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Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt,Robert Sedgewick, Princeton University, New Jersey
Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt,Robert Sedgewick, Princeton University, New Jersey
Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt,Robert Sedgewick, Princeton University, New Jersey
Analytic Combinatorics aims at predicting precisely the properties of large structured combinatorial configurations, through an approach based extensively on analytic methods. Generating functions are the central objects of study of the theory.
Analytic combinatorics starts from an exact enumerative description of combinatorial structures by means of generating functions: these make their first appearance as purely formal algebraic objects. Next, generating functions are interpreted as analytic objects, that is, as mappings of the complex plane into itself. Singularities determine a function's coefficients in asymptotic form and lead to precise estimates for counting sequences. This chain of reasoning applies to a large number of problems of discrete mathematics relative to words, compositions, partitions, trees, permutations, graphs, mappings, planar configurations, and so on. A suitable adaptation of the methods also opens the way to the quantitative analysis of characteristic parameters of large random structures, via a perturbational approach.
Theapproach to quantitative problems of discrete mathematics provided by analytic combinatorics can be viewed as an operational calculus for combinatorics organized around three components.
Symbolic methods develops systematic relations between some of the major constructions of discrete mathematics and operations on generating functions that exactly encode counting sequences.
Complex asymptotics elaborates a collection of methods by which one can extract asymptotic counting information from generating functions, once these are viewed as analytic transformations of the complex domain. Singularities then appear to be a key determinant of asymptotic behaviour. […]
Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt,Robert Sedgewick, Princeton University, New Jersey
Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt,Robert Sedgewick, Princeton University, New Jersey
We combine in the three appendices definitions and theorems related to key mathematical concepts not covered directly in the text. Generally, the entries in the appendices are independent, intended for reference while addressing the main text. Our own Introduction to the Analysis of Algorithms [538] is a gentle introduction to many of the concepts underlying analytic combinatorics at a level accessible to any college student and is reasonable preparation for undergraduates or anyone undertaking to read this book for self-study.
This appendix contains entries that are arranged in alphabetical order, regarding the following topics:
Arithmetical functions; Asymptotic notations; Combinatorial probability; Cycle construction; Formal power series; Lagrange inversion; Regular languages; Stirling numbers; Tree concepts.
The corresponding notions and results are used throughout the book, and especially in Part A relative to Symbolic Methods. Accessible introductions to the subject of this appendix are the books by Graham–Knuth–Patashnik [307], and Wilf [608], regarding combinatorial enumeration, and De Bruijn's vivid booklet [142], regarding asymptotic analysis. Reference works in combinatorial analysis are the books by Comtet [129], Goulden–Jackson [303], and Stanley [552, 554].
Arithmetical functions
A general reference for this section is Apostol's book [16]. First, the Euler totient function ϕ(k) intervenes in the unlabelled cycle construction (pp. 27, 84, 165, as well as 729 below). It is defined as the number of integers in [1 ‥ k] that are relatively prime to k.
Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt,Robert Sedgewick, Princeton University, New Jersey
FastSLAM is a framework for simultaneous localization and mapping using a Rao-Blackwellized particle filter (RBPF). But, FastSLAM is known to degenerate over time due to the loss of particle diversity, mainly caused by the particle depletion problem in resampling phase. In this work, improved particle filter using geometric relation between particles is proposed to restrain particle depletion and to reduce estimation errors and error variances. It uses a KD tree (k-dimensional tree) to derive geometric relation among particles and filters particles with importance weight conditions for resampling. Compared to the original particle filter used in FastSLAM, this technique showed less estimation error with lower error standard deviation in computer simulations.
A much beloved and widely used example showing the elegance and simplicity of lazy functional programming represents itself as “The Sieve of Eratosthenes.” This paper shows that this example is not the sieve and presents an implementation that actually is.
