Super Solutions framework [13], from the field of constraint programming, to solve the problem of finding a robust solution. A weighted super solution guarantees that any subset of bids likely to be withdrawn can be repaired to form a new solution of at least a given revenue by making limited changes. Secondly, we introduce an auction model that uses a form of leveled commitment contract [26, 27], which we have called mutual bid bonds, to improve solution reparability by facilitating backtracking on winning bids by the bid-taker. We then examine the trade-off between robustness and revenue in different economically motivated auction scenarios for different constraints on the revenue of repair solutions. We also demonstrate experimentally that fewer winning bids partake in robust solutions, thereby reducing any associated overhead in dealing with extra bidders. Robust solutions can also provide a means of selectively discriminating against distrusted bidders in a measured manner.

Robust solutions for combinatorial auctions

EnergeTIC is a recent industrial research project carried out in Grenoble on optimizing energy consumption in data-centres. The efficient management of a data-centre involves minimizing energy costs while ensuring service quality. We study the problem formulation proposed by EnergeTIC. First, we focus on a key sub-problem: a bin packing problem with linear costs associated with the use of bins. We study lower bounds based on Linear Programming and extend the bin packing global constraint with cost information. Second, we present a column generation model for computing the lower bound on the original energy management problem where the pricing problem is essentially a cost-aware bin packing with side constraints. Third, we show that the industrial benchmark provided so far can be solved to near optimality using a large neighborhood search.

The authors acknowledge their industrial partners (Bull, Schneider Electric, Business & Decision and UXP) as well as several public research institutions (G2Elab, G-SCOP and LIG). The authors from UCC are supported by Science Foundation Ireland Grant No. 10/IN.1/I3032.

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Bin Packing with Linear Usage Costs --- An Application to Energy Management in Data Centres

This report documents the programme and the outcomes of Dagstuhl Seminar 11201 "Constraint Programming meets Machine Learning and Data Mining". Our starting point in this seminar was that machine learning and data mining have developed largely independently from constraint programming till now, but that it is increasingly becoming clear that there are many opportunities for interactions between these areas: on the one hand, data mining and machine learning can be used to improve constraint solving; on the other hand, constraint solving can be used in data mining in machine learning. This seminar brought together prominent researchers from both communities to discuss these opportunities.

Constraint Programming meets Machine Learning and Data Mining (Dagstuhl Seminar 11201)

This paper formalises a packing problem that emerges as a core sub-problem for managing workload consolidation in data centres. As a generalisation of the Bin Packing (BP) problem, it considers a set of tasks (items) to be assigned to a set of machines (bins) under capacity constraints (CPU usage) on each machine. Unlike classic BP settings, items have a lifespan. We define the cost of using a bin as the product of the bin's capacity and the time for which it is used. This problem will be referred to as the Temporal Bin Packing problem (TBP). We formalise the problem and present optimisation models using Mixed Integer Programming (MIP) and Constraint Programming (CP) for two contrasting but equivalent perspectives on the problem. The Packing model (PA) extends traditional BP models while the Temporal model (TP) explicitly models time with a sequence of packing problems. In addition, symmetry breaking techniques are developed. Finally, we introduce both a lower bound and an upper bound on the objective function. Our empirical results suggest that the TBP is a rather challenging problem for complete solvers to prove optimality. While breaking symmetry considerably reduces the computational effort for both PA and TP models, the Packing model using CP should be considered for larger instances.

The Temporal Bin Packing Problem: An Application to Workload Management in Data Centres

The heavy-tailed phenomenon that characterises the runtime distributions of backtrack search procedures has received considerable attention over the past few years. Some have conjectured that heavy-tailed behaviour is largely due to the characteristics of the algorithm used. Others have conjectured that problem structure is a significant contributor. In this paper we attempt to explore the former hypothesis, namely we study how variable and value ordering heuristics impact the heavy-tailedness of runtime distributions of backtrack search procedures. We demonstrate that heavy-tailed behaviour can be eliminated from particular classes of random problems by carefully selecting the search heuristics, even when using chronological backtrack search. We also show that combinations of good search heuristics can eliminate heavy tails from quasigroups with holes of order 10 and 20, and give some insights into why this is the case. These results motivate a more detailed analysis of the effects that variable and value orderings can have on heavy-tailedness. We show how combinations of variable and value ordering heuristics can result in a runtime distribution being inherently heavy-tailed. Specifically, we show that even if we were to use an oracle to refute insoluble subtrees optimally, for some combinations of heuristics we would still observe heavy-tailed behaviour. Finally, we study the distributions of refutation sizes found using different combinations of heuristics and gain some further insights into what characteristics tend to give rise to heavy-tailed behaviour.

Barry O'Sullivan

Papers

Robust solutions for combinatorial auctions

Bin Packing with Linear Usage Costs --- An Application to Energy Management in Data Centres

Constraint Programming meets Machine Learning and Data Mining (Dagstuhl Seminar 11201)

The Temporal Bin Packing Problem: An Application to Workload Management in Data Centres

The Impact of Search Heuristics on Heavy-Tailed Behaviour