In all educational contexts, technological developments and changes in pedagogical theory mean that any picture of current practice and attitudes must be dynamic. In many countries, the learning outcomes of foreign language courses now include intercultural communicative competence (ICC), although the precise model for teaching ICC varies even across the English-speaking world. Internet-mediated approaches are widely used to support intercultural learning. In China, the geographical scale of the country and the speed and extent of contemporary socio-economic evolution, allied to long-established and distinctive cultures of learning, make the interface of new technologies and intercultural learning objectives particularly interesting and significant. A small-scale study of college teachers’ and learners’ perceptions of intercultural classroom instruction, with a special focus on Internet mediation, was conducted in mid-2007, using questionnaires and semi-structured questions, to explore the professional, personal and technical issues associated with Internet-mediated learning of languages and cultures. The results show that textbooks remain the predominant authority, while Internet tools are used as a source of information rather than a means of communication. Findings suggest recognition by teachers and students of the potential of the medium, and of the validity of intercultural goals for foreign language classes, although there are some divergences between the views of teachers and students. However, it is suggested that national policy, local incentives and resources and above all educational traditions do not yet allow optimal use of Internet-mediated approaches.
This paper presents an adaptive actuator failure compensation method, which compensates for uncertainties due to unknown actuator failures for redundant manipulator systems. The method is first developed for manipulators whose joints are concurrently actuated. While physical realization of concurrently actuated manipulators and the advantages of their use have been understood before, in this paper failure modeling, controller structure, and adaptive update rules for handling uncertainties from the actuator failures are studied. The adaptive actuator failure compensation method is then expanded for a cooperating multiple manipulator system with uncertain actuator failures. Dynamic equations of such a multiple manipulator system in the task space are derived and the adaptive actuator failure compensation problem is formulated in the task space, for which a compensation controller structure is proposed with stable adaptive parameter update laws. The adaptive control scheme is able to compensate for the uncertainties of system parameters and actuator failures in a more general sense. For both cases, closed-loop system stability and asymptotic tracking are proved, despite uncertain system failures.
One of the basic topics of question answering (QA) dialogue systems is how follow-up questions should be interpreted by a QA system. In this paper, we shall discuss our experience with the IMIX and Ritel systems, for both of which a follow-up question handling scheme has been developed, and corpora have been collected. These two systems are each other's opposites in many respects: IMIX is multimodal, non-factoid, black-box QA, while Ritel is speech, factoid, keyword-based QA. Nevertheless, we will show that they are quite comparable, and that it is fruitful to examine the similarities and differences. We shall look at how the systems are composed, and how real, non-expert, users interact with the systems. We shall also provide comparisons with systems from the literature where possible, and indicate where open issues lie and in what areas existing systems may be improved. We conclude that most systems have a common architecture with a set of common subtasks, in particular detecting follow-up questions and finding referents for them. We characterise these tasks using the typical techniques used for performing them, and data from our corpora. We also identify a special type of follow-up question, the discourse question, which is asked when the user is trying to understand an answer, and propose some basic methods for handling it.
As a means of transmitting not only data but also code encapsulated within functions, higher-order channels provide an advanced form of task parallelism in parallel computations. In the presence of mutable references, however, they pose a safety problem because references may be transmitted to remote threads where they are no longer valid. This paper presents an ML-like parallel language with type-safe higher-order channels. By type safety, we mean that no value written to a channel contains references, or equivalently, that no reference escapes via a channel from the thread where it is created. The type system uses a typing judgment that is capable of deciding whether the value to which a term evaluates contains references or not. The use of such a typing judgment also makes it easy to achieve another desirable feature of channels, channel locality, that associates every channel with a unique thread for serving all values addressed to it. Our type system permits mutable references in sequential computations and also ensures that mutable references never interfere with parallel computations. Thus, it provides both flexibility in sequential programming and ease of implementing parallel computations.
In this paper, the optimization of architectural parameters for a class of translational parallel kinematic machine (PKM) is performed with the particle swarm optimization (PSO) to achieve the best accuracy characteristics. The conventional error transformation matrix (ETM) is derived based on the differentiation of kinematic equations, and a new error amplification index (EAI) over a usable workspace is proposed as an error performance index for the optimization. To validate the efficiency of the PSO method, both the traditional direct search method and the genetic algorithm (GA) are implemented as well. The simulation results not only show the advantages of PSO method for the architectural optimization, but also reveal the necessity to introduce the EAI for the optimal design. And the results are valuable for architectural design of the PKM for machine tool applications.
The application of mobile technologies to learning has the potential to facilitate the active participation of learners in the creation and delivery of content. Mobile technologies can also provide a powerful connection between a variety of formal and informal learning contexts and can help to build a community of learners. However these versatile tools present challenges to educators and learners alike. The paper discusses the pedagogical challenges that result from the introduction of mobile technologies in language learning in the context of an intensive week of study abroad. We describe and evaluate a pilot project that uses mobile blogging to promote a constructivist, situated and informal learning experience of the foreign language and culture based on theories of active learning. We aim to encourage interaction and a sense of community among learners outside formal educational environments and in different locations as we ask them to engage with the foreign culture by capturing, sharing and reflecting on their experiences for their peers.
In this paper, finding the maximum load carrying capacity of mobile manipulators for a given two-end-point task is formulated as an optimal control problem. The solution methods of this problem are broadly classified as indirect and direct. This work is based on the indirect solution which solves the optimization problem explicitly. In fixed-base manipulators, the maximum allowable load is limited mainly by their joint actuator capacity constraints. But when the manipulators are mounted on the mobile bases, the redundancy resolution and nonholonomic constraints are added to the problem. The concept of holonomic and nonholonomic constraints is described, and the extended Jacobian matrix and additional kinematic constraints are used to solve the extra DOFs of the system. Using the Pontryagin's minimum principle, optimality conditions for carrying the maximum payload in point-to-point motion are obtained which leads to the bang-bang control. There are some difficulties in satisfying the obtained optimality conditions, so an approach is presented to improve the formulation which leads to the two-point boundary value problem (TPBVP) solvable with available commands in different softwares. Then, an algorithm is developed to find the maximum payload and corresponding optimal path on the basis of the solution of TPBVP. One advantage of the proposed method is obtaining the maximum payload trajectory for every considered objective function. It means that other objectives can be achieved in addition to maximize the payload. For the sake of comparison with previous results in the literature, simulation tests are performed for a two-link wheeled mobile manipulator. The reasonable agreement is observed between the results, and the superiority of the method is illustrated. Then, simulations are performed for a PUMA arm mounted on a linear tracked base and the results are discussed. Finally, the effect of final time on the maximum payload is investigated, and it is shown that the approach presented is also able to solve the time-optimal control problem successfully.
Recent years have seen the emergence of Web2.0, in which users are not only passive recipients of the featured content, but actively engaged in constructing it. Sites such as ‘Facebook’ and ‘Myspace’ are typical examples of this, as are blogs that allow users to present themselves online, to write about their daily lives or even to establish themselves as an authority on a particular subject. Due to the opportunities for self-reflection and interactive learning offered by blogs, they have also become one of the emerging tools in language pedagogy and higher education. At the same time, peer feedback is a technique that is increasingly used by educators instead of, or in addition to, tutor feedback, due to its potential to develop students’ understanding of standards, to initiate peer feedback, and to engage the student in the process of learning and assessment.
This paper is concerned with the question to what extent blogs can facilitate peer feedback and what issues need to be addressed for them to be a valuable tool in this process. After reviewing the recent literature on peer feedback and the specific issues emerging from providing feedback through computer mediated communication (CMC) technologies, the paper presents the results from a pedagogic research project in an advanced German language class in which blogs were used for this purpose. Drawing on students’ blogs as well as the responses given by students in questionnaires and focus groups and responses by experienced tutors in interviews, the paper argues that blogs are potentially valuable tools for peer feedback, but entail the need to address specific issues regarding the choice of CMC tool for feedback tasks, training in the use of interactive online tools and the roles of teachers and students.
The Functional Payout Framework (fpf) is a Haskell application that uses an embedded domain-specific functional language to represent and process exotic financial derivatives. Whereas scripting languages for pricing exotic derivatives are common in banking, fpf uses multiple interpretations to not only price such trades, but also to analyse the scripts to provide lifecycle support and more. This paper discusses fpf in relation to the wider trading workflow and our experiences in using a functional language in such a system as both an implementation language and a domain-specific language